Multi-temporal Optimal Power Flow Including Storage...iii Resumo A otimização da exploração dos...

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Faculdade de Engenharia da Universidade do Porto

Multi-temporal Optimal Power Flow Including Storage

Diogo Domingos Lopes de Freitas

Mestrado Integrado em Engenharia Eletrotécnica e de Computadores

Supervisor: Prof. Dr. José Nuno Moura Marques Fidalgo

Co-Supervisor: Dr. Leonel de Magalhães Carvalho

<January 2018>

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© Diogo Domingos Lopes de Freitas, 2018

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Resumo

A otimização da exploração dos Sistemas Elétricos de Energia exige o recurso a técnicas

avançadas, capazes de lidar com problemas complexos, de natureza multi-temporal, não-linear

e combinatória. O OPF (Optimal Power Flow) constitui um problema de otimização, que é

resolvido para ajudar a encontrar uma solução ótima para os trânsitos de potência da rede

Neste trabalho, pretende-se desenvolver uma ferramenta para resolver o problema de OPF

incluindo a otimização dos recursos de armazenamento de energia. Esta ferramenta foi

implementada em MATLAB, aproveitando as funções disponíveis na biblioteca MATPOWER.

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Abstract

With the growth of renewable energy sources and other distributed generation sources,

electricity grids are becoming more complex. Renewable production has many advantages but

has the disadvantage of the inherent variability, which requires conventional production to

back it up when the weather does not allow for renewable production.

One of the most promising technologies for electricity grids are energy storage systems.

Storage systems are gaining more importance as renewable generation increases in the electric

system, and it is seen as one of the tools to help smooth the variability of renewable energy

sources, among other advantages.

In this study, the main objective was to develop a Multi-temporal Optimal Power Flow

methodology, able to integrate storage and to deal with AC constraints. The multi-temporal

problem formulation allows the optimization of the charging and discharging schedule, in order

to evaluate the benefits of storage integration.

The proposed approach is based on a two-blocks system. The first block uses the MATPOWER

Optimal Scheduling Tool (MOST), responsible for the initial DC OPF and optimization of the

global dispatch for the time interval considered, while defining the storage unit charge and

discharge periods that would minimize the overall production cost. The second block is an AC

OPF, applied for each hour individually, that aims at computing losses and checking all system

constraints, namely reactive power flows and limits. In the last step, the AC information (losses,

constraint violation) are re-integrated in the MOST tool to produce the final production

schedule.

The proposed methodology was validated through simulations studies on the IEEE 30 bus

system

During this study, several case studies are put into test to analyse the influence of the

storage unit on various aspects of the system, with the main objective being always to diminish

the system’s production cost.

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Palavras-Chave

MATPOWER, MOST, Otimização, Sistemas de Armazenamento de Energia, Transito de

Potências Ótimo, Unit Commitment

Keywords

Energy Storage System, MATPOWER, MOST, Optimal Power Flow, Optimization, Unit

Commitment

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Appreciations

Firstly, I would like to deeply thank the supervisor of this dissertation, Professor Doctor José

Nuno Moura Fidalgo for letting me develop this study with him, for all the support and attention

he gave to me during the semester, and for the continuous help during the best and the worst

moments of this study.

I would also like to thank the Co-Supervisor of this dissertation, Doctor Leonel de Magalhães

Carvalho, for providing an incredible insight to the subject, and helping with the elaboration

of the work itself. Without his knowledge, this work would not be so complete.

Special thanks to Doctor Carlos Murillo-Sánchez, one of the developers of MATPOWER and

MOST, for being able to debate ideas and help me implement the code to have the simulation

program up and running. He was a great help to this work and I am deeply thankful of all the

support he and Doctor Ray Zimmerman provided me.

I also thank the institution that is the Faculdade de Engenharia da Universidade do Porto,

for being the house that took me since 2011 and that helped making me what I am today.

Special thanks must be given to my family, my girlfriend, and my friends. To my family,

especially my parents, that supported me through all my education, that were always there to

motivate me even when they knew they could not help. And to my brother, that always tried

to cheer me on, especially during the course of this study.

I also need to thank my girlfriend Sara, for helping me have the strength to face all adversity.

She has put up with me through all the panic moments, all the scares, all the rough days, but

as also been there for me for every victory, every smile, every moment of joy. Although she

denies it, she is a major part of this work and a major part of what I achieved. Without her, I

would probably not be writing these words. And for that I will be eternally grateful. She is the

woman of my dreams and I hope I can make her proud with my doings.

Finally, I would like to thank my friends. That throughout the entire adventure that was

university, were there to support me, to hear me complain, to see me cry in despair. I thank

all of my friends for everything and for being always there for me, especially Filipe, that was

the one who followed closer all the work of this Dissertation; Rodrigues, for always being there

to help me with IT and programming, and Pedro, for being a partner in the tough years that

were the early years of university.

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Table of contents

..................................................................................... 1

Introduction ............................................................................................ 1 1.1 - Context ........................................................................................ 1 1.2 - Objectives .................................................................................... 2 1.3 - Dissertation Structure ....................................................................... 2

..................................................................................... 5

Energy Storage Systems – Technologies and applications ........................................ 5 2.1. Introduction .................................................................................. 5 2.2. Existing Types of Energy Storage Systems ................................................ 6 2.2.1. Pumped Hydroelectric Storage (PHS) ................................................ 6 2.2.2. Compressed Air Energy Storage (CAES) .............................................. 7 2.2.3. Flywheel Energy Storage ............................................................... 8 2.2.4. Battery Energy Storage Systems (BESS) .............................................. 9 2.2.4.1. Lead-Acid Battery .................................................................. 10 2.2.4.2. Lithium-Ion Battery ................................................................. 11 2.2.4.3. Sodium-Sulfur (NaOS) Battery ..................................................... 12 2.2.4.4. Nickel-cadmium (NiCd) Battery ................................................... 13 2.2.5. Flow Battery Energy Storage (FBES) ................................................ 14 2.2.6. Capacitors and Supercapacitors ..................................................... 15 2.2.7. Superconducting Magnetic Energy Storage ......................................... 16 2.2.8. Hydrogen Storage and Fuel Cell ..................................................... 18 2.2.9. Thermal Energy Storage .............................................................. 19 2.2.10. Hybrid Electrical Energy Storage ................................................. 20 2.3. Energy Storage Systems Applications .................................................... 21 2.3.1. Load Leveling ........................................................................... 21 2.3.2. Impact on long distance energy transport ......................................... 23 2.3.3. Congestion Management in the Power Grid ........................................ 24 2.3.4. Renewable Energy Sources Penetration Increase ................................. 24 2.3.5. Deployment of the Smart Grid Concept ............................................ 27 2.3.6. Continuity and Flexibility of Supply ................................................. 30 2.4. Chapter Summary ........................................................................... 31

.................................................................................... 33

Problem Formulation................................................................................. 33 3.1. Introduction and Context .................................................................. 33 3.2. General Optimal Power Flow Formulation .............................................. 33 3.3. Expanding the OPF formulation ........................................................... 36 3.4. Methodology ................................................................................. 39 3.5. Software Description ....................................................................... 41 3.5.1. MATPOWER ............................................................................. 41 3.5.2. Matpower Optimal Scheduling Tool (MOST) ....................................... 41

.................................................................................... 43

Presentation of the Study Case ..................................................................... 43 4.1. Introduction and Context .................................................................. 43 4.2. Network and Load Characteristics ........................................................ 44 4.2.1. Network Configuration, description and characteristics ......................... 44 4.2.2. Load Profile and Load per bus ....................................................... 48

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.................................................................................... 53

Results and Discussion ............................................................................... 53 5.1. Introduction ................................................................................. 53 5.2. Case 1 – Initial Case: Influence of Storage in multiperiod AC OPF ................... 54 5.2.1. Results Without Storage .............................................................. 54 5.2.1.1. Results for MOST without considering the Storage unit ....................... 54 5.2.1.2. Results for the Multi-Period AC OPF without considering Storage ........... 55 5.2.1.3. Results for MOST with losses compensation without Storage ................ 60 5.2.1.4. Final observations .................................................................. 64 5.2.2. Results with the inclusion of the Storage unit ..................................... 65 5.2.2.1. Results for MOST with a Storage unit and without loss compensation ...... 66 5.2.2.2. Results of AC OPF With Storage................................................... 69 5.2.2.3. Results for MOST with loss compensation and storage ........................ 75 5.2.2.4. Final Observations .................................................................. 78 5.2.3. Case 1 Conclusions .................................................................... 79 5.3. Case 2 – Avoiding generator start with the use of the Storage Unit ................. 80 5.3.1. Storage Profile Definition............................................................. 81 5.3.2. Multiperiod AC OPF Analysis ......................................................... 82 5.3.2.1. Without Storage ..................................................................... 82 5.3.2.2. With Storage ......................................................................... 85 5.3.3. MOST with Lost compensation analysis ............................................. 89 5.3.3.1. Without the Storage Unit .......................................................... 89 5.3.3.2. With the Storage Unit .............................................................. 91 5.3.4. Case 2 Conclusions .................................................................... 96 5.4. Case 3 – Analyzing the influence of the storage unit location on the system losses

97 5.4.1. First Iteration of MOST ................................................................ 97 5.4.2. Multiperiod AC OPF with the Storage unit on Bus 5 ............................... 99 5.4.3. MOST with loss compensation with the storage unit on Bus 5 ................. 104 5.4.4. Case 3 Conclusions .................................................................. 107

.................................................................................. 109

Conclusions and Future Works .................................................................... 109 6.1. Conclusions ................................................................................ 109 6.2. Future Works .............................................................................. 111

References ................................................................................. 113

Annex A .................................................................................... 119

Per Bus Load for each hour of the system ...................................................... 119

Annex B .................................................................................... 123

Case 1 - Generator Production for each hour in MOST without the storage unit .......... 123

Annex C .................................................................................... 125

Case 1- Generator Production for each hour of the system for the AC OPF ............... 125

Annex D .................................................................................... 127

Case 2 - Storage Unit charge level ............................................................... 127

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List of Figures

Figure 2-1 - Simple layout of a pump hydroelectric storage plant [3] .............................. 6

Figure 2-2 - Schematic of a Compressed Air Energy Storage System operation [1] ............... 7

Figure 2-3 - Flywheel Energy Storage system description [1] ........................................ 8

Figure 2-4 - Simple diagram of how a battery energy storage system works [1] ................. 10

Figure 2-5 - Example and scheme of a lead-acid battery [17] ...................................... 11

Figure 2-6 - Simple scheme of the way of operation for a Li-ion battery. The movement of the Li+ ions from the anode to the cathode forces the electrons to circulate and create electric current [19] ................................................................................ 12

Figure 2-7 - Simple schematic of the constitution of a Sodium-Sulfur battery [22] ............. 13

Figure 2-8 - Scheme of how a Nickel-Cadmium battery is constituted [24] ....................... 13

Figure 2-9 - Simple diagram of the operation of a redox flow battery (Vanadium Redox Flow Battery) [1] .......................................................................................... 14

Figure 2-10 - Simple schematic of a Supercapacitor [3] ............................................. 16

Figure 2-11 - Simple scheme of the composition and operation of a SMES system [3] .......... 17

Figure 2-12 - Simple scheme of Hydrogen Storage and Fuel Cell system [3] ...................... 18

Figure 2-13 - Simple schematic of a Sensible Heat storage system, being integrated into a wind generation unit [3] ........................................................................... 20

Figure 2-14 – Variation of electric energy costs for the Iberian Market, in 10-07-2010 [42] ... 21

Figure 2-15 - Simple scheme for a load leveling solution with an ESS [43] ....................... 22

Figure 2-16 - Basic representation of a conventional use of an ESS [44] .......................... 23

Figure 2-17 - – Evolution of RES in the European scenario [45] ..................................... 25

Figure 2-18 - Evolution of the different types of energy generation installed capacities [46] ........................................................................................................ 25

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Figure 2-19 - RES capacity progress up to 2030 [47] ................................................. 26

Figure 2-20 - Simple Scheme of a PV system with Energy Storage [50] ............................ 27

Figure 2-21 - A simple schematic of a Smart Grid, where all the active parts of the grid are connected [52] ...................................................................................... 28

Figure 3-1 - Methodology flow chart .................................................................... 39

Figure 4-1 - One-line scheme of the IEEE 30 Bus Network [63] ..................................... 44

Figure 4-2 - Load chart of the total system load during the 24 hours ............................. 50

Figure 5-1 - Generator total production over 24 hours .............................................. 55

Figure 5-2 - Generator total production over 24 hours .............................................. 56

Figure 5-3 - Difference of production between MOST and the AC OPF for all system's running hours .................................................................................................. 57

Figure 5-4 - Comparison of the system total generation between MOST and the AC OPF ...... 57

Figure 5-5 - System per hour dispatch .................................................................. 58

Figure 5-6 - System AC losses over time ............................................................... 58

Figure 5-7 - Comparison of system total generation with the system's losses .................... 59

Figure 5-8 - System loss percentage in all periods .................................................... 59

Figure 5-9 - System Production curves, for each generator, during the 24 hours ................ 60

Figure 5-10 - Difference in Production in all generators in MOST without and with loss compensation ........................................................................................ 61

Figure 5-11 - System Total Production comparison ................................................... 62

Figure 5-12 - Difference in production for all generators between MOST with loss compensation and AC OPF ......................................................................... 63

Figure 5-13 - Total system production comparison between MOST with loss compensation and the AC OPF ...................................................................................... 63

Figure 5-14 - Graphical comparison of the economic dispatch obtained in the three steps of the simulation ....................................................................................... 65

Figure 5-15 - Comparison of dispatches for MOST with and without storage ..................... 66

Figure 5-16 - Generator and Storage unit production curve for MOST, for the 24 hours of the system ................................................................................................ 67

Figure 5-17 - Difference in production for each generator in MOST with and without storage ........................................................................................................ 68

Figure 5-18 - Added Production comparison between MOST with and without Storage ......... 68

Figure 5-19 - Analysis of the peak shaving effect caused by the storage .......................... 69

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Figure 5-20 - Comparison of the economic dispatch for the AC OPF with and without the storage unit .......................................................................................... 70

Figure 5-21 -Comparison of the dispatches per hour of the AC OPF with and without storage ........................................................................................................ 70

Figure 5-22 – Production of all generators for the multi-period AC OPF with Storage .......... 71

Figure 5-23 - Difference in production in the AC OPFs with and without storage ................ 71

Figure 5-24 - Difference in production between the AC OPF and MOST with storage unit ...... 72

Figure 5-25 - Total losses comparison between the AC OPF with and without the storage unit .................................................................................................... 73

Figure 5-26 -Comparison of system total production with the system total production ........ 74

Figure 5-27 -System total loss percentage per hour .................................................. 74

Figure 5-28 - Comparison of the economic dispatches of MOST with loss compensation, with and without the storage unit ...................................................................... 75

Figure 5-29 - Generator Production for MOST with loss compensation and storage unit ........ 76

Figure 5-30 - Average percentage difference between MOST with loss compensation and the AC OPF, both with storage ......................................................................... 77

Figure 5-31 - Average Percentage Error of MOST compared to AC OPF ............................ 77

Figure 5-32 - Difference in generator production between MOST with loss compensation, with and without storage unit ..................................................................... 78

Figure 5-33 - Comparison of the system's total dispatch for all the steps of the simulation for the multiperiod OPF with Storage ............................................................ 79

Figure 5-34 - Storage Unit Charge over time obtained from MOST ................................. 81

Figure 5-35 - Individual Generator production during the 24 hours of the multiperiod OPF ... 82

Figure 5-36 - System Total production in the 24 hours of the AC OPF ............................. 83

Figure 5-37 - System total losses over the 24 hours of the system ................................. 84

Figure 5-38 - Percentage of losses over generation for the multiperiod AC OPF ................. 84

Figure 5-39 - Comparison of the economic dispatch for the AC OPF without storage /1) and with storage (2) ..................................................................................... 85

Figure 5-40 – Evolution of the production for each generator and the storage unit in the AC OPF considering Storage ........................................................................... 86

Figure 5-41 - Comparison of the individual Generator production in the multiperiod AC OPF, with and without the storage unit ................................................................ 86

Figure 5-42 – Comparison of the production from Generator 5 in the AC OPF with and without Storage ............................................................................................... 87

Figure 5-43 - Comparison of System's total production between Case 1 and Case 2’s multiperiod AC OPF with Storage ................................................................. 87

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Figure 5-44 - System total conventional generation, with the inclusion of the storage unit ... 88

Figure 5-45 - Difference in total production between AC OPF with and without storage ....... 88

Figure 5-46 - Comparison of the system's losses for the AC OPF with and without storage ..... 89

Figure 5-47 - Evolution of generator production for MOST with the AC losses consideration .. 90

Figure 5-48 - System total production for MOST when considering the AC Losses ............... 90

Figure 5-49 - Comparison of the system's economic dispatch for MOST, with and without the storage unit .......................................................................................... 91

Figure 5-50 - Generation comparison between MOST with the storage unit considered, and MOST without considering the storage ........................................................... 92

Figure 5-51 - Individual generator production for MOST with the storage unit ................... 92

Figure 5-52 - Generator 5 production in MOST with and without the storage unit in the system ................................................................................................ 93

Figure 5-53 - Difference in individual generator production between the multiperiod AC OPF and MOST with loss compensation ................................................................ 93

Figure 5-54 - Average difference (in percentage) between the multiperiod AC OPF and MOST for all the generators of the system .............................................................. 94

Figure 5-55 - Total System production comparison between the multiperiod AC OPF and MOST .................................................................................................. 95

Figure 5-56 - Comparison of the economic dispatch between the multiperiod AC OPF (1) and MOST (2) .............................................................................................. 95

Figure 5-57 - Individual Generator and Storage Production ......................................... 98

Figure 5-58 - Storage Unit power input/output profile .............................................. 98

Figure 5-59 - Storage Unit Charge levels at the end of each hour after the first iteration of MOST .................................................................................................. 99

Figure 5-60 - Comparison of Economic dispatch between Case 2 and Case 3 multiperiod AC OPF .................................................................................................. 100

Figure 5-61 - Individual Generator Production over the 24 hours for the multiperiod AC OPF with the storage unit on Bus 5 .................................................................. 100

Figure 5-62 - Difference in total production between Case 3 and Case 2 multiperiod AC OPF ...................................................................................................... 101

Figure 5-63 - Difference between the active losses obtained in Case 3 and Case 2 ........... 102

Figure 5-64 - Comparison of system losses between the AC OPF with the storage on Bus 5 and without storage .............................................................................. 102

Figure 5-65 - Comparison of the loss percentage for the AC OPF without storage and with storage in bus 1 and 5 ............................................................................ 103

Figure 5-66 - Graphical Representation of the economic dispatches presented in Table 5-16 ...................................................................................................... 104

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Figure 5-67 - Individual generator production for MOST with the storage unit located in Bus 5 ..................................................................................................... 105

Figure 5-68 - Difference in generator production between MOST in Case 3 and in Case 2 ... 105

Figure 5-69 - Comparison of individual generator production between MOST and the AC OPF, both with the storage on Bus 5 .................................................................. 106

Figure 5-70 - Total system production comparison between MOST and the AC OPF ........... 107

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List of Tables

Table 4-1 - Generator characteristics .................................................................. 45

Table 4-2 - Characteristics of Voltage and Bus Bar classification .................................. 45

Table 4-3 - System Line Parameters .................................................................... 47

Table 4-4 – Transformer data for the system in study ............................................... 48

Table 4-5 - Capacitor banks information ............................................................... 48

Table 4-6 – Load per hour to be applied to the network ............................................ 49

Table 4-7 – Original Per Bus of the IEEE 30 Bus Case ................................................. 51

Table 5-1 - Value of the system total dispatch when running MOST ............................... 54

Table 5-2 - System dispatch for the 24 hours AC OPF ................................................ 56

Table 5-3 - Economic dispatch for MOST with loss consideration .................................. 60

Table 5-4 - Comparison between the economic dispatches of the various steps of the simulation ............................................................................................ 64

Table 5-5 - Economic dispatch for MOST with storage ............................................... 66

Table 5-6 - Economic dispatch for the AC OPF with Storage Unit ................................. 70

Table 5-7 - Economic dispatch of the system with MOST considering losses and storage ....... 75

Table 5-8 – Table summary of all the economic dispatches of the simulation steps with Storage ............................................................................................... 79

Table 5-9 - Case B generation cost function ........................................................... 81

Table 5-10 - Economic dispatch for the multiperiod AC OPF without Storage .................... 82

Table 5-11 - Economic dispatch for the multiperiod AC OPF with storage ........................ 85

Table 5-12 - Economic dispatch for MOST when considering the AC losses ....................... 89

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Table 5-13 - Economic Dispatch value comparison of MOST with and without the storage unit .................................................................................................... 91

Table 5-14 - Economic Dispatch for the multiperiod AC OPF with the storage unit on Bus 5 .. 99

Table 5-15 - Total Active losses for the 24 hours of the system for each of the study cases . 103

Table 5-16 - Values for the economic dispatch of MOST with loss compensation (Case 3 and Case 2) and multiperiod AC OPF for Case 3 ................................................... 104

Table A-1 - System MW Load, per bus, for each hour of the system ............................. 120

Table A-2 - System MVar load, per bus, for each hour of the system ............................ 121

Table B-1 - Generator production, per hour, for MOST without the storage unit .............. 123

Table C-1 - Individual Generator Production, per hour, for the multiperiod AC OPF without storage .............................................................................................. 125

Table D-1 - Storage Unit Charge Level ............................................................... 127

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Symbols and Abbreviations

List of Abbreviations

AC Alternate Current

AFC Alkaline Fuel Cell

BESS Battery Energy Storage Systems

BSS Battery Storage Systems

CAES Compressed Air Energy Storage

DC Direct Current

DG Distributed Generation

DMFC Direct Methanol Fuel Cell

DP Disperse Production

EES Electric Energy Storage

ESS Energy Storage Systems

EV Electric Vehicle

FBES Flow Battery Energy Storage

FES Flywheel Energy Storage

HV High Voltage

MCFC Molten Carbonate Fuel Cell

MOST Matpower Optimal Scheduling Tool

NaOS Sodium Sulfur

NiCd Nickel-Cadmium

PAFC Phosphoric Acid Fuel Cell

PEMFC Proton Exchange Membrane Fuel Cell

PHS Pumped Hydroelectric Storage

PSB Polysulfide Bromine

PV Photovoltaic

RES Renewable Energy Sources

SMES Superconducting Magnetic Energy

SOFC Solid Oxide Fuel Cell

TES Thermal Energy Storage

VRB Vanadium Redox Flow

ZnBr Zinc Bromine

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Introduction

1.1 - Context

Electrical energy systems are changing. The growth of the electricity grid and the constant

growing demand by the consumers changes the system every day, with networks becoming more

complex and harder to operate.

