Reliability assessment of power systems considering reactive power sources

This paper presents a technique to evaluate system and load point reliability indices of power systems considering reactive power shortages due to the failures caused by reactive powe

Abstract— Reactive power plays a significant rule in power

system reliability and security Reactive power is considered as

the network constraint in conventional reliability evaluation

techniques The impact of the failures of reactive power sources

such as synchronous condensers and compensators on system

reliability has not been considered in the existing reliability

techniques This paper presents a technique to evaluate system

and load point reliability indices of power systems considering

reactive power shortages due to the failures caused by reactive

power sources The reliability indices due to the reactive power

shortages are separated from those due to the real power

shortages Two reliability indices related to reactive power

shortage are proposed The IEEE 30-bus system is modified and

analyzed to illustrate the proposed technique The results provide

very important information for system planners and operators

for reactive power management

Index Terms— Reactive power, power system reliability

I INTRODUCTION

he objective of reactive power provision is to maintain

power system reliability and security Reactive power

reserve is a basic requirement for maintaining voltage

stability The adequate reactive power reserve is expected to

maintain system integrity under both normal and post

contingency operation As one of the well established

ancillary services, reactive power support and voltage control

plays a vital role in the operation of both conventional and

restructured power systems The effect of reactive power on

system stability and security has been well investigated

[1]-[8] Large area blackout usually occurs in a heavily loaded

system which does not have adequate local reactive reserves

Heavily loaded systems not only have high reactive power

demand but also high reactive power losses in the lines

During a disturbance, the real power component of line

loadings does not change significantly, whereas the reactive

power flow can change dramatically [1]

The reason is that the voltage drop resulting from a

contingency reduces the reactive power generation from line

charging, thereby increasing reactive power losses Sufficient

reactive reserves should be available to meet the Var changes

following a disturbance How much more reactive power a

power system can deliver depends on the operating condition

The authors are with the School of EEE, Nanyang Technological

University 1 , Singapore (e-mail: epwang@ntu.edu.sg ) and Power Engineering

School, Taiyuan university of Technology 2 , China

and the location of the reserves Many approaches have been developed in reactive power management and monitoring in order to improve the reliability of the system with respect to voltage stability/security problems [1]-[8]

Therefore it is important to consider the impact of reactive power in power system reliability evaluation in order to obtain more accurate reliability indices Reliability evaluation techniques have been well developed [9]-[12] The reactive power is usually considered as the network constraints in those techniques During post contingency load shedding, the network violation is alleviated through the proportional or priority load shedding without considering the rule of reactive power The estimation of post-contingency voltages and reactive power generation and flows was discussed using sensitivities [13] Though employing piecewise linear estimates, the effect of equipment limits on the estimates was captured The effect of shunt capacitor on distribution system

reliability was studied [14] The composite system reliability

was investigated from the standpoint of voltage limits and generator real/reactive power constraints in [15] The expected value of curtailed kWh due to lack of reactive power generation or due to exceeding of voltage limits and the expected value of voltage irregularity were also investigated [15]

However the following problems are either ignored or seldom considered in the existing reliability evaluation techniques Firstly most existing techniques for power system reliability evaluation ignored the impact of the failures of reactive power resources such as synchronous condensers and

various compensators on system reliability Secondly most reliability evaluation techniques concerned more on the

problems caused by real power shortage rather than those caused by reactive power unbalance during post contingency load shedding Thirdly, the reliability indices due to the reactive power shortage were seldom considered separately with those due to the real power losses System operators could not find the information related to the reliability problems caused by reactive power shortage from the existing reliability indices provided by the conventional reliability

evaluation techniques Therefore there is a need to find a

relationship between the reactive power and system reliability with respect to voltage violations and system

reliability

This paper presents a technique to evaluate system and load point reliability of a power system considering reactive power shortage due to failures caused by reactive power sources such as generators, synchronous condensers and

