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Dynamic stability improvement via coordination of static var compensator and power system stabilizer control actions
Electric Power Systems Research 58 (2001) 37 – 44 www.elsevier.com/locate/epsr
Dynamic stability improvement via coordination of static var compensator and power system stabilizer control actions M.A. Al-Biati a,*, M.A. El-Kady b, A.A. Al-Ohaly b a
Gulf Hygienic Industries Ltd., PO Box 99883, Riyadh 11625, Saudi Arabia b King Saud Uni6ersity, PO Box 800, Riyadh 11421, Saudi Arabia Accepted 21 March 2001
Abstract Power system controllers such as the static var compensators and the power system stabilizers are receiving a wide interest since many technical studies have proven their effects on damping system oscillations and stability enhancement. This paper is mainly concerned with coordinating the control actions of static var compensators and power system stabilizers to achieve improved dynamic performance of the power system using the newly developed concept of ‘domains of influence’. Novel sensitivity-based algorithms are presented for the purpose of effectively identifying the domains of influence of various control parameters on critical dynamic system modes. Applications to the Saudi Consolidated Electric Company (SCECO) power system show that significant improvement in power network stability can be achieved via coordinating the control actions of both static var compensator and power system stabilizer instead of using them individually in an uncoordinated manner. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Power system controller; Saudi Consolidated Electric Company (SCECO); Compensator
1. Introduction Present day interconnected power systems are typical examples of large-scale, complex multi-variable systems. The electrical energy generated is transmitted over an interconnected network, which in turn supplies the demand power to the load centers. Due to the increase in system size and the tendency to operate systems near their stability limits, emphasis has been placed on the design of additional control schemes to maintain the dynamic performance of the system at acceptable levels. Generally, it is not only required to know whether a system is stable or not, but also to evaluate the performance or quality of stability [1 – 3]. In the past, utilities in the Kingdom of Saudi Arabia have not vigorously considered the use of reactive power compensating devices or power system stabilizing equipment. This is mainly due to the fact that, until recently, the system was operating far from the stability limit and the generation * Corresponding author. Tel.: + 966-1-4985622; fax: +966-14983903. E-mail address: [email protected] (M.A. El-Kady).
capacity has not been fully utilized. At present, this is not the case as the load has been growing very fast over the past several years. The practice, until recently, has been to use as many generating units at one time as possible to reduce the amount of reactive power absorbed by each unit. With the vast increase in both demand and cost of power, this can no longer be acceptable from the economic point of view. Dynamic instability, which is the main subject of this paper, is related to several factors including the high loading levels of modern electrical power systems, the design of lower-cost synchronous generators and the use of high-gain and quick-acting excitation systems. Dynamic stability is closely related to the eigenvalues of the system (state) matrix. Several computational techniques for calculating the eigenvalues of realistic power systems have been developed [4–6]. In order to improve the damping of electromechanical oscillations when necessary, such systems should be designed to allow proper processing of stabilization signals, usually derived from the machine rotor-speed or electrical power. Counter measures available include the use of power system stabilizer (PSS) and static var compensator (SVC) to improve system performance [7–10].
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The idea behind the PSS is to feed a signal containing the oscillation of the generator. This signal introduces positive damping to generator oscillations only if suitable design and appropriate tuning for the PSS parameters are met. On the other hand, the installation of SVC devices, on which we will emphasize in this paper, would change the system reactive power distribution resulting in an immediate voltage variation. The electric output from surrounding generators is immediately affected before any rotor angle oscillation or regulation has taken place. Experience with stabilizer application is rapidly developing but geographically loose interconnections have shown that the straightforward course of applying stabilizers at all new power plants can be ineffective because these machines are not necessarily located at the best points for damping the troublesome modes. The identification of optimum sites for stabilizers is a complicated process. This paper aims at a proposed scheme for choosing appropriate locations for the SVC and/or PSS control equipment as well as coordinating their actions to enhance power system steady-state stability. In the paper, previous research work is extended to include and coordinate both PSS and SVC dynamic controls in the power system, using a well-coordinated numerical eigenvalue sensitivity technique and a so-called ‘domain of influence’ concept. In particular, the paper is concerned mainly with modeling, analysis and computation of the effects of various control devices on the dynamic behavior of power systems. Of a special interest, the problem of coordinating the control actions of different SVC and PSS devices will be studied. The numerical sensitivity-based algorithms will be used for the purpose of effectively identifying the domains of influence of various control parameters on critical dynamic system modes. As an illustration, the proposed scheme will be applied to the interconnected portion of Saudi consolidated electric company (SCECO) power system containing Central, Eastern and Qassim regions. The power system for those three connected areas will be considered in this paper and special considerations will be given to improving the SCECO network stability by coordinating the actions of SVC and PSS devices. Section 2 provides a general background, illustrates the control effects of PSS and SVC and presents the new sensitivity based algorithm for effective coordination of PSS and SVC control actions in order to improve dynamic stability. It also provides a general description of the overall computerized procedure and outlines the set of extensive software modules developed during the course of the present study. Section 3 presents a full-scale practical application to the SCECO power system while Section 4 introduces the concept of PSS and SVC domains of influence and demonstrates its applications. Section 5 summaries the contributions made in this paper and the conclusions of the work.
2. Sensitivity-based SVC/PSS coordination methodology and software In the present study of PSS and SVC effects on the system eigenvalues (dynamic modes), it is required to locate the system eigenvalues for a certain operating conditions. In addition, it is also necessary to examine the possible movement of the critical subset of these dynamic modes under changes in system control and design parameters around the chosen base-case condition. This can generally be achieved by either eigenvalue re-calculation for different parameter settings, or by using eigenvalue sensitivities around the base case– case (nominal) values. The second approach is much more efficient and convenient, especially for large-scale systems. Most approaches reported on in the literature have used analytical eigenvalue sensitivity formulas [11–14]. Nonetheless, in the present study, an efficient, well-coordinated numerically based sensitivity algorithm is used because of its simplicity, ease in coding and true applicability to large-scale systems because all it requires is a sparsity-oriented eigenvalue analysis routine. Nevertheless, the use of the numerical sensitivity technique is also associated with several challenging issues that need to be resolved for successful implementation as will be described in this paper.