At the same time, environmental issues are becoming more serious. Energy production is

swiftly moving from the conventional production using big thermal powerplants to a more

distributed generation panorama, with renewable energy sources gaining a bigger role on the

energy production scenario. With renewable generation, the environmental issues caused by

thermal powerplants can be avoided. Production sources like solar and wind power generation

do not release pollutant gases to the atmosphere, nor generate toxic waste like the one that is

obtained from nuclear reactors. Renewable energy sources provide clean energy, that goes well

with the current global panorama of searching for a more sustainable and environmentally

friendly way of living.

Renewable energy sources also provide cheaper power to the network, with the overall

production costs being diminished when renewable sources start to replace thermal plants.

Since the fuel used by these plants is considered free, the overall cost of their energy is lower

when it is available for market than the prices offered by thermal powerplants.

However, the growth of renewable energy sources has its limitations. Renewable production

is very weather dependent, and can have a variable behavior, ending up being impossible to

rely solely on renewable sources to supply an entire energy network. When the weather

conditions are not the most appropriate and there are no more generation units available, there

might be blackouts since renewable generation will not be enough to supply all the loads.

Introduction

2

Energy storage might be a key part of that scenario. With the addition of storage units to

the network, the variable effect of renewable generation can be mitigated, with energy storage

units being able to help to store electricity in periods with surplus of renewable energy and

supply the loads when there is generation deficit or high price.

Electric energy storage can be a big part of today’s energy systems even without considering

renewable generation. Storage units can contribute to energy production costs reduction by

diminishing the amount of energy that is produced by the conventional plants during peak hours

where, normally, the electricity cost is more expensive.

1.2 - Objectives

The main objective of this dissertation is to study the influence that the addition of a storage

unit can have in an electric energy system, specially the influence that the storage unit can

have on the multi-temporal scheduling of generating units during a period of 24 hours.

To perform this study, a simulation tool was needed that could perform a multi-temporal

Optimal Power Flow (OPF) with storage and determine the optimal operation cost for the 24

hours of the simulation. Since there was no direct tool capable of giving the desired results,

the first objective was to develop an algorithm that could perform the multi-temporal OPF for

the network in question, while considering the storage unit, a variable load profile, and

transformer and capacitor banks tap optimization.

After the development of the algorithm, the objective was to use it in order to see the

influence that the storage unit would have on various aspects, namely, to determine the

influence that the addition of storage would have on the system’s economic dispatch for the

24 hours of the problem.

In addition to the study of the economic dispatch, it was also interesting to see the influence

that the storage unit would have in the system’s behavior, and how could certain aspects of

the system’s performance could be improved by adding the storage unit and studying its

installation location.

1.3 - Dissertation Structure

This dissertation is divided into seven different chapters. The first chapter is an introductory

chapter, where the context of the problem is presented, and the objectives and structure of

the study are presented.

Introduction

3

The second chapter contains a small presentation of some of the different storage

technologies that exist in electric energy systems, giving a simple explanation of how the

various technologies work, the advantages and the disadvantages, and some of the scenarios

where energy storage systems can be installed. This chapter is also used to present the various

applications that energy storage systems can have in the energy grid, and how can they be used

to improve various aspects of the energy supply.

Chapter 3 describes the mathematical formulation for the problem. The objective with this

chapter was to give a simple and concise explanation of the OPF problem addressed in this

dissertation and the mathematical formulation behind the simulation tools used, like

MATPOWER and MOST.

Chapter 4 presents the case study to contextualize the reader with the network used for the

simulations, and all its characteristics. The load profile used is also presented together with all

other relevant data to better understand and reproduce the simulations made.

Chapter 5 presents the various case study that were analyzed and presents all the results

and discussion of those results. Each case study consists of a different scenario and tackles a

new objective that is meant to be achieved with the usage of the storage unit. Each study case

has conclusions and discussion around the results obtained so that the reader can understand

the logic of each result and understand the purpose of each study.

Chapter 6 is the last chapter of this dissertation and it serves to present the final conclusions

that were obtained from this study, as well as presenting future research that can be done to

improve this work and to explore new aspects that this dissertation did not cover.

Introduction

4

Energy Storage Systems – Technologies and applications

5


2.1. Introduction

This dissertation starts by providing a general look at the different technologies for electrical

energy storage (EES) that currently exists. Even though the main objective of this dissertation

is not the storage systems themselves, it is important to present a brief overview of the existing

technologies to better contextualize the actual purpose of this study.

There are many different types of EES currently available worldwide. Energy storage is

becoming more and more important in the electricity grid and its importance is growing as

energy needs become more and more demanding and the control of the system is becoming

more difficult.

Therefore, it is important to underline that the main goal this chapter is to contextualize

the proposed study: analyze the influence of storage systems on a multi-period OPF in HV

systems. For more detailed information about the different storage systems, it is recommended

for the reader to consult the list of bibliographical references in this dissertation.


6

2.2. Existing Types of Energy Storage Systems

2.2.1. Pumped Hydroelectric Storage (PHS)

Pumped hydroelectric storage is one of the EES with the richest history, better technical

development and larger energy storage capacity. This is represented by the following numbers:

in 2012, PHS had an installed capacity of around 120 GW worldwide, and it represented 99% of

global storage capacity and contributed to 3% of the world’s total power generation [1] [2].

The operation mode is very simple. A PHS plant consists of two water reservoirs, separated

vertically. When power demand is lower, the excess energy will power the pumps that will

move the water to the top reservoir. Then during peak hours, when load demands are greater

than the production capabilities, the water flows to the lower level reservoir, running through

the turbines that will act as primary units to the generators that will produce electrical energy

to supply load demands [1]. Figure 2-1 shows a simple model of a PHS plant.

Figure 2-1 - Simple layout of a pump hydroelectric storage plant [3]

The storage capacity depends on the height of the reservoirs and the volume of water that

they can store. The rated power of the PHS plant will depend on:

• Water Pressure

• Flow rate between reservoirs

• Rated power of turbines and motors/generation units

PHS plants can exist ranging from 1MW to up to 3000MW of installed power. They operate

at approximately 70-80% efficiency and can have a lifespan of up to 40 years [4] [5].

The greatest problem in PHS systems is that they are very dependent on the geographical

location of the PHS plant. The ecological impact that PHS have is also worth mentioning. PHS

plants are often responsible for the alteration of the fauna of the installation locale, and can


7

cause the retaining of sand, rocks, and even fish and other living organisms that otherwise

would follow the natural flow of the river [6]. Other than that, their installation cost is

considerably large and the elevated construction time that it takes to build a fully operational

PHS plant are also setbacks for this technology, that still is one of the most common EES

technologies in the world [1].

2.2.2. Compressed Air Energy Storage (CAES)

Compressed air energy storage (CAES) is a type of ESS that can provide more than 100MW of

power from a single CAES plant [1].

The way of operation is the following: during the charging mode, a reversible

motor/generator group activates a chain of air compressors that will inject air into the air

storage units, storing the air at high pressures for later deflation of the air tanks; in the

discharging mode, which typically occurs during peak load hours, the stored air will be released,

heated, and then will be directed to the turbines, activating them, who consequently activate

the generator groups that will end up producing energy to supply the loads [1]. A simple scheme

of how a CAES system operates is shown in Figure 2-2.

Figure 2-2 - Schematic of a Compressed Air Energy Storage System operation [1]

The compressed air energy storage powerplants can be built with a wide arrange of

capacities, similarly to the PHS powerplants. The plant capacity will be dependent of the air

storage unit’s capacities, the flow of air that can run through the turbines, and the

motor/generator unit rated power output.


8

There are many practical uses for this kind of technology, all of them very similar to the

ones found on every EES. More details on these applications can be found in 2.3

The bigger barriers to CAES powerplants is the need for an appropriate location. Many CAES

systems are installed on abandoned mines or large caves, so that they can use the existing

topology for compressed air storage. This geographical requirement will end up being reflected

on the overall cost for the plant installation. If the cost for building the caves and air reservoirs

can be avoided, then the overall system cost will diminish. Another disadvantage of CAES plants

is the low cycle efficiency, reflected on the operation costs of the plant and the energy that is

lost [1].

2.2.3. Flywheel Energy Storage

Flywheel Energy Storage (FES) systems are composed by five major components [7]:

• The Flywheel

• Group of bearings

• Reversible Motor Generator

• Power Electronics Unit

• Vacuum Chamber

FES systems use electric energy to accelerate or deaccelerate the flywheel. That will result

in an increase or decrease of the amount of stored kinetic energy transferred from or to the

flywheel through the integrated motor generator. When a flywheel loses speed, the energy that

is lost is injected to the grid, analogously to how a battery works when it discharges [1]. Figure

2-3 shows a simple scheme of how a FHS system works.

Figure 2-3 - Flywheel Energy Storage system description [1]


9

FES systems can be split into two major groups [8]:

1. Low-Speed FES – These types of FES systems use steel as the main material for the

flywheel and have rotation speeds of under 6000 rpm. They are usually used for

short-term and medium/high power applications

2. High-Speed FES – These types of FES systems use carbon fiber as the main material

for the flywheel, making it lighter, allowing for bigger rotation speed. They can

operate to up to 10000 rpm. They use non-contact magnets to eliminate the wear

of the bearings, improving overall system efficiency. The applications for High-

Speed FES are always expanding but they are mainly used in high power quality and

ride-through capacity in industries like the aerospace industry.

The main weakness of flywheel energy storage systems is that the flywheel suffers from

idling losses when the system is on standby, leading to high self-discharges of up to 20% of the

stored capacity per hour [9]. Another setback for FES is that they can only provide power in

short notice at a very modest rate, so the rate of response to fast fluctuations of the system is

not the best. FES systems usually work in parallel with other EES that can provide a fast response

at punctual load fluctuations, like Battery storage systems (2.2.4) or even use fuel generators

as a backup to respond to those fast responses [1].

2.2.4. Battery Energy Storage Systems (BESS)

Rechargeable batteries are one of the most used energy storage systems, not only in

industrial and power grid applications, but also in the everyday life (for instance, in cellphones

and laptops).

A BESS consists on several electrochemical cells connected in parallel and in series that will

produce electricity at a desired voltage, being the electricity a result of chemical reactions

that occur inside the battery. Each cell contains two electrodes of opposing poles (one anode

and one cathode) and an electrolyte that can be solid, liquid or even viscous [10] [11].

The battery cell can convert energy in a bidirectional way: it can make the conversion from

chemical to electrical energy (discharge) and from electrical to chemical (charge).


10

Figure 2-4 - Simple diagram of how a battery energy storage system works [1]

During the discharge process, the electrochemical reactions occur in both the anode and the

cathode. At the eyes of the circuit to which the battery is connected, electrons are emitted by

the anode and collected by the cathode. When the battery is in charge mode, the opposite

reaction occurs. The battery is charged by applying an external voltage to both the electrodes.

A simple scheme of the structure of a BESS, and how it operates is shown on Figure 2-4.

Battery storage systems can have different types of applications, being able to integrate

almost every general application for EES. For more detail on EES applications, please attend to

2.3

A BESS applied to the energy grid is relatively fast to be built and implemented, with

installation time going only up to 12 months in the worst-case scenario [12]. The installation

site can be very flexible, usually with the battery being installed inside a house, a building or

close to vital facilities of the installation that the battery will power.

The main setbacks for BESS are the relatively low cycling times and the still high

maintenance cost. These factors are the main reason why battery storage systems are not still

implemented in a larger scale in the electric system [1]. It is also important to realize that the

disposal or recycling of a battery is a process that must be made with extreme care because of

the toxic nature of some battery components that are released when dismantling it [13].

Batteries have various chemicals that must be treated in the appropriate manner, to avoid

pollution of the ground, water, and even the atmosphere, that can also be polluted by the

gasses that batteries can release.

2.2.4.1. Lead-Acid Battery

Composition: Anode – PbO2; Cathode – Pb; Electrolyte – Sulfuric Acid

Pros:

• Fast Response Times;

• Small daily self-discharge rate (less than 0,3% of total capacity);

• Relatively high efficiency per operation cycle (63-90%);


11

• Low Capital Costs (50-600$/kWh) [9] [14] [15] ;

Cons:

• Relatively low life cycles (Around 2000 charge-discharge cycles);

• Low energy Density (50-90 Wh/L);

• Low specific energy (25-50 Wh/Kg) [14] [16];

• Bad performance at low temperatures [1];

Examples of Application:

• Secondary backup PSU for data centers and telecommunication structures;

• Energy Management Applications;

• Hybrid and Electric Vehicles application [14] ;

Figure 2-5 - Example and scheme of a lead-acid battery [17]

2.2.4.2. Lithium-Ion Battery

Composition: Anode – Graphitic Carbon; Cathode – Lithium Metal Oxide (LiCoO2, LiMO2);

Electrolyte – Non-Aqueous Organic liquid with dissolved Lithium salts [18].

Pros [9] [13] [14]:

• Fast Response time (approximately few milliseconds);

• Good Performance on a small-scale form (1500 – 10000 W/L)

• Great values for energy density;

• High specific energy (75-200 Wh/Kg);

• High cyclic Efficiency (Around 97%);

Cons [1]:

• Requires an on-board computer to manage its operation, increasing the system total

cost;


12

• Charge-discharge cycles can affect Li-ion batteries total lifespan, making it shorter

after some cycles;

Examples of Application:

• Energy Grid applications, like frequency control, peak shaving and renewable

sources integration;

• Hybrid and Electric Vehicles;

Figure 2-6 - Simple scheme of the way of operation for a Li-ion battery. The movement of the Li+

ions from the anode to the cathode forces the electrons to circulate and create electric current [19]

2.2.4.3. Sodium-Sulfur (NaOS) Battery

Composition: Molten Sodium and Molten Sulfur as electrodes. Electrolyte – Solid Beta

Alumina. The chemical reactions must occur at around 574-624 Kelvin, to ensure liquid state of

the electrodes and guaranteeing the correct and safe operation of the battery [20];

Pros [2] [18] [21]:

• High energy density (150 – 300 Wh/L);

• Close to null daily self-discharge;

• Rather high energy capacity, compared to other batteries (up to 244.8 MWh);

• High impulse operation capacity;

• Inexpensive and non-toxic materials lead to high recyclability of the batteries

(approximately 99%);

Cons [1] [14] [18]:

• High Operating Costs (80$/kW/Year);

• Requires a separated System to ensure that temperatures maintain themselves at

the desired range;


13

Figure 2-7 - Simple schematic of the constitution of a Sodium-Sulfur battery [22]

2.2.4.4. Nickel-cadmium (NiCd) Battery

Composition: Uses nickel hydroxide and metallic cadmium as electrodes. Electrolyte –

Aqueous alkali solution [1].

Pros [1]:

• High and Robust reliabilities;

• Low maintenance Costs

Cons [13] [23]:

• Toxic materials used as electrodes can cause environmental disasters if not dealt

with appropriately;

• Maximum capacity drastically decreases after charge-discharge cycles, if the battery

isn’t fully discharged before the next charge (Memory effect).

Examples of Application [1]:

• Not many successes in using NiCd batteries at a big scale as utility ESS in the power

grid. Usage has been discontinued due to the options referred before being safer

and more reliable options

Figure 2-8 - Scheme of how a Nickel-Cadmium battery is constituted [24]


14

2.2.5. Flow Battery Energy Storage (FBES)

Flow batteries store energy in two soluble redox couples that are contained in external tanks

with liquid electrolyte. The electrolytes in the tanks can be pumped from inside the tanks to

the cell stacks, which consist in two electrolyte flow compartments that are divided by ion

selective membranes. The operation of a flow battery is based on reduction-oxidation reactions

of the electrolyte solutions. While the battery is charging, one of the electrolytes will be

oxidized at the anode of the battery. At the same time, the other electrolyte will be reduced

at the cathode, converting the electrical energy supplied to the battery to chemical energy.

When the battery discharged, the process works in reverse, to convert chemical energy into

electrical energy [1].

There are two possible categorizations for flow batteries: Redox Flow batteries and Hybrid

flow batteries. The category depends of all electroactive components being dissolved or not in

the electrolyte [1].

Figure 2-9 - Simple diagram of the operation of a redox flow battery (Vanadium Redox Flow

Battery) [1]

A major advantage of FBES systems is that the rated power of the system is not dependent

on the system total storage capacity: it is instead determined by the size of the electrodes and

the number of cells in the stack. On the other hand, the storage capacity is determined by the

concentration and the amount of the electrolyte [2] [25].


15

FBES systems also have very low self-discharge rates, since the electrolytes are stored in

separated sealed tanks, thus avoiding self-discharges of the battery [14] [18].

The major setbacks for this kind of technology include the low performance of the battery

that occurs from non-uniform pressure drops and the transfer limitation of the reactant mass.

This technology also includes high maintenance costs and more complex system requirements

for its integration in an electric system, while compared to other batteries and other ESS [26].

The practical examples of FBES systems have demonstrated the ability to operate in an

interval of a few hundred kW, up to a few MW. Still, currently there are not many commercially

available FBES systems available [14] [27]. Investigation is being made to diminish the operating

costs of the FBES and to improve its efficiency and reliability, ultimately making this technology

more suitable for practical ESS applications.

The main types of FBES are [1]:

• Vanadium Redox Flow Battery (VRB)

• Zinc Bromine (ZnBr) Flow Battery

• Polysulfide Bromine (PSB) Flow Battery

2.2.6. Capacitors and Supercapacitors

Capacitors are composed of at least two electrical conductors, separated by a thin layer of

insulator. The conductors usually are metallic foils, and the insulators can be made of ceramic,

glass or a plastic film. When the capacitor is charged, the energy is stored on the dielectric

material, in the form of an electrostatic field [14]. Capacitors are traditionally selected if the

amount of energy to be stored is not too large and if the operating voltage to be deployed is

variable. Differently from traditional BESS (2.2.4), capacitors have a higher power density and

have shorter charging times. On the other hand, their capacity is fairly limited, the energy

density is lower than the ones on BESS and the high self-discharge losses [14] are points to be

taken into consideration when using a capacitor as an EES. However, and bearing in mind the

said characteristics, capacitors can still be used in certain situations: power quality control,

and high voltage power correction. They can also be used to level out the output of power

supplies and help with energy recovery in mass transit systems.

Supercapacitors, or electric double-layer capacitors, contain two conductor electrodes, an

electrolyte and a porous membrane separator [18], similarly to the flow battery. Figure 2-10

shows how the composition of a supercapacitor


16

Figure 2-10 - Simple schematic of a Supercapacitor [3]

Supercapacitors have both the characteristics of traditional capacitors, but also from

electrochemical batteries. Energy is charged as static charge on the surfaces between on the

edges between the conductors and the electrolyte.

The main advantages of superconductors as ESS are the large lifespan, of around 10000

charging cycles, and the high energy efficiency, that can go from 84 to 97% [28]. The

disadvantages of this technology are the daily self-discharge rates that can be quite high (up

to 40% self-discharge rate) and the capital cost for installing a supercapacitor that can be

superior than 6000$/kWh [14]. It also worth noting that supercapacitors and capacitors are

usually used in short term applications rather than long-term ESS usage. They usually are used

as pulse power controllers, bridging power to a certain equipment, UPS devices and other

applications. [1]

2.2.7. Superconducting Magnetic Energy Storage

Superconducting Magnetic Energy Storage (SMES) systems are usually divided into three main

parts of their composition: a superconducting coil unit, a power conditioning subsystem, and a

refrigerator and vacuum subsystem [3] [29]. The system stores the energy in the magnetic field

that is generated by the direct current that flows through the superconductor coil. The coil

itself was previously cryogenically cooled to a temperature below the superconducting critical

temperature.

When electric current passes through a coil, the electric energy is dissipated in the form of

heat. This happens due to the resistance of the wires of the coil. However, if the coil’s wires

are made of a superconducting material, like mercury or vanadium, and if they are under their

superconducting state, resistance is close to null, making it able for the electric energy to be

stored without significant losses.


17

When the SMES system is discharging, it can release the stored energy in the AC form using

an integrated power converter. The amount of stored energy is dictated by the self-inductance

of the coil and the current that flows through it [30]. Figure 2-11 shows a simple schematic of

a SMES system.

Figure 2-11 - Simple scheme of the composition and operation of a SMES system [3]

The main advantages of SMES technology are its high-power density that can be up to

4000W/L, response times that can be around the 1 millisecond, quick discharge times, of around

1 minute for a full discharge of the SMES system. The high efficiency levels of around 95% and

the long lifetime (up to 30 years) are also points that need to be taken into consideration when

considering this technology as an ESS [28] [31] [32]. Comparing the SMES systems to the battery-

based systems, SMES systems can be fully discharged with little degradation compared to

conventional batteries, even after a large amount of charge-discharge cycles.

The major cons of this type of storage system are the high initial installation costs, that can

be as high as 10000$/kWh, or 7200$/kW. They have a daily self-discharge rate of around 10%

to 15% of total installed capacity and can contribute to damaging the environment due to their

strong magnetic field. [14] [15]. Also, worth mentioning is that the coil, being supercooled, is

very sensitive to small temperature variations that can end up causing a loss of stored energy

in power and energy management situations. It is expected that these kinds of systems will

have a growing impact on the integration of variable renewable energy sources due to their

fast response times [33].


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2.2.8. Hydrogen Storage and Fuel Cell

EES systems based on hydrogen storage and fuel cells are usually separated into two

different processes: one for storing energy and the other to produce the electric energy.

Hydrogen production is commonly achieved by using a water electrolysis unit that uses water

to obtain the hydrogen. Hydrogen can then be stored in high pressure containers for later use

[1] [18]. For converting the hydrogen into electric energy, the fuel cell is the main part of the

system, being a key technology in hydrogen-based ESS.

Fuel cells use the stored hydrogen’s chemical energy and oxygen from the air to obtain

electric energy [34]. The chemical reaction is the one described on Equation 2-1:

2𝐻2 + 𝑂2 → 2𝐻2𝑂 + 𝐸𝑛𝑒𝑟𝑔𝑦 (2-1)

Apart from the electric energy that is released, heat is also a part of the products of the

reaction in Equation 2-1.

