Modelling and control coordination of power systems with facts devices in steady state operating mode

LIST OF PRINCIPAL SYMBOLS SYMBOLS USED IN CHAPTER 2 V, I vectors of the nodal voltages and nodal currents respectively |V|, θ vectors of the system voltage magnitudes and phase angles

Modeling and Control Coordination of Power Systems with FACTS Devices in

Steady-State Operating Mode

by Van Liem NGUYEN

Achieving International Excellence

This thesis is presented for the degree of Doctor of Philosophy

of The University of Western Australia

Energy Systems Centre School of Electrical, Electronic and Computer Engineering

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my supervisor, Associate Professor T T Nguyen, for providing me the opportunity to undertake this research, along with his excellent guidance, constant support and invaluable encouragement throughout my PhD candidature at The University of Western Australia

I would like to thank the staff at the Energy Systems Centre for their assistance and the use of the facilities of the Centre Thanks are also extended to all the postgraduate students studying at the Energy Systems Centre for their friendship, support and encouragement

I would like to express my boundless gratitude towards my parents, especially my beloved Father who passed away during the course of my PhD study, my sisters and brothers for their love and constant encouragement throughout my study I would also like to thank my wife, Kim Loan, for her love, patience, support and understanding during every stage of my life and my work Thanks also go to my loved children, Thanh Luan and Ngoc Lam, who give me the motivation and objective to work and study I would like to dedicate the thesis to my family

Finally, I would like to express my special appreciation to the scholarship granted by the Government of Vietnam through Project 322, the Ad hoc scholarship awarded by the Energy Systems Centre and SIRF Scholarship provided by The University of Western Australia

ABSTRACT

This thesis is devoted to the development of new models for a recently-implemented FACTS (flexible alternating current transmission system) device, the unified power flow controller (UPFC), and the control coordination of power systems with FACTS devices in steady-state operating mode The key objectives of the research reported in the thesis are, through online control coordination based on the models of power systems having FACTS devices, those of maximising the network operational benefit and restoring system static security following a disturbance or contingency

Based on the novel concept of interpreting the updated voltage solutions at each iteration in the Newton-Raphson (NR) power-flow analysis as dynamic variables, the thesis first develops a procedure for representing the unified power flow controllers (UPFCs) in the steady-state evaluation Both the shunt converter and series converter control systems of a UPFC are modeled in their dynamical form with the discrete time variable replaced by the NR iterative step in the power-flow analysis The key advantage of the model developed is that of facilitating the process of UPFC constraint resolution during the NR solution sequence Any relative priority in control functions pre-set in the UPFC controllers is automatically represented in the power-flow formulation

Although the developed UPFC model based on the dynamic simulation of series and shunt converter controllers is flexible and general, the number of NR iterations required for convergence can be large Therefore, the model is suitable mainly for power system planning and design studies For online control coordination, the thesis develops the second UPFC model based on nodal voltages The model retains all of the flexibility and generality of the dynamic simulation-based approach while the number of iterations required for solution convergence is independent of the UPFC controller dynamic responses

Drawing on the constrained optimisation based on Newton’s method together with the new UPFC model expressed in terms of nodal voltages, a systematic and general method for determining optimal reference inputs to UPFCs in steady-state operation is

developed The method is directly applicable to UPFCs operation with a high-level line optimisation control (LOC) for maximising the network operational benefit By using a new continuation technique with adaptive parameter, the algorithm for solving the constrained optimisation problem extends substantially the region of convergence achieved with the conventional Newton’s method

Having established the foundation provided by the comprehensive models developed for representing power systems with FACTS devices including the UPFC, the research,

in the second part, focuses on real-time control coordination of power system controllers, with the main purpose of restoring power system static security following a disturbance or contingency

At present, as the cost of phasor measurement units (PMUs) and wide-area communication network is on the decrease, the research proposes and develops a new secondary voltage control where voltages at all of the load nodes are directly controlled, using measured voltages The new secondary voltage control avoids the possible degradation of the performance of the existing coordinated secondary voltage control which is based on the direct voltage control at only a limited number of load nodes The control strategy developed is fully adaptive to any changes in loads and/or system configuration

However, to achieve the lowest possible system operating cost, real-time corrective control rather than preventative control is required Depending on the nature of the disturbance or contingency, secondary voltage control might not be able to provide the necessary corrective control to restore power-flow security In order to provide a comprehensive control scheme which has the capability of restoring power system static security in its entirety, the final research contribution made in the thesis is that of developing a coordinated secondary control scheme for restoring voltage and/or power-flow security subsequent to a disturbance/contingency, and, simultaneously, minimising the network active- or reactive-power loss The active- or reactive-power loss minimisation leads to optimal reactive-power schedule for generators and compensators together with system voltage profile while only a limited number of load nodes referred

to as the pilot nodes are selected for direct control In addition to the voltage control function, the new scheme includes FACTS devices of the series form or UPFC to

achieve the corrective control for removing transmission circuit overloading For enhancing the accuracy in control and coordinating the time responses of the power system primary controllers and secondary control, each secondary control cycle is subdivided into a number of steps which is adaptive to the nature of the disturbance/contingency

State-of-the-art computer systems for implementing the comprehensive secondary control law developed are referred to, and discussed in the thesis