Reliability Assessment of Power Systems

Considering Reactive Power Sources

Peng Wang1,2, Member, IEEE, Wenping Qin2, Xiaoqing Han2, Yi Ding1, Xinghui Du2

T

978-1-4244-4241-6/09/$25.00 ©2009 IEEE

compensators The reliability indices due to the reactive

power shortages are separated from those due to the real

power losses The reliability indices related to reactive power

shortages are proposed to provide more information to system

operators and planners The IEEE test system is modified and

analyzed to illustrate the proposed technique

Section II discusses the important characteristics of reactive

power sources and load The real and reactive power models

of generator, transmission line, compensator and load are also

presented The reliability evaluation techniques and load

shedding methods will be discussed and the reliability indices

associated with Var shortage during the post contingency are

proposed in Section III The modified IEEE 30-bus system

has been analyzed using the proposed techniques and the

results are presented in IV Section V concludes the paper

II REACTIVE POWER CHARICTERISTICS AND MODELING

There are three aspects that differentiate reactive power

from active power in power system operation Firstly, it is not

efficient to transfer reactive power over a long distance

because the reactive power loss in transmission system is

significant Reactive power losses are typically about ten

times of the active power losses due to the inductive nature of

transmission lines Therefore it is better to compensate the

reactive power locally Secondly, the main role of reactive

power is to maintain voltage stability/security of power

systems The effect of reactive power on system reliability in

terms of energy not supplied is indirect and should be

calculated based on reactive power shortage and voltage

violation Thirdly, the total reactive power loss in the

transmission network often exceeds the total reactive power

load The reactive power loss changes with system

configuration and operation condition [7]-[8] Reactive power

requirement for releasing voltage violation after a contingency

are heavily dependent on reactive power reserve distributions

in the system In order to determine and re-dispatch real and

reactive power reserve for post contingency restoration, the

models of various real and reactive power sources have to be

studied

A Generator

A generator can provide both capacitive and inductive

reactive power According to a NERC planning standard

guideline [4], reactive capability within 0.9 lagging and 0.95

leading should be available A physical constraint in Var

provision by a generator is its generation capability constraint

which represents the hard physical limitation of a generator's

capability for the simultaneous production of real and reactive

power A typical generation capability curve is shown in Fig

1

The real power output of a generator is usually limited to a

value within the MVA rating by the capability of its prime

mover [16] When real power and terminal voltage of a

generator is fixed, the armature and field winding heating

limits restrict its reactive power output The armature heating

limit is a circle with radius R1 =V t I acentered on the origin

C1(0, 0) and given by the following equation:

2 a t 2

P + ≤ (1)

Fig 1 Typical generation PQ curves

The field heating limit follows a circle with radius

d

i t

E V

R = , centered at

⎟⎟⎠

⎞

⎜⎜⎝

⎛ −

d

2 t 2

X

V , 0

C and given by Equation 2

2

d

i t 2

d

2 t 2

X

E V X

V Q P

⎟⎟⎠

⎞

⎜⎜⎝

⎛

≤

⎟⎟⎠

⎞

⎜⎜⎝

⎛ + + (2)

where Vt is the voltage magnitude at the generator bus, Ia is the steady state armature current, Ei is the excitation voltage magnitude, Xd is the synchronous reactance, P and Q are real

and reactive power output, respectively The machine rating

S R is the intersection point of the two circles The corresponding rated real power output is denoted by PR The

reactive power capability limits of generator can be determined by:

( )

d

2 t 2 2

d

i t

V P X

E V P

⎟⎟⎠

⎞

⎜⎜⎝

⎛

≤ for P<PR (3)

a t max

Q ≤ − for P>PR (4)

In real time operation, actual reactive power reserve Q r

from a generator can be determined using the capability curves as

Q r =Q max( )P −Q current (5)

where Qcurrent is the reactive power dispatched in the normal

operation

In most conventional reliability techniques, constant

maximum and minimum reactive power limits Qmax and Qmin

are used in AC power flow analysis The reactive power model for synchronous condenser is similar to generator In this paper the maximum reactive power provided by a

generator is assumed to be QR when the real power output is

P R

B Transmission line

An equivalent π model is used to represent a long line in

Fig 2

Y ’ / 2

Z ’

