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HomeMy WebLinkAboutAnchorage Fairbanks Transient Network Analyzer-APA-83-C-0051 1983TT. III. ALASKA POWER AUTHORITY Anchorage - Fairbanks Intertie Voltage and Load Flow Study .......... Dynamic Stability Analysis. .......... Control System Study ANCHORAGE-FAIRBANKS INTERTIE STATIC VAR SYSTEMS (230 kV Pt. Mackenzie Area Transmission] VOLTAGE AND LOAD FLOW STUDIES FOR ALASKA POWER AUTHORITY APA Contract No. APA-83-C-0051 Report by Carl E. Grund ELECTRIC UTILITY SYSTEMS ENGINEERING DEPARTMENT GENERAL ELECTRIC COMPANY DECEMBER 1983 1.0 INTRODUCTION Steady-state voltage and load flow studies have been performed for the Alaska Power Authority Anchorage to Fairbanks Intertie Static Var Systems. These studies have been performed by the Electric Utility Systems Engineering Department of the General Electric Company in Schenectady, New York, to satisfy the requirements of Contract No. APA-83-C-0051. These studies represent the power system in accordance with the specification; that is, the Pt. Mackenzie transmission area was represented as 230 kV and the Cantwell to Watana line was not in service. The requirements for the studies were given in the specification and are restated below for convenience. 2.0 APA STUDY SPECIFICATION 4.1.2 “To perform voltage study to verify proper performance of the SVS over the normal control and design range and to identify voltage conditions for excursions beyond the normal control and design range. This study shall also include investigation of overvoltage at the SVS bus that may occur for: a. Maximum capacitive vars being produced at any system voltage dispatch. b. Maximum capacitive vars being produced at any system voltage level with concurrent failure of a shunt reactor, thyristor or control system. Information from this voltage study will be utilized to apply proper voltage ratings to the capacitors, filter equipment, protective equipment, non-gated thyristors and to confirm overexcitation requirements for the supplied power transformers, whether dedicated or being acquired separately. Note: Feasibility studies for SVS performance indicated that non-concurrent loss of the inductive component of the SVS at the respective substations will result in overvoltage at the SVS buses of 1.07 per unit at Gold Hill, 1.21 per unit at Healy and 1.07 per unit at Teeland, on a continuous basis. Therefore, the transformer windings connected to the SVS have been specified for overexcitation capability of 1.10 per unit at Gold Hill, 1.20 per unit at Healy and 1.1 per unit at Teeland. 4.1.3 Perform load flow studies to observe the voltage, real power and reactive power flow patterns in the intertie system during steady-state conditions. The load flow cases shall involve pertinent combinations of generation dispatch, customer demand level and intertie power flow conditions with normal and facility outage (out-of-service) system configurations. The SVS shall provide a continuous control to maintain the voltage of the designated bus. Note: The voltage study and the load flow studies may be combined, provided that all of the requirements of the Paragraphs 4.1.2 and 4.1.3 are addressed in the study and the study report.” 3.0 POWER SYSTEM DEFINITION The power system was modeled based on the data supplied on magnetic tapes by Commonwealth Associates (CA). This information was used in the studies performed by General Electric as the basis of all power system impedances, load levels, generation dispatch, and transformer tap ratios. The impedances of the SVS transformers were changed based on the new information of the final design values. The CA load flows were translated to the General Electric ILF load flow program and repeated without any modifications to provide a convenient technical bridge between the CA studies and the new studies performed by General Electric Company. The results of the translated CA load flows are presented as reference cases without discussion in Figures 1, 6, and 11 of this report (cases APAlA, APA2A, and APA1OA, respectively). The voltage levels of the SVS controlled bus in the CA load flow cases established the desired voltage level of the SVS's for these buses in the new study. 4.0 RESULTS The load flow study requirements of Paragraphs 4.1.2 and 4.1.3 are combined and are described in two separate categories: 1. Performance Under Normal Conditions 2. Performance Under Abnormal Conditions. The load flow study results are given on one-line diagrams which show the bus voltages and the line power flows of the Intertie system, including its Anchorage and Fairbanks terminations. 