LIST OF PRINCIPAL SYMBOLS

SYMBOLS USED IN CHAPTER 2

V, I vectors of the nodal voltages and nodal currents respectively

|V|, θ vectors of the system voltage magnitudes and phase angles

respectively

f vector function associated with nonlinear power-flow equations

h vector function associated with operating limits of individual

power system elements

|V hsvc |, V svcref SVC high-voltage node voltage magnitude and its reference,

respectively

(inductive) limit values respectively

P lsvc SVC low-voltage node active-power

X tcr(α) variable inductive reactance

X tcsc(α) TCSC effective reactance

αLlim, αClim TCSC delay angle limits in inductive region and capacitive

region respectively

X Llim , X Clim TCSC inductive reactance and capacitive reactance limits

respectively

P line , P linesp transmission line active-power flow and its specified value,

respectively

reactance limits respectively

reference, respectively

SYMBOLS USED IN CHAPTER 3

V E , V B UPFC shunt converter and series converter voltage sources,

respectively

V K , V L , V i voltage phasors at nodes K, L and i, respectively

|V B|, θB UPFC series converter voltage magnitude and phase angle,

Z E , Z B UPFC shunt converter and series converter coupling transformers

leakage impedances, respectively

Y E , Y B UPFC shunt converter and series converter coupling transformers

admittances, respectively

Y Ki element (K,i) of network nodal admittance matrix

P Ksp , Q Ksp specified active- and reactive-power load demands at node K,

respectively

f PEB residual function associated with the net active-power exchange

between the UPFC and the network

f Vupfc , f Pupfc , f Qupfc residual functions associated with the voltage control,

active-power control and reactive-active-power control, respectively, of the UPFC of the UPFC

V ref , P ref , Q ref UPFC reference values for the voltage magnitude, active-power

flow and reactive-power flow respectively

X B , X E UPFC series converter and shunt converter coupling transformers

inductive reactance respectively

|Y B|, αB UPFC series converter coupling transformer admittance module

and angle, respectively

P Kinj , Q Kinj total active- and reactive-power injections of the UPFC at node K

P KM0 , Q KM0 active- and reactive-power flows in the transmission line between

nodes K and M after the removal of the UPFC series voltage source

P Minj , Q Minj active- and reactive-power injections of the UPFC at node M

Z KM impedance of the transmission line between node K and M

transmission line reactive-power flow at node K

operation related to the voltage control function at node K

SYMBOLS USED IN CHAPTER 4

V ref , P ref , Q ref UPFC voltage, active-power and reactive-power references,

respectively

V K (t) voltage phasor at node K at t

reference for voltage magnitude at node K

I E (t) shunt converter current phasor at t

V dc (t), V dcref DC voltage at t and its reference value

I Ep (t), I Eq (t) in-phase and quadrature components, respectively, of the UPFC

shunt converter current at t with respect to the reference given by

V K (t)

I Epref (t), I Eqref (t) in-phase and quadrature components, respectively, of required

shunt converter current at t

V Ep (t), V Eq (t) in-phase and quadrature components, respectively, of the shunt

converter voltage source at t

|V E (t)|, θ E (t) magnitude and phase angle, respectively, of the shunt converter

voltage source at t

θK (t) phase angle of voltage phasor V K (t)

V L (t), V K (t) voltage phasors of nodes L and K, respectively, at t

I B (t) UPFC series converter current phasor at t

V Bp (t), V Bq (t) in-phase and quadrature components of the UPFC series

converter voltage at t

|V B (t)|, θ B (t) magnitude and phase angle, respectively, of the UPFC series

converter voltage at t

V K (p), V L (p) voltage phasors of node K and L, respectively, at step p

V B (p), I B (p) UPFC series converter voltage and current phasor, respectively,

at step p

θK (p) phase angle of the voltage phasor of node K at step p

I Bp (p), I Bq (p) in-phase and quadrature components, respectively, of the UPFC

series converter current phasor with respect to the reference given

by V K (p) at step p

I Bpref (p), I Bqref (p) in-phase and quadrature components, respectively, of the required

UPFC series converter current phasor at step p

∆I Bp (p), ∆I Bq (p) differences between the in-phase and quadrature components of

the UPFC series converter current phasor and their required

values, respectively, at step p

P B (p) active-power exchange between the UPFC shunt and series

converters at step p

∆V K (p) difference between the voltage magnitude of node K and its

reference value at step p

V Bp (p+1), V Bq (p+1) in-phase and quadrature components of the UPFC series converter

voltage phasor at step p+1

|V B (p+1)|, θ B (p+1) magnitude and phase angle, respectively, of the UPFC series

converter voltage phasor at step p+1 phase angle of the series converter voltage phasor at step p+1

|V B (p+1)|, θ B (p+1) magnitude and phase angle, respectively, of the UPFC series

converter voltage at step p+1

I Ep (p+1), I Eq (p+1) in-phase and quadrature components of the UPFC shunt

converter current phasor at step p+1

I E (p+1), ψ E (p+1) magnitude and phase angle, respectively, of the UPFC shunt

converter current at step p+1

X B UPFC series converter transformer reactance

K 1 , K 2 , K 3 coefficients derived from the UPFC controller gains

V Bmax maximum allowable limit of the UPFC series converter voltage

magnitude

V Lmin , V Lmax minimum and maximum allowable limits of the UPFC line side

voltage magnitude respectively

P Bmax maximum allowable limit of active-power exchange between the

UPFC shunt and series converters

I Bmax maximum allowable limit of the UPFC series converter current

I Emax maximum allowable limit of the UPFC shunt converter current

k Newton-Raphson iterative step in the range where the second

level of control is active

P line active-power flow in the transmission line controlled by UPFC

SYMBOLS USED IN CHAPTER 5

V F , |V F |, θ F voltage phasor, its magnitude and phase angle, respectively, at

node F

I Ep , I Eq active-power and reactive-power components of the UPFC shunt

converter current, respectively

P Ksp , Q Ksp specified active- and reactive-power at node K respectively

αref reference value for the UPFC phase shift between the line side

voltage V L and busbar voltage V K

V Bref, θBref series voltage magnitude and phase angle reference signal inputs

to the UPFC

V Lref reference value for the UPFC line-side voltage reference

P E , P Emax active-power flow in the DC link and its maximum limit,

respectively

SYMBOLS USED IN CHAPTER 6

V ref , V refopt desirable and optimal values, respectively, of the UPFC voltage

reference

Q Shref , Q Shrefopt desirable and optimal values, respectively, of the UPFC

high-voltage side node reactive-power reference

P ref , P refopt desirable and optimal values, respectively, of the UPFC

V Bref , V Brefopt desirable and optimal values, respectively, of the UPFC series

