Dynamic security constrained optimal power flow/VAr ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 1, FEBRUARY 2001

Dynamic Security Constrained Optimal Power Flow/VAr Planning Ebrahim Vaahedi, Fellow, IEEE, Yakout Mansour, Fellow, IEEE, Chris Fuchs, Member, IEEE, Sergio Granville, Senior Member, IEEE, Maria de Lujan Latore, Member, IEEE, and Hamid Hamadanizadeh

Abstract—Traditionally Security Constrained Optimal Power Flow and VAr planning methods consider static security observing voltage profile and flow constraints under normal and post contingency conditions. Ideally, these formulations should be extended to consider dynamic security. This paper reports on a B.C. Hydro/CEPEL joint effort establishing a Dynamic Security Constrained OPF/VAr planning tool which considers simultaneously static constraints as well as voltage stability constraints. This paper covers the details of formulation and implementation of the tool together with the test results on a large scale North American utility system and a reduced Brazilian system. Index Terms—OPF, VAr planning, voltage stability.

I. INTRODUCTION

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RADITIONALLY, the Security Constrained OPF [1] and VAr planning methods [2], [3] have provided optimal conditions considering static security constraints under normal and contingency conditions. This feasibility definition considering only static security constraints is not sufficient when considering the operation and planning practices in the utilities concerned with voltage stability and other dynamic security constraints. The operation and planning criteria for such utilities include provisions for both static and dynamic security and thus coordinated OPF/VAr planning approaches are needed which can simultaneously satisfy both of these constraints. In the review of the literature, there are a few references which address voltage stability margin calculation using optimization techniques [4], [5]. Reference [6] provides a remedial action formulation to fulfill voltage stability requirement but it does not consider static security constraints. Reference [7] was the first paper to provide a VAr planning formulation to consider both voltage profile and voltage stability requirements. The formulation can consider only one case and hence it is not security constrained. A recent paper [8] realized the need for a tool, which satisfies static and dynamic constraints for congestion management application in a deregulated market.

Manuscript received December 9, 1999. The work reported in this project was developed under a joint agreement on OPF and VAr Planning tool development between B.C. Hydro and CEPEL. E. Vaahedi was with B.C. Hydro, Burnaby, Canada. He is now with Perot Systems, Alhambra, CA. Y. Mansour and C. Fuchs are with B.C. Hydro, Burnaby, Canada. S. Granville and M. de Lujan Latore are with CEPEL, Rio De Janeiro, Brazil. H. Hamadanizadeh is with Powertech Labs, Surrey, Canada. Publisher Item Identifier S 0885-8950(01)02305-7.

Fig. 1. Changing system characteristic to resolve violation of voltage constraint at operating condition A.

In this paper, the formulation of a Dynamic Security Constrained OPF/VAr Planning tool (DSC OPF)1 will be described followed by the implementation of the method. The results obtained applying the developed tool on a large-scale North American utility system and a reduced Brazilian system are also examined and discussed. II. FORMULATION The objective of a Dynamic Security Constrained OPF/VAr Planning tool is to identify the best control actions to ensure the voltage security of an operating condition. The operating condition is voltage secure if, for a given set of contingencies, it meets the following criteria: • The pre-contingency and post-contingency voltages and VAr reserves must be within specified limits. • The voltage stability margin of the pre-contingency and post-contingency cases must be greater than specified limit. The voltage stability margin is defined in terms of a stress pattern. A stress pattern specifies how much load (active and/or reactive) or generation is increased in one or more groups of buses. To explain this in a simple way, consider Figs. 1–3 which give a simple system characteristic of voltage against its active or reactive load. In Fig. 1, the voltage profile constraints are not satisfied therefore, the solution of the OPF/VAr planning tool should 1In the rest of this document abbreviation DCS OPF is used to indicate Dynamic Security Constrained OPF/VAr Planning.

