Sizing, Costing and Competitiveness Analysis of Large ... · di erent business cases: industrial...

eeh power systemslaboratory

Vytis Gumbrys

Sizing, Costing and CompetitivenessAnalysis of Large Scale Electrical Energy

Storage

Master ThesisPSL 1518

EEH – Power Systems LaboratorySwiss Federal Institute of Technology (ETH) Zurich

Examiner: Prof. Dr. Goran Andersson, ETH ZurichSupervisor: Dr. Vipluv Aga, ALSTOM Renewable PowerSupervisor: Dr. Osvaldo Rodrıguez Villalon, ETH Zurich

Zurich, September 3, 2015

Acknowledgements

First and foremost, I would like to thank my supervisors Dr. Vipluv Agaand Dr. Osvaldo Rodrıguez Villalon for their guidance and help throughoutthe course of this thesis. I am especially grateful for the opportunity to learnabout the energy storage and the photovoltaic industries from the extensiveknowledge of Dr. Vipluv Aga.

In addition, I would like to express my gratitude to Prof. Dr. GoranAndersson for his support during my studies at ETH Zurich and for givingme the opportunity to write this thesis in collaboration with the RenewableSteam Plants department of Alstom.

I would also like thank my colleagues at the Renewable Steam Plantsdepartment for creating a great working environment. A special thank yougoes to Christos Tsolakis with whom I tackled many interesting and chal-lenging tasks in photovoltaic and energy storage fields over the last year.Lastly, I would like to thank Enrico Conte for guiding me through his ther-modynamic model and Yannick Laborde for helping me with the electricalsizing calculations.

ii

Abstract

The increasing share of renewable energy sources calls for large scale elec-trical energy storage solutions. There are many applications where energystorage can be beneficial and it is key for ensuring reliable supply of theelectrical energy. In addition, there are several technologies that competefor the place in the growing energy storage market. Thus, it is importantto identify suitable technologies for specific applications as well as size theinstalled capacity in an optimum way for maximising the potential benefits.

This thesis investigates sizing and competitiveness of three large scaleelectrical energy storage technologies: lithium-ion batteries, vanadium redoxbatteries and the molten salt energy storage. First, a mixed integer linearprogramming optimisation for achieving minimum LCOE or maximum NPVconfigurations of combined storage and PV plants is described. After that,a bottom-up costing of the molten salt energy storage is presented with afocus on sizing and costing of the electrical integration equipment. Theelectrical sizing according to the international standards is explained andverified using NEPLAN software. Finally, the cost estimate obtained for themolten salt energy storage system is used to compare the competitivenessof this technology with vanadium redox and lithium-ion batteries in threedifferent business cases: industrial peak shaving, diesel replacement in amine and electrical energy time shift.

It was demonstrated that the optimisation presented can be used forsizing combined storage and PV plant with yearly input data. Sizing andcosting of the molten salt energy storage system revealed that the electricalintegration equipment contributes 3% - 6% towards the total cost of thesystem and that the most expensive part of the system is the dischargingcycle. The business case analysis demonstrated that only the diesel replace-ment business case can ensure desired financial returns. In addition, it wasshown that the molten salt energy storage is the most suitable technologyfor the diesel replacement and the electrical energy time shift business cases.On the other hand, vanadium redox battery was identified as the preferredtechnology for the peak shaving business case.

iii

Contents

List of Figures x

List of Tables xi

List of Acronyms xii

1 Introduction 11.1 Growth of the energy storage market . . . . . . . . . . . . . . 11.2 Overview of electricity storage technologies . . . . . . . . . . 2

1.2.1 Lithium-ion batteries . . . . . . . . . . . . . . . . . . . 21.2.2 Assumptions for lithium-ion batteries . . . . . . . . . 21.2.3 Vanadium redox batteries . . . . . . . . . . . . . . . . 41.2.4 Assumption for vanadium redox batteries . . . . . . . 41.2.5 Molten salt storage . . . . . . . . . . . . . . . . . . . . 6

1.3 Overview of economic assessment criteria . . . . . . . . . . . 81.3.1 Levelised cost of electricity . . . . . . . . . . . . . . . 81.3.2 Net present value . . . . . . . . . . . . . . . . . . . . . 81.3.3 Internal rate of return . . . . . . . . . . . . . . . . . . 8

1.4 Goals of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 91.5 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . 9

2 Mixed Integer Linear Optimisation 112.1 Sizing for the minimum LCOE . . . . . . . . . . . . . . . . . 112.2 Sizing for the maximum NPV . . . . . . . . . . . . . . . . . . 142.3 Constraint explanations . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Power balance . . . . . . . . . . . . . . . . . . . . . . 162.3.2 Implementation of efficiencies . . . . . . . . . . . . . . 172.3.3 Achieving desired fulfilment factor . . . . . . . . . . . 172.3.4 PV production . . . . . . . . . . . . . . . . . . . . . . 17

2.4 Technology specific constraints . . . . . . . . . . . . . . . . . 172.4.1 Additional constraints for molten salt storage . . . . . 172.4.2 Additional constraints for vanadium redox batteries . 182.4.3 Additional constraints for lithium-ion batteries . . . . 18

iv

CONTENTS v

3 Electrical Equipment Sizing 193.1 Modes of operation . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Determining loads and sources . . . . . . . . . . . . . . . . . 223.3 Load flow analysis . . . . . . . . . . . . . . . . . . . . . . . . 223.4 Selecting transformers . . . . . . . . . . . . . . . . . . . . . . 233.5 Short circuit current calculations . . . . . . . . . . . . . . . . 23

3.5.1 Voltage factor . . . . . . . . . . . . . . . . . . . . . . . 233.5.2 Short circuit impedances . . . . . . . . . . . . . . . . . 233.5.3 Referring impedances . . . . . . . . . . . . . . . . . . 273.5.4 Thevenin equivalent circuits . . . . . . . . . . . . . . . 283.5.5 Formulas for calculating short circuit currents . . . . . 33

3.6 Rated continuous current calculation . . . . . . . . . . . . . . 343.7 Calculation comparison with NEPLAN model . . . . . . . . . 34

3.7.1 Voltage levels . . . . . . . . . . . . . . . . . . . . . . . 343.7.2 Electrical component characteristics . . . . . . . . . . 343.7.3 Load flow calculation comparison . . . . . . . . . . . . 343.7.4 Short circuit current calculation comparison . . . . . . 36

4 Costing 384.1 Cost models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.1.1 Circuit breaker cost model . . . . . . . . . . . . . . . . 384.1.2 Circuit breaker cost model sensitivity . . . . . . . . . 40

4.2 Costing non-electrical equipment . . . . . . . . . . . . . . . . 424.3 Molten salt storage cost breakdown . . . . . . . . . . . . . . . 42

5 Case Studies 445.1 Case 1: industrial peak shaving . . . . . . . . . . . . . . . . . 44

5.1.1 Industrial demand profile . . . . . . . . . . . . . . . . 445.1.2 Electricity tariffs for case 1 . . . . . . . . . . . . . . . 455.1.3 Sizing for case 1 . . . . . . . . . . . . . . . . . . . . . 465.1.4 Dispatch profiles for case 1 . . . . . . . . . . . . . . . 465.1.5 IRR graph comparison for case 1 . . . . . . . . . . . . 495.1.6 Conclusions for case 1 . . . . . . . . . . . . . . . . . . 49

5.2 Case 2: diesel replacement in a mine . . . . . . . . . . . . . . 515.2.1 Gold mine demand profile . . . . . . . . . . . . . . . . 515.2.2 Electricity cost produced by diesel generators . . . . . 515.2.3 Locations . . . . . . . . . . . . . . . . . . . . . . . . . 525.2.4 Sizing for case 2 . . . . . . . . . . . . . . . . . . . . . 525.2.5 Dispatch profiles for case 2 . . . . . . . . . . . . . . . 535.2.6 LCOE comparison for case 2 . . . . . . . . . . . . . . 555.2.7 IRR comparison for case 2 . . . . . . . . . . . . . . . . 555.2.8 Conclusions for case 2 . . . . . . . . . . . . . . . . . . 57

5.3 Case 3: electrical energy time shift . . . . . . . . . . . . . . . 575.3.1 Input price profile for case 3 . . . . . . . . . . . . . . . 57

CONTENTS vi

5.3.2 Electricity tariffs for case 3 . . . . . . . . . . . . . . . 575.3.3 Sizing for case 3 . . . . . . . . . . . . . . . . . . . . . 585.3.4 Dispatch profiles for case 3 . . . . . . . . . . . . . . . 585.3.5 IRR comparison for case 3 . . . . . . . . . . . . . . . . 615.3.6 Conclusions for case 3 . . . . . . . . . . . . . . . . . . 62

6 Discussion and Conclusion 636.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A Electrical component characteristics 65

B Electrical cost share variation 67

C Sizing for Case 2 69

D Sizing Dependency on the FF for Case 2 72

E Sizing for Case 3 76

Bibliography 78

List of Figures

1.1 Predicted utility scale storage market growth [1]. . . . . . . . 11.2 Schematic diagram of a lithium-ion battery [2]. . . . . . . . . 31.3 Schematic diagram of a vanadium redox battery [3]. . . . . . 51.4 Schematic diagram of a molten salt storage integration with

a PV plant [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Electrical heater example for the molten salt storage charging

system [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 Explanatory diagram for the power balance constraint. . . . . 16

3.1 Electrical integration scheme for the molten salt storage withadvanced charging system. . . . . . . . . . . . . . . . . . . . . 20

3.2 Electrical integration scheme for the molten salt storage withelectric heater charging system. . . . . . . . . . . . . . . . . . 21

3.3 Standard transformer sizes in kVA from IEEE Std.C57.12.00[6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 Thevenin circuit with equivalent impedance Zk. . . . . . . . . 283.5 Positive sequence equivalent circuit for ”Charging from PV”

mode of operation. . . . . . . . . . . . . . . . . . . . . . . . . 293.6 Zero sequence equivalent circuit for ”Charging from PV”mode

of operation with Yy main transformer. . . . . . . . . . . . . 293.7 Zero sequence equivalent circuit for ”Charging from PV”mode

of operation with Dy main transformer. . . . . . . . . . . . . 303.8 Positive sequence equivalent circuit for ”Discharging” mode of

operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.9 Zero sequence equivalent circuit for ”Discharging” mode of

operation with Yy main transformer. . . . . . . . . . . . . . . 313.10 Zero sequence equivalent circuit for ”Discharging” mode of

operation with Dy main transformer. . . . . . . . . . . . . . . 313.11 Molten salt storage electrical integration system model in NE-