voltage magnitude reference

θBref, θBrefopt desirable and optimal values, respectively, of the UPFC series

voltage angle reference

Z ref , Z refopt desirable and optimal values, respectively, of the UPFC series

impedance reference

x i , X refi the ith elements of vector x and X ref, respectively

W i weighting factor associated with x i

S k , S spk apparent power flow in transmission line k at either sending- or

receiving end, and the specified value to which power flow S k is

W weighting factors associated with S k and V l, respectively, which

reflect the relative priority in control assigned to the individual controlled quantities

S ks , S kr apparent power flows at the sending- and receiving-end of

transmission line k, respectively

Z L , Y L series impedance and shunt admittance of the transmission line

W V , W P , W Q weighting factors associated with voltage, active- and

reactive-power flow controls, respectively

|V C |, P C , Q C voltage magnitude at node C, active- and reactive-power flows on

transmission line SC at node C

SYMBOLS USED IN CHAPTER 7

|V pl |, V plsp , V n measured, set-point and nominal values, respectively, of the

voltage magnitude at the pilot node

generator i

|V geni |, V refgeni measured and reference values, respectively, of the voltage

magnitude of generator i

∆V refgeni variation of the voltage magnitude reference of generator i

I exi exciter current of generator i

Q n nominal reactive-power of the controlling generator

V plsp vector of the set-point voltage magnitudes at the pilot nodes

Q gensp vector of the set-point reactive-power of the controlling

generators

V 0 refgen vector of the pre-specified voltage references for the controlling

generators

|V plk| measured voltage magnitude at pilot node k

|V geni |, V refgeni measured and reference values, respectively, of the voltage

magnitude of controlling generator i

Q geni measured reactive-power of controlling generator i

I exi exciter current of generator i

n gen number of controlling generators

αC control gain of the coordinated secondary voltage control

p , (p+1) current step and next step, respectively, of the control procedure Notation ||.|| norm of a vector

C Vpl sensitivity matrix associated with voltage variations at pilot nodes

to the voltage reference variations of the controlling generators

C Q sensitivity matrix associated with the generator reactive-power

variation to the voltage reference variations of the controlling generators

λV, λQ, λU weighting factors associated with the pilot node voltages,

controlling generator reactive-powers and controlling generator terminal voltage references, respectively

∆V genmax vector of the maximum allowable variations of the controlling

generator voltage magnitudes

V plmin ,V plmax vectors of the minimum and maximum allowable voltages at pilot

nodes

V senmin , V senmax vectors of the minimum and maximum allowable voltage

magnitudes at the sensitive nodes

V hgenmin , V hgenmax vectors of the minimum and maximum allowable voltage

magnitudes at the high voltage side of the controlling generators

V vector of the measured voltage magnitudes at the high-voltage

sides of controlling generators

C Vsen sensitivity matrix associated with voltage variation at the sensitive

nodes to the voltage reference variations of the controlling generators

C hgen sensitivity matrix associated with voltage variation at the high

voltage side nodes of the controlling generators to the voltage reference variations of the controlling generators

a, b and c diagonal matrices the diagonal elements of which are coefficients

of the straight lines representing operating diagrams for the controlling generators (P,Q,V)

ED ij electrical distance between nodes i and j

sensitivities of the voltage magnitude change at nodes i and j to

their injected reactive-power change, respectively

sensitivity of the voltage magnitude change at node j to the

injected reactive-power change at node i

sensitivity of the voltage magnitude change at node i to the

injected reactive-power change at node j

SYMBOLS USED IN CHAPTER 8

P load , Q load vectors of the load node active- and reactive-power, respectively

∆P load , ∆Q load vectors of the active- and reactive-power variations at load nodes

of the slack node

∆θ vector of the changes in nodal voltage phase angles excluding that

of the slack node which is chosen as the phase angle reference

P gen vector of the generator active-power

∆P gen vector of the generator active-power variations

|V gen| vector of the voltage magnitudes at the generator terminals

∆|V gen| vector of the changes in voltage magnitudes at the generator

terminals

∆V genref vector of the changes in the reference inputs to the excitation

controllers

P lsvc vector of nodal active-power at the nodes on the low voltage sides

of the SVC coupling transformers

∆P lsvc vector of the active-power variation at the nodes on the low

voltage sides of the SVC coupling transformers

|V hsvc| vector of the voltage magnitudes at the nodes on the high voltage

sides of the SVC coupling transformers

a svc diagonal matrix the elements of which are reactance slopes of

SVCs

V svcref vector of the SVC voltage references

∆V svcref vector of the changes in the SVC voltage references

P lsta vector of nodal active-power at the low voltage side nodes of the

STATCOM coupling transformers

|V hsta | vector of voltage magnitudes at high voltage side nodes of the

STATCOM coupling transformers

a sta diagonal matrix the elements of which are reactance slopes of

STATCOMs

∆V staref vector of the changes in the STATCOM voltage references

n node number of the power system nodes

∆|V L| vector of the changes in the load nodes voltage magnitudes

∆|V C| vector of the changes in the voltage magnitudes of the slack node,

generator nodes, low-voltage side nodes of SVCs and STATCOMs

C v system voltage sensitivity matrix which gives the linear relation

between the system voltage variation and the changes in controllers references

C vL , C vC submatrices of matrix C v associated with ∆|V L | and ∆|V C|,

respectively

Q gen vector of the generator reactive-powers

V target vector of the specified target voltage magnitudes at the load

nodes

ε vector of the differences between the specified target values and

the current values of voltage magnitudes at the load nodes

∆V Cmin , ∆V Cmax vectors of the deviations between the current operating voltage

magnitudes and the allowable minimum and maximum voltage magnitudes of the slack node, generator nodes, low-voltage nodes

of SVCs and STATCOMs

∆Q genmin , ∆Q genmax vectors of the differences between the minimum and maximum

reactive-power limits of generators, respectively, and their current operating reactive-powers