4.1 Performance of the SVS's Over the Normal Control and Design Range SVS performance was investigated for normal operation by analysis of three nominal power flow conditions as given in Table 1. The nominal power flow conditions are indicated by the index “X", where the number of the index is the same as that used by Commonwealth Associates in the feasibility studies. The second index “Y" gives the type of SVS model used. For Y = A, a direct translation of base case data as provided by CA is given. The SVS is modeled on the low or tertiary winding. For Y = B, a SVS is modeled on the controlled bus and for Y = C the SVS is modeled as a generator within the control range and as fixed capacitive or inductive shunt for voltages outside of the control range. The third index “"Z" indicates the SVS outage that is simulated. Heavy capacitive loading of the SVS occurs for the 70 MW power transfer conditions. Heavy reactive absorption by the SVS's occurs for the zero power transfer condition. The power flow results for the SVS's are given in Tables 2, 3 and 4. The power flow information for the Intertie is given on the one-line diagrams in Figures 1 through 15. In the tables, the desired SVS controlled bus voltage is the same as that used in the CA reference Table 1 Power Flow Case Identification APAXYZ X= 1: 70 MW Anchorage to Fairbanks, Healy Generator On 2s 70 MW Anchorage to Fairbanks, Healy Generator Off 10: O MW Anchorage to Fairbanks, Healy Generator Off Y= A: Translated Commonwealth Associates Cases B&C: New Cases Z= 1: Teeland SVS Out of Service 2's Healy SVS Out of Service 3: Gold Hill SVS Out of Service cases. The actual high side voltage is equal to the desired voltage as long as the SVS is within its control range. The high side MVAR limits are dependent on the SVS transformer impedance and the operating voltage. The SVS MVAR maximum is defined as positive for capacitive SVS operation and negative for reactive operation. The magnitude of the SVS controlled bus voltage was not the same in the CA reference cases APAlA, APA2A and APA1OA. Hence, the desired voltage for the controlled bus is slightly different between Tables 2, 3 and 4. In practice, the desired SVS voltage and MVAR steady-state operating point is adjustable and can be changed as power system conditions change. The operating point is dependent upon the SVS reference setpoint, SVS control gain (slope of the voltage-MVAR characteristic) and the system operating condition. Therefore, in the performance of load flow cases, where only one steady-state operating condition is examined at a time, it is not necessary to relate operating points to a specific SVS voltage reference setpoint and slope. The nominal SVS loading is given in the Tables 2, 3, and 4 by the MVAR “at Rated Voltage" in per unit based on maximum available MVAR. For the maximum power transfer cases, the maximum loading at the Healy SVS is 72% of maximum for the case with the Healy unit on-line (Table 2, Case APA1B). The Teeland maximum loading is at 70% for the Healy unit off-line (Table 3, Case APA2B) and the Gold Hill SVS has a maximum loading of 67% for the Healy unit on-line. These nominal loadings provide additional range for dynamic control of bus voltages. A heavy reactive power absorption condition is given by case APA10 (Table 4). The nominal reactive absorption is at or near the limit for the Teeland and Gold Hill SVS and approximately 50% for the Healy SVS. 4.2 Over- and Undervoltages for SVS Outages The SVS control system is designed to prevent SVS failures that result in uncontrolled operation at maximum reactive power generation or absorption. Therefore, a loss of control of reactive power results in an automatic disconnect of the SVS. Heavy reactive power absorption and generation conditions were tested for each SVS outage. Cases APAI1BX and APA2BX test the effect of SVS outages for heavy reactive power generation. The Teeland and Gold Hill SVS outages will produce a 3% voltage decrease at the SVS bus. That is, the actual ac voltage is 3% below its desired value as given in Tables 2 and 3. For the Healy SVS failure, the voltage reduction is 6% with the Healy generator on-line and 5% with the Healy generator off-line. For the heavy reactive power absorption case (APA10CX) the SVS outages produced the following overvoltages at the SVS controlled buses. For the Teeland SVS failure, the voltage rises 4% above its desired value. The remaining SVS‘s are able to regulate their desired high side voltages. For the Gold Hill SVS failure, the SVS controlled bus voltage rise is 1% above the desired value and the remaining SVS‘'s are within their control range. The Healy SVS failure produces a 6% voltage rise and the Gold Hill SVS is unable to regulate its high side voltage but the voltage rise is only 2%. In summary, for both maximum reactive power absorption and generation, Teeland and Gold Hill SVS outages will produce voltage changes less than 5% of desired. A Healy SVS outage will produce 6% change for maximum absorption as well as generation. These voltage changes will produce undervoltages for Teeland and Healy SVS outages for heavy power transfer and overvoltage for a Healy SVS outage for zero power transfer (Tables 2, 3 and 4). 