-Fig 2 Equivalent π model of a transmission line

The real and reactive power losses along a transmission line

depend on line parameters such as series impedance Z’, and

parallel admittance Y’, and bus voltages at the sending and

receiving ends [16] The equations to calculate the real and

reactive power losses for short, medium and long lines can be

found in [16] Heavily loaded transmission lines lead to large

inductive reactive power losses In this case generators and

compensators need to produce sufficient reactive capability to

maintain the reactive power balance and to keep voltages

within the specified limits

C Var Compensators

Compensation devices can provide both capacitive and

inductive reactive power for a power system A reactive

power compensator is usually connected between a bus and

ground There are static and dynamic Var compensators in

power systems A basic dynamic Var generation arrangement

using a fixed capacitor with a thyristor-controlled inductor is

shown in Fig.3 The constant capacitive Var generation QC of

the fixed capacitor is opposite to the variable Var absorption

QL(γ) of the thyristor-controlled inductor to yield the total

variable Var output QT(γ) =QL(γ)-Qc For a specific voltage V,

the required positive or negative QT(γ) can be obtained by

changing turn off angle γ of thysistor It is assumed Var

compensators can provide both capacitive and inductive

reactive power

Fig.3 A typical thyristor-controlled Var compensator and its Q output

D Load

Load at a bus of a bulk power system is the aggregation of

the associated sub-transmission network and various loads

Therefore modeling such an aggregate load requires the

network parameters of sub-transmission system and the

profile of each individual load A typical PV curve is shown in

Fig 4 which addresses the proper voltage profile at a load bus

in a power system [17] It can be seen from the curve that bus

voltage is reduced as load increases The real Pb and reactive

Qb power at point b correspond to values at the low limit of the bus voltage c is the point of system voltage collapse when the reactive power provided by system is less than the

required reactive power Qc to maintain voltage level at Vc The

reactive safety margin can be defined using the curve as:

Q r =Q current −Q b (6)

Fig.4 A typical PV curve at a load bus

III RELIABILITY INDICES AND EVALUATION TECHNIQUE

A Component reliability models

A power system component such as generator, synchronized condenser, transmission line and reactive device can be represented using the two-state reliability model [18]

as shown in Fig 5 The availability A and unavailability U can

be calculated based on failure rate and repair rate using the following equations

Down

μ Fig 5 Two-state model of a component

A

μ λ

μ +

= (7)

U

μ λ

λ +

= (8)

B Basic system reliability indices

Considering an N-component power system, the basic reliability parameters such as the probability p i, departure rate λ , frequency Fi i , the total real power generation capacity

P i and reactive power generation capacity Qi for state i with M

failed components can be determined using the following equations respectively:

∏

∏

= +

=

1

j j N

1 M

p (9)

∑ +∑

= +

N M j

M

j j j i

λ (10)

V

L

SW

I c

I Q

L

C

QL(γ)

QT(γ)

Qc γ

Q

V

P(Q)

O

a

b

c

Pb (Qb)

P current (Q current ) P c (Q c )

i

i P

F = λ (11)

∑

=

=Ngi

1

k k

P (12)

∑=

=Nqi

1

k k

Q (13)

where Aj, Uj, λ andj μ are the availability, the unavailability, j

the failure rate and the repair rate of component j respectively,

P k is the available real power capacity of generator k, Qk is

reactive power capacity of compensator or generator k, and

N gi is the total number of generators and N qi is the total

number reactive power sources

C Load point and system reliability indices

Two conventional annualized reliability indices of the

expected load curtailment (ELC) and the expected energy not

supplied (EENS) can be calculated using the proposed

technique The EENS due to the real power shortage (EENSP)

and reactive power shortage (EENSQ) are separately

calculated The expected MVarh shortage (EVarS)

considering the failures of reactive power sources and the

expected Var not supplied EVNS are defined to provide more

reliability information for system planners and operators The

annualized reliability indices for annual constant load can be

calculated using the following equations:

∑

=NC

1

F LC ELC (14)

∑

=NC

1

EENS (15)

=NC

1

EENS (16)

∑

=NC

1

EVNS (17)