∆B svcmin , ∆B svcmax vectors of the differences between the inductive limits and

capacitive limits of SVCs, respectively, and their current operating susceptances

∆I stamin , ∆I stamax vectors of the differences between the minimum and maximum

current limits of STATCOMs, respectively, and their operating currents

0

ref

V vector of the current controllers reference settings

V ref vector of optimal reference settings for the controllers

SYMBOLS USED IN CHAPTER 9

X tcsc , X tcscref TCSC reactance and its reference value, respectively

stcsc , rtcsc TCSC sending-end and receiving-end node nodes, respectively

system excluding the TCSC

system excluding the TCSC

V stcsc , V rtcsc nodal voltages at nodes stcsc and rtcsc, respectively

values, respectively, of the TCSC reactance

∆Xtcsc TCSC reactance variation

∆Xtcscmin, ∆Xtcscmax differences between the TCSC minimum and maximum reactance

limits, respectively, and the TCSC reactance at the current operating condition

∆X tcsc vector of the changes in TCSC reactances

∆X tcscref vector of the changes in TCSC reactances references

P tcsc, Q tcsc vectors of the nodal active- and reactive-power at nodes stcsc’s of

all TCSCs, respectively

∆X tcscmin , ∆X tcscmax vectors of the differences between the minimum and maximum

reactance limits of TCSCs and their reactance at the current operating condition, respectively

∆R ref vector of the changes in the reference input signals to controllers

S S , S R apparent power flows at the sending-end and receiving-end

∆V min , ∆V max vector of deviations between the allowable minimum and

minimum values and the current operating values of system voltage magnitudes, respectively

∆X tcscmin , ∆X tcscmax vectors of the differences between the minimum and maximum

reactance limits of TCSCs (they are dynamic limits depending on the TCSC operating condition), respectively, and their current operating reactance

∆S bmax vector of the differences between the maximum power flow limits

of all branches and their current operating apparent power flow

SYMBOLS USED IN CHAPTER 10

R upfcref vector of UPFC reference settings for controlled quantities

f C , f R , h vector functions in the UPFC steady-state model associated with

circuit constraints, control functions and operating limits

P upfcref , Q upfcref reference settings for the active- and reactive-power flows

∆R upfcref vector of the changes in UPFC reference input settings

h 0 value of vector h at the current operating point

P gensp , V gensp scheduled active-power generation of the generator and the

specified voltage magnitude at the generator terminal, respectively

P Hsp , Q Hsp specified active- and reactive-power demands at the high-voltage

side node of the transformer, respectively

|V G |, |V H| voltage magnitudes at the low- and high-voltage side nodes of the

transformer, respectively

node of the transformer

P H , Q H nodal active- and reactive-power at the high-voltage side node of

the transformer, respectively

T min , T max minimum and maximum values, respectively, of the LTC

transformer voltage ratio

∆T ltc vector of the changes in LTC transformer voltage ratios

∆R ref vector of the changes in reference input signals to controllers,

which can include generators, SVCs, STATCOMs, TCSCs, UPFCs and LTC transformers

∆V ltcref vector of the changes in the LTC transformer voltage references

∆V upfcref vector of the changes in the UPFC voltage

∆P upfcref , ∆Q upfcref vectors of the changes in the UPFC active- and reactive-power

references, respectively

∆R ref1 vector of the changes in reference input signals to the subset of

controllers, which participate in the secondary control

∆|V| 1, ∆θ1 vectors of the changes in voltage magnitudes and phase angles at

the pilot nodes, important nodes together with those at other nodes, which are needed for forming the changes in circuit power flows, controller operating quantities and objective function

∆T ltc1 , ∆X tcsc1 vectors of the changes in LTC transformers voltage ratios and

TCSCs reactances, respectively, which participate in the secondary control

Q gen, Qsl, Q com total reactive-powers generated from generators, slack node and

compensators, respectively

Q load total reactive-power consumed by loads

Q loss , Q gain total reactive-power loss in the series reactances and the total

reactive-power gain from shunt-path capacitances of transmission circuits, respectively

C vpl matrix partition of C v associated with the pilot nodes, which gives

the sensitivity of the pilot node voltage magnitudes with the control variables

|

|V pli0 initial value for the voltage magnitude of pilot node i immediately

after a contingency/disturbance

|V pli| measured value for the voltage magnitude of pilot node i in

response to secondary control

C L sensitivity matrix associated with constrained quantities

C S submatrix of the sensitivity matrix C L associated with the power

flows in the critical transmission circuits

S 0 , S max vectors of the current circuit loadings in the critical transmission

circuits and their maximum allowable limits, respectively

βmax, βmin upper and lower allowable limits of the changes in apparent

power flow, respectively

C H matrix partition of C L associated with controller operating

quantities, which gives their sensitivities with the control variables

H 0 , H min , H max vectors of the current values for controller operating quantities,