4.3 Intertie Operation for AC Line or Transformer Outages Power flow conditions are given in Table 5 for major ac line or transformer outages near the Anchorage and Fairbanks termination of the Intertie. The Pt. Mackenzie 230 kV bus is the termination of the Intertie in the Anchorage system and the Gold Hill 69 kV bus is the termination in the Fairbanks system. The terminating ac systems may Table 5 Power Flow Conditions for AC Line/Transformer Outages 1984 System, Pt. Mackenzie 230 kV Transmission Load Flow Case Figure No. Line/Transformer Outage Results APA1B41 16 Pt. Mackenzie-University Operation of Intertie 230 kV Unaffected APA1B42 Ly) Pt. Mackenzie 230/138 kV Operation of Intertie Unaffected APA1B51 18 Gold Hill-Zehnder 69 kV Power Transfer Reduced from 70 to 58 MW APA10B51 19 Gold Hill-Zehnder 69 kV Operation of Intertie Unaffected have a single outage without disruption of Intertie operation. The opening of any other line segment along with the Intertie will result in temporary shutdown of the Intertie and operation may be restored for isolated operations. The Teeland load may be served from Fairbanks with the opening of the Pt. Mackenzie to Teeland 230 kV line. The line outages selected are those which are connected to the Intertie terminating buses. In the Fairbanks system, two 69 kV lines are in service from Gold Hill to Zehnder. Opening either line will decrease the short circuit capacity at the Gold Hill 69 kV bus. At the Anchorange termination, the Pt. Mackenzie line to University and the 230/138 kV transformer may have an impact on Intertie operation. The results indicate that a single contingency at the Anchorage or Fairbanks termination has a negligible impact on the operation of the Intertie. The outage of one of two lines from Gold Hill to Zehnder causes a 17% reduction in the power transfer of the Intertie because the line removal produces load disconnection. 5.0 CONCLUSIONS For the power system conditions considered, a. With all three SVS's in service, each SVS should remain within its normal control range and be able to maintain the desired control bus voltage. b. With one SVS out of service, the remaining SVS‘s may operate outside of their normal control range. The controlled bus voltage deviation from desired will be 6% or less. The outage of the Healy SVS is the most critical to the voltage control of the Intertie. c. The voltage changes produced by SVS outages appear small enough so that before and after outage voltages should be within their allowed operating range of +5% of nominal. a. For heavy SVS MVAR generation, the Intertie voltages should be set close to their maximum value so that the voltage reduction due to a SVS outage will not cause Intertie voltages to drop below their minimum values. The converse is true for heavy SVS MVAR absorption. AC line or transformer outages near the Intertie terminations have a negligible effect on Intertie voltages. However, the power transfer is reduced from 70 to 58 MW from Anchorage for the Gold Hill-Zehnder 69 kV line outage. The voltages at the SVS controlled buses remained within +5% of nominal for all conditions studied. e@ fable 2 Normal and SVS Failure Power Flow Conditions for 70 MW Power Transfer to Fairbanks, Healy Generator On-Line, 1984 System, Pt. Mackenzie 230 kV Transmission Load Intertie ——SUS_Equipment Bus____ aie Bk aoe aa Flow SVS Voltage Over/ SVS Controlled Bus Wolters —_Voltage Fig. Controlled SVS In Under- Voltage (%) MVAR Voltage i Case_ No. Bus Service Voltage Desired _Actual Max. Actual (pu) Max. Actual (pu) APA1B 2 Teeland 138 yes no 98.7 98.7 20.9 10.5 0.973 22. 11.3. (.51) Healy 138 yes 102.2 102.2 25.0 17.6 1.087 22. 15.8 (.72) Gold Hill 69 yes 101.0 101.0 34.9 23.0 1.034 $3. 22.0 (.67) APA1B1 3 Teeland no under 98.7 96.1 - oO. 0.973 - - Healy yes 102.2 10252 25.0 22.3 1.104 22. 19.8 (.90) Gold Hill yes 101.0 101.0 34.9 23.0 1.034 33. 22.0 (.67) APA1B2 4 Teeland yes under 98.7 98.7 20.9 20.5 0.985 22 21.6 (.98) Healy no 102.2 96.6 - Oo. 0.966 - ~ Gold Hill yes 101.0 101.0 34.9 34.8 1.045 33. 33.0 (1.0) APA1B3 5 Teeland yes no 98.7 98.7 20.9 11.1 0.974 22. 11.9 (.54) Healy yes 102.2 102.2 25.0 23.8 1.110 22. 