8760 p VarS EVarS NC

1

i Qi× i×

=∑= (18)

where NC is the total number of considered contingencies,

Pi

LC and LC Qiare the real power load curtailment due to real

power and reactive power shortage for state i respectively,

Qi

QC are the reactive power load curtailment due to reactive

power shortage for state i , VarS Qi is the Var shortage which

cause the voltage drop, and LC i =LC Pi +LC Qi

D Load shedding

Network violations for a contingency can be released using

load shedding and real and reactive power re-dispatch Load

shedding technique is more complicated when considering

both real and reactive power shortage In real time operation,

different power systems may have different load curtailment

strategies such as proportional, priority and wheeling load

shedding, and the corresponding direct load control

equipments are required for the implementation of those

strategies, which should and can be considered in reliability

evaluation A two step curtailment strategy is presented in this

section to illustrate load shedding with considering reactive

power shortage For each contingency state, the corresponding total real power available capacity is firstly compared with the total real power demand (load plus estimated transmission loss) If the total real power capacity is less than total real power demand, the real and related reactive power of the load

at each bus in the system is curtailed using the proportional load shedding technique After the load shedding due to the real power shortage, AC power flow is performed to check network violations and generation adequacy If the total real power generation is sufficient for the total demand and the voltage violations exist, the violations are due to reactive power shortage Because the reactive power cannot be delivered efficiently through a long distance due to the transmission loss, the reactive power is usually compensated locally Therefore the load shedding related to the reactive power shortage should be in the local buses with the low voltage, which is different with the load shedding approach due to the real power shortage In this technique, the load shedding due to reactive power shortage is usually performed

at the nodes with voltage violation If the voltage violation still exists after the load shedding at those buses, the load shedding is expanded to the surrounding nodes

E Determination of reactive power shortage

In order to determine reactive power shortage under a contingency state, reactive power is injected step by step at the node with the low voltage to raise the voltage When the voltage reaches its low limit, the corresponding reactive

power injected is the reactive power shortage VarSQi in

equation (18)

F Procedure of reliability evaluation

Based on the proposed models, equations and techniques, the procedure of the AC power flow based reliability evaluation considering reactive power include the following steps:

Step1: Input basic network data, load data, generation data, and basic reliability data

Step2: Determine system state using contingency analysis and

calculate basis system reliability indices for state i

Step3: Calculate total system real and reactive power capacity

P i and Qi respectively

Step4: If Pi is less than the total real power demand, cut real

and reactive load proportionally at each load bus and update

EENS P, EVNSQ and ELC Otherwise go to next step

Step5: Determine line overflow violations using AC power flow analysis

Step6: If there is the line overflow, gradually cut the load at the ending bus of the line and go to Step5 Otherwise update

EENS P , EVNSQ and ELC, and go to next step

Step7: Determine voltage violations using AC power flow analysis Go to next step if there is voltage violation Otherwise go to Step14

Step8: If the real power capacity is sufficient, gradually increase reactive power injection at the node with low voltage Step9: Perform AC power flow analysis Go to Step8 if there

is voltage violation Otherwise update EVarS and go to next

step

Step10: Remove the reactive power injected at Step8

Step11: Gradually cut the load at the bus with low voltage

Step12: Perform AC power flow and check the voltage

violations

Step13: Go to Step11 if there is voltage violation Otherwise

update EENSQ , EVNS Q and ELC and go to Step14

Step14: If all contingencies are considered go to next step

Otherwise go to Step2 for next state

Step15: Calculate system reliability indices

IV SYSTEM STUDIES

The IEEE 30-bus system [19] as shown in Fig 6 is analyzed

to illustrate the proposed technique The system is selected

due to its requirements of the reactive power compensation

caused by special radial configuration from two generation

stations to the remote load centers

Fig 6 The single line diagram of IEEE 30-bus system

There are two generation buses in the system Generation

bus 1 consists of 4×60MW units Generation bus 2 consists of

3×40MW units In order to illustrate the effect of reactive

power reserve on system reliability, the system has been

modified The reactive power limits of the generators, synchronous condensers and static Var compensators have been changed The reactive power limits and the reliability parameters for each generator and condenser are shown in Table A1 The reliability parameters of the transmission lines are shown in Table A2 Annual constant load is used in analysis The real and reactive power load is bundled together using fixed power factor, which means that real and reactive power must be curtailed at the same percentage during the real or reactive power shortage