their minimum and maximum values, respectively

R ref10 vector of the current reference settings for controllers

R ref1min , R ref1max vectors of the minimum and maximum allowable values for

controllers reference setting, respectively

GLOSSARY

FACTS Flexible Alternating Current Transmission System

IGBT Insulated Gate Bi-polar Transistor

TCSC Thyristor Controlled Series Capacitor

TVR Tertiary Voltage Control

TABLE OF CONTENTS

Chapter 1 Introduction 1

1.1 BACKGROUND AND SCOPE OF THE RESEARCH 11.2 OBJECTIVES 31.3 OUTLINE OF THE THESIS 41.4 CONTRIBUTIONS OF THE THESIS 6

Chapter 2 Review of Steady-State Models of Power System Elements 8

2.1 INTRODUCTION 82.2 NODAL FORMULATION OF POWER SYSTEM MODEL 92.3 FACTS DEVICES MODELS 112.3.1 Modeling principle 122.3.2 Static VAr compensator (SVC) 122.3.3 Thyristor controlled series capacitor (TCSC) 172.3.4 Static synchronous compensator (STATCOM) 242.4 FACTS DEVICE CONTROLLER 282.4.1 General 282.4.2 FACTS controller input signal derivation 292.4.3 Application of the dq0 transformation for phasor calculation 302.5 SYSTEM MODEL 322.6 CONCLUSION 33

Chapter 3 Review of Steady-State Models of UPFC 34

3.1 INTRODUCTION 343.2 UPFC STRUCTURE AND OPERATING PRINCIPLES 353.3 POWER LOSSES IN UPFC OPERATING CONDITION 373.4 UPFC CONTROL MODES AND OPERATING LIMITS 393.4.1 Shunt Converter 393.4.2 Series Converter 40

3.4.3 Stand alone shunt and series compensation 423.4.4 Operating limits 423.5 DECOUPLED UPFC MODEL 433.6 TWO-VOLTAGE SOURCE MODEL 453.7 POWER INJECTION MODEL 513.8 IDEAL TRANSFORMER UPFC MODEL 583.9 CONCLUSIONS 59

Chapter 4 Dynamic Simulation-Based UPFC Steady-State Model 60

4.1 INTRODUCTION 604.2 UPFC DYNAMICAL MODEL 614.3 UPFC DYNAMICAL REPRESENTATION

IN POWER-FLOW ANALYSIS……….……… 664.3.1 Principle 664.3.2 Implementation for Power-flow Analysis 664.4 SERIES VOLTAGE SOURCE 714.4.1 Definitions 714.4.2 Transfer Function Simulation 714.5 SHUNT CURRENT SOURCE 734.5.1 Definition 734.5.2 Transfer Function Simulation 734.6 UPFC SECOND LEVEL CONTROL 744.7 SIMULATION RESULTS 774.7.1 System Configuration 774.7.2 Case Study 1 774.7.3 Case Study 2 804.7.4 Case Study 3 854.8 CONCLUSION 90

Chapter 5 Nodal-Voltage Model of UPFC 92

5.1 INTRODUCTION 925.2 NEW UPFC MODEL DEVELOPMENT PRINCIPLES 935.3 UPFC NEW MODEL EQUATIONS 965.3.1 Circuit Constraints 965.3.2 Interaction between the Shunt Converter and Series Converter 975.3.3 Control Function Equations 975.3.4 Discussion 1015.4 UPFC INEQUALITY CONSTRAINTS 1035.4.1 General 1035.4.2 Shunt Converter Current Limit 1035.4.3 Active-Power Exchange Limit 1045.4.4 Series Injected Voltage Limit 1055.4.5 Series Converter Current Limit 1055.4.6 Line-side Voltage Limit 1065.5 COMPARISON BETWEEN THE NEW UPFC MODEL

AND OTHER ONES………1065.5.1 Two-Voltage Source Model 1065.5.2 Power Injection Model 1075.6 CONCLUSIONS 107

Chapter 6 Application of Nodal-Voltage UPFC Model for LOC 109

6.1 INTRODUCTION 109

COMBINED WITH LOC 1106.2.1 Principal Concepts 1106.2.2 OPF Formulation with Specified UPFC References 1136.2.3 OPF Formulation without Pre-specification of UPFCs References 1146.3 SOLUTION PROCEDURE BY NEWTON’S METHOD 118

6.4 APPLICATION OF THE CONTINUATION METHOD 1226.4.1 General Concept 1226.4.2 Adaptive Scheme 1226.5 CASE STUDY 4 1266.5.1 Power System Description 1266.5.2 Performance Study with Series Compensation 1276.5.3 UPFC Application Studies 1286.6 CONCLUSIONS 130

Chapter 7 Review of Secondary Voltage Control in Transmission Network 131

7.1 INTRODUCTION 1317.2 VOLTAGE CONTROL REQUIREMENTS 1327.3 HIERARCHICAL VOLTAGE CONTROL STRUCTURE 1337.3.1 General 1337.3.2 Primary voltage control 1347.3.3 Secondary voltage control 1357.3.4 Tertiary voltage control 1367.4 SECONDARY VOLTAGE CONTROL SCHEMES 1377.4.1 Former Secondary Voltage Control 1377.4.2 Coordinated Secondary Voltage Control (CSVR) 1427.5 PILOT NODE SELECTION 1517.5.1 General 1517.5.2 Simple rule 1527.5.3 Combined electrical distance and typology analysis 1537.5.4 Optimisation-based selection using linearised network model 1547.5.5 Optimisation-based selection using nonlinear network model 1557.6 CONCLUSION 155

Chapter 8 Application of Wide-Area Network of Phasor Measurements for Secondary Voltage Control in Power Systems with FACTS Controllers 157

8.1 INTRODUCTION 157

8.3 SENSITIVITY MATRIX OF POWER SYSTEM 1608.3.1 Load 1608.3.2 Generator 1628.3.3 SVC 1638.3.4 STATCOM 1648.3.5 Slack Node 1658.3.6 System Sensitivity Matrix 1668.3.7 Discussion 1698.3.8 Controller Sensitivity Matrices 1698.4 CONTROL STRATEGY 1718.5 SECONDARY VOLTAGE CONTROL LOOP 1748.6 SIMULATION RESULTS 1758.6.1 Case Study 5 1778.7 CONCLUSIONS 180

