Valuation Of Reactive Power

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 4, NOVEMBER 2001

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Valuation of Dynamic Reactive Power Support Services for Transmission Access Wilsun Xu, Senior Member, IEEE, Yi Zhang, Luiz C. P. da Silva, Student Member, IEEE, Prabha Kundur, Fellow, IEEE, and Allan A. Warrack

Abstract—Competitive procurement of reactive power support services is rapidly becoming a reality for deregulated electricity markets. It has resulted in a great need to quantify the value of reactive power support from var sources. This paper presents research results on the development of new concepts and schemes for equitable reactive power support valuation. Performance characteristics of the proposed method are determined and practical application issues are addressed. The validity of the method is verified through sensitivity studies. This work emphasizes that the valuation of reactive power support services should be based on their contributions to system security and stability. The dynamic var is the primary concern for the reactive power valuation problem. Index Terms—Ancillary services, open access, reactive power support, voltage security.

I. INTRODUCTION

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HE RESTRUCTURED electricity market identifies the supply of reactive power as a key type of system support services. As the knowledge on managing real power transactions over an open- accessed network gradually matures, how to qualify and compensate reactive power support service is becoming an urgent research subject. From the perspective of generator owners, proper compensation of individual generators reactive power output and reserve provides a clear market signal for them to balance the need for real and reactive power generation. From the perspective of transmission administrators or operators, it is critical to recognize and capitalize on the varied importance of different reactive power sources so that the system security and stability can be maximized through a competitive pricing mechanism. Research on methods for valuation or pricing of reactive power support has become quite active recently [1]. Most of the published works are focused on determining the cost of reactive power transportation, using the ideas of real power wheeling [2]. Optimization theories are the main tools to determine the spot prices, marginal costs, wheeling costs, etc., for the reactive power [3]–[5]. Some of the optimization methods include static security constraints such as voltage profiles and line overloading [4]. A common characteristic of these works is that they are essentially the extension of the real power wheeling ideas to the reactive power domain. Such a formulation is Manuscript received Arpil 7, 2000; revised June 29, 2001. This work was supported by the Natural Science and Engineering Council of Canada strategic grant. W. Xu, Y. Zhang, L. C. P. da Silva, and A. Warrack are with the University of Alberta, Edmonton, AB, Canada (e-mail: [email protected]). P. Kundur is with Powertech Labs Inc., Surrey, BC, Canada. Publisher Item Identifier S 0885-8950(01)09429-9.

questionable since the reactive power is not a commodity and cannot be shipped over a long distance. “Wheeling” of reactive power has no practical use. Furthermore, there is no distinction between the static and dynamic vars in such methods. It is the dynamic vars that are of much greater value in terms of supporting open access [6]–[8]. What is interested by industry is to determine the relative importance or values of the dynamic var sources such as generators in a system. There is, therefore, a need to formulate and solve the problem from a different perspective. This has led the authors to introduce the concept of “value curves” to quantify the relative importance of dynamic var sources [9]. An Equivalent Reactive Compensation (ERC) method was proposed to determine the value curves [9]. In this paper, the concept and method are further improved by addressing practical application issues. Performance characteristics of the method are investigated using two real-life large-scale power systems. The validity of the method is demonstrated through sensitivity studies.

II. THE CONCEPT OF VALUE CURVE AND ITS DETERMINATION A typical scenario that requires to value reactive support services is as follows: two real power producers are injecting reactive power to a system. One producer is close to the load center and the other is far away. It is required to compensate the two reactive power sources differently. Equal compensation is not desirable since it gives a wrong signal to the suppliers of system support services and could eventually harm system security. It is clear that a simple, qualitative generator ranking scheme is not sufficient for this problem. What is needed is a quantitative index that can represent the value (or the perceived usefulness) of the reactive power output of each producer. The value should vary as the output changes. The reactive power reserve level of the producer should also be reflected in the index. We envision that an ideal solution to this problem is a set of value curves shown in Fig. 1. Each curve represents the value of the var produced by the respective var in terms of contributing to the system margin. It should be noted that the value curves essentially measure the relative importance of the var sources. They have no direct relationship with the cost (investment cost or opportunity cost) of the sources. A var source could have a high cost yet have a low value. In this case, it may not be profitable for the source to offer reactive support service. Therefore, the value, not the cost, is the main factor affecting the compensation level a var source could expect to get. With the value curves, transmission administrators can develop technically sound compensation schemes.