PLAN. Components connected to the main busbar from leftto right: steam turbine generator, synchronous generator,synchronous motor, electric heater, auxiliary loads, PV plant. 35

vii

LIST OF FIGURES viii

4.1 Molten salt storage costing procedure. First a thermody-namic model is used to obtain electrical load list and sizingfor non-electrical equipment. After that, electrical equipmentis sized and overall cost numbers for the molten salt storageare obtained. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Example of transformer cost approximation with a linear costmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Circuit breaker cost data [7]. . . . . . . . . . . . . . . . . . . 404.4 Circuit breaker cost model sensititivity to the changes of short

circuit current rating. . . . . . . . . . . . . . . . . . . . . . . 414.5 Circuit breaker cost model sensitivity to the changes of con-

tinuous current rating. . . . . . . . . . . . . . . . . . . . . . . 414.6 Cost breakdown of molten salt storage with the advanced

charging system. . . . . . . . . . . . . . . . . . . . . . . . . . 434.7 Cost breakdown of molten salt storage with the electric heater

charging system. . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.1 Industrial load profile [8]. . . . . . . . . . . . . . . . . . . . . 455.2 Molten salt storage EH dispatch profile for the industrial peak

shaving application. . . . . . . . . . . . . . . . . . . . . . . . 475.3 Molten salt storage AD dispatch profile for the industrial peak

shaving application. . . . . . . . . . . . . . . . . . . . . . . . 475.4 VRB dispatch profile for the industrial peak shaving application. 485.5 Lithium-ion battery dispatch profile for the industrial peak

shaving application. . . . . . . . . . . . . . . . . . . . . . . . 485.6 15% IRR curves with 0.05 e/kWh off-peak price for the indus-

trial peak shaving application. Locations indicated by dots: 1- California, US, 2- Japan, 3 - Maharashtra, India, 4 - Australia. 50

5.7 15% IRR curves with 0.1 e/kWh off-peak price for the indus-trial peak shaving application. Locations indicated by dots: 1- California, US, 2- Japan, 3 - Maharashtra, India, 4 - Australia. 50

5.8 Gold mine load profile [9]. . . . . . . . . . . . . . . . . . . . . 515.9 Molten salt EH dispatch for first 10 days in Yass, Australia

for the diesel replacement application. . . . . . . . . . . . . . 535.10 Molten salt AD dispatch for first 10 days in Yass, Australia

for the diesel replacement application. . . . . . . . . . . . . . 545.11 VRB dispatch for first 10 days in Yass, Australia for the diesel

replacement application. . . . . . . . . . . . . . . . . . . . . . 545.12 Lithium-ion battery dispatch for first 10 days in Yass, Aus-

tralia for the diesel replacement application. . . . . . . . . . . 555.13 LCOE for optimum storage and PV configurations for the

mine business case. . . . . . . . . . . . . . . . . . . . . . . . . 565.14 IRR for optimum storage and PV configurations for the mine

business case. . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

LIST OF FIGURES ix

5.15 Input electricity price profile for the business case 3. . . . . . 585.16 First 10 days of dispatch for molten salt EH in South Africa

for the business case 3. . . . . . . . . . . . . . . . . . . . . . . 595.17 First 10 days of dispatch for molten salt AD in South Africa

for the business case 3. . . . . . . . . . . . . . . . . . . . . . . 595.18 First 10 days of dispatch for VRB in South Africa for the

business case 3. . . . . . . . . . . . . . . . . . . . . . . . . . . 605.19 First 10 days of dispatch for lithium-ion batteries in South

Africa for the business case 3. . . . . . . . . . . . . . . . . . . 605.20 Business case 3 15% IRR curves for high GHI area (2275

kWh/m2). Locations indicated by dots: 1 - California, US, 2- Japan, 3 - Maharashtra, India, 4 - Zimbabwe. . . . . . . . . 61

5.21 Business case 3 15% IRR curves for low GHI area (1442kWh/m2). Locations indicated by dots: 1 - California, US, 2- Japan, 3 - Maharashtra, India, 4 - Zimbabwe. . . . . . . . . 62

B.1 Electrical integration cost share dependency on the storagesizing for the molten salt storage with advanced charging. Pch

- charging power rating, Pdisch - discharging power rating, E- energy rating. . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.2 Electrical integration cost share dependency on the storagesizing for the molten salt storage with electric heating charg-ing. Pch - charging power rating, Pdisch - discharging powerrating, E - energy rating. . . . . . . . . . . . . . . . . . . . . 68

C.1 Sizing of molten salt EH strorage for the case 2. . . . . . . . . 69C.2 Sizing of molten salt AD strorage for the case 2. . . . . . . . 70C.3 Sizing of VRB for the case 2. . . . . . . . . . . . . . . . . . . 70C.4 Sizing of lithium-ion batteries for the case 2. . . . . . . . . . . 70C.5 PV sizing for the case 2. . . . . . . . . . . . . . . . . . . . . . 71C.6 Energy rating sizing for the case 2. . . . . . . . . . . . . . . . 71

D.1 Ratio of installed PV power and discharging power rating vs.fulfilment factor for the electric heater molten salt storageconfiguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

D.2 Ratio of installed charging and discharging power rating vs.fulfilment factor for the electric heater molten salt storageconfiguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

D.3 Energy rating vs. fulfilment factor for the electric heatermolten salt storage configuration. . . . . . . . . . . . . . . . . 73

D.4 Ratio of installed PV power and discharging power ratingvs. fulfilment factor for the advanced molten salt storageconfiguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

LIST OF FIGURES x

D.5 Ratio of installed charging and discharging power rating vs.fulfilment factor for the advanced molten salt storage config-uration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

D.6 Energy rating vs. fulfilment factor for the advanced moltensalt storage configuration. . . . . . . . . . . . . . . . . . . . . 75

E.1 Molten salt storage EH sizing for the business case 3. . . . . . 76E.2 Moten salt storage AD sizing for the business case 3. . . . . . 76E.3 VRB sizing for the business case 3. . . . . . . . . . . . . . . . 77E.4 Lithium-ion sizing for the business case 3. . . . . . . . . . . . 77E.5 Energy capacity sizing for the business case 3. . . . . . . . . . 77

List of Tables

1.1 Assmptions for lithium-ion batteries . . . . . . . . . . . . . . 31.2 Assmptions for vanadium redox batteries . . . . . . . . . . . 4

3.1 Load flow calculation for sizing main transformer comparisonwith NEPLAN . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2 Three-phase to ground short circuit current calculation com-parison with NEPLAN for the main circuit breaker . . . . . . 36

3.3 Three-phase to ground short circuit current calculation com-parison with NEPLAN for the main busbar . . . . . . . . . . 36

3.4 Three-phase to ground short circuit current calculation com-parison with NEPLAN synchronous machines and PV plant. 36

3.5 Single-phase to ground short circuit current calculation com-parison with Neplan for the main circuit breaker. . . . . . . . 37

3.6 Single-phase to ground short circuit current calculation com-parison with Neplan for the main busbar. . . . . . . . . . . . 37

3.7 Single-phase to ground short circuit current calculation com-parison with Neplan synchronous machines and PV plant. . . 37

5.1 Capacity charges and peak to off-peak electricity price ratios.In the table: λcap - capacity charge for the peak power drawnfrom the grid over a month, λog - off-peak electricity tariff, λpg- peak electricity tariff. . . . . . . . . . . . . . . . . . . . . . . 45

5.2 Resulting sizing for the industrial peak shaving business case. 465.3 Levelised cost of electricity produced by diesel generators. . . 525.4 Locations considered for the business case 2. . . . . . . . . . . 525.5 Peak and off-peak electricity tariffs considered in business case

3. In the table: λog - off-peak electricity tariff, λpg - peakelectricity tariff. . . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.1 Grid characteristics [4]. . . . . . . . . . . . . . . . . . . . . . 65A.2 PV plant characteristics [4]. . . . . . . . . . . . . . . . . . . . 65A.3 Transformer characteristics [4]. . . . . . . . . . . . . . . . . . 66A.4 Synchronous machine characteristics [4]. . . . . . . . . . . . . 66

xi

List of Acronyms

CAPEX Capital ExpenditureCSP Concentrated Solar PowerFF Fulfilment FactorGHI Global Horizontal IrradiationIEC International Electrotechnical CommissionIRR Internal Rate of ReturnLCOE Levelised Cost of ElectricityMILP Mixed Integer Linear ProgrammingNPV Net Present ValueOPEX Operating ExpenditurePV PhotovoltaicSOC State of ChargeVBA Visual Basic for ApplicationsVRB Vanadium Redox Battery

xii

Chapter 1

Introduction

1.1 Growth of the energy storage market

The energy storage becomes crucial for ensuring safe and reliable operationof the future electricity systems as the share of renewable energy sourceskeeps increasing. Thus, experts predict a large and fast growth of the elec-trical energy storage market in the coming years, which is illustrated infigure 1.1. This growing market will need storage solutions for several differ-ent applications: industrial peak shaving, price arbitrage, ancillary services,diesel replacement in off-grid locations, T&D deferral and other.

Figure 1.1: Predicted utility scale storage market growth [1].

1

CHAPTER 1. INTRODUCTION 2

1.2 Overview of electricity storage technologies

There are several energy storage technologies that are likely to compete forthe growing energy storage market. In this thesis three technologies forlarge scale electrical energy storage are investigated: lithium-ion batteries,vanadium redox batteries and the molten salt electricity storage. A shortoverview of these technologies is presented below.

1.2.1 Lithium-ion batteries

Lithium-ion batteries are a type of rechargeable batteries that are used invarious applications from consumer electronics to utility scale energy storagesolutions. The lithium-ion batteries have a cathode made of lithium metaloxide (usually LiCoO2 or LiMO2) and an anode made of graphitic carbon.The electrolytes in lithium-ion batteries are lithium salts like LiClO4. Thesebatteries work by transferring lithium ions from the negative electrode tothe positive during discharging and in opposite direction when charging [10].A schematic of a lithium-ion battery is presented in figure 1.2.

Advantages of lithium-ion batteries:

1. High cycle efficiency ∼90% [11].

2. Fast response time [10].

3. High energy density [10].

Disadvantages of lithium-ion batteries:

1. Energy and power ratings are coupled.

2. Depth of discharge have a significant impact on the lifetime [10].

1.2.2 Assumptions for lithium-ion batteries

Lifetime and costs are extremely important parameters when analysing thecompetitiveness storage technologies. The energy capital cost for lithium-ionbatteries varies significantly across different literature sources. The energycapital cost used in this thesis were based on two literature sources: 356e/kWh [11] and 503 e/kWh [1]. The average of these two numbers weretaken for the analyses and a 430 e/kWh cost number was used. Otherassumptions and respective sources are summarised in table 1.1.