Chapter 9 Secondary Control for Restoring Power System Security 182

9.1 INTRODUCTION 1829.2 LINEARISED MODEL OF TCSC 1859.2.1 General 1859.2.2 Linearised TCSC Model 1859.3 SENSITIVITY MATRIX OF POWER SYSTEM 1889.4 ACTIVE-POWER LOSS OBJECTIVE FUNCTION 1919.5 TRANSMISSION LINE POWER FLOW 1929.6 CONTROL STRATEGY 1949.7 MULTI-STEP SECONDARY CONTROL 195

9.8 SECONDARY CONTROL LOOP 1979.9 SIMULATION RESULTS 1979.9.1 System Configuration 1979.9.2 Case Study 6 1999.10 CONCLUSIONS 203

Chapter 10 Robust Pilot-node Based Secondary Control Scheme for Security Restoration in Restructured Power Systems 205

10.1 INTRODUCTION 20510.2 LINEARISED UPFC MODEL FOR SECONDARY CONTROL 20710.3 LINEARISED MODEL FOR GENERATOR TRANSFORMER 20910.4 LINEARISED MODEL OF POWER SYSTEM 21210.4.1 Sensitivity Matrix for Dependent Variables 21210.4.2 Sensitivity Matrix for Constrained Quantities 21410.5 CHOICE OF OBJECTIVE FUNCTION IN SECONDARY CONTROL 21510.6 SECONDARY CONTROL STRATEGY 21810.7 COMPUTER SYSTEMS FOR SECONDARY CONTROL 225

SECONDARY CONTROL RESPONSES 22610.9 SECONDARY CONTROL LOOP 22710.10 REPRESENTATIVE STUDIES 22910.10.1 Power System Description 22910.10.2 Case Study 7: Load Demand Change 23010.10.3 Case Study 8: Transmission Line Outage 23310.11 CONCLUSIONS 238

Chapter 11 Conclusions and Future Work 240

11.1 CONCLUSIONS 24011.2 FUTURE WORK 24211.2.1 Real-time implementation of the new secondary control 243

11.2.2 Priority for power-flow control in secondary control 24311.2.3 Control coordination for power system stability improvements 243

Bibliography……… ……… 244 Appendices…….……… 253

Chapter 1

Introduction

With the competitive market environment in which power systems at present operate, the need for optimal system operation and at the same time maintaining system security

is on the increase, and represents a challenge to system operators

Since the availability of computer systems, extensive research has been carried out in the context of real-time control coordination [1] of power systems controllers for improving system performance in relation to system stability [2 – 7], frequency control [8 – 11], power-flow control [12], voltage control [13 – 15] and system security [16] More recently, advanced FACTS (flexible alternating current transmission system) controllers including the unified power flow controller (UPFC) have been available and used in many power systems, with the aim of enhancing their performance, and utilisation However, it has been acknowledged that, to derive the maximum possible benefit from these controllers, it is required to coordinate their controls in real time optimally and efficiently

The complexity encountered in power system responses has led to their subdivisions

respectively relate With this acknowledgement, the research presented in the thesis has the focus on power system steady-state mode of operation and the related issues of system static security following a disturbance or contingency

Underlying the control coordination is the system model for deriving the required control strategy and its implementation By control coordination is meant, within the context of steady-state mode of operation, the coordinated adjustments of individual input references to participating power system controllers for achieving specified control objective(s) Although most of the aspects in modeling power systems in their steady operation have been extensively investigated and reported in the open literature, there are remaining issues to be addressed in relation to modeling the FACTS device of UPFC type which has recently been developed and applied in power system [17] The first part of the research is devoted to the development of new UPFC steady-state models which offer the flexibility in representing a wide range of UPFC controls and operations together with the robustness in achieving the convergence in iterative solution sequences required in power-flow analysis and control

The application of the new UPFC model based on network nodal voltage variables in the analysis of power systems having UPFCs with line optimisation control (LOC) [18] will be developed and presented in the thesis Prior to the development of the new UPFC model, it has been difficult, if not impossible, to represent a UPFC with LOC in power-flow control studies The new development will provide a comprehensive power-flow analysis facility required for the optimal and simultaneous control coordination of multiple UPFCs with LOC and other FACTS devices to achieve maximum network operational benefit

The comprehensive steady-state model of power systems with FACTS devices provides the foundation for the second part of the research in the field of secondary control which has the main function of power system security restoration, following a disturbance or contingency Although the voltage aspect of system static security has been investigated extensively and reported in the literature, which has led to the development of secondary voltage control schemes and their applications in power systems [19 – 23], the research and development of real-time control schemes for restoring transmission circuit power-flow security subsequent to a contingency have been very limited

Schemes which are based on generation rescheduling and/or load shedding for achieving power-flow security are not desirable, particularly in a restructured power system operating in the electricity market environment With the availability of FACTS devices of both the shunt and series forms having high-speed responses, the research proposes and develops a new secondary control scheme for providing the real-time control coordination of power system controllers which include the generator excitation controllers, FACTS devices of both shunt and series forms, the UPFC and load-tap-changing (LTC) transformers to restore both voltage and power-flow security following

a disturbance/contingency

The above control objective is achieved by the real-time and optimal coordination of the reference settings of all of the participating controllers provided by the new secondary control strategy The limited scope of the existing coordinated secondary voltage control (CSVR), which focuses on only voltage security aspect, will be augmented and extended through the new secondary control to provide a comprehensive corrective control measure for system static security restoration The practical benefits achieved with the new control scheme include the following:

• Avoiding/reducing the need for using generation rescheduling/load shedding in corrective control