2.1. Sensiti6ity e6aluation methodology An estimated value ui of a specific eigenvalue EVi due to a change DPk in a certain parameter Pk can be obtained using Taylor series expansion around the base value EVoi as follows: EVi = EVoi +
)
)
#EVi 1 #EV2i (DPk ) + (DPk )2 2 #P 2k P o #Pk P o k
+… In this equation, the term
k
)
#EVi 1is defined as the #Pk P o k
first-order sensitivity coefficient of the eigenvalue EVi with respect to the parameter Pk at P ok, where the subscript k stands for the parameter location. If the series expansion is terminated after the first derivative term of the series, the estimation is a first-order approximation, which is valid only for small parameter changes. Since, for complex eigenvalues: EVi = EVRi + jEVIi
(1)
Then, the sensitivity for mode i with respect to Pk parameter is given by Sik =
#EVi #EVRi #EVIi = +j #Pk #Pk #Pk
(2)
The normalized sensitivities for real and imaginary parts of eigenvalues are as follows:
M.A. Al-Biati et al. / Electric Power Systems Research 58 (2001) 37–44
NSRik = NSIik =
P #EVRi · , EVRoi #Pk o k
P ok #EVIi · . EVIoi #Pk
(3) (4)
3. Application to SCECO power system A special-purpose computer program has been developed in order to classify, organize and display all sensitivity outputs (after mode alignment) in a master information file. In this master file, a unique six-digit indexed code is used to identify each PSS and SVC control parameter in the system as will be demonstrated in subsequent sections. Along with these parameter codes, base-case parameter and mode values as well as the associated mode sensitivities are included in the master file. In this section, the sequence of technical steps involved will be demonstrated through a practical application to the power grid of the Saudi consolidated electric company-Center (SCECO-C). The power system under study consists of three regions namely SCECO Central, SCECO East and Qassim. The transmission system of SCECO-C consists of 132 kV double circuit ring network enclosed by a semi ring of 380 kV transmission network. The 132 kV ring is also connected through the generation and load grid substations through underground 132 kV cables. The system is provided with reactors at certain substations to compensate for the capacitive reactive power produced by the network. The SCECO-C is interconnected with SCECO-E by three tie lines of which one is a double circuit 230 kV overhead transmission line. The second and third lines are 380 kV double-circuit overhead transmission lines. JADIDA substation in SCECO-E is considered as a reference bus (infinite bus). Qassim is interconnected with Riyadh via a double circuit 380 kV transmission line. Fig. 1 shows the system configuration where system buses have been renumbered for easy reference. The network under study contains 11 generator buses, 111 load buses, a reference bus and 230 branches (lines and transformers). The system data fed to the load flow program is prepared from a test-operating scenario based on practical system operation data. The maximum demand considered was 3626 MW (load flow base-case peak demand value). The results of load flow solution represent the initial condition for the dynamic stability analysis.
3.1. Parameter selection for PSS and SVC sensiti6ities The SCECO system has three types of excitation systems resulting in different PSS parameter settings. In the present study, the stabilizers have been placed at eight generators from the total of 11 generators, namely
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Shedquem, Faras, PP8A, PP8B, PP8C, PP5, Qurrayyah and Qassim. The PSS gain Ks at each generator was chosen for the sensitivity analysis. Two SVC control parameters were chosen for the sensitivity analysis, namely the constant Kh and the firing angle h. By varying each SVC parameter separately, best values of SVC parameters have been identified. These parameter settings have been fixed for all SVC controllers and used in the subsequent sensitivity analysis. The approximate parameter settings are: h=70° =1.22 radian; XC = 6; XT = 0.1; Kh = 50; ~h = 0.20; K =0.25. A preliminary pilot study had been conducted to quickly identify suitable candidate locations in the network for the SVC devices by placing static reactors at suggested locations and then examining the resulting approximate effects on the system dynamic modes. A total of 38 buses have been selected for possible placement of the SVC devices.
3.2. Effect of placing SVC and PSS controls From the output results of the 38 location runs, it was concluded that the system stability could be improved by different degrees according to the individual scenarios of SVC placement. Examples of two cases of interest were considered, where the SVC has been placed on buses 121 and 112, respectively, and its speed signal has come from generator c 11. The top part of Table 1 shows the first ten eigenvalues, in descending order of the real part values, where it is clear that several system dynamic modes have been improved in both cases. The effect of PSS placement depends mainly on the PSS parameter settings. Among the eight different locations for the PSS, the best effect was obtained when the PSS was placed at the Qurrayyah plant. The bottom part of Table 1 shows the first ten eigenvalues, where again, it is clear that the system stability has been improved since two of five originally unstable modes became stable.
3.3. Dynamic control sensiti6ities From the results of the 38 SVC location runs and the eight PSS generator location runs, it is evident that a tremendous impact on the oscillation damping and dynamic stability has been made. On the other hand, the more difficult task of selecting the best combination of SVC and PSS placement and control settings is far more challenging. The best direction for such tasks is to study the eigenvalue sensitivities with respect to changes in the dynamic control parameters of interest. In this respect, the eigenvalue first-order sensitivities with respect to various PSS and SVC control parameters are calculated numerically as was illustrated earlier. These sensitivities, together with the most probable ranges of variations of the associated control parame-
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Fig. 1. System configuration for PSS/SVC placement study.
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ters during system operation, are then used to establish the most significant effects caused by varying individual PSS and SVC device parameters. With the aid of the computed dynamic mode sensitivities, those parts (buses) of the power grid, which are relatively more affected by one (or more) control device than others, can be identified. Therefore, the domains of influence associated with individual dynamic controls can be established as will be described in the next section.
4. Domains of PSS and SVC influence For the SCECO power system under consideration, the analysis of the previous section produced a total of 84 output sensitivity tables for the system eigenvalues with respect to changes in the control parameter values. In view of such large amount of data, it is very important to have an efficient method of organizing and displaying these sensitivity results in such a way that the relative influence of different PSS and SVS parameters on individual eigenvalues can be clearly identified. We shall refer to such display as the ‘domains of influence’ of the PSS and SVC parameters. In practice, the utility engineers would use these domains of influence charts and maps to quickly determine the most effective control actions required to correct (stabilize) a specific power system dynamic mode. In the work of this paper, three methods of representing sensitivity data are introduced. Each method has its own advantage in terms of the effectiveness of identifying and displaying PSS and SVC domains of
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influence. For the SCECO power system under consideration, different groups of PSS and SVC parameters as well as different mode groups will be considered to demonstrate the thinking process involved in identifying corrective actions to improve dynamic modes in real power utility applications.
