Excerpt

## TABLE OF CONTENTS

**PREFACE **

**ACKNOWLEDGEMENTS **

**List of Tables**

**List of Figures **

**CHAPTER 1 **

**INTRODUCTION**

1.1 Background of work proposed

1.2 Definitions of Voltage Stability

1.2.1 Definitions according to CIGRE

1.2.2 Definitions according to Hill and Hiskens

1.2.3 Definitions according to IEEE

1.3 Literature Survey

1.4 Overview of work presented in the book

**CHAPTER 2 **

**PROBLEM DEFINITION**

2.1 Problem formulation and Approach

2.2 What is Voltage Instability Problem

2.3 Causes of Voltage Instability

2.4 Workflow

**CHAPTER 3 **

**MODEL AND COMPONENT DESCRIPTION**

3.1 IEEE 14 Bus Power System Network

3.2 Polynomial Loads

3.3 Static Var Compensator

3.4 Static Synchronous Compensator

**CHAPTER 4 **

**SOFTWARE FLOW ROUTINE**

4.1 Binary Search Algorithm

4.2 Fast Decoupled Load Flow Approach

4.3 Power System Analysis Toolbox

**CHAPTER 5 **

**RESULTS AND ANALYSIS**

5.1 Analysing the load models

**CHAPTER 6 **

**CONCLUSION AND FUTURE PROSPECTS**

6.1 Conclusion

6.2 Future Prospects

**BIBILOGRAPHY **

**APPENDIX **

## PREFACE

*A lot of research has happened in Electrical Engineering in the field of Power Engineering with regards to Power System Stability and related issues. The research work presented as part of this book only adds to this multitude of findings in the area of Load Modelling which plays an important role in Voltage Stability Analysis. We addressed the Voltage Instability issues arising in the presence of Polynomial Loads with Computational Intelligence as a tool to solve this issue.*

## ACKNOWLEDGEMENTS

*I wish to express my heartfelt and profound gratitude to management of Andhra Loyola Institute of Engineering and Technology in encouraging and extending their support to carry out such technical research work to enhance and empower our research abilities.*

* I would also like express my deep sense of gratitude and thank my family, friends and colleagues who have aided me in the completion of this work and guiding me in the right direction whenever necessary to execute this research book to be helpful to many a student, faculty and research community.*

## LIST OF TABLES

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## LIST OF FIGURES

Abbildung in dieser Leseprobe nicht enthalten

## CHAPTER 1

## INTRODUCTION

### 1.1 Background of work proposed

Modern power systems are continuously operating under much stressed conditions and this is making the system to operate closer to their thermal operating limits. Operation of power system is becoming difficult owing to the following reasons:

a. Increased competition in power sector.

b. Social and environmental burdens; resulting to limited expansion of transmission network.

c. Lack of initiatives to replace the old voltage and power flow control mechanisms.

d. Imbalanced load-generation.

Aforementioned factors are causing power system stability problems. A power system operating under stressed conditions shows a different behaviour from that of a non-stressed system. As the system is operating close to the stability limit, a relatively small disturbance is enough to push the system to become unstable. As the power system is normally a interconnected system, its operation and stability will be severely affected.

### 1.2 Definitions of Voltage Stability

In literature several definitions of voltage stability are found which are based on time frames, system states, size of disturbance etc. During voltage instability, a broad spectrum of phenomena will occur.

#### 1.2.1 Definitions according to CIGRE

CIGRE 1 defines voltage stability in a general way similar to other dynamic stability problems. According to CIGRE,

“A power system at a given operating state is small-disturbance voltage stable if, following any small disturbance; voltages near loads are identical or close to the pre-disturbance values”.

A power system at a given operating state and subject to a given disturbance is voltage stable if voltages near loads approach post-disturbance equilibrium values. The disturbed state is within the region of attraction of the stable post-disturbance equilibrium.

A power system undergoes voltage collapse if the post-disturbance equilibrium volt-ages are below acceptable limits.