The failures up to second order have been considered in the

analysis The proposed annual load point and system EENSP,

EENS Q and ELC have been calculated and the results are

shown in Table 1 It can be seen from Table 1 that load point

at bus 26 has highest EENSP followed by the load point at bus

5 The highest EENSP at bus 26 is because of the single

transmission line connected to the bus and the high

probability of the first order failure The higher EENSP at bus

5 is due to the highest load for the second order failure

Unlike EENSP the load point at bus 29 has highest EENSQ

followed by the load point at bus 30 This is because the long transmission line from reactive power compensators to the

two buses The results also show that the system EENSQ caused by the voltage violation is about 28 percent of EENSP

due to real power shortage and should be considered in reliability evaluation

Bus # EENS P

(MWh/yr)

EENS Q

(MWh/yr)

ELC

(MW/yr)

5 139311.10 92880.21 23155.98

12 15307.69 5663.05 1751.07

17 16085.15 1987.96 1999.76

21 48446.32 7938.02 8470.37

26 1124030.00 34429.42 147960.80

29 11319.81 182601.40 25045.13

30 49995.85 105795.30 22653.80 System 1606505.00 453599.00 249534.50

The proposed annual load point and system EVNSQ and

EVarS are also calculated and the results are shown in Table 2

The EVarS results show that the voltage violations caused

by Var shortage can be released using the reactive power injection at those nodes instead of shedding the load

Therefore EVarS provide the system operator with very

important information for post contingency restoration Both

real and reactive power shortage will cause the reactive power

curtailments because real and reactive power loads are

bundled by the fixed power factor

Bus # EVNS Q

(Mvarh)/yr

EVarS

(Mvarh)/yr

5 46832.64 73617.88

7 19520.02 9238.56

8 54565.78 10443.33

12 14042.91 6356.84

14 3046.91 2009.08

17 11647.11 2373.76

19 6642.29 560.42

20 1149.61 15.31

21 36085.98 9261.80

23 3216.00 587.33

24 9707.84 764.81

26 761273.60 39626.82

29 72720.46 199034.20

30 27924.83 90334.29 System 1101236.00 444224.40

V CONCLUSIONS

This paper presents a technique to evaluate system and load

point reliability of power systems considering reactive power

shortage due to failures caused by reactive power sources

such as synchronous condensers and compensators The

reliability indices due to the reactive power shortage are

separated from those due to the real power shortage The

reactive power shortage is calculated through the reactive

power injection at the nodes with low voltage The IEEE

30-bus system is modified and analyzed to illustrate the proposed

technique The results provide very important information and

different ways for system operator to alleviate the network

violations and for system planner to determine the optimal

location for installing new reactive power compensators

VI REFERENCES [1] B Leonardi, V Ajjarapu, “Investigation of various generator reactive

power reserve (GRPR) definitions for online voltage stability/security

assessment”, Proc of IEEE PES General Meeting, Jul 2008

[2] I El-Samahy, K Bhattacharya, C Caizares, M F Anjos, Jiuping Pan, “A

Procurement Market Model for Reactive Power Services Considering

System Security”, IEEE Trans on Power Systems, vol 23, no 1, pp.137–

149, Feb 2008

[3] T Plavsic, I Kuzle, “Zonal reactive power market model based n optimal

voltage scheduling”, AFRICON 2007, pp 1–7, Sept 2007

[4] N Yorino, M Eghbal, E.E El-Araby, Y Zoka, “Dynamic Security

Constrained VAR Planning for Competitive Environments”, Power and

Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 2008 IEEE, pp 1–8, Jul 2008