4.1. Domains of PSS/SVC influence – by modes In this method of representation the sensitivities of different control parameters for a particular group are displayed against various dynamic modes (eigenvalues). Using such display, the relative impact of a particular control parameter on the respective modes can easily be identified and assessed. Table 2 shows the sensitivities of the real part of Qassim power plant modes with respect to the changes in the gain parameter of the PSS located at Qassim (Parameter 111000), the changes in firing angle of the SVC located at bus 40 and controlled by the Qassim power plant (Parameter 111040), and the changes in firing angle of the SVC located at bus 121 and controlled by Qassim power plant (Parameter 111121). The parameter codes are assigned to indicate the controlling bus (first three digits) and the SVC location bus (last three digits). The relative impact of a particular control parameter on the respective dynamic system modes can be assessed by examining the associated dynamic mode sensitivities. In this regard, it was shown that the Qassim power plant real modes are highly affected by certain SVC parameters, especially those located at bus
Table 1 System modes improved by SVC and PSS placement No.
Original system modes
System modes with SVC located at bus 121
System modes with SVC located at bus 112
System modes with PSS at Qurrayyah
1
0.469553 + j0.000000 0.047739 +j4.871110 0.047739 −j4.871110 0.025666 + j1.945050 0.025666 −j1.945050 −0.100045 + j0.000000 −0.192844 +j1.103310 −0.192844 −j1.103310 −0.231421 + j0.155905 −0.231421 −j0.155905
0.443938+j0.000000
0.453571+j0.000000
0.468323+j0.000000
0.110913+j4.819560
0.111251+j4.813420
0.025368+j1.945140
0.110913–j4.819560
0.111251−j4.813420
0.025368−j1.945140
−0.003914+j2.120920
−0.019816+j2.211120
−0.100045+j0.000000
−0.003914−j2.120920
−0.019816−j2.211120
−0.193789+j1.102590
−0.047740+j0.453371
−0.049445+j0.450290
−0.193789−j1.102590
−0.047740−j0.453371
−0.049445−j0.450290
−0.231447+j0.155914
−0.100047+j0.000000
−0.100046+j0.000000
−0.231447−j0.155914
−0.235368+j1.116780
−0.199392+j1.116120
−0.273013+j7.3226940
−0.235368−j1.116780
−0.199392−j1.116120
−0.273013−j7.326940
2 3 4 5 6 7 8 9 10
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Table 2 Influence of SVC at bus c121 on Qassim modes (Sensitivities of real part) Seq-c Mode-
P-111000
P-111040
P-111121
0.151E−02 0.151E−02 0.100E−03 0.100E−03 0.496E−04 0.496E−04 0.126E−01 0.126E−01 −0.261E−01 −0.496E−04 −0.196E−04 −0.496E−04
−0.850E−03 −0.850E−03 – – 0.107E−01 0.107E−01 −0.123E−02 −0.123E−02 0.184E−02 −0.340E−01 0.203E−03 0.119E−01
– – – – −0.291E−01 −0.291E−01 0.254E−02 0.254E−02 0.111E−01 0.803E−01 0.821E−04 −0.311E−01
c 1 2 3 4 5 6 7 8 9 10 11 12
4 5 85 86 91 92 56 57 51 107 80 113
121. Also, the sensitivity of mode c107 with respect to the SVC parameter at bus 40 is about 1000 times its sensitivity with respect to the PSS parameter at the same power plant. One of the groups analyzed (the fifth group), emphasizes the concept of the PSS local effects. The set of modes considered includes those associated with generator c 4. In this respect, the PSS at generator c4 has the largest effect on generator c4 modes such as c 7, c 8, c 15 and c 16. On the other hand, the strong electrically coupled generators c1 and c 11 also affect these modes, more than other modes (such as c 19 and c 20). In the previous case scenarios, the selected mode groups were studied in respect to the real part of the corresponding eigenvalues. The results obtained would be of a prime interest to those studies concerned with the dynamic stability of the system in relation to the damping effects. Similar analysis can be performed on the imaginary part of the eigenvalues as the performance index of interest. As was mentioned earlier in the paper, the imaginary part of the eigenvalues relates directly to the frequency of oscillations encountered. Nevertheless, the study reported on in this paper was concerned more with the task of finding effective dynamic control schemes which stabilize the system by increasing the damping effects and, consequently, moving the real part of influenced eigenvalues more towards the negative range of values.
4.2. Domain of PSS/SVC influence – by parameters In this method of representation, a selected mode group associated with one of the system generators is represented against the SVC or PSS control parameters. Using this method, the most affected eigenvalues (dynamic modes) by changes in a particular parameter can be quickly identified and assessed. Using a set of applications to the SCECO power system, similar to those
considered in the previous sub-sections, this method of representation will be demonstrated. The set of real modes considered for demonstration in this paper are those associated with generator c 1, namely modes c 22, c 81 and c37. The PSS control parameters used are those of the PSS gain at generators c1, c2 and c 3. Also, the firing angles of the SVC controlled by generator c1 and placed on buses 59, 90 and 97, respectively, have been considered as control parameters in this case scenario. From the results obtained, it is shown that the SVC firing angle for the SVC located at bus 59 and controlled by generator c 1 represents the most influencing parameter on modes c22 and c 37, while the PSS gain located at generator c 1 is the most influencing control parameter on mode c 81. Also, the SVC located at bus 59 is considered as a major control parameter affecting mode c 81. A list of calculated sensitivities were obtained for generator c 11 modes, namely modes c51, c 80 and c 107 with respect to perturbations in the PSS gain located at generator c 11, the four SVC firing angles located at buses 121, 40, 112 and 97, respectively, and controlled by generator c 11 as well as the SVC gain located at bus 112 and controlled by generator c 11. It was clear that the PSS at generator c11 represents the most affecting control parameter on mode c 51, while the SVC control parameters located at buses 40 and 112 are the most influential parameters on modes c 80 and c 107, respectively.
