Modeling and Control of Distributed Generation based Micro-grids for

Power Quality Studies

BY

AHSAN SHAHIDB.S., University of Engineering and Technology, Lahore, 2012

THESIS

Submitted as partial fulfillment of the requirementsfor the degree of Master of Science in Electrical and Computer Engineering

in the Graduate College of theUniversity of Illinois at Chicago, 2014

Chicago, Illinois

Defense Committee:

Vahe Caliskan, AdvisorMilos Zefran, ChairWenjing Rao

Copyright by

AHSAN SHAHID

2014

TABLE OF CONTENTS

CHAPTER PAGE

1 INTRODUCTION TO DISTRIBUTED GENERATION . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Distributed Generation Technologies . . . . . . . . . . . . . . . . 21.3 Distributed Generation Components . . . . . . . . . . . . . . . . 31.4 Need for Distributed Generation . . . . . . . . . . . . . . . . . . 4

1.4.1 Electricity Market Reforms . . . . . . . . . . . . . . 51.4.2 Eco-friendly Concerns . . . . . . . . . . . . . . . . . . 7

1.5 Micro-grid Explained . . . . . . . . . . . . . . . . . . . . . . . . . 91.5.1 Architecture of a Micro-grid . . . . . . . . . . . . . . 101.5.2 Advantages . . . . . . . . . . . . . . . . . . . . . . . . 121.5.3 Ongoing Research in Micro-grids . . . . . . . . . . . 13

2 PROBLEMS WITH DG AND MICRO-GRIDS . . . . . . . . . . . . 142.1 Voltage Regulation and Losses . . . . . . . . . . . . . . . . . . . 142.2 Voltage Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Islanding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4 Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Transmission Pricing Issues . . . . . . . . . . . . . . . . . . . . . 222.6 Integration with the Grid . . . . . . . . . . . . . . . . . . . . . . 22

3 PROPOSED MODELING AND CONTROL . . . . . . . . . . . . . 233.1 Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 Source . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1.2 Grid Circuit Breaker . . . . . . . . . . . . . . . . . . 26

3.2 Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.1 Power Transformer . . . . . . . . . . . . . . . . . . . 283.2.2 Transmission Line . . . . . . . . . . . . . . . . . . . . 30

3.3 Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.4 Micro-grid Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.4.1 Micro-source . . . . . . . . . . . . . . . . . . . . . . . 333.4.2 Voltage Source Inverter . . . . . . . . . . . . . . . . . 333.4.3 Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.5 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.6 Control of Micro-grids . . . . . . . . . . . . . . . . . . . . . . . . 393.7 Power Flow in Micro-grids . . . . . . . . . . . . . . . . . . . . . . 43

4 SIMULATION AND RESULTS . . . . . . . . . . . . . . . . . . . . . . 48

iii

TABLE OF CONTENTS (Continued)

CHAPTER PAGE

4.1 Power Quality test . . . . . . . . . . . . . . . . . . . . . . . . . . 484.1.1 Sinusoidal Pulse Width Modulation based Micro-

grid Inverter . . . . . . . . . . . . . . . . . . . . . . . 504.1.2 Space Vector Pulse Width Modulation based Micro-

grid Inverter . . . . . . . . . . . . . . . . . . . . . . . 554.2 Power Sharing Test . . . . . . . . . . . . . . . . . . . . . . . . . . 604.3 Reliability Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . . 655.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

CITED LITERATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Appendix A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

iv

LIST OF TABLES

TABLE PAGE

I IEEE ALLOWED HARMONIC CONTENT . . . . . . . . . . . . . . 21

II POWER FLOW RESULTS USING POWERWORLD SIMULATOR 39

III SIMULATION PARAMETERS FOR SPWM BASED MICRO-GRIDINVERTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

IV SIMULATION PARAMETERS FOR SVPWM BASED MICRO-GRIDINVERTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

v

LIST OF FIGURES

FIGURE PAGE

1 Distributed Resources in a Power Network (Source:EPRI) . . . . . . . . 2

2 Reduction of Pollution due to Distributed Generation . . . . . . . . . . . 8

3 Line Diagram of Distributed Generation based Power Systems . . . . . 10

4 Line Diagram of a Micro-grid . . . . . . . . . . . . . . . . . . . . . . . . . 11

5 GE Drop Curve showing the Borderline of Irritation (see IEEE 519-1992for further details) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6 Unintentional Islanding (Source:Nova Energy Specialists) . . . . . . . . 18

7 Model of a Generation Source and its MATLAB Equivalent . . . . . . . 24

8 Load Flow Parameter Options . . . . . . . . . . . . . . . . . . . . . . . . . 25

9 MATLAB Model of a Circuit Breaker . . . . . . . . . . . . . . . . . . . . 27

10 Control Parameters of a Circuit Breaker . . . . . . . . . . . . . . . . . . . 27

11 Transformer Model and its MATLAB Equivalent . . . . . . . . . . . . . 28

12 Transformer Parameter Selection . . . . . . . . . . . . . . . . . . . . . . . 29

13 General Transmission Line Model and its MATLAB Equivalent . . . . . 30

14 Transmission Line Parameters Selection . . . . . . . . . . . . . . . . . . . 32

15 Fuel Cell Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

16 Voltage Source Inverter (VSI) Model . . . . . . . . . . . . . . . . . . . . . 34

17 MATLAB Implementation of Fuel Cell based VSI . . . . . . . . . . . . . 35

18 MATLAB Model of Three-Phase Load and its Parameters . . . . . . . . 36

vi

LIST OF FIGURES (Continued)

FIGURE PAGE

19 System Model under Consideration . . . . . . . . . . . . . . . . . . . . . . 37

20 MATLAB/Simulink Model of the System under Consideration . . . . . 37

21 Lumped System Model with Three Generators . . . . . . . . . . . . . . . 38

22 Generalized Model of Controller for Micro-grids . . . . . . . . . . . . . . 40

23 Voltage vs. Reactive Power Droop . . . . . . . . . . . . . . . . . . . . . . 41

24 Active Power vs. Frequency Droop . . . . . . . . . . . . . . . . . . . . . . 42

25 Grid-tied Inverter with DC Prime Mover . . . . . . . . . . . . . . . . . . 44

26 Power Filter Model Connected at the Output of Micro-grid Inverter . . 49

27 Micro-grid Inverter Model based on Sinusoidal Pulse Width Modulation(SPWM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

28 Line-Line voltage, Line-Neutral Voltages and Phase Currents of SPWMbased Micro-grid Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

29 FFT Analysis of Output Voltage in Grid-connected Mode . . . . . . . . 53

30 FFT Analysis of Output Voltage in Islanded Mode without Control . . 54

31 FFT Analysis of Output Voltage in Islanded Mode with Control . . . . 54

32 Space Vector Modulation based Micro-grid Inverter . . . . . . . . . . . . 55

33 Time Calculations for Space Vectors . . . . . . . . . . . . . . . . . . . . . 56

34 Output Voltages of Space Vector Modulation based Micro-grid Inverter 58

35 Voltage and Current Profile of the System before Proposed Control . . 58

36 Voltage and Current Profile of the System after Proposed Control . . . 59

37 Harmonic Analysis of Voltages Injected by Controlled Micro-grid Inverter 59

38 Droop Control based Voltage Source Model . . . . . . . . . . . . . . . . . 60

vii

LIST OF FIGURES (Continued)

FIGURE PAGE

39 Droop Control Model for Active and Reactive Power Sharing . . . . . . 61

40 FFT Analysis; Low Voltage Operation I . . . . . . . . . . . . . . . . . . . 61

41 FFT Analysis; Low Voltage Operation II . . . . . . . . . . . . . . . . . . 62

42 MATLAB/Simulink Model of the System with Over-current Relay andParallel Feeder Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

43 Pre and Post-fault Grid Phase Currents . . . . . . . . . . . . . . . . . . . 64

44 Parametric Analysis of Total Harmonic Distortion (THD) in DifferentControl Strategies Applied to Micro-grid . . . . . . . . . . . . . . . . . . . 66

45 Distributed System with three DG Units . . . . . . . . . . . . . . . . . . 67

46 Switching Sequence in Space Vector Pulse Width Modulation . . . . . . 74

47 Switching States and Sectors in Space Vector Modulation . . . . . . . . 75

48 Control Modes showing Transitions among Sources . . . . . . . . . . . . 79

49 State Transition Diagram for Fault and Normal Operating States withAssociated Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

viii

LIST OF ABBREVIATIONS

DERs Distributed Energy Resources

DG Distributed Generation

EPRI Electric Power Research Institute

PCC Point of Common Coupling

EPA Environmental Protection Agency

IEA International Energy Agency

SRECs Solar Renewable Energy Credits

LTC Load Tap Changer

ANSI American National Standards Institute

SAIDI System Average Interruption Duration Index

SCR Silicon Controlled Rectifier

IGBT Insulated Gate Bipolar Transistor

FACTS Flexible AC Transmission Systems

THD Total Harmonic Distortion

VA Voltage Ampere

DSA Direct Stability Assessment

OPF Optimal Power Flow

ix

LIST OF ABBREVIATIONS (Continued)

VSI Voltage Source Inverter

SVC Static VAR Compensator

APF Active Power Filter

PPF Passive Power Filter

SPWM Sinusoidal Pulse Width Modulation

SVPWM Space Vector Pulse Width Modulation

CPS Cyber-physical System

x

SUMMARY

With the advent of modern power grids constituted by non-conventional and renewable

distributed energy resources (DERs), considerable interest has been developed to solve the

potential issues related to power quality, harmonic distortions, voltage unbalance and frequency

restoration. The core issues with distributed generation (DG) systems of today are power

fluctuation, harmonic distortions to the main power system and inefficient power sharing which

lead to decreased efficiency and raise reliability concerns. These problems are directly instigated

by interface inverters in a micro-grid configuration in grid-connected as well as in islanded

modes. A flexible and seamless inverter control mechanism with desired modulation and a

degree of operability is the need of hour especially for these type of systems.

In smart or micro-grids based on DG, an adaptive and distributed rather than lumped or

centralized control is highly desirable so as to adapt to the real-time dynamics of the system.