0885–8950/01$10.00 © 2001 IEEE

VAAHEDI et al.: DYNAMIC SECURITY CONSTRAINED OPTIMAL POWER FLOW/VAr PLANNING

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Fig. 4. Preventive control design in DSC OPF. Fig. 2. Changing system characteristic to resolve minimum voltage stability margin requirement.

Fig. 3. Changing system characteristic to resolve voltage profile and voltage stability constraints.

change system characteristic such that it moves the existing operating condition A to a point anywhere between points B and C. Now consider Fig. 2 in which it is assumed that due to our for this opercriteria we need a voltage stability margin of ating condition to satisfy voltage stability requirements. Hence the system characteristic would have to change such that point A moves to points B, C, or others which ensure the operating . Now let us consider the condition has a margin larger than combination of these two curves. The acceptable solution is the one which satisfies both constraints. Therefore, all the characteristics crossing between A and B are acceptable. The derivation of preventive and corrective remedial actions is the combination of two distinct problems one for the original base case (operating point) and the other one for the stressed base case. The details of the formulation for preventive and corrective designs are separately described in the following subsections. A. Preventive Control , are sought For the preventive design, remedial controls, in the pre-contingency ( refers to base case) such that:

1) The original base case and all its post-contingency cases have no voltage or VAr reserve violation. 2) The stressed base case and its post-contingency cases have solution. It should be noted that although the selected preventive controls have the same settings for the two cases, the local controls can take different values from the original base case to the stressed base case. If a selected preventive control itself has active (enabled) local control, e.g., a switched shunt with local voltage control, its control setting, e.g., the voltage range, must be adjusted accordingly. This is to ensure that the control does not move from the original case to the stress or contingency cases, or if it moves for local control, it will not cause security violations. The flow chart describes the formulation as illustrated in Fig. 4. Alternatively if the stressed base case and its contingency cases can be considered as contingency cases for the original base case, the flow chart will turn into a security constrained contingencies as shown in Fig. 5. This OPF which has formulation requires the tool to be able to consider two sets of constraints under the contingency conditions. B. Corrective Control ( to ) In the corrective design remedial measures, and contingencies ( are sought for the base case to ) to ensure that: • The original base case and its contingencies have no voltage or VAr reserve violation. • The stressed base case and its contingencies have solutions. Fig. 6 which provides the flow chart for this formulation indicates a formulation using two security constraint OPF’s coordinated by a higher level block. III. IMPLEMENTATION The preventive and corrective solutions provided in the above flowcharts are obtained through a three level hierarchical decomposition scheme where each sub-problem is solved by interior point method. The following four types of operation sub-problems should be dealt with: 1) A base case problem where preventive controls are designed to ensure the feasibility of the base case operating

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 1, FEBRUARY 2001

Fig. 7.

Fig. 5. Preventive control design in DSC OPF.

Fig. 6. Corrective control design in DSC OPF.

condition in terms of static security constraints, e.g., voltage levels, VAr reserve limits, circuit flow limits. 2) A stressed base case where controls are designed to ensure the solvability of the stressed base case. 3) A contingency case problem where corrective controls are designed to ensure the feasibility of a contingency base case in terms of static security constraints, e.g., voltage levels, VAr reserve limits, circuit flow limits. 4) A stressed contingency case where corrective controls are designed to ensure the solvability of the stressed contingency base case. The final solution is obtained by the iterative resolution of all subproblems, as illustrated in Fig. 7. Each time the base case

Three level hierarchical scheme.

