Voltage Stability

CHAPTER 6 CHAPTER 6 : VOLTAGE STABILITY : VOLTAGE STABILITY IN ELECTRICAL POWER SYSTEMSIN ELECTRICAL POWER SYSTEMS

Ho Chi Minh City, 2008

TRANSIENT PROCESSES IN TRANSIENT PROCESSES IN ELECTRICAL POWER SYSTEMSELECTRICAL POWER SYSTEMS

CONTENTSCONTENTS

11. GENERAL CONCEPTION TO VOLTAGE . GENERAL CONCEPTION TO VOLTAGE STABILITYSTABILITY

22. BASIC CHARACTERISTIC OF . BASIC CHARACTERISTIC OF NETWORKNETWORK ELEMENTSELEMENTS

33. RELATION BETWEEN VOLTAGE, ACTIVE . RELATION BETWEEN VOLTAGE, ACTIVE POWER, AND REACTIVE POWER (P-U-Q)POWER, AND REACTIVE POWER (P-U-Q)

44. CONCLUSION. CONCLUSION

PURPOSES THE PURPOSE OF THE PRESENTATION To present the general conceptions of To present the general conceptions of Voltage stability. Voltage stability. How does the basic characteristic of How does the basic characteristic of network elements influence in voltage network elements influence in voltage stability ?stability ? To consider the relation between (P-U-Q) To consider the relation between (P-U-Q) in voltage stability.in voltage stability.

1. GENERAL CONCEPTION1. GENERAL CONCEPTION

Voltage stabilityVoltage stability is the ability of a power system to is the ability of a power system to maintain steady acceptable voltages at all buses in the maintain steady acceptable voltages at all buses in the system under normal operating conditions and after being system under normal operating conditions and after being subjected to disturbance.subjected to disturbance.

A system enters a state of voltage instability :A system enters a state of voltage instability : A disturbanceA disturbance Increase in load demandIncrease in load demand Change in system condition causes a progressive Change in system condition causes a progressive and uncontrollable decline in voltageand uncontrollable decline in voltage The main factor causing instabilityThe main factor causing instability is inability of theis inability of the power system to meet the demand for reactive powerpower system to meet the demand for reactive power


A criterion for voltage stability is that, At a given A criterion for voltage stability is that, At a given operating condition for every bus in the system, bus operating condition for every bus in the system, bus voltage magnitude increase as reactive power injection at voltage magnitude increase as reactive power injection at the same bus increase.the same bus increase.

Voltage instability is essentially a local phenomenon.Voltage instability is essentially a local phenomenon.

Voltage collapse is more complex than simple voltage Voltage collapse is more complex than simple voltage instability.instability.

The heart of the problem is usually the voltage drop The heart of the problem is usually the voltage drop that occurs when active power and reactive power flow that occurs when active power and reactive power flow through inductive reactance associated with the through inductive reactance associated with the transmission network.transmission network.

The following are some example about voltage instability The following are some example about voltage instability had been responsibility for several major network collapses:had been responsibility for several major network collapses:

Florida system disturbance of December 28, 1981Florida system disturbance of December 28, 1981

French system disturbances of December 19, 1978French system disturbances of December 19, 1978 and January 12, 1987and January 12, 1987

Northern Belgium system disturbance of August 4, 1982Northern Belgium system disturbance of August 4, 1982

Swedish system disturbance of December 27, 1983 Swedish system disturbance of December 27, 1983


2. BAISIC CHARACTERISTIC OF NETWORK ELEMENTS2. BAISIC CHARACTERISTIC OF NETWORK ELEMENTS

GENERATORGENERATOR

TRANSMISSION SYSTEMTRANSMISSION SYSTEM

LOADLOAD

2.1 TRANSMISSION SYSTEM CHARACTERISTICS2.1 TRANSMISSION SYSTEM CHARACTERISTICS

Characteristic of a simple radial system fo illustration of Characteristic of a simple radial system fo illustration of voltage stability phenomenonvoltage stability phenomenon

Constant voltage

Figure 1 Figure 1 Schematic diagram Schematic diagram

The characteristics of interest are the relationships among the transmitted power (PR ), receiving end voltage (VR) and the reactive power injection (QC ).