21.0 (.95) Gold Hill no 101.0 98.2 - oO. 0.972 ~ - Notes: 1. Per unit of maximum. @ ble 3 Normal and SVS Failure Power Flow Conditions for 70 MW Power Transfer to Fairbanks, Healy Generator Off-Line, 1984 System, Pt. Mackenzie 230 kV Transmission Load Intertie ——__SV¥5_Equipment Bus____ uipe mk ss ed Flow SVS Voltage Over/ SVS_ Controlled Bus Voltage i Waltacs(@\ 15. o eMVARLUULUL steeeaieeeEssisicaiencs Fig. Controlled SVS In Under- Voltage (%) MVAR Voltage i Case No. Bus Service Voltage Desired _Actual Max. Actual (pu) Max. Actual (pu) APA2B 7 Teeland 138 yes no 99.9 99.9 21.4 14.7 0.989 22. 15.3 (.70) Healy 138 yes 102.2 102.2 25.0 11.0 1.063 een 10.1 (.46) Gold Hill 69 yes 102.0 102.0 35.9 22.2 1.047 33. 20.8 (.63) APA2B1 8 Teeland no under 99.9 96.4 0. Oo. 0.940 - - Healy yes 102.2 102.2 25.0 17.4 1.087 22. 15.7 (.71) Gold Hill yes 102.4 102.4 35.9 22.2 1.047 33. 20.7 (.63) APA2B2 9 Teeland yes no 99.9 99.9 21.4 21.2 0.993 22. 22.0 (1.0) Healy no 102.2 97.5 oO. oO. 0.975 - - Gold Hill yes 102.4 102.4 35.9 32.1 1.057 a. 29.7 (.90) APA2B3 10 Teeland yes no 99.9 99.9 21.4 14.9 0.990 22. 15.5 (.70) Healy yes 102.2 102.2 25.0 16.4 1.083 22. 14.8 (.67) Gold Hill no 102.4 99.6 oO. oO. 0.996 - - Notes: 1. Per unit of maximum. @ fable 4 Normal and SVS Failure Power Flow Conditions for 0 MW Power Transfer to Fairbanks, Healy Generator Off-Line, 1984 System, Pt. Mackenzie 230 kV Transmission SVS Equipment Bus Load Intertie MVAR at Rated Flow SVS Voltage Over/ SVS Controlled Bus Voltage ———— on vane Fig. Controlled SVS In Under- Voltage (%) MVAR Voltage i Case_ No. Bus Service Voltage Desired _Actual Max. Actual (pu) Max. Actual (pu) APA1OC 12 Teeland 138 yes no 97.8 97.8 -17.7 -19.6 0.934 -22. -19.9 (.90) Healy 138 yes 101.4 101.4 -14.5 -30.2 0.960 -33. -14.9 (.45) Gold Hill 69 yes 101.6 101.6 - 5.1 - 5.1 1.011 - 5. -5. (1.00) APA1OC1 13 Teeland no no 97.8 101.4 oO. 0. 0.989 oO. oO. (---) Healy yes 101.4 101.4 -20.0 -30.2 0.939 -33. -21.1 (.64) Gold Hill yes 101.6 101.6 - 5.1 - 5.1 1.011 -5 -4.9 (.98) APA10C2 14 #Teeland yes over 97.8 99.2 -20.1 -19.6 0.944 -22. -22. (1.00) Healy no 101.4 107.5 0. 0. 1.075 0. 0. (---) Gold Hill yes 101.6 103.2 - 5.3 -5.1 1.026 -5. -5~. (1.00) APA10C3 15 #£Teeland yes no 97.8 97.8 -17.8 -19.6 0.934 -22 -19.9 (.90) Healy yes 101.4 101.4 -15.8 -30.2 0.956 -33 -16.3 (.49) Gold Hill no 101.6 102.3 0. 0. 1.023 oO. oO. (---) Notes: 1. Per unit of maximum. ig oF] 10 FIG.! APALA se ister o. sary 48 oettietlng § 0. 1 13° 7 6? GOL DHL PU 1 1.0 40 1.03 MEATS. che 0.9g3 15:48:46 08:32:57 PAIBI AE AUU 0.96PU ot pu® ootnu™ 2,96 PU 9.95 PU 9.97PU S114 5110 xd 116 aoe BARES, 220! 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"EB. 30 a 13:57:48 133. sett icity 0 og 8 Ww 14 is > 1-04 0 1 o.satt elan,,§ ee Fo 5 ~1.65° 1 46! = 1 oF PGMs tee 03 on fieittt, o's 1.03809 1 KXT 233° 1.9 08 3 1.090 1 ate oct 1° 1.0@pb" 0.49% < - <E 4 > 4 < y 3 3 3 7 7 3 < oF Fo oe |e 08:31:34 rgstettio 5 0.9080 =Sos7% si i tof 3 3—O Svs 1 sBRNING Ss 0.97PU -4.34° 44 13 goto 1 igolome 1 séoton 3 fusexy 3 0.98 ES rhe yo ae ese 1ogo 10178 28s.e1e orp “6b cre i 1 a4 13 1 3 2 6 es 6 4 4 < <-|> oF a3 Svs oF] 10:18:35 selid $110 Fels $145 S66 5133 $146 140 114BELUGA Ss 108 LIGTEELND_ |S L4STEECND. S 4eTEELND 5 iyswiliow os L46TLKINA Ss igocnTWeL os 0. 90 57 6 0.908 NE a 0.96PU —=8. 99° o.9zs 9-S9FU =8.00° 0. 98PU , =33.96° 0.9980 KEM og 1-01FU -32-88° H Z 0. FP = e+ 10 7 14 16% < 1 16 S131 TD HRNING Ss 0. 9PPUN NES? 77% 13 nas hub 4GOLOHL 4 gest 3 0.98PU °=60.13" 4.0 1.0120" 66. i 1 = 19 19 = 4 08:51:09 r1aBeLUda 5 LLOPTARNE |S O.98PU 10.442 0-96PU 6.44° i Fe 7 0.9880 goer ake s o. shi! B36 3 4Got DHL 1 igolme a boi! 1 0.99PU °=46.97° 5 9 1.01PU=s2.28¢ 1.0170 OS ee 1 eri = i>ye70 + is is 22¢F 10 10 <_- <_|> oe SVS oF 10 orpdMeNls, W 11818847 FIG. 19 APA OBS! inal 0. 98PU seta) BELUGA Ss 64° Fe 110. S116 $145 $. ae, S133 2 rte S140 L4STEELNI Ss 46TEELND 5S LSSWILLOW OS 1 46TLKTN, Ss J4OCNTWEL S oughta, o.9bPUTEEDNE a 0. 9580 Wibod 0. seh pee ea 1 ree hse de 2 FAS “4 4 3 3 Ss — pron ch) EEO SVS . - iz § 132 L32HCRAE S 1.00PU "=6.23° 1.50° a 5.109 S142 Hl es OSPT MK) S igor Ake s NGS < r.ogo 0-960" Bhb0¢ 0. 9680" Bikae O-se~ . S14) 3 el = 1 yreteng é + 3 17 3 1 6 7 GHEALY SNENANA 3 GOLDHL 1 4 1.08 Putt. 3 V.02@PU3-0S° . 1.090 1.02PU" 4.422 4 ? e Tops f 7 O z s 0 ta Svs . 5 goneaty 1.00PU ANCHORAGE-FAIRBANKS INTERTIE STATIC VAR SYSTEMS (230 kV Pt. Mackenzie Area Transmission] DYNAMIC STABILITY ANALYSIS for ALASKA POWER AUTHORITY APA Contract No. APA-83-C-0051 Report by Carl E. Grund ELECTRIC UTILITY SYSTEMS ENGINEERING DEPARTMENT GENERAL ELECTRIC COMPANY DECEMBER 1983 1.0 Introduction ........ 2.0 APA Study Specification 3.0 Power System Definition .. 3.1 AC System Model .... 3.2 SVS Model ....... 4.0 Dynamic Performance Results 4.1 AC System Faults ... 4.1.1 Fairbanks Faults 4.1.2 Anchorage Faults 4.2 Loss of a Single SVS 4.2.1 Teeland .... 