This work supports the proposition of distributed control techniques for interface inverters in

micro-grids and utilizes added controllers to yield harmonic mitigation, proper power sharing

and improved power quality. MATLAB/Simulink has been employed to simulate a distributed

power system that can operate in synchronization with the utility grid as well as independently

from the grid with desirable controls. Control loops are ameliorated for system level power

quality improvement and frequency adjustment so as to make the system efficient, reliable and

power dense. The design scheme has been validated with the help of simulations.

xi

CHAPTER 1

INTRODUCTION TO DISTRIBUTED GENERATION

1.1 Motivation

The first power plants provided DC voltages to be distributed physically close to the point

of generation. Being a DC system, the supply voltage level was limited and so was the distance

over which the power could be transmitted. Balancing demand and supply was partly done by

using local storage i.e. batteries, which were directly tied to the DC grid. Today small-scale

generation along with local storage is becoming more popular. There is a renewed interest

in small-scale electricity generation from bio-fuels, wind and solar, small hydro-power, marine

and geothermal energy. The incorporation and integration of these non-conventional energy

sources resulted in a new term called ”Distributed Generation (DG)” which stands for on-site

generation in electricity markets (1). Although it is a fairly new concept, the idea behind is not

new since the DC grids worked on more or less the same principles. The aim behind replacing

regular remote utility generation and transmission system is the aging, deterioration costs and

energy losses over long transmission networks. Another motivation is that the green energy

production effectively reduces the CO2 emission (2).

Distributed generation includes the application of small generators, typically ranging in capacity

up to 10,000 kW, distributed throughout a power system, to provide the electric power needed

by consumers (3). As usually applied, the term distributed generation includes use of small

1

2

Figure 1. Distributed Resources in a Power Network (Source:EPRI)

electric power generators, whether located on the utility system, at the site of a utility customer,

or at an isolated site not connected to the main or utility grid. Typical distributed generators use

traditional power generation paradigms for example, diesel, combustion turbine, combined cycle

turbine, low-head hydro, or other rotating machinery. In addition, DG includes renewable power

generation methods such as wind, solar, etc. These renewable generators are often compiled

together into the ”DG” category because of their smaller size. Figure 1 (4), (5) shows how DG

is visualized.

1.2 Distributed Generation Technologies

Distributed generation is like an internet of power with the resources scattered throughout

the power system. DG technologies include the following distributed generation and distributed

storage systems:

3

Distributed Generators:

1. Small localized generators

2. Wave-energy harvesting

3. Photovoltaic panels

4. Bio-fuel generation

5. Wind turbines

6. Tidal dams

Distributed Storage:

1. Fuel Cells

2. Flywheels

3. Local batteries

4. Super Capacitive storage

5. Superconducting electromagnetic storage

1.3 Distributed Generation Components

The distributed generation system, as mentioned earlier, is an internet of power sources

combined together to perform in an efficient, reliable and flexible manner. DG system com-

ponents include micro-grids, loads, storage systems, control and communication circuitry and

grid-interactive inverters.

4

Micro-grid: A micro-grid can be defined as a small scale power supply network that can

incorporate small power generation sources to invigilate load demand. It is a very reliable

system of short range transmission as even if the micro-grid is disconnected from main grid,

the system continues to supply electricity in the vicinity.

Loads: Loads include regular household appliances and industrial machinery. They also

include commercial units and governmental facilities like lighting equipment, water-supply fil-

tration units, etc.

Grid-interactive Inverters: These inverters effectively remove the harmonics in converted

output power of renewable sources like solar or wind. These are used in interfacing micro-grid

with the main power network and provide different controls for voltage and frequency.

Tie Line: Sometimes known as common grid bus, It is the Point of Common Coupling

(PCC) of micro-grid and main or utility grid. When a fault happens, the tie line is opened so

that the fault does not affect micro-grid and connected loads.

1.4 Need for Distributed Generation

The progress in distribution technologies has been around for a while, but was not widely

implemented due to ”economy of scale” (6). Distributed generation avoids the need for the

developing new transmission and distribution lines. The grid acts as a backup supply at least

so as to increase the system reliability (7). Although reliability at the moment, is not an issue

in the advanced nations’ high voltage systems yet this will change rapidly in the following years

thanks to aging, crowding and deterioration of transmission systems. This section discusses

5

those major driving forces which emphasize the importance and need of distributed generation

systems. All the benefits of DG can be narrowed down to following two major aspects:

1. Electricity Market Reforms

2. Eco-friendly Concerns

1.4.1 Electricity Market Reforms

There is an increased interest of electricity suppliers in DG because they see it as a tool

that can help them to fill in niches in a free market. In such a market customers will look

for the service best suited to them. In free markets, it is important to adjust to the changing

requirements in the most flexible way. Distributed generation technologies generally provide

this flexibility because of their small sizes, persistence, flexibility and the short construction

times compared to many types of larger central power plants. DG technologies help electricity

suppliers to provide the desired type of electric service to consumers with regards to the fact

that different weight are given by customers to different features of electricity supply. In short

distributed generation allows players in the electricity sector to respond in a flexible way to the

changing market situations.

Reliability and Persistence: A major motivator for distributed generation is reliability

of supply considerations. Reliability problems refer to continual interruptions (i.e. voltage

drops to zero called outages) and blackouts in electricity supply (7). The importance of reli-

able electric supply is known by customers through energy markets liberalization. Most of the

under-developed countries have low reliability levels, basically due to low technical standards

6

and insufficient funds. Customers have no choice but to purchase electricity from a single state-

owned enterprise. The situation can change in free markets, because in conventional power

system high reliability levels imply more generation investment and infrastructure maintenance

costs. Because of the cost-effectiveness incentives coming from the introduction of DG technolo-

gies and re-regulation of the power supply utilities, reliability levels will increase (8). Having

a reliable power supply is very important for the industry (refining, paper, metal, chemicals,

petroleum, and telecommunication). When these industries find the reliability to be too low of

the grid-supplied electricity, they decide to invest in DG units so as to increase the reliability

standards to high overall.

Power Quality: The relation between distributed generation and power quality is ambigu-

ous but important. On one hand, some experts stress the potential negative effect on power

quality caused by the installation of distributed generation, while others emphasize the restora-

tive effects of distributed generation for power quality complications in a power network (8).

For example, in areas where the utility grid is weak and voltage support is difficult, DG can

contribute because connecting it generally leads to a rise of voltage in the network. The poten-

tial positive effects of distributed generation for voltage support and power factor corrections

are highly appreciated.

Cost-effectiveness and Localized Generation: Distributed generation serves as a sub-

stitute for investments in transmission and distribution capacity (demand for distributed gen-

eration from transmission and distribution companies) or as a bypass for transmission and

distribution costs (demand for distributed generation from electricity customers). Ofcourse,

7

this is possible only to the extent that alternative primary fuels are available in the premises.

Furthermore, increased use of DG technologies can end in new congestion problems for other

networks such as the ”gas transport network” (8).

According to the International Energy Agency (IEA), on-site production could result in cost

savings in transmission and distribution up-to 30 % of electricity costs. As such, it has been

seen as one of the biggest potential drivers for the distributed generation demand. ”In gen-

eral, smaller the customer size, larger the share of transmission and distribution costs in the

electricity price (above 40% for households)” (8).

Supporting Devices: Distributed generation can contribute in facilitation of a power

network. These contributions include services necessary to maintain unrelenting and stable

operation of the grid, but not supplying the consumers directly. This may be the capability to

generate on demand of the grid operator, for instance to stabilize a dropping frequency due to

a sudden or excess demand of power (e.g. a power plant switching off).

1.4.2 Eco-friendly Concerns

At present, environmental policies or concerns are one of the major factors for the demand

for ”distributed generation” as environmental regulations emphasize the companies in the elec-

tricity market to look for ”green energy” and cost-effective solutions (8). Distributed generation

can play a role here as it allows optimizing the energy demand of firms that have a large con-

sumption of both heat and electricity (9). Most governments are now making policies aiming

to promote the use of renewable energy. As a result, an increased impact of DG technologies

as renewable energy sources is observed except for large hydro power projects which have a

8

Figure 2. Reduction of Pollution due to Distributed Generation

decentralized nature. It reduces pollution because of less emission of fatal gases as shown in

Figure 2 (9).

Beneficial to Society: It is suggested by the environmentalists and academicians that

DG technologies are capable of providing remarkable benefits to a society. Power plants that

are large and centralized, emit substantial amounts of particulate matter, hydrocarbons, sulfur

oxides, carbon monoxide and nitrogen compounds. It is noted by the Environmental Protection

Agency (EPA) that the relation between sulfur oxide emissions and the phenomena of acid rain

is increasingly destroying the marine biodiversity and aquatic habitat. Interestingly, recent

studies have confirmed that widespread use of DG technologies is a cause of reduction in above

mentioned emanations.

Moreover, because DG technologies have the ability to remain independent of the grid, they can

provide emergency power for public services, residences, communications stations and natural

gas based power systems. Thus, DG can facilitate a country in increasing its miscellany of energy

9

resources. As evident, some of the DG technologies like solar photovoltaic panels, wind turbines

and low-head hydro consume essentially no fossil fuels while others including fuel cells, micro-

turbines and some internal combustion units operate by burning natural gas. This increasing

diversity helps shield the economy from price shocks, interruptions, and fuel shortages.

Source of Revenue: By introducing a law for power sellers to have a certain fraction

of green energy per unit production (RPS), residential system owners can save a substantial

amount of money on their utility bills by installing a solar system depending on the size of their

system (10). Homeowners can also sell green energy in the form of Solar Renewable Energy

Credits (SRECs). Energy suppliers buy these SRECs to meet their RPS goals. Thus this

legislation also ensures that the market for SRECs will remain stable and strong in the future,

which will spur solar development and investment.

1.5 Micro-grid Explained

Technology, economy and environmental incentives are changing the face of power gen-

eration, transmission and distribution network (11). Construction of new and large power

generating plants is costly and takes time. Smart and micro-grids represent an entirely new

approach to meet the customer needs. It is local and on-the-spot generation. It consists of small

generating units having capacity of 15-10,000 kW. Micro-grid generation resources include re-

ciprocating engines, gas turbines, micro-turbines, fuel cells, wind energy, solar energy, and other

small energy sources. Energy storage devices are batteries, superconducting coils, flywheels,

super capacitors, fuel cells etc. It is shown in Figure 3 (12) that how they are integrated in a

supply system.