Figure 1.2: Schematic diagram of a lithium-ion battery [2].

Table 1.1: Assmptions for lithium-ion batteries

Assumption Unit Source

Roundtrip efficiency 90 % [11]

Lifetime with 80 % DoD 3650 no. cycles [12]

Energy to power ratio 1 - [13]

Power capital cost 125 e/kW [11]

Energy capital cost 430 e/kWh

OPEX 2 % of CAPEX p.a.


1.2.3 Vanadium redox batteries

Vanadium redox flow batteries work by storing energy in two electrolytetanks separated by an ion selective membrane. These batteries use vanadiumions in different oxidation states in order to store chemical potential energy[10]. A schematic of a vanadium redox flow battery is illustrated in figure1.3.

Advantages of vanadium redox batteries:

1. Power rating is independent from the energy storage capacity [10].

2. Quick response time [10].

3. Long lifetime [10].

4. Relatively high effiency ∼75% [11].

Disadvantages of vanadium redox batteries:

1. Low energy density [10].

2. High operating and manufacturing cost [10].

3. Complex system [10].

1.2.4 Assumption for vanadium redox batteries

Similarly to the case for the lithium-ion batteries, the indicated energy cap-ital cost varies significantly across literature. The energy capital cost usedin this thesis were based on two literature sources: 398 e/kWh [11] and 622e/kWh [1]. The average of these two numbers were taken and 510 e/kWhwas used in the business case analyses. Other assumptions and respectivesources are summarised in table 1.2.

Table 1.2: Assmptions for vanadium redox batteries

Assumption Unit Source

Roundtrip efficiency 75 % [11]

Lifetime 13000 no. cycles [11]

Power capital cost 334 e/kW [11]

Energy capital cost 510 e/kWh

OPEX 2 % of CAPEX p.a.


Figure 1.3: Schematic diagram of a vanadium redox battery [3].


1.2.5 Molten salt storage

The final storage technology investigated in this thesis is the molten saltenergy storage. A similar technology is usually used in combination withconcentrated solar power (CSP) plants. However, a possibility of integratingsuch storage technology with PV plants was considered in this case. Thistype of storage uses molten salt as a working fluid to transfer the energy.The electricity from renewable energy sources can be converted to heat andstored in a hot molten salt tank. The energy can be recovered by transferringthe molten salt from the hot molten salt tank to the cold molten salt tankand producing water vapour while doing this. The produced water vapouris then used for running a steam power cycle to recover the stored energy[10]. A schematic of molten salt storage integration with PV power plant isillustrated in figure 1.4.

In order to convert the electricity produced by renewable energy sourcesto high grade heat a charging system is needed. Two variants of chargingtechnology for the molten salt electricity storage were considered in thisthesis. The first one is based on electrical process heaters. An example ofthe electrical heater that can be used in the charging cycle is presented infigure 1.5. The second variant is based on a thermodynamic heat pumpcycle for converting electricity to high grade heat. This variant can achieveround-trip efficiency of around 50% compared to the round-trip efficiencyof around 40% which can be achieved by the electrical heater variant. Thedisadvantage of the heat-pump variant is that it requires more equipmentand as a result makes more complex system. The heat-pump charging systemwill be referred to as an advanced (AD) charging system in the rest of thethesis.

Advantages of molten salt storage:

1. Low energy capital cost [10].

2. Decoupled energy rating, charging and discharging power capacities.

3. Long lifetime (> 25 years).

Disadvantages of molten salt storage:

1. Low round-trip efficiency [10].


Electrical Power when produced

Cold Molten Salt

Hot Molten Salt

Charging System converts electricity to

high grade heat

Electrical Heater

Conventional steam turbine power block

Electrical Power when needed to Grid (NEM)

Discharge, Qout

ChargeQin

Heat Pump

Charging system Coverts electrity to high grade heat

Figure 1.4: Schematic diagram of a molten salt storage integration with aPV plant [4].

Figure 1.5: Electrical heater example for the molten salt storage chargingsystem [5].


1.3 Overview of economic assessment criteria

Below a short explanation of the economic assessment criteria used as sizingobjectives or competitiveness indicators is given.

1.3.1 Levelised cost of electricity

Levelised cost of electricity (LCOE) allows comparing different electricitygeneration technologies by taking into account the investment and operatingcosts as well as the total power generation over the lifetime of the project[14].

LCOE =

C +∑n

i=1

A(t)

(1 + r)i∑ni=1

L(i)

(1 + r)i

(1.1)

C Initial investment cost.A Annual total costs.L Energy production used for covering the load.r Interest rate.i Year of the project.n Project lifetime.

1.3.2 Net present value

Net present value (NPV) is the difference between present value of revenuesand present value of expenses over the project lifetime [15].

NPV = −C +

n∑i=1

R(i)−A(i)

(1 + r)i= −C +

n∑i=1

cf

(1 + r)i(1.2)

C Initial investment cost.R Annual revenue.A Annual total costs.cf Annual cash flow.r Interest rate.i Year of the project.n Project lifetime.

1.3.3 Internal rate of return

Internal rate of return (IRR) is the discount rate which would make theNPV over the project lifetime equal to zero.


NPV = −C +

n∑i=1

cf

(1 + IRR)i= 0 (1.3)

1.4 Goals of the thesis

The main focus of the thesis is a comparison of lithium-ion batteries, vana-dium redox batteries and the molten salt energy storage in large scale elec-trical energy storage applications. The first step for such comparison is costoptimum sizing of storage technologies for a specific application. In addition,to make this comparison possible, a bottom-up cost estimate was needed forthe molten salt storage and its electrical integration integration system. Thekey goals formulated for this thesis are summarised below:

• Formulate optimisation problem for optimum sizing of combined stor-age and PV plants.

• Develop a sizing methodology for electrical equipment used for themolten salt storage and PV plant integration.

• Obtain a bottom up cost estimation for a combined molten salt energystorage and PV plant.

• Compare competitiveness of vanadium redox batteries, lithium-ionbatteries and the molten salt energy storage.

• Identify the most competitive energy storage technologies for specificapplications.

• Evaluate whether large scale storage technologies can achieve desirablefinancial returns with current energy price levels.

1.5 Outline of the thesis

• Chapter 2 - explains the formulation of the mixed integer linear pro-gramming problem, which was used for sizing the required chargingpower, discharging power, energy rating and PV size for combinedstorage and PV plants.

• Chapter 3 - outlines the methodology used for sizing the electricalintegration equipment.

• Chapter 4 - overviews the bottom-up costing procedure of moltensalt energy storage system.


• Chapter 5 - presents the competitiveness analysis of molten salt stor-age, vanadium redox and lithium-ion batteries in three different busi-ness case studies.

• Chapter 6 - summarizes the results and suggests possibilities for fu-ture work.

Chapter 2

Mixed Integer LinearOptimisation

In this chapter a mixed integer linear optimisation model for sizing chargingpower, discharging power, energy rating of the storage device and size of thePV plant is presented. Two models with different objective functions wereformulated to increase the flexibility of sizing depending on the economicgoals of the project. One objective function tries to minimise the levelisedcost of electricity (LCOE) while the other tries to maximise the net presentvalue (NPV) of the project. LCOE and NPV were selected as objectivesbecause these are typical criteria used for comparing projects in the energysector.

2.1 Sizing for the minimum LCOE

The formulation for sizing the storage in order to achieve the minimumlevelised cost of electricity (LCOE) value is presented in this section. Theinitial investment and operational costs are considered in this formulation.In addition, the cost of electricity bought from the grid or produced bya diesel generator is also taken into account when calculating the LCOE.In this way, the optimum ratio between energy delivered from a combinedPV/storage plant and energy drawn from the grid or diesel generator can beachieved. The objective function and constraints are presented below withthe explanation of the variables and coefficients:

11

CHAPTER 2. MIXED INTEGER LINEAR OPTIMISATION 12

min : LCOE =

C +n∑

i=1

O(i) +∑8760

t=1 λg(t) · Pg(t) + λcap · Pmaxg

(1 + r)i

n∑i=1

∑8760t=1 L(t)

(1 + r)i

C = λpv · Ppv + λins · P ins + λouts · P out

s + λes · Es

s.t. PVgen(t)− PVcurt(t)− Pch(t) + Pdisch(t) + Pg(t) = L(t)

ηch · Pch(t)− Pdisch(t)

ηdisch+ SOC(t) = SOC(t+ 1)

SOC(1) = SOC(8760)PVgen(t) = Ppv · PV norm

gen (t)

SOC(t) ≥ 0PVgen(t) ≥ 0PVcurt(t) ≥ 0

Pch(t) ≥ 0Pdisch(t) ≥ 0SOC(t) ≤ Es

Pch(t) ≤ P ins

Pdisch(t) ≤ P outs

Pdisch(t) ≤ SOC(t)Pdisch(t) ≤ L(t)PVcurt(t) ≤ PVgen(t)∑nt=1 Pg(t) ≤ (1− ff) ·

∑nt=1 L(t)

Ppv ≥ 0P ins ≥ bmin

in

P outs ≥ bmin

out

Es ≥ 0(2.1)


C Investment cost (e).O Annual operation and maintenance cost (e).r Interest rate.

Ppv Installed PV power size (MW)P ins Installed storage charging power (MW).P outs Installed storage discharging power (MW).Es Installed storage energy size (MWh).

PVgen(t) Power generated by the PV plant (MW).PVcurt(t) PV power curtailed (MW).Pch(t) Power flowing into the storage (MW)Pdisch(t) Power flowing out of the storage (MW)SOC(t) State of charge (MWh)Pg(t) Power from the grid (MW).Pmaxg Maximum power from the grid (MW).

L(t) Load (MW).

PV normgen Normalised PV generation (MWh/MW).

ff Load fulfilment factor.

λg Electricity tariff (e/MWh)λcap Peak grid capacity charge (e/MW p.a.)λpv Cost of PV (e/MW)λins Cost of input storage power (e/MW)λouts Cost of output storage power (e/MW)λes Cost of storage energy (e/MWh)

ηch Storage charging efficiency.ηdisch Storage discharging efficiency.

t Time step in hours.i Year of the project.n Project lifetime.

bminin Minimum operating point of the charging cycle (MW).bminout Minimum operating point of the discharging cycle (MW).