4.2.2 Healy ..... 4.2.3 Gold Hill 5.0 Summary .......26-. Index oOo WON N VY WY Ds} ~ o 1.0 INTRODUCTION Power flow and voltage studies were reported in the previous report. This report discusses dynamic stability results. The study concentrates on the operation of the intertie following severe faults near the terminating ac systems and loss of a single SVS with 70 MW transfer from Anchorage to Fairbanks with the Healy generator on-line at 25 MW output. Faults directly on the Intertie result in the opening of the Intertie with subsequent separation of the Anchorage and Fairbanks power systems. Therefore, such conditions were not investigated in this study. The power system was represented in accordance with the specification; that is, the Pt. Mackenzie transmission area was represented as 230 kV and the Cantwell to Watana line was not in service. All of the 230 kV submarine cable capacitance from Pt. Mackenzie to the University substation was assumed to be compensated with shunt reactors (60 MVAR total). 2.0 APA STUDY SPECIFICATION The following study is in accordance with paragraph 4.1.4 of the specification which defines the dynamic stability analysis requirements. The specification is repeated here for convenience: “4.1.4 Perform a dynamic stability analysis, starting from system conditions defined by load flow cases, to verify that the SVS will meet the requirements of controlling power frequency overvoltages and damping oscillations during and after disturbances in the system and thus provides improved system stability.” This study concentrates on power system stability. The control of overvoltages is addressed in more detail in the TNA study. 3.0 POWER SYSTEM DEFINITION 3.1 AC System Model The ac system network is modeled in detail (as used in previous power flow studies) and only minor network reduction was performed to combine machines in the same plant. Figure 1 gives the power flow diagram for the Intertie with generator network reductions in the Anchorage and Fairbanks power systems. The effects on the Intertie are negligible. The machines in the Fairbanks power system were modeled in detail except for the Fort Wainwright machine which was modeled classically, i.e., constant mechanical power and constant voltage behind transient reactance. The following machines were modeled in detail including sub-transient effects, excitation systems and prime movers: Healy Zehnder North Pole Chena The following plants in the Anchorage system were each modeled classically as separate single machines: Beluga Bernice Lake Copper Lake Eklutna International Anchorage ML&P Station 1 Anchorage ML&P Station 2 The classical machine model for Anchorage generation facilitates the machine representation. Primary focus is on the dynamics of the Fairbanks system due to its small size relative to the Anchorage system. 3.2 SVS Model The SVS was modeled as a thyristor controlled reactor (TCR) in parallel with a capacitor in series with the SVS transformer (Figure 2). The SVS steady-state characteristics are given in Table 1. Table 1 Steady-State Characteristics SVS Rated Voltage MVAR TCR Rated Voltage Capacitive Inductive MVAR Teeland 22. 22. a4, Healy 22. 33. 55: Gold Hill 33. 5. 38. The SVS dynamic model represents the control of the TCR with 5% slope (gain = 20) from full off to full on with a time constant of 0.15 second. The time delay of the thyristor firing is represented by a 2 ms delay. The block diagram is given in Figure 2. The dynamics of the three SVS are identical. Regulator Limiter Delay - my ref + z -1/R a Tall 1+ st, |—— Sa a —_—S - 1 0 Yn R = 0.05 pu (Gain = 20) T) = .150 seconds T faa -002 seconds ! Figure 2. SVS Block Diagram age 4.0 DYNAMIC PERFORMANCE RESULTS The predisturbance condition for the power system was based on a standard power flow model of the system. The case with 70 MW transfer from Anchorage to Fairbanks with the Healy generator on-line showed larger voltage deviations for loss of an SVS compared to the case with the Healy generator off-line. Normally, the case with additional generation on-line will provide improved performance over the case with generation off-line. However, for these simulations, the case with Healy generation on-line has 25 additional MW of transfer from Healy to Fairbanks. This increased transfer is carried over approximately 50% of the Intertie and, therefore, represents a worst case operating condition from a power system dynamic stability point of view. This case with Healy generation on-line is also analyzed for dynamic performance in the subsequent paragraphs. The dynamic simulations fall into two categories: Le AC System Faults in the Terminating Systems (Anchorage and Fairbanks) of the Intertie. 