operation problem find new control set point values which make base case operation feasible, the stressed base case is simulated to verify if the power flow is solvable and the contingency operations are simulated to verify feasibility given the control rules from base case to contingencies. In turn, there is an iterative procedure between each contingency operation and the stressed contingency operation. The contingency operation subproblem will only send information to the base case operation after the iterative procedure between the base case and stressed base case has converged. In the simulation of the stressed cases no control optimization is allowed. Also each stressed contingency case is defined by applying the corresponding contingency modifications to the stressed base case as shown in Fig. 7. Control set points, which do not correspond to corrective controls, are sent to the stressed contingency cases by the stressed base case. Control set points which correspond to corrective control, with the exception of ULTC blocking, are sent to the stressed contingency cases by the corresponding contingency base case. For ULTC blocking which is a corrective voltage stability measure, the tap values are sent to the stressed contingency case by the stressed base case. The feedback information from the stressed contingency case to the contingency case is designed to provide information on the effectiveness of the corrective controls. The hierarchical scheme above is implemented through Benders decomposition [9], [10]. The base case configuration is associated to an optimization problem whose objective function is the cost of generation redispatch plus the sum of fictitious reactive injection. During its optimization a sufficient number of preventive control is released so that at its optimal solution total fictitious injection of reactive power is equal to zero. The stressed base case, contingency cases and stressed contingency

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cases are associated to optimization problems whose objective function are the sum of fictitious injections of active and reactive power. The information from the stressed base case to the base case, from the contingency case to the base case and from the stressed contingency case to the contingency cases indicated in Fig. 7 corresponds to the Benders cuts. The overall optimization finishes when fictitious injections of active and reactive power are equal to zero in all sub-problems. Each sub-problem represented in Fig. 7 is solved through interior point methods [11], [12] which have proved to be very effective in dealing with voltage collapse problems [6]. Consider the optimization problems in the following form: Min (1) Subject to

Fig. 8.

Primal–dual direct interior point method.

Fig. 9.

Bifurcation diagrams.

(1.1)

(1.2) is the objective function and represents the where equality constraints. The first step in the application of the primal–dual algorithm to problem (1) is to incorporate constraint (1.2) as a logarithmic barrier function: Min (2) Subject to

(2.1) where is the barrier parameter. The basic idea of the algorithm is to solve approximately problem (2) for each value of and force go to zero; at the limit, the optimal solution of problem (1) is obtained. For each value of one iteration of the Newton–Raphson algorithm is applied to the nonlinear system of equations derived from the optimality conditions of problem (2). A crucial point in the method is the control of the primal and dual variables in its iterative process. Fig. 8 shows the basic steps of the interior point method applied here; for further details see [6], [12]. IV. NUMERICAL RESULTS WITH A SMALL SYSTEM The ideas of the paper are first illustrated using a reduced system obtained from a large-scale Brazilian utility system. As shown in the system diagram given in Appendix, the system has 11 buses and 15 circuits. The main load center of this system is located at Coxipó 138 kV substation with a peak load of 260 MW. In the numerical experiments with this system, load variations have been considered, keeping a constant power factor at

bus Coxipó 138 kV. The load types are all constant PQ. The control list consists of the three manually controlled transformers, indicated on the on-line diagram. For results validation, the Continuation Power Flow and Point of Collapse Program—PFLOW developed by Alvarado and associates [13] has been used. For this study the following three cases have been considered observing the conditions for the normal case and one contingency: 1) The original case with initial tap values for the three manually controlled transformers. 2) Maximizing Voltage Stability margin by adjusting the three manually controlled transformers. 3) Satisfying voltage stability margin requirement while observing voltage profile limits under normal condition and a contingency. The original case with no voltage profile violations has a voltage stability margin of 11.4% as shown in the curve called Tap-ori in Fig. 9. Optimizing the tap positions to maximize