2.2 Sizing for the maximum NPV

The formulation for sizing the storage in order to achieve the maximum netpresent value (NPV) is presented in this section. This kind of formulation ismore suitable when the storage is used for taking the advantage of differentelectricity prices throughout the day. The objective function and constraintsare presented below with the explanation of the variables and coefficients:

max : NPV = −C +

n∑i=1

∑8760t=1 λg(t) · Pg(t)−O(i)

(1 + r)i

C = λpv · Ppv + λins · P ins + λouts · P out

s + λes · Es

s.t. PVgen(t)− PVcurt(t)− Pch(t) + Pdisch(t) + Pg(t) = L(t)


ηdisch+ SOC(t) = SOC(t+ 1)

SOC(1) = SOC(8760)PVgen(t) = Ppv · PV norm

gen (t)

SOC(t) ≥ 0PVgen(t) ≥ 0PVcurt(t) ≥ 0

Pch(t) ≥ 0Pdisch(t) ≥ 0SOC(t) ≤ Es

Pch(t) ≤ P ins

Pdisch(t) ≤ P outs

Pdisch(t) ≤ SOC(t)Pdisch(t) ≤ L(t)PVcurt(t) ≤ PVgen(t)∑nt=1 Pg(t) ≤ (1− ff) ·

∑nt=1 L(t)

Ppv ≥ 0P ins ≥ bmin

in

P outs ≥ bmin

out

Es ≥ 0(2.2)


C Investment cost (e).O Annual operation and maintenance cost (e).R Annual revenue (e).r Interest rate.

Ppv Installed PV power size (MW)P ins Installed storage charging power (MW).P outs Installed storage discharging power (MW).Es Installed storage energy size (MWh).

PVgen(t) Power generated by the PV plant (MW).PVcurt(t) PV power curtailed (MW).Pch(t) Power flowing into the storage (MW)Pdisch(t) Power flowing out of the storage (MW)SOC(t) State of charge (MWh)Pg(t) Power from the grid (MW).L(t) Load (MW).

PV normgen Normalised PV generation (MWh/MW).

ff Load fulfilment factor.

λg Electricity tariff (e/MWh)λpv Cost of PV (e/MW)λins Cost of input storage power (e/MW)λouts Cost of output storage power (e/MW)λes Cost of storage energy (e/MWh)

ηch Storage charging efficiency.ηdisch Storage discharging efficiency.

t Time step in hours.i Year of the project.n Project lifetime.

bminin Minimum operating point of the charging cycle (MW).bminout Minimum operating point of the discharging cycle (MW).


2.3 Constraint explanations

In this section the most important constraints used in the optimisation for-mulation are explained in more detail.

2.3.1 Power balance

The constraint in equation 2.3 makes sure that the load is fully covered bythe PV plant, storage device and the grid at any given time. This balanceis schematically illustrated in figure 2.1.

PVgen(t)− PVcurt(t)− Pch(t) + Pdisch(t) + Pg(t) = L(t) (2.3)

PV plant

Storage

Grid

Load

Pg

L

PchPdisch

PVcurt

PVgen

Figure 2.1: Explanatory diagram for the power balance constraint.


2.3.2 Implementation of efficiencies

In order to formulate the linear optimisation problem the energy storagetechnologies were modelled with charging and discharging efficiencies as il-lustrated in equation 2.4.


ηdisch+ SOC(t) = SOC(t+ 1) (2.4)

2.3.3 Achieving desired fulfilment factor

Fulfilment factor is defined as a ratio between demand that is covered usingpower produced by the PV plant and power drawn from the grid. Theconstraint presented in equation 2.5 allows user to define a minimum desiredfulfilment factor.

8760∑t=1

Pg(t) ≤ (1− ff) ·8760∑t=1

L(t) (2.5)

2.3.4 PV production

The constraint in equation 2.6 was used to simulate the energy productionfrom a PV plant. The matrix PV norm

gen was obtained for each consideredlocation by a PV plant simulation program PVSyst. This matrix containsnormalised production from a PV plant for each hour in MWh/MW.

PVgen(t) = Ppv · PV normgen (t) (2.6)

2.4 Technology specific constraints

There are significant technical differences between storage technologies con-sidered. Thus, specific constraints had to be added for each technology.

2.4.1 Additional constraints for molten salt storage

Charging and discharging power ratings are decoupled in the molten saltenergy storage system. Thus, separate variables for charging and dischargingpower were used in the mixed integer linear optimisation. Because at anygiven time the storage can either charge or discharge, a constraint whichforces one of these variables to become zero was necessary. In order toachieve this constraints presented in equations 2.7 to 2.11 were introduced.This kind of formulation is based on the description in [16].

Pch(t)− ych(t) · ∞ ≤ 0 (2.7)


Pdisch(t)− ydisch(t) · ∞ ≤ 0 (2.8)

ych(t) + ydisch(t) ≤ 1∀t ∈ Z (2.9)

0 ≤ ych(t) ≤ 1,∀t ∈ Z (2.10)

0 ≤ ydisch(t) ≤ 1,∀t ∈ Z (2.11)

2.4.2 Additional constraints for vanadium redox batteries

One of the key differences between molten salt storage and vanadium redoxbatteries is that the power conversion system in vanadium redox batterieshave the same charging and discharging capacity. Thus, an additional con-straint presented in equation 2.12 was introduced for the vanadium redoxbattery sizing.

P ins = P out

s (2.12)

2.4.3 Additional constraints for lithium-ion batteries

Similarly to the case for vanadium redox batteries, the power conversionsystem for lithium-ion batteries have the same charging and dischargingcapacity. In addition, the power and the energy ratings of lithium-ion bat-teries are coupled to each other. Thus, a constraint which ensures a specifiedenergy to power ration was introduced as presented in equation 2.14.

Another difference for lithium-ion batteries is that the lifecycle of suchbatteries strongly depend on the depth of discharge under which batteriesare operated. Thus, an additional constraint presented in equation 2.15was introduced, which ensure that the battery is operated with a maximumdepth of discharge of 80%.

P ins = P out

s (2.13)

Es =E

P· P in

s (2.14)

SOC(t) ≥ 0.2 · Es (2.15)

Chapter 3

Electrical Equipment Sizing

The electrical equipment illustrated in figures 3.1 and 3.2 had to be sized inorder to obtain a bottom-up cost figure for the molten salt storage electricalintegration scheme. The main electrical components were sized: transform-ers, busbars and circuit breakers. This sizing was done by implementingmethodologies of electrical standards into an Excel based model with VisualBasic for Applications (VBA) macros.

3.1 Modes of operation

The electrical integration scheme for the molten salt storage system is sup-posed to operate at a number of different modes. Thus, the sizing had tobe done for all of them to ensure that the system can function in all modesof operation. After the sizing was done for all modes, the largest size forcomponents were chosen to fulfil the criteria under all modes of operation.The following key modes of operation were considered in sizing calculations:

• Mode 1 - charging using PV power. Components connected:synchronous motor, synchronous generator, electric heater, PV plant,auxiliary molten salt and water pumps.

• Mode 2 - starting charging using grid power. Components con-nected: synchronous motor, electric heater, auxiliary molten salt andwater pumps.

• Mode 3 - discharging. Components connected: steam turbine gen-erator, auxiliary molten salt and water pumps.

19

CHAPTER 3. ELECTRICAL EQUIPMENT SIZING 20

Grid

G

Steam turbine

Main transformer

PV

Motor drive

M

Electric heaterdrive

Electric heater

MSynchronous motor

Hot molten salt pump

M

Cold moltensalt pump

M

Feed water pump

Auxiliary transformer

G

Other aux. loads

Main circuit breaker

Synchronous generator

PV transformer

Electric heater transformer

Main bus

Figure 3.1: Electrical integration scheme for the molten salt storage withadvanced charging system.


Grid

G

Steam turbine

Main transformer

PV

Electric heaterdrive

Electric heater

M

Hot molten salt pump

M

Cold moltensalt pump

M

Feed water pump

Auxiliary transformer

Other aux. loads

Main circuit breaker

PV transformer

Electric heater transformer

Main bus

Figure 3.2: Electrical integration scheme for the molten salt storage withelectric heater charging system.


3.2 Determining loads and sources

Loads and sources inside the molten salt storage system needed to be de-termined in order to size the electrical equipment. Loads consist of the syn-chronous motor, the electric heater, various molten salt and water pumps.Sources include two synchronous generators used in the system. These loadsand sources were estimated by modifying thermodynamic model for themolten salt storage [4] and extracting the loads which fulfil desired sizes ofcharging power, discharging power and energy rating produced by the linearoptimisation discussed in chapter 2.

3.3 Load flow analysis

The primary purpose of the load flow analysis was sizing of the transformers.The load flow analysis was done in a simplistic manner. In each mode ofoperation power flows through the main transformer and main busbar wereestimated using the following formulas:

Smode1main =

∣∣∣Spv + Sgen − Smot − Seh − Schaux

∣∣∣ (3.1)

Smode2main =

∣∣∣−Smot − Seh − Schaux

∣∣∣ (3.2)

Smode3main =

∣∣∣Sst − Sdischaux

∣∣∣ (3.3)

Smode1main Main transformer loading during operation mode 1.Smode2main Main transformer loading during operation mode 2.Smode3main Main transformer loading during operation mode 3.Spv PV power.Sgen Synchronous generator power.Smot Synchronous motor power.Seh Electric heater power.Sst Steam turbine power.Schaux Charging auxiliaries power.Sdischaux Discharging auxiliaries power.

In addition, the effect of transformer consumption of reactive power hadto be taken into account as well. The equation 3.4 [17] was used to correctfor this consumption of reactive power.

Qconstrafo ≈ ukr ·

S2

Sn(3.4)


Qconstrafo Reactive power consumption by a transformer.

ukr Transformer short-circuit voltage in p.u..S Apparent power flowing through the transformer.Sn Nominal apparent power of the transformer.

Equivalent calculations were also done for sizing other transformers usedin the system.

3.4 Selecting transformers

Transformers usually come in standard sizes. Thus, transformer power rat-ings were selected based on the table illustrated in figure 3.3. After the loadflow calculation, the transformer with a power rating that is closest to thecalculated load was chosen.

3.5 Short circuit current calculations

In order to correctly size busbars and circuit breakers the short circuit cur-rent calculations have to be performed. These calculations were done usingIEC 60909 standard. According to the standard several steps have to be fol-lowed in order to estimate the short circuit currents. First, the short circuitimpedances are estimated. Then the impedances are referred to the trans-former side where the fault is present. After that, an equivalent Thevenincircuit at the fault point is obtained and standard formulas for short circuitcurrents are applied. During sizing procedure three-phase to ground andsingle-phase to ground short circuit currents were considered. The method-ology and formulas used for the short circuit currents are based on twosources: [18] and [19].

3.5.1 Voltage factor

The IEC 60909 standard uses a voltage factor c for calculating the maximumshort circuit currents. This factor allows accounting for voltage variationsin time and space, changing of transformer taps and subtransient behaviourof generators and motors. According to the IEC standard voltage factor of1.1 is used for calculating maximum short circuit currents in systems withvoltages of more than 1 kV [18].

