Transient Instability Risk Assessment V. Vitta1 Fellow vvittal@ iastate.edu
J. D. McCalley Senior Member j d m @ iastate.edu
N. Abi-Samra Senior Member
[email protected]
W. Fu
V. Van Acker Student Member
[email protected]
Student Member wfu @ iastate.edu
Electric Power Research Institute Palo Alto, CA.
Iowa State University Ames, Iowa Abstract This paper presents an approach to calculate risk of transient instability of an operating point for a power system. Risk is defined as the product of the probability of transient instability and the cost consequences of this instability in the event that it occurs. This measure combines the security aspects with the economics and gives an objective idea of the ‘danger’ associated with any operating point. The approach also accounts for the presence of special protection systems (SPS) and demonstrates the approach for the most common type of SPSgeneration rejection scheme (GRS). Keywords probabilistic risk, transient stability assessment, generation rejection scheme (GRS), reliability
1.
Introduction
This paper presents an approach to assess risk of transient instability in power systems. A framework for probabilistic security assessment was presented in [11 where a severity function is suggested to evaluate the technical and economic consequences of a scenario. We propose a similar approach where the security aspects of an operating point are coupled to the economics of it through a measure of risk. This way it is possible to measure the degree of risk inside the secure region as well as outside of it. The first steps towards this approach were presented in [2]. An extension of that work is the topic of this paper; here the probability and impact models used here are more elaborate and accurate. In addition, different ways to display risk information are proposed and some suggestions are given of how risk can be used for determining operating limits. This risk value is equivalent to the expected cost of tripping generation due to either loss of synchronism or controlled trip. It is defined as the product of the probability of having this event occur over a certain period of operation with the consequences of the event. This computed risk index is useful for making decisions related to operating limits or it can be used to compare alternatives for enhancing stability performance. Finally, it enables dynamic security to be assessed and compared together with overload and voltage security using the same risk index [3-51. Therefore, we may use it to obtain a composite measure of security. Special protection systems (SPS) (also called remedial action schemes or RAS) are designed to detect abnormal
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system conditions, typically contingency-related, and initiate pre-planned, corrective action to mitigate the consequence of the abnormal condition and provide acceptable system performance [6]. SPS can provide rapid corrective actions and are often used to increase the transfer capability of the network. However, excessive reliance on SPS can result in increased risk. Because SPS are normally armed only under stressed conditions, when their failure would result in very severe consequences, this risk can be significant. In addition to the risk caused by failure to operate when required, SPS also contributes risk via unintended operation and unplanned interaction with other SPS. There are many types of SPS in use today; 93 schemes and 113 special protection schemes were reported in operation in the 1988 CIGRE’s survey [7] and in the 1992 IEEE-CIGRE’s survey [8,9], respectively. Since the most commonly used SPS type in industry is generator rejection scheme (GRS) [7-91, we will extend our analysis to also include the GRS case.
2.
Risk Calculation
We will use the following notation: Fi : event that there is a fault on circuit i. A : fault type random variable. We define one phase to ground, two phase to ground, three phase to ground and phase to phase fault, represented by 1, 2, 3, 4, respectively, as all possible values of A. N, : number of critical circuits. N, : total number of events considered in the study. Ei :initiating event. The first N, initiating events correspond to ‘“-1” outages, i.e., nFi nFi+, FN, Ei = nF2...
c-,
a . 1
i = l,...,N,
and the N,
+ 1 initiating event is no fault, i.e.
nFN, E ~ ~=+ , nF2 n-.. Outage events Ei+i> N , + 1 correspond to simultaneous outage of two or more circuits. Note that normally, N, 2 N, + 1 . Also we have:
pre-contingency operating point; it is a vector of critical pre-contingency controllable parameters which significantly influence the postcontingency system performance. T: GRS tripping event Risk(.) ,Im(.) ,Pr(.) : risk ,impact, respectively, probability of an event K: transient instability event, i.e., it is the trip of a certain generator due to loss of synchronism. The risk of a generation plant without GRS comes from the potential of having a fault on a nearby circuit that will cause the units at the plant to lose synchronism with the rest of the system. The significant factors here are the identification of the faulted circuit, the fault type and location on the line, and most importantly the operating condition, typically characterized by the generation level of the plant at risk. A GRS is designed to trip some pre-selected generating unit(s) at a plant in order to prevent loss of the entire plant. Each operation of a GRS is classified into one of the following categories:
X:
GRS trips when a contingency occurs ( T n E i ) , i = 1 , 2 , . . . , N c , N c+ 2 , . . - , N , 2 . The GRS does not trip when a contingency occurs 1.