There are six major groups of fuel cells [35]:

• Alkaline Fuel Cell (AFC)

• Phosphoric Acid Fuel Cell (PAFC)

• Solid Oxide Fuel Cell (SOFC)

• Molten Carbonate Fuel Cell (MCFC)

• Proton Exchange Membrane Fuel Cell (PEMFC)

• Direct Methanol Fuel Cell (DMFC)

Although there isn’t much extension over each type of fuel cell and their applications, it is

worth mentioning the different types of technology that exist. In Figure 2-12 we present a

simple illustration of how a Hydrogen Storage and Fuel cell system is

Figure 2-12 - Simple scheme of Hydrogen Storage and Fuel Cell system [3]


19

The production of electric energy using fuel cells and hydrogen storage has some advantages

that are worth mentioning: electricity production using fuel cells is, in general, less noisy and

produces less pollution than conventional fossil fuel energy production. It is also a more

efficient electric energy production than those who use fossil fuels [36]. Besides, it is a

technology that is easily scalable, variating from 1kW to hundreds of MW of installed

production. Its compact design can also facilitate the integration in certain scenarios. And the

combination of hydrogen storage and fuel cell technology can help providing steady electrical

supply to the grid or to the system where it is applied. This technology is also a serious

candidate for transportation purposes, being an alternative to fossil fuels on motorized vehicles

[35]. The dual integration of hydrogen storage and fuel cell can offer power independence and

capacity in energy production, storage and usage, due to the separate process. The system can

store energy in the hydrogen deposit, while the fuel cell can continue to produce energy.

Although hydrogen storage with fuel cells is still in development stage, there are already

some concerns with the technology. First, the disposal of exhaust fuel cells is an issue, due to

the toxic materials used as electrodes or catalysts. The degradation of these materials must be

taken into consideration, and in due time they must be recycled to toxic waste.

Another point of current research is the costs of implementation of this technology.

Research has been made towards cost reduction and the improvement and corroboration of the

durability of hydrogen storage with fuel cells [29]. These issues need to be tackled before this

type of ESS can be considered for mass implementation.

2.2.9. Thermal Energy Storage

Thermal Energy Storage (TES) systems can accommodate a variety of technology that can

store available heat in insulated repositories. This heat can be stored using various techniques

that this paper will not detail [37].

TES systems normally are composed by a storage reservoir, a chiller or a built-up

refrigeration system, pipes, pumps and control systems. They can be split into two different

groups of TES, depending on the operation temperature: low temperature TES and high

temperature TES.

Most common low temperature TES exploit underground aquifers or are based on the

cryogenic technique. On the other hand, high-temperature TES can include latent heat TES,

sensible heat TES and concrete thermal storage [14] [38].


20

Figure 2-13 - Simple schematic of a Sensible Heat storage system, being integrated into a wind

generation unit [3]

The technologies before mentioned have different applications, in specific scenarios,

depending on their characteristics. An example of said applications is the usage of latent heat

storage systems in buildings and in situations where the space is more reduced, due to their

high storage energy density, which gives the system a good performance, even with a small

dimension reservoir [39]. Other example is the application of cryogenic energy storage that is

being used in research and is expected to be used in future power grid management situations.

TES systems have various characteristics that are worth being mentioned: They can store

large amount of energy without being a major environmental and safety reliability. They also

have a small self-discharge ratio that varies from 0.05 to 1% of total system capacity. As said

before, they have a good energy density, allowing for small reservoirs to be used (80 to 500

Wh/L) and also possess a good specific energy for the system itself (80-250 Wh/Kg). This is a

technology that is also quite cheap, with the initial capital cost variating from 3 to 60$/kWh

[14] [40]. But although these aspects, it is still worth mentioning that TES systems have a low

cycle efficiency rating, that variates from 30 to 60%, being this still one of the major research

and development bumps that needs to be overcome.

Due to the characteristics of this technology, there are many research and study cases being

developed in order to better integrate TES systems in the power grid. The main applications

that TES systems are being used for are load shifting cases and even electricity generation for

heat engine cycles. Peak shaving and industrial power backup are also fields where TES systems

are being implemented [14].

2.2.10. Hybrid Electrical Energy Storage

Hybrid Electrical Energy Storage Systems are not an ESS technology for itself. Basically,

hybrid energy storage combines two or more EES technologies into one installation in order to

take advantage of the various advantages of each ESS. This can be used to achieve specific of

a certain usage scenario, meet harsh conditions for the ESS operation, and overall, to improve


21

the performance of the ESS, with each technology used helping to overcome the disadvantages

that each has.

One of the examples of Hybrid Electrical Energy Storage systems, ADELE, uses CAES and TES

technologies to improve the overall efficiency of the storage system and to avoid the

consumption of fossil fuels for energy production [41].

Other example of a hybrid storage system is the combined application of supercapacitors

and storage batteries. This will offer a high storage capacity while still offering very fast charge

and discharge times for prompter actuation when needed.

2.3. Energy Storage Systems Applications

2.3.1. Load Leveling

The demand in power systems varies along the day. In Portugal, peak demand usually occurs

when people arrive home after work and during the evening. This variation of demand is

reflected in the cost of energy [2]. Usually, electricity prices are higher during peak-demand

periods and lower during the off-peak periods. This happens due to the fact that more expensive

generators have to be turned on to fulfill the user demands, resulting in an increase of

electricity price [2]. In Figure 2-14 we can see how the price of electricity changes during a day

for the Iberian Electric Energy Market (MIBEL). The bars indicate the price of energy for each

hour, the blue line indicates the total market energy, including the bilateral contracts, and the

orange line indicates the total energy commercialized in the daily market.

Figure 2-14 – Variation of electric energy costs for the Iberian Market, in 10-07-2010 [42]

A useful tool to even the electricity prices during the day is called Load Leveling. Load

leveling consists of using the energy stored during low demand periods to supply the loads

during peak demand periods. This reduces the need for drawing power from the grid, making

0.00

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it less demanding for the gird infrastructure and for the peaking power plants [43]. An example

of this is shown in Figure 2-15.

Figure 2-15 - Simple scheme for a load leveling solution with an ESS [43]

Being Pmax the maximum power that the grid can supply to the load through the existing

lines, when the demand is bigger than Pmax, there are only two solutions [43]:

1. Increase the grid infrastructure/generator capabilities

2. Install an ESS on the energy system

The ESS will charge during the hours of less power consumption, when the energy price is

cheaper. When the demand surpasses Pmax, the ESS will discharge and suppress the needs of the

load, without needing extra energy from the grid. This allows for a postponement of

investments to reinforce the infrastructure of the grid, without compromising the quality of

service for the consumers. The ESS, in particular a Rechargeable Battery Storage System (BSS),

is a good quality solution, being able to be easily connected to the electrical grid. They can

provide advantages not just for the consumer, but also for the energy-providers, helping them

meet peak-demands and critical loads, while not being constrained by the limitations of the

electrical grid.


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2.3.2. Impact on long distance energy transport

Nowadays, power grids are bigger than ever, and its complexity keeps growing as power

demands are getting bigger every day. Consumers have loads that keep increasing and whose

location can be very far from the generation facilities [2].

With the increasing number of disperse production (DP) sources, this problem tends to

become less disturbing for the grid management. However, Disperse Production still is not a

standard in every grid, so we still see a lot of the conventional production in the power systems,

with that energy being transporter through the grid and distributed to the loads. Long distance

transport of energy has some issues, including the high amount of losses, the higher chances of

service interruption [2] and the price of the infrastructure necessary to supply the loads.

ESS can help in these scenarios. While it does need to charge with energy obtained from the

grid, the ESS will help diminish the power flow during peak times. With the ESS charged, it can

feed loads to which he is connected. This means that the loads will not need to request energy

from the power plants, diminishing the amount of energy that needs to be transported from

the generation location to the consumer. This will lead to less congestion issues and fewer

losses in the grid, reflecting in the reduction of the price of delivering energy to the consumer.

Figure 2-16 - Basic representation of a conventional use of an ESS [44]

The reduction of energy flowing from the main power plants to the consumers will reflect

in other ways that will be better explained thorough this chapter.


24

2.3.3. Congestion Management in the Power Grid

The congestion in the grid reflects on the problem mentioned in 2.3.2. As the distance

between the loads and the generators increases, the flow of energy from one point to another

tends to get bigger, as more and more energy is produced to suppress the growing needs of the

consumers [2]. This can lead to the congestion of the electrical lines, who have physical

limitations to the amount of energy they can transport at a given time. The loads might not be

properly supplied, and it can cause problems in the safety and reliability of the system.

The grid operators try to predict when these congestions might happen, by calculating the

future dispatch for the production facilities and the estimated power flow for that given day

[2]. However, these predictions might be nullified as unexpected situation might occur that

can lead to the congestion of some lines (per example, if one or more major lines happen to go

off-service, the power flow will have to be redirected, which can lead to congesting other

transmission or distribution lines).

Grid dispatch cannot solve all the congestion problems that exist in a real scenario. When

these kinds of problems start to be recurrent, it is a sign that the grid needs to be reinforced

in order to prevent them. The most common solutions for solving congestions in the grid is line

reinforcement: replacement of older lines by new ones with larger capacity or installing new

lines in parallel with the older ones [2].

ESS can help in dealing with this situation. When installed in the appropriate locations of

the grid, such as key substations in the end of lines that are usually heavy loaded, the ESS can

store energy during off-peak periods, when the loads are smaller [2]. Then, at peak hours,

power flows in the grid will not be so big and there is less need for peak production at the

powerplants. After charging, the ESS can provide energy to the loads when demand is higher,

and the lines are already operating at full capacity, eliminating the problems caused by line

congestion. The installation of the ESS will also allow grid upgrade postponement that would

be required due to the effects of line congestion. [2]

2.3.4. Renewable Energy Sources Penetration Increase

Renewable energy sources (RES) are becoming more and more usual in the actual scenario

of the energy system. Figure 2-17 shows the results of a study made by the European

Environment Agency, where we can see the evolution of RES penetration in the European Energy

panorama.


25

Figure 2-17 – Evolution of RES in the European scenario [45]

The tendency is for RES penetration to grow more and more, as traditional energy production

methods tend to decrease [45]. A study made by the Imperial College of London shows a

prediction of the evolution of the different generation capacities that will be operating in

Europe up to 2030 [46]. As shown in Figure 2-18, the tendency is for the decrease of

conventional fossil fuel production facilities, to be replaced by RES.

Figure 2-18 - Evolution of the different types of energy generation installed capacities [46]

It is still important to consider the role of DG in this scenario. As DG will increase, and more

and more consumers will have production capability, conventional thermal plants will be only

used in order to complement renewable generation (due to weather reasons, intermittency,

etc.).


26

Figure 2-19 - RES capacity progress up to 2030 [47]

At the same time, the consumer needs for energy will increase accordantly, as electrical

vehicles and other bigger loads will start to be connected to the grid. As that happens, it is

important to assure that the quality of service will not be compromised by the bigger

penetration of RES on the system. Although RES can be environmental friendly and produce

cheaper energy than traditional sources, that comes along with some problems for the grid and

for the quality of service.

a. Frequency Regulation

RES are very weather dependent, and that results in production systems that can go from

on to off very quickly. RES like solar and wind power have a very intermittent and do not

contribute to frequency regulation the same way that conventional thermal generators do [43].

The conservation of energy principle states that the produced energy must be equal to the

loads at all time. RES generation depends on weather conditions and have no frequency

regulation abilities. With that said, in what concerns frequency regulation, a system with a

large penetration of RES is more vulnerable, because conventional generators need to

compensate not only load fluctuation but also RES intermittency. An ESS can help in this

situation, serving as a frequency regulator for the system, maintaining the output signal of the

powerplant with characteristics within the ones accepted by the network [2].

b. Power Fluctuation

Renewable Energy sources will always have the problem of being weather dependent for

their operation. This means that, with the current technology, an electric system cannot count

on RES alone for supplying every load of the system. If a grid only has RES with no other backup,

power outages will be frequent when the weather conditions do not allow for PV and Wind

production [2].


27

That is why RES, like solar and wind power, need to be backed up by conventional fossil fuel

power plants, whose output is more stable and can produce energy at any given time. That

way, when RES production fails, the balance between generation and consumption will be

maintained by the activation of conventional power plants. It is estimated that for every 10%

of wind penetration in the grid, there is a need of around 2% to 4% of wind installed capability

that will need to be supplied by conventional production sources [43].

Another problem that contributes to the power fluctuation of the system is that RES

production can be rather inconsistent. PV plants are very dependent of solar irradiance, which

can cause fast variations of power output [48].

ESS can help in scenarios of power fluctuation [2]. Large-scale ESS can help preventing loss

of load caused by RES intermittency, providing stable supply to the loads thanks to the energy

arbitrage of ESS [49]. The location of storage can also be a factor In fighting power outages and

output fluctuation of RES. For example, when installing an ESS next to a wind farm, the power

output will be more stable and power levels will be better regulated thanks to ESS nullifying

the fluctuation of the wind farm. [49].

ESS installation near consumption points is also interesting to mitigate power fluctuations

for the consumer. If the user has any type of load who needs a continuous supply, an ESS can

provide a stable backup in case of RES failure or a power outage [2].

Figure 2-20 - Simple Scheme of a PV system with Energy Storage [50]

2.3.5. Deployment of the Smart Grid Concept

a. What is the Smart Grid

The electric grid that exists nowadays is becoming outdated. The grid was initially built to

be a one-way path from generation to consumption, without being ready for distributed

generation [2]. It is not prepared for real-time communication between the grid assets and the


28

grid operators, which makes the job of operating the grid more complicated and mainly based

on predictions and estimations. Grid operators rely heavily on predictions (of consumption,

power flows, weather conditions and so on) to make dispatches for the future days and to

predict how the grid would have to react to the expected situations.

Smart Grids consist in the implementation of new technologies in the grid that will allow for

real time communication and for real time information delivery to the grid operator [2] [51].

Not only that, but Smart grids also allow for a bigger system control, being it tap control,

generator output, RES control, and overall system overlook through sensors and measurement

instruments located thorough the energy grid. This will make the grid operator fully aware of

what is happening at any point of the grid at any given moment and provide total control of

the system, being it the generation side or the demand side [2].

Advantages of the smart grid include [51]:

• Better efficiency regarding energy transmission;

• Quicker restoration periods after failure;

• Reduced management and grid operation costs;

• Increased integration of Renewable Energy Sources and other distributed

generation;

• More information and control for the common user;

Figure 2-21 - A simple schematic of a Smart Grid, where all the active parts of the grid are

connected [52]

b. ESS and Smart Grid applications

ESS can play an essential role in future Smart Grid. as it will contribute to a deeper

integration of microgeneration, to congestion management, to load control (of electric

vehicles, for instance) [2]. In short, it will make the system work better, more reliable and

safer.

The first point worth mentioning is the ability for ESS to control power flows and to help

mitigating congestions when installed on the consumer side of substations [2]. The effects of


29

ESS in relieving congestions are deeper explained in point 2.3.3. On top of that, the ESS can

also be a method to control voltage levels in the grid, through power injections or absorptions

to help maintain voltage in a desired level [2].

Another usage for ESS in Smart Grid integration is the ability for the ESS to provide stable

power to existing equipment in the grid, to avoid power outages [2]. An example of an ESS

system that can act as a mobile energy source are electric vehicles (EV). In fact, EV can act as

mobile storage systems that can be used by the grid operator in case of emergency or other

kind of need to power some parts of the system that require immediate energy. This way, the

EV will not act purely as a load when it is charging, but can also act as an ESS, avoiding the

need to use other energy sources (e.g. thermal powerplants) to feed the system [2].

Lastly, another way that ESS can help with Smart Grid integration is by acting as an Energy

Management System (EMS) for houses and buildings [2]. With Smart Grid technology, users can

verify their consumptions in real time. This will allow for changes in their energy spending

patterns, and help with making the houses and buildings more energy efficient [2]. Smart Grids

also allow for the optimization of the consumers’ individual resources accordingly to the

network’s resources and needs. The storage system will work according with the building owner

desire, with overview of its operation by the grid operator. The ESS will allow the condominium

manager to store energy during periods of low consumption, and use the stored energy during

peak periods, to allow for fewer costs with electric energy [2]. This will be particularly useful

in cases where the buildings have local generation, like PV systems, where the energy produced

in periods of low consumption can be used in peak periods, making the building self-sufficient

and independent from the energy of the grid.

c. Smart Microgrids

Smart microgrids can be a classification for various things. A smart building with an ESS can

be treated as a smart microgrid. At the same time, an isolated grid inside the main energy

network, with its own production, load and storage can also be defined as a microgrid [2]. An

isolated grid is an energy system, usually of small size, who has stable production at all times

to be able to supply its loads [53].

ESS are a key part of Smart Microgrids. Microgrids must be capable of changing its size and

infrastructure at a given point, to follow the demands of its loads. The same happens with the

ESS installed in those networks. [2]. Smart Microgrids should also be available to cooperate with

surrounding microgrids in case of need [2]. This control must be made by the grid operators,

that through Smart Grid technology can control the power flow through the connection of the

adjacent grids, and the production of each of the microgrids.


30

But a key factor for Smart microgrids is the autonomy [2]. ESS play a key part in microgrid

autonomy. When operating disconnected from the main grid (Island mode), ESS will help

providing the loads with stable supply, if the installed production is not sufficient at a given

point [2]. It is up to the Microgrid operator to fully optimize its resources to achieve the best

isolated performance. And Smart Grid technology is crucial in these situations, because allows

for total remote control and monitorization of the grid, leading to a better operation and better

quality of service for the users.

A study was made in Azores, Portugal [54], where a system working on island mode was put

into test with and without an ESS. The results were the following:

• Without the ESS, the variation of 350 kW of load would end up resulting in around

3Hz of frequency oscillation in the system;

• With the ESS, a variation of 300 kW of load in the system was barely noticed on the

system frequency, with the frequency practically constant value of around 50 Hz.

This example was just to show how ESS can affect microgrids, even in conditions where

these are located in an island, making them more stable and more secure, and allowing for the

implementation of microgrids to be expanded.

2.3.6. Continuity and Flexibility of Supply

One of the fundamental characteristics of electricity transport and distribution is the fact

that the service must be continuous, with the minimum number of interruptions possible [2]. It

also must adapt itself to the flexible demands of the consumer, to provide the correct amount

of energy at any given time [2]. If the right amount of electricity cannot be provided at a given

time, that can result in the decline of service quality indexes, power spikes or, in the worst-

case scenario, power outages and blackouts [2].

To avoid these situations, and for continuous supply of energy to the costumers to be

achieved, grid operators rely on forecasts to analyze the fluctuation of demand and

intermittency of renewable production, so that production can be as accurate as possible,

bearing into consideration all the factors that might cause disturbances in normal service [2].

For example, RES units are unable to adapt their power injections in the system accordingly

to the system’s total load [2]. The output of the facility is dictated by the weather conditions.

RES are also not capable of doing system frequency control, with this happening due to the fact

that, once again, as RES units cannot control their power output, the power injection cannot

be controlled to adjust to frequency variations in the system. For RES to be able to do this kind


31

of control, phase-shifter inverters would have to be installed, raising the total cost of the

system [2].

An energy storage system could help compensating both the kilowatt and the frequency

control functionalities in production facilities, being it renewable or traditional production

facilities [2]. The ESS can act as a reserve energy storage that can be used in cases of high load

variations that cannot be compensated by regular generation. In this scenario, the storage

system would charge in periods of low demand, and that stored energy could be used later to

act as the kilowatt function normally acts, by discharging and supplying its energy to the grid

to suppress the unexpected growth in demand.

As far as frequency control is regarded, ESS can help in maintaining frequency levels within

desired in the grid. Through power consumption (charging) and power injection (discharging),

the ESS can help mitigating frequency variations in the grid, the same way generators do, but

in a more efficient way, since there is no need for extra fuel consumption to inject energy into

the grid, unlike conventional thermal power plants. And, since RES do not have control of their

power output, the ESS can work together with the renewable production, in order to make

them more suitable to work in the grid, as detailed on 2.3.4.

2.4. Chapter Summary

This chapter goal was to give a short, yet overall, presentation of the different types of

storage technologies and the various applications that ESS can have in the energy network.

There are several ESS technologies, each with their own set of benefits and disadvantages.

It is up to the user and the project manager to choose for each specific case which is the best

ESS to use.

The same point is valid for the different applications that ESS have. According to the main

goal that they are purposed to fulfill, ESS can have different implications in the operation of

the energy system. The focus of the objective of the storage unit must be defined when

installed, in order to better optimize the installation location and the storage unit

characteristics.

With an introduction to ESS made, the core objective of this dissertation can now be better

explored, having the theoretical background of how an ESS operates been covered.


32

Problem Formulation

33

Problem Formulation

3.1. Introduction and Context

The goal of the present dissertation is to develop a 24-hour unit commitment optimization

tool, with storage, and AC restrictions, such as active losses. Such restrictions are obtained by

running an AC OPF for each of the periods in study

For this purpose, it is necessary to lay down the concept of the AC OPF and to describe how

is it applied in the context of this research work.

This chapter has the purpose of introducing the mathematical concepts that support the

optimization method developed, as well as the AC OPF. It is not in the scope of this thesis to

enter in much detail on the mathematical algorithms to solve this problem, but it is important

to highlight the objective of the technique developed and how is that objective achieved.

Other important aspect that this chapter is the methodology used to achieve the results

presented in Chapter 5. In a simple way, it is intended to present the computational steps

necessary to simulate the multi-temporal OPF with the addition of an ESS. A short presentation

of the software used is made to contextualize its function for the purpose of this dissertation.

3.2. General Optimal Power Flow Formulation

To solve any kind of OPF problems, the first step is to identify the different types of variables

that will be fundamental to the determination of any system’s OPF.

These variables can be divided into three sets [55]:

Problem Formulation

34

• Control Variables – u;

• State Variables – x;

• Parameters – p;

The main objective of the OPF is to minimize energy production costs while respecting the

system restrictions. That can be represented by the following equations [56]:

min𝑥

𝑓(𝑥) (3-1)

subject to:

𝑔(𝑥) = 0 (3-2)

ℎ(𝑥) ≤ 0 (3-3)

𝑥𝑚𝑖𝑛 ≤ 𝑥 ≤ 𝑥𝑚𝑎𝑥 (3-4)

Where f(x) is the objective function, g(x)=0 represent the equality constraints, h(x) are the

inequality constraints, like the line flow or voltage limits.

The state variables set, x, is the optimization vector for the standard AC OPF and consists

of [56]:

Where θ is the phase angles of the bus voltages (except the slack bus), Vm represents the

magnitude of the bus voltages in the busbars without generators, Pg and Qg represent the

generator’s injected active (P) and reactive (Q) power [55] [56].