3.5.2 Short circuit impedances

In this section the formulas used for estimating the short circuit impedancesof components used in the system are outlined.


Figure 3.3: Standard transformer sizes in kVA from IEEE Std.C57.12.00 [6].


Grid short circuit impedance

The following formulas were used for estimating grid short circuit impedance:

Zgrid =cV 2

n

Sgrid(3.5)

Xgrid =Zgrid√

1 + (Rgrid

Xgrid)2

(3.6)

Rgrid = Xgrid ·Rgrid

Xgrid(3.7)

Zgrid Grid short circuit impedance.Xgrid Grid short circuit reactance.Rgrid Grid short circuit resistance.Sgrid Grid short circuit power.Vn Rated grid voltage.c Voltage factor.

Transformer short circuit impedance

The following formulas were used for estimating transformer short circuitimpedances:

Ztrafo =ukr

100%× V 2

n

Strafo(3.8)

Rtrafo =uRr

100%× V 2

n

Strafo(3.9)

Xtrafo =√Z2trafo −R2

trafo (3.10)

Ztrafo Transformer short circuit impedance.Xtrafo Transformer short circuit reactance.Rtrafo Transformer short circuit resistance.Strafo Rated apparent power of the transformer.Vn Rated grid voltage.ukr Short-circuit voltage at rated current in per cent.uRr Rated resistive component of the short-circuit voltage in per cent.


Synchronous machine short circuit impedance

The following formulas were used for estimating short circuit impedances ofsynchronous motors and generators:

X′′d = x

′′d ×Kg ×

V 2g

Sg(3.11)

Kg =VnVg

c

1 + x′′d sin(φg)

(3.12)

Rg = X′′d ×

Rg

Xg(3.13)

X′′d Sub-transient reactance of the synchronous machine.

x′′d Relative subtransient reactance .Kg Correction factor.Vn Nominal voltage of the system.Vg Rated voltage of the synchronous machine.Sg Apparent power of the synchronous machine.φg Phase angle.c Voltage factor.Rg Short circuit resistance of the synchronous machine.

PV plant short circuit impedance

PV plant short circuit impedance was calculated using the same method asfor the grid. In this case the maximum short circuit power was set to be thesame as the PV plant nominal power. This assumption was taken becauseinverters used in the PV plants do not allow the flow of short circuit currentsfrom the DC side to the AC side. Thus, the maximum current that a PVplant can add to the short circuit faults is the current which is flowing at themaximum possible PV power. The formulas for estimating PV plant shortcircuit impedance are presented below:

Zpv =cV 2

pv

Spv(3.14)

Xpv =Zpv√

1 + (Rpv

Xpv)2

(3.15)

Rpv = Xpv ×Rpv

Xpv(3.16)


Zpv PV plant short circuit impedance.Xpv PV plant short circuit reactance.Rpv PV plant short circuit resistance.Spv PV plant power rating.Vpv Rated inverter output voltage.c Voltage factor.

Electric heater short circuit impedance

The following formulas were used for estimating electric heater short circuitimpedance:

Zeh =cV 2

eh

Seh(3.17)

Reh = Zeh × cos(φeh) (3.18)

Xeh =√Z2eh −R2

eh (3.19)

Zeh Electric heater impedance.Xeh Electric heater reactance.Reh Electric heater resistance.Seh Electric heater power rating.Veh Rated electric heater voltage.cos(φeh) Power factor of the electric heater.c Voltage factor.

3.5.3 Referring impedances

Because the electrical integration scheme involves transformers the impedanceshave to be referred to the transformer side on which the short circuit currentis estimated. The following formulas were used for that:

n =Vt2 × (1 + tp)

Vt1(3.20)

Zt1 =Zlv

n2(3.21)

Zt2 = Zhv × n2 (3.22)


n Transformer winding ratio.Vt2 Nominal secondary voltage of the transformer.Vt1 Nominal primary voltage of the transformer.tp Specified tap setting.Zt1 Impedance on the primary side of the transformer.Zt2 Impedance on the secondary side of the transformer.

3.5.4 Thevenin equivalent circuits

In order to calculate the short circuit current on the main bus the equivalentThevenin circuit for this fault have to be obtained as illustrated in figure3.4.

Short circuit calculations were performed for operation modes 1 and3. The operation mode 2 was not considered in short circuit calculations,because the operation mode 1 has all the same components connected tothe system with the addition of PV plant. Thus, the short circuit currentswould be more severe during operation mode 1 compared to operation mode2.

Vth

Zth

Shortcircuit

Figure 3.4: Thevenin circuit with equivalent impedance Zk.

Equivalent circuits for operation mode 1

The equivalent positive and zero sequence circuits of an electrical integrationsystem in the ”Charging from PV” mode can be seen in figures 3.5, 3.6 and3.7. The grid connection type (Wye or Delta) is subject of the local grid


codes. Thus, zero sequence connection of both types were implemented toincrease the flexibility of the calculations.

Vgrid(1)

Vexp(1)

Zmot(1)

Zgen(1)

Zgrid(1)

Ztrafo(1)

Vpv(1)

Zpv(1)

Zeh(1)

Zt_eh(1)

Zt_pv(1)

Zaux(1)

Zt_aux(1)

Figure 3.5: Positive sequence equivalent circuit for ”Charging from PV”mode of operation.

Zmot(0)

Zgen(0)

Zgrid(0)

Zt_main(0)

Zpv(0)

Zeh(0)

Zt_eh(0)

Zt_pv(0)

Zaux(0)

Zt_aux(0)

Figure 3.6: Zero sequence equivalent circuit for ”Charging from PV” modeof operation with Yy main transformer.


Zmot(0)

Zgen(0)

Zt_main(0)

Zpv(0)

Zeh(0)

Zt_eh(0)

Zt_pv(0)

Zaux(0)

Zt_aux(0)

Zgrid(0)

Figure 3.7: Zero sequence equivalent circuit for ”Charging from PV” modeof operation with Dy main transformer.

Equivalent circuits for operation mode 3

Similarly to the case for the operation mode 1, the equivalent single-phasecircuits of an electrical integration system in the ”Discharging” mode wereobtained as illustrated in figures 3.8, 3.9 and 3.10.

Vgrid(1)

Vst(1)

Zst(1)

Zgrid(1)

Ztrafo(1)

Zaux(1)

Zt_aux(1)

Figure 3.8: Positive sequence equivalent circuit for ”Discharging” mode ofoperation.


Zst(0)

Zgrid(0)

Zt_main(0)

Zaux(0)

Zt_aux(0)

Figure 3.9: Zero sequence equivalent circuit for ”Discharging” mode of op-eration with Yy main transformer.

Zst(0)

Zt_main(0)

Zaux(0)

Zt_aux(0)

Zgrid(0)

Figure 3.10: Zero sequence equivalent circuit for ”Discharging” mode of op-eration with Dy main transformer.


Thevenin impedance for the operation mode 1

In order to calculate the short circuit currents on the main bus the equiv-alent Thevenin impedances had to be calculated. It was assumed that theimpedances for positive and negative sequence are the same and that gridconnection can be Wye or Delta type. Equation 3.23 was used for estimat-ing the impedance of circuit presented in figure 3.5, equation 3.24 was usedfor estimating impedance of the circuit illustrated in figure 3.6 and equation3.25 was used for estimating impedance of the circuit illustrated in figure3.7.

Z1 = Z2 = (Zgrid(1) + Zt main(1)) ‖ Zgen(1) ‖ Zmot(1) ‖‖ (Zeh(1) + Zt eh(1)) ‖ (Zaux(1) + Zt aux(1)) ‖ (Zpv(1) + Zt pv(1))

(3.23)

ZY y0 = (Zgrid(0) + Zt main(0)) ‖ Zgen(0) ‖ Zmot(0) ‖‖ (Zeh(0) + Zt eh(0)) ‖ (Zaux(0) + Zt aux(0)) ‖ (Zpv(0) + Zt pv(0))

(3.24)

ZDy0 = Zt main(0) ‖ Zgen(0) ‖ Zmot(0) ‖‖ (Zeh(0) + Zt eh(0)) ‖ (Zaux(0) + Zt aux(0)) ‖ (Zpv(0) + Zt pv(0))

(3.25)

Thevenin impedance for the operation mode 3

Thevenin impedance calculations for the faults occurring on the main busbarwere also performed for the operation mode 3. Equation 3.26 was used forestimating the impedance of circuit presented in figure 3.8, equation 3.27was used for estimating impedance of the circuit illustrated in figure 3.9 andequation 3.28 was used for estimating impedance of the circuit illustrated infigure 3.10.

Z1 = Z2 = (Zgrid(1) + Zt main(1)) ‖ Zst(1) ‖ (Zaux(1) + Zt aux(1)) (3.26)

ZY y0 = (Zgrid(0) + Zt main(0)) ‖ Zst(0) ‖ (Zaux(0) + Zt aux(0)) (3.27)

ZDy0 = Zt main(0) ‖ Zst(0) ‖ (Zaux(0) + Zt aux(0)) (3.28)


3.5.5 Formulas for calculating short circuit currents

The final step of calculating short circuit impedances is applying the formu-las presented in this subsection. Three-phase to ground initial symmetricshort circuit current is calculated using formula:

I′′k =

cVn√3Z1

(3.29)

I′′k Initial symmetrical three-phase to ground short-circuit current.Vn Nominal voltage.Z1 Equivalent positive sequence Thevenin impedance.c Voltage factor.

One-phase to ground initial symmetric short circuit current is calculatedusing formula:

I′′k1 =

√3cVn

Z1 + Z2 + Z0(3.30)

I′′k1 Initial symmetrical one-phase to ground short-circuit current.Vn Nominal voltage.Z1 Equivalent positive sequence Thevenin impedance.Z2 Equivalent negative sequence Thevenin impedance.Z0 Equivalent zero sequence Thevenin impedance.c Voltage factor.

Once the initial short circuit currents are calculated, the peak shortcircuit currents can be estimated using formulas below:

ip = k√

2I′′k (3.31)

ip1 = k√

2I′′k1 (3.32)

k = 1.02 + 0.98e−3R/X (3.33)

ip Peak three-phase to ground short-circuit current.ip1 Peak one-phase to ground short-circuit current.

I′′k Initial symmetrical three-phase to ground short-circuit current.

I′′k1 Initial symmetrical one-phase to ground short-circuit current.k Constant factor.R/X Resistance and reactance ratio at the fault location.


3.6 Rated continuous current calculation

Rated continuous current is another important characteristic for estimatingthe cost of circuit breakers and busbars. The continuous operating currentwas calculated using equation 3.34. It was calculated for 90% of the voltagelevel, which would result in the highest operating currents. This was doneaccording to IEC standards, which define the allowable variation of voltageduring an operation of the electrical system. The allowable voltage variationis ± 10% for the medium voltage systems operating from 1 kV to 35 kVvoltage [20].