The expression for Current I in The expression for Current I in figure1figure1 is is When I and E are When I and E are phasorsphasors

LD LN

EIZ Z

(1)

2 2( cos cos ) ( sin sin )s

LN LD LD LN

EI

Z Z Z Z

(2)



Figure 2Figure 2 Receiving voltage current and power Receiving voltage current and power as a function of load demand for The system in as a function of load demand for The system in figure1

From figure2 • Power transmitted is maximum when the voltage

drop in the line is equal in magnitude to VR, that is when

• As ZLD is decreased gradually, I increase and VR decrease, Initially, at high value of ZLD the increase in I dominates over the decrease in VR and hence Pr increase rapidly with decrease in ZLD

( / ) 1LN LDZ Z


From the view point of Voltage stabilityFrom the view point of Voltage stability The relationship between PThe relationship between PRR and V and VRR is of interest. This is of interest. This

shown in shown in figure3figure3 for the system under consideration for the system under consideration when the load power factor is equal to 0.95 lagwhen the load power factor is equal to 0.95 lag


(4)(4) coscos..2

LD

SLDRR Z

EFZ

IVP

)cos(.212

LD

LD

LD

LD

ZZ

ZZF (5)(5)

(3)(3)S

LN

LDLDR E

ZZ

FIZV ..1.


Figure 3: VRR-PRR characteristics of the system of figure1 with difference load-power factor

The principal causes of voltage instabilityThe principal causes of voltage instability

The load on transmission lines is too highThe load on transmission lines is too high

The voltage sources are too far from The voltage sources are too far from the load centresthe load centres

The source voltages are too lowThe source voltages are too low

There is insufficient load reactive compensation There is insufficient load reactive compensation


2.2 GENERATOR CHARACTERISTICS Generator AVRs are the most important means of voltage control in EPS

Under normal conditions the terminal voltages of G maintained constant

During conditions of low - system voltages, the active power demand on G may exceed their field current

When the active power out is limited, the terminal voltage is nolonger maintained constant

The generator field current is automatically limited by an overexcitation limiter (OXL)

VVRR

Curve 1(Vi – regulated)

b) The VR – PR characteristics

Curve 2 (excitation of G1 at its limit)

AACC

BB

PA PMAX2 PMAX1

VVCRT1CRT1

VVCRT2CRT2

PPRR

VRV1

Es

PR + jQRP1

G1

a) Schematic diagrams

2.2 GENERATOR CHARACTERISTICS

Figure 4Figure 4 Impact of loss of regulation of intermediatebus voltage

2.2 GENERATOR CHARACTERISTICS

These results demonstrate the importance of These results demonstrate the importance of maintaining the voltage control capability of generators.maintaining the voltage control capability of generators.

They show that the degree of voltage stability cannot They show that the degree of voltage stability cannot be judged base only on how close the bus voltage is to be judged base only on how close the bus voltage is to the normal voltage levelthe normal voltage level

Load characteristics and distribution system voltage Load characteristics and distribution system voltage control devices are among the key factor influencing control devices are among the key factor influencing system voltage stability.system voltage stability. Loads whose active and reactive components vary with Loads whose active and reactive components vary with voltage interact with the transmission characteristic by voltage interact with the transmission characteristic by changing the power flow through the system.changing the power flow through the system. The system voltages settle at values determined by the The system voltages settle at values determined by the composite character of the transmission system and loads.composite character of the transmission system and loads.

The industrial loads, with large components of The industrial loads, with large components of induction motors will change little.induction motors will change little.

The loads consist of resistance, inductance and The loads consist of resistance, inductance and capacitance.capacitance.

2.3 LOAD CHARACTERISTICS2.3 LOAD CHARACTERISTICS

2.3 LOAD CHARACTERISTICS2.3 LOAD CHARACTERISTICS

Therefore, representation of load characteristic Therefore, representation of load characteristic should consideration the effects of thermostats and should consideration the effects of thermostats and other load regulation devices.other load regulation devices.

Industrial and commercial motors are usually Industrial and commercial motors are usually controlled by contactor; so, the voltage drop will cause controlled by contactor; so, the voltage drop will cause many motors to drop out.many motors to drop out.

Distribution system voltage regulators and transformer Distribution system voltage regulators and transformer ULTCs attempt to hold constant voltage at the point of ULTCs attempt to hold constant voltage at the point of consumption.consumption.

2.4 CHARACTERISTIC OF REACTIVE 2.4 CHARACTERISTIC OF REACTIVE COMPENSATING DEVICESCOMPENSATING DEVICES

Here, we brietly describe how these devises influence voltage stabilityHere, we brietly describe how these devises influence voltage stability Shunt capacitorsShunt capacitors

Shunt capacitor have a number of inherent limitations.Shunt capacitor have a number of inherent limitations. In heavily shunt capacitor compensated systems, the voltageIn heavily shunt capacitor compensated systems, the voltage regulation tends to be poor.regulation tends to be poor.

Beyond a certain level of compensation, stable operation Beyond a certain level of compensation, stable operation unattainable with shunt capacitor.unattainable with shunt capacitor.

The reactive power generated by shunt capacitor is proportional to The reactive power generated by shunt capacitor is proportional to the square of voltage; during system conditions of low voltage the var the square of voltage; during system conditions of low voltage the var support drops thus compounding the problem.support drops thus compounding the problem.