#### 1.2.2 Definitions according to Hill and Hiskens

Hill and Hiskens have proposed definitions which define static and dynamic stability issues. For the system to be stable, the static stability definition with respect to the following must be true 3.

i. The voltages must be viable i.e. they must lie within an acceptable band.

ii. The power system must be in a voltage marginal operable point.

A marginal operating point implies that if reactive power is injected into the system or a voltage source increases its voltage, a voltage increase is expected in the network.

For the dynamic stability behaviour of the system the following are the concepts:

a. Small disturbance voltage stability: A power system at a given operating state is small disturbance stable if following any small disturbance, its voltages are identical to or close to their pre-disturbance equilibrium values.

b. Large disturbance voltage stability: A power system at a given operating state and subject to a given large disturbance is large disturbance voltage stable if the voltages approach post-disturbance equilibrium values.

Voltage collapse: A power system at a given operating state and subject to a given large disturbance undergoes voltage collapse if it is voltage unstable or the post-disturbance equilibrium values are nonviable.

#### 1.2.3 Definitions according to IEEE

According to IEEE 1, the following formal definitions of terms related to voltage stability are given:

“Voltage stability refers to the ability of a power system to maintain steady voltages at all buses in the system after being subjected to a disturbance from a given initial operating condition”.

It depends on the ability to maintain or restore equilibrium between load demand and power supply from the power system. Instability that may result occurs in the form of a progressive fall or rise of voltages of some buses. A possible outcome of voltage instability is loss of load in an area, or tripping of transmission lines and other elements by their protections leading to cascading outages that in turn may lead to loss of synchronism of some generators

### 1.3 Literature Survey

The fundamental concepts of power system modelling and operation by Prabha Kundur 11 defines voltage stability as "Voltage stability is concerned with the ability of a power system to maintain steady voltages at all buses in the system under normal operating conditions, and after being subjected to a disturbance".

The stability problems involved in power system operation are well presented in 1. Types of voltage stability and factors affecting it are well explained in 2.

Power system voltage stability by C W Taylor 2 has proposed as Power system synchronous or angle instability phenomenon limits power transfer, especially where transmission distances are long. This is well recognized and many methods have been developed to improve stability and increase allowable power transfers. The synchronous stability problem has been fairly well solved by fast fault clearing, thyristor exciters, power system stabilizers (PSSs), and a variety of other stability controls such as generator tripping. Fault clearing of severe short circuits can be less than three cycles and the effect of the faulted line outage on generator acceleration and stability may be greater than that of the fault itself. The severe multiphase short circuits are infrequent on extra high voltage (EHV) transmission networks. Nevertheless, more intensive use of available generation and transmission, more onerous load characteristics, greater variation in power schedules, and other negative aspects of industry restructuring pose new concerns. Recent large-scale cascading power network failures have levelled up the concerns.

Prabha Kundur 11 in his literature, Power System Dynamics and Stability has proposed a general description of the power system stability phenomena including fundamental concepts, classification, and definition of associated terms. A historical review of the emergence of different forms of stability problems as power systems evolved and of the developments of methods for their analysis and mitigation is presented. Requirements for consideration of stability in system design and operation are discussed.

Power flow analysis by I A Hiskens 3 is used extensively in the planning, design and operation of electrical systems. In power flow analysis, it is normal to assume that the system is balanced and that the network is composed of constant, linear, lumped-parameter branches. (In the most basic form of the power flow, transformer taps are assumed to be fixed. This assumption is relaxed in commercial power flows though.) Therefore nodal analysis is generally used to describe the network. However, because the injection/demand at bus bars is generally specified in terms of real and reactive power, the overall problem is nonlinear. Accordingly, the power flow problem is a set of simultaneous nonlinear algebraic equations. Numerical techniques are required to solve this set of equations

Hingorani and Gyugyi 4 present a practical approach to FACTS that will enable electrical engineers working in the power industry to understand the principles underlying this advanced system. Understanding Flexible AC Transmission System will enhance expertise in equipment specifications and engineering design, offering an informed view of the future of power electronics in AC transmission systems. The Flexible AC Transmission Systems (FACTS) -- a new technology based on power electronics offers an opportunity to enhance controllability, stability, and power transfer capability of AC transmission systems. Pioneers in FACTS and leading world experts in power electronics applications Narain G Hingorani and Laszlo Gyugyi have teamed together to bring you the definitive book on FACTS technology.