2. Sudden Loss of an SVS. Simulation results are indexed in Table 2. Most cases have a 2 second time duration. Two cases were extended to 8 seconds to check steady- state stability. Table 2 Simulation Results Case and Figure Identifications Case No. Case ID Fault Loss of SVS Figures 2 APA1B5A Gold Hill 3-11 2 APA1B5B Zehnder 12-20 3 APA1B4A Pt. Mackenzie 21-29 4 APA1B4B University 30-38 D APA1B3A Teeland 39-44 6 APA1B3B Healy 45-50 7 APA1B3C Gold Hill 51-55 Faults in the terminating systems of the Intertie give the dynamic performance of the Intertie subsequent to the weakening of the terminating ac system as well as the stability of the Fairbanks power system with respect to the Anchorage system. The simulations of loss of SVS give voltage drop and recovery characteristics of the Intertie as well as the adjustment of other var sources near the Intertie such as the remaining SVS units and the machines modeled with excitation systems. 4.1 AC System Faults The case descriptions start with a complete discussion of all plots for case 1. Other cases are discussed only to point out significant differences in results. All plots are included for all cases for the sake of completeness and for a comparison of cases. 4.1.1 Fairbanks Faults Case 1 represents a three-phase fault at Gold Hill on the Gold Hill to Zehnder 69 kV line with breaker opening at Gold Hill at 6 cycles and at Zehnder at 36 cycles after fault initiation. This scenario represents a severe fault in the Fairbanks ac terminating system of the Intertie. Simulation results are given in Figures 3 through 11. Figure 3 gives the Intertie power (pu of 100 MVA) and the SVS controlled voltages Wy): Teeland 138 kV Healy 138 kV Gold Hill 69 kV The voltages settle to their post-disturbance equilibria which are slightly above the pre-disturbance values showing effective SVS performance. The Intertie power is reduced due to the loss of load (10.6 MW) in the Fairbanks area with the line removal. Figure 4 gives the SVS terminal voltages (v,) in per unit. The Healy SVS bus has the highest terminal voltage (1.11 pu) at fault clearing time. Figure 5 gives the SVS reactor output (rated voltage MVAR) in per unit of its rating. The post-fault steady-state output is increased because capacitive MVAR requirements are reduced due to a reduction in Intertie transfer and an increase in ac system voltage sensitivity (line removal). During the fault, the reactors of all SVS's are almost completely shut off allowing maximum dynamic voltage support. The SVS output (MVAR) at the high side terminal of the SVS transformer is given in Figure 6. The post-fault SVS outputs are lower than the pre-fault values (14 vs. 21 MVAR for Gold Hill) because of the reduced power flow on the Intertie. Figure 7 gives Healy generator simulation results. The steady-state angle oscillations (after 4 seconds) are negligible. Figure 8 gives machine angles relative to the Beluga plant in the Fairbanks and Anchorage systems. The Chena plant shows significant oscillations due to its proximity to the fault. Figure 9 shows the damping of the Chena machine speed oscillations. The machine excitation system outputs (field voltage in pu) are given in Figure 10, and Figure 11 gives machine prime mover outputs of those machines which are modeled in detail. Excitation output is lower after fault removal because of higher system impedances. The prime mover outputs of the Healy and Chena plants are rate limited because their rate limits are 1/50th of those of the other two units (.1 vs 5 pu/second). The North Pole machine has a significant prime mover output deviation during and after the fault. Case 2 is a repeat of case 1 except that the fault is applied at the Zehnder terminal of the line instead of at the Gold Hill terminal. This case represents a more severe disturbance to the Intertie but a less severe disturbance to the machines in the Fairbanks systems. The simulation results are given in Figures 12-20 for a 2 second simulation. The severity of the disturbance can be assessed by comparing the machine speeds for the two fault scenarios (Figures 9 and 18). The Gold Hill fault produces significantly larger machine speed oscillations for the Chena and North Pole machines. 