The
( T n E i ) , i=1,2,-..,N,,Nc +2,...,N, 3. The GRS trips when there is no contingency (T E N , + I ) 4. The GRS does not trip when there is no contingency
(T nEN,+I 1 . According to these categories, the risk for a system with a GRS comes from three sources: If a GRS fails to take corrective measures when armed and initiated, the plant may or may not experience an out of step condition, depending on the pre-fault operating condition, and fault type and location. 2 . If a GRS takes action promptly and correctly as designed, system stability will be maintained, but nonzero impact will occur via a controlled trip of a block of generation capacity. 3. If a GRS takes an unnecessary action when there is no outage for a critical line, then non-zero impact occurs via a controlled trip of a block of generation capacity. This is called a nuisance trip. Therefore the significant factors for a plant with GRS are the same as those without GRS plus the reliability level of the GRS itself. In the case when there is no GRS, we desired to find the risk over the next time period (e.g., 1 hour) associated with the transient instability event K, given operating condition, X , due to all possible N , events. This is 1.
-
Risk(K /X) = Pr(K /X)Im(K / X) N.
i=l
In the case of where we have GRS, we desire to find the risk over the next time period associated with either the transient instability event K or a GRS trip T due to all possible N , events. This is
Risk(K U T / E ) =
NT
Pr((K
nrnEi ) / X)
i=l
x Irn((K nf n
)/
X)+
N,
Pr((T n
/~
)
x
(2)
i=L
Im((T nEi ) / X) Here, the first term expresses the risk from source 1, which is the same as that given by eq.1 if we assume the GRS fails with probability 1.0. The second term expresses the risk from source 2 ( i # N , + 1 , GRS trips as desired) and from sources 3 ( i = N , + 1 , GRS nuisance trips). In what remains, we will drop the notational dependency on X , leaving the reader to be cognizant of it throughout.
2.1 Probability The event K may only occur following the occurrence of a fault F;. Following assumptions typically made for operational and facility planning, we further assume that protective systems work properly and a fault on circuit i causes outage of circuit i, i.e., event Ei follows F;. We first consider the case of no-GRS. Because A=l, A=2, A=3, A=4 are mutually exclusive and exhaustive events, we obtain for the probability term in eq.1: A
Pr(K nE; n( A = n))
Pr(K nE; ) = n=l
=
Pr(Ei n ( A = n)) Pr(K /(EiA ( A = n)))
(3)
n=l 4
/ ( E i n ( A = n))) n=l
I
II
m
Eq.(3) requires three probabilities inside the summation. For the first one (I), Pr(Ei) , we assume the fault process on a circuit is a homogeneous Poisson process. We also assume the failure rate of circuit i is Ai. Then the fault probability in unit time is i = l;.., N, Pr(Fj.)= l-e-', Since F,, F 2 , . . . , F., are independent of each other, we have
207
-
-
Pr(Ei)=Pr(q n ~ - . n F~ , n F- , ,I, - - . F , ~ )
= Pr(560MW, the risk increase is again more gradual, but not zero, since the impact is still increasing due to higher generation levels. R& -us
The fault type probability for a three-phase fault, twophase to ground fault, single phase to ground fault and line-to-line fault are 6.2, 10, 75 and 8.8%, respectively. The number of faults per hour for line 12-13 and line 13-23 are 4.65E-6 and 9.30E-6, respectively.
G m e r b
a
Figure 2 - Risk versus generation at bus 130
Figure 1 - IEEE RTS 24 bus system 1
It is assumed that the units are producing at c,ig = $19/MW, and in case of tripping of these units, their supply can be replaced at a cost of C,,,~ = $32/MW. The down time for a tripped unit is 10 hours. The fixed start up and repair costs are estimated at $156,000 per unit. Simulations were done to determine what the amount of load to be shed for different power levels of at the generators at risk. The cost of this interruption is assumed to be very high, C1-d = 200 $/MWh.
3.1 Risk versus parameter plots Figure 2 illustrates the influence of the generation level on the risk. The horizontal X-axis represents the total generations of the three units at Bus 13. The more these units are supplying the higher the probability that they will loose synchronism in case of a fault in the neighborhood. The increase in generation at Bus 13 is compensated by a
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Figure 3 - Risk versus load at Bus 130 Figure 3 represents the variation in Bus 13 load compensated by variation in Bus 21 Generation, holding Bus 13 generation constant. Under these conditions, risk decreases as Bus 13 load increases. This influence is caused by off loading of the faulted line as the load at Bus 13 and the generation at Bus 23 are increased.
