IEEE PES Task Force on Benchmark Systems for Stability Controls

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1 IEEE PES Task Force on Benchmark Systems for Stability Controls Report on Benchmark #2 The Brazilian 7 Bus (Equivalent Model) Version 1 - October 23 rd, 214 Fernando J. de Marco, Leonardo Lima and Nelson Martins The results presented in this report correspond to time-domain simulations of different disturbances and eigenvalue calculations for the Benchmark System #2 performed with and /PacDyn software. This system, as described in [1], is oscillatory unstable without power system stabilizers. All linear techniques for locating stabilizers (e.g., transfer function residues, participation factors, etc.) indicate that the unstable mode can be stabilized by a PSS at Itaipu (bus #4). However, the key characteristic of this system is the presence of a zero in the transfer function associated with the PSS at Itaipu (bus #4) that precludes proper damping of the mode with just one PSS at Itaipu [1]. Therefore, stabilizers at the other machines (except the equivalent machine at bus #7) are necessary to eliminate this poorly located transfer function zero and thus achieve sufficient damping for the unstable oscillation mode. Time domain simulations The main objective associated with the selection of these disturbances is to assess the system damping and the effectiveness of the proposed stabilizers in providing damping to these oscillations. Both disturbances excite the unstable interarea mode of.85 Hz. Results are presented for the system without PSS, with PSS at Itaipu only, and with PSS at all generators except the equivalent (at bus #7). The first set of simulations comprises the connection of a 5 Mvar reactor at the Ivaiporã 765 kv bus (bus #6) at t = 1. second. The reactor is disconnected 1 ms later, without any further changes in the system topology. The second set of simulations corresponds to a 2% step in voltage reference at the Itaipu machine (bus #4), applied at t = 1. second. The step is removed (i.e., 2% step is applied) at t = 11. seconds. Eigenanalysis The eigenanalysis consists in the calculation of the linear system eigenvalues and participation factors. The results are summarized in tables.

2 1. System model 1.1 /PacDyn Dynamic Simulation Models The models and associated parameters for the dynamic simulation models used in the /PacDyn setup are described in this section. 1.1.a) Synchronous Machines The generator model used to represent the salient pole units is the library model Synchronous Machine Model 2, shown in the block diagram in Figure 1, which is a 5 th order dynamic model. Saturation effects are neglected in all cases. Details about the implementation of the model are available in the software documentation [2]. a) Quadrature axis b) Direct axis Figure 1: Block Diagram for the s synchronous Machine Model b) Excitation Systems The excitation systems of all generators are represented by the s library model Voltage Regulator Model 2 shown in Figure 2, with the parameters in Table 1.

3 Figure 2: Block Diagram for the Anatem s Voltage Regulator Model 2. Table 1: Parameters of the Automatic Voltage Regulators Modeled in Parameter T m K a T 1 T 2 T 3 T 4 L min L max Value. s 3. pu. s.5 s 1. s 1. s -4. pu 5. pu 1.1.c) Power System Stabilizers The power system stabilizers are represented in by the library model Stabilizer Model 1 shown in the block diagram in Figure 3, with the parameters in Table 2. Figure 3: Power System Stabilizer Modeled in. Table 2: Parameters of the Power System Stabilizers Modeled in. Parameter Value Units 1, 2 and 3 Unit4 K 3 pu 48 pu T 3. s 3. s T 1.3 s.52 s T 2.75 s.65 s T 3.3 s.52 s T 4.75 s.65 s L min -.1 pu -.1 pu L max.1 pu.1 pu

4 1.2 Dynamic Simulation Models The models and associated parameters for the dynamic simulation models used in the setup are described in this section. 1.2.a) Synchronous Machines The generator model used to represent the salient pole units is the PSS E model GENSAE, shown in the block diagram in Figure 4. This is a 5 th order dynamic model with the saturation represented by the geometric (exponential) function S = S1. E X, where X = ln(s1.2/s1.)/ln(e1.) and E is the input. Speed damping D is set to zero for all generators, as should be the case when using sub-transient generator models. Details about the implementation of the model are available in the software documentation [3]. Figure 4: Block Diagram for the Model GENSAE. The details associated with the representation of the saturation of the generators should not dramatically interfere with the results of a small-signal (linearized) analysis of the system performance. On the other hand, the proper representation of saturation is extremely important