4.1.2 Anchorage Faults Cases 3 and 4 represent severe faults near the Anchorage termination of the Intertie. Case 3 simulates a fault applied at the Pt. Mackenzie terminal of the line to University (line 110-107). Case 4 simulates the fault at the University end of the same line. The line is opened at the faulted end at 5 cycles and at the far end at 30 cycles after fault initiation. These faults result in first swing instability of the Fairbanks system as shown by the machine angles of the Chena and North Pole machines (Figures 26 and 35). The machine speed traces also clearly show the system separation between the Fairbanks and the Anchorage machines (Figures 27 and 36). This system separation is also indicated by the machine angles which exceed 140° at 0.5 second for the Machines in the Fairbanks system relative to the Beluga plant. Comparing North Pole machine speeds for the two cases (Figures 27 and 36), it appears that the fault at University is more severe. The simulation results past about 0.5 second are of no consequence because the Intertie would probably be opened on a rate of change of power or other signal indicating the separation of the Anchorage and Fairbanks systems. Comparing the Anchorage with the Fairbanks faults, the latter is clearly stable and the former case is clearly unstable. One reason for this difference in stability is the difference in machine acceleration caused by the two fault locations. A fault at the Anchorage termination of the Intertie results in acceleration of the Anchorage machines and in deceleration of the Fairbanks machines. This difference in acceleration of machines in the two ac systems causes rapid angular separation and loss of synchronism. For the fault near the Fairbanks terminal, both ac systems experience acceleration and, therefore, a reduced difference in accelerating torques. This results in higher stability margins for Fairbanks faults with Intertie power flow from Anchorage to Fairbanks. 4.2 Loss of a Single SVS Loss of an SVS was modeled by setting the SVS current and reactive flow to zero at a time of 0.1 second. This represents the sudden disconnection of a SVS such as might occur for certain equipment contingencies. The results of the simulations will be discussed by a detailed description of the case of the loss of the Teeland SVS and by a summary of the overall dynamic performance for the loss of one of the other two SVS. Detailed dynamic simulation results of the Intertie, SVS and ac systems are given in Figures 39-56 for the Teeland loss of SVS. The Teeland and Gold Hill cases have 2 second simulation times and the Healy case has a 8 second time duration to evaluate steady-state stability. 4.2.1 Teeland Loss of SVS Figure 39 gives the important Intertie parameters: ac power (in per unit on the system base of 100 MVA) from Gold Hill to Nenana (bus 4 to bus 5). This flow includes the nominal 70 MW flow from Anchorage to Fairbanks at the Healy 138 kV bus as well as the flow of the Healy generator. The steady-state flow is 81 MW of which 80 is delivered at the Gold Hill 69 kV bus termination of the Intertie in Fairbanks. The effect of the Teeland loss of SVS on the power transfer is negligible. The loss of SVS results in an immediate controlled voltage reduction of 2% as shown in Figure 39 and Table 2. Since excitation systems are not modeled for machines near the Teeland SVS, the transient voltage change is also 2%. The effect on the other SVS controlled voltages is negligible. Figure 40 gives the dynamic performance of the thyristor controlled reactor (TCR). The Healy TCR turns completely off at about 1.0 second for maximum SVS MVAR output. The Gold Hill TCR changes from about 33 to 30 percent on. Figure 41 gives SVS MVAR output. The Teeland SVS output goes to zero at a time of 0.1 second. The Healy SVS output responds to the dynamics of the ac systems. Figure 42 gives the dynamic response characteristics of the Healy generator. Parameter variations for the 2 second simulation are negligible. Figure 43 gives machine excitation system outputs for machines modeled in detail. The Healy machine excitation increases slightly due to the Teeland loss of SVS. Figure 44 gives machine speeds for representative machines in the Anchorage and Fairbanks areas. Machine speed deviations are negligible. Table 2 Intertie Voltage Sensitivity for Loss of SVS Sub- Steady- Transient Transient State Sub-Transient Voltage Voltage Voltage Change Voltage Change Change Change in Sensitiyjty SVS Figures (pu) (pu) (pu) MVAR_ (AV/AQ) (pu) ql) Teeland 39-44 -02 -02 -03 9. 0.2 Healy 45-50 -06 -05 -06 19. 0.3 Gold Hill 51-56 -04 -02 -03 el. 0.2 Notes: (1) Modeling of machines near Teeland without excitation systems (2) AQ in per unit of 100 MVA. 4.2.2 Loss of Healy SVS Figures 45-50 give simulation results for the loss of the Healy SVS. This outage produces the largest deviation of the SVS controlled voltage (Figure 45). The controlled voltages stay above 95% of rated voltage. Both the Teeland and Gold Hill SVS MVAR outputs increase significantly (Figure 47). The Healy generator excitation system output increases to compensate for the loss of MVAR due to the SVS outage (Figure 48). 