A study of effect of different static load models and system operating constraints and static voltage stability has proposed by Cheng Hong Gu uses continuation power flow to simulate P-V curves to analyze the effects of different load model and system operating constraints on power system static voltage stability. It is found that the critical points with ZIP and exponential function load model are relatively similar. While to restrict generators’ reactive power output, it would be unfavourable for voltage stability. Transmission line active and apparent power limits have quite similarly influences on voltage stability. But current limits are different, which are much serious. In addition, nodal voltage amplitude low limits are better among 0.90-0.95p.u and upper limits almost have no influences.

Continuation power flow (CPF) method proposed by Venkataramana Ajjarapu 8 was used for finding the continuous power flow solutions starting from base load condition to steady state voltage stability limit. The main difference between CPF and conventional power flow method can be observed as the operating point approaches critical point. In conventional power flow as the operating point comes close to critical point, power flow will not converge. In CPF method, divergence problem doesn't arise and it uses predictor-corrector 8 process to find the next operating point. As the critical point is approached, loading factor reaches maximum and starts decreasing. The tangent component corresponding to is zero at critical point and becomes negative after that. From the tangent vector, information about weak buses can be obtained.

V Ajjarapu in 8 presented computational techniques for voltage stability sssessment and control. V Ajjarapu and C Christy talked about continuation power flow tool for assessment of voltage stability in 9.

Voltage stability indices are helpful in determining the proximity of a given operating point to voltage collapse point. These indices are simple, easy to implement and computationally inexpensive. Voltage stability indices can be used for both on-line or o -line studies. In literature, several indices are proposed. Voltage stability indices are derived from power flow equations. Fast Voltage Stability Index (FVSI) proposed by I.Musirin et al. in 10 is applied for a standard IEEE 14 bus system at various loading scenarios. If the index value approaches one then it is inferred that voltage point is reached.

Power System Analysis Toolbox in short PSAT as termed by many 6 is a Matlab supportive toolbox for static and dynamic analysis and control of electric power systems. Federico Milano began writing PSAT in September 2001, while he was studying as Ph.D. student at the Universit´a degli Studi di Genova, Italy, and completed the first public version in November 2002, when he was a visiting scholar at the University of Waterloo, Canada.

Binary Search Algorithm 7 was proposed by Ancy Oommen. In computer science, a binary search or half-interval search algorithm finds the position of a specified input value within an array sorted by key value. For binary search, the array should be arranged in ascending or descending order. Advantages of binary search method are that it can interact poorly with the memory hierarchy (i.e. caching) because of its random-access nature. There are also disadvantages of binary search algorithm that is in any language we must provide an ordered list, usually an array, for the algorithm to search. Arrays are either static in size or, if dynamic, require special processing when they grow in size. A linked list does not work, because we need to make random access to the elements.

### 1.4 Overview of work presented in the book

Chapter 1 presents a brief introduction to voltage stability problem along with a detailed literature review

Chapter 2 details the problem statement of the proposed work presented as part of this book.

Chapter 3 presents the model and component description of systems being used and tested.

Chapter 4 discusses the methods adopted and material utilized in the research work.

Chapter 5 discusses the simulation results and necessary actions.

Chapter 6 concludes on the research work presented in this book and the scope for improvements to be observed in this area.

## CHAPTER 2

## PROBLEM DEFINITION

### 2.1 Problem formulation and Approach

Load modelling has been identified as an essential tool for voltage stability studies in order to address instability issues for any power system operating in long run. Load modelling has been addressed in 14 using cat swarm optimization for different static load models with a solution of UPFC in identifying its optimal size and location.

Accurate modelling of loads continues to be a difficult task due to several reasons. Lack of precise information on the composition of the load, changing of load composition with time like day and week, seasons, weather, through time and more such factors influence the load models. Electrical utility analysts and their management need evidence of the benefits in improved load representation to justify the effort and expense of collecting and processing load data along with modification of computer programs using load models.