5 for transient stability and the determination of rated and ceiling conditions (minimum and maximum generator field current and generator field voltage) for the excitation system. The assumed saturation factors S(1.) =.1 and S(1.2) =.1 essentially neglect saturation effects. 1.2.b) Excitation Systems All excitation systems are considered identical and are represented by the same dynamic model and set of parameters. It is used the PSS E simplified excitation system model SEXS [3], shown in Figure 5, with the parameters presented in Table 3. Figure 5: Block Diagram for the Model SEXS. Table 3: Dynamic Model Data for the Excitation Systems ( Model SEXS) Parameters Description Symbol Value Unit TGR block 1 transient gain T A /T B 1 TGR block 1 denominator time constant Exciter gain Exciter time constant Max. AVR outpu Min. AVR outpu T B K T E E min E max c) Power System Stabilizers This benchmark system considers power system stabilizers (PSS) in all machines except the machine connected to bus #7 (EQUIVALENT). All PSSs are derived from rotor speed deviation and have the same structure, namely two lead-lag blocks, one wash-out block, and a gain. The IEEE Std (25) model PSS1A [4] are used to represent the power system stabilizers. This model can be represented in PSS E by the IEEEST model [3]. The block diagram of the IEEEST model is shown in Figure 6 and the used parameters are given in Table 4. The output limits are set to +/ 1%, while the logic to switch off the PSS for voltages outside a normal operation range is ignored (parameters V CU and V CL set to zero). The input signal is rotor speed deviation. s pu s pu pu

6 Input Signal 2 1+A 5S +A 6S 2 (1 +A 1S +A 2 2S )(1 +A 3S +A ) 4S 1+sT 2 1+sT 1 1+sT 3 1+sT 4 L SMAX Output Limiter K S st 5 1+sT 6 V SS V S = V SS,if (V CU > V CT >V CL ) V S =, if (V CT < V CL ) V S =, if (V CT < V CU ) VOTHSG L SMIN Figure 6: Power System Stabilizer ( Model IEEEST). Table 4: Dynamic Model Data for Power System Stabilizers ( Model IEEEST) Parameters Buses Description Symbol Unit 1, 2, nd order denominator coefficient A 1 2 nd order denominator coefficient A 2 2 nd order numerator coefficient A 3 2 nd order numerator coefficient A 4 2 nd order denominator coefficient A 5 2 nd order denominator coefficient A 6 1 st lead-lag numerator time constant T 1 s st lead-lag denominator time constant T 2 s nd lead-lag numerator time constant T 3 s nd lead-lag denominator time constant T 4 s Washout block numerator time constant T 5 s 3 3 Washout block denominator time constant T 6 s 3 3 PSS gain K S pu 1 16 PSS max. output L Smax pu.1.1 PSS min. output L Smin pu Upper voltage limit for PSS operation V CU pu Lower voltage limit for PSS operation V CL pu

7 2. Comparison of results /PacDyn vs 2.1Time-domain simulation results The time-domain responses for the two perturbations simulated with and programs are compared in Sections 2.1.a) and. An acceptable matching is qualitatively appreciated between the results of both programs, for the cases with and without PSS. 2.1 a) Case A: 5 MVAr Reactor Applied to Bus #6 4 3 CaseA-noPSS - Gen # CaseA-PSSita - Gen # CaseA-allPSS - Gen # Figure 7: Output power Response of Generator #1 to a 5 MVAr Reactor Applied to Bus #6. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

8 CaseA-noPSS - Gen # CaseA-PSSita - Gen # CaseA-allPSS - Gen # Figure 8: Output power Response of Generator #2 to a 5 MVAr Reactor Applied to Bus #6. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