4.2.3 Loss of Gold Hill SVS Figures 51-56 give simulation results for the loss of the Gold Hill SVS. This outage results in excitation system output increases for the machines in the Fairbanks system (especially Zehnder) to supply reactive flow lost due to the loss of SVS (Figure 55). This SVS outage results in the highest frequency of oscillation of the machine speed deviations (Figure 56). A high frequency of oscillation indicates a steady-state stable system and, therefore, this SVS loss is the least severe in terms of reducing the steady-state stability of the Fairbanks system with respect to the Anchorage systen. Comparing the frequencies of oscillation of machine speeds in Figures 44 and 50 for the Teeland and Healy SVS outages, it appears that both SVS have an approximately equal reduction in the steady-state stability of the power systems. The Healy case was simulated for 8 seconds and steady-state stability is indicated. 5.0 SUMMARY For stability considerations, the worst operating condition of the Intertie is with 70 MW transfer from Anchorage to Fairbanks with the Healy generator on-line. This case is simulated for faults in the Intertie terminations at Anchorage and at Fairbanks, as well as for loss of SVS. For faults near the Fairbanks termination of the Intertie, the overall power system is transiently and steady-state stable. However, faults in the Anchorage termination of the tie result in a transiently unstable system and separation of the Fairbanks and Anchorage systems. For the condition studied, the loss of a single SVS results in transient and steady-state voltage reductions. Other system var sources such as excitation systems increase MVAR output to compensate for the loss of SVS. The Teeland and Healy SVS outages result in a larger reduction of the steady-state stability limit than the Gold Hill SVS outages. Nevertheless, the ac systems are steady-state stable even after the loss of the Healy SVS. -10- SAS » o43°39-_ ngco't 1 GIN3HOPT vit £ +94 40 até =-|> , ++ Z & 23 >sbt — a < vi 3B vz aie e2ta9- Ndto-t 099° 9 Natore jo" o98°9- Ngtork 292° 1S Ndas"0 ofa6f- | Agzc-k og t xcisnad SWayo9¢ HG 2051 1 VAWN3NS Paik Z ft tt St a ai I Sip ct z wis e60°S- Ndl6-0 too 8 43-9" 096° jor 3 oNtwaatet stmt igel eee 1gedte ? ters 2 § fee — -—-__ —__-- ‘ ob9'Ol- NdZ6"0 Ag Sas gu§t bois & vs 22 T ef oF9'Ol~ a o obo t Qd96°0 2593'S 636-0 s Guagarsee Ens got S Vonr38bit Shis oO burs ddivday tole \2 TOW A-F/HEALY ON.2 GOLD WILL-ZEHNDER FAULT INTERTIE P,V Fig. 3 1 LINE 4-5 POUERR 2 TEELAND 136KU .W.. —.. 3 HEALY 138KV 4 GOLD HILL 69KV USER_1LAPAJAPAIBS.PLT;3 1.5 1.4 1.3 1.2 1.1 1.0 @.7 0.6 @.5 324 @.S @.3 @.1 — : ~ ae ee at se a ~~ ~ _ “. 23-NOV-1983 4.0 TIME IN SECONDS 6.0 8.8 COR A-F/HEALY GOLD HILL-ZEHNDER FAULT SUS TERMINAL VOLT (PU) Fig. a 15.0 13.7 1 TEELAND Se 12.4 BMEALY em ee em no SF GOLD WILL weccxceccecscece cons 11.1, ‘ : : ' : : ' : ’ ‘ : . : ' : ’ : ‘ ‘ : : : ® 2.8 4.8 6.8 8.8 213 TIME IN SECONDS USER_1:CAPAIAPAIBS .PLT;3 23-NOU-1983 TOA A-F HEALY ON/: @ GOLD HILL-ZEHNDER FAULT SUS REACTOR OUTPUT (PU) 1 TEELAND ES 2 MEALY a ee eee 3 ODT htcttcrtctccncen @.8 2.8 4.0 6.0 8.8 213 TIME IN SECONDS USER_1 :CAPAIAPAIBS.PLT;3 23-NOV-1983 TOR A-F/HEALY 0N/23 GOLD HILL-ZEHNDER FAULT SUS OUTPUT (MUAR) Fig. G 1 TEELAND —— 2MEALV eee 3 GOLD HILL eee eeeeeeeeeeeeeeees USER_1:LAPAJAPALBS.PLT;3 $@.0 44.0 -10.8 0.0 213 2.0 23-NOU-1983 4.0 TIME IN SECONDS TAU A-F/HEALY ON; GOLD HILL-ZEHNDER FAULT HEALY GENERATOR 5.8 Fig . “] 4.5 1 ANGLE (DEG) ae 2 SPEED (H2) 0 CD 3 EXC OUTPUT (PU) on... eeeeeeeeeeeee 25 4 PM OUTPUT (PU) . 3.8 2.5 2.8 1.5 1.0 @.5 0.0 10% -1 4 USER_1:CAPAJAPAIBS .PLT;3 4.8 3.6 3.2 2.8 2.4 2.8 1.6 1.2 0.4 3 612.8 607.2 604.8 602.4 600.8 $97.6 $95.2 592.8 590.4 588.8 10% -1 2.8 23-NOU-1983 4.0 TIME IN SECONDS 6.0 8.0 TRA AHF “HEALY ON/ GOLD HILL-ZEHNDER FAULT MACHINE ANGLES (DEG) Fig.& 1 CHENA ——— 2 NORTH POLE = _._._._-—. 3 BELUGA = —§—-_ ne ececccsccnsssenses 4 EKLUNTA S INTERNATIONAL USER_1 CAPAJAPALBS.PLT;3 43215 2.8 23-NOV-1983 4.0 TIME IN SECONDS 6.8 TA A-F HEALY ONY GOLD HILL-ZEHNDER FAULT MACHINE SPEEDS (HZ) 606.0 Fi gq: q 604.8 1 CHENA ee ee 603.6 2 NORTH POLE 1 = ~uue 3 BELUGA 8 rasatssceccemseenseess 4 EKLUNTA eee 6ee.4 S INTERNATIONAL 601.2 | 600.05) 598.8 | 597.6 $96.41 $95.2 594.0 0.0 2.0 4.0 6.8 8.0 10% -1 93215 TIME IN SECONDS USER_1:CAPAJAPAIBS.PLT;3 23-NOU-1983 TORU A-F HEALY @ GOLD HILL-ZEHNDER FAULT MACH EXC OUT (PU) VOLT Fig. 10 1 HEALY a 22N0R 8 aa. SN oe rarccpnvecscceosscets 4 CHENA 0.0 2.8 4.0 6.0 8.0 3214 TIME IN SECONDS USER_1 sCAPAJAPAIBS.PLT;3 23-NOU-1983 ORY A-F/HEALY ON. GOLD HILL-ZEHNDER FAULT MACH PR OUT (PUD -wrw 3 in USER_1tCAPAJAPAIBS.PLT;3 2.0 23-NOV-1983 4.0 TIME IN SECONDS ZO A-F HEALY ON/23: ZEHNDER-GOLD HILL FAULT INTERTIE P,V 1.5 Fig. (2 1.4 1 LINE 4-5 POWER 1.3 2 TEELAND 138