The interest in load modelling has increased in the last few decades, and power system load modelling has become a new research area in power systems stability itself 5. Several studies have reported the critical effect of load representation in voltage related stability studies. This leads to identification of accurate load models than the traditionally used ones.

Though the wok presented here is a known theory to many a researchers, it happens to readdress stability issues by comparing two flexible AC transmission network devices namely Static Var Compensator and Static Compensator in terms of their performance in application to two of the very important load models commonly encountered namely Voltage Dependent load and frequency dependent load. We present a simple binary search procedure to locate and size of the power electronic devices.

### 2.2 What is Voltage Instability Problem?

Voltage stability problem is significant since it affects the power system reliability and security. Stability of voltage 2 is related to the ability of a power system to maintain acceptable voltages at all buses under normal and post perturbed operating conditions in a given power system network. Definitions proposed by various authors related to voltage stability are mentioned in Chapter 1. Voltage instability is an a-periodic, dynamic phenomenon. As most of the loads are voltage dependent and during disturbances, voltages decrease at a load bus will cause a decrease in the power consumption. However loads tend to restore their initial power consumption with the help of distribution voltage regulators (DVR), load tap changers (LTC) and thermostats. These control devices try to adjust the load side voltage to their reference voltage. The increase in voltage will be accompanied by an increase in the power demand which will further weaken the power system stability. Under these conditions voltages undergo a continuous decrease, which is small at starting and leads to voltage collapse.

When a single machine is connected to a load bus then there will be pure voltage instability. When a single machine is connected to infinite bus then there will be pure angle instability. When synchronous machines, infinite bus and loads are connected then there will be both angle and voltage instability but their influence on one another can be separated 2. The dynamics involved in voltage instability are restricted to load buses with LTC, restorative loads etc. These load voltage control devices are operated for few minutes to several minutes. So, generator dynamics can be substituted by appropriate equilibrium conditions. Under stressed conditions, coupling between voltage and active power is not weak 2. So, insufficient active power in the system also leads to voltage instability problems.

The following are the main contributing factors 2 to voltage instability problem.

- Increased stress on power system.

- Insufficient reactive power resources.

- Load restoring devices in response to load bus voltages.

- Unexpected and or unwanted relay operation following a drop in voltage magnitude.

- Line or generator outages.

- Increased consumption in heavy load centres.

Even though voltage instability phenomenon is dynamic in nature, both static and dynamic analysis methods 2 are used. To operate the system safely, system is to be analyzed for various operating conditions and contingencies. In most cases, the system dynamics affecting voltage stability are usually quite slow and much of the problem can be analyzed using static analysis that gives information about the maximum load-ability limit 3 and factors contributing to instability problem. Static approach involves computation of only algebraic equations and it is faster than dynamic approach. Static analysis takes less computational time compared to dynamic analysis and conventional power flow is used in the static analysis. A number of static voltage stability analysis methods 5 are proposed in the literature for analyzing the problem.

### 2.3 Causes of Voltage Instability

There are three main causes of voltage instability:

1. Load dynamics: Loads are the driving force of voltage instability. Load dynamics are due to the following devices.

Load tap changing (LTC) transformer role is to keep the load side voltage in a defined band near the rated voltage by changing the ratio of transformer. As most of the loads are voltage dependent, a disturbance causing a voltage decrease at a load bus will cause a decrease in the power consumption. This tends to favour stability. However, the LTC will then begin to restore the voltage by changing the ratio step by step with a predefined timing. The increase in voltage will be accompanied by an increase in the power demand which will further weaken the power system stability.

Thermostat will control the electrical heating. The thermostat acts by regularly switching the heating resistance on and off. In the case of a voltage decrease, the power consumption, hence the heating power will be reduced. Therefore, the thermostat will tend to supply the load during a longer time interval. The aggregated response of a huge group of this kind of loads is seen as a restoration of the power, comparable to the one of the LTC .Induction motors have dynamic characteristics with short time constants. Restoration process occurs following voltage reduction because the motor must continue to supply a mechanical load with a torque more or less constant.