9 CaseA-noPSS - Gen # CaseA-PSSita - Gen # CaseA-allPSS - Gen #3 Figure 9: Output power Response of Generator #3 to a 5 MVAr Reactor Applied to Bus #6. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

10 1 5 CaseA-noPSS - Gen # CaseA-PSSita - Gen # CaseA-allPSS - Gen # Figure 1: Output power Response of Generator #4 to a 5 MVAr Reactor Applied to Bus #6. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

11 CaseA-noPSS - Gen # CaseA-PSSita - Gen # CaseA-allPSS - Gen # Figure 11: Output power Response of Generator #7 to a 5 MVAr Reactor Applied to Bus #6. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

12 2.1.b) Case B: Step applied to the AVR reference of Generator # CaseB-noPSS - Gen # CaseB-PSSita - Gen # CaseB-allPSS - Gen # Figure 12: Output power response of Generator #1 to step applied to the AVR reference of Generator #4. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

13 CaseB-noPSS - Gen # CaseB-PSSita - Gen # CaseB-allPSS - Gen # Figure 13: Output power response of Generator #2 to step applied to the AVR reference of Generator #4. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

14 CaseB-noPSS - Gen # CaseB-PSSita - Gen # CaseB-allPSS - Gen # Figure 14: Output power response of Generator #3 to step applied to the AVR reference of Generator #4. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

15 CaseB-noPSS - Gen # CaseB-PSSita - Gen # CaseB-allPSS - Gen # Figure15: Output power response of Generator #4 to step applied to the AVR reference of Generator #4. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

16 -15-2 CaseB-noPSS - Gen # CaseB-PSSita - Gen # CaseB-allPSS - Gen # Figure 16: Output power response of Generator #7 to step applied to the AVR reference of Generator #4. Top: no PSS; Center: PSS at Itaipu; Bottom: PSS at all generators.

17 2.2 Eigenanalysis 2.2.a) PacDyn vs PSSPLT Comparison This section provides the system eigenvalues calculated with both software for the cases with no PSS, with PSS at generator #4 only, and with PSS at all generators. In the first case, good matching is observed for the electromechanical modes. In the last two cases (with PSS), the results obtained with PSSPLT highly depend on the processed signal. System with no PSS Imag (rad/s) a) Imag (rad/s) b) Real (1/s) Real (1/s) Figure 17: Eigenvalues Calculated with PSS E Program PSSPLT and PacDyn for the system with no PSS. a) Complete set of eigenvalues; b) Enlarged view in the region of the electromechanical modes. System with PSS at generator #4 5 a) 15 b) 4 1 Imag (rad/s) 3 2 Imag (rad/s) Real (1/s) Real (1/s) Figure 18: Eigenvalues Calculated with PSS E Program PSSPLT and PacDyn for the system with PSS at generator #4 (Itaipu). results from Table 11 (Itaipu active power). a) Complete set of eigenvalues; b) Enlarged view in the region of the electromechanical modes.

18 5 a) 15 b) 4 1 Imag (rad/s) 3 2 Imag (rad/s) Real (1/s) Figure 19: Eigenvalues Calculated with PSS E Program PSSPLT and PacDyn for the system with PSS at generator #4 (Itaipu). results from Table 12 (Santiago active power). a) Complete set of eigenvalues; b) Enlarged view in the region of the electromechanical modes. System with PSS at all generators Real (1/s) 5 a) 15 b) 4 1 Imag (rad/s) 3 2 Imag (rad/s) Real (1/s) Real (1/s) Figure 2: Eigenvalues Calculated with PSS E Program PSSPLT and PacDyn for the system with PSS at all generators. results from Table 13 (Itaipu active power). a) Complete set of eigenvalues; b) Enlarged view in the region of the electromechanical modes. 6 5 a) 15 b) 4 1 Imag (rad/s) 3 2 Imag (rad/s) Real (1/s) Real (1/s) Figure 21: Eigenvalues Calculated with PSS E Program PSSPLT and PacDyn for the system with PSS at all generators. results from

19 (Santiago active power). a) Complete set of eigenvalues; b) Enlarged view in the region of the electromechanical modes.