The most inexpensive means of providing reactive power, voltage The most inexpensive means of providing reactive power, voltage support.support. To extend the voltage stability limits by correcting the receiving end PF. To extend the voltage stability limits by correcting the receiving end PF.

Regulated shunt compensation Regulated shunt compensation Static var system (SVS) of finte size will regulate up to its maximumStatic var system (SVS) of finte size will regulate up to its maximum capacitive output. capacitive output.

Synchronous condensor has an internal voltage source. It continues toSynchronous condensor has an internal voltage source. It continues tosupply reactive power down to relatively low voltages and contributessupply reactive power down to relatively low voltages and contributes to a more stable voltage performance.to a more stable voltage performance.

Series capacitorsSeries capacitorsThe reactive power supplied by series capacitors is proportional toThe reactive power supplied by series capacitors is proportional to square of line current and is independent of voltage bus.square of line current and is independent of voltage bus.

Series capacitors reduce both the characteristic impedance ( Zc) and Series capacitors reduce both the characteristic impedance ( Zc) and The electrical length (The electrical length (θθ) of the line.) of the line.

2.4 CHARACTERISTIC OF REACTIVE 2.4 CHARACTERISTIC OF REACTIVE COMPENSATING DEVICESCOMPENSATING DEVICES

3. RELATIVE BEWEENT P-U-Q

22 2 2( ) ( ) [ ( ) ]L L

EU UP U Q UX X

jIXU

E

I

θΦ

c. Voltage phasor diagramc. Voltage phasor diagram

1

2

PL+ jQLX

U

b. System equivalent circuitb. System equivalent circuit

EEPL+ jQL

a. System schematica. System schematic

XSinUE

XCosXIUCosIUUPL

......)(

XUCos

XEU

XSinXIUSinIUUQL

2....)( As:

CosCos22θθ + S + Sinin22θθ = 1 = 1

If P and Q are independent of U, PL(U)=Pn, QL(U)=Qn

U2/X

Qn

Pn

Figuire6:Relative P-Q corresponding to U

22

24 /n

nPEQ

X E X


22 2 2( ) ( ) [ ( ) ]L L

EU UP U Q UX X

(3)(3)

B

A

PPnn

Figuire7: Relative P-Q when U change

QQnn(4)(4)

XUQP

XUE

nn

22

2.

If P and Q depend on U as quadratic function of U; Pn and Qn unlimited

2

22

2

( )

( )

n

n nL n

n

Pp U

P G UU UU

Load is shown as : Y=GLoad is shown as : Y=Gnn+jB+jBnn

2

22

2

( )

( )

n

n nL n

n

QQ U

Q B UU UU

Any values of GAny values of Gnn,B,Bn n ;substitute P ;substitute PLL,Q,QLL into (3): into (3):

2 2( ) ( 1)n n

EUG X B X



Figure 6: QFigure 6: Qnn and P and Pn n when the load characteristic changeswhen the load characteristic changes

QQnn

PPnn

UUnn

PPLL, Q, QLL

UU

PPnn

QQnn



PPLL, Q, QLL

UU

PPnn

2

.

NNL UUQQ

QQnn

PPnn



QQnn

PPnn

PPLL, Q, QLL

UU

2

.

NNL UUQQ

2

.

NNL UUPP



PPLL, Q, QLL

UU

2

.

NNL UUQQ

2

.

NNL UUPP

QQnn

PPnn

CONCLUSIONCONCLUSION Three key concepts of voltage stability are the load

characteristics as seen from the bulk power network, the available means for voltage control at generators and in the network the ability of network to transfer power particularly reactive power from the point of production to the point of consumption.

Voltage stability depens on the relationship beween Q-U-P.

The network element characteristics have important influences on system stability.

The fundamental causes of voltage instability is identified as incapability of combined transmission and generation system to meet excessive load demand in either real power or reactive power form.

THANKSTHANKS

R

X

Un

I

2 2

n

n

UI

R X

2.nQ I jX

2

2 2n

n

UQ X

R X

(1)

2

2 2( )U

Q U XR X

In general: (2)

From (1) , (2) :2 2

2( )nn nUQ U

Q U UU

2( ) ( / )n nQ U U U Q

2( ) ( / )n nP U U U PAs above: As above:

Equivalent circuit


2.3 CHARACTERISTIC OF REACTIVE 2.3 CHARACTERISTIC OF REACTIVE COMPENSATING POWERCOMPENSATING POWER

2.3 CHARACTERISTIC OF REACTIVE 2.3 CHARACTERISTIC OF REACTIVE COMPENSATING POWERCOMPENSATING POWER

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Voltage Stability

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