2. Transmission system: Each transmission element, line or transformer, has a limited transfer capability. It is dependent on several factors like the impedance of the transmission element, the power factor of the load and the presence of voltage controlled sources (generators or Static Var Compensator-SVC) at one or both extremities of the element and the voltage set point of these sources.

The presence of reactive compensation devices (mechanically switched capacitors or reactors).

Generation system: When the power system flows increase, the transmission system consumes more reactive power. The generators must increase their reactive power output. Operating point of generator can be found from it's capability curve. But due to over-excitation limiter (OEL) and stator current limiter (SCL), voltage can't be controlled after this limiters are activated.

### 2.4 Workflow

STEP-1: Design the 14-bus power system based on the standard IEEE 14-bus power system data.

STEP-2: Perform power flow analysis

STEP-3: Connect the polynomial load models in the power system and run power flow.

STEP-4: Compare the voltage profile before and after placement of loads.

STEP-5: Incorporate the Static Var Compensator & STATCOM at optimal location through binary search procedure and run the power flow routine.

STEP-6: Compare voltage magnitude profiles and maximum load ability limit

## CHAPTER 3

## MODEL AND COMPONENT DESCRIPTION

### 3.1 IEEE 14 Bus Power System Network

We are testing our polynomial load model on IEEE 14 bus power network as shown in the figure 3.1 which was constructed with the help of power system analysis toolbox in matrix laboratory. The test system consists of twenty one branches, fourteen buses, and eleven loads totalling 259 MW with 81.4 MVAR. The tolerance limit for bus voltages in P.U. was assumed to be 5%. Bus 1 is assumed as slack bus. We are applying continuation power routine with fast decoupled iterative approach. The number of iteration limit in power flow routine is set to twenty counts.

Abbildung in dieser Leseprobe nicht enthalten

Figure 3.1: IEEE 14 Bus Power System Network

### 3.2 Polynomial Loads

One of the commonly observed load model at most of the distribution centres is a polynomial load. The approach that can be employed in modelling this polynomial load is the constant impedance, constant current and constant power classes commonly called the ZIP model 6. Constant impedance load examples include residential loads and lighting loads such as bulbs etc. Constant current load examples include transistors, transducers and incandescent lamps. Constant power loads are switching regulators and industrial loads. A constant current load is the one which varies its internal resistance to achieve a constant current regardless of the voltage which is being fed to it (within certain extent) and therefore the power will vary.

A constant power load varies it's impedance on change of input voltage to keep the power constant. A good example of a constant power load is a switching regulator. Since this has to maintain its power into its load, it must draw the same power from its source even if the source changes voltage.

The polynomial or ZIP loads are loads whose powers are a quadratic expression of the bus voltage, as follows:

Abbildung in dieser Leseprobe nicht enthalten

Where, V0 is the initial voltage at the load bus as obtained by the load ﬂow solution, g is the conductance, IP is active current, Pn is active power, b is susceptance, IQ is reactive current and Qn is reactive power.

ZIP loads can be included directly in the power ﬂow analysis in which case, the initial voltage is not known V0, thus the following equations will be used:

Abbildung in dieser Leseprobe nicht enthalten

### 3.3 Static Var Compensator

A Static VAR Compensator 4 is a set of electrical device for providing fast-acting reactive power on high-voltage electricity transmission networks. Static VAR compensator in short SVC is part of the flexible AC transmission system device family, regulating voltage, power factor, harmonics and stabilizing the system. Unlike a synchronous condenser which is a rotating electrical machine, a static VAR compensator has no significant moving parts (other than internal switchgear). Prior to the invention of the SVC, power factor compensation was the preserve of large rotating machines such as synchronous condensers or switched capacitor banks.

**[...]**

- Quote paper
- Gutha Naveen Kumar (Author), 2019, Power Transmission Network Security under Loaded Conditions, Munich, GRIN Verlag, https://www.grin.com/document/498580

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