• Avoiding the need for preventative control This will lower the system operating cost, which is one of the key desirable aspects in a competitive electricity market

Also discussed in the thesis is a key enabling aspect in relation to the computer systems for implementing in real-time the comprehensive secondary control strategy developed The recent advances in computer technology, particularly that for implementing a cluster of low-cost and high-performance processors, make it entirely feasible and practical for carrying out extensive numerical processing tasks within the time frames

of the individual steps in the secondary control loop with substantial margins

1.2 OBJECTIVES

Given the context of the research described in Section 1.1 the thesis has the following

(a) Developing new UPFC steady-state models The models are to fulfil the analysis requirements for a wide range of UPFC control functions and operations, and at the same time, represent the relative priorities in individual UPFC control functions (b) Applying the modeling approach developed in (a) for representing UPFCs with LOC in power system A comprehensive power-flow analysis facility based on constrained optimisation combined with the new UPFC model formed in terms of nodal voltages only will be developed for control coordination of power system controllers, including UPFCs with LOC for maximising the network operational benefit

(c) Investigating and developing an improved secondary voltage control scheme where system voltages are controlled directly through the use of wide-area measurement systems (WAMS) for obtaining network voltage phasors of all of the load nodes Degradation of the existing secondary voltage control performance due to the control of only a limited number of network nodes referred to as the pilot nodes will be eliminated

(d) Developing a comprehensive secondary control scheme which includes in the control coordination the FACTS controllers of the series form and UPFCs The power-flow control achieved with these controllers will augment the secondary voltage control to maintain system static security in its entirety

1.3 OUTLINE OF THE THESIS

The thesis is organised in eleven main chapters Starting with the background and scope

of the research, the first chapter presents the objectives, outline and contributions of the thesis

Chapter 2 reviews and discusses the existing steady-state models, which give a foundation for the analysis and online control coordination to be developed in subsequent chapters, for conventional items of plant together with shunt and series FACTS devices

In Chapter 3 is presented a general overview of the previously-reported steady-state models for the UPFC Their key disadvantages which severely limit the scope for representing UPFCs in their wide range of control functions are identified in the review The first new steady-state model for the UPFC is developed in Chapter 4 The model is based on the explicit dynamic simulation of both the shunt converter and series converter controllers The model is a viable and useful one for power system power-flow study involving UPFC applications, particularly in the context of off-line evaluations related to system planning (including operational planning) and design

In relation to online control applications, Chapter 5 develops the second new UPFC steady-state model based on the nodal voltages The model which is expressed in terms

of sets of equations and inequality constraints is a comprehensive and flexible one suitable for steady-state analysis of a power system with embedded UPFCs

Chapter 6 applies the general and flexible UPFC model derived in Chapter 5 in developing an optimisation-based method for steady-state analysis of power systems having UPFCs with line optimisation control (LOC) In the method, optimal reference inputs to UPFCs as required in LOC are determined using constrained optimisation

In Chapter 7, a comprehensive overview of the secondary voltage control is presented

On tracing through the evolution of secondary voltage control scheme, key issues which require further research and development are identified

Chapter 8 is devoted to the development of a new scheme for the secondary voltage control which is based on the application of wide-area network of phasor measurements, and applied to power systems having FACTS controllers such as the SVC (static VAr compensator) and STATCOM (static synchronous compensator)

Chapter 9 develops a general secondary control scheme which includes the power-flow aspect of the power system security in the control law Thyristor-controlled series capacitor (TCSC), which is a FACTS device of the series form used mainly for power-flow control, is considered in the secondary control

In Chapter 10 is developed a robust and comprehensive secondary control scheme The scheme can either include directly all load nodes in the control or use only a limited

number of nodes with phasor measurement units (PMUs) Objective function based on active-power loss or reactive-power loss is developed and applied in the secondary control for countering the adverse effects of voltage measurements only at a limited number of nodes on the control performance FACTS devices which are available and in current use are incorporated in the overall secondary control scheme

The overall conclusion in Chapter 11 summarises the main features and advances of the research reported in the thesis Future research work is also suggested and included in the chapter

The thesis has made five original contributions as described in the following:

(a) Development of a new dynamic simulation-based steady-state model for the UPFC The UPFC controllers together with their operating constraints are represented in a dynamic form in an overall Newton-Raphson (NR) power-flow analysis A key advance made is the use of the NR iterative step, which now has the role of the discrete time-variable, in the interface between the UPFC controller responses and network solutions in individual NR iterations With explicit UPFC controller representation, issues or difficulties encountered in the previous models in relation

to UPFC constraint resolution and relative control priorities are eliminated

(b) Development of a new model for the UPFC using only nodal voltages as variables The UPFC model developed in (a) is suitable mainly for off-line studies in system planning and design as the number of NR iterations required for convergence can

be high The new nodal-voltage-based model, while retaining the desirable features

of the model developed in (a), leads to a more efficient power-flow analysis procedure where the number of iterations required for convergence does not depend

on the UPFC controller dynamic responses

(c) Development of an optimisation-based method for steady-state analysis of power systems having UPFCs with LOC The efficient nodal-voltage-based UPFC model

in (b) is combined with a constrained optimisation procedure to provide a comprehensive software facility for steady-state analysis and power-flow control

studies for power systems having multiple UPFCs with LOC and other FACTS devices The analysis facility has a direct application in control coordination of these FACTS devices for achieving maximum network operational benefit

In relation to the algorithm used in the analysis procedure, a novel continuation method is developed for solving the nonlinear constrained optimisation problem The approximate predictor-corrector technique which has hitherto been used in the conventional continuation method is not required in the new development

(d) Development of a new secondary voltage control scheme based on the application

of wide-area network of phasor measurements In the new scheme, the voltage control performance is enhanced as comprehensive information derived from the wide-area network measurements is directly used in forming the control law