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 1, FEBRUARY 2001

voltage stability margins increases the margin to 14.7% as shown in the curve Tap-otim in Fig. 9. Now despite the larger voltage stability margin, the new tap values are not satisfactory because they result in voltage limit violations at the normal operating conditions. As shown in Fig. 9, voltage level for the Coxipó 138 kV bus in the un-stressed base case is close to 1.1 pu well outside the limit band of [0.95, 1.05]. Finally, in the third case the required voltage stability of 12.9% was specified for the normal case and for one contingency case. With the initial tap values, the original base case has no operating limit violation as mentioned before. However when these tap values are considered in the stressed base case, the required margin is not attained which is reflected by nonzero fictitious active injections in the optimization solution corresponding to this case. This results in the computation of a Benders cut which is sent to the original base case. Taking into account the Benders cut and the base case operating limits, a new set of tap values is computed. As a result, in the final solution of the optimization problem associated to this case, the problem has no nonzero fictitious injections of active or reactive power. This means that in addition to ensuring the required margin, the new set of tap values does not result in any base case voltage limit violations. Fig. 9 shows the bifurcation diagram associated to the new set of tap values (Tap-dsc curve) indicating that the voltage level for Coxipó 138 kV bus in the un-stressed case is lower (1.027 pu) than in the preceding case.

V. RESULTS OF A LARGE BASE CASE UTILITY SYSTEM In this section, the application of the to a North American electric utility system with 1449 buses, 2511 circuits, 778 transformers and 240 generators is covered. Two studies are conducted on this system. The specifications of the first study are given below: MVA • A minimum voltage stability margin of at the major load center had to be observed under the normal and contingency conditions. • Static operating constraints were required to be observed under the normal and contingency conditions. • The contingency considered included the loss of a 500 kV line and a 200 Mvar shunt (200 Mvar). • The Preventive control list included voltage set points for generators, switchable shunts and ULTC’s, manual capacitor and reactor switching and manual transformer tap adjustment. For the corrective controls, only manual capacitor and reactor switching and manual transformer tap adjustment were allowed. Under normal operating conditions, no preventive control needed to be activated since there were no operating constraints violations. Also the load margin was achieved with no fictitious injections in the stressed base case. For the contingency case on the other hand, the set points were not satisfactory, The optimization ended with 8.6 MVAr of fictitious injections

distributed at four buses with no corrective control activation. The injections were deducted from the loads in the simulation of the stressed contingency case. As a result no additional fictitious injection was necessary for this case. Then a Benders cut was generated from the un-stressed contingency case to the base case. With the Benders cut the base case is resolved to compute a new set of set points. A generator and a switched shunt voltage set points were adjusted. The new set points still ensure the load margin for the base case but were not satisfactory for the contingency case. After two iterations between the contingency case and the stressed contingency case a new Benders cut was generated and sent to the base case. The overall iterative procedure converged at the fourth iteration. A total of 11 preventive controls were activated (the voltage set points of a generator and 10 switched shunts) and no corrective controls were necessary. In the second case a more severe contingency resulting in the loss of two parallel 500 kV lines was considered. The margin and operating constraint data were the same as before. The control data were as follows: • Preventive control: voltage setting points for generators, switchable shunts and ULTC, manual capacitor and reactor switching, manual transformer tap adjustment and generator redispatch. • Corrective control list consisted in manual capacitor and reactor switching, manual transformer tap adjustment. This case converged after three iterations for resolving the violations in the base case sub-problems (stressed and unstressed) and a number of iterations between the un-stressed and stressed contingency cases. At the end, the following controls were activated: 1) Preventive Controls: 6 generation redispatch, 3 generator voltage settings and 6 switched shunt voltage settings; 2) Corrective Controls: 3 load shedding. Amount of load curtailed was 140 MW.

VI. CONCLUSION This paper introduces the concept of a Dynamic Security Constrained OPF/VAr Planning tool which simultaneously considers static constraints as well as voltage stability constraints. The novel formulation and implementation of the method which has been extensively covered in the paper, is based on a three level hierarchical decomposition scheme where each sub-problem is solved by the interior point method. The test results conducted on a large-scale North American utility system and a reduced Brazilian system validated the soundness and practicality of the approach. Also the interior point algorithm used in the optimization of sub-problems proved to be effective and robust in dealing with unsolvable power flows. Finally, the approach explained here is very general and can be used as part of any application requiring the consideration of static and dynamic constraints such as ATC/TTC calculation tools and VAr Planning methods.