0885–8950/01$10.00 © 2001 IEEE

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Fig. 2.

Fig. 1. Value curves for assessing dynamic reactive power sources.

A. Equivalent Reactive Compensation Method An Equivalent Reactive Compensation (ERC) method was proposed to determine the value curves [9]. The basic idea of the method is as follows: if a var source reduces its output, the network voltage profiles and margins will change. To maintain the same degree of system security, var compensations must be added to the system. The total amount of compensation added is, in effect, a direct measure of the value or importance of the missing var output from source . The compensation can be realized, for example, by fictitious condensers distributed across the system. The condensers serve as “thermometers” to provide an uniformed measurement on the impact of varying the output of any physical var sources. The following is the procedure to implement this idea: 1) Establish a solved case for the system condition of interest; 2) Add fictitious condensers to each load bus. The output of these condensers are zero at the base case. There are no reactive power limits for the condensers; 3) Hold the reactive power output of all existing dynamic reactive sources at the base case levels. This can be done buses injecting the base case by representing them as reactive power; 4) For the dynamic var source whose value is to be determined, vary its reactive power output from zero to its var limit. The total reactive power output of all fictitious con, are calculated in the process; densers, called as a function of , the output of the study 5) Plot source. This curve, called compensation curve, therefore on the system; measures the impact of 6) Steps 4) to 5) can be repeated for all physical dynamic var sources of interest. A family of curves can be generated. Each curve represents one var source. The most important generation. In sources are those that require a lot of other words, the shortage of var output from these sources has to be made up in large amount from other sources across the system. The computation effort of the above procedure is comparable curve. Namely, the value to that needed for calculating a curve of each source involves the calculation of 10 to 20 power buses because flow cases. For each case, most buses are of the existence of the fictitious condensers. The chance of encountering numerical problems is therefore lower than that of curves. Sample results of the ERC method applied to a the

A simple system for concept illustration.

simple 5-bus system (Fig. 2) are shown in Fig. 3. The system consists of three generators (buses 1, 2 and 3) feeding a load center (bus 5). There is a distant slack bus (bus 4) that supplies almost no power to the load but serves as a reference to the system. The fictitious condenser is added to bus 5 in this case. Fig. 3(a) shows the results for the case of different generator distances. The closest generator (G1) has the highest value for almost entire curve. The index of G3 has a large varidecreases the index first exceeds other curves and ation. As then stops before reaching zero. Although this appears in contradiction to common perception, the results are correct. Further study shows that the phenomenon is caused by the need for G3 to ship its real power to the system over a long distance. If there , the system has to provide a lot of var to is a shortage of gets too low, the generator make up the difference. When becomes incapable of shipping its real power to the system. An important implication of these results is that the var output of a generator has two purposes. One is to support the shipment of its own generated power into the grid and the other is to support the system voltage. To verify this conclusion, a case with zero real power output from G1 and G3 is analyzed. In this case, the sole purpose of the generators is to provide reactive power support. Results, shown in Fig. 3(b), confirm the common understanding that G1 is more valuable due to a shorter distance to the load center. It is fair to say that the ERC method may not be the only one suitable for determining the value curves. During the course of this project, we have tried two other types of methods. The first type is the sensitivity-based methods. The key idea here is first to define a security index and then to determine the effect of each generator output on the index. A typical security index is curve. A var source the system margin determined from the that causes a higher security index response can be considered as more important. The main problem encountered by this method is that the sensitivities are close to zero for many var sources. This is because most var source sources, if acting by themselves alone, have little impact on improving system margin. The second type is the stress-based methods. These methods monitor the responses of individual var sources when the system is being stressed. Reactive sources that are most responsive to stresses can be considered as the highly valuable ones. Sample forms of stresses are the line outage, generator outage, or load increase. This type of methods did not work well either. The methods require to freeze the output of all var sources except the one whose value needs to be determined during the stress process. For large scale systems, this approach seldom results in converged power flow solutions since a single var source is normally insufficient for the system to deal with stresses that have a system wide impact. Due to space limitation, detailed discussions on these methods are omitted.

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(a) Fig. 3.

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(b)

Compensation curves for the test system. (a) All generators have P output. (b) G1 and G3 have no P output.

amount of monetary compensation for reactive power support is shown in the following equation: (2) where monetary compensation for var source ; value of produced or reserved var of the source; total monetary compensation available; total value of all var sources. can be established using simple or compliParameter cated economic principles. III. A GENERALIZED EQUIVALENT REACTIVE COMPENSATION METHOD

Fig. 4. Value curves for the test system.