Pg and Qg, along with the tap positions of the transformers and the capacitor banks, and the

storage unit active generation are the system’s control variables, u. So the vector of control

variables will be as follows:

Control Variables: u = [ Pg1 Pg2 Pg3 Pg4 Pg5 Pg6 Psc Qg1 Qg2 Qg3 Qg4 Qg5 Qg6 T1 T2 T3 T4 C1 C2 ]

where T represents the transformer tap position and C the capacitor tap position.

The objective function presented in Equation 3-1 consists of the aggregation of the

individual cost functions of each generator [56]:

min

𝜃,𝑉𝑚,𝑃𝑔,𝑄𝑔

∑ 𝑓𝑝𝑖(𝑃𝑔

𝑖

𝑛𝑔

𝑖=1

) + 𝑓𝑞𝑖(𝑄𝑔

𝑖 )

(3-6)

𝑥 =

[ 𝜃𝑉𝑚𝑃𝑔𝑄𝑔]

(3-5)

Problem Formulation

35

Where ng stands for the number of the system’s generators. 𝑓𝑝𝑖(𝑃𝑔

𝑖) stands for the part of the

objective minimization function f related with the active power generation. Complementary,

𝑓𝑞𝑖(𝑄𝑔

𝑖 ) stands for the minimization function f but considering the reactive power generation.

As for the constraints, the equality function g(x) = 0 represent the set of equations that

defines the balance between generated and consumed power. Assuming g(x) is divided into

active and reactive sub-equations, the power balance equations would be [56]:

𝑔𝑃(𝜃, 𝑉𝑚 , 𝑃𝑔) = 𝑃𝑏𝑢𝑠(𝜃, 𝑉𝑚) + 𝑃𝑑 − 𝑃𝑔 (3-7)

𝑔𝑄(𝜃, 𝑉𝑚, 𝑃𝑔) = 𝑄𝑏𝑢𝑠(𝜃, 𝑉𝑚) + 𝑄𝑑 − 𝑄𝑔 (3-8)

Where 𝑃𝑏𝑢𝑠 and 𝑄𝑏𝑢𝑠 stand for the injected active and reactive power, respectively, in each

of the system’s bus bars. 𝑃𝑑 and 𝑄𝑑 are the bus’s load demands.

As we interested in a full AC modeling of the system, the equations above described can be

adjusted according to the system’s bus bar types [56]:

𝑔(𝑥) = [𝑔𝑃

𝑖 (𝜃, 𝑉𝑚 , 𝑃𝑔)

𝑔𝑄𝑗(𝜃, 𝑉𝑚 , 𝑄𝑔)

] ∀𝑖 ∈ 𝑃𝑉𝐵𝑢𝑠 ∪ 𝑃𝑄𝐵𝑢𝑠

∀𝑗 ∈ 𝑃𝑄𝐵𝑢𝑠 (3-9)

Where PVBus and PQBus represent the PV and PQ bus bars present in the system.

The inequality constraints represent the branch flow limits and are represented by two

groups of nl nonlinear functions, one group corresponding to the bus where the line begins, and

the other group to the bus where the line ends. Each of the group of nonlinear equations are

functions of the bus bars’ voltage angle and magnitude as can be seen in the equation below

[56]:

ℎ𝑓(𝜃, 𝑉𝑚) = |𝐹𝑠(𝜃, 𝑉𝑚)| − 𝐹𝑚𝑎𝑥 ≤ 0 (3-10)

ℎ𝑒(𝜃, 𝑉𝑚) = |𝐹𝑒(𝜃, 𝑉𝑚)| − 𝐹𝑚𝑎𝑥 ≤ 0 (3-11)

Since the line flows in our case are expressed in MVA, the flow function, F can be expressed

as [56]:

𝐹𝑠(𝜃, 𝑉𝑚) = 𝑆𝑠(𝜃, 𝑉𝑚) (3-12)

𝐹𝑒(𝜃, 𝑉𝑚) = 𝑆𝑒(𝜃, 𝑉𝑚) (3-13)

With 𝑆𝑠 and 𝑆𝑒 being the complex power injections at the start and at the end bus bar,

respectively. 𝑆𝑏𝑢𝑠 can be expressed as [56]:

Problem Formulation

36

𝑆𝑏𝑢𝑠(𝑉) = [𝑉]𝐼∗ = [𝑉]𝑌𝑏𝑢𝑠∗ 𝑉∗ (3-14)

Where 𝑌𝑏𝑢𝑠∗ is the conjugate of the admittance matrix of the system that relates the nodal

current injections to the complex node voltages.

The last part of the general OPF formulation worth mentioning concerns the variable limits.

These include several constraints to keep all the system control variables within the maximum

and minimal limits imposed by the system. Therefore, they can branch out as [56]:

𝜃𝑖𝑟𝑒𝑓

≤ 𝜃𝑖 ≤ 𝜃𝑖𝑟𝑒𝑓

, 𝑖 = 𝑆𝑙𝑎𝑐𝑘 𝐵𝑢𝑠 (3-15)

𝑣𝑚𝑖,𝑚𝑖𝑛 ≤ 𝑣𝑚

𝑖 ≤ 𝑣𝑚𝑖,𝑚𝑎𝑥 , 𝑖 = 1… 𝑛𝑏 (3-16)

𝑝𝑔𝑖,𝑚𝑖𝑛 ≤ 𝑝𝑔

𝑖 ≤ 𝑝𝑔𝑖,𝑚𝑎𝑥 , 𝑖 = 1… 𝑛𝑔 (3-17)

𝑞𝑔𝑖,𝑚𝑖𝑛 ≤ 𝑞𝑔

𝑖 ≤ 𝑞𝑔𝑖,𝑚𝑎𝑥 , 𝑖 = 1… 𝑛𝑔 (3-18)

where nb represents the number of buses in the system and ng the number of generators.

3.3. Expanding the OPF formulation

In 3.2 the formulation for a generic AC OPF was presented. This formulation is valid for a

single instant or point in time. However, in this study we need to consider some adjustments,

so that it could transform a generic OPF into an unit commitment optimization tool for a 24

hours span, with the consideration of storage.

Starting with the objective function found in 3.2, the presented function performs a single

period optimization of a generic AC OPF formulation. However, the objective function used in

MOST and ultimately used in this study takes into consideration the multiple time frames where

the system is tested, whose optimization of the global cost is the goal.

Another aspect of this study is the influence of the storage unit on the results of the multi-

temporal OPF, so that parameter also must be taken into consideration in the final objective

function.

Generally, the main objective of the multi-temporal OPF is the same as any other OPF

problem: To minimize the objective function, in this case, the overall energy production costs

of the system

min𝑥

𝑓(𝑥) (3-19)

Problem Formulation

37

The difference in this scenario is the f(x) function that has more elements, ending up being

as [57, 58]:

𝑓(𝑥) = 𝑓𝑝(𝑝, 𝑞) + 𝑓𝑠(𝑠0, 𝑝𝑠𝑐 , 𝑝𝑠𝑑) + 𝑓𝑢𝑐(𝑢, 𝑣, 𝑤) (3-20)

Where 𝑓𝑝(𝑝) stands for the initial objective function, being the function of optimization of

the expected cost of active power dispatch, fs is the storage cost and fuc the unit commitment

cost. Being this a multitemporal problem, the dispatch optimization function becomes [57, 58]:

𝑓𝑝(𝑝, 𝑞) = ∑ ∑𝑓𝑝𝑖(𝑃𝑔

𝑖

𝑛𝑔

𝑖=1

)

𝑇

𝑡=1

= ∑∑(𝐶𝑝𝑖 ∗ 𝑝𝑔

𝑖

𝑛𝑔

𝑖=1

)

𝑇

𝑡=1

(3-21)

𝑓𝑠(𝑠0, 𝑝𝑠𝑐 , 𝑝𝑠𝑑) represents the optimization of the storage unit costs. For this problem, the

cost associated to the storage unit is divided in two parts: The charging cost that is dictated by

the cost of the additional production that the conventional generators must supply, in order to

charge the storage unit. The discharge cost is set to zero, as the energy cost was considered

during the charge period. This function however is responsible for optimizing the costs of stored

energy, initial stored energy and the value loss of any leftover energy that the storage unit

retains [57, 58]

𝑓𝑠(𝑠0, 𝑝𝑠𝑐 , 𝑝𝑠𝑑) = 𝐶𝑠0𝑇 𝑠0 − (𝐶𝑡𝑠0

𝑇 𝑠0 + 𝐶𝑡𝑠𝑐𝑇 𝑝𝑠𝑐 + 𝐶𝑡𝑠𝑑

𝑇 𝑝𝑠𝑑) (3-22)

Where 𝑠0 stands for the initial stored energy of the unit (in this study, the initial storage

level in each day is set to zero), 𝑝𝑠𝑐 is the charging power input and 𝑝𝑠𝑑 is the discharging power

output of the storage unit, 𝐶𝑠0𝑇 represents the cost of initial stored energy that the battery

might have, for the full 24 hours of the system (T), 𝐶𝑡𝑠𝑐𝑇 and 𝐶𝑡𝑠𝑑

𝑇 represent the cost of charge

and discharge of the storage unit, for the period t.

With the addition of the storage unit to the system, some other constraints must be added

to the ones referred in 3.2. Starting with the storage dispatch definition and the consequent

storage limits, those can be defined by [57, 58]:

𝑝𝑡,𝑖 = 𝑝𝑠𝑐𝑡,𝑖 + 𝑝𝑠𝑑

𝑡,𝑖 (3-23)

𝑝𝑠𝑐𝑡,𝑖 ≤ 0 (3-24)

𝑝𝑠𝑑

𝑡,𝑖 ≥ 0 (3-25)

Now to set the constraints for the energy level of the storage unit, it is required to define

the maximum and minimal levels of energy that the unit can have, so that MOST can do the

control of the unit’s charge levels [57, 58]:

Problem Formulation

38

𝑠𝑡,𝑖 ≥ 𝑆𝑚𝑖𝑛𝑡,𝑖

(3-26)

𝑠𝑡,𝑖 ≤ 𝑆𝑚𝑎𝑥𝑡,𝑖 (3-27)

It is also important to define the state of charge of the storage unit for each period [59].

𝑆𝑂𝐶𝑡 = 𝑆𝑂𝐶𝑡−1 + (𝜂𝑑 ∗ 𝑝𝑠𝑐𝑡,𝑖 −

𝑝𝑠𝑑𝑡,𝑖

𝜂𝑑

) (3-28)

𝑆𝑂𝐶𝑚𝑖𝑛 ≤ 𝑆𝑂𝐶𝑡 ≤ 𝑆𝑂𝐶𝑚𝑎𝑥

𝑆𝑂𝐶1 = 𝑆𝑂𝐶24

𝑝𝑠𝑐𝑡,𝑖 ∗ 𝑝𝑠𝑑

𝑡,𝑖 = 0

(3-29)

(3-30)

(3-31)

Now for the unit-commitment aspect of the simulation, the objective function 𝑓𝑢𝑐(𝑢, 𝑣, 𝑤) is

a simple combination and optimization of no load scenario costs, and start-up and shutdown

costs for the installed generators, and it is optimized by following Equation 3-32

𝑓𝑢𝑐(𝑢, 𝑣, 𝑤) = ∑ ∑𝐶𝑃𝑡,𝑖(0)𝑢𝑡,𝑖 + 𝐶𝑣

𝑡,𝑖𝑣𝑡,𝑖 + 𝐶𝑤𝑡,𝑖𝑤𝑡,𝑖

𝐼𝑡

𝑖=1𝑡∈𝑇

(3-32)

Where 𝑢𝑡,𝑖 stands for a binary commitment vector for unit i, in the time period t. It is 1 if

the unit is online and 0 if the unit is not operational. 𝑣𝑡,𝑖 and 𝑤𝑡,𝑖 stand for the unit’s binary

startup and shutdown states. If the unit has a start in period t, vector v is 1. Similarly, if a unit

has a shutdown even in period t, vector w is 1. 𝐶𝑣𝑡,𝑖 and 𝐶𝑤

𝑡,𝑖 represent the i unit startup and

shutdown costs, for period t.

To integrate the unit commitment and optimization in the problem, some constrains need

to be considered. First, the constraints of power injections and commitment [57, 58]

𝑢𝑡,𝑖𝑃𝑚𝑖𝑛𝑡,𝑖 ≤ 𝑝𝑡,𝑖 ≤ 𝑢𝑡,𝑖𝑃𝑚𝑎𝑥

𝑡,𝑖 (3-33)

𝑢𝑡,𝑖𝑄𝑚𝑖𝑛𝑡,𝑖 ≤ 𝑞𝑡,𝑖 ≤ 𝑢𝑡,𝑖𝑄𝑚𝑎𝑥

𝑡,𝑖 (3-34)

Then a constraint to control the startup and shutdown events in the system [57, 58]

𝑢𝑡,𝑖 − 𝑢(𝑡−1),𝑖 = 𝑣𝑡,𝑖 − 𝑤𝑡,𝑖 (3-35)

0 ≤ 𝑣𝑡,𝑖 ≤ 1 (3-36)

0 ≤ 𝑤𝑡,𝑖 ≤ 1 (3-37)

𝑢𝑡,𝑖 ∈ {0,1} (3-38)

It is important to underline that the mathematical formulation used in this problem was

adapted based on the generic OPF formulation used in an AC OPF implementation. Then they

Problem Formulation

39

were also adapted according to the formulation considered in MATPOWER and MOST, as these

are the tools used in this simulation study. Moreover, the formulation was also adapted to the

proposed study case.

3.4. Methodology

The flow chart in Figure 3-1 describes the main steps of the methodology used to process

the simulations in this study, that led to the results presented in Chapter 5.

The flow chart presented is the graphical representation of the steps took to achieve the

results that are presented in this study.

The first step of the work was to define the MATPOWER case file that contains all the

network data, being it bus, generator, branches and even generation costs data. This step is

crucial so that the calculations can be made with the correct data information, allowing the

results to be as accurate as possible, and correctly applicable to the network in question. In

addition, this step is when the load profile of the system is loaded into MOST. The shape of this

profile was based on a real Portuguese load scenario, and adapted to the system in question

(IEEE 30-bus system). Since this is a multi-temporal problem, the load of the system is variable

over time. That is why the system load cannot be introduced directly into the MATPOWER

Figure 3-1 - Methodology flow chart

Problem Formulation

40

network case file (which is a single instant tool). In MOST, the load data is charged into the

algorithm by using a designated MOST function for applying variable load profiles to a network.

In case of the AC OPF, the load can be loaded directly from an Excel file after the network case

load, and applying it to each bus bar.

After the data preparation and introduction, the next thing to do is the first run MOST for

the initial introduced data. The goal of MOST initial run is to define the charge/discharge profile

of the storage unit, if it exists, and do a first DC OPF and optimization for the multi-temporal

problem. This provides an initial picture of how the system will behave, namely when storage

exists, it helps defining how the storage will work during the whole 24-hours period. When

executing the initial MOST run, if the program fails to converge, it is an indication that the

initial state of the system might not lead to an acceptable result. Whether if it is due to

excessive load, voltage constraints that are too harsh, or other constraints that might be too

demanding for the system to converge to a real solution. However, it is important to underline

that this initial run of MOST has the primary function of defining the storage dispatch for the

24 hours of the problem and verifying that the system is converging and able to proceed the

simulations.

When MOST converges, the results obtained can be used to help preparing the multi-period

AC OPF. Since there is no way of doing a multi-temporal AC OPF using MATPOWER, the solution

found was to run an AC OPF for each hour of the system. The data obtained from MOST, namely

the storage settings for each hour, is the starting point for the AC OPF, but being aware that

the other results could be rather different from it, since the AC OPF takes into consideration

line limitations, reactive flow, voltage limits and system losses. The initial MOST is responsible,

as said before, for defining the storage charge and discharge times that are used in the AC

OPF’s formulation. In this (AC OPF) step, the storage i unit is modeled as a negative generator

when it is charging, and a normal positive generator when it is discharging. In both situations,

the cost function of the storage energy is set to zero.

Note that MOST is a DC-based approach and, as so, it does not consider power losses (or

other AC constraints). Thus, the final step consists in running MOST again, but this time by

adding the MW losses obtained in the AC OPF to the system’s load, in order to include the

system’s losses in MOST. This will approximate the results of the AC OPF and of MOST, but

allowing for MOST to do the unit-commitment and overall system optimization. The process is

considered to be iterative, and the result is considered acceptable if the margin of error

between the AC OPF results and MOST are similar enough, depending on the user. If the result

is not acceptable, the AC restrictions must be reintroduced into MOST, until the final results

are the desired ones.

If the final MOST run is a success, the results of all three steps can now be analyzed, finishing

the procedure for calculating the multi-period OPF with storage unit and overall system’s

commitment optimization.

Problem Formulation

41

3.5. Software Description

All of the simulations done in this study used MATLAB and its extension for power system

analysis, MATPOWER. MATPOWER was a key role to execute all the optimal power flow

simulations, with focus especially on the AC OPFs that were executed. MATPOWER is also the

base where MOST is built, so all of the simulations had a base in MATPOWER. In this point, it

shall be given a brief introduction to each of the particular groups of MATLAB and MATPOWER

that were used in this study.

3.5.1. MATPOWER

MATPOWER was initially developed by Ray D. Zimmerman, Carlos E.Murillo-Sánchez and

Dequiang Gan from the Power Systems Engineering Research Center, located at Cornell

University [60, 56].

It is a package of files for MATLAB whose intent is to help in solving power flow and optimal

power flow situations. Its intent is to provide a simple to use and to modify simulation tool for

students, researchers and educators [56].

The initial reason for the development of MATPOWER were the computational requirements

of a Cornell’s university project named PowerWeb, that consists in an online tool for power

flow simulations and analysis [61].

Matpower has various tools and functions for the study of power systems and power flows

in a certain network. In this situation, it was mainly used to calculate the system’s AC OPFs for

each hour, and as a backbone to all the MOST simulations, that use MATPOWER as a cornerstone

for all of its procedures.

More details about MATPOWER and all of its functionalities can be found on the MATPOWER

user’s manual [62].

3.5.2. Matpower Optimal Scheduling Tool (MOST)

Since its sixth version, MATPOWER has included an extra set of programs and respective

implementations for electric power systems scheduling problems. These are known as

Matpower Optimal Scheduling Tool, or MOST.

MOST was initially being developed to help extending the AC optimal power flow already

existing in MATPOWER. But after development, MOST ended up being a tool for solving many

stochastic and multiperiod problems for power systems. This was done while considering new

aspects of the grid that have not had a simple modeling technique before on MATPOWER. With

Problem Formulation

42

MOST, it was now simpler to solve various problems that involved renewable energy sources,

energy storage systems, localized generation reserves, and other aspects that are more detailed

on the MOST User’s Manual [58].

MOST can be used for a variety of scenarios and problems. From simple single period

economic dispatches, to solving multiperiod optimal power flows while managing the charge

and discharge of a storage system, and combining unit commitment to the solution. This last

example was what was made with MOST during this dissertation.

Although the advantages of MOST and the help it brought during this study, it’s worth

mentioning that at the date of this dissertation, MOST can only solve problems while using a

DC model of the network. So, although the input data is a general MATPOWER complete network

data file, based on an AC model, MOST can only work with DC power flow models of the

network.

Presentation of the Study Case

43


4.1. Introduction and Context

This chapter aims at introducing the energy grid used during the course of this study,

presenting its characteristics and the various parts that define the grid as it is.

During this study, various networks were used for testing the algorithms in use. When the

implementation of the algorithms was already considered to be successful, a definite network

was chosen. This definitive network was the IEEE 30-bus system [63] and the load profile that

was applied to the system was obtained by adapting a typical HV load diagram from a

Portuguese HV grid.

The goal with using the IEEE 30-bus system was to achieve results that could be easily

understood and replicated by other researchers, and to try and use a standard network case

for more reliability of the achieved results.

So, in this chapter, the IEEE 30 Bus case is described, bearing in mind that some adaptations

(load level, for instance) were required in the MATPOWER case file, and consequent

simulations.


44

4.2. Network and Load Characteristics

4.2.1. Network Configuration, description and characteristics

As previously mentioned, the network used for the definitive part of this project was an IEEE

30 Bus bar System. This network is based on a real portion of the American Electric Power

system [63]. This network was adopted for this study because it is important to work with public

accessible networks for allowing the replicability of the proposed approach. Besides there are

already implementations of this grid as Matpower case files and for more global interpretation

of the system itself and the results obtained. A one-line scheme of the grid itself can be found

in Figure 4-1.

Figure 4-1 - One-line scheme of the IEEE 30 Bus Network [63]

The network has 6 generators connected to it, used to supply the loads of the system. The

information about the generators is summarized in Table 4-1


45

Table 4-1 - Generator characteristics

Location

(bus) Pmin

(MW) Pmax (MW)

Qmin

(MVar) Qmax

(Mvar) a ($/h)

b ($/MWh)

c ($/((MW)2)h))

G1 1 0 80 -20 150 0.02 2 0

G2 2 0 80 -20 60 0.0175 1.75 0

G3 13 0 50 -15 62.5 0.0625 1 0

G4 22 0 55 -15 48.7 0.00834 3.25 0

G5 23 0 30 -10 40 0.025 3 0

G6 27 0 40 -15 44.7 0.025 3 0

The generators have a production cost for each of the generation units that can be

approximated by a quadratic function, just like the one on Equation 4-1. It is important to

underline that the cost data for the generators are the same as can be found on the IEEE 30

Bus Case. And although the cost functions might be out of date when compared to current

generator costs, for the purposes of this study, this was not seen as an issue.

𝐶(𝑃𝑔) = 𝑎 + 𝑏𝑃𝑔 + 𝑐𝑃𝑔2 (4-1)

As the name indicates, the network is composed by 30 bus bars, with some of them having

loads connected to them, and others not. Since this is a multiperiod problem, that covers the

network for the whole day, load in each bus will vary from hour to hour. The details about the

load for each bus at each hour will be detailed in 4.2.2.

As for the voltage levels at each bus bar, the accepted range of voltage levels go from 0.9

p.u. to 1.1 p.u. Table 4-2 presents the maximum and minimum voltage levels accepted for each

bus bar, as well as the bus type classification and the base voltage for the network zones on

which the bus bars are located.

Table 4-2 - Characteristics of Voltage and Bus Bar classification

Bus Type of Bus Bar Vbase (KV) Vmax (p.u.) Vmin (p.u.)