4.3. Domains of SVC/PSS influence – topological display Here, we use a topological display to demonstrate the problem-solving approach involved in correcting unstable dynamic modes by identifying the most effective control actions. As was stated before, the original system (without any PSS and SVC controls) has five unstable modes. The unstable dynamic mode c1 (for the set of system operating conditions assumed) belongs to generator c 5, while the unstable conjugate modes c 2 and c 3 belong to generator c 10. Also, the unstable modes c4 and c 5 belong to generator c11. From the PSS and SVC domains of influence, the most influencing parameters on the above five modes can be identified. The mode sensitivities with respect to various parameters have been classified into three ranges, namely high-influence, medium-influence and low-influence as shown in Fig. 2. The parameters chosen were those scattered around mode c1, according to the original power system topology, as well as those determined from available system designers’ experience and power system engineering judgement. From the results obtained, it was clear that the control parameters, which have the most
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influence on mode c1, are: 1) the SVC firing angle parameter of the SVC device located at bus 59 and controlled by generator c 5, 2) the SVC firing angle parameter of the SVC device located at bus 44 and controlled by generator c 5, 3) the SVC firing angle parameter of the SVC device located at bus 98 and controlled by generator c1, and 4) the SVC firing angle parameter of the SVC device located at buses 112 and controlled by generator c11. Therefore, in order to improve the interaction mode c 1, using the most effective control actions available, one or more of these three SVC control parameters should be used. Similarly, in order to improve the conjugate modes 2 and 3, the most influencing parameters have been selected from the tabulated and ordered dynamic sensitivity values. The results obtained showed that the dynamic control parameter representing the PSS gain at generator c 10 has the most effect on the critical modes c2 and c 3. We now recall that the original system eigenvalue pattern, discussed in Section 3, was improved by the application of a PSS device at generator c 10 (Qurrayyah). Such improvement resulted in the stabilization of modes c2 and c 3, which were originally unstable. This finding is now confirmed, but in a much faster way, using dynamic control parameter sensitivities. In a similar manner, the dynamic control
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parameters, which most influence the critical conjugate modes c4 and c 5, were identified by examining the sensitivities of these modes with respect to variations in various parameters. It was concluded that the firing angle parameters of the three SVC devices located at buses 121, 112 and 98 have the most influence on the these two modes. This fast and elegant sensitivity-based result also confirms what was previously reported on using extensive full-scale dynamic stability computer runs. In summary, the results of the sensitivity analysis indicate that the five unstable modes could be corrected, most effectively, by placing a coordinated combination of one PSS at generator c 10, one SVC at bus 98 controlled by generator c 11 and one SVC at bus 112 controlled by generator c 11. The resulting modes for this arrangement were confirmed using the dynamic stability program which showed all system modes being stable for the coordinated SVC/PSS placement considered.
5. Conclusions This paper has presented a new sensitivity-based methodology for easy and effective coordination of
Fig. 2. Domains of control parameter influence on critical dynamic mode c1.
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parameter control actions associated with power system stabilizers and static var compensators for the purpose of improving the dynamic performance of electric power systems. The present study showed that coordination of SVC and PSS control devices can significantly increase power system damping as compared with cases where either type is used alone to damp system oscillations. The paper demonstrated the effect of SVC and PSS equipment on system stability by examining the numerically calculated eigenvalue sensitivities of the dominant eigenvalues with respect to various candidate locations. These sensitivities are calculated by simulating the installation of SVC devices on different bus locations and/or PSS devices on different generator exciters. The proposed methodology calculates and displays the domains of influence of various control parameters on the system dynamic modes (eigenvalues). Using these domains of influence, proper assessment and corrective actions can be made to improve dynamic performance by correcting the problem (unstable or weak) modes using the most effective combination of control actions. Practical applications of the sensitivitybased methodology were carried out for the SCECO-C system connected to Qassim and SCECO-E. The steady-state stability of the system and the associated dynamic mode sensitivities with respect to PSS and SVC control parameters have been evaluated. The application study confirmed that the proper coordination of PSS and SVC control actions would have a significant effect on the system dynamic stability. In this respect, it was found that placing a power system stabilizer at the Qurrayyah power plant coupled with placing two static var compensators at buses 98 and 112 with control signals from the Qassim power plant would stabilize the dynamic system performance. The practical operating scenario considered in the paper is regarded as a likely future scenario in which the system operates close to its dynamic stability limits. While no dynamic instability has actually occurred in the SCECO-C power system to-date, observations and measurements of the actual system dynamic behavior seam to confirm the findings of the paper. Notable improvements in the system dynamic response to disturbances have already been witnessed with some PSS and SVC devices in place. It is believed that the present work would pave the way for a number of future
.
studies on the coordination of PSS and SVC control actions based on the concept of ‘domains of influence’ introduced in this paper.