B. The Value Curve curves contain good technical information. But The they are not suitable for assessing the “value” of each source. A transform is proposed to convert the compensation curve into a value curve. This method is summarized as follows [9]: (1) is the compensation curve for the th reactive where is the lowest permissible var output of the source. source. The value curves corresponding to Fig. 3(a) are shown in Fig. 4. is the most valuable one. As analyzed The figure shows that before, this is true since the value includes two components, one for shipping generated power and the other for supporting the system. The figure indicates that G3 has zero value in the range . It also makes sense since G3 must generate at of 0 to to start shipping power into the system. least The value curve represents the system-wide var savings one can achieve if the output of a dynamic var source is increased. More savings a generator can give to the system implies more important it is to support system security. The value curves can Var curves to price the rebe further transformed into dollar active power of different dynamic reactive power suppliers. For example, a possible (and simplistic) method to determine the

The ERC method summarized in the previous section has demonstrated a potential to solve the reactive source valuation problem. There is a problem, however, due to the indiscriminate use of fictitious condensers. Since all load buses are equipped with ideal condensers, the contribution of each condenser can be significantly influenced by its distance to the study generator [6]. It has no relationship to the size of bus load. As the fictitious var injections can also be viewed as shedding of reactive loads, it is desirable to relate the contribution of each fictitious source to its bus load size. The distribution of the equivalent var injections would reflect the system loading pattern more accurately in this way. Two methods have been proposed to solve this problem. The first method is to represent the fictitious condensers with a SVC – characteristic instead of the ideal constant voltage characteristic. The slope of the – characteristic is a function of the bus load size. If a bus has a smaller load, the slope of its fictitious SVC will be larger. It will take a larger voltage variation for the SVC to produce the same amount of var injection. Thus the amount of var output from a fictitious source becomes directly related to its load size. The second method is to set reactive output limits for the fictitious generators. The var limit can be set in proportion to the size of bus MVA load as follows (3)

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(a) Fig. 5.

(b)

k

Output of fictitious condensers as affected by constant . (a) Distribution of condenser output. (b) Number of condensers with significant

(a) Fig. 6.

Q output.

(b)

Sample results for the BC Hydro system. (a) Compensation curves. (b) Value curves.

where reactive limit for condenser at bus ; and real and reactive loads at the bus; constant applied to all fictitious condensers. Typical value of is 15% to 100%, depending on the convergence characteristics of the study system. A larger gives better load flow convergence. With the var limits, condensers connected to buses with small loads are unable to inject large amount var into the system. More fictitious condensers will share the var shortage. Extensive case studies on large scale systems have shown that the limit model have more advantages. One of the main disadvantages of the SVC model is that the – slopes cannot be very large due to load flow convergence restrictions. But small – slopes are unable to produce sufficient differentiation among the outputs of condensers at different load buses. The SVC model is also more difficult to implement. The limit model is therefore adopted for use as a generalized ERC method. Fig. 5(a) illustrates the method’s performance. The -axis is load bus number ordered by the amount of fictitious injection and the -axis is the output from the fictitious condensers. It can be seen that as the constant gets smaller, more condensers contribute to support the system. Fig. 5(b) also demonstrates that the limit method can get more condensers to contribute with var support. This chart plots the number of condensers outputting more than

1% of total injected ( ). The results show that, for the model ( ), there are only 4 condensers contributing. For %, the contributing condensers are about 10. the case of Another significant improvement to the basic ERC method is that one can add fictitious condensers to selected zones or areas only. With this approach, the value of a generator’s var output can be quantified with respect to its support to specific load centers. IV. PERFORMANCE CHARACTERISTICS The ERC method has been tested extensively on two large-scale power systems. One is a 1200-bus BC Hydro system and the other is a 1800-bus Alberta system. This section presents performance characteristics of the method. The method is implemented using the var limit model and the fictitious condensers are added to the entire study area. A. Basic Performance Characteristics Sample compensation and value curves are shown in Figs. 6 and 7. These curves are obtained for the base case conditions. The results suggest that both the compensation and the value curves follow similar trends to those observed from the small test case. Some compensation curves have negative values. This is because the generators have a very small or even negative var

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(a) Fig. 7.