1 SLACK 132 1,1 0,9

2 PV 132 1,1 0,9

3 PQ 132 1,1 0,9

4 PQ 132 1,1 0,9

5 PQ 132 1,1 0,9

6 PQ 132 1,1 0,9

7 PQ 132 1,1 0,9

8 PQ 132 1,1 0,9

9 PQ 1 1,1 0,9

10 PQ 33 1,1 0,9

11 PQ 11 1,1 0,9

12 PQ 33 1,1 0,9

13 PV 11 1,1 0,9

14 PQ 33 1,1 0,9

15 PQ 33 1,1 0,9

16 PQ 33 1,1 0,9

17 PQ 33 1,1 0,9

18 PQ 33 1,1 0,9


46

Table 4-3 - Characteristics of Voltage and Bus Bar classification (Continuation)

19 PQ 33 1,1 0,9

20 PQ 33 1,1 0,9

21 PQ 33 1,1 0,9

22 PV 33 1,1 0,9

23 PV 33 1,1 0,9

24 PQ 33 1,1 0,9

25 PQ 33 1,1 0,9

26 PQ 33 1,1 0,9

27 PV 33 1,1 0,9

28 PQ 132 1,1 0,9

29 PQ 33 1,1 0,9

30 PQ 33 1,1 0,9

Defining the Slack bus bar is crucial to the correct calculation of the power flow. Since the

I2R losses of the system are not known prior to the OPF, the slack bus will help compensate any

lack of excess of active or reactive power flow in the grid to achieve the best result possible.

The slack bus has its phase angle for the voltage usually set to zero, also meaning that this bus

bar will be the reference for other busses phase angle delays.

The network in study has 41 branches, connecting the various bus bars between themselves.

The line characteristics (R, X, B) are presented per unit (p.u.). R stands for the line resistance

and X for its electrical reactance. Together, R and X give the line impedance, Z. Z is given by

the following equation [64]:

𝑍 = 𝑅 + 𝑗𝑋 (4-2)

B stands for the line charging susceptance and it is the measurement of the line ability to

conduct a changing current caused by a passive element with time-variable properties (Like

inductive and capacitive lines) [65]. Table 4-4 presents the main line characteristics.


47

Table 4-4 - System Line Parameters

Line From Bus To Bus R (p.u.) X (p.u.) B (p.u.)

1 1 2 0,02 0,06 0,03

2 1 3 0,05 0,19 0,02

3 2 4 0,06 0,17 0,02

4 3 4 0,01 0,04 0

5 2 5 0,05 0,2 0,02

6 2 6 0,06 0,18 0,02

7 4 6 0,01 0,04 0

8 5 7 0,05 0,12 0,01

9 6 7 0,03 0,08 0,01

10 6 8 0,01 0,04 0

11 6 9 0 0,21 0

12 6 10 0 0,56 0

13 9 11 0 0,21 0

14 9 10 0 0,11 0

15 4 12 0 0,26 0

16 12 13 0 0,14 0

17 12 14 0,12 0,26 0

18 12 15 0,07 0,13 0

19 12 16 0,09 0,2 0

20 14 15 0,22 0,2 0

21 16 17 0,08 0,19 0

22 15 18 0,11 0,22 0

23 18 19 0,06 0,13 0

24 19 20 0,03 0,07 0

25 10 20 0,09 0,21 0

26 10 17 0,03 0,08 0

27 10 21 0,03 0,07 0

28 10 22 0,07 0,15 0

29 21 22 0,01 0,02 0

30 15 23 0,1 0,2 0

31 22 24 0,12 0,18 0

32 23 24 0,13 0,27 0

33 24 25 0,19 0,33 0

34 25 26 0,25 0,38 0

35 25 27 0,11 0,21 0

36 28 27 0 0,4 0

37 27 29 0,22 0,42 0

38 27 30 0,32 0,6 0

39 29 30 0,24 0,45 0

40 8 28 0,06 0,2 0,02

41 6 28 0,02 0,06 0,01


48

The network has 4 active transformers, dividing the system into four different voltage zones,

as we can see in Table 4-2. The transformers characteristics can be found in Table 4-5

Table 4-5 – Transformer data for the system in study

Transformer From Bus

To Bus Vpri (kV) Vsec (kV) X (p.u) Taps (sec)

min avg max

T1 6 9 132 1 0.208 0.9 1 1.1

T2 6 10 132 33 0.556 0.9 1 1.1

T3 4 12 132 33 0.256 0.9 1 1.1

T4 28 27 132 33 0.396 0.9 1 1.1

The system also has two capacitor banks installed. Capacitor banks are used in power grids

to increase the system’s power factor, serving as a regulator for voltage levels a controller of

the reactive power flows. Capacitor banks help controlling the reactive power flows by

supplying the reactive loads with current to help mitigate their needs [66] [67]. Table 4-6

presents the characteristics of the capacitor banks installed in our network.

Table 4-6 - Capacitor banks information

Bus Bar QNom (Mvar) Tap positions

0% 50% 100%

10 19 0 Mvar 9.5 Mvar 19 Mvar

24 4.3 0 Mvar 2.15 Mvar 4.3 Mvar

For optimization purposes, the capacitor banks have been equipped with taps as well, so

that they can work under three different operation modes: At 0%, or turned off, at 50% or at

100% of their total capacity

4.2.2. Load Profile and Load per bus

The original data provided for this network included only load data for a steady-state

problem analysis. Considering that this study consists on a 24-hours multi-temporal optimization

of the OPF, a load profile must be considered in order to simulate the load variations along the

day. This load profile was adapted from a Portuguese high voltage network, and adapted to the

network in study to avoid convergence problems. The IEEE 30 Bus Case is a network that in its


49

initial state is already under heavy load, and load profile alterations might cause convergence

problems in future OPF calculations.

Being this said, Table 4-7 presents the overall system load profile, after the adaptation of

the Portuguese load information.

Table 4-7 – Load per hour to be applied to the network

Hour Total Load

(MW)

1 50

2 34

3 38

4 31

5 37

6 40

7 51

8 64

9 95

10 127

11 139

12 157

13 161

14 164

15 158

16 162

17 160

18 167

19 180

20 192

21 207

22 210

23 204

24 177

The idea with this was to try and replicate as accurate as possible the load fluctuations that

happen in a power grid during a day, with peak consumption time occurring during the evening

hours, and the periods of lower demand corresponding to hours with more people sleeping,

usually named the off-peak hours. In Figure 4-2 it can be seen a chart that shows the evolution

of the system load during the 24 hours of the problem.


50

Figure 4-2 - Load chart of the total system load during the 24 hours

As for the load per bus, being that different buses have different loads attached to them in

the static scenario of the IEEE 30 Bus Network, when applying an external load profile, the load

of each bus is going to change according to the new load scenario to be simulated. The original

load of each bus in the IEEE 30 Bus case can be found in Table 4-8

0.00

50.00

100.00

150.00

200.00

250.00

0 5 10 15 20

Syst

em t

ota

l Lo

ad (

MW

)

TIme of day (Hours)

Load Profile applied to the IEEE 30 Bus Case


51

Table 4-8 – Original Load Per Bus in the IEEE 30 Bus Case

Bus Pd Qd

1 0 0

2 21,7 12,7

3 2,4 1,2

4 7,6 1,6

5 0 0

6 0 0

7 22,8 10,9

8 30 30

9 0 0

10 5,8 2

11 0 0

12 11,2 7,5

13 0 0

14 6,2 1,6

15 8,2 2,5

16 3,5 1,8

17 9 5,8

18 3,2 0,9

19 9,5 3,4

20 2,2 0,7

21 17,5 11,2

22 0 0

23 3,2 1,6

24 8,7 6,7

25 0 0

26 3,5 2,3

27 0 0

28 0 0

29 2,4 0,9

30 10,6 1,9

The current challenge is a situation where the load will change from hour to hour. This was

achieved by applying the load profile mentioned in Table 4-7 to the 30 buses of our network.


52

This was done by using a MOST functions, called “getprofile” and “ex_load_profile”. These

functions, after slight alteration, allow for the application of a load profile of user defined

length, applying it to the system for the MOST calculations for DC OPF and Unit Commitment.

More detail about MOST operation and the functions that were used to run our tests can be

found in MOST will apply the total load of the system for each period, defined by the profile

inserted by the before mentioned functions. Then the software will adapt the total system load

to the network in use, distributing it accordingly to the previously existing load. So, since the

bus bar with the biggest attached load in the initial network data was bus bar nº7, after MOST

applies the load profile, for each period, the bus bar with the biggest attached load will also

be bus bar nª7.

The table containing the load for each bus and for each period of the day can be found in

the Annex A.

Results and Discussion

53


5.1. Introduction

As explained in Chapter 3, the methodological process is divided into two different

simulation steps: The first consists in applying MOST to run a multiperiod DC OPF and dispatch

optimization, to obtain an optimized charge and discharge profile for the storage unit, and for

knowing how the generators will act during the various hours of the day. The second part of

the simulation consists in applying an AC OPF for each hour of the day, using MOST results as a

start point and locking the storage production as was dispatched by MOST. This will help

eliminate any restriction breaks that might occur during the first step of the simulation, since

MOST does not take into consideration AC system restrictions and limit violations. This sequence

of procedures makes the results obtained more reliable and simulates a multi-period AC OPF

with storage consideration and global optimization for the 24 hours of the study.

In this chapter, the results of the simulations ran will be presented, compared, and discussed

so the conclusions that were made during this paper can be validated and put into context. Its

presented various Cases of study, each one tackling a different aspect of the study that was

meant to be tackled.

In the end of this chapter it is hoped that the reader will be able to understand the potential

of the implemented tool to appraise the various effects that storage units can have in the

system


54

5.2. Case 1 – Initial Case: Influence of Storage in multiperiod AC

OPF

Case 1 is the initial set of solutions that were obtained. It is the solution for the initial

problem, with the network with the data that was originally provided in 4.1.

In Case1, it was intended to study the influence that the storage unit would have in the AC

OPF for the IEEE 30 Bus Case presented, and analyze what would differ from doing the set of

simulations with and without the storage unit. The ESS used in the simulation was a simple

50MWh battery that was easily put into the simulations by using one of MOST incorporated

functions for adding storage units to the system. As previously mentioned, the storage unit is

exemplified as an additional generator for the system, that is seen by MATPOWER as a negative

generator when it is charging, and as an additional positive generator when the battery is set

do discharge.

As the simulation has various steps, the results will be presented according to the various

steps made and the conclusions and remarks will be made along the presentation of the results.

5.2.1. Results Without Storage

5.2.1.1. Results for MOST without considering the Storage unit

When running the MOST for the optimization of the DC Optimal Power flow and dispatch,

the value of de objective function can be found in Table 5-1

Table 5-1 - Value of the system total dispatch when running MOST

Economic dispatch ($) 8428,63


55

The production for each generator can be found in Figure 5-1. The detailed information

about the production values at any hour is depicted in Annex B

As was expected, the system production curves follow how the load demand evolves too.

When the system total load is bigger, generation will also be higher. It is also curious to notice

that generators 4,5 and 6, being the most expensive generators, only start producing when the

system total load is bigger. Generator 5 and 6 have the same production values, due to their

cost being the same.

Since MOST works only with the DC model of the network, and does the DC OPF and dispatch

optimization disregarding the system losses and AC restrictions, this step of the simulation is

mainly interesting to define the storage unit charge and discharge profile. The goal now is with

the single-period AC OPF try and replicate the results of MOST for the supposed better final

results.

5.2.1.2. Results for the Multi-Period AC OPF without

considering Storage

To do a multi-period AC OPF, it was decided to use the single-period AC OPF tool from

MATPOWER, and apply it individually to each hour of our system, while using the values we

obtained in 5.2.1.1 (namely the storage dispatch) for reference and limitation. The idea was

to keep the results between steps as close as possible. However, we must keep in mind that

the calculations in MOST do not consider system losses and the AC limitations imposed by the

AC OPF. Therefore, the results could not be the same.

The value for the total dispatch of all the hours of the system can be seen in Table 5-2

0

10

20

30

40

50

60

70

0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (hours)Generator 1 Generator 2 Generator 3 Generator 4 Generator 5 Generator 6

Figure 5-1 - Generator total production over 24 hours


56

Table 5-2 - System dispatch for the 24 hours AC OPF


As far as the production in each generator evolves in the system, in Figure 5-2 it can be seen

the production for each generator over time. As in 5.2.1.1, for more detailed information about

the production of each generator, please refer to Annex C

Figure 5-2 - Generator total production over 24 hours

Again, just like it happened in 5.2.1.1, the system production will follow the load curve

presented in the data of the problem in Chapter 4.

Comparing the results obtained in 5.2.1.1 and the results obtained in the AC OPF simulation,

the production values for each generator are not very different, with the biggest difference

happening in Generator 6 at hour 22, and being a difference of only 1,75 MW. This shows the

similarity of both steps of the problem. However, it must be taken into consideration that MOST

does not consider system losses, therefore the production in the AC OPF is always going to be

bigger due to said losses. The difference of production in each generator can be found in Figure

5-3.

0

10

20

30

40

50

60

-1 4 9 14 19 24

Pro

du

ctio

n (

MW

)

Time (hours)

Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Gen 6


57

Comparing the total generation curve for both 5.2.1.1 and 5.2.1.2, the similarities between

the two are even more noticeable.

As shown in Figure 5-4 the total system production in both cases is very similar, with the

bigger differences occurring in the peak hours and even then, the production in both cases does

not differ too much. The main reasons that cause the differences between them are the system

losses, that are inexistent in MOST, but exist in the AC OPF, and the more demanding

restrictions that exist in the AC OPF regarding line limits and voltage violation constrains. The

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tota

l Pro

du

ctio

n (

MW

)

Time period (Hour)MOST Total Generation AC OPF Total Generation

Figure 4 - Comparison of the system total generation between MOST and the AC OPF

Figure 5-3 - Difference of production between MOST and the AC OPF for all system's running hours

Figure 5-4 - Comparison of the system total generation between MOST and the AC OPF

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pro

du

ctio

n D

iffe

ren

ce (

MW

)

TIme (hours)

Diference between MOST and AC OPF

Generator 1 Generator 2 Generator 3

Generator 4 Generator 5 Generator 6


58

AC OPF is stricter that MOST’s DC OPF and therefore, the power flow will be affected to achieve

all the constraint restrictions.

Since the AC OPF is applied for each hour of the problem, it can also be presented the data

for the economic dispatch for each hour of the problem. That data can be found in Figure 5-5

Figure 5-5 - System per hour dispatch

Energy cost is bigger during periods of bigger load demand because the more expensive

generators (4,5 and 6) had to be put online, with the power that they produce being more

expensive than the power produced by the cheapest generators (1,2 and 3).

Also, since this is an AC OPF, system losses are something that must be considered as well.

Figure 5-6 shows the evolution of the system losses over time

0

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Syst

em D

isp

atch

($

)

Time Period (Hours)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

-1 4 9 14 19 24

Syst

em L

oss

es (

MW

)

Time (hours)

Figure 5-6 - System AC losses over time


59

As expected, losses are higher when load (and production) is also higher, and the power

flowing in the lines is bigger, resulting in more IR2 losses. However, the losses in the system are

rather small when compared to the system total production, as it can be seen in Figure 5-7

To make for an easier understanding, in Figure 5-8 the system total losses for each hour are

presented as a percentage of the system total generation. As it can be seen, system losses are

very low, with the average percentage value for system losses being 0,80%, which can

considered pretty standard for high voltage networks.

For the energy grid used in this study, having these kinds of losses is quite satisfactory, with

peak loss percentage being around 1.2%.

0 50 100 150 200 250

1

3

5

7

9

11

13

15

17

19

21

23

MW

Tim

e (h

ou

rs)

Systel Total Production (MW) System total losses (MW)

Figure 5-7 - Comparison of system total generation with the system's losses

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Syst

em L

oss

es (

%)

Time perod (Hour)

Figure 5-8 - System loss percentage in all periods


60

5.2.1.3. Results for MOST with losses compensation without

Storage

Since MOST does not consider the AC losses, as a way of achieving more similar results to

the results achieved in 5.2.1.2, it was decided to test the addition of the MW losses obtained

in the AC OPF to the total per-hour load of the system, and then run MOST again and analyze

if the results became closer. Note that closer results mean that AC OPF conditions (in this case,

losses) are also included by the DC approach performed by MOST.

MOST distributes the added losses as load between the bus bars, according to the already

existing load. So, the busses with more load would be the ones with more losses share to be

added. This is an approximation technique, and it is known that the added losses might not be

an exact representation of the system real line losses.

The value of the dispatch for the system’s total activity can be found in Table 5-3

Table 5-3 - Economic dispatch for MOST with loss consideration


As far as generation is regarded, the generation profile is quite similar to the one found in

the AC OPF, with the generation profiles having the same tendencies as the ones found in the

previous steps.

Comparing the results to the ones obtained in 5.2.1.1, it is plausible to assume that the

production of the generators from MOST with losses compensation is going to be bigger than

0

10

20

30

40

50

60

70

0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (hours)

Generator 1 Generator 2 Generator 3 Generator 4 Generator 5 Generator 6

Figure 5-9 - System Production curves, for each generator, during the 24 hours


61

the results obtained for MOST without considering the system losses obtained in the AC OPF,

since we increased the system load to “simulate” the AC losses in the DC OPF used in MOST.

This difference can be compared in Figure 5-10 and Figure 5-11.

As we can see in Figure 5-10, just like it happened between the results in 5.2.1.1 and

5.2.1.2, the biggest difference in production between generators from one simulation to the

other happens during the times of biggest production, where the production from the

generators in MOST with loss compensation is higher due to the higher load.

In Figure 5-11, we can see the difference in total production for each hour of the system

between the two simulations. Again, as expected, the total production in MOST with loss

compensation is higher, although not by much, reinforcing that the losses are pretty standard

for the type of network that it is considered.

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20

Pro

du

ctio

n D

iffe

ren

ce (

MW

)

Time (hours)Generator 1 Generator 2 Generator 3 Generator 4 Generator 5 Generator 6

Figure 5-10 - Difference in Production in all generators in MOST without and with loss compensation


62

Although it is interesting to compare both MOST calculations, MOST with loss compensation

is calculated to approach its results to the results obtained with the multiple AC OPFs that are

calculated in 5.2.1.2. Therefore, it is more interesting to compare both results between

themselves to see how much more similar they are than the initial MOST run and the AC OPF.

Starting with the system production per generator, the differences in absolute value are

presented in Figure 5-12. The maximum value of MW difference between generators is less than

1,4 MW, showing once again the similarities between both processes.

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Syst

em T

ota

l Pro

du

ctio

n (

MW

)

Time (Hours)

MOST without Loss Compensation Total Generation MOST with Loss Compensation Total Production

Figure 5-11 - System Total Production comparison


63

But the similarities are bigger when total system production is analyzed. When total production

in MOST with loss compensation and the AC OPF are compared in Figure 5-13, the productions

are very similar, with the differences being minimal (less than 1MW) in all periods. That is a

corroboration of the proposed approach: MOST can be used to optimize the dispatch for the 24

hours of the problem, and to program the charging and discharging periods of the storage unit,

as it shall be seen ahead

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20

Pro

du

ctio

n D

iffe

ren

ce (

MW

)

Time (hours)

Generator 1 Generator 2 Generator 3 Generator 4 Generator 5 Generator 6

Figure 5-12 - Difference in production for all generators between MOST with loss compensation and AC OPF

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tota

l Pro

du

ctio

n (

MW

)

Time (Hour)

Total System Production for MOST with Loss compensation Multiperiod AC OPF

Figure 5-13 - Total system production comparison between MOST with loss compensation and the AC OPF


64

5.2.1.4. Final observations

As final observations of the results without the storage unit, it is important to underline that

this step of the study is mainly to validate that all the algorithms are working as they should,

and that are ready to have the storage unit introduced to see its influence on the network and

on the optimal power flow of this system.

With that being said, one final study is the comparison between the economic dispatches of

all three steps of the simulation. Although they have been presented in the previous sections

(5.2.1.1, 5.2.1.2 and 5.2.1.3), no direct comparison was made between them. Optimizing the

dispatch while maintain the system security constraints respected is the main goal of the

optimal power flow, and our goal is to optimize the dispatch with the introduction of the

storage and with the reconfiguration of transformer tap positions and capacitor banks.

The dispatch of the three steps of the simulation (MOST without loss compensation, Multi-

period AC OPF and MOST with loss compensation) can be found in Table 5-4.

Table 5-4 - Comparison between the economic dispatches of the various steps of the simulation

Step of the Simulation Economic Dispatch ($)

MOST without loss compensation (5.2.1.1) 8428,63

Multiperiod AC OPF (5.2.1.2) 8535,98

MOST with Loss Compensation (5.2.1.3) 8537,18

The clear biggest difference happens between the dispatch obtained in MOST without

considering losses. It provides the cheapest result of all the simulations, but it must be taken

into consideration that the production values obtained are not viable, since the total system

production for each hour is not enough when we consider the AC constraints, namely the

reactive flow and the system losses that cannot be ignored. That is why it is mandatory in this

study to do the AC OPF for the 24 hours of the problem and then re-do MOST while considering

the MW losses that exist in the AC OPF.


65

When comparing the AC OPF to the final run of MOST, the losses obtained are much closer

to each other, with the cost difference being only 1,20$. This shows that the co-integration of

MOST and the AC OPF can provide very similar results, giving more ground to stand to the results

obtained. A more graphical comparison between all the dispatches can be seen in Figure 5-14.

With the algorithm put to test, and with the OPF calculation and optimization completed,

the influence that the storage unit will have on the results of the OPF can now be studied and

analyzed, as shown in 5.2.2.

5.2.2. Results with the inclusion of the Storage unit

After testing the system and the algorithm for the OPF solution, the real interest is now in

adding the storage system to the network and analyze its influence on the results of the OPF

and the dispatch of the system. The following results will be presented in the same order that

were presented in 5.2.1, comparing the results with storage to the same simulation step, but

without the storage system.

The storage unit used in this case was a 50MWh battery storage system, located in bus bar

1.

8360

8380

8400

8420

8440

8460

8480

8500

8520

8540

8560

MOST without losscompensation (4.2.1.1)

Multiperiod AC OPF (4.2.1.2) MOST with Loss Compensation(4.2.1.3)

Eco

no

mic

dis

pat

ch

Figure 5-14 - Graphical comparison of the economic dispatch obtained in the three steps of the simulation


66

5.2.2.1. Results for MOST with a Storage unit and without loss

compensation

Running MOST with the storage system enabled allows for an immediate improvement in the

economic dispatch over the results obtained in 5.2.1.1. As expected, the value of the dispatch

is lower when the system has the storage unit, since it allows for peak-shaving. That means

that the system generators produce a little more in the off-peak hours to charge the storage

device, but the accumulated energy can be spared during peak hours, when energy production

is more expensive due to the more expensive generators. The result of the economic dispatch

can be found in Table 5-5.