References [1] F.P. deMello, Power System Dynamics-Overview, Symposium on Adequacy and Philosophy of Modelling: Dynamic System Performance at 1975 Winter Power Meeting, IEEE Publication 75CH0790-4-PWR (1975). [2] F.P. deMello, C. Concordia, Concept of synchronous machine stability as affected by excitation control, IEEE Transactions on Power Apparatus and Systems 88 (1969) 316 – 329. [3] Charles Concordia, Power System Stability, Proceedings of the International Symposium on Power System Stability, Ames, Iowa, CIGRE (WG 38/02) (1985) 13 – 15. [4] N. Martins, Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies, IEEE Transactions on Power Systems 1 (1986) 217 – 226. [5] A. Semlyen, L. Wang, Sequential computation of the complete eigensystem for the study zone in small signal stability analysis of large power systems, IEEE Transactions on Power Systems 3 (1988) 715 – 725. [6] P. Kundur, G.J. Rogers, D.Y. Wong, L. Wang, M.G. Lauby, A comprehensive computer program package for small signal stability analysis of power systems, IEEE Power Engineering Society, Winter Power Meeting, Paper No. 90-WM007-5 (1990). [7] S.E.M. Oliveira, Effect of excitation systems and power system stabilizers on synchronous generator damping and synchronising torques, IEE Proceedings 136 (1989). [8] A. Olwegand, Improvement of transmission capacity by thyristor controlled reactive power, IEEE Transactions on Power Apparatus and Systems 100 (1981). [9] E.Z. Zhou, Application of static var compensators to increase power system damping, IEEE Transactions on Power Systems 8 (1993). [10] A.A. Al-Ohaly, Z. Elrazaz, Shunt reactors as counter measure for reactive power surplus: location and impact on system stability performance, Canadian Electric Engineering Journal 12 (1987). [11] J.E. Van Ness, J.M. Boyle, F.P. Imad, Sensitivity of large multiple-loop systems, IEEE Transactions on Automatic Control 10 (1965) 308 – 318. [12] M. Laughton, Matrix analysis of dynamic stability in synchronous multi machine systems, IEE Proceedings 113 (1966) 325 – 336. [13] M.A. Al-Biati, Coordination of SVC and PSS to enhance steady state stability, Master of Engineering thesis, King Saud University (1995). [14] M.A. Pai, K.R. Padiyar, Sensitivity based selection of control parameters for multi-machines power systems, IEEE Transactions on Power Apparatus and Systems 99 (1980) 1320.
Dynamic stability improvement via coordination of static var compensator and power system stabilizer control actions M.A. Al-Biati a,*, M.A. El-Kady b, A.A. Al-Ohaly b a
Gulf Hygienic Industries Ltd., PO Box 99883, Riyadh 11625, Saudi Arabia b King Saud Uni6ersity, PO Box 800, Riyadh 11421, Saudi Arabia Accepted 21 March 2001
Abstract Power system controllers such as the static var compensators and the power system stabilizers are receiving a wide interest since many technical studies have proven their effects on damping system oscillations and stability enhancement. This paper is mainly concerned with coordinating the control actions of static var compensators and power system stabilizers to achieve improved dynamic performance of the power system using the newly developed concept of ‘domains of influence’. Novel sensitivity-based algorithms are presented for the purpose of effectively identifying the domains of influence of various control parameters on critical dynamic system modes. Applications to the Saudi Consolidated Electric Company (SCECO) power system show that significant improvement in power network stability can be achieved via coordinating the control actions of both static var compensator and power system stabilizer instead of using them individually in an uncoordinated manner. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Power system controller; Saudi Consolidated Electric Company (SCECO); Compensator
1. Introduction Present day interconnected power systems are typical examples of large-scale, complex multi-variable systems. The electrical energy generated is transmitted over an interconnected network, which in turn supplies the demand power to the load centers. Due to the increase in system size and the tendency to operate systems near their stability limits, emphasis has been placed on the design of additional control schemes to maintain the dynamic performance of the system at acceptable levels. Generally, it is not only required to know whether a system is stable or not, but also to evaluate the performance or quality of stability [1 – 3]. In the past, utilities in the Kingdom of Saudi Arabia have not vigorously considered the use of reactive power compensating devices or power system stabilizing equipment. This is mainly due to the fact that, until recently, the system was operating far from the stability limit and the generation * Corresponding author. Tel.: + 966-1-4985622; fax: +966-14983903. E-mail address: [email protected] (M.A. El-Kady).
capacity has not been fully utilized. At present, this is not the case as the load has been growing very fast over the past several years. The practice, until recently, has been to use as many generating units at one time as possible to reduce the amount of reactive power absorbed by each unit. With the vast increase in both demand and cost of power, this can no longer be acceptable from the economic point of view. Dynamic instability, which is the main subject of this paper, is related to several factors including the high loading levels of modern electrical power systems, the design of lower-cost synchronous generators and the use of high-gain and quick-acting excitation systems. Dynamic stability is closely related to the eigenvalues of the system (state) matrix. Several computational techniques for calculating the eigenvalues of realistic power systems have been developed [4–6]. In order to improve the damping of electromechanical oscillations when necessary, such systems should be designed to allow proper processing of stabilization signals, usually derived from the machine rotor-speed or electrical power. Counter measures available include the use of power system stabilizer (PSS) and static var compensator (SVC) to improve system performance [7–10].
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The idea behind the PSS is to feed a signal containing the oscillation of the generator. This signal introduces positive damping to generator oscillations only if suitable design and appropriate tuning for the PSS parameters are met. On the other hand, the installation of SVC devices, on which we will emphasize in this paper, would change the system reactive power distribution resulting in an immediate voltage variation. The electric output from surrounding generators is immediately affected before any rotor angle oscillation or regulation has taken place. Experience with stabilizer application is rapidly developing but geographically loose interconnections have shown that the straightforward course of applying stabilizers at all new power plants can be ineffective because these machines are not necessarily located at the best points for damping the troublesome modes. The identification of optimum sites for stabilizers is a complicated process. This paper aims at a proposed scheme for choosing appropriate locations for the SVC and/or PSS control equipment as well as coordinating their actions to enhance power system steady-state stability. In the paper, previous research work is extended to include and coordinate both PSS and SVC dynamic controls in the power system, using a well-coordinated numerical eigenvalue sensitivity technique and a so-called ‘domain of influence’ concept. In particular, the paper is concerned mainly with modeling, analysis and computation of the effects of various control devices on the dynamic behavior of power systems. Of a special interest, the problem of coordinating the control actions of different SVC and PSS devices will be studied. The numerical sensitivity-based algorithms will be used for the purpose of effectively identifying the domains of influence of various control parameters on critical dynamic system modes. As an illustration, the proposed scheme will be applied to the interconnected portion of Saudi consolidated electric company (SCECO) power system containing Central, Eastern and Qassim regions. The power system for those three connected areas will be considered in this paper and special considerations will be given to improving the SCECO network stability by coordinating the actions of SVC and PSS devices. Section 2 provides a general background, illustrates the control effects of PSS and SVC and presents the new sensitivity based algorithm for effective coordination of PSS and SVC control actions in order to improve dynamic stability. It also provides a general description of the overall computerized procedure and outlines the set of extensive software modules developed during the course of the present study. Section 3 presents a full-scale practical application to the SCECO power system while Section 4 introduces the concept of PSS and SVC domains of influence and demonstrates its applications. Section 5 summaries the contributions made in this paper and the conclusions of the work.