Fig. 8.

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(b)

Sample results for the Alberta system. (a) Compensation curves. (b) Value curves.

Variation of valuation results with respect to constant k.

output at the base case. The value curve is not affected by the existing var output. Those who are familiar with either test systems may notice that some remote generators exhibit high value curves. This phenomenon is again caused by the reactive power needed for those generators to send their own real power output into the grid. The total values of the vars from such generators are therefore high. The impact of constant on the valuation results was investigated. This study calculates the value of each generator with as a parameter. Fig. 8 plots the value results when the generators produce 50% of their maximum var output. The figure suggests that for most generators, the values are not sensitive to the constant . Two large remote generators (MCA and REV) exhibited some degrees of value variation. This is due to the fact that to compensate these remote generators need a lot more their var output reductions. Many far away fictitious condensers therefore will participate as a smaller is used. The total becomes large. In spite of these variations, consistent var valuation results can be maintained if a system specific is chosen and used consistently. The impact of system loading levels on the var valuation results was also investigated. This is done by calculating the value curve nose point case. curves for the base case and for the Fig. 9(a) shows the value results when each generator has 20% and 50% output respectively. It can be seen that the values of

supports are larger in the nose point case. It makes sense intuitively. Another reason for the value increase is that the large generators produce more real power at the nose point. More reactive power must be produced by these generators to support the shipment of their increased real power output. This case further demonstrates the need to separate the two functions of a generator’s reactive power output. An attempt is made here to determine the impact of real power shipment on the value index. Fig. 9(b) shows the var value per MW generator output. It can be seen that the order of the generators has changed. Some smaller generators that are close to load centers exhibit more values per MW output. Two large generators have smaller per MW values at the nose point case. Our explanation is that a larger portion of the var output of these generators is used to support their increased real power output at the nose point case. Results obtained from the Alberta system are similar to those from the BC Hydro system. B. Contingency Study Results The purpose of contingency studies is twofold. Firstly, it is a way to verify the performance of the ERC method. Secondly, the impact of contingencies on reactive power support valuation is itself a subject of interest. It is important to know how the contingencies change the valuation results. The procedure of contingency studies is as follows: Apply a line contingency to the base case and establish a post-contingency case; Determine the compensation and value curves for the post-contingency case; Repeat the above process for different contingencies; and Determine the value difference between the contingency case and the base case; This procedure deals with each contingency case as a new case. The value of a generator is expected to be different for different contingencies. 15 critical contingencies are selected for each system. This study produced more than 400 value curves. Test results on both systems show that the post-contingency value curves are also monotonically-increasing curves. To

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(a) Fig. 9.

(b)

Comparison of var values between two load levels. (a) Total value of var support. (b) Value per MW output.

(a) Fig. 10.

(b)

Generator var value change with respect to line contingencies. (a) BC Hydro system. (b) Alberta system.

(a)

(b)

Fig. 11. Total value change as a function of line contingencies. (a) BC Hydro system. (b) Alberta system.

facilitate the digestion of the results, the differential value curves and data between the base case and the contingency cases are used. Fig. 10 shows the changes of the value results at 50% generator var output for three different contingencies. As expected, some generators exhibit significant value change and the contingencies increase the value of reactive power support services. Fig. 11 shows the total value change of all test generators with respect to different contingencies. It is noted

from the results that the critical contingencies cause more value change than the non- critical contingencies. Fig. 12 correlates total value change with the pre-contingency line flow. A good correlation can also be observed from the figure. Both Figs. 11 and 12 demonstrate that the ERC method has a good agreement with engineering judgment. The results have shown that different load patterns and system configurations will result in different value curves for the same

XU et al.: VALUATION OF DYNAMIC REACTIVE POWER SUPPORT SERVICES FOR TRANSMISSION ACCESS

(a) Fig. 12.

(b)

Correlation of total value change with pre-contingency line flow. (a) BC Hydro system. (b) Alberta system.

(a) Fig. 13.