Table 5-5 - Economic dispatch for MOST with storage


The difference between the result above and the result obtained in 5.2.1.1 can be seen in

Figure 5-15.

As expected, the storage unit helps dropping the economic dispatch from 8428,63$ to

8395,68$. This results in a difference of 32,95$ each day, a monthly 988,36$ saving, and an

annual system dispatch cost saving of 11860,31$.

8370

8380

8390

8400

8410

8420

8430

8440

MOST with no Storage MOST with Storage

Syst

em T

ota

l Dis

pat

ch (

$)

Figure 5-15 - Comparison of dispatches for MOST with and without storage


67

Another interesting point of analysis is the production of each generator during the 24 hours

of the system, now with the added storage.

Analyzing Figure 5-16, there are several aspects that are worth mentioning. First, it is

interesting to see that even with the storage unit, the production curves for the conventional

system’s generators still tend to follow the load profile curve as happened before. That is what

was expected. However, it is curious to see that in this case, Generator 3 is constantly

producing 17,99MW during all the 24 hours of the system. This might occur due to the system

constraints, being it line or voltage limitations that force this generator to only produce this

amount during the entire 24 hour period.

Looking at the ESS curve, it can clearly be seen the different charging and discharging

periods of the storage unit. The ESS will charge in the periods of lowest demand, where the

energy required to charge the battery can be supplied by the cheapest generators (Generator

1 and 2) without compromising the remaining loads. After charging, the storage unit will keep

its charge (with the efficiency of the storage of 95% taken into consideration) until the peak

demand periods, where it will discharge and serve as an additional generator, supplying up to

18,62 MW on hour 22, where the demand is the highest.

Comparing the results obtained with the ones obtained in 5.2.1.1, there are significant

differences in generator production, as we can see in Figure 5-17 as it presents the difference

in production for both scenarios, with the results being compared by the absolute difference.

-20

-10

0

10

20

30

40

50

60

70

-1 4 9 14 19 24

Pro

du

ctio

n (

MW

)

Time (hours)

Gen.1 Gen.2 Gen.3 Gen.4 Gen.5 Gen.6 ESS

Figure 5-16 - Generator and Storage unit production curve for MOST, for the 24 hours of the system


68

The main reason for the difference between the two simulations is the storage system

addition. With it, the system will have to produce more during charging periods than it would

have to if there was no storage. The reverse situation happens during peak hours, where the

storage unit is discharging. Here, in reverse to what happened during off-peak hours, the

storage unit will make the generators produce less power to supply the loads, since it will be

responsible for part of the supply.

Another interesting aspect to analyze is the total added production of all the generators and

compare it to the results obtained in 5.2.1.1

Figure 5-17 - Difference in production for each generator in MOST with and without storage

0

50

100

150

200

250

0 5 10 15 20

Tota

l Pro

du

ctio

n (

MW

)

Time (hours)

MOST with Storage MOST without Storage

Figure 5-18 - Added Production comparison between MOST with and without Storage

-8

-6

-4

-2

0

2

4

6

8

10

0 5 10 15 20

Pro

du

ctio

n D

iffe

ren

ce (

MW

)

TIme (hours)

Gen.1 Gen.2 Gen.3 Gen.4 Gen.5 Gen.6


69

Looking at Figure 5-18, we can see a difference between the production curves from MOST

with and without the storage unit. What happens is that the storage unit will help smooth the

production curve, making the generators produce a bit more in the less demanding hours, but

also diminishing the production in peak hours, as said before.

It is more interesting to analyze the peak shaving phenomenon that happens with the

addition of the storage unit. Storage, in a way, can be seen to the system as a positive and

negative load. A positive load when it is charging, and a negative load when it is discharging.

Therefore, when we consider the system total load and add the battery as a variable load, we

can clearly see the shaving of the minimal and maximal value of the load curve.

With this, the system generators will see the system total load as smaller in the periods of

higher demand, thus leading to the diminishing of the total energy production cost.

5.2.2.2. Results of AC OPF With Storage

Similarly, to the approach used in 5.2.1.2, to perform the multiperiod AC OPF, an AC OPF

was applied for each of the hour of study. The difference now was the storage unit that must

be considered.

As explained in Chapter 3, the way chosen to consider storage in the AC OPF was treating it

like an additional generator that could go from -Pmax to Pmax. Although the AC OPF tends to

define the production of the generators, storage unit production is locked to the values

obtained in MOST in 5.2.2.1. The AC OPF serves mainly to adapt the generator production to

help the integration of limits and security constraints and feed the loads while taking into

consideration the existing line losses that cannot be overlooked in the AC version of the OPF.

-50

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Load

(M

W)

Time (hours)

System total load Storage Unit as a load Total Load + Storage

Figure 5-19 - Analysis of the peak shaving effect caused by the storage


70

The result of system dispatch can be found in Table 5-6.

Table 5-6 - Economic dispatch for the AC OPF with Storage Unit

Comparing the result with the one obtained in the AC OPF without the storage unit, it is

clear that the dispatch is going to be smaller than the one obtained in 5.2.1.2.

Analyzing the influence of the storage in the long-term scenario, the difference seen in

Figure 5-20 represents a daily saving of 60,40$. That represents a monthly saving of 1811,93$

and a yearly saving of 21743,13$.

It is interesting to analyze the difference in the hourly dispatch for the AC OPF with and

without the storage unit


8440

8450

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8470

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8490

8500

8510

8520

8530

8540

8550

AC OPF's Dispatch With Storage AC OPF's Dispatch without Storage

Eco

no

mic

Dis

pat

ch C

ost

($

)

Dispatch Comparison

Figure 5-20 - Comparison of the economic dispatch for the AC OPF with and without the storage unit

0

100

200

300

400

500

600

700

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Eco

no

mic

Dis

pat

ch (

$)

Time of day (Hours)

Dispatch per hour of the AC OPF with Storage Dispatch per hour of the AC OPF without Storage

Figure 5-21 -Comparison of the dispatches per hour of the AC OPF with and without storage


71

Looking at the system per-generator production, the production charts are very similar to

the ones already obtained before, since the load of the system is the same.

Comparing the production of the generators with the production existing in the AC OPF with

and without the storage unit, the production curves differences are mainly because the total

production for the AC OPF with storage is bigger in the off-peak periods and will be smaller in

the peak hours. These differences exist due to the power that needs to be generated to charge

the storage unit in the less load demanding hours, and due to the power that is saved from

being produced, due to the charge existing in the storage unit that will help supply the loads.

This is analogous to what happened when comparing MOST with and without the storage unit.

Figure 5-22 – Production of all generators for the multi-period AC OPF with Storage

-8

-6

-4

-2

0

2

4

6

8

0 5 10 15 20

Dif

fere

nce

in P

rod

uct

ion

(M

W)

Time (hours)

Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Gen 6

Figure 5-23 - Difference in production in the AC OPFs with and without storage

-40

-20

0

20

40

60

-1 4 9 14 19 24Pro

du

ctio

n (

MW

)

Time (hours)Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Gen 6 BESS


72

Analyzing Figure 5-23, we can see that when the difference in production is positive (storage

system charging) means that the production in the AC OPF with storage is bigger than the

production without storage. The contrary happens after 20:00, when the storage unit starts

discharging, meaning that the generators can ease their production.

It is also interesting to compare the variation of the production curve of each generator with

the ones obtained in 5.2.2.1 to see how much differs from the multi-period AC OPF.

In this case, there is clearly some considerable differences between the multiperiod AC OPF

and MOST, both with the storage unit. As it happened in 5.2.1.2, differences will always exist

between the AC OPF and the initial run of MOST, mainly because of the lack of line losses in

that simulation, while on the AC OPF they are taken into consideration. The main difference

happens in generator 3, who MOST had locked production at 17.99MW. This generator has

differences of up to 6MW approximately higher production in MOST, since the AC OPF tends to

prioritize other generators, mainly because of MVA line limitations.

Another interesting aspect to analyze in the AC OPF is the system total losses and see the

influence that the storage unit can have on those losses. Figure 5-25 presents the comparison

of system losses between the multiperiod AC OPF with and without the storage unit

-8

-6

-4

-2

0

2

4

6

0 5 10 15 20

Dif

fere

nce

in P

rod

uct

ion

(M

W)

time (hours)

Gen 1 Gen 2 Gen 3 Gen 4 Gen 5 Gen 6 (13)

Figure 5-24 - Difference in production between the AC OPF and MOST with storage unit


73

Interestingly, the total value of the system losses is slightly bigger when we add the storage

unit to the system. This can be justified by the location of the storage unit that might be

located connected to a line that produces more IR2 losses when power flows through it. A way

of seeing if this is correct would be by retrying the simulations, but having the storage unit

being located in another bus bar, connected to a line with other characteristics to see if the

losses would suffer any variation.

Although the losses slight increase when compared to the multiperiod AC OPF without the

storage unit, the losses obtained in this step of the simulation are still very acceptable,

especially when compared to the system total production, the average loss value is only 0,81%

of the system’s production. This value is backed up by Figure 5-26, where it can be seen how

insignificant the system losses are for each hour.

0

0.5

1

1.5

2

2.5

3

3.5

0 5 10 15 20

Losses for the AC OPF w/Storage Losses for the AC OPF w/o Storage

Figure 5-25 - Total losses comparison between the AC OPF with and without the storage unit


74

Another example of how small the losses on the system are can be found in Figure 5-27. As

it can be seen, the percentage losses for each hour are significantly low, with the exception of

the periods of higher demand and higher production, and even in those periods the losses are

only as high as 1,40% of the system’s total generation.

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tota

l Pro

du

ctio

n -

Loss

es

Hour of the day

Total Production Total Losses

Figure 5-26 -Comparison of system total production with the system total production

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Loss

per

cen

tage

(%

)

Hour of the day

Figure 5-27 -System total loss percentage per hour


75

5.2.2.3. Results for MOST with loss compensation and storage

The last step in the simulation is to adjust MOST by adding the active losses obtained in the

AC OPF to the system load of MOST, to try to approximate its results to the ones obtained for

the AC multiperiod OPF.

Starting with analyzing the economic dispatch of the problem, in Table 5-7 we can see the

value of the economic dispatch obtained with MOST with the storage unit being considered,

but also with the losses being taken into account

Table 5-7 - Economic dispatch of the system with MOST considering losses and storage

When comparing to the value obtained in 5.2.1.3, it is clear that the system dispatch is

smaller, just like it happened with the AC OPF and with MOST without loss compensation. It is

clear that the addition of the storage unit makes the overall dispatch of the system to become

less expensive.

The value of the dispatch is like the one found in 5.2.2.2, just showing how the two

simulations are like each other, confirming once more the process taken. A direct comparison

between the economic dispatches of all the calculations using the storage unit will be done in

Figure 5-28.


8440

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8480

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8500

8510

8520

8530

8540

8550

MOST Dispatch with loss compensation+ storage

MOST Dispatch with loss compensation

Eco

no

mic

Dis

pat

ch (

$)

Figure 5-28 - Comparison of the economic dispatches of MOST with loss compensation, with and without the storage unit


76

In this case, the reduction of the system dispatch cost would result in daily savings of 63,06

$, that result in monthly savings of 1 891,68 $, and in a year, the system operator would save

up to 22 700,20$.

It is also interesting to see how the production of the generators evolve with the presence

of the ESS. Figure 5-29 shows the production of each generator over time. The results are very

similar to the ones obtained in the AC OPF with the storage unit, as it can be seen in Figure

5-29. Compared to the results obtained in 5.2.1.3, it is clear that some differences exist, but

that was to be expected, since it was introduced the storage system to the grid.

It is interesting to notice that in this situation, Generator 5 and 6 have the same production

curve, and appear in Figure 5-29 as only one curve.

The production of the generators is quite similar to what was obtained in the AC OPF. In

Figure 5-30 it can be seen the differences in MW between MOST with loss compensation and

storage and the AC OPF with storage. Figure 5-31 shows the average percentage differences

between the two simulations, as to show the similarities between them and how small the

differences are.

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-10

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pro

du

ctio

n (

MW

)

time (Hours)

Gen.1 Gen.2 Gen.3 Gen.4 Gen.5 Gen.6 ESS

Figure 5-29 - Generator Production for MOST with loss compensation and storage unit


77

As it can be seen, the variations between MOST with loss compensation and the results

obtained in 5.2.2.2 are quite small, with the biggest difference happening in Generator 1 and

being less than 2MW. It is also important to mention that the storage unit has a very slight

variation. This happens because the storage profile used in the AC OPF is the same one used in

MOST without the loss compensation. So, when the losses are added to MOST, there is a slight

difference in the storage profile, but nothing too significant. When looking at Figure 5-31, it

can be seen how similar the two processes are, with the biggest average difference happening

in Generator 6, and being less than 4,50%.

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20

Pro

du

ctio

n D

iffe

ren

ce (

MW

)

time (hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27)

Gen 5 (23) Gen 6 (13) Storage (1)

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

5.00%

Gen1 Gen2 Gen3 Gen4 Gen5 Gen6 Storage

Dif

fere

nce

per

cen

tage

(%

)

Figure 5-30 - Production difference between MOST with loss compensation and AC OPF, both with storage

Figure 5-30 - Average percentage difference between MOST with loss compensation and the AC OPF, both with storage

Figure 5-31 - Average Percentage Error of MOST compared to AC OPF


78

When comparing the results for MOST with loss compensation with storage to the same step

of the simulation, without the storage unit, the difference is noticeable, and that was to be

expected due to the inclusion of the storage unit.

As it can be seen, the difference in this case only happens on the periods where the storage

unit is operational. Although the periods where differences exist are smaller, the difference

from one simulation to another is bigger, when we look at the values of MW production. These

differences happen simply because of the storage unit, that when charging leads to bigger

production of the generators, but when discharging eases off the production of the conventional

machines.

5.2.2.4. Final Observations

As a final remark of the analysis of the initial MOST run, the multi-period AC OPF, and the

final MOST run, with the load adjustment for simulating the AC losses, it is interesting to

compare the economic dispatches obtained in all three steps of the simulation

-8

-6

-4

-2

0

2

4

6

8

0 5 10 15 20

Dif

fere

nce

in P

rod

uct

ion

(M

W)

Time (hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27) Gen 5 (23) Gen 6 (13)

Figure 5-32 - Difference in generator production between MOST with loss compensation, with and without storage unit


79

Table 5-8 – Table summary of all the economic dispatches of the simulation steps with Storage

Step of the Simulation Economic Dispatch ($)

MOST without loss compensation

(5.2.2.1)

8395,69

Multiperiod AC OPF (5.2.2.2) 8475,59

MOST with Loss Compensation (5.2.2.3) 8474,12

Similarly to what happened when the system had no storage unit, the most similar results

exist between the multiperiod AC OPF and the MOST run where loss compensations were

considered. It is also interesting to see that MOST with loss compensation presents a less

expensive dispatch than all the other simulations, specially the AC OPF, making it the best

value achieved for our simulation. This happens because MOST optimizes the dispatch for the

full 24 hours, while the AC OPF does individual optimal power flows for each hour of the system.

Figure 5-33 illustrates Table 5-8 for an easier view of the similarities and differences between

all three dispatches.

5.2.3. Case 1 Conclusions

This case study had the objective of analyzing the influence of the storage unit in the

multiperiod OPF’s economic dispatch and how it could help improving it.

8340

8360

8380

8400

8420

8440

8460

8480

8500

MOST without losscompensation (4.2.2.1)

Multiperiod AC OPF (4.2.2.2) MOST with Loss Compensation(4.2.2.3)

Syst

em T

ota

l Dis

pat

ch (

$)

Figure 5-33 - Comparison of the system's total dispatch for all the steps of the simulation for the multiperiod OPF with Storage


80

Looking at the results obtained in all of the previous steps, it is clear that the storage unit

can provide immediate reduction of the cost of energy production in our system. With peak-

shaving, the storage unit helps decreasing the production in peak hours, helping the more

expensive generators not needing to produce so much, reducing the overall cost of the system’s

production. That was the main goal with this case study, so it is safe to say that the results

obtained are very acceptable.

An interesting point of analysis is the fact that the overall system losses increased a little

when the storage unit was added to the multiperiod AC OPF. This might be due to the line

where the storage was connected, that was already a very flow heavy line, and whose

characteristics might help in producing more transmission losses. It would be interesting to

analyze the influence of the storage unit, but this time on a more favorable location. Note

however that the total cost (objective function) is lower when storage is considered, and this

is the most relevant fact.

Another aspect that is interesting to analyze is trying to use the storage unit to avoid turning

on one of the generators and see the influence that would bring to the system and for the

overall dispatch of it.

5.3. Case 2 – Avoiding generator start with the use of the

Storage Unit

One of the interesting uses of storage units is, in addition to the system dispatch decrease,

the capacity for the storage unit to supply the system loads, avoiding for the use of conventional

generation. This by itself is something that would, on normal conditions, diminish the system’s

overall production costs. The OPF tends to prioritize the cheapest generators, so if one of them

was to be left out, it would be expected to be the most expensive one.

Besides economic advantages, the ability to not use a generator that without storage would

be needed can be of great interest when analyzing the environmental side. Conventional

generators usually are thermal generators that pollute the atmosphere with the emission of

carbon-heavy gasses. If the storage unit can avoid using one of the generators, the total

emissions would decrease, helping the energy grid to be more “eco-friendly”.

In this Case Scenario, the storage unit will be used to achieve the load supply of the system

while avoiding turning on one of the generator. For this to occur, the cost function of the

conventional generators had to be adjusted. The new cost function of each generator can be

found in Table 5-9.


81

Table 5-9 - Case 2 generation cost function

Generator n a ($/h) b ($/MWh) c ($/((MW)2)h))

G1 3 0,02 2 0

G2 3 0,0175 1,75 0

G3 3 0,0625 1 0

G4 3 0,00834 5 0

G5 3 0,025 4,44 0

G6 3 0,025 3 0

When penalizing Generators 4, 5 and 6, the OPF will prioritize generators 1, 2 and 3, only

turning on the remaining generators when it is really needed. In this case it shall be presented

the influence that the storage unit will have on avoiding putting one of the generators to use.

5.3.1. Storage Profile Definition

For defining the storage profile, the process used was the same as in Case 1: Running MOST

with and without the storage unit to see how the algorithm optimizes the charge and discharge

moments of the unit. The results of the initial MOST run will not be presented since the

important results are the ones from the multi-period AC OPF and MOST when considering the

loss compensations.

With that being said, the behavior of the storage unit can be presented in Figure 5-34.

Figure 5-34 - Storage Unit Charge over time obtained from MOST

0

5

10

15

20

25

30

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Sto

rage

Lev

el (

MW

h)

Time (hours)


82

The exact charge values can be found in Annex D. Bearing in mind that the considered

storage unit has a 95% performance rate, being that 95% of the absorbed energy can be

outputted to the network. It is also worth mentioning that the considered storage unit is

modeled as a 50MWh storage unit, with a rated power of 20MW for each period.

With this storage profile, the interest now is to see how this will affect the system’s

optimization and how can it avoid putting one of the most expensive generators online.

5.3.2. Multiperiod AC OPF Analysis

5.3.2.1. Without Storage

When looking at the initial run of the AC OPF without considering storage, like it happened

in Case A, the first thing to analyze is the result of the system’s total economic dispatch. The

dispatch result can be found in Table 5-10.

Table 5-10 - Economic dispatch for the multiperiod AC OPF without Storage


Looking now at the production of each generator, like it happened in Case 1, production is

significantly bigger when the peak periods occur (Around 19:00 until 23:00) as more loads are

connected to the grid and the need for production is bigger. Figure 5-35 shows the evolution of

the production during the 24 hours of the day.

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (hours)


Figure 5-35 - Individual Generator production during the 24 hours of the multiperiod OPF


83

The evolution of the generators production is like what happened in Case 1, but in this case

the most important aspect to highlight is the production of Generator 5. During the period

between 19:00 and 23:00, generator 5 is required to inject power into the grid, to suppress the

production needs of the system loads. When the storage is added, the intention is to avoid the

activation of Generator 5, as it shall be seen ahead.

When analyzing the system’s total added generation, the production curve can be seen in

Figure 5-36. As mentioned before, the production is bigger on the evening when load

consumption is bigger, and during the off-periods production is smaller since load demand is

smaller as well.

The final interesting aspect to analyze in this stage of the results is the system’s total losses.

Losses occur the proportionally to the system’s load: when load is higher, losses will be higher

too. The system’s total losses can be found in Figure 5-37.

0

50

100

150

200

250

0 5 10 15 20 25 30

Pro

du

ctio

n (

MW

)

Time (hours)

Figure 5-36 - System Total production in the 24 hours of the AC OPF


84

Looking at the system losses as a percentage over generation (Losses/Total Generation), it

can be seen how small the system losses are when compared to the total production, with the

biggest loss percentage being 1,71%, and with the average system losses being at 1,09%

0

0.5

1

1.5

2

2.5

3

3.5

4

-1 4 9 14 19 24

Loss

es (

MW

)

Time (Hours)

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

1.80%

2.00%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Loss

Per

cen

tage

(%

)

Time (hours)

Figure 5-38 - Percentage of losses over generation for the multiperiod AC OPF

Figure 5-37 - System total losses over the 24 hours of the system


85

5.3.2.2. With Storage

With the addition of the storage unit, the overall system economic dispatch has an

immediate decrease in value, with the storage allowing for the production in peak hours to be

diminished, when energy production is more expensive. The value for the dispatch can be found

in Table 5-11.

Table 5-11 - Economic dispatch for the multiperiod AC OPF with storage


When compared to the results of the AC OPF without the storage unit, there is a clear

reduction in the overall energy production costs for the system. With the addition of the storage

unit, the dispatch has a reduction of 101,63$. This represents a monthly saving of 3048,83$ and

an annual saving of around 36.585,96$. The comparison between the dispatch of the

multiperiod AC OPF with and without the storage unit can be found in Figure 5-39

Figure 5-39 - Comparison of the economic dispatch for the AC OPF without storage /1) and with storage (2)

Now looking at the generator production, this is the point of bigger emphasis of this case.