2. Sensitivity-based SVC/PSS coordination methodology and software In the present study of PSS and SVC effects on the system eigenvalues (dynamic modes), it is required to locate the system eigenvalues for a certain operating conditions. In addition, it is also necessary to examine the possible movement of the critical subset of these dynamic modes under changes in system control and design parameters around the chosen base-case condition. This can generally be achieved by either eigenvalue re-calculation for different parameter settings, or by using eigenvalue sensitivities around the base case– case (nominal) values. The second approach is much more efficient and convenient, especially for large-scale systems. Most approaches reported on in the literature have used analytical eigenvalue sensitivity formulas [11–14]. Nonetheless, in the present study, an efficient, well-coordinated numerically based sensitivity algorithm is used because of its simplicity, ease in coding and true applicability to large-scale systems because all it requires is a sparsity-oriented eigenvalue analysis routine. Nevertheless, the use of the numerical sensitivity technique is also associated with several challenging issues that need to be resolved for successful implementation as will be described in this paper.
2.1. Sensiti6ity e6aluation methodology An estimated value ui of a specific eigenvalue EVi due to a change DPk in a certain parameter Pk can be obtained using Taylor series expansion around the base value EVoi as follows: EVi = EVoi +
)
)
#EVi 1 #EV2i (DPk ) + (DPk )2 2 #P 2k P o #Pk P o k
+… In this equation, the term
k
)
#EVi 1is defined as the #Pk P o k
first-order sensitivity coefficient of the eigenvalue EVi with respect to the parameter Pk at P ok, where the subscript k stands for the parameter location. If the series expansion is terminated after the first derivative term of the series, the estimation is a first-order approximation, which is valid only for small parameter changes. Since, for complex eigenvalues: EVi = EVRi + jEVIi
(1)
Then, the sensitivity for mode i with respect to Pk parameter is given by Sik =
#EVi #EVRi #EVIi = +j #Pk #Pk #Pk
(2)
The normalized sensitivities for real and imaginary parts of eigenvalues are as follows:
M.A. Al-Biati et al. / Electric Power Systems Research 58 (2001) 37–44
NSRik = NSIik =
P #EVRi · , EVRoi #Pk o k
P ok #EVIi · . EVIoi #Pk
(3) (4)
3. Application to SCECO power system A special-purpose computer program has been developed in order to classify, organize and display all sensitivity outputs (after mode alignment) in a master information file. In this master file, a unique six-digit indexed code is used to identify each PSS and SVC control parameter in the system as will be demonstrated in subsequent sections. Along with these parameter codes, base-case parameter and mode values as well as the associated mode sensitivities are included in the master file. In this section, the sequence of technical steps involved will be demonstrated through a practical application to the power grid of the Saudi consolidated electric company-Center (SCECO-C). The power system under study consists of three regions namely SCECO Central, SCECO East and Qassim. The transmission system of SCECO-C consists of 132 kV double circuit ring network enclosed by a semi ring of 380 kV transmission network. The 132 kV ring is also connected through the generation and load grid substations through underground 132 kV cables. The system is provided with reactors at certain substations to compensate for the capacitive reactive power produced by the network. The SCECO-C is interconnected with SCECO-E by three tie lines of which one is a double circuit 230 kV overhead transmission line. The second and third lines are 380 kV double-circuit overhead transmission lines. JADIDA substation in SCECO-E is considered as a reference bus (infinite bus). Qassim is interconnected with Riyadh via a double circuit 380 kV transmission line. Fig. 1 shows the system configuration where system buses have been renumbered for easy reference. The network under study contains 11 generator buses, 111 load buses, a reference bus and 230 branches (lines and transformers). The system data fed to the load flow program is prepared from a test-operating scenario based on practical system operation data. The maximum demand considered was 3626 MW (load flow base-case peak demand value). The results of load flow solution represent the initial condition for the dynamic stability analysis.
3.1. Parameter selection for PSS and SVC sensiti6ities The SCECO system has three types of excitation systems resulting in different PSS parameter settings. In the present study, the stabilizers have been placed at eight generators from the total of 11 generators, namely
39
Shedquem, Faras, PP8A, PP8B, PP8C, PP5, Qurrayyah and Qassim. The PSS gain Ks at each generator was chosen for the sensitivity analysis. Two SVC control parameters were chosen for the sensitivity analysis, namely the constant Kh and the firing angle h. By varying each SVC parameter separately, best values of SVC parameters have been identified. These parameter settings have been fixed for all SVC controllers and used in the subsequent sensitivity analysis. The approximate parameter settings are: h=70° =1.22 radian; XC = 6; XT = 0.1; Kh = 50; ~h = 0.20; K =0.25. A preliminary pilot study had been conducted to quickly identify suitable candidate locations in the network for the SVC devices by placing static reactors at suggested locations and then examining the resulting approximate effects on the system dynamic modes. A total of 38 buses have been selected for possible placement of the SVC devices.
3.2. Effect of placing SVC and PSS controls From the output results of the 38 location runs, it was concluded that the system stability could be improved by different degrees according to the individual scenarios of SVC placement. Examples of two cases of interest were considered, where the SVC has been placed on buses 121 and 112, respectively, and its speed signal has come from generator c 11. The top part of Table 1 shows the first ten eigenvalues, in descending order of the real part values, where it is clear that several system dynamic modes have been improved in both cases. The effect of PSS placement depends mainly on the PSS parameter settings. Among the eight different locations for the PSS, the best effect was obtained when the PSS was placed at the Qurrayyah plant. The bottom part of Table 1 shows the first ten eigenvalues, where again, it is clear that the system stability has been improved since two of five originally unstable modes became stable.
3.3. Dynamic control sensiti6ities From the results of the 38 SVC location runs and the eight PSS generator location runs, it is evident that a tremendous impact on the oscillation damping and dynamic stability has been made. On the other hand, the more difficult task of selecting the best combination of SVC and PSS placement and control settings is far more challenging. The best direction for such tasks is to study the eigenvalue sensitivities with respect to changes in the dynamic control parameters of interest. In this respect, the eigenvalue first-order sensitivities with respect to various PSS and SVC control parameters are calculated numerically as was illustrated earlier. These sensitivities, together with the most probable ranges of variations of the associated control parame-
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Fig. 1. System configuration for PSS/SVC placement study.