VAAHEDI et al.: DYNAMIC SECURITY CONSTRAINED OPTIMAL POWER FLOW/VAr PLANNING

APPENDIX REDUCED BRAZILLIAN SYSTEM DIAGRAM

Fig. 10.

Brazillian system diagram.

ACKNOWLEDGMENT The authors would like to thank Prof. Alvarado, from University of Wisconsin, for permission to use the academic version of the Point of Collapse and Continuation Power Flow programs in this research work. They also appreciate the valuable assistance of J. O. Soto and A. Bianco in preparing this paper.

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[7] O. O. Obadina and G. J. Berg, “VAr planning for power system security,” IEEE Trans. on Power Systems, vol. 5, May 1989. [8] D. Shirmohammadi et al., “Transmission dispatch and congestion management in the emerging energy market structures,” IEEE Trans. on Power Systems, Nov. 1998. [9] J. F. Benders, Partitioning Procedure for Solving Mixed Variables Programming Problems: Numerishe Mathematics, 1962, pp. 238–262. [10] S. Granville and M. C. A. Lima, “Application of decomposition techniques to VAr planning,” IEEE/PES Trans. on Power Systems, vol. 9, no. 4, Nov. 1994. [11] N. Karmarkar, “A new polynomial time algorithm for linear programming,” Combinatorica, vol. 4, 1984. [12] S. Granville, “Optimal reactive dispatch through interior point methods,” IEEE Trans. on Power Systems, vol. 9, no. 1, Feb. 1994. [13] C. A. Canizares and F. L. Alvarado, “Point of collapse and continuation method for large scale AC/DC systems,” IEEE Trans. on Power Systems, vol. 7, no. 1, Feb. 1993.

Ebrahim Vaahedi presently is an Associate of the Energy Office of the Perot Systems. Previously he was the Manager of the Control Center Technologies Department of B.C. Hydro where this work was carried.

Yakout Mansour is presently the Vice President of the Grid Operation and Inter-Utility Affairs Division of B.C. Hydro.

Chris Fuchs presently works as a Senior Engineer in the Control Center Technologies Department of B.C. Hydro.

REFERENCES [1] B. Stott, O. Alsac, and A. J. Monticelli, “Security analysis and optimization,” Proceedings of the IEEE, vol. 75, no. 12, Dec. 1987. [2] S. Granville, M. V. F. Pereira, and A. Monticelli, “An integrated method for VAr sources planning,” IEEE Trans. on Power Systems, vol. 3, May 1988. [3] Y. Hong, D. I. Sun, S. Lin, and C. Lin, “Multi-year multi-case optimal VAr planning,” IEEE Trans. on Power Systems, vol. 5, Nov. 1990. [4] O. O. Obadina and G. J. Berg, “Determination of voltage stability limit in multi-machine power systems,” IEEE Trans. on Power Systems, vol. 3, Nov. 1988. [5] T. Van Custem, “A method to compute reactive power margins with respect to voltage collapse,” IEEE Trans. on Power Systems, vol. 6, Feb. 1991. [6] S. Granville, S. J. Mello, and A. Melo, “Application of interior point methods to power flow unsolvability,” IEEE Trans. on Power Systems, vol. 4, May 1996.

Sergio Granville received the B.Sc. degree in mathematics in 1971, the M.Sc. degree in applied mathematics in 1973, both from PUC/RJ, and the Ph.D. degree in operations research in 1978 from Stanford University. Since 1986, he has been a Senior Researcher at CEPEL.

Maria de Lujan Latore received the B.Sc. degree in mathematics in 1991 from UNR-Rosario, the M.Sc. degree in system engineering from COPPE/UFRJ in 1995 where she is presently taking her D.Sc. degree in system engineering.

Hamid Hamadanizadeh is presently a Senior Analytical Engineer in the System Studies Group of Powertech Labs.