20 2.2.b) PacDyn Results Table 5: Eigenvalues Calculated with PacDyn for the system without PSS # Real Imaginary Module Freq. (Hz) Damp(%) Part. Factor DELT S Santiago # DELT FOZ AREIA # WW S Segredo # EQ' S Segredo # WW EQUIV SE # EQ' EQUIV SE # EQ'' ITAIPU # ED'' S Santiago # E DELT EQUIV SE # ED'' S Segredo # EQ'' S Santiago # EQ'' FOZ AREIA # EQ'' S Segredo # x 5 AVR-G7 # x 5 AVR-G4 # x 5 AVR-G3 # ED'' FOZ AREIA # ED'' EQUIV SE # EQ' EQUIV SE # EQ' S Santiago # EQ' S Segredo # E

21 Table 6: Eigenvalues Calculated with PacDyn for the system with PSS at generator #4 (Itaipu) # Real Imaginary Module Freq. (Hz) Damp(%) Part. Factor WW ITAIPU # WW S Santiago # DELT FOZ AREIA # WW EQUIV SE # EQ' S Segredo # DELT ITAIPU # ED'' EQUIV SE # ED'' S Santiago # E E DELT ITAIPU # ED'' S Segredo # EQ' ITAIPU # EQ'' S Santiago # EQ'' FOZ AREIA # EQ'' S Segredo # EQ' ITAIPU # x 5 AVR-G7 # x 5 AVR-G3 # ED'' FOZ AREIA # ED'' ITAIPU # EQ' ITAIPU # EQ' ITAIPU # EQ' S Santiago # x 8 PSSDW # EQ' S Segredo # x 3 PSSDW # E E

22 Table 7: Eigenvalues Calculated with PacDyn for the system with PSS at generators #1, #2, #3 and #4. # Real Imaginary Module Freq. (Hz) Damp(%) Part. Factor WW S Santiago # WW ITAIPU # WW S Segredo # EQ'' S Santiago # WW FOZ AREIA # 1 x 5 AVR-G3 # WW EQUIV SE # DELT ITAIPU # x 5 PSSDW # ED'' EQUIV SE # ED'' FOZ AREIA # DELT FOZ AREIA # DELT FOZ AREIA # x 5 PSSDW 11 # x 5 PSSDW 11 # ED'' S Segredo # EQ' ITAIPU # ED'' S Santiago # EQ' ITAIPU # ED'' S Santiago # x 5 AVR-G7 7 # ED'' ITAIPU # EQ' FOZ AREIA # EQ' ITAIPU # EQ' ITAIPU # x 8 PSSDW 11 # x 8 PSSDW 33 # x 8 PSSDW # x 8 PSSDW 33 # EQ' S Segredo # x 3 PSSDW # x 3 PSSDW 22 # x 3 PSSDW # DELT FOZ AREIA #

23 2.2.c) Results PSS E auxiliary program PSSPLT 1 can estimate the dominant modes of a system by decomposing its oscillatory response. The following tables show the results using the Least Square decomposition method applied separately to time-domain responses of the speeds of machines #2 and #4. Table 8 shows the original JCITA system eigenvalues. It can be seen that there is a complex pair with positive real part which characterizes an unstable mode. Erro! Fonte de referência não encontrada. and Erro! Fonte de referência não encontrada. show the system with PSS at the Itaipu Generator (#4), where the poor damping achieved is characterized. Erro! Fonte de referência não encontrada. and Erro! Fonte de referência não encontrada. show the system eigenvalues with PSSs in all machines (except the equivalent generator #7). No PSS Table 8: Eigenvalues Calculated with PSS E Program PSSPLT for the system without PSS. PTI INTERACTIVE POWER SYSTEM SIMULATOR-- SUN, NOV :38 IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM EIGENVALUES: NO. REAL IMAG DAMP FREQ E E E E E E E E-2 1 Provided as part of the PSS E installation, for users with the proper license. Consult the software vendor if you are not sure about your license.