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ters during system operation, are then used to establish the most significant effects caused by varying individual PSS and SVC device parameters. With the aid of the computed dynamic mode sensitivities, those parts (buses) of the power grid, which are relatively more affected by one (or more) control device than others, can be identified. Therefore, the domains of influence associated with individual dynamic controls can be established as will be described in the next section.
4. Domains of PSS and SVC influence For the SCECO power system under consideration, the analysis of the previous section produced a total of 84 output sensitivity tables for the system eigenvalues with respect to changes in the control parameter values. In view of such large amount of data, it is very important to have an efficient method of organizing and displaying these sensitivity results in such a way that the relative influence of different PSS and SVS parameters on individual eigenvalues can be clearly identified. We shall refer to such display as the ‘domains of influence’ of the PSS and SVC parameters. In practice, the utility engineers would use these domains of influence charts and maps to quickly determine the most effective control actions required to correct (stabilize) a specific power system dynamic mode. In the work of this paper, three methods of representing sensitivity data are introduced. Each method has its own advantage in terms of the effectiveness of identifying and displaying PSS and SVC domains of
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influence. For the SCECO power system under consideration, different groups of PSS and SVC parameters as well as different mode groups will be considered to demonstrate the thinking process involved in identifying corrective actions to improve dynamic modes in real power utility applications.
4.1. Domains of PSS/SVC influence – by modes In this method of representation the sensitivities of different control parameters for a particular group are displayed against various dynamic modes (eigenvalues). Using such display, the relative impact of a particular control parameter on the respective modes can easily be identified and assessed. Table 2 shows the sensitivities of the real part of Qassim power plant modes with respect to the changes in the gain parameter of the PSS located at Qassim (Parameter 111000), the changes in firing angle of the SVC located at bus 40 and controlled by the Qassim power plant (Parameter 111040), and the changes in firing angle of the SVC located at bus 121 and controlled by Qassim power plant (Parameter 111121). The parameter codes are assigned to indicate the controlling bus (first three digits) and the SVC location bus (last three digits). The relative impact of a particular control parameter on the respective dynamic system modes can be assessed by examining the associated dynamic mode sensitivities. In this regard, it was shown that the Qassim power plant real modes are highly affected by certain SVC parameters, especially those located at bus
Table 1 System modes improved by SVC and PSS placement No.
Original system modes
System modes with SVC located at bus 121
System modes with SVC located at bus 112
System modes with PSS at Qurrayyah
1
0.469553 + j0.000000 0.047739 +j4.871110 0.047739 −j4.871110 0.025666 + j1.945050 0.025666 −j1.945050 −0.100045 + j0.000000 −0.192844 +j1.103310 −0.192844 −j1.103310 −0.231421 + j0.155905 −0.231421 −j0.155905
0.443938+j0.000000
0.453571+j0.000000
0.468323+j0.000000
0.110913+j4.819560
0.111251+j4.813420
0.025368+j1.945140
0.110913–j4.819560
0.111251−j4.813420
0.025368−j1.945140
−0.003914+j2.120920
−0.019816+j2.211120
−0.100045+j0.000000
−0.003914−j2.120920
−0.019816−j2.211120
−0.193789+j1.102590
−0.047740+j0.453371
−0.049445+j0.450290
−0.193789−j1.102590
−0.047740−j0.453371
−0.049445−j0.450290
−0.231447+j0.155914
−0.100047+j0.000000
−0.100046+j0.000000
−0.231447−j0.155914
−0.235368+j1.116780
−0.199392+j1.116120
−0.273013+j7.3226940
−0.235368−j1.116780
−0.199392−j1.116120
−0.273013−j7.326940
2 3 4 5 6 7 8 9 10
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Table 2 Influence of SVC at bus c121 on Qassim modes (Sensitivities of real part) Seq-c Mode-
P-111000
P-111040
P-111121
0.151E−02 0.151E−02 0.100E−03 0.100E−03 0.496E−04 0.496E−04 0.126E−01 0.126E−01 −0.261E−01 −0.496E−04 −0.196E−04 −0.496E−04
−0.850E−03 −0.850E−03 – – 0.107E−01 0.107E−01 −0.123E−02 −0.123E−02 0.184E−02 −0.340E−01 0.203E−03 0.119E−01
– – – – −0.291E−01 −0.291E−01 0.254E−02 0.254E−02 0.111E−01 0.803E−01 0.821E−04 −0.311E−01
c 1 2 3 4 5 6 7 8 9 10 11 12
4 5 85 86 91 92 56 57 51 107 80 113
121. Also, the sensitivity of mode c107 with respect to the SVC parameter at bus 40 is about 1000 times its sensitivity with respect to the PSS parameter at the same power plant. One of the groups analyzed (the fifth group), emphasizes the concept of the PSS local effects. The set of modes considered includes those associated with generator c 4. In this respect, the PSS at generator c4 has the largest effect on generator c4 modes such as c 7, c 8, c 15 and c 16. On the other hand, the strong electrically coupled generators c1 and c 11 also affect these modes, more than other modes (such as c 19 and c 20). In the previous case scenarios, the selected mode groups were studied in respect to the real part of the corresponding eigenvalues. The results obtained would be of a prime interest to those studies concerned with the dynamic stability of the system in relation to the damping effects. Similar analysis can be performed on the imaginary part of the eigenvalues as the performance index of interest. As was mentioned earlier in the paper, the imaginary part of the eigenvalues relates directly to the frequency of oscillations encountered. Nevertheless, the study reported on in this paper was concerned more with the task of finding effective dynamic control schemes which stabilize the system by increasing the damping effects and, consequently, moving the real part of influenced eigenvalues more towards the negative range of values.