With the addition of the storage unit, the goal was to avoid turning on one of the most expensive

generators. Looking at Figure 5-40, it can be seen how the production of each generator evolves

when the storage unit is considered in the AC OPF. When comparing to the results obtained in

5.3.2.1, other than the expected differences in the behavior of each generator due to the

addition of storage, it is interesting to look at the production curve of Generator 5. With the

8760

8780

8800

8820

8840

8860

8880

8900

8920

8940

1 2

Eco

no

mic

Dis

pat

ch (

$)


86

addition of the storage unit, Generator 5 does not produce energy for the system. This means

that with the help of the energy stored during off-peak periods, the storage unit can help the

system supply all the loads in the system, while using less generators. Figure 5-41 compares the

production for all generators between the AC OPF with and without storage. Figure 5-42 shows

the production of Generator 5 for both processes, so it can be clearer to see that when the

storage unit is added to the system, Generator 5 does not produce any power during the whole

24 hours of the system

-8

-6

-4

-2

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2

4

6

8

0 5 10 15 20

Dif

fere

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in P

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(M

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Time (hours)


-20

0

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0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (Hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27)

Gen 5 (23) Gen 6 (13) Storage (1)

Figure 5-40 – Evolution of the production for each generator and the storage unit in the AC OPF considering Storage

Figure 5-41 - Comparison of the individual Generator production in the multiperiod AC OPF, with and without the storage unit


87

Like it happened in Case 1, the differences occur mainly because the production in the low

consumption periods is slightly higher when the storage unit is considered for the unit to charge.

Symmetrically, on higher demand periods, the production of the generators is smaller in the AC

OPF with the storage unit, because the storage unit itself will inject power into the grid,

relieving the generators.

Comparing now the two situations total production, the results obtained with the addition

of the storage unit are like the ones obtained in Case 1. With the addition of the storage unit,

the overall production increases during off-peak hours, when the storage unit needs to charge,

and decreases during peak hours. Although Generator 5 does not produce any power in this

case, when the storage unit is added, the overall total produced power is not very different

from the total power produced in the multiperiod AC OPF in case 1 with the storage unit. This

happens mainly because the load profile is the same. So, although one of the most expensive

generators is not enabled, the production must be covered by the cheapest generators.

Figure 5-42 – Comparison of the production from Generator 5 in the AC OPF with and without Storage

0

50

100

150

200

250

0 5 10 15 20

Tota

l Pro

du

ctio

n (

MW

)

Time (Hours)

Case 2 Data Case 1 Data

Figure 5-43 - Comparison of System's total production between Case 1 and Case 2’s multiperiod AC OPF with Storage

0

1

2

3

4

5

6

7

8

0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (hours)Without Storage With Storage


88

Now comparing the system’s losses with and without the storage unit, the results are similar

to what was seen in Case 1. When the storage unit is added, there is a slight increase in the

system’s losses with the addition of storage, especially during peak times. This happens mainly

due to the transmission lines that supply the bus bar where the storage unit is located. This will

be tested more deeply in Case 3, so in this case the presented loss results will just be presented

and compared in Figure 5-46.

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-15

-10

-5

0

5

10

15

20

0 5 10 15 20

Dif

fere

nce

in P

rod

uct

ion

(M

W)

TIme (hours)

Figure 5-45 - Difference in total production between AC OPF with and without storage

0

50

100

150

200

250

0 5 10 15 20

Tota

l Pro

du

ctio

n (

MW

)

Time (hours)

Figure 5-44 - System total conventional generation, with the inclusion of the storage unit


89

5.3.3. MOST with Lost compensation analysis

5.3.3.1. Without the Storage Unit

After the multiperiod AC OPF study, it is now time to enter the final step in the simulation

algorithm. By adding the MW losses obtained in the AC OPF to the load profile applied to MOST,

it is possible to “replicate” the AC losses in a calculation that, by itself, does not consider

losses. Although this is not an ideal scenario, since the line losses are distributed by the

generators accordingly to their load (larger loads get a larger share of the total losses), the

results obtained are not very different from the ones obtained in the AC OPF.

Starting with a look at the system’s economic dispatch, the result can be found in Table

5-12. Being this the final step of the algorithm, with the consideration of the system’s AC losses

Table 5-12 - Economic dispatch for MOST when considering the AC losses


Looking now at the generators production curves over the 24 hours of the study, the

tendency is the same as in the previous simulations. Production is bigger during peak load

periods and there is less production during off-peak periods, as would be expected

Figure 5-46 - Comparison of the system's losses for the AC OPF with and without storage

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 5 10 15 20

Act

ive

Loss

es (

MW

)

Time (Hours)

AC OPF without Storage AC OPF With Storage


90

Figure 5-48 shows the system’s overall total production curve. Figure 5-47 and Figure 5-48

data is interesting mainly to compare it to the data that will be obtained when the storage unit

is added, to see how the storage will influence the system total production, but more

importantly, to see if in fact there is one generator whose production is avoided.

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (Hours)

Gen.1 Gen.2 Gen.3 Gen.4 Gen.5 Gen.6

Figure 5-47 - Evolution of generator production for MOST with the AC losses consideration

0

50

100

150

200

250

0 5 10 15 20

Pro

du

ctio

n (

MW

)

Time (hours)

Figure 5-48 - System total production for MOST when considering the AC Losses


91

5.3.3.2. With the Storage Unit

With the addition of the storage unit, the first aspect that is interesting to compare is the

difference in the economic dispatch, when compared to the calculations made in MOST but

without storage.

Table 5-13 - Economic Dispatch value comparison of MOST with and without the storage unit

MOST simulation Economic Dispatch ($)

without storage 8915,57

with storage 8820.92

For a more visual analysis of the data presented in Table 5-13, Figure 5-49 presents a

representation of the both economic dispatches of the system, for MOST with and without

storage unit.

Similarly to the AC OPF analysis in 5.3.2, the main point of interest is to see the comparison

of the system’s individual and total production between MOST with and without the storage

unit.

Starting off with the individual generator production over time, the production curve is like

the ones found before, but with the values of production being smaller on peak times due to

the storage unit that was added. On an inverse note, the production is slightly bigger during

off-peak periods, due to the loading of the storage unit. The individual production curves can

be found on Figure 5-50 and the comparison between the production curves between MOST

with storage unit and without can be found on Figure 5-51.

8760.00

8780.00

8800.00

8820.00

8840.00

8860.00

8880.00

8900.00

8920.00

8940.00

without storage with storage

Eco

no

mic

Dis

pat

ch (

$)

Figure 5-49 - Comparison of the system's economic dispatch for MOST, with and without the storage unit


92

When looking at the individual generator production, Generator 5 is offline during the entire

24 hours of the system. This happens due to the inclusion of the storage unit in the grid that

will help the system with the production in the peak periods, avoiding turning on the most

expensive generator, just like it happened in the AC OPF. This is illustrated in Figure 5-52 that

shows the difference in Generator 5 production when comparing MOST with and without

storage.

-20

0

20

40

60

80

100

0 5 10 15 20

Pro

du

ctio

n (

MW

)

TIme (hours)

Gen.1 Gen.2 Gen.3 Gen.4 Gen.5 Gen.6 Storage

-20

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-5

0

5

10

15

20

25

0 5 10 15 20

Pro

du

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n D

iffe

ren

ce (

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)

Time (Hours)


Figure 5-50 - Individual generator production for MOST with the storage unit

Figure 5-51 - Generation comparison between MOST with the storage unit considered, and MOST without considering the storage


93

To validate the result obtained in MOST, it is interesting to compare them to the results

obtained in the AC OPF, where all the restrictions are considered, including reactive flows and

line limitations.

Starting with analyzing the difference in the individual production for each of the

generators. Those differences can be seen in Figure 5-53.

The two simulations present very similar results. The storage profile is the same for both

scenarios as expected (because storage dispatch is set by the first run of MOST). As for the

conventional generators go, there are always some expected differences, since the AC OPF

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pro

du

ctio

n (

MW

)

Time (Hours)

No Storage With Storage

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 5 10 15 20

Ind

ivid

ual

Pro

du

ctio

n (

MW

)

Time (hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27)

Gen 5 (23) Gen 6 (13) Storage (1)

Figure 5-52 - Generator 5 production in MOST with and without the storage unit in the system

Figure 5-53 - Difference in individual generator production between the multiperiod AC OPF and MOST with loss compensation


94

considers more restrictions and parameters than the DC OPF that MOST uses. However, the

differences are not very significant, with the biggest difference happening during peak hours

and not being even 2MW. In Figure 5-54 it is presented the average difference between the

multiperiod AC OPF and MOST, in percentage. It shows that the differences are quite small,

with the biggest difference being in Generator 6, with an average difference, for all the 24

hours of the study, of 4.03%

When looking at the total production, the differences in MOST and the multiperiod AC OPF

continue to be very small, with the multiperiod AC OPF requiring a slightly bigger production

than MOST, mainly because of the losses. Although compensated in MOST, the loss value that

was used for compensation is the one obtained from the AC OPF without the storage unit. When

adding the storage unit, there is also a slight increase in the system losses, that will not be

corrected in MOST. The addition of the losses would lead to a new dispatch of the storage unit

and would force an entire new cycle of the process. And since the variations are rather small,

in this study it was accepted the slight deviation in results. There are also the line limitations,

that are not considered in MOST that tend to increase some generators production more than

others due to the lines’ capacities.

Overall, the total system production is very similar, and the results can be compared in

Figure 5-55.

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27) Gen 5 (23) Gen 6 (13) Storage (1)

Ave

rage

diif

fere

nce

(%

)

Figure 5-54 - Average difference (in percentage) between the multiperiod AC OPF and MOST for all the generators of the system


95

Lastly, it is interesting to analyze the difference in the economic dispatch between the

multiperiod AC OPF and MOST, when both are using the storage unit.

As it can be seen, the differences between the two are not very big, with the AC OPF having

a slightly more expensive dispatch than the one that it can be found with MOST. This happens

mainly because MOST does a global system optimization for the 24 hours of the system, while

the multiperiod AC OPF does an OPF for each hour, what in the end might not end up being the

global optimal when considering the 24 hours scenario of the problem. But the both dispatches

are pretty similar, with a difference of 10.25$. In case 1 the difference achieved was smaller

between both dispatches, but it must be taken into consideration that the cost functions of the

generators were changed to force Generator 5 not to turn on with the addition of storage.

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tota

l Pro

du

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n (

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)

TIme (hours)AC OPF MOST

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8740

8760

8780

8800

8820

8840

1 2

Eco

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Dis

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$)

Figure 5-55 - Total System production comparison between the multiperiod AC OPF and MOST

Figure 5-56 - Comparison of the economic dispatch between the multiperiod AC OPF (1) and MOST (2)


96


The main objective with this Case of study was to see if it was possible to avoid using one

of the most expensive system generators by adding the storage unit. Although with the initial

cost functions used in Case 1 that did not happen, with the changes made to the cost functions

of the most expensive generators of the system, it was possible to fulfill all the load demands

without using one of the most expensive generators, in this case Generator 5.

This shows that with the addition of storage unit in the current energy grid, avoiding the

usage of some of the most expensive conventional generators becomes a reality, especially

when combined with the renewable energy sources, that allied with the storage units, can lead

to a major contribution in avoiding thermal generators usage.

Another aspect that should be referred is that the value of the economic dispatches

increased from Case 1 to Case 2, simply because of the change of the cost function of the

generators, without changing the load profile applied to the system. This leads to an overall

economic dispatch increase. But when the values of the economic dispatch between the

simulations with storage and without storage for both cases, the biggest differences occur in

Case 2. Again, the influence of the cost functions tends to make the energy production costs to

highlight differences in terms of energy produced, especially when we consider that the

generator that is avoided in Case 2 is highly penalized in its cost function when compared to

Case 1.

But being this Case mainly a proof of concept (that storage units can lead to avoiding turning

some generators online), the results obtained can be considered successful, with the main goal

being achieved with Generator 5 not being online at any moment during the 24 hours of the

study, when the system had the storage unit operational.


97

5.4. Case 3 – Analyzing the influence of the storage unit

location on the system losses

During the simulation of the last two cases, although all the results were satisfactory, and

the main objective of the simulation was achieved, with the decrease of the overall system’s

economic dispatch, one aspect that was still curious was the increase of the system total active

losses every time that the storage unit was activated.

Although the increase in the system losses was expected, it was still a desire to try and

explore the importance that the location of the storage would have in the overall system losses.

Therefore, in this case study, the location of the storage unit was changed for the

simulations in MOST and in the multiperiod OPF, to see what changes that would bring to the

final results and particularly to the system’s active losses.

In Case 3, instead of having the storage unit located in Bus Bar 1, the storage unit was

changed to be closer to the bus bar with the biggest load attached. Therefor the storage unit

was moved from Bus bar 1 to Bus Bar 5.

The process of simulation will be the same as in the previous cases:

• running the first iteration of MOST to define the charge and discharge periods of the

storage unit;

• running the multiperiod AC OPF to analyze all the restrictions of the system;

• and finally doing an iteration of MOST while considering the active losses obtained

in the AC OPF to see how it affects the overall optimization of the system.

5.4.1. First Iteration of MOST

The first iteration of MOST has the main goal of defining the storage profile and dividing the

applied load profile between the bus bars according to the load data defined in the IEEE 30 Bus

case. Being it so, it is only interesting to analyze the results of MOST with the storage unit

considered. On top of that, there is only interest in analyzing the results from the multiperiod

AC OPF and the second iteration of MOST, because it is only on those stages where losses are

considered.

Being it so, the value of system economic dispatch will be ignored, and the focus will be on

the generator production and more importantly, on the storage profile defined by MOST.

Starting with the individual generator production, the evolution of the production of each

generator and the storage unit can be found in Figure 5-57.


98

With the first iteration of MOST, the storage profile defined for the rest of the simulation

can be seen in Figure 5-58. In Figure 5-59 it is shown the state of charge of the storage unit, as

defined by MOST, remembering that the storage unit used has an efficiency of 95%, being that

only 95% of the power used to charge the battery actually can be used as output power.

-20.00

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0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pro

du

ctio

n (

MW

)

time (Hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27)

Gen 5 (23) Gen 6 (13) Storage (5)

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-15.00

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-5.00

0.00

5.00

10.00

15.00

20.00

25.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Po

wer

Inp

ut/

ou

tpu

t (M

W)

Time (Hours)

Figure 5-57 - Individual Generator and Storage Production

Figure 5-58 - Storage Unit power input/output profile


99

With the storage profile defined, it is now possible to do the multiperiod AC OPF simulations

and verify the influence that the new location of the storage unit has in the losses.

5.4.2. Multiperiod AC OPF with the Storage unit on Bus 5

With the storage profile defined in MOST, it is possible to do the AC OPF with the

consideration of the storage unit now located in Bus 5. Being that there was nothing else

changed in the network, there was no need to re-do the multiperiod AC OPF without the storage

unit, since it has been done already in the study of Case 2, and can be found in 5.3.2.1.

With that said, the first thing to verify is if the change of location in the storage unit had

any change in the economic dispatch when compared to the one obtained in Case 2. The

economic dispatch for the multiperiod AC OPF in this case is presented in Table 5-14, while the

comparison with the economic dispatch obtained in Case 2 can be found in Figure 5-60.

Table 5-14 - Economic Dispatch for the multiperiod AC OPF with the storage unit on Bus 5

Economic Dispatch ($) 8826.64

0.00

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10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Sto

rage

Ch

arge

(M

Wh

)

Time (hours)

Figure 5-59 - Storage Unit Charge levels at the end of each hour after the first iteration of MOST


100

When looking at the two dispatches, the dispatch in Case 3 is slightly smaller than the one

obtained in Case 2. This is a first indicator that the position of the storage unit can benefit the

system, and although the main goal in this case is to see what it does to the active losses, it

cannot be ignored any type of improvements that the new location of the unit will do to the

system.

Since the decrease of the system economic dispatch means that the power production of

the generators had changed, it is important to analyze the individual generator production.

8804

8809

8814

8819

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8829

8834

Economic Dispatch Case 3 Economic Dispatch Case 2

Eco

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Dis

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60

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100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Pro

du

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n (

MW

)

Time (hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27)Gen 5 (23) Gen 6 (13) Storage (5)

Figure 5-60 - Comparison of Economic dispatch between Case 2 and Case 3 multiperiod AC OPF

Figure 5-61 - Individual Generator Production over the 24 hours for the multiperiod AC OPF with the storage unit on Bus 5


101

Looking at Case 3 and Case 2 total production, the difference can be found in Figure 5-62.

The difference shown helps understanding better the difference in the system total dispatch.

As there is less power being produced in Case 3 during peak hours, where power production is

more expensive, it is understandable that the overall system’s economic dispatch is smaller.

Although there is slightly more production in Case 3 during off-peak hours, that extra production

can be taken care of by the less expensive generators, contrarily to what happens during peak

periods.

Taking a more detailed look at the system overall losses, that was the main point of this

study case, the difference of the location of the storage unit did indeed cause a slight decrease

of the system’s total losses. When comparing the MW losses to the ones obtained in Case 2,

there is a decrease from 1.79 MW average active losses in Case 2 to 1.76 MW average active

losses in Case 3. This corresponds to a decrease from 43.02 MW to 42.18 MW of total losses over

the 24 hours of the study. The difference for each hour can be found in Figure 5-63.

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Dif

fere

nce

in P

rod

uct

ion

(M

W)

Time (hours)

Figure 5-62 - Difference in total production between Case 3 and Case 2 multiperiod AC OPF


102

It is interesting to compare the losses difference between the results obtained in this study

case, with the storage unit located in Bus 5 to the results obtained for the multiperiod AC OPF

without the storage unit being considered. Figure 5-64 shows the difference of the system’s

losses for the AC OPF without storage and the AC OPF with the storage on bus 5.

Although the MW losses are still bigger in the AC OPF scenario with the storage unit, the

difference now to the losses obtained in the AC OPF without storage are smaller than what

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

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5.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Act

ive

Loss

es (

MW

)

Time (hours)AC OPF with storage on Bus 5 (Case 3) AC OPF With Storage on Bus 1 (Case 2)

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Act

ive

loss

es (

MW

)

Time (hours)

AC OPF With Storage on Bus 5 AC OPF without storage

Figure 5-63 - Difference between the active losses obtained in Case 3 and Case 2

Figure 5-64 - Comparison of system losses between the AC OPF with the storage on Bus 5 and without storage


103

happened when the storage unit was located in bus 1. This shows that the position of the storage

unit in the grid will have an influence on the system’s losses, as was intended to be proven. In

Figure 5-65 it is shown a comparison of the active losses percentage over the active generation

for all three cases: No storage, storage in bus bar 1 and in bus bar 5.

As shown, the overall system losses with the storage unit, at least in the two positions that

were tested, all lead to having slightly bigger system losses when compared to the AC OPF

without the storage unit. However, it is also clear that when the storage unit changed positions

losses also changed, so the position of the storage unit will indeed influence the losses that the

system will have. Table 5-15 shows the total loss value for the 24 hours of the system study for

each of the cases shown in Figure 5-65.

Table 5-15 - Total Active losses for the 24 hours of the system for each of the study cases

Total Active Losses (MW)

Case 3 Case 2 No Storage

42.18 43.02 41.17

With the conclusion of the multiperiod AC OPF, the study can now proceed to the second

iteration of MOST, where the new losses will be implemented into the system load, and see the

results that MOST will provide and compare them to the ones obtained in Case 2.

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Loss

per

cen

tage

(%

)

Time (hours)

AC OPF with Storage (Bus 5) AC OPF with Storage (Bus 1) AC OPF without Storage

Figure 5-65 - Comparison of the loss percentage for the AC OPF without storage and with storage in bus 1 and 5


104

5.4.3. MOST with loss compensation with the storage unit on

Bus 5

With the addition of the MW losses obtained in the AC OPF, it is possible to make the results

obtained in MOST to be closer to the ones obtained in the multiperiod AC OPF. It is interesting

to see how the change of the storage position will influence the results of MOST with the loss

compensation, when compared to the results obtained in Case 2.

Starting with analyzing the economic dispatch obtained from MOST and comparing it to the

results obtained in both MOST with loss compensation in Case 2 and the multiperiod AC OPF

obtained in this study case. The difference between all three situations can be found in Table

5-16, and for a more visual comparison Figure 5-66.

Table 5-16 - Values for the economic dispatch of MOST with loss compensation (Case 3 and Case 2)

and multiperiod AC OPF for Case 3

Economic Dispatch ($)

Case 3 MOST with Loss Compensation 8821.96

Case 2 MOST with Loss Compensation 8820.917

Case 3 AC OPF 8826.64

When comparing the results obtained between Case 3 and Case 2’s MOST with the loss

compensation, the differences obtained are minimal, with the overall system dispatch only

8818

8819

8820

8821

8822

8823

8824

8825

8826

8827

8828

Case 3 MOST with LossCompensation

Case 2 MOST with LossCompensation

Case 3 AC OPF

Eco

no

mic

Dis

pat

ch (

$)

Figure 5-66 - Graphical Representation of the economic dispatches presented in Table 5-16


105

increasing about 1$ in the entire 24 hours of the study. In this scenario, the cost of the dispatch

increased with the relocation of the storage unit, but the change is insignificant.

When comparing the results obtained in the AC OPF with the ones obtained in the final

iteration of MOST, it can be seen that the economic dispatch obtained with MOST is less

expensive than the one obtained with the AC OPF.

Analyzing the production value of MOST with the storage unit located in bus 5, the

production curves of each generator are as expected, as can be seen in Figure 5-67, but the

most interesting aspect is comparing it to the production values obtained in MOST but with the

storage unit located in bus 1. That comparison can be seen in Figure 5-68.

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0

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40

60

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100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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(M

W)

Time (hours)


Figure 5-67 - Individual generator production for MOST with the storage unit located in Bus 5

Figure 5-68 - Difference in generator production between MOST in Case 3 and in Case 2


106

As shown in Figure 5-68, the differences between the generators’ productions in both study

cases is barely minimal, with the differences in all of the generators being smaller than 0.06MW.

The biggest difference happens for hour 20 and it happens for the storage unit, whose

production was bigger in case 2 by 0.32MW.

The comparison between the multiperiod AC OPF and MOST with the consideration of losses,

both of them with the storage unit located in Bus 5, the difference in individual generator

production is slightly different from MOST to the AC OPF, mainly due to the reasons explained

before in Case 1 and 2: The AC OPF has more restrictions, considers line limitations and the

reactive flow, therefore the results might suffer slight variations with the AC OPF giving priority

to some generators other than the ones used by MOST. The difference in individual generator

production can be found in Figure 5-69.

But when looking at the system total production, it is clear that the differences in total

produced energy are very small, with the total production being pretty much the same for all

of the hours in study, showing the similarities that exist in both processes, as one results from

the other.