[5] F Dong, B H Chowdhury, M L Crow, L Acar, “Improving voltage

stability by reactive power reserve management”, IEEE Trans on Power

Systems, vol 20, no 1, pp 338–345, Feb 2005

[6] S K Parida, S N Singh, S C Srivastava, “Voltage security constrained

localized reactive power market”, 2006 IEEE, Power India Conference,

pp 6, Apr 2006

[7] S Hao, A Papalexopoulos, “Reactive power pricing and management”,

IEEE Trans on Power Systems, vol 12, no 1, pp 95– 104, Feb 1997

[8] A Rajabi, H Monsef, “Valuation of dynamic reactive power based on

probability aspects of power system”, Universities Power Engineering

Conference, UPEC 2007 42nd International, pp 1169–1174, Sept 2007

[9] R N Allan, R Billinton, A M Breipohl, and C H Grigg, “Bibliography

on the Application of Probability Methods in Power System Reliability

Evaluation: 1987-1991”, IEEE Trans on Power Systems, vol 9, no 1, pp

41–49, Feb 1994

[10] R N Allan, R Billinton, A M Breipohl, and C H Grigg, “Bibliography

on the Application of Probability Methods in Power System Reliability

Evaluation”, IEEE Trans on Power Systems, vol 14, no 1, pp 51–57,

Feb 1999

[11] R Billinton, M Fotuhi-Firuzabad, and L, Bertling, , “Bibliography on the Application of Probability Methods in Power System Reliability Evaluation1996-1999”, IEEE Trans on Power Systems, vol 16, no 4,

pp 595–602, Nov 2001

[12] Y Ding, P Wang, “Reliability and price risk assessment of a restructured

power system with hybrid market structure”, IEEE Trans on Power

Systems, vol 21, no 1, pp 108–116, Feb 2006

[13] P A Ruiz, P W Sauer, “Voltage and Reactive Power Estimation for

Contingency Analysis Using Sensitivities”, IEEE Trans on Power

Systems, vol 22, no 2, pp 639–647, May 2007

[14] A A Sallam, M Desouky, H Desouky, “Shunt capacitor effect on

electrical distribution system reliability,” IEEE Trans on Reliability, vol

43, no 1, pp 170–176, Mar 1994

[15] P L Noferi, L Paris, “Effects of voltage and reactive power constraints

on power system reliability”, IEEE Trans on Power Apparatus and

Systems, vol 94, no 2, pp 482–490, Mar 1975

[16] J J Grainger, W D Stevenson, Jr Power system analysis New York:

McGraw-Hill, 1994

[17] V C Thierry, V Costas, Voltage Stability of Electric Power Systems, Boston/London/Dordrecht: Kluwer Academic Publishers, 1998

[18] R Billinton, R N Allan, Reliability Evaluation of Power Systems, 2nd

ed., New York and London: Plenum Press, 1996

[19] O Alsac, B Stott, “Optimal Load Flow with Steady State Security”, IEEE

Trans on Power Apparatus and Systems, vol 93, no 3, pp 745-751,

May 1974

Appendix

Compensator

T ABLE A2

1 2 1 876

1 3 1 876

2 4 1 876

3 4 1 876

2 5 1 876

2 6 1 876

4 6 1 876

5 7 1 876

6 7 1 876

6 8 1 876

6 9 1 876

6 10 1 876

9 11 1 876

9 10 1 876

4 12 1 876

12 13 1 876

12 14 1.5 876

12 15 1.5 876

12 16 1.5 876

14 15 1.5 876

16 17 1.5 876

15 18 1.5 876

18 19 1.5 876

19 20 1.5 876

10 20 1.5 876

10 17 5 876

10 21 5 876

10 22 5 876

21 22 5 876

15 23 5 876

22 24 1.5 876

23 24 1.5 876

24 25 1.5 876

25 26 5 876

25 27 5 876

28 27 1.5 876

27 29 5 876

27 30 5 876

29 30 5 876

6 28 1 876

Peng Wang (M’00) received his B.Sc degree from Xian Jiaotong University,

China, in 1978, the M Sc degree from Taiyuan University of Technology,

China, in 1987, and the M Sc and Ph.D degrees from the University of

Saskatchewan, Canada, in 1995 and 1998, respectively Currently, he is an

associate professor of Nanyang Technological University, Singapore

Qin Wenping received her B.S (1995) and M.S (2001) degrees in College of

Electrical & Power Engineering of Taiyuan University of Technology (TUT),

Taiyuan, China (e-mail: qinwenping@tyut.edu.cn) Currently, she is a lecturer in

TUT and a visiting scholar in Nanyang Technological University, Singapore

Her research interests include power system reliability analysis, security assessment, stability analysis and protection