24 Table 9: Eigenvalues Calculated with PSS E Program PSSPLT for the system without PSS. Results obtained processing generator #4 speed. CHANNEL FILE: run_fault_bus_6_rea_5_pss_none.out IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM CHANNEL: CHNL# 34: [SPD 4[ITAIPU 765.]1] TIME INTERVAL: SEC. MODAL COMPONENTS COMP. EIGENVALUE EIGENVECTOR NO REAL IMAGINARY MAGNITUDE ANGLE REMARKS E FREQ.:.866 HZ E-5 -- TCNST:.46 SC E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ. PERC. ERROR: SIGNAL/NOISE: 34.7 METHODS: EIGENVALUE - LEAST SQUARE, EIGENVECTOR - LEAST SQUARE ORDER: 3 Table 1: Eigenvalues Calculated with PSS E Program PSSPLT for the system without PSS. Results obtained processing generator #2 speed. CHANNEL FILE: run_fault_bus_6_rea_5_pss_none.out IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM CHANNEL: CHNL# 32: [SPD 2[S. SANTIAGO 5.]1] TIME INTERVAL: SEC. MODAL COMPONENTS COMP. EIGENVALUE EIGENVECTOR NO REAL IMAGINARY MAGNITUDE ANGLE REMARKS E-5 -- TCNST:.368 SC E FREQ.:.872 HZ E FREQ.: 1.61 HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ. PERC. ERROR: 3.64 SIGNAL/NOISE: 27.1 METHODS: EIGENVALUE - LEAST SQUARE, EIGENVECTOR - LEAST SQUARE ORDER: 27

25 PSS at Itaipu Table 11: Eigenvalues Calculated with PSS E Program PSSPLT for the system with PSS at generator #4. Results obtained processing generator #4 speed. NUMBER OF SELECTED DATA POINTS IS 86 AND TIME STEP IS.8 SELECT AN NPLT OF 8 TO REDUCE THE NUMBER OF POINTS TO ABOUT 1 EFFECTIVE NUMBER OF DATA POINTS IS 286 AND EFFECTIVE TIME STEP IS.25 CHANNEL FILE: run_fault_bus_6_rea_5_pss_ita.out IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM CHANNEL: CHNL# 34: [SPD 4[ITAIPU 765.]1] TIME INTERVAL: SEC. MODAL COMPONENTS COMP. EIGENVALUE EIGENVECTOR NO REAL IMAGINARY MAGNITUDE ANGLE REMARKS E FREQ.:.618 HZ E E FREQ.:.929 HZ E E-6 -- TCNST: SC E FREQ.: 2.26 HZ E-7 -- TCNST:.8 SC E FREQ.: HZ E FREQ.: HZ E FREQ.: 5.14 HZ E FREQ.: 4.27 HZ E FREQ.: HZ E FREQ.: 7.66 HZ E FREQ.: 9.2 HZ. PERC. ERROR: SIGNAL/NOISE: METHODS: EIGENVALUE - LEAST SQUARE, EIGENVECTOR - LEAST SQUARE ORDER: 42

26 Table 12: Eigenvalues Calculated with PSS E Program PSSPLT for the system with PSS at generator #4. Results obtained processing generator #2 speed. NUMBER OF SELECTED DATA POINTS IS 967 AND TIME STEP IS.8 SELECT AN NPLT OF 9 TO REDUCE THE NUMBER OF POINTS TO ABOUT 1 EFFECTIVE NUMBER OF DATA POINTS IS 322 AND EFFECTIVE TIME STEP IS.25 CHANNEL FILE: run_fault_bus_6_rea_5_pss_ita.out IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM CHANNEL: CHNL# 32: [SPD 2[S. SANTIAGO 5.]1] TIME INTERVAL: SEC. MODAL COMPONENTS COMP. EIGENVALUE EIGENVECTOR NO REAL IMAGINARY MAGNITUDE ANGLE REMARKS E E FREQ.:.928 HZ E FREQ.:.613 HZ E FREQ.: 1.51 HZ E FREQ.: 2.27 HZ E-6 -- TCNST: SC E FREQ.: 7.99 HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: 9.99 HZ E FREQ.: 4.23 HZ. PERC. ERROR: SIGNAL/NOISE: METHODS: EIGENVALUE - LEAST SQUARE, EIGENVECTOR - LEAST SQUARE ORDER: 41