-2.00

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-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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du

ctio

n d

iffe

ren

ce (

MW

)

Time (hours)

Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27)Gen 5 (23) Gen 6 (13) Storage (5)

Figure 5-69 - Comparison of individual generator production between MOST and the AC OPF, both with the storage on Bus 5


107


The main objective with this third study case was to analyze the influence that the storage

unit location could have on the system’s total losses. It was also seen that the location of the

storage unit ended up having an effect in the system’s dispatch as well.

Starting with the system total losses, it was clear that changing the location of the storage

unit from bus 1 to bus 5 ended up reducing the system total active losses, even if just slightly.

Being only two locations tested, it is interesting to see what influence other locations could

have in the system normal operation, but since this study was mainly a proof of concept, the

results obtained were considered satisfactory

It was also interesting to see how the location ended up influencing the system’s dispatch

as well, although very slightly.

This study case illustrates the impact that storage location can have in the overall system

performance. Another interesting aspect to consider is that, although in this study the overall

losses of the system increased when compared to the situation without the ESS, the total

economic dispatch decreased every time that the storage unit was added to the system. Being

the optimization of the economic dispatch the overall goal of this study, the results obtained

can be classified as satisfactory.

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Tota

l Pro

du

ctio

n (

MW

)

Time of day (Hours)Conventional Production MOST with Losses Conventional Production for thr AC OPF

Figure 5-70 - Total system production comparison between MOST and the AC OPF


108

Conclusions and Future Works

109


6.1. Conclusions

This study presents a solution for implementing a 24 hours multi-period optimal power flow

with the consideration of storage and with global unit commitment optimization, while

respecting the constraints of an AC optimal power flow. The technique used for achieving this

objective was an iterative procedure using MOST and MATPOWER’s AC OPF calculations. The

first iteration of MOST would be responsible for the definition of the storage unit charge and

discharge profiles and the load applied to each bus of the system. Then, while using the storage

profile defined by the first iteration of MOST, 24 AC OPF’s would be run to try and replicate a

multi-period AC OPF, with the objective of checking if the power flow would not violate any of

the AC constraints of the OPF. Then finally, a final iteration of MOST is ran, while adding the

AC losses to the load profile applied in MOST, in order to obtain more similar results to the ones

obtained in the AC OPF, but with MOST doing the global optimization of the system for the 24

hours of the simulation.

The results obtained during the course of the simulation can lead to various conclusions

regarding the influence that the storage unit inclusion in the IEEE 30-bus network OPF.

First, the inclusion of the storage unit reflects in a decrease of the total energy production

cost. The energy production cost, or system’s economic dispatch, was the focus of the study,

and was the function that the algorithm aimed to minimize. With the inclusion of the storage

unit, it was clear that the overall cost for energy production was lower than the one obtained

in the scenario where no storage unit was considered in the system. This would happen due to

the peak-shaving effect that the storage unit would have in the system. It would force the

generators to produce a bit more during off-peak periods, where the energy cost is cheaper

since the production can be covered by the cheapest generators, to charge the storage unit.


110

But in the other hand, the storage unit would discharge during peak hours, allowing for the

more expensive generators to produce less energy. This relief of generator production during

peak hours is enough to diminish the overall economic dispatch for the total of the period of

study (24 hours).

With the conclusion that the storage unit helps with the diminishing of the system’s overall

economic dispatch, the next point of interest was to see if it was possible to use the storage

system to avoid turning one of the generators on, leaving its production to be distributed by

the system’s cheapest generators and the storage unit. For that objective to be achieved, the

cost functions of generators 4 and 5 were changed to penalize these generators so that the

system would only use them as a last resort to supply the loads. What was concluded was that

with the inclusion of the storage unit, the system could avoid using Generator 5, that was

previously being used then the storage unit was not operational. This showed that with the

addition of storage units to the electric networks, the possibility of avoiding the usage of some

of the conventional generators is a reality, with the storage unit helping to supply the loads

during the most critical periods. This possibility is very interesting, especially when analyzing

the environmental impact of conventional energy production, that could be seriously improved

if then number of thermal generators used to supply the system’s loads were to be diminished.

That diminishing is a possibility, especially when combining storage units with renewable

sources, leading to a cleaner energy supply.

The final point of study of this dissertation was the study the influence that the location of

the storage unit could have in the system’s overall performance, like the economic dispatch

and the power injection levels. But the main reason that lead to this study case was to analyze

the influence that different locations of the storage unit would have on the system’s active

losses. When the storage unit was added in the previous study cases, the overall system active

losses suffered a slight increase when compared to the initial, no storage added, case. With

the addition of the storage unit in Bus 1, the active power flow in the branches that were

connected to that bus was supposed to increase, which might lead to an overall increase in the

system’s total losses. So with the new location of the storage unit in this last study case, with

the storage unit located in the bus with the highest load demands, it could be seen that the

active losses did indeed decrease when compared to the active losses found with the storage

unit in Bus 1, but were still slightly bigger than the ones found when the system had no storage

unit. Still, the decrease in active losses when compared to the results obtained with the storage

unit located in Bus 1 are enough to conclude that the location of the storage unit can contribute

to the performance of the system, especially when losses is regarded. When locating the storage

unit in a bus bar whose branches connected to it have better characteristics, it is expected that

the power flow in those branches will not result in as many active losses as the power flow that

happens in lines that are under heavier load and whose characteristics are not so beneficial for

the flow of power on them.


111

Overall, the main objectives intended with this dissertation were achieved. The creation of

a solution for the study of storage unit influence of a network while using global period

optimization, tap position optimization and respect for the AC constraints while using only

MATPOWER tools ended up giving very satisfactory results, and the results obtained for all the

study cases were the ones that were expected, corroborating the initial premise of the

dissertation: Storage units are beneficial for the system, resulting mainly in economic, but also

environmental benefits.

6.2. Future Works

Although the obtained results were positive, and the study done during this dissertation

achieved good results and conclusions, there are aspects that could be improved or studied

more deeply.

The first aspect that could be improved was the computational aspect of the entire range

of iterations, from the first MOST run, to the multi-period AC OPF, and to the final MOST run.

The process was not fully optimized, as the programming of all the algorithms could be

improved to make the process faster and less troublesome for whoever tries to replicate the

obtained results. On top of this, the ideal operation mode for this type of algorithm is to make

it an iterative algorithm. Create a way to make the process be as such as that the restrictions

of the AC OPF would work as an input for MOST, and then run it. After the MOST run, do another

AC OPF simulation and verify if the results are better than the first ones. If not, re-input the

AC restrictions again into MOST and do this until the results are the ones desired. During this

work it was only done one iteration of the described process due to lack of time to better

optimize the results.

Another aspect that could be improved is the reactive flow focus and optimization. During

this study, the main focus was the active power flow and the active aspects of the grid, mainly

because MOST only deals with DC OPF and with the active aspects of the power flow. Therefore,

even though the reactive constraints were respected with the help of the multiperiod AC OPF,

the reactive power flow was not optimized. Maybe with deeper study of the reactive side of

the problem, and with a better optimization of MOST to deal with the reactive flow, the

obtained results could be improved.

Continuing with the optimization of the MOST programming and calculations, one of the

aspects that has room for improvement is the adaptation of MOST to consider the AC losses.

The original MOST programming does not consider losses, since it only tackles the DC OPF of

the system. The solution found was the addition of the active losses found in the AC OPF into

the load profile that MOST uses for its calculations. Although the results obtained were

considered satisfactory, perhaps with better optimization of this solution, or with the

integration of a different solution, the results achieved could be even more similar between


112

the multi-period AC OPF and the final iteration of MOST. Another aspect that MOST ignores that

it would be a good challenge for the future is the line flow limits. MOST does not consider line

limitations, so the results obtained are also constrained by that factor. If in the future, a way

of adding the consideration of line limits to the MOST calculations was found, the results

obtained would be even more reliable and close to the ones found in the AC OPF.

There are more aspects of this problem that could be studied, like the influence of more

storage units in the grid, or how the network would behave to different types of storage and

different locations. Even the consideration of renewable sources in this problem would be an

interesting addition to it. The study made was limited to the time available and the results

obtained are the ones intended, but there is always more aspects of every problem that can be

better studied or analyzed in a different way.


113

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Per Bus Load for each hour of the system

119

Annex A



120

Table A-1 - System MW Load, per bus, for each hour of the system

Bus/Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 3.83 2.60 2.91 2.37 2.83 3.06 3.91 3.91 7.27 9.72 10.64 12.02 12.33 12.56 12.10 12.40 12.25 12.79 13.78 14.70 15.85 16.08 15.62 13.55

3 0.42 0.29 0.32 0.26 0.31 0.34 0.43 0.43 0.80 1.08 1.18 1.33 1.36 1.39 1.34 1.37 1.35 1.41 1.52 1.63 1.75 1.78 1.73 1.50

4 1.34 0.91 1.02 0.83 0.99 1.07 1.37 1.37 2.55 3.41 3.73 4.21 4.32 4.40 4.24 4.34 4.29 4.48 4.83 5.15 5.55 5.63 5.47 4.75

5 16.62 11.30 12.63 10.30 12.30 13.30 16.95 16.95 31.58 42.21 46.20 52.19 53.51 54.51 52.52 53.85 53.18 55.51 59.83 63.82 68.80 69.80 67.81 58.83

6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

7 4.02 2.74 3.06 2.49 2.98 3.22 4.10 4.10 7.64 10.22 11.18 12.63 12.95 13.19 12.71 13.03 12.87 13.44 14.48 15.45 16.65 16.89 16.41 14.24

8 5.29 3.60 4.02 3.28 3.92 4.23 5.40 5.40 10.06 13.44 14.71 16.62 17.04 17.36 16.73 17.15 16.94 17.68 19.05 20.32 21.91 22.23 21.59 18.74

9 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

10 1.02 0.70 0.78 0.63 0.76 0.82 1.04 1.04 1.94 2.60 2.84 3.21 3.29 3.36 3.23 3.32 3.27 3.42 3.68 3.93 4.24 4.30 4.17 3.62

11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

12 1.98 1.34 1.50 1.23 1.46 1.58 2.02 2.02 3.75 5.02 5.49 6.20 6.36 6.48 6.24 6.40 6.32 6.60 7.11 7.59 8.18 8.30 8.06 7.00

13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

14 1.09 0.74 0.83 0.68 0.81 0.88 1.12 1.12 2.08 2.78 3.04 3.43 3.52 3.59 3.46 3.54 3.50 3.65 3.94 4.20 4.53 4.59 4.46 3.87

15 1.45 0.98 1.10 0.90 1.07 1.16 1.48 1.48 2.75 3.67 4.02 4.54 4.66 4.75 4.57 4.69 4.63 4.83 5.21 5.56 5.99 6.08 5.90 5.12

16 0.62 0.42 0.47 0.38 0.46 0.49 0.63 0.63 1.17 1.57 1.72 1.94 1.99 2.03 1.95 2.00 1.98 2.06 2.22 2.37 2.56 2.59 2.52 2.19

17 1.59 1.08 1.21 0.98 1.17 1.27 1.62 1.62 3.02 4.03 4.41 4.99 5.11 5.21 5.02 5.14 5.08 5.30 5.72 6.10 6.57 6.67 6.48 5.62

18 0.56 0.38 0.43 0.35 0.42 0.45 0.58 0.58 1.07 1.43 1.57 1.77 1.82 1.85 1.78 1.83 1.81 1.89 2.03 2.17 2.34 2.37 2.30 2.00

19 1.68 1.14 1.27 1.04 1.24 1.34 1.71 1.71 3.18 4.26 4.66 5.26 5.40 5.50 5.30 5.43 5.36 5.60 6.03 6.44 6.94 7.04 6.84 5.93

20 0.39 0.26 0.29 0.24 0.29 0.31 0.40 0.40 0.74 0.99 1.08 1.22 1.25 1.27 1.23 1.26 1.24 1.30 1.40 1.49 1.61 1.63 1.58 1.37

21 3.09 2.10 2.35 1.91 2.28 2.47 3.15 3.15 5.87 7.84 8.58 9.69 9.94 10.13 9.76 10.00 9.88 10.31 11.11 11.86 12.78 12.97 12.60 10.93

22 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

23 0.56 0.38 0.43 0.35 0.42 0.45 0.58 0.58 1.07 1.43 1.57 1.77 1.82 1.85 1.78 1.83 1.81 1.89 2.03 2.17 2.34 2.37 2.30 2.00

24 1.53 1.04 1.17 0.95 1.14 1.23 1.57 1.57 2.92 3.90 4.27 4.82 4.94 5.03 4.85 4.97 4.91 5.13 5.53 5.89 6.35 6.45 6.26 5.43

25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

26 0.62 0.42 0.47 0.38 0.46 0.49 0.63 0.63 1.17 1.57 1.72 1.94 1.99 2.03 1.95 2.00 1.98 2.06 2.22 2.37 2.56 2.59 2.52 2.19

27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

29 0.42 0.29 0.32 0.26 0.31 0.34 0.43 0.43 0.80 1.08 1.18 1.33 1.36 1.39 1.34 1.37 1.35 1.41 1.52 1.63 1.75 1.78 1.73 1.50

30 1.87 1.27 1.42 1.16 1.38 1.50 1.91 1.91 3.55 4.75 5.20 5.87 6.02 6.13 5.91 6.06 5.98 6.25 6.73 7.18 7.74 7.85 7.63 6.62


121

Table A-2 - System MVar load, per bus, for each hour of the system

Bus/Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 2.24 1.52 1.70 1.39 1.66 1.79 2.29 2.29 4.26 5.69 6.23 7.04 7.21 7.35 7.08 7.26 7.17 7.48 8.07 8.60 9.28 9.41 9.14 7.93

3 0.21 0.14 0.16 0.13 0.16 0.17 0.22 0.22 0.40 0.54 0.59 0.66 0.68 0.69 0.67 0.69 0.68 0.71 0.76 0.81 0.88 0.89 0.86 0.75

4 0.28 0.19 0.21 0.18 0.21 0.23 0.29 0.29 0.54 0.72 0.78 0.89 0.91 0.93 0.89 0.91 0.90 0.94 1.02 1.08 1.17 1.19 1.15 1.00

5 3.35 2.28 2.55 2.08 2.48 2.68 3.42 3.42 6.37 8.51 9.32 10.53 10.79 10.99 10.59 10.86 10.73 11.20 12.07 12.87 13.88 14.08 13.68 11.87

6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

7 1.92 1.31 1.46 1.19 1.42 1.54 1.96 1.96 3.65 4.88 5.35 6.04 6.19 6.31 6.08 6.23 6.15 6.42 6.92 7.38 7.96 8.08 7.85 6.81

8 5.29 3.60 4.02 3.28 3.92 4.23 5.40 5.40 10.06 13.44 14.71 16.62 17.04 17.36 16.73 17.15 16.94 17.68 19.05 20.32 21.91 22.23 21.59 18.74

9 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

10 0.35 0.24 0.27 0.22 0.26 0.28 0.36 0.36 0.67 0.90 0.98 1.11 1.14 1.16 1.12 1.14 1.13 1.18 1.27 1.35 1.46 1.48 1.44 1.25

11 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

12 1.32 0.90 1.01 0.82 0.98 1.06 1.35 1.35 2.51 3.36 3.68 4.15 4.26 4.34 4.18 4.29 4.23 4.42 4.76 5.08 5.48 5.56 5.40 4.68

13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

14 0.28 0.19 0.21 0.18 0.21 0.23 0.29 0.29 0.54 0.72 0.78 0.89 0.91 0.93 0.89 0.91 0.90 0.94 1.02 1.08 1.17 1.19 1.15 1.00

15 0.44 0.30 0.34 0.27 0.33 0.35 0.45 0.45 0.84 1.12 1.23 1.38 1.42 1.45 1.39 1.43 1.41 1.47 1.59 1.69 1.83 1.85 1.80 1.56

16 0.32 0.22 0.24 0.20 0.23 0.25 0.32 0.32 0.60 0.81 0.88 1.00 1.02 1.04 1.00 1.03 1.02 1.06 1.14 1.22 1.31 1.33 1.30 1.12

17 1.02 0.70 0.78 0.63 0.76 0.82 1.04 1.04 1.94 2.60 2.84 3.21 3.29 3.36 3.23 3.32 3.27 3.42 3.68 3.93 4.24 4.30 4.17 3.62

18 0.16 0.11 0.12 0.10 0.12 0.13 0.16 0.16 0.30 0.40 0.44 0.50 0.51 0.52 0.50 0.51 0.51 0.53 0.57 0.61 0.66 0.67 0.65 0.56

19 0.60 0.41 0.46 0.37 0.44 0.48 0.61 0.61 1.14 1.52 1.67 1.88 1.93 1.97 1.90 1.94 1.92 2.00 2.16 2.30 2.48 2.52 2.45 2.12

20 0.12 0.08 0.09 0.08 0.09 0.10 0.13 0.13 0.23 0.31 0.34 0.39 0.40 0.41 0.39 0.40 0.40 0.41 0.44 0.47 0.51 0.52 0.50 0.44

21 1.98 1.34 1.50 1.23 1.46 1.58 2.02 2.02 3.75 5.02 5.49 6.20 6.36 6.48 6.24 6.40 6.32 6.60 7.11 7.59 8.18 8.30 8.06 7.00

22 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

23 0.28 0.19 0.21 0.18 0.21 0.23 0.29 0.29 0.54 0.72 0.78 0.89 0.91 0.93 0.89 0.91 0.90 0.94 1.02 1.08 1.17 1.19 1.15 1.00

24 1.18 0.80 0.90 0.73 0.87 0.95 1.21 1.21 2.25 3.00 3.29 3.71 3.81 3.88 3.74 3.83 3.78 3.95 4.26 4.54 4.89 4.96 4.82 4.18

25 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

26 0.41 0.28 0.31 0.25 0.30 0.32 0.41 0.41 0.77 1.03 1.13 1.27 1.31 1.33 1.28 1.31 1.30 1.36 1.46 1.56 1.68 1.70 1.66 1.44

27 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

28 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

29 0.16 0.11 0.12 0.10 0.12 0.13 0.16 0.16 0.30 0.40 0.44 0.50 0.51 0.52 0.50 0.51 0.51 0.53 0.57 0.61 0.66 0.67 0.65 0.56

30 0.34 0.23 0.25 0.21 0.25 0.27 0.34 0.34 0.64 0.85 0.93 1.05 1.08 1.10 1.06 1.09 1.07 1.12 1.21 1.29 1.39 1.41 1.37 1.19


122

Case 1 - Generator Production for each hour in MOST without the storage unit

123

Annex B


Table B-1 - Generator production, per hour, for MOST without the storage unit

Hour Gen.1 Gen.2 Gen.3 Gen.4 Gen.5 Gen.6

1 14.15 23.32 12.53 0 0 0

2 7.66 15.89 10.45 0 0 0

3 9.28 17.75 10.97 0 0 0

4 6.44 14.5 10.06 0 0 0

5 8.87 17.28 10.84 0 0 0

6 10.09 18.68 11.23 0 0 0

7 14.56 23.78 12.66 0 0 0

8 19.84 29.81 14.35 0 0 0

9 29.5 40.86 17.44 0 3.6 3.6

10 35.1 47.26 19.23 9.24 8.08 8.08

11 36.96 49.38 19.83 13.69 9.57 9.57

12 39.75 52.57 20.72 20.37 11.8 11.8

13 40.37 53.27 20.92 21.86 12.29 12.29

14 40.83 53.81 21.07 22.97 12.66 12.66

15 39.9 52.74 20.77 20.75 11.92 11.92

16 40.52 53.45 20.97 22.23 12.42 12.42

17 40.21 53.1 20.87 21.49 12.17 12.17

18 41.29 54.34 21.21 24.09 13.03 13.03

19 43.31 56.64 21.86 28.91 14.64 14.64

20 45.16 58.76 22.45 33.36 16.13 16.13

21 47.48 61.41 23.2 38.93 17.99 17.99

22 47.95 61.94 23.34 40.05 18.36 18.36

23 47.02 60.88 23.05 37.82 17.62 17.62

24 42.84 56.1 21.71 27.8 14.27 14.27


124

Case 1- Generator Production for each hour of the system for the AC OPF

125

Annex C


Table C-1 - Individual Generator Production, per hour, for the multiperiod AC OPF without storage

Hora Gen 1 (1) Gen 2 (2) Gen 3 (22) Gen 4 (27) Gen 5 (23) Gen 6 (13)

1 14.14632 23.43012 12.65453 0 0 0

2 7.661668 15.94571 10.49311 0 0 0

3 9.28168 17.81412 11.03144 0 0 0

4 6.446823 14.54526 10.09064 0 0 0

5 8.876605 17.34685 10.89673 0 0 0

6 10.09197 18.74899 11.30111 0 0 0

7 14.55201 23.89885 12.79034 0 0 0

8 19.83055 30.00262 14.56367 0 0 0

9 28.86726 40.48771 17.63677 0 4.472826 4.289569

10 33.99249 46.45674 19.45106 10.82668 8.656616 8.669024

11 35.88269 48.66105 20.12658 15.04269 10.20205 10.2919

12 38.72874 51.98248 21.14904 21.35316 12.52921 12.74223

13 39.36478 52.72458 21.37822 22.74713 13.04866 13.29101

14 39.8422 53.28174 21.55047 23.79217 13.4386 13.70322

15 38.88769 52.16792 21.20628 21.70172 12.65903 12.87934

16 39.52388 52.91024 21.4356 23.09552 13.17861 13.42836

17 39.20571 52.53897 21.32087 22.39871 12.91875 13.15373

18 40.31997 53.8394 21.72305 24.83681 13.82884 14.11596

19 42.39427 56.26182 22.47466 29.35912 15.52344 15.91066

20 44.31476 58.50642 23.17394 33.52696 17.09287 17.57629

21 46.71743 61.34671 24.05118 38.68791 19.06249 19.6877

22 47.19759 61.90982 24.22774 39.73264 19.45595 20.10592

23 46.2375 60.784 23.87492 37.64318 18.66929 19.26991

24 41.91501 55.70195 22.30067 28.31616 15.13187 15.49561


126

Case 2 - Storage Unit charge level

127

Annex D


Table D-1 - Storage Unit Charge Level

Hour Storage Charge

(MWh)

1 0

2 11,4

3 19

4 33,25

5 41,8

6 47,5

7 47,5

8 47,5

9 47,5

10 47,5

11 47,5

12 47,5

13 47,5

14 47,5

15 47,5

16 47,5

17 47,5

18 47,5

19 47,5

20 46,87

21 31,24

22 12,62

23 0

24 0


128

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