Iph =Sn√

3× 0.9Vn(3.34)

Iph Rated continuous current.Sn Power of the load connected.Vn Phase to phase bus voltage.

3.7 Calculation comparison with NEPLAN model

A model was created using NEPLAN software package in order to verify thatthe calculations presented in this chapter provide accuracy of an acceptablelevel. This model is presented in figure 3.11. The same inputs were usedwith the simplified Excel model and NEPLAN model and the comparisonof results for the molten salt storage systems with the advanced chargingsystem is presented in this section.

3.7.1 Voltage levels

For the comparison 66 kV grid voltage was assumed. The bus voltage wasset to 20 kV, the electric heater input voltage was set to 0.69 kV and theauxiliary load supply voltage was set to 0.6 kV.

3.7.2 Electrical component characteristics

The electrical component characteristics used to compare the developed Ex-cel model and the NEPLAN model are summarized in the Appendix A.

3.7.3 Load flow calculation comparison

As it can be seen in the table 3.1 the simplified load flow calculations pro-vide similar results to the NEPLAN model. Newton-Raphson method wasselected when performing the load flow calculation in NEPLAN. This con-firms that the simplified method for load flow calculations is valid.


Figure 3.11: Molten salt storage electrical integration system model inNEPLAN. Components connected to the main busbar from left to right:steam turbine generator, synchronous generator, synchronous motor, elec-tric heater, auxiliary loads, PV plant.

Table 3.1: Load flow calculation for sizing main transformer comparisonwith NEPLAN

Mode of operation Strafomain Excel Strafo

main NEPLAN Difference

(-) (MVA) (MVA) (%)

1 28.13 27.43 2.55

2 56.60 56.59 0.02

3 25.45 25.41 0.16


3.7.4 Short circuit current calculation comparison

In this sub-section the short circuit calculation comparison between Exceland NEPLAN models are presented. Three-phase to ground and single-phase to ground faults were considered.

Three-phase to ground short circuit calculation comparison

As it can be seen in tables 3.2, 3.3 and 3.4 the initial symmetrical shortcircuit values for the main components were really close. The differencebetween calculations were within 5%.

Table 3.2: Three-phase to ground short circuit current calculation compar-ison with NEPLAN for the main circuit breaker

Mode of oper. I′′k Excel I

′′k NEPLAN Diff. ip Excel ip NEPLAN Diff.

(-) (kA) (kA) (%) (kA) (kA) (%)

1 2.197 2.206 0.41 5.766 5.514 4.57

3 1.100 1.104 0.36 2.859 2.742 4.27

Table 3.3: Three-phase to ground short circuit current calculation compar-ison with NEPLAN for the main busbar



(-) (kA) (kA) (%) (kA) (kA) (%)

1 23.294 23.341 0.20 60.234 60.374 0.23

3 15.421 15.556 0.87 40.276 40.618 0.84

Table 3.4: Three-phase to ground short circuit current calculation compar-ison with NEPLAN synchronous machines and PV plant.

Type of breaker I′′k Excel I


(-) (kA) (kA) (%) (kA) (kA) (%)

Steam turbine 4.589 4.589 0 11.775 11.981 1.72

Synchronous motor 8.255 8.255 0 21.182 21.352 0.80

Synchronous generator 2.206 2.205 0.05 5.659 5.704 0.79

PV 2.003 1.916 4.54 4.917 4.955 0.77


Single-phase to ground short circuit calculation comparison

An equivalent comparison for single-phase to ground fault calculations arepresented in tables 3.5, 3.6 and 3.7. As it can be seen there were higherdifferences for short-circuit values compared to three-phase short circuit cal-culations, with one instance of 17% deviation. This can be explained bythe fact that single-phase to ground faults are unsymmetrical compared tothree-phase to ground which are symmetrical. Thus, the simplifications as-sumed resulted in higher errors, but as discussed in chapter 4 the accuracyis still acceptable for the cost estimation of electrical equipment.

Table 3.5: Single-phase to ground short circuit current calculation compar-ison with Neplan for the main circuit breaker.


′′k Neplan Diff. ip Excel ip Neplan Diff.

(-) (kA) (kA) (%) (kA) (kA) (%)

1 2.637 2.837 7.05 6.922 7.091 2.38

3 1.277 1.542 17.19 3.322 3.830 13.26

Table 3.6: Single-phase to ground short circuit current calculation compar-ison with Neplan for the main busbar.



(-) (kA) (kA) (%) (kA) (kA) (%)

1 24.967 24.942 0.08 64.560 64.515 0.07

3 14.868 14.942 0.50 38.830 39.015 0.47

Table 3.7: Single-phase to ground short circuit current calculation compar-ison with Neplan synchronous machines and PV plant.

Type of breaker I′′k Excel I


(-) (kA) (kA) (%) (kA) (kA) (%)

Steam turbine 5.453 6.066 10.11 13.991 15.838 11.66

Synchronous motor 10.222 11.446 10.69 26.230 29.606 11.40

Synchronous generator 2.288 2.282 0.26 5.870 5.903 0.56

PV 2.001 1.921 4.16 4.937 4.970 0.66

Chapter 4

Costing

Molten salt storage integration with a source of electricity for obtaining highgrade heat is not a well researched area. As a result, cost estimates cannot beeasily obtained as in the case for lithium-ion or vanadium redox flow batter-ies. Thus, a bottom-up costing of molten salt storage system had to be done.As illustrated in figure 4.1 this required several steps to be performed. Inthe first step an existing thermodynamic model for molten salt storage wasused to obtain electrical load list consisting of motors, pumps and electri-cal heaters and non-electrical equipment sizes like heat exchangers, storagetanks, required molten salt mass, etc. The electrical load list was then usedto size transformers and circuit breaker used in the integration system of themolten salt storage. This was done using methodology described in chapter3. After that, the electrical and non-electrical equipment was costed usingcost models.

4.1 Cost models

An example of a cost model is presented in figure 4.2. As it can be seenthe cost figures are not present on the graph. This is because the majorityof the cost data used in estimating the total cost of the molten salt storagesystem was based on confidential supplier data, which cannot be disclosed.

4.1.1 Circuit breaker cost model

In this section the methodology for obtaining cost models is outlined byusing and example for a circuit breaker cost model, which was based on apublicly available data.

The data illustrated in figure 4.3 was taken to derive a cost model for thecircuit breakers. It can be seen that two major cost drivers for circuit breakercost are the continuous current rating and short circuit current rating. Itcan be observed that the RMS and peak short circuit currents follow the

38

CHAPTER 4. COSTING 39

Storage chargingpower rating (MW)

Storage dischargingpower rating (MW)

Storage energyrating (MWh)

Thermodynamic molten salt storage model

Non-electrical component sizes

Electrical sizing & overall costing tool

Eq

uip

me

nt

cost

fu

nctio

ns

Ele

ctri

cal e

qu

ipm

en

t sp

ecs

Electrical load list

Charging power cost (Euro/MW)

Discharging powercost (Euro/MW)

Storage energycost (Euro/MWh)

Electrical integration cost (Euro)

Figure 4.1: Molten salt storage costing procedure. First a thermodynamicmodel is used to obtain electrical load list and sizing for non-electrical equip-ment. After that, electrical equipment is sized and overall cost numbers forthe molten salt storage are obtained.

Figure 4.2: Example of transformer cost approximation with a linear costmodel.


same pattern. Thus, only the RMS value was used to derive the cost modelin order to avoid multicollinearity, which can be caused by highly correlatedindependent variables [21].

Figure 4.3: Circuit breaker cost data [7].

The cost model obtained by performing the regression analysis with thedata from figure 4.3 is presented in equation 4.1. The circuit breaker costmodel had a coefficient of determination R2 = 0.9539. This indicates thatthe linear approximation of the change in cost is valid and that the selectedcost drivers suitably approximate the change in cost of the circuit breakers.

CCB = 18262.26 + 2329.88× Icont + 207.08× I ′′k (4.1)

CCB Circuit breaker cost (e)Icont Continuous operating current (kA)

I′′k Initial symmetrical short circuit current (kA).

4.1.2 Circuit breaker cost model sensitivity

In this section the sensitivity of the circuit breaker cost model to the changesof the short circuit current rating and the continuous current rating areinvestigated. This was done to see if the inaccuracies present in the shortcircuit calculations can be tolerated.

As illustrated in figures 4.4 and 4.5 the circuit breaker cost model ismore sensitive to the changes in continuous current rating compared to thechanges in the short circuit current rating. It can be seen from the figure4.4 that 10% change in short circuit current rating results in less than 2%change in the cost of a circuit breaker. Thus, it can be concluded that theinaccuracies seen in chapter 3 are acceptable.


Figure 4.4: Circuit breaker cost model sensititivity to the changes of shortcircuit current rating.

Figure 4.5: Circuit breaker cost model sensitivity to the changes of contin-uous current rating.


4.2 Costing non-electrical equipment

Electrical equipment makes only a small part of molten salt storage system.In order to obtain a bottom-up cost estimate of the overall solution a ther-modynamic molten salt energy storage model was used and the equipmentwas costed using confidential data from [4].

4.3 Molten salt storage cost breakdown

The cost breakdown for the molten salt storage system is described in thissection. The cost breakdown for the molten salt energy storage system withadvanced charging system is presented in figure 4.6 and the cost breadownfor the molten salt energy storage with electric heater charging system ispresented in figure 4.7. It can be seen that electrical part of the cost is fairlysmall. It is 3% when advanced charging system is used and around 6% whenthe electric heater based charging system is used. These are typical percent-ages that depend on the storage parameters. The variations depending onthe storage parameters are illustrated in Appendix B. Electric heater con-figuration has more significant electrical cost share because additional largetransformer is needed for connecting electrical heaters to the main busbar.This is because electrical heaters are supplied using low voltage levels.

It also can be noticed that the largest share of the cost is dedicated forthe discharging cycle, which include all costs related to building a steam cy-cle for recovering the energy from the molten salt tanks. In addition, figures4.6 and 4.7 show that the advanced molten salt charging cycle takes up alot more share of the cost compared to electric heater charging cycle. Thiscan be explained by the fact that the advanced cycle requires a lot moreequipment and the technology is not as mature as the electric heater tech-nology. Finally, the suitability of molten salt storage system in applicationswere large quantities of energy have to be stored with relatively low powerrating requirement is demonstrated by the low share of energy capital cost(8% - 9%).


Figure 4.6: Cost breakdown of molten salt storage with the advanced charg-ing system.