3.2
GRS risk illustration
Figure 5 shows a portion of the IEEE Reliability Test System together with an illustration of the SPS logic. Lines 12--13 and 13--23 are critical lines. Without SPS, outage of either of these two outlet transmission lines may result in a plant-out-of-step condition. To improve
the transient stability performance of this plant, a GRS is installed. When the GRS detects a line outage on either of these two lines, it trips promptly only one generator to keep the other two generators in service. The GRS logic is simple: when there is a fault on a critical line, the breakers on this line open: an “open” signal (high level signal) from any breaker energizes the output of the OR gate. The high level signal from the OR gate output, together with the high level arming signal, sets the AND gate output in high level, which is input to the 2 out of 3 voting scheme. When two or more of the voting scheme input signals are high signals, the voting scheme output signal is high; otherwise, it is low. The high level signal from the voting scheme will trip the selected generator. Here, we assume breakers and the voting scheme are fully reliable. Breakers are external to GRS; so assuming they are 100% reliable helps to isolate the SPS influence. Their failure potential can be included in this analysis if desired. Assuming a fully reliable voting scheme is used to simplify the illustration.
4
Risk(K UT) =
c 2
=
Risk(Ei) i=l
Pr(K n T nEi) Im(K n T nE i )
(1 1)
i=l
3
+
Pr(T nEi ) Im(T nEi ) + Pr( E, ) Im(E4)
i=l
The risk expression for the system without GRS is 4
Risk(K) = =
2
Risk(Ei) i=l
(12)
Pr( K nEi ) Im(K nEi ) + Pr(E4) x Im(E4)
i=l
Based on eqs. 11 and 12, we obtain Figure 6, which shows that the generation level 573 MW is the optimal arming point; while using the worst-case scenario (three phase fault at Bus 13) gives us the arming point 430 MW. By arming the GRS at the generation level 430 MW, the system risk is actually increased by $6.09/hr. Hence the traditional worst-case scenario method to determine the arming point can unnecessarily increase risk. On the other hand, when the GRS is armed at the generation level 600 MW, the system risk is decreased by $1.80/hr, which could be subsequently used as an indication of worth to the system of operating a GRS.
Bus 23
IT p1 RI
2 U
.f
N
line 12-13
y-‘
and for generation levels above the arming point, risk with armed GRS is smaller than risk with GRS not armed. In our example, the total risk expression for the system with GRS is
Bus 13 9I
Bus 12
, I
8 -
Figure 5 - GRS logic circuit and voting scheme
I
In present industry practice, the GRS arming point is obtained deterministically with worst-case scenario simulation regardless of arming time2. The three phase fault is the most severe fault, but due to the rarity of its occurrence, its influence on risk may be less than the influence of the two phase fault or one phase fault. Therefore the deterministic arming point which is obtained only considering the three phase fault is not always equal to the probabilistic arming point which accounts for the influence from all four types of faults. The RBSA criteria for identifying the optimal arming point is : “arm to minimize risk.” Therefore, if we plot risk vs. generation level for GRS unarmed and GRS armed, the optimal arming point is when the two curves cross. In other words, for generation levels operating below the arming point, risk with armed GRS is larger than risk with GRS not armed, Arming time is the time duration for which GRS is expected to be armed.
210
1
-’
Riskwithwt GRS,
440
460
480
500 520 540 Generationat Bus 13 in MW
560
580
M
Figure 6 - Determination of Optimal Arming Point
4.
Risk-based generation limits
An important contribution of the risk approach to the security assessment is the ability to develop risk-based limits. Presenting these limits in a graphical form as under the deterministic approach will facilitate the interpretation of the limits by the system operator. From Figure 2, the deterministic generation limit would be 450
MW. Up to this level, none of the selected contingencies will cause the generation to go out of step. On the other hand, it is also clear that exceeding this value only makes the risk increase slightly. It is only when the generation level goes beyond 550 MW that the risk starts growing steeply. Therefore, the slight increase in risk of operating beyond the traditional limit should be compared against the economic benefits of supplying more power. The level at which a company is willing to supply depends on the attitude of the operator towards risk and is a decisionmaking problem. To fix these limit, a threshold risk value needs to be determined. The operating region will then be defined by an area delimited by a constant risk contour. Several ways exist to define such a threshold risk-value. One way is to use judgement or experience based on what has previously been defined as acceptable operating points in the past. We recommend applying this method initially in order to gain experience with the risk index and to provide a link to the deterministic approach and to make the transition from one approach to another more acceptable for the system operators. This method could be applied by computing risk for acceptable operating points where system response to a contingency is stabilized through generation rejection. The tripping of a unit leads to a certain cost, that, when multiplied by the frequency of fault occurrence, corresponds to a certain amount of risk that has been accepted. This value could be used as a threshold riskvalue. The limiting operating conditions are then defined by all operating conditions having an associated risk equal to this threshold value. This is called the equal risk criterion [3].