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(b)

Correlation of QERC with the system PV margin reduction. (a) BC Hydro system. (b) Alberta system.

generator, which is expected. Each value curve can be used to establish a compensation price for system support services. Although this approach is more accurate, it is somewhat cumbersome. We propose a comprehensive value curve for application in different operating scenarios. This value curve can simply be a weighted summation of all value curves for each generator. For example, the following equation can be used to construct such a curve for particular generator: (4) where combined value curve for the study generator; value curve for th contingency (including base case); weighting factor for each case. V. VERIFICATION STUDIES Verification of the proposed method is a challenging task since we are dealing with a new concept and there are no “correct”results available for comparison. In fact, if there were a technique that could thoroughly verify the ERC method, the technique itself would be a good tool for reactive support valuation. In spite of this problem, the validity of the proposed method can be checked indirectly by assessing its relationship with system power transfer capabilities, as the goal of reactive

support valuation is to enhance system security [7], [8]. Several voltage stability related indices are therefore used for the purpose of verification: •

Margin: If a generator is very important, withdrawing its var support will likely lead to significant reduction of system margin. • Generator Output Sensitivity: Generators will increase their reactive power output if a system’s reactive power demand increases. Important generators are expected to have more significant increase in their output. • Impact of Contingencies: When contingencies are applied to a system, the reactive power output of each generator will increase. Important generators are expected to output more reactive power. margins is done The correlation of ERC results with the as follows: for each test generator, an ERC index is calculated. margins calculated from the base The reduction of system case and a case without the test generator’s var support is also determined. The ERC index is then compared to the margin reduction index. A positive correlation between the two indices would indicate the usefulness of the ERC method. Fig. 13 shows the correlation results. A good correlation is observed. The generator output sensitivity method monitors the var outputs of all dynamic var sources as the system reactive

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(a) Fig. 14.

(b)

Correlation of QERC with the generator output sensitivity. (a) BC Hydro system. (b) Alberta system.

(a) Fig. 15.

(b)

Correlation of QERC with contingency impact. (a) BC Hydro system. (b) Alberta system.

indicate that sufficient correlation does exist. The GENESE generator in Fig. 15(b) has a small reserve and it reaches limit early when contingency is implemented. As a result, its post-contingency var increase is small. All correlation study results indicate that the ERC method can provide a consistent measurement of the value of reactive power support. The imperfect correlation shown in some of the results is more likely due to indirect comparisons rather than the performance of the ERC method. Fig. 16.

Determining the value of reactive power reserve.

load increases. If a generator is important, it tends to output more reactive power. The reason to increase reactive loads only is to maintain the same real power generation pattern for the system. Fig. 14 shows the correlation results for a 2% reactive load increase. A general correlation pattern can be noted from the figure. The discrepancies are caused by the fact that the generator output sensitivity is not a true sensitivity: all generators respond to the load increase. True sensitivity indices cannot be obtained for this verification study due to convergence problems. The correlation with contingency impact is done by applying 15 critical contingencies to the test systems. The resulting total var output increase of each generator, for all contingenresults. Important cies, is used to correlate with the generators are expected to exhibit more noticeable var output responses to the contingencies. The results, shown in Fig. 15,

VI. THE VALUE OF REACTIVE POWER RESERVE There are two types of reactive power support from dynamic var sources. One type is the produced reactive power and the other is the reactive reserve. The value of produced var can be obtained from the value curve directly. The value of reactive reserve, on the other hand, cannot be calculated as the difference between the value of produced var and that at the generator limit. This is because the var reserves of some (remote) generators may not be fully utilized by the system. The maximum potential contribution of each var source can be detercurve method. We propose to mined using the well-known curve nose point use the var output of each source at the as the maximum potential var contribution of that source. The value of reactive power reserves can be determined according is the maximum var a source can to Fig. 16. In the figure, inject to the system when the system is stressed to the limit (i.e.,

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(a) Fig. 17.

(b)

Values of produced versus reserved reactive power support. (a) BC Hydro system. (b) Alberta system.

curve nose point). For important var sources, is typi. But for remote generators, it is possible that cally equal to is less than . This means that the var capability of the generator cannot be fully utilized due to system constraints. Fig. 17 shows the results obtained from both test systems. It can be seen that reserves of some generators indeed have less values than those of other generators, although the produced var has a is contingency delot more value. It should be noted that pendent. Therefore the total reserve value should be determined using a formula similar to (4). VII. CONCLUSION AND FUTURE WORK This paper has presented a systematic investigation on the subject of how to assess the relative importance of different dynamic var sources. An alternative formulation, the value curve, has been introduced for the var valuation problem. An Equivalent Reactive Compensation method has been proposed to address the problem. Extensive test results indicate that the ERC method is capable to accomplish such a task. The method provides not only a rank of the sources but also a quantitative value index for different source output levels. Main contributions of this work can be summarized as follows: 1) The papers have established an alternative framework for valuing and compensating dynamic reactive power support services. It is the dynamic reactive power support that has critical importance to system security. The concept of value curve is introduced. 2) A method has been proposed to solve the problem. The key idea of this method is to determine an equivalent value for the produced or reserved var of each dynamic var source. The equivalence makes it possible to compare the var support from different sources on a common basis. 3) Extensive analysis and case studies have been conducted. As a result of these studies, major issues related to reactive support valuation are clarified and an adequate foundation for further work in this area has been established. The test results also verified the performance of the proposed method. As a new area of research, our work can only address some of the key issues related to reactive support valuation. A lot more