Figure 4.7: Cost breakdown of molten salt storage with the electric heatercharging system.

Chapter 5

Case Studies

In this chapter three business case studies are presented to compare thecompetitiveness of the molten salt energy storage, lithium-ion batteries andvanadium redox batteries. The first business case investigates the industrialpeak shaving case where a large scale storage device is used for reducingthe peak consumption of an industrial customer. In the second businesscase, a diesel replacement with a combined PV and storage plant in a min-ing application is considered. Finally, the third business case investigatespower dispatch shifting to high electricity price hours by a combined PVand storage plant.

5.1 Case 1: industrial peak shaving

Electricity bill for a large industrial customer often consists of two parts: onethat is paid for the energy used and the second one paid for the maximumpower drawn from the grid during a month. In addition, such customersoften have different electricity prices for high and low demand hours. Thus,such customer could potentially save money by reducing the peak powerdrawn from the grid and using more of its electricity during low priorityhours.

5.1.1 Industrial demand profile

The demand profile for an industrial customer was taken from [8]. It is ademand profile of a factory manufacturing parts for the automotive industry.This profile was given without dimensions, but with per unit values. In orderto obtain the profile seen in figure 5.1 it was scaled by multiplying per unitvalues by 10 MW.

44

CHAPTER 5. CASE STUDIES 45

Figure 5.1: Industrial load profile [8].

5.1.2 Electricity tariffs for case 1

Electricity tariff information in four different countries were collected inorder to perform the business case analysis. Electrical energy tariff duringpeak and off-peak hours as well as the capacity charge for the peak powerdrawn from the grid were found. This information is summarised in table5.1.

Important point to make is that electricity tariffs in California have dif-ferentiation between summer and winter periods, but for the sake of simplic-ity the average between these two were taken. In addition, the electricitytariffs for Australia only reflect the grid charges without the generation costs.Thus, only the ratio of peak and off-peak tariffs are representative, but notthe absolute numbers.

Table 5.1: Capacity charges and peak to off-peak electricity price ratios. Inthe table: λcap - capacity charge for the peak power drawn from the gridover a month, λog - off-peak electricity tariff, λpg - peak electricity tariff.

Location λcap λog λpg Source

(e/kW per month) (e/kWh) (e/kWh) (-)

California, US 21.92 0.067 0.112 [22]

Japan 11.90 0.114 0.305 [4]

Maharashtra, India 4.2 0.040 0.055 [23]

Australia 1.35 0.019 0.009 [24]


5.1.3 Sizing for case 1

The sizing was done according to LCOE minimising optimisation formula-tion presented in chapter 2. The following assumptions were taken for sizingstorage devices:

• Industrial load profile from figure 5.1.

• Peak shaving the demand to maximum of 21 MW.

• Off-peak electrcity price of 0.05 e/kWh and peak electricity price of0.1 e/kWh with peak electrcity hours between 8h and 20h.

• Capacity charge of 20 e/kW per month.

• 25 year project lifetime.

• 8% interest rate.

The sizing using these assumptions for different batteries is presented intable 5.2.

Table 5.2: Resulting sizing for the industrial peak shaving business case.

Storage type P ins P out

s Es

(-) (MW) (MW) (MWh)

Lithium-ion 121.50 121.50 121.50

VRB 20.80 20.80 107.38

Molten salt storage EH 21.00 20.80 270.16

Molten salt storage AD 21.00 20.80 270.84

5.1.4 Dispatch profiles for case 1

The corresponding dispatch profiles for sized batteries are presented in fig-ures 5.2, 5.3, 5.4 and 5.5. It can be seen that systems with the molten saltenergy storage needs to draw much more energy during the off-peak hoursto fulfil the peak demand compared to lithium-ion and vanadium redox bat-teries. This can be explained by the fact that the molten salt energy storagehas lower efficiency compared to lithium-ion and vanadium redox batteries.


Figure 5.2: Molten salt storage EH dispatch profile for the industrial peakshaving application.

Figure 5.3: Molten salt storage AD dispatch profile for the industrial peakshaving application.


Figure 5.4: VRB dispatch profile for the industrial peak shaving application.

Figure 5.5: Lithium-ion battery dispatch profile for the industrial peak shav-ing application.


5.1.5 IRR graph comparison for case 1

In order to compare the competitiveness of different storage solutions iso-IRR curves were drawn with peak/off-peak electricity price ratio on thex-axis and capacity charge on the y-axis. The purpose of such graphs is toidentify conditions, which would be needed in order to achieve the desiredreturns from the investment into storage. 15% IRR was assumed to be thetarget for desired financial returns as it is a typical financial target used inthe industry.

The following formulas were used for calculating the annual revenue ofthe storage device investment in order to estimate the IRR:

cf = Electricity bill without storage− Electricity bill with storage−O&M(5.1)

cf = λcap · (Pmaxl − Pmax

g ) · 12 +8760∑t=1

λg(t) · (Pl(t)− Pg(t))−O&M (5.2)

cf Annual cash flow (e).Pmaxl Maximum power of the load profile (kW).Pmaxg Maximum power drawn from the grid with storage (kW).

Pl Load power (kW).Pg Power drawn from the grid (kW).λg Electricity tariff (e/kWh)λcap Peak grid capacity charge (e/kW per month)O&M Annual operation and maintenance costs (e).t Time step in hours.

The resulting IRR graphs are presented in figures 5.6 and 5.7. Two off-peak electricity price levels (0.05 e/kWh and 0.1 e/kWh) were consideredto investigate of changing electricity price levels.

5.1.6 Conclusions for case 1

The following conclusions were drawn from this business case analysis:

• No storage technology could achieve the desired financial return withelectricity price levels observed in the countries considered.

• The lithium-ion batteries performed the worst economically.

• The vanadium redox batteries performed the best economically.

• More efficient storage technologies become more competitive with in-creasing electricity price levels.


Figure 5.6: 15% IRR curves with 0.05 e/kWh off-peak price for the indus-trial peak shaving application. Locations indicated by dots: 1 - California,US, 2- Japan, 3 - Maharashtra, India, 4 - Australia.

Figure 5.7: 15% IRR curves with 0.1 e/kWh off-peak price for the industrialpeak shaving application. Locations indicated by dots: 1 - California, US,2- Japan, 3 - Maharashtra, India, 4 - Australia.


5.2 Case 2: diesel replacement in a mine

This business case aims to replace the diesel based generation used in remotelocations. A typical example of a consumer that could be interested inreplacing large amounts of diesel are mining sites, which are often locatedin off-grid locations. The replacement of diesel can be done by combiningPV power plant with large scale energy storage technologies as consideredin this business case.

5.2.1 Gold mine demand profile

The demand profile shape for a mine was taken from [9]. Because the focusof the thesis is large scale electrical storage, the profile presented in [9] wasdoubled in magnitude to better represent the storage size range consideredin the thesis. The resulting profile is illustrated in figure 5.8.

Figure 5.8: Gold mine load profile [9].

5.2.2 Electricity cost produced by diesel generators

In order to do the sizing of the combined PV and storage plant a cost ofelectricity produced by diesel generators was needed as an input to the sizingoptimisation. Thus, literature was reviewed and three sources indicatinglevelised cost of electricity produced by diesel generators were found. Theinformation found is summarised in table 5.3. As it can be seen from thedata collected there is an uncertainty regarding the electricity cost producedby diesel generators. Thus, an average of these numbers were taken and


diesel generation lifecycle cost of 0.35 e/kWh was used in this business caseanalysis.

Table 5.3: Levelised cost of electricity produced by diesel generators.

Cost in original currency Cost in e Source

0.539 $/kWh 0.493 e/kWh [25]

0.297-0.332 $/kWh 0.271-0.303 e/kWh [26]

0.4975 AUD/kWh 0.338 e/kWh [27]

5.2.3 Locations

In order to investigate the effect of different solar irradiation, four differ-ent locations were considered. Location with respective global horizontalirradiation (GHI) levels are summarised in table 5.4.

Table 5.4: Locations considered for the business case 2.

Location GHI, kWh/m2 p.a. PV technology

Upington, South Africa 2275 1-axis polycrystalline

Jodhpur, India 2051 1-axis polycrystalline

Yass, Australia 1851 1-axis polycrystalline

Taubate, Brazil 1442 fixed-axis polycrystalline


The sizing was done according to LCOE minimising optimisation formula-tion presented in chapter 2. The following assumptions were taken for sizingstorage devices:

• Gold mine load profile from figure 5.8.

• Levelised cost of electricity produced by diesel generators: 0.35 e/kWh.

• Fulfilment factor of 70%.



The sizing using these assumptions is presented in Appendix C. Becausethe sizing was done for a specific fulfilment factor, the sizing trends for differ-ent fulfilment factors were also investigated. This information is important


because it can suggest which parts of the system usually stay similar sizeand which change a lot. This can help standardizing certain parts of thesystem to drive the costs down. The sizing dependency on the fulfilmentfactor are presented in Appendix D.


Dispatch profiles for the first 10 days in Yass, Australia are presented in fig-ures 5.9, 5.10, 5.11 and 5.12. It can be noticed that there is significantly morePV curtailment for vanadium redox and lithium-ion batteries compared tothe molten salt storage technology. This can be explained by the fact thatthe energy capital cost is expensive for vanadium redox and lithium-ion bat-teries compared to the molten salt storage. Thus, it is more optimal tohave largely oversized PV plant in order to achieve desired fulfilment factorinstead of further expanding energy storing capacity for vanadium redox orlithium-ion batteries.

Figure 5.9: Molten salt EH dispatch for first 10 days in Yass, Australia forthe diesel replacement application.


Figure 5.10: Molten salt AD dispatch for first 10 days in Yass, Australia forthe diesel replacement application.

Figure 5.11: VRB dispatch for first 10 days in Yass, Australia for the dieselreplacement application.


Figure 5.12: Lithium-ion battery dispatch for first 10 days in Yass, Australiafor the diesel replacement application.

5.2.6 LCOE comparison for case 2

The levelised cost of electricity for the optimum storage and PV configura-tions is presented in figure 5.13. It can be seen that only the molten saltstorage (EH and AD) and VRB can bring significant improvement to theLCOE.

5.2.7 IRR comparison for case 2

The following formulas were used for calculating the annual revenue of thestorage device investment in order to estimate the IRR:

cf =Cost of supplying load with diesel generators only−− Cost of supplying the load with PV/storage plant−O&M

(5.3)

cf =

8760∑t=1

λg · (Pl(t)− Pg(t))−O&M (5.4)

The IRR graph which shows how IRR changes with changing GHI forall storage technologies considered is illustrated in figure 5.14.


Figure 5.13: LCOE for optimum storage and PV configurations for the minebusiness case.