27 PSS at All Machines Table 13: Eigenvalues Calculated with PSS E Program PSSPLT for the system with PSS at generator1 #1, #2, #3 and #4. Results obtained processing generator #4 speed. NUMBER OF SELECTED DATA POINTS IS 693 AND TIME STEP IS.8 SELECT AN NPLT OF 6 TO REDUCE THE NUMBER OF POINTS TO ABOUT 1 EFFECTIVE NUMBER OF DATA POINTS IS 231 AND EFFECTIVE TIME STEP IS.25 CHANNEL FILE: run_fault_bus_6_rea_5_pss_all.out IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM CHANNEL: CHNL# 34: [SPD 4[ITAIPU 765.]1] TIME INTERVAL: SEC. MODAL COMPONENTS COMP. EIGENVALUE EIGENVECTOR NO REAL IMAGINARY MAGNITUDE ANGLE REMARKS E FREQ.:.778 HZ E FREQ.:.544 HZ E FREQ.: HZ E E-6 -- TCNST: SC E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: 9.5 HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ. PERC. ERROR:.8675 SIGNAL/NOISE: METHODS: EIGENVALUE - LEAST SQUARE, EIGENVECTOR - LEAST SQUARE ORDER: 43

28 Table 14: Eigenvalues Calculated with PSS E Program PSSPLT for the system with PSS at generator1 #1, #2, #3 and #4. Results obtained processing generator #2 speed. NUMBER OF SELECTED DATA POINTS IS 783 AND TIME STEP IS.8 SELECT AN NPLT OF 7 TO REDUCE THE NUMBER OF POINTS TO ABOUT 1 EFFECTIVE NUMBER OF DATA POINTS IS 261 AND EFFECTIVE TIME STEP IS.25 CHANNEL FILE: run_fault_bus_6_rea_5_pss_all.out IEEE BENCHMARK SYSTEM BRAZILIAN 7-BUS EQUIVALENT SYSTEM CHANNEL: CHNL# 32: [SPD 2[S. SANTIAGO 5.]1] TIME INTERVAL: SEC. MODAL COMPONENTS COMP. EIGENVALUE EIGENVECTOR NO REAL IMAGINARY MAGNITUDE ANGLE REMARKS E FREQ.:.769 HZ E-5 -- TCNST:.294 SC E-5 -- TCNST:.7 SC E FREQ.: 1.53 HZ E-6 -- TCNST: 5.49 SC E FREQ.: HZ E FREQ.: 6.92 HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ E FREQ.: HZ. PERC. ERROR: 4.59 SIGNAL/NOISE: METHODS: EIGENVALUE - LEAST SQUARE, EIGENVECTOR - LEAST SQUARE ORDER: 42

29 References [1] MARTINS, Nelson; LIMA, L. T. G. Eigenvalue and Frequency Domain Analysis of Small-Signal Electromechanical Stability Problems, IEEE Symposium on Application of Eigenanalysis and Frequency Domain Method for System Dynamic Performance, 1989,.p [2] CEPEL, Users Manual V1.4.6 (in Portuguese), March 212. [3] Siemens PTI, 32. Online Documentation, June 29. [4] IEEE Recommended Practice for Excitation System Models for Power System Stability Studies, IEEE Standard 421.5(25), April 26.

Aug 2015 PES-TR18. Benchmark Systems for Small-Signal Stability Analysis and Control. IEEE Power & Energy Society TECHNICAL REPORT

Aug 2015 PES-TR18. Benchmark Systems for Small-Signal Stability Analysis and Control. IEEE Power & Energy Society TECHNICAL REPORT IEEE Power & Energy Society Aug 25 TECHNICAL REPORT PES-TR8 Benchmark Systems for Small-Signal Stability Analysis and Control PREPARED BY THE Power System Dynamic Performance Committee Power System Stability