5.
work, including A. Irizarry-Rivera, Hua Wan, Weihui Fu, Vincent Van Acker, Sanyi Zhao, and Youjie Dai. References [l] Cigre Task Force 38.03.12,“Power System Security Assessment: a position paper,” Final Report, June.97. [2] McCalley J.D., Fouad, A..A., Vittal V., Irizarry-Rivera, A., Agrawal, B.L., Fanner, R. G., “A Risk-based security index for determining operating limits in stability-limited electric power systems” IEEE Trans. Pwr. Sys., Vol. 12, No. 3, Aug. 1997 [3] Wan H., McCalley J., Vittal V., “Increasing Thermal Rating by Risk Analysis”, PE-090-PWRS-0-1-1998, to appear in IEEE Transactions on Power Systems. [4] Wan H., McCalley J., Vittal V., “Risk Based Voltage Security Assessment”. submitted for review to the IEEE Transactions in Power Systems. [5] W. Fu., McCalley J., Vittal V., Risk-based Assessment of Transformer Thermal Overloading Capability”, Proceedings of the 30th North American Power Symposium, Cleveland, Ohio, October 1998 [6] NERC Planning Standards, September, 1997. [7] W. H.Winter and B. K. LeReverend, “Operational Performance of Bulk Electricity System Control Aids, ”Performances de fonctionnement des aides ala conduite d’un reseau electrique, Electra, No. 123, Marchlmars 1989, pp. 97-101. [8] P.M. Anderson and B. LeReverend, “Industry Experience with Special Protection Schemes,” Electra, No. 155, August 1994. pp. 103127. [9] P.M. Anderson and B. LeReverend, “Industry Experience with Special Protection Schemes,” Discussion, IEEE Trans. Pwr. Sys., Vol. 11, No. 3, Aug. 1996 [lo] W. Fu, S. Zhao, J. McCalley, V. Vittal, and N. Abi-Samra, “Riskbased Assessment of Transient Stability with A Generation Rejection Scheme,” under review by IEEE Trans. Pwr. Systems. [ l l ] Van Acker V., McCalley J., Vittal V., “Risk-based Transient Stability Assessment using Neural Networks”, Proceedings of the 30th North American Power Symposium, Cleveland, Ohio, October 1998
Conclusions
In this paper the concept of risk of transient instability is presented. An approach is proposed to calculate risk corresponding to one operating point and the required mathematical expressions of the probability and impact are derived. The approach is applied to a portion of the IEEE RTS and the results are displayed in the form of risk variation plots and contours of constant risk plots. An approach to assess the risk of transient instability with a GRS in use is, and it integrates the effect of GRS reliability. Risk-based security assessment with GRS in use is also presented. Finally, a way to obtain operating limits based on risk is discussed. Acknowledgements The authors would like to thank the Foundation of Science and Technology, Portugal - PRAXIS XXI Program BD/9298/96 for the financial support granted to V. Van Acker. Funding for this work came from the EPRI Contract W08604-01, and the National Science Foundation, Grant ECS9502790. The authors also acknowledge the contributions of graduate students previously or presently involved in this
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Vijay Vittal is professor of electrical and computer engineering at Iowa State University. He received his PhD from Iowa State University. He is recipient of the 1985 Presidential Young Investigator Award and an IEEE Fellow. James D. McCalley is an associate professor of electrical engineering at Iowa State University, where he has been employed since 1992. He received his PhD from Georgia Tech. He was employed by Pacific Gas & Electric Company as a transmission planning engineer from 1986 to 1990. He is a registered professional engineer in California, and an IEEE senior member. Nicholas Abi-Samra has a Bachelor of Engineering degree from the American University of Beirut and a Masters of Science in Electrical Power Engineering from the University of Missouri. From 1977 to 1997, he was with Westinghouse Electric Corporation. He joined EPRI in August 1997. Currently he is Manager, Systems Planning, Grid Operations and Planning. Weihui Fu received his B.S.and M.S. degree from Shanghai Jiaotong University, China in 1991 and 1994 respectively. He is currently working towards his Ph.D. in Electrical Engineering at Iowa State University. He is a student member of the IEEE. Vincent Van Acker received his Engineering degree from the University of Ghent, Belgium in 1992 and his M. S from the University of Porto, Portugal in 1995. He is currently a research assistant at Iowa State University where he is pursuing a PhD degree.