4.2. Domain of PSS/SVC influence – by parameters In this method of representation, a selected mode group associated with one of the system generators is represented against the SVC or PSS control parameters. Using this method, the most affected eigenvalues (dynamic modes) by changes in a particular parameter can be quickly identified and assessed. Using a set of applications to the SCECO power system, similar to those
considered in the previous sub-sections, this method of representation will be demonstrated. The set of real modes considered for demonstration in this paper are those associated with generator c 1, namely modes c 22, c 81 and c37. The PSS control parameters used are those of the PSS gain at generators c1, c2 and c 3. Also, the firing angles of the SVC controlled by generator c1 and placed on buses 59, 90 and 97, respectively, have been considered as control parameters in this case scenario. From the results obtained, it is shown that the SVC firing angle for the SVC located at bus 59 and controlled by generator c 1 represents the most influencing parameter on modes c22 and c 37, while the PSS gain located at generator c 1 is the most influencing control parameter on mode c 81. Also, the SVC located at bus 59 is considered as a major control parameter affecting mode c 81. A list of calculated sensitivities were obtained for generator c 11 modes, namely modes c51, c 80 and c 107 with respect to perturbations in the PSS gain located at generator c 11, the four SVC firing angles located at buses 121, 40, 112 and 97, respectively, and controlled by generator c 11 as well as the SVC gain located at bus 112 and controlled by generator c 11. It was clear that the PSS at generator c11 represents the most affecting control parameter on mode c 51, while the SVC control parameters located at buses 40 and 112 are the most influential parameters on modes c 80 and c 107, respectively.
4.3. Domains of SVC/PSS influence – topological display Here, we use a topological display to demonstrate the problem-solving approach involved in correcting unstable dynamic modes by identifying the most effective control actions. As was stated before, the original system (without any PSS and SVC controls) has five unstable modes. The unstable dynamic mode c1 (for the set of system operating conditions assumed) belongs to generator c 5, while the unstable conjugate modes c 2 and c 3 belong to generator c 10. Also, the unstable modes c4 and c 5 belong to generator c11. From the PSS and SVC domains of influence, the most influencing parameters on the above five modes can be identified. The mode sensitivities with respect to various parameters have been classified into three ranges, namely high-influence, medium-influence and low-influence as shown in Fig. 2. The parameters chosen were those scattered around mode c1, according to the original power system topology, as well as those determined from available system designers’ experience and power system engineering judgement. From the results obtained, it was clear that the control parameters, which have the most
M.A. Al-Biati et al. / Electric Power Systems Research 58 (2001) 37–44
influence on mode c1, are: 1) the SVC firing angle parameter of the SVC device located at bus 59 and controlled by generator c 5, 2) the SVC firing angle parameter of the SVC device located at bus 44 and controlled by generator c 5, 3) the SVC firing angle parameter of the SVC device located at bus 98 and controlled by generator c1, and 4) the SVC firing angle parameter of the SVC device located at buses 112 and controlled by generator c11. Therefore, in order to improve the interaction mode c 1, using the most effective control actions available, one or more of these three SVC control parameters should be used. Similarly, in order to improve the conjugate modes 2 and 3, the most influencing parameters have been selected from the tabulated and ordered dynamic sensitivity values. The results obtained showed that the dynamic control parameter representing the PSS gain at generator c 10 has the most effect on the critical modes c2 and c 3. We now recall that the original system eigenvalue pattern, discussed in Section 3, was improved by the application of a PSS device at generator c 10 (Qurrayyah). Such improvement resulted in the stabilization of modes c2 and c 3, which were originally unstable. This finding is now confirmed, but in a much faster way, using dynamic control parameter sensitivities. In a similar manner, the dynamic control
43
parameters, which most influence the critical conjugate modes c4 and c 5, were identified by examining the sensitivities of these modes with respect to variations in various parameters. It was concluded that the firing angle parameters of the three SVC devices located at buses 121, 112 and 98 have the most influence on the these two modes. This fast and elegant sensitivity-based result also confirms what was previously reported on using extensive full-scale dynamic stability computer runs. In summary, the results of the sensitivity analysis indicate that the five unstable modes could be corrected, most effectively, by placing a coordinated combination of one PSS at generator c 10, one SVC at bus 98 controlled by generator c 11 and one SVC at bus 112 controlled by generator c 11. The resulting modes for this arrangement were confirmed using the dynamic stability program which showed all system modes being stable for the coordinated SVC/PSS placement considered.
5. Conclusions This paper has presented a new sensitivity-based methodology for easy and effective coordination of
Fig. 2. Domains of control parameter influence on critical dynamic mode c1.
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parameter control actions associated with power system stabilizers and static var compensators for the purpose of improving the dynamic performance of electric power systems. The present study showed that coordination of SVC and PSS control devices can significantly increase power system damping as compared with cases where either type is used alone to damp system oscillations. The paper demonstrated the effect of SVC and PSS equipment on system stability by examining the numerically calculated eigenvalue sensitivities of the dominant eigenvalues with respect to various candidate locations. These sensitivities are calculated by simulating the installation of SVC devices on different bus locations and/or PSS devices on different generator exciters. The proposed methodology calculates and displays the domains of influence of various control parameters on the system dynamic modes (eigenvalues). Using these domains of influence, proper assessment and corrective actions can be made to improve dynamic performance by correcting the problem (unstable or weak) modes using the most effective combination of control actions. Practical applications of the sensitivitybased methodology were carried out for the SCECO-C system connected to Qassim and SCECO-E. The steady-state stability of the system and the associated dynamic mode sensitivities with respect to PSS and SVC control parameters have been evaluated. The application study confirmed that the proper coordination of PSS and SVC control actions would have a significant effect on the system dynamic stability. In this respect, it was found that placing a power system stabilizer at the Qurrayyah power plant coupled with placing two static var compensators at buses 98 and 112 with control signals from the Qassim power plant would stabilize the dynamic system performance. The practical operating scenario considered in the paper is regarded as a likely future scenario in which the system operates close to its dynamic stability limits. While no dynamic instability has actually occurred in the SCECO-C power system to-date, observations and measurements of the actual system dynamic behavior seam to confirm the findings of the paper. Notable improvements in the system dynamic response to disturbances have already been witnessed with some PSS and SVC devices in place. It is believed that the present work would pave the way for a number of future
.
studies on the coordination of PSS and SVC control actions based on the concept of ‘domains of influence’ introduced in this paper.
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