follow up research is needed to improve the proposed method for eventual industry use. New methods could also be developed. Our next research effort will focus on the following two subjects: 1) Develop concepts and methods to separate the value of reactive support that is used for helping the shipment of real power from that for improving system security. 2) Extend the proposed method to the cases where var sources absorb reactive power and establish a comprehensive valuation method for the cases of var generation and absorption. In the long run, there is a need to develop concepts and techniques for valuing both dynamic and static var support services in a unified framework, since the static var support is often used to increase reserves for dynamic var sources and for loss minimization. There is a tradeoff between the objectives to increase security and reduce losses. The overall value of a var source should reflect such constraints. New applications could also be identified for the value curve concept and the ERC method. ACKNOWLEDGMENT The authors would like to thank the Alberta power industry (such as the Transmission Administrator of Alberta) for input and support of this project. REFERENCES [1] W. W. Hogan, “Markets in real electric networks require reactive prices,” Energy Journal, vol. 14, no. 3, pp. 171–200, 1993. [2] F. C. Schweppe, M. Caramanis, and R. Bohn, “The costs of wheeling and optimal wheeling rates,” IEEE Trans. Power Systems, vol. 1, no. 1, pp. 63–73, 1986. [3] Y. Z. Li and A. K. David, “Wheeling rates of reactive power flow under marginal cost pricing,” IEEE Trans. Power Systems, vol. 9, no. 3, pp. 1263–1269, 1994. [4] X. Ma, A. A. El-Keib, and T. A. Haskew, “Marginal cost-based pricing of wheeling transactions and independent power producers considering security constraints,” Electric Power Systems Research, vol. 48, no. 2, pp. 73–78, 1998. [5] M. L. Baughman, S. N. Siddiqi, and J. W. Zarnikau, “Advanced pricing in electrical systems. Part I: Theory,” IEEE Trans. Power Systems, vol. 12, no. 1, pp. 489–495, 1997. [6] S. Hao and A. Papalexopoulos, “Reactive power pricing and management,” IEEE Trans. Power Systems, vol. 12, no. 1, pp. 95–104, 1997.

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[7] C. Taylor, “Discussion on ‘Reactive power pricing and management’, by S. Hao and A. Papalexopoulos,” IEEE Trans. Power Systems, vol. 12, no. 1, pp. 95–104, 1997. [8] P. Kundur, Power System Stability and Control. New York: McGrawHill, 1994. [9] W. Xu, Y. Zhang, L. da Sliva, and P. Kundur, “Competitive procurement of dynamic reactive power support service for transmission access,” in Proceedings of IEEE PES Summer Meeting, Seattle, July 2000, paper no. 0-7803-6423-6/00/.

Wilsun Xu (M’90–SM’95) is presently a full professor at the University of Alberta and is a member of a NSERC strategic project team to research open access issues.

Yi Zhang worked as a postdoctoral fellow at the University of Alberta in 1999 and is currently with RTDS Inc.

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Luiz C. P. da Silva is working toward a Ph.D. degree at UNICAMP. At present, he is a visiting Ph.D. student at the University of Alberta, Canada. His research interests are power system voltage stability.

Prabha Kundur (F’85) is currently President and CEO of Powertech Labs Inc. at Surrey, B.C and an adjunct professor of UBC. Dr. Kundur is a member of a NSERC strategic project team to research open access issues.

Allan A. Warrack received the Ph.D. degree from the Economics at the Iowa State University in 1967. He is currently a full professor at the Faculty of Business, University of Alberta. He has been actively involved in the regulation and restructuring of Alberta’s power industry since 1975. Dr. Warrack is a member of a NSERC strategic project team to research open access issues.