Figure 5.14: IRR for optimum storage and PV configurations for the minebusiness case.



The following conclusions can be drawn for the mine business case:

• Molten salt storage is the most competitive technology for the dieselreplacement and can bring desired financial returns in locations withGHI of at least ∼1440 kWh/m2.

• VRB can bring desired financial returns in locations with GHI of atleast ∼1700 kWh/m2.

• Lithium-ion batteries can bring desired financial returns in locationswith GHI of at least ∼1900 kWh/m2.

• Lithium-ion batteries do not bring additional financial benefit com-pared to stand-alone PV plant if there is no requirement for the min-imum fulfilment factor.

5.3 Case 3: electrical energy time shift

In this business case a combined storage and PV plant owner tries to max-imise the profits under varying electricity price profile. The idea is to chargethe storage using excess PV power during the day and discharge it duringhigh priority hours when the power from the PV plant is not available anymore.

5.3.1 Input price profile for case 3

The electricity price profile illustrated in figure 5.15 was as an input to thesizing process according to maximum NPV.

5.3.2 Electricity tariffs for case 3

Electricity tariffs used for the comparison are listed in table 5.5.

Table 5.5: Peak and off-peak electricity tariffs considered in business case 3.In the table: λog - off-peak electricity tariff, λpg - peak electricity tariff.

Location λog λpg Source

(e/kWh) (e/kWh) (-)

California, US 0.067 0.112 [22]

Japan 0.114 0.305 [4]

Maharashtra, India 0.040 0.055 [23]

Zimbabwe 0.108 0.108 [4]


Figure 5.15: Input electricity price profile for the business case 3.


The sizing was done according to NPV maximising optimisation formulationpresented in chapter 2. The sizing of the storage devices are summarised inAppendix E. These results were obtained using the following assumptions:

• Electricity price profile from figure 5.15.

• Fulfilment factor of at least 60%.




Example disptach profiles are presented in figure 5.16, 5.17, 5.18 and 5.19.Similarly to the business case 2, large amounts of PV energy are curtailedduring the days with a lot of solar irradiation when lithium-ion or vanadiumredox batteries are used. In addition, it can be seen that the molten saltenergy storage system dispatches the energy during the whole day with alower power output compared to lithium-ion and vanadium redox batteries.This can be explained by the fact that the most expansive part of the moltensalt energy storage is the discharging cycle while energy capacity is relativelycheap. In comparison, lithium-ion and vanadium redox batteries have highercosts for the energy capacity relative to costs for the power capacity.


Figure 5.16: First 10 days of dispatch for molten salt EH in South Africafor the business case 3.

Figure 5.17: First 10 days of dispatch for molten salt AD in South Africafor the business case 3.


Figure 5.18: First 10 days of dispatch for VRB in South Africa for thebusiness case 3.

Figure 5.19: First 10 days of dispatch for lithium-ion batteries in SouthAfrica for the business case 3.


5.3.5 IRR comparison for case 3

Similarly to the first business case, iso-IRR curves were drawn to investigatewhat conditions would be needed for the investments in storage to be worth-while. In addition, because the production from a PV plant depends highlyon the location, high and low GHI countries were considered for the analysis.The graphs used for determining the competitiveness of the business case 3are presented in figures 5.20 and 5.21.

The following formulas were used for calculating the annual revenue ofthe storage device investment in order to estimate the internal rate of return:

cf = Revenue from selling electricity−O&M (5.5)

cf =

8760∑t=1

λg(t) · (L(t)− Pg(t))−O&M (5.6)

Figure 5.20: Business case 3 15% IRR curves for high GHI area (2275kWh/m2). Locations indicated by dots: 1 - California, US, 2 - Japan, 3- Maharashtra, India, 4 - Zimbabwe.


Figure 5.21: Business case 3 15% IRR curves for low GHI area (1442kWh/m2). Locations indicated by dots: 1 - California, US, 2 - Japan, 3- Maharashtra, India, 4 - Zimbabwe.


The following conclusions can be drawn for the third business case:

1. Molten salt thermal storage is the most competitive in the businesscase where the energy needs to be shifted to the evening with the highpriority hours.

2. The 15% IRR target is not likely to be reached in most countries. Ahigh GHI like in South Africa and high electricity prices like in Japanare needed at the same time.

Chapter 6

Discussion and Conclusion

6.1 Conclusions

A mixed integer linear programming optimisation formulations for minimis-ing LCOE and maximising NPV were presented in the thesis. This opti-misation was successfully used to obtain sizing of stand alone storage orcombined storage and PV plants with yearly input data.

In addition, electrical sizing methodology for the molten salt storagesystem integration system was combined with an existing thermodynamicmodel. The load flow calculations were performed with simple addition ofapparent power of loads and sources and the short circuit calculations weredone following methodology of the IEC 60909 standard. The validity of theelectrical sizing calculations was verified with the NEPLAN model.

Moreover, the bottom-up costing was done for the molten salt storagesystem. It was shown that electrical integration part takes up a relativelysmall part of the total cost. For the electric heater molten salt storage variantthe electrical integration scheme accounted for 6% of the total cost. Incomparison, the advanced molten salt storage electrical integration schemeaccounted for about 3% of the total cost. The difference between these twosystems can be explained by the fact that an additional large transformeris needed for connecting the electrical heaters to the main bus and that thetotal cost of the advanced molten salt storage system is higher compared tothe electrical heater molten salt storage system. In addition, the bottom-up costing revealed that the discharging steam cycle contributes the largestshare of the cost for molten salt storage system.

Obtained cost numbers for the molten salt storage were used to comparecompetitiveness of the large scale electrical energy storage technologies inthree different business cases. It was shown that at current electricity pricelevels the investment in the peak-shaving business case does not bring desiredfinancial returns (15% IRR). Moreover, it was shown that the most suitabletechnology for peak shaving applications would be VRB, while lithium-ion

63

CHAPTER 6. DISCUSSION AND CONCLUSION 64

batteries performed the worst. The diesel replacement business case wasalso analysed. The molten salt energy storage was identified as the mostcompetitive technology and it was shown that this technology can bringdesired financial returns in locations with GHI over ∼1440 kWh/m2. Incomparison, VRB brought desired financial returns in locations with GHIover ∼1700 kWh/m2 while lithium-ion batteries achieved this in locationswith GHI over ∼1900 kWh/m2. The final business case considered waselectrical energy time shift. The aim in this business case was maximisationof NPV under an electricity price tariff with differentiation between peak andoff-peak hours. Analysis of the last business case showed that the molten saltenergy storage is the most competitive technology for this application. Inaddition, it was demonstrated that with current price levels the investment incombined PV and storage plant is unlikely to bring desired financial returns.Very large spread between peak and off-peak electricity prices and high GHIlocation are needed at the same time.

6.2 Future work

There are several ways how the thesis could be extended. The possibilitiesfor future work are listed below:

• Consider technology learning for the future storage technology costreduction.

• Consider the incentive schemes for storage and renewable energy tech-nologies and investigate how they affect the profitability of large scaleelectrical storage projects.

• Extend business cases for ancillary service applications that large scaleelectrical energy storage can provide.

• Introduce a detailed model for operation and maintenance costs fordifferent storage technologies.

• Consider the costs for disposing and recycling the batteries after theend of their lifetime.

Appendix A

Electrical componentcharacteristics

Table A.1: Grid characteristics [4].

Sgrid 1000 MVA

Rgrid/Xgrid 0.1

Zgrid(0)/Zgrid(1) 4.3

Table A.2: PV plant characteristics [4].

Ppv 70 MW

Rpv/Xpv 0.1

Zpv(0)/Zpv(1) 1

65

APPENDIX A. ELECTRICAL COMPONENT CHARACTERISTICS 66

Table A.3: Transformer characteristics [4].

Type Strafo ukr(1) uRr(1) ukr(0) uRr(0)

(-) (MVA) (%) (%) (%) (%)

Main transformer Yd 60 11 0.24 8.8 0.19

Auxiliary transformer Dy 1.5 5.7 0.75 4.56 0.6

PV transformer Yd 70 6 1.1 4.8 0.88

Table A.4: Synchronous machine characteristics [4].

P xd′′(1) xd

′′(0) Rg/Xg cos(φg)

(MW) (%) (%) (-) (-)

Synchronous motor 61.79 19.4 8.2 0.07 1

Synchronous generator 12.86 21.3 19 0.07 0.8

Steam turbine generator 22.38 18.1 9.5 0.07 0.85

Appendix B

Electrical cost sharevariation

Figure B.1: Electrical integration cost share dependency on the storagesizing for the molten salt storage with advanced charging. Pch - chargingpower rating, Pdisch - discharging power rating, E - energy rating.

67

APPENDIX B. ELECTRICAL COST SHARE VARIATION 68

Figure B.2: Electrical integration cost share dependency on the storage siz-ing for the molten salt storage with electric heating charging. Pch - chargingpower rating, Pdisch - discharging power rating, E - energy rating.

Appendix C

Sizing for Case 2

Figure C.1: Sizing of molten salt EH strorage for the case 2.

69

APPENDIX C. SIZING FOR CASE 2 70

Figure C.2: Sizing of molten salt AD strorage for the case 2.

Figure C.3: Sizing of VRB for the case 2.

Figure C.4: Sizing of lithium-ion batteries for the case 2.

APPENDIX C. SIZING FOR CASE 2 71

Figure C.5: PV sizing for the case 2.

Figure C.6: Energy rating sizing for the case 2.

Appendix D

Sizing Dependency on theFF for Case 2

Figure D.1: Ratio of installed PV power and discharging power rating vs.fulfilment factor for the electric heater molten salt storage configuration.

72

APPENDIX D. SIZING DEPENDENCY ON THE FF FOR CASE 2 73

Figure D.2: Ratio of installed charging and discharging power rating vs.fulfilment factor for the electric heater molten salt storage configuration.

Figure D.3: Energy rating vs. fulfilment factor for the electric heater moltensalt storage configuration.


Figure D.4: Ratio of installed PV power and discharging power rating vs.fulfilment factor for the advanced molten salt storage configuration.

Figure D.5: Ratio of installed charging and discharging power rating vs.fulfilment factor for the advanced molten salt storage configuration.


Figure D.6: Energy rating vs. fulfilment factor for the advanced molten saltstorage configuration.

Appendix E

Sizing for Case 3

Figure E.1: Molten salt storage EH sizing for the business case 3.

Figure E.2: Moten salt storage AD sizing for the business case 3.

76

APPENDIX E. SIZING FOR CASE 3 77

Figure E.3: VRB sizing for the business case 3.

Figure E.4: Lithium-ion sizing for the business case 3.

Figure E.5: Energy capacity sizing for the business case 3.

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