(e) Development of a new and comprehensive secondary control scheme in which both the voltage security and power-flow security are taken into account The scheme developed is robust in its performance, even with a limited number of PMUs installed in the power system

The thesis is supported by four publications as follows:

1 Nguyen, T.T., and Nguyen, V.L.: ‘Application of wide-area network of phasor measurements for secondary voltage control in power systems with FACTS controllers’, Proceedings of IEEE PES General Meeting, San Francisco, USA, June

2005, 3, pp 2927-2934

2 Nguyen, T.T., and Nguyen, V.L.: ‘Dynamical model of unified power flow controllers in load-flow analysis’, Proceedings of IEEE PES General Meeting, Montreal, Canada, June 2006

3 Nguyen, T.T., and Nguyen, V.L.: ‘Representation of line optimisation control in unified power flow controller model for power-flow analysis’, IET Generation, Transmission and Distribution, 2007, 1, (5), pp 714 – 723

4 Nguyen, T.T., and Nguyen, V.L.: ‘Power system security restoration by secondary control’, Proceedings of IEEE PES General Meeting, Florida, USA, June 2007

Chapter 2

Review of Steady-State Models of Power System Elements

Central to the analysis, design and control of a power system is the modeling of the

individual components or items of plant in the system Different forms and levels of

details in modeling have been developed, which represent the system response

characteristics essential to the analysis/design/control relevant to the particular

operating mode of the power system under consideration Models are often classified on

the basis of the time frame of the system responses Electromagnetic transient models

are relevant in the investigation related to fast and high-frequency transient phenomena

Transient stability and small-disturbance stability models are adopted in the studies of

electromechanical oscillations of low frequency in the power system A steady-state

operating condition which represents an equilibrium of the power system after all of the

transient responses have been damped out is appropriately investigated or studied using

static models in which all of the relationships among voltage and current variables are

expressed in terms of algebraic equations

Within the category of static or steady-state models, there are different levels of details

in representing the system and its components Phase-variable models are required when operating unbalances are the focus of the system study However, for most steady-state system studies in practice related to system control and operation where operating unbalances are not of a concern, the system voltage and current variables are represented by those in the positive-phase sequence, and the individual system elements are modeled by a single-phase equivalent with parameters also in the positive-phase sequence

With nonlinear loads and controllers based on power electronic systems, there are always harmonic components in power system waveforms even in the steady-state operation In practice, the harmonic distortions are to be complied with National or International standards, which are of very low levels in comparison with the supply-frequency components There are harmonic frequency-domain models previously developed for the analysis and evaluations of harmonic distortions However, when the focus is on system studies related to operation and control in steady-state condition, the common practice adopted is to use the models at the supply frequency which is specified in formulating all of the system control objectives in steady-state condition

As outlined in the Introduction, the present thesis is devoted to the modeling, analysis and control in steady-state operating mode Therefore, the subsequent sections in this chapter will review and discuss the steady-state models of a power system together with its elements, and the system equations which form a foundation for response evaluations FACTS devices of the shunt and series forms recently developed will be included in the review together with other conventional elements of a power system

It has been accepted that, for modeling a power system in its steady state operating mode, the nodal formulation in which system nodal voltages are the variables provides the most general, flexible and systematic procedure for analyses including those related

to power-flow studies, security assessment and control Based on nodal voltage variables, steady-state models have been well-established for conventional elements:

completeness, these models are summarised in Appendices A and B With these models, the complete network nodal equation set is formed and expressed in the following vector/matrix form:

YV

I= (2.1)

In (2.1):

V and I are the vectors of the nodal voltages and nodal currents, respectively, and

Y is the nodal admittance matrix of the network

Elements of Y are formed from the network element parameters as given Appendix A

The linear nodal equation set in (2.1) combined with static load models to lead to the nonlinear power-flow equation set for individual power network nodes:

0 u

θ

V

f( , , )= (2.2)

In (2.2):

f is a vector function of |V|, θ and u;

|V| and θ are the vectors of system voltage magnitudes and phase angles,

respectively, and

u is the vector of control variables

The control variables in (2.2) are the controllers output signals which are to be determined simultaneously with the network voltage variables to achieve specified steady-state control objectives For example, the off-nominal tap position of a load-tap-changing (LTC) transformer is a control variable

In addition, there are operating limits to be considered in the models of individual power system elements The operating constraints are grouped and expressed in:

0 u

The explicit form of individual equations in (2.2) and inequalities in (2.3) is given in Appendix B

To maximise the utilisation of individual items of plant, particularly in a competitive market environment following the deregulation and restructuring of the power supply industry, the use of power electronics based controllers is on the increase in modern power systems at present These controllers are collectively referred to as FACTS (flexible AC transmission systems) devices

The next section and Chapter 3 will review and discuss the operating principles and existing models of individual FACTS devices currently used in power system steady-state studies

‘FACTS’ is the acronym for Flexible AC Transmission Systems The concepts of FACTS which have been gaining popularity internationally for increasing steady-state power transfer limits as well as improving power system dynamic response were introduced by Dr N Hingorani from the Electric Power Research Institute in the USA The concept was first mentioned in the EPRI Journal in 1986 and then in the luncheon speeches during the IEEE PES Summer meeting in July 1987, in San Francisco, and at the 1988 American Power Conference [24] The philosophy of FACTS is to use power electronic controlled devices to control voltages and/or power flows in a transmission network so that transmission lines can be utilised up to their full capability as well as the dynamic response of the power network can be improved

This section focuses on shunt and series FACTS devices which are widely used, including the static VAr compensator (SVC), static synchronous compensator (STATCOM) and thyristor-controlled series capacitor (TCSC) The steady-state models

of these FACTS devices which have been developed in previously-published research works will be reviewed in the following sections