10

Figure 3. Line Diagram of Distributed Generation based Power Systems

1.5.1 Architecture of a Micro-grid

A micro-grid is a small scale power supply network incorporated with small power generation

sources having a reliable system of short range transmission as even if the main grid goes out of

service, the micro-grid continues to supply the consumers (13). Essential features of this type

of a power system are reliability, flexibility in network topology, efficiency, load management

and power control.

Micro-grid is generally viewed as a cluster of micro-sources (small and/or renewable energy

sources). There are two operating modes of a micro-grid; grid-connected mode and islanded

mode. In the grid-connected mode, micro-grid is connected to centralized power plant (macro-

grid) through a tie line and operates in synchronization with the utility grid. In islanded mode,

11

it is disconnected from the utility grid and operates independently and autonomously meeting

the load requirements at any time as shown in Figure 4 (13), (14).

Figure 4. Line Diagram of a Micro-grid

12

1.5.2 Advantages

Micro-grids use renewable resources, hence they are more environment friendly with no

emission of harmful gases. They can use fuel cells which produce electricity from hydrogen and

oxygen gases and emit only water vapors. Nitrogen oxides and carbon dioxide emissions are

associated with reforming of natural gas or other fuels to produce fuel cells hydrogen supply.

Also, it increases reliability as it can be isolated from main grid in case of fault or outage of

the utility grid; power continues to flow in the power system. For remote and isolated areas,

micro-grid is the best solution to provide power quickly and cost-effectively with very less or

no transmission line losses. Comparatively, a centralized power generating unit converts 50%

of fuel into electricity emitting pollutant gases and then transmission line losses are up to 15%

of it, which is considerable.

Furthermore, micro-grids back up the main power or utility grid when power demand and costs

are high. One of the greatest benefits of micro-grids is that they are better positioned than

the main power/utility grid to meet the unknown or future needs of customers. They can

increase the overall electricity production quickly and efficiently through small local generators.

Ultimately, it comes down to a point where there is no need to wait for companies to build

large and centralized power plants that are costly and take time to build and provide relatively

less reliable power to the end users.

13

1.5.3 Ongoing Research in Micro-grids

Some of the research dimensions currently being explored in the area of micro-grids explained

in (15), (16), (17), (18), (19), (20) are as follows:

1. Development of robust and efficient control methods for frequency and voltage stability.

2. Development of flexible, seamless and improved approaches for micro-grid inverters and

their synchronization with the utility grid and loads.

3. Development of new and improved techniques to meet power quality benchmarks and

reliability standards.

CHAPTER 2

PROBLEMS WITH DG AND MICRO-GRIDS

This chapter focuses on the issues related to DG and micro-grids which include voltage

regulation, voltage flicker, harmonic distortion, islanding, reliability and other factors. These

are discussed in detail in the following subsections.

2.1 Voltage Regulation and Losses

Radial distribution systems are generally controlled by means of Load Tap Changer (LTC)

transformers at substations, additional line regulators on feeders, and switched capacitors on

feeders. Through the application of these devices, customer service voltages are usually upheld

within the ranges quantified by IEEE standard. Voltage regulation practice is based on radial

power flows from the substation to the loads and DG introduces meshed power flows that in-

terfere with the efficiency of standard voltage regulation practice.

As an example, if a DG unit is applied just downstream of a voltage regulator or LTC trans-

former that is using significant line drop compensation, the regulation controls will be unable

to properly measure feeder demand. Note that with distributed generation the voltage becomes

lower on the feeder. In this example, the voltage is reduced because the DG reduces the ob-

served load at the line drop compensator control. This confuses the regulator into setting a

voltage lower than is required to maintain adequate service levels at the tail end of the feeder.

This is the opposite effect of voltage support. one possible solution to this problem is shifting

14

15

the DG unit to the upstream side of the regulator (if possible) or adding regulator controls to

compensate for the DG output, but it brings its own set of issues.

DG may also result in high voltage at some electric customers. For example, a small residential

DG system that shares a common distribution transformer with several other residences may

raise the voltage on the secondary enough to cause high voltage at these customers. This can

occur if the distribution transformer serving these customers is located at a point on the feeder

where the primary voltage is near or above the American National Standards Institute (ANSI)

upper limit i.e. 126+ volts on a 120 volt base. Normally, without DG, there would be voltage

drop across the distribution transformer and secondary conductors and voltage at the customer

service entrances would be less than the primary. The presence of the DG may introduce reverse

power flow to counter-act this normal voltage drop, perhaps even raising voltage somewhat, and

the service voltage may actually be higher at the customer services than on the primary side of

the distribution transformer; it may even exceed the ANSI upper limit. This has shown that

both high and low service voltages can occur due to the incompatibility of DG with the radial

power flow based voltage regulation approach used in most utility systems.

2.2 Voltage Drop

DG may cause visible voltage flicker (21). Flicker can either be simple or a concerning issue

regarding its analysis methods and mitigation approaches. Generally, it may be prominent due

to machine starting (e.g. induction generator) or due to the step changes in the output of DG

unit causing a significant voltage change (drop or rise) on the respective feeder. The frequent

repetition of these events may be harmful to the loads and drop of lighting loads can become

16

noticeable to the customers. For prohibition, one approach is to determine the magnitude and

number of changes of voltage occurring per unit time and see if these are above the visibility

or irritation threshold levels of the General Electric (GE) drop curve (Figure 5). If above the

threshold, or if customer complaints occur, mitigation must be considered.

Figure 5. GE Drop Curve showing the Borderline of Irritation (see IEEE 519-1992 for further

details)

Mitigation approaches include reduced voltage starts on induction generators as well as

speed matching. Synchronous generators might require tighter synchronization and voltage

matching. Inverters might be controlled to limit inrush currents and changes in output levels.

The drop curve approach is very useful and straightforward for determining the drop malfunc-

17

tions due to machine starting. It provides necessary information of output fluctuations in case

of a well defined fluctuation rate.

It is possible for Output fluctuations of a DG (even smoother ones from solar or wind systems)

possibly cause ”hunting” of an upstream regulator. While a visible drop may not be created

by fluctuations of a DG unit alone, the hunting regulator can create noticeable visible volt-

age flicker (22). These problems may become complicated with time and handling strategies.

Therefore, the operator must be adequately familiar with the interactions between the DG units

and the rest of power transmission and distribution system.

2.3 Islanding

Islanding is referred to as when a DG unit (or group of DG units) continues to energize a

specific zone of the power system that has been isolated from the utility grid. This isolation can

be the result of an upstream breaker operation, fuse functions, or switches which sectionalize

the power system into different zones (23). Only if the generator(s) can self-excite and sustain

the load in the islanded zone, islanding can take place. In most cases it is not desirable for a DG

to island with any part of the utility system because this can lead to safety and power quality

problems that affect the utility system and loads. For example, during the routinely reclosing

operations, if an islanding condition develops on a feeder, the islanded DG units speedily go out

of phase with the utility system in the ”dead period”. After this event, if reclosing is done, the

utility system will now connect with the islanded portion as out of phase. This happens when

reclose-blocking into the energized portion is not provided with breaker controls and damages

the DG units supporting the island, the utility equipment and customer loads.

18

Figure 6. Unintentional Islanding (Source:Nova Energy Specialists)

19

Unintentional islanding has been demonstrated in Figure 6 (23). Islanding also increases the

likelihood that DG sources may be allowed to subject to the island with out of range voltage

and frequency conditions during its existence (24). Also, a serious safety threat can be posed

during downed conductors and utility repair operations as the utility workers or common people

may come in contact with the energized zones which would be de-energized otherwise. The

restoration of service may be delayed as line workers try to disable the respective island. This

impacts reliability indices such as the System Average Interruption Duration Index (SAIDI)

which is commonly used by electric utilities for reliability indication at various parts of a power

system.

2.4 Harmonics

”The combination of technology innovation in power electronics, electricity deregulation,

economics, customer value, and energy demand are beginning to converge causing the electric

power industry to shift from a few large concentrated generation centers to a more distributed

and dispersed generation infrastructure” (25). Nevertheless, distributed generators introduce

harmonics into the power system. The types and severity of harmonics depend on the power

converter technology and interconnection configuration. From the standpoint of harmonic dis-

tortion, two key questions arise from the potential use of distributed generation as:

1. What would be the harmonic impact on the distribution circuit by these distributed

resources?

2. How much of the existing feeder load can be supplied by these distributed resources before

IEEE 519-1992 voltage limit compliance is violated (25)?

20

Harmonic problems are tied with the switching device technology, the nature of the char-

acteristic harmonics, equipment ratings, and loading conditions of the host distribution feeder.

From the standpoint of harmonic modeling and simulation, a DG unit is usually a converter-

inverter type topology and is treated as a non-linear load injecting harmonics into the distri-

bution circuit (26). Under the present framework of IEEE 519-1992, the supplier of electricity

is responsible for the quality of the voltage supplied. The end-user is responsible for limiting

harmonic current injections based on the size of the end-use load relative to the capacity of

the system. Distributed resources such as micro-turbines, fuel cells, and photovoltaic arrays

are small relative to system capacity, but the smaller sizes are much more likely to achieve

significant penetration levels. It is therefore reasonable to address the question of allowable

penetration by assuming a harmonic injection at the limit levels specified (25).

Inverters are particularly concerned over which the possible harmonic current contributions

they may make to the utility system. Partially, these concerns arise due to the use of Silicon

Controlled Rectifier (SCR) type inverters. They are line-commutated and inject high levels of

harmonic current through the distributed system. Most types of new inverter topologies are

based on Insulated Gate Bipolar Transistors (IGBTs) that use pulse-width-modulation (PWM)

to generate the injected ”sine” wave. They are capable of generating much cleaner output and

normally meet the standards set by IEEE 519-1992 (see Table I below).

The table shows allowed odd harmonics. Even harmonics are limited to be 25% of odd

values. Other source of harmonics may be rotating machinery such as synchronous generators.

Depending on the design of the generator windings (pitch of the coils), core non-linearity,

21

Harmonic Order Allowed % relative to Fun-

damental

<11th 4%

<11th to<17th 2%

<17th to<23rd 1.5%

<23rd to<35th 0.6%

<35th or greater 0.3%

Total Harmonic Distortion

(THD)

5%

TABLE I

IEEE ALLOWED HARMONIC CONTENT

grounding and other factors, there can be significant harmonics present in the system. Triple

harmonics are additive in the neutral; and the third harmonic is often the most prevalent.

Synchronous generators are often specified with a 2/3 pitch for the windings as much less third

harmonic is produced than those with other pitches. Unfortunately a 2/3 pitch machine has a

lower impedance to third harmonic and may cause more harmonic current to flow from other

sources connected in parallel with it (27). The feeder penetration of harmonics is limited by

the grounding arrangement of the generator and step-up transformer.

22

2.5 Transmission Pricing Issues

The allocation of fixed or marginal costs for different generation types may be changed by

transmission pricing. ”Generally, transmission charges are related to one or more of the fol-

lowing; the distance electricity is transmitted, the amount of electricity transmitted and the

reservation, if any, made by the generator for access to transmission lines known as capacity

reservation” (28). ”How these pricing schemes would affect the cost of renewable-based gener-

ation depends on how the characteristics of renewable generation, intermittence and capacity

factor, distance from load centers, and coincidence with peak load relate to these factors” (28).

Details of these factors can be seen from the reference given.

2.6 Integration with the Grid

For reasons of reliability and efficiency, distributed generation resources would be intercon-

nected to the same transmission grid as central power stations. Various technical and economic

issues occur while integrating these resources into a grid to form a network. Technical problems

are faced in the areas of voltage stability, harmonics and power quality, reliability, protection

and control (29). Grid-wide functions e.g. voltage and frequency control and allocation of

reserves may be affected by the large scale deployment of distributed generation technologies.

As a result of smart grid functions, virtual power plants and grid energy storage such as power

to gas stations are added to the grid.

CHAPTER 3

PROPOSED MODELING AND CONTROL

In MATLAB/Simulink, ”SimPowerSystemsTM toolbox provides component libraries and

analysis tools for modeling and simulating electrical power systems. Models of electrical power

components, including three-phase machines, electric drives and components are offered in

libraries for applications such as flexible AC transmission systems (FACTS) and renewable

energy systems. Harmonic analysis, calculation of total harmonic distortion (THD), load flow,

and other key electrical power system analyses are automated” (30).

From modeling point of view, a traditional power system consists of three parts. 1) Generation

2) Transmission and 3) Distribution. They along-with their components are described in the

following sections.

3.1 Generation

3.1.1 Source

Typical model of a generation source (hydro or nuclear) is shown in Figure 7. Generator

and coupling transformer ratings are specified by the generation capacity of a power plant.

”The Three-Phase Source block implements a balanced three-phase voltage source with

an internal R-L impedance where the three voltage sources are connected in Y with a neutral

connection that can be internally grounded or made accessible” (31). The internal resistance

and inductance of source are specified either directly by entering R and L values or indirectly

23

24

Figure 7. Model of a Generation Source and its MATLAB Equivalent

by specifying the source inductive short-circuit level and X/R ratio. Block parameters for

specifications are shown in Figure 8. The internal phase-to-phase voltage in volts RMS (Vrms)

and phase angle of the internal voltage generated by phase A, in degrees can be specified (31).

Phase B and C of internal voltages lag phase A by 120 and 240 degrees, respectively which

means that three voltages are generated in positive sequence. The internal connection of the

three internal voltage sources may be Y, Yn or Yg. The three-phase inductive short-circuit

power, in volts-amperes (VA) is used to compute the internal inductance L at specified base

voltage. ”This parameter is available only if Specify impedance using short-circuit level

is selected” (31). The frequency of source is in hertz (Hz).

The load flow tool of the PowerGui block specifies the parameters on the Load Flow tab.

”These load flow parameters are used for model initialization only, they have no impact on the

block model and on the simulation performance” (31). The Generator Type parameter in

load flow tab specifies the voltage source type from the following:

25

Figure 8. Load Flow Parameter Options

1. Swing is selected for the implementation of a generator with controls for magnitude of

terminal voltage and its phase angle. The load flow bus block which is connected to the

voltage source terminals, provides the specifications for reference voltage magnitude and

angle.

2. PV is selected for the implementation of a generator with controls for output voltage

magnitude V active power P. Active power and voltage are specified by active power

generation P and swing or PV bus voltage parameters of the load flow tab whereas

minimum reactive power Qmin and mamximum reactive power Qmax parameters control

min and max reactive powers, respectively.

26

3. PQ is selected for the implementation of a generator with controls for output active and

reactive powers. Active power generation P and reactive power generation Q parameters

of this block specify P and Q, respectively.

3.1.2 Grid Circuit Breaker

A circuit breaker is implemented by the Breaker block shown in Figure 9. ”The opening

and closing times can be controlled either from an external Simulink signal (external control

mode), or from an internal control timer (internal control mode)” (32). A series Rs-Cs snubber

circuit comes with the model which can be connected to the circuit breaker. If the breaker block

is connected in series with a current source, an inductive circuit or an open circuit, a snubber is

necessary. ”When the breaker block is set in external control mode, a Simulink input appears

on the block icon. The control signal connected to the Simulink input must be either 0 or 1 (0

to open the breaker, 1 to close it)” (32). It can be specified by using a ”constant” block.

In the internal control mode, the dialog box of this block specifies the switching times of the

breaker. Resistance Ron implies that the breaker is closed. ”The Ron value can be set as small

as necessary in order to be negligible compared with external components (a typical value is 10

mohms). When the breaker is open, it has an infinite resistance” (32). These parameters can

be selected as desired by the user as shown in Figure 10.

3.2 Transmission

Transmission in a power system refers to transmitting the bulk generated power to an

intermediate substation where it can be supplied to load centers depending on the demand. A

transmission network is formed by the interconnection of various transmission lines with each

27

Figure 9. MATLAB Model of a Circuit Breaker

Figure 10. Control Parameters of a Circuit Breaker

28

other. The whole power network with transmission and distribution systems is known as the

”power grid”, or just ”the grid” (33). Transmission system consists of power transformers,

transmissions lines and compensation equipment. They are described as follows:

3.2.1 Power Transformer

Model of an ideal transformer and its MATLAB equivalent are shown in Figure 11.

Figure 11. Transformer Model and its MATLAB Equivalent

This block implements a three-phase transformer using three single-phase transformers.

When activated, the saturation characteristic is the same as the one described for the Saturable

Transformer block. If the fluxes are not specified, the initial values are automatically adjusted

so that the simulation starts in steady state. The leakage inductance and resistance of each

winding are given in per unit (p.u) based on the transformer nominal power on the nominal

voltage of the winding (V1 or V2) (34).

29

Figure 12. Transformer Parameter Selection

The two windings of the transformer can be connected as follows:

1. Y

2. Accessible neutral Y

3. Grounded Y

4. Delta lagging Y by 30 degrees (D1)

5. Delta leading Y by 30 degrees (D11)

A parameter selection block for customization is apparent form Figure 12. ”The D1 and

D11 notations refer to the clock convention that assumes that the reference Y voltage phasor

30

Figure 13. General Transmission Line Model and its MATLAB Equivalent

is at noon (12:00) on a clock display. D1 and D11 refer to 1:00 p.m. (delta voltages lagging

Y voltages by 30 degrees) and 11:00 a.m. (delta voltages leading Y voltages by 30 degrees)

respectively” (35).

3.2.2 Transmission Line

A transmission line is a material medium or structure that forms a path for directing the

transmission of energy from one place to another, such as electromagnetic waves or acoustic

waves, as well as electric power. It can be of long length, medium length and short (50km or

less). The power is produced at a relatively low voltage (2.3-30 kV) depending on the size of

the unit at the power station. The transformer at that power station steps up the generator

terminal voltage to a higher voltage (115-765 kV AC, varying by the transmission system and

by the country) for transmitting it to long distances (33). General model of a transmission line

and its MATLAB equivalent are shown in Figure 13 (36).

31

The Three-Phase Pi Section Line block implements a balanced three-phase transmission

line model with parameters lumped in a pi section. As opposed to the Distributed Parameter

Line model where the resistance, inductance, and capacitance are uniformly distributed along

the line, the three-phase pi section line block lumps the line parameters in a single pi section (36).

The line parameters R, L, and C are specified as positive- and zero-sequence parameters that

take into account the inductive and capacitive couplings between the three phase conductors,

as well as the ground parameters. This method of specifying line parameters assumes that

the three phases are balanced. The self and mutual resistances (Rs, Rm), self and mutual

inductances (Ls, Lm) of the three coupled inductors, as well as phase capacitances Cp and

ground capacitances Cg, are deduced from the positive- and zero-sequence RLC parameters

which can be specified in the tab shown in Figure 14.

This transmission line model is helpful in realistic modeling of a power transmission system and

studying different effects due to transmission such as electromagnetic interference issues and

how they play a role depending on the length of line.

3.3 Distribution

”An electric power distribution system is the final stage in the delivery of electrical power as

it carries electricity from the transmission system to individual consumers” (37). Transformers

are used on large scale to connect distribution substations to the transmission system and

lower the transmission voltage to medium voltage (2.3-30 kV). This medium-voltage power is

transfered to the distribution transformers located near the customer’s premises, through the

primary distribution lines. This medium voltage is again lowered to the utilization level for

32

Figure 14. Transmission Line Parameters Selection

33

household appliances by distribution transformers. They typically feed several customers at

this voltage level through the secondary distribution lines. ”Customers demanding a much

larger amount of power may be connected directly to the primary distribution level” (37). The

distribution system comprises of transformers (usually step-down), wires and load centers.

In modern power systems or system based on distributed generation, distribution is rather

integrated with embedded power sources (mostly renewable), storage devices, power electronic

equipment and distributed loads. This is described in detail the next section.

3.4 Micro-grid Modeling

3.4.1 Micro-source

Micro-source is usually a small power source integrated in the power network. Renewable

energy sources are commonly used as micro-sources. Fuel cells are considered to be an important

resource in micro-grid due to advantages like high efficiency, low pollution and flexible molecular

structure. MATLAB provides a model for fuel cell in SimPowerSystems toolbox as shown in

Figure 15. The fuel cell stack block implements a generic model parameterized to represent

most popular types of fuel cell stacks with hydrogen and air. It is rated at 380-400V DC.

3.4.2 Voltage Source Inverter

A Voltage Source Inverter (VSI) is necessary for interfacing micro-source (DC) to the three-

phase distributed AC power system. As shown in Figure 16, it comprises a DC source, and an

inverter with a filter to produce sinusoidal output.

The VSI topology uses a multi-leg inverter to convert DC voltage into AC at nominal

frequency (50 or 60 Hz). The DC link is a parallel capacitor which regulates the DC bus

34

Figure 15. Fuel Cell Model

Figure 16. Voltage Source Inverter (VSI) Model

voltage ripple and stores energy for the system. The inverter is composed of insulated gate

bipolar transistor (IGBT) semiconductor switches. There are other alternatives to the IGBT

are insulated gate commutated thyristors (IGCTs) and injection enhanced gate transistors

(IEGTs) although IGBT is used extensively in most VSIs. The IGBT switches create a pulse-

35

width-modulated (PWM) voltage output that regulates the voltage and frequency. MATLAB

model of an uncontrolled VSI is shown in Figure 17.

Figure 17. MATLAB Implementation of Fuel Cell based VSI

3.4.3 Load

The Three-Phase Series RLC Load block and its parameters tab shown in Figure 18

implement a balanced three-phase load as a series-combination of RLC elements. ”At the

specified frequency, the load exhibits a constant impedance. The active and reactive powers

absorbed by the load are proportional to the square of the applied voltage” (38).

If constant Z is selected, nominal phase-to-phase voltage Vn, active power P, and reactive

power (QL-QC) are used to determine the load impedance. Impedance is kept constant during

the load flow solution. The effective P and Q vary proportionally to the square of the bus

voltage as calculated by the load flow tool.

36

If constant PQ is selected, the active power P and reactive power Q are kept constant and

equal to the values specified on the parameters tab of the block dialog box (38).

Figure 18. MATLAB Model of Three-Phase Load and its Parameters

3.5 System Model

The high level diagram of the system under consideration is shown in Figure 19. The

figure shows there is one main centralized power plant, whose power is transmitted through

transmission lines to the receiving station where it is transmitted to the distribution substation.

At the receiving station PCC, there is availability of power from the distribution resources. In

case main grid G is not available due to fault or maintenance purposes, power can be supplied

37

Figure 19. System Model under Consideration

Figure 20. MATLAB/Simulink Model of the System under Consideration

to loads through distributed generation based micro-grids A and B. MATLAB/Simulink model

of this system can been seen from Figure 20.

In grid-connected mode, power is being supplied to loads through the main grid G. Micro-

grids A and B are connected to both the grid G and distribution generation systems. In case

38

of island (fault or unavailability of the grid), no power is supplied to the loads through the grid

and power demands are fulfilled through DG micro-grids. This adds flexibility, efficiency, and

reliability to the system.

Figure 21. Lumped System Model with Three Generators

A non-distributed or lumped analogue of above mentioned system which has three power

sources can be modeled using Direct Stability Assessment Tools (DSA) such as PowerWorld

Simulator for Optimal Power Flow (OPF) solutions as shown in Figure 21. This is a 3-Machines

6-Bus system. Active and reactive power flow can be studied. Note that there are no distributed

sources in this system and consequently no controls for micro-grids. The system if subjected to

fault, is not reliable. Voltage and currents at different buses are shown in Table II.

39

Bus Number Bus Type Voltage (pu) Angle (deg)

1 Slack 1.0000 0.00

2 PV 1.0000 6.28

3 PV 1.0000 4.50

4 PQ 0.9790 3.18

5 PQ 0.9545 -1.81

6 PQ 0.9675 -1.41

TABLE II

POWER FLOW RESULTS USING POWERWORLD SIMULATOR

A detailed block diagram of this distributed system shown in Figure 20 will be analyzed for

different situations in the next chapter. It will be studied that how power is managed in this

type of a system and what are the controls desired to maintain an efficient, reliable and power

dense operation. For now, the control design of this system is presented and different control

loops are discussed for power, voltage and frequency.

3.6 Control of Micro-grids

The job of micro-source controls is to make sure that the micro-grid can connect to or

isolate itself from the grid in a rapid and seamless fashion, new micro-sources can be added to

the system without modification of existing equipment, power set-points can be independently

40

chosen, active and reactive power can be independently controlled, and it can meet the dynamic

load demand (39).

Each micro-source controller must autonomously respond effectively to system changes without

requiring data from the loads, the static switch or other sources. The generalized block diagram

of the control is shown in Figure 22 (39). The blocks on the left are used to calculate the real

time values of active power, reactive power and the voltage magnitude. The control generates

the desired voltage magnitude and angle at the inverter terminals. The gate pulse generator

is responsible for appropriate firing pulses (to the inverter) to track the control’s requests.

Operating the inverter as a voltage behind an impedance results in P≈δ and Q≈|V| (39). The

two droop controls described below are implemented in separate blocks.

Figure 22. Generalized Model of Controller for Micro-grids

41

1. Voltage (V) vs. Reactive Power (Q) Droop: Integration of large numbers of micro-

sources into a micro-grid is not possible with basic unity power factor controls as voltage

regulation is necessary for local reliability and stability. Systems with high penetrations of

micro-sources without local voltage control, can experience voltage and/or reactive power

oscillations which is not desirable. Voltage control must also ensure that there are no large

circulating reactive currents between the sources. These currents can exceed the ratings

of the micro-sources even with small errors in voltage set-points. This situation requires

a voltage vs. reactive power droop controller so that, as the reactive power generated

by the micro-source tends to be more capacitive, the local voltage set-point is reduced.

Conversely, as it tends to be more inductive, the voltage set-point is increased (39). This

is shown in Figure 23 (40).

Figure 23. Voltage vs. Reactive Power Droop

42

2. Active Power (P) vs. Frequency (ω) Droop: When the micro-grid is connected to

the utility grid, loads get power both from the grid and local micro-sources, depending

on the customer’s situation. If the grid power is lost because of IEEE 1547 events,

voltage drops, faults, blackouts, etc., the micro-grid can transfer to island operation,

autonomously. To regulate the output power in such situations, each source exhibits a

constant negative slope (droop) on the Pω plane. Figure 24 shows that the slope is chosen

by allowing the frequency to drop by a given amount, ∆ω, as the power spans from zero

to Pmax shown by the dashed line (41). It also shows the power set-points Po1 and Po2

for two units. This is the amount of power injected by each source when connected to

the grid, at system frequency (40). Let us analyze two situations where this regulation is

needed.

Figure 24. Active Power vs. Frequency Droop

43

Case1: If the system transfers to island when importing from the grid, the generation

needs to increase power to balance the power in islanded mode. In this case, the new

operating point will be at a frequency lower than the nominal value. Hence, both sources

would increase their power output with unit 2 at its maximum power point (39), (40).

Case2: If the system transfers to island when exporting power to the grid, the new

frequency will be higher, corresponding to a lower power output from the sources with

unit 1 at its zero power point (39), (40).

The characteristics shown in Figure 24 are steady state characteristics. The slope is fixed in

the region where the unit is operating within its power range. As soon as any limit is reached,

the slope tends to become vertical. The droop is the locus where the steady state points are

constrained to come to rest, but during dynamics the trajectory has deviations from these

characteristics.

3.7 Power Flow in Micro-grids

Typically, a DG or a micro-grid consists of a DC prime mover, interface converter (inverter

in this case) and an LC filter which is coupled to the AC main (utility grid) using an inductor

as shown in Figure 25 (40).

The main role of inverter (VSI) is to control the voltage amplitude and phase angle for

the injection of desired active and reactive power. Magnitude of output voltage and frequency

depends on real and reactive power of micro-source. Output power for this model is given as

S = V × [(E∠g − V ∠0) /jXg] (3.1)

44

Figure 25. Grid-tied Inverter with DC Prime Mover

As,

S = P + jQ (3.2)

P = [(E × V ) /Xg]× sin (g) (3.3)

Q = (V/Xg)× [E × cos (g)− V ] (3.4)

Where V is grid voltage and E is the amplitude of inverter output voltage. Xg is the

reactance which can be taken as resistive in low voltage networks. The voltage source inverter

controls both the magnitude and phase of its output voltage. The relationship between the

inverter voltage, system voltage, and the inductors reactance determines the flow of active and

reactive power from the system. The active and reactive powers injected by the DG units to

the common grid bus can be given by the following set of equations

45

P =

(EV

Zcos Φ− V 2

Z

)cos θ +

EV

Zsin Φ sin θ (3.5)

Q =

(EV

Zcos Φ− V 2

Z

)sin θ − EV

Zsin Φ cos θ (3.6)

Where, Φ is the power angle and Z and θ are the magnitude and phase of impedance, respec-

tively. When the network is predominantly resistive, we can substitute Z=R, θ=0 in equations

3.5 an 3.6 to give the following set of equations

P =

(EV

Rcos Φ− V 2

R

)(3.7)

Q = −EVR

sin Φ (3.8)

For practical applications, power angle Φ is usually small, so P/Q decoupling approximation

(sin Φ= Φ, cos θ=1) can be assumed for the simplification of control design. Hence the new

set of equations will be

P ≈ V

R(E − V ) (3.9)

Q = −EVR

Φ (3.10)

Consider that by increasing the output voltage amplitude, the delivered real power becomes

high and by increasing the power angle, reactive power becomes low.

Accurate power sharing among the sources and loads is guaranteed by the droop control tech-

46

nique. This method mainly referring to the frequency of the power electronics inverter, is similar

to the traditional power system frequency adjustment (42). System voltage and frequency regu-

lation can decouple active power-frequency and reactive power-voltage droop curves. There are

two types of controls of the inverter. One of them is using activefrequency (P -ω) and reactive

power-voltage (Q-V ) droops. Another is using active power-voltage (P -V ) and reactive power-

frequency (Q-ω) droops. In both cases, VSI acts as a voltage source, with the magnitude and

frequency of the voltage controlled by droops (43). Each control mode has its own applications;

some are better than others. Generalized droop equations (44) can be written as

ω = ωo − k (P ) (3.11a)

V = Vo − k (Q) (3.11b)

where,

kp: frequency droop coefficient

kq: voltage droop coefficient

ω0: nominal frequency

V0: rated phase voltage magnitude

P : active power output of micro-grid inverter

Q : reactive power output of micro-grid inverter

47

We have witnessed from equations 3.9 and 3.10 that if output voltage is increased, the

delivered active power becomes high and if power angle is increased, the reactive power is

decreased, which shows opposite characteristics to the conventional droop method. We conclude

that P -V droop and Q-ω boost functions are the true measure of active and reactive power

sharing in low voltage or resistive networks. The equations so obtained to get the control of

frequency and voltage are as follows

ω = ωo + kq (Qo −Q) (3.12a)

E = Eo − kp (Po − P ) (3.12b)

Active and reactive powers with their nominal and rated values are shown. kq is frequency

boost coefficient and kp is the voltage droop coefficient. These control equations are imple-

mented in MATLAB/Simulink and synthesized with the proposed system model. The results

will be presented in the next chapter.

CHAPTER 4

SIMULATION AND RESULTS

The system under consideration consists of a utility grid with bulk generation from a large

generator rated at 500MW, 11KV and two micro-grids connected through a Point of Common

Coupling (PCC) to the utility grid and distributed loads. Micro-grids have DC sources rated at

400V DC. Circuit breakers (reclosers) are installed for interfacing micro-grids with the utility

grid forming different zones. Each micro-grid has a voltage source inverter provided with the

droop control model. The droop control model provides a voltage reference signal at the output.

This reference signal depends on the actual active and reactive power output of the inverter

and maintains power sharing. An additional gain is used to maintain system stability (45). The

model of main grid along-with the transmission and distribution transformers, circuit breakers,

micro-grids and distributed loads have all been simulated in MATLAB/Simulink as shown in

section 3.5 Figure 20. The analysis of system level power quality, reliability and dynamic

performance is done in the following sections.

4.1 Power Quality test

Power quality covers a lot of issues in the domain of distributed power systems and power

electronic systems. Some of the notable issues have been described in detail in chapter 2.

Traditionally, we use Power Filter (PF) or Static Var Compensator (SVC) to improve power

quality of microgrid. PF includes Active Power Filter (APF) and/or Passive Power Filter

48

49

(PPF). PPF can mitigate some harmonics, but it is uncontrollable, and has bad real-time

performance. SVC can mitigate some harmonics, compensate reactive power at a high rate,

and weaken the three-phase imbalance of the microgrid (46). It is cheap in reactive power

compensation, however, uncontrollable in harmonic mitigation. Model of power filter considered

in this system is shown in Figure 26 which is a three-phase passive filter of 2nd order. It is rated

at 500 Hz cut-off frequency with inductance 150 mH and capacitive power 3 KVAR. The filter

is installed at the output of three-phase voltage source inverter forming a DG or a micro-grid

sub-system.

Figure 26. Power Filter Model Connected at the Output of Micro-grid Inverter

The use of inverters on the large scale providing power to a micro-grid system can create

higher order harmonics due to internal switching. Those harmonics must be compensated

50

in order to get the improved voltage profile at the loads. Harmonics produce fluctuation in

the output voltage especially in the islanded mode of operation of the micro-grid. Though

harmonics are always present in the power system but they should be within the standards set

by IEEE which are:

1. A single harmonic content less than 3%

2. Total Harmonic Distortion (THD) no more than 5%

Each inverter must be able to respond quickly and effectively to load changes. Mostly,

inverter control modulation scheme decides the amount of harmonic pollution present at a

specific time in the system. Commonly used modulation techniques are sinusoidal and space

vector methods with PWM control. In general, PWM technique changes the duty cycle of a

square wave to control the power output.

4.1.1 Sinusoidal Pulse Width Modulation based Micro-grid Inverter

Most commonly used for voltage source inverter is the Sinusoidal Pulse Width Modulation

(SPWM) technique. Sinusoidal PWM shown in Figure 27 uses many more square waves (at a

much higher frequency) to mimic the shape of a sine wave. Sinusoidal PWM technique, gives an

output wave that is very easy to filter into a pure sine wave because very little energy has to be

absorbed and later released during the cycles of the higher frequency signal. This means a much

cleaner output with smaller inductors and capacitors can be obtained. Simulation parameters

used for micro-grid inverter are shown in Table III.

Voltage and current waveforms including line-line voltage, line-neutral voltages and phase

currents of SPWM based micro-grid inverter are shown in Figure 28.

51

Figure 27. Micro-grid Inverter Model based on Sinusoidal Pulse Width Modulation (SPWM)

Parameter Value

DC Link Voltage Vdc=380V

Fundamental Frequency f=50Hz

Switching Frequency fs=1MHz

Sampling Time ts=10−6sec

Filter 2nd Order Low Pass

Cut-off Frequency fo=500Hz

TABLE III

SIMULATION PARAMETERS FOR SPWM BASED MICRO-GRID INVERTER

52

Figure 28. Line-Line voltage, Line-Neutral Voltages and Phase Currents of SPWM based

Micro-grid Inverter

53

FFT analysis of these waveform shows that very less amount of harmonic content is present

which is a consequence of normal operating condition in grid-connected mode as adequate

voltage and frequency support needed at the load side is fulfilled by the main grid. This is

verified by checking the Total Harmonic Distortion (THD). Figure 29 shows the results.

Figure 29. FFT Analysis of Output Voltage in Grid-connected Mode

A comparison of controlled and uncontrolled islanded mode of operation in terms of power

quality has been done using the FFT analysis of the output (see Figure 30 and Figure 31)

which shows that an uncontrolled micro-grid system can insert a significant amount of harmonic

content into the system which not only violates the IEEE standard but also poses threats to

the loads. So islanded mode without proper control can raise significant concerns regarding

harmonic distortions and power quality.

54

Figure 30. FFT Analysis of Output Voltage in Islanded Mode without Control

Figure 31. FFT Analysis of Output Voltage in Islanded Mode with Control

Islanded mode is referred to as when the main or utility grid is out of service due to some

fault or adverse environmental conditions. The system load in this case has to be supplied

by the micro-grids based on micro-sources in order to ensure maximum reliability. In this

case, power quality is an important issue to be taken care of and the control scheme has to

be designed accordingly so as to limit the harmonic content to as low as possible. It can be

55

witnessed that fundamental of the output voltage is still close to the rated DC value of fuel

cells but it has a lot of harmonic content due to intermittent switching and unbalance of system

voltage and frequency in the absence of utility grid. Micro-sources with control are able to

reduce the harmonic content below 5% which is in accordance with the IEEE allowed limit.

4.1.2 Space Vector Pulse Width Modulation based Micro-grid Inverter

Space vector pulse-width-modulation (SVPWM) is used for micro-grid inverters because of

its fast real-time response, low harmonic content and high efficiency. It is a digital modulating

technique where the objective is to generate PWM load line voltages that are in average equal

to reference load line voltages (47). This is done in each sampling period by properly selecting

the switch states for VSI and by proper calculation of the period of times they are used. The

selection and calculation times are based upon the space vector transformation. Figure 32

shows a space vector modulation based micro-grid inverter model.

Figure 32. Space Vector Modulation based Micro-grid Inverter

56

Figure 33. Time Calculations for Space Vectors

The reference voltage is followed by the three-phase voltages by calculations of proper on

and off duration of sequences (voltage vector) represented by adjacent sides of the sector.

These durations can be calculated by building a MATLAB model as shown in Figure 33.

Simulation parameters for SVPWM based micro-grid inverter are used as in Table IV. Three

phase voltages injected by space vector modulation based micro-grid inverter in Figure 34 show

smooth waveforms leading to power dense grid operation.

In grid-connected mode, harmonic content in the system is very less and a smooth operation

is yielded whereas islanded mode requires proper control. The waveforms in Figure 35 show

that without applying the proposed strategy the harmonics present in the system are around 9%

which violate IEEE 519-1992 power quality standard. Applying the proposed control strategy,

the harmonic content is mitigated to 0.27% in grid-connected and 0.95% in islanded modes

respectively. The results are shown in Figure 36.

57

Parameter Value

DC Link Voltage Vdc=400V

Fundamental Frequency f=60Hz

Switching Frequency fz=10KHz

Sampling Time tz=10−3sec

Filter 2nd Order Low Pass

Cut-off Frequency fo=500Hz

Modulation Index m=0.85

TABLE IV

SIMULATION PARAMETERS FOR SVPWM BASED MICRO-GRID INVERTER

58

Figure 34. Output Voltages of Space Vector Modulation based Micro-grid Inverter

Figure 35. Voltage and Current Profile of the System before Proposed Control

59

Figure 36. Voltage and Current Profile of the System after Proposed Control

FFT analysis of output waveforms in Figure 37 proves the effectiveness of proposed control

strategy. It shows that the THD is finally reduced to 0.27% and with a fairly close fundamental

component of voltage i.e. 400V.

Figure 37. Harmonic Analysis of Voltages Injected by Controlled Micro-grid Inverter

60

4.2 Power Sharing Test

To maintain proper power sharing among the loads, droop control is required. Droop

control mainly refers to the frequency tuning of micro-gird inverter which is similar to the

traditional power system frequency adjustment. System voltage and frequency regulation can

decouple active power-frequency and reactive power-voltage droop curve. The voltage source

inverter (VSI) in a micro-grid configuration, acts like a voltage source with the magnitude and

frequency of the voltage controlled by respective droops and therefore emulating the behavior

of a synchronous machine. The methodology is described in detail in (39). MATLAB/Simulink

models of droop control based voltage source and droop control subsytem described in chapter

3 are shown in Figure 38 and Figure 39.

Figure 38. Droop Control based Voltage Source Model

For verification of power sharing considerations at system level, the system was simulated

under low voltage condition. Results are as desired (see Figure 40 and Figure 41). It can be

61

Figure 39. Droop Control Model for Active and Reactive Power Sharing

seen that when system voltage goes low and current goes higher, the controllers are able to

maintain appropriate power sharing and do not violate IEEE standard for power quality.

Figure 40. FFT Analysis; Low Voltage Operation I

62

Figure 41. FFT Analysis; Low Voltage Operation II

4.3 Reliability Test

DG has the potential to increase system reliability and power quality due to the decen-

tralization of supply. Increase in reliability levels can be obtained if DG is allowed to operate

autonomously in transient conditions. Thanks to the redundancy gained in parallel operation,

if a grid goes out, the micro-grid can continue seamlessly in islanded mode. The expense of

secondary on-site power backup is thus reduced or perhaps eliminated, because, in effect, the

micro-grid and main grid do this already (39).

The micro-grid paradigm provides a general platform to approach power management issues.

In terms of energy source security, that multiple small generators are more efficient than relying

on a single large one for lowering electric bills. Small generators are better at automatic load

following and help avoid large standby charges seen by sites using a single generator. Having

multiple DGs on a microgrid makes the chance of all-out failure much less likely (48).

63

For testing the reliability of the system under consideration, an over current relay has been built

so that when the fault happens, the relay opens for a duration of fault clearing and isolates the

grid from the distributed generation based micro-grids. This in one way, protects the whole

system and in the other way ensures uninterrupted power supply to the loads as micro-grids

can operate independently in islanded mode with their control mechanisms. Model of the sys-

tem with over current relay has been shown in the Figure 42. A parallel load has also been

connected for redundancy.

Figure 42. MATLAB/Simulink Model of the System with Over-current Relay and Parallel

Feeder Load

To verify that the system exhibits a real-time application, a fault condition has been simu-

lated on grid side in which a three phase fault occurs on the grid causing the system to switch

64

to off-grid or islanded mode. The fault is simulated at 0.15s and goes on for the duration of

0.06s. The system changes its state and after operating for 60ms goes back to the normal op-

erating state. This is demonstrated in Figure 43. Meanwhile the other energy sources continue

to supply energy to the system to ensure reliability. This proves the effectiveness of proposed

control scheme for quick system recovery maintaining reliability when the transients happen.

Figure 43. Pre and Post-fault Grid Phase Currents

CHAPTER 5

CONCLUSIONS AND FUTURE WORK

5.1 Conclusions

Distributed generation is replacing conventional power systems to a wide extent because of

its increased reliability, efficiency and the ability to integrate distributed energy resources in

it. If the issues associated with DG like power fluctuation and power quality can be addressed

effectively, the future grid can be made much more reliable, efficient and power dense. This

works puts forth effective modules to take care of power fluctuation problems in order to in-

crease micro-grid reliability, efficiency and power density. For that matter, loads are effectively

supplied from the main grid as well as distributed energy resources in case of grid absence.

The control of micro-grid inverter has been ameliorated with improved efficiency and dynamic

performance. A seamless and flexible real-time solution has been proposed to take care of key

issues related to power quality. Parametric results highlight the effectiveness and validation

of the approach in which system level power quality has been improved avoiding the need of

additional controllers for system integration as used to be done earlier. The flexibility of manip-

ulation and digital implementation renders it more useful in micro-grid inverter applications.

With these features, the system contributes to the research in terms of performance, sustain-

ability and economics. Furthermore, a comparison with previously reported results has been

65

66

Figure 44. Parametric Analysis of Total Harmonic Distortion (THD) in Different Control

Strategies Applied to Micro-grid

done in Figure 44 for validation of design scheme which shows that power quality is significantly

improved.

In order to study the transient behavior of the modeled system, a fault condition has been

simulated with the help of an over-current relay to check the recovery time of the system. It

is observed that the system has the capability to operate and switch between its states flexibly

and reliably even in case of transient conditions.

67

5.2 Future Work

In future, I plan to integrate other intermittent Distributed Energy Resources (DERs)

besides fuel cells and renewable energy sources like photovoltaic, wind turbines etc. within

the system and apply the control scheme. Power sharing for that case will also be studied

taking into account the intermittent nature of renewable energy sources. This work can be

extended to include energy storage techniques as well. The switches considered are ideal. Solid

state switches can be used to reduce internal and switching loses and dimensionality of the

problem can be increased as shown in Figure 45. A probabilistic model of fault conditions and

perturbations in various system parameters can also be integrated with it.

Figure 45. Distributed System with three DG Units

CITED LITERATURE

1. Marsdon, J.: Distributed generation systems: A new paradigm for sustainable energy.

2. DOE: The potential benefits of distributed generation and rate-related issues that mayimpede their expansion, 2007.

3. NREL: Using distributed energy resources, 2002.

4. Khan, U. N.: Impact of ditributed generation on electrical power network”.www.academia.edu.

5. Epri white paper, ”integrating distribution resources into electric utility distribution sys-tem”. Technology Review, 2011.

6. Lovins: Small is profitable: The hidden economic benefits of making electrical resourcesthe right size, 2002.

7. Mazidi, P. and Sreenivas, G. N.: Reliability assessment of a distributed generation con-nected distribution system. International Journal of Power System Operation andEnergy Management(IJPSOEM), 2011.

8. EUSUSTEL: European sustainable electricity; comprehensive analysis of future europeandemand and generation of european electricity and its security of supply. 2007.

9. Tsikalakis, A. and Hatziargyriou., N.: Environmental benefits of micro-grids operation.2006.

10. Joern Hoppmann, Jonas Volland, T. S. S. V. H. H.: The economic viability of batterystorage for residential solar photovoltaic systems - a review and a simulation model.2014.

11. Kaplan, S. M. and Sissine, F.: Smart grid: modernizing electric power transmission anddistribution. page 217, 2009.

12. Belmans, R.: Distribution grid. 2005.

68

CITED LITERATURE (Continued) 69

13. Lasseter, R.; Akhil, A. M. C. S. J. D. J. G. R. A. S. M. R. Y. and J., E.: White paper onintegration of distributed energy resources, the certs microgrid concept. TechnicalReport.

14. Piagi, P. and Lasseter, R. H.: Autonomous control of microgrids. 2006.

15. Savaghebi, M. Jalilian, A.: A new control strategy for distributed generation inter-face converters to compensate micro-grid harmonics. In International Symposiumon Power Electronics, Electrical drives, Automation and Motion, pages 908–913.

IEEE, 2010.

16. Savaghebi, M. Jalilian, A.: Voltage harmonic compensation of a micro-grid operating in is-landed and grid-connected modes. In Iranian Conference on Electrical Engineering,pages 1–6. IEEE, 2011.

17. Savaghebi, M. Jalilian, A. V. J. G. J.: Selective compensation of voltage harmon-ics in islanded micro-grid. In Power Electronics, Drive Systems and TechnologiesConference, pages 279–285. IEEE, 2011.

18. Zhou Niancheng, Chi Yuan, W. Q.: Control strategies for microgrid power quality en-hancement with back-to-back converters connected to a distribution network. In15th International Conference on Harmonics and Quality of Power, pages 384–389.IEEE, 2012.

19. Shabestary, S.M.A. Saeedmanesh, M. R.-K. A. J. E.: Real-time frequency and voltage con-trol of an islanded mode micro-grid. In Iranian Conference on Smart Grids, pages1–6. IEEE, 2012.

20. Dehghani, M.T. Vahedi, A. S.-M. G. J.: Voltage quality improvement in islanded microgridssupplying non-linear loads. In Power Electronics and Drive Systems Technology,pages 360–365. IEEE, 2012.

21. Pepermans G., Driesen J., H. D. B. R. D. W.: Distributed generation: Definition, benefitsand issues. Energy Policy, 36:787–798, 2005.

22. Schipman, K. and Delinc, F.: The importance of good power quality. 2010.

23. Nova Energy Specialists, L.: Interconnection of ditributed generation to power systemstraining course, 2013.

CITED LITERATURE (Continued) 70

24. Pilo, F. ; Celli, G. . M. S.: Improvement of reliability in active networks with intentionalislanding, 2004.

25. Bhowmik, A. ; Maitra, A. . H. S. . S. J.: Determination of allowable penetration levelsof distributed generation resources based on harmonic limit considerations. IEEETransactions on Power Delivery, 18:619–624, 2003.

26. Shahid, A. and Azhar, H.: A modular control design for optimum har-monic compensation in micro-grids considering active and reactive power shar-ing. In IEEE 16th, International Conference on Harmonics and Quality of Power(ICHQP), pages 601–605. IEEE, 2014.

27. El-Samahy, I. ; El-Saadany, E.: The effect of dg on power quality in a deregulated en-vironment. In Power Engineering Society General Meeting, IEEE, volume 3, pages2969–2976. IEEE, 2005.

28. DOE: Electric power annual report, 2011.

29. J.A. Pecas Lopes, N. Hatziargyriou, J. M. P. D. N. J.: Integrating distributed genera-tion into electric power systems: A review of drivers, challenges and opportunities.Electric Power Systems Research, 77:1189–1203, 2007.

30. Mathworks: Sim power systems; model and simulate electrical power systems.

31. Mathworks: Three-phase source.

32. Mathworks: Circuit breaker.

33. Hughes, T. P.: Networks of power: Electrification in western society. pages 119–122, 1993.

34. Mathworks: Three-phase transformer(two windings).

35. Standard, I.: Power transformer - part 1: General. 2000.

36. Mathworks: Three-phase pi section line.

37. Brown, R. E.: Electric Power Distribution Reliability. CRC Press, 2008.

38. Mathworks: Three-phase series rlc load.

CITED LITERATURE (Continued) 71

39. Piagi, P. and Lasseter, R. H.: Autonomous control of microgrids. In IEEE PowerEngineering Society General Meeting. IEEE, 2006.

40. Lasseter, R. H.: Microgrids. Technical report, 2002.

41. Lu, J. and Niu, M.: Overview on Microgrid Research and Development, volume 105. 2010.

42. Yongqin Gu, Peiqiang Li, Y. P. H. O. D. H. Y. H.: Development of microgrid coordinationand control overview. In IEEE Innovative Smart Grid Technologies Aisa (ISGTAsia), pages 1–6, 2012.

43. Peas Lopes, J.A. ; Moreira, C. . M. A.: Defining control strategies micro-grids islandedoperation. Transaction on Power Systems, IEEE, 21(2):916–924, 2006.

44. Dobakhshari, A.S. ; Azizi, S. . R. A.: Control of microgrids: Aspects andprospects. In Networking, Sensing and Control (ICNSC), Proceedings. 2006 IEEEInternational Conference on, pages 38–43. IEEE, 2011.

45. Majumder, R.: Defining control strategies micro-grids islanded operation. Transaction onPower Systems, IEEE, 28(3):3243–3252, 2013.

46. Tuo Dong, Linchuan Li, Z. M.: A combined system of apf and svc for power quality im-provement in microgrid. In IEEE Power Engineering and Automation Conference(PEAM), pages 1–4. IEEE, IEEE, 2012.

47. Rashid, M. H.: Power Electronics, Circuits, Devices and Applications. Prentice Hall, 2004.

48. Marnay, C. and Bailey, O.: The certs micro-grid and the future of macro-grid. Technicalreport, Technical report, 2004.

49. Kashif, S.A.R. ; Saqib, M. . Z. S. . K. A.: Implementation of neural network based spacevector pulse width modulation inverter-induction motor drive system. In ICEEThird International Conference on Electrical Engineering, pages 1–6. IEEE, 2009.

50. Ahmad, W. and Ali, S. M. U.: Comparative study of svpwm (space vector pulse width mod-ulation) and spwm (sinusoidal pulse width modulation) based three phase voltagesource inverters for variable speed drive. IOP Conference Series; Materials Scienceand Engineering, 2013.

CITED LITERATURE (Continued) 72

51. Kinsy, Khan, C. M. C. D.: Time predictable computer architecture for cyber-physicalsystems: Digital emulation of power electronic systems. In 32nd IEEE Real-TimeSystems Symposium (RTSS), pages 305–316. IEEE, 2011.

52. Le Xie ; Yun Zhang ; Ilic, M.: Multi-scale integration of physics-based and data-driven models in power systems. In IEEE/ACM Third International Conferenceon Cyber-Physical Systems (ICCPS), pages 129–137. IEEE, 2012.

53. Shahid, A.: A cyber-physical approach for stochastic hybrid control and safety verificationof smart grids. In IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia),pages 721–725. IEEE, 2014.

APPENDICES

73

74

Appendix A

SPACE VECTOR PULSE WIDTH MODULATION

Space vector pulse width modulation used for micro-grid inverter is described in detail in

this section. The selection and calculation times for switching the inverter are based upon the

Space Vector (SV) transformation as shown in Figure 46 (47).

Figure 46. Switching Sequence in Space Vector Pulse Width Modulation

Any three-phase set of variables that add up to zero in the stationary (abc) frame can be rep-

resented in a complex plane by a complex vector that contains a real (α) and an imaginary (β)

75

Appendix A (Continued)

component. For instance, the vector of three-phase line-modulating signals V abcc = [VcaVcbVcc]

T

can be represented by the complex vector−→Vc = V

αβc = [VcαVcβ]T by means of the following

transformation:

Vcα =2

3[Vcα − 0.5 (Vcb + Vcc)] (A.1)

Vcα =

√3

3[(Vcb − Vcc)] (A.2)

If the line-modulating signals V abcc are three balanced sinusoidal waveforms with an amplitude

V̂c and angular frequency ω,the resulting modulating signal in the αβ stationary frame becomes

a vector−→Vc = V

αβc of fixed module Vc which rotates at frequency ω as shown in Figure 47 (47).

Figure 47. Switching States and Sectors in Space Vector Modulation

76

Appendix A (Continued)

”SVPWM determines the on and off states of six switches used in inverter to control the

output voltage and frequency where the reference voltage vector always remains inside the poly-

gon” (49). The limit on maximum value of the reference voltage is defined by the case when an

inscribed circle of polygon is obtained. The arrangement of three switches forms eight switching

patterns (000, 100, 110, 010, 011, 001, 101, and 111). ”Sequence 000 and 111 short circuit the

load terminal therefore zero voltage across load while a hexagon is formed with six non-zero

vectors representing the voltage because of other switching sequences in d-q frame” (49).The

angle between two non-zero adjacent vectors is 60 degrees. Corresponding hexagon is shown in

Figure 45.

To ensure that the generated voltage in one one sampling period Ts is on average equal to the

vector−→Vc following expression should hold

−→Vc · Ts =

−→Vi · Ts +

−−→Vi+1 · Ti+1 +

−→Vz · Tz (A.3)

The solution of the real and imaginary parts of above equation gives

Ti = Ts · V̂c · sin(π

3− θ)

(A.4)

Ti+1 = Ts · V̂c · sin (θ) (A.5)

Tz = Ts − Ti − Ti+1 (A.6)

For different voltages, Ts remains the same whereas T1 and T2 are changed. ”To change

the frequency, rate of change of angle β is varied. Time it takes the reference vector to complete

77

Appendix A (Continued)

one revolution over the circle decides the output frequency” (49).

An observation shows that SVPWM exhibits superior performance due to less harmonic dis-

tortion (i.e. THD), greater power factor and less switching losses. ”SVPWM utilizes advance

computational switching technique to reduce THD. It also reduces switching losses because of

the changing of any one switching state which results in one single phase voltage change every

time” (50).

78

Appendix B

CYBER-PHYSICAL MODELING AND HYBRID CONTROL

The smart grid concept is an example of a complex cyber-physical system (CPS) that ex-

hibits intricate interplay between control, sensing, and communication infrastructure on one

hand, and power processing and actuation on the other hand (51). ”The extensive use of

computation, sensing, and communication, tightly coupled with power processing calls for a

fundamental reassessment of some of the prevailing paradigms in the real-time control and

communication abstraction” (51).

The electric power industry is being undergone by profound architectural changes as our so-

ciety is emphasizing more sustainable utilization of energy. On the physical power grid layer,

increasing presence of dispersed, heterogeneous, and variable resources such as wind, solar etc.

generation require major operating paradigm shift to ensure affordability and maximum relia-

bility. On the information layer, recent smart grid momentum leads to large-scale deployment

of sensing, computation, and communication technologies, which renders modeling and control-

ling dispersed resources such as frequency responsive loads based on available massive real-time

data (52).

The system studied in this thesis can also be modeled as a smart grid which is operated based

on stochastic nature of hybrid systems. This type of system models can capture the interaction

between probabilistic elements, discrete and continuous dynamics, and interplay between them.

Thus it can promise to be able to deal with the complexity of the system governing its ability

79

Appendix B (Continued)

to perform the operation safely in a real-time environment.

The control process of combination of micro-sources in different modes is discrete. For each

micro-source and the main grid itself, the control process is continuous. Therefore, a smart grid

is clearly a hybrid system (53). A finite Hybrid Automata (HA) can be formed for an operating

model of a smart grid in order to achieve hybrid control. The total number of power sources in

this system is three. A main grid G and two micro-grids A and B.

Figure 48. Control Modes showing Transitions among Sources

Turning on and off of main and micro grids involves different modes that can be represented

as discrete states and different combinations can be formed. According to the system described

above, there are eight possible modes of operation due to three sources of power. Each mode

shows a switching scheme for main and micro-grids. Assuming that system is always at least

reliable, Figure 48 shows different enumerated modes.

A, B and G are different states representing switching mode of each power source in the sequence

80

Appendix B (Continued)

[ABG]. Turn-on condition is represented by 1 and turn-off condition is represented by 0. G=1

in all states represents grid-connected mode and G=0 represents islanded mode. For the sake

of clarity, we observe that the state [110] representing G of islanded mode shows that both A

and B are ON while G is OFF which also indicates off-grid condition. From here, when B goes

OFF, the system moves to the state [100] which represents A where only one power source is

available.

To observe the system dynamic behavior, we study the transition probabilities for having a

fault condition as we ideally want our system to switch to the power sources which are not

affected by fault. For the sake of understanding the algorithm, lets assume that fault happens

on the system with 25% probability then we assign 0.25 probability value to fault operating

condition and 1-0.25=0.75 probability value to the normal operating condition which is shown

in the form of a state transition diagram with associated probabilities in Figure 49. Here I

represents fault condition in which system switches to islanded mode.

Figure 49. State Transition Diagram for Fault and Normal Operating States with Associated

Probabilities

81

Appendix B (Continued)

Probability matrix which is P = [0.75 0.25; 0.25 0.75] in this case, takes into account the

probability of transition among the states. It is desirable for the system that it changes its state

(possibly goes to islanded mode) with more probability when fault happens. This will ensure

the reliability of the supply. Probability analysis shows that for fault being more probable,

system is more likely to switch to the fault operating condition. For, example if there is a fault

on main grid G then system will switch to micro-grid A or B or both to ensure the supply to

the load centers. When fault is least likely, system will retain its normal state in grid-connected

mode where simple controls can do the job. Once the system goes to islanded mode, then

switching it back to grid-connected mode depends on the recovery time of the grid from fault

condition.

VITA

NAME: Ahsan Shahid

EDUCATION: B.S., Electrical Engineering, UET Lahore, 2012

M.S., Electrical and Computer Engineering, UIC, 2014

PUBLICATIONS: Ahsan Shahid; A Cyber-Physical Approach for Stochastic Hybrid Control

and Safety Verification of Smart Grids, IEEE PES ISGT, Asia, 2014.

Ahsan Shahid, Hasan Azhar; A Modular Control Design for Optimum Har-

monic Compensation in Micro-grids considering Active and Reactive Power

Sharing, 16th IEEE Int’l Conference on Harmonics and Quality of Power, 2014

Ahsan Shahid; Simulation based Analysis of Regenerative DC Motor Drives

for Vehicular Power Systems, 6th IEEE PES APPEEC, 2014.

Ahsan Shahid, Anwar Shabir; Microchip based Embedded System Design

for Achievement of High Power Factor in Electrical Power Systems, 5th IEEE

PES APPEEC, 2013.

EXPERIENCE: Teaching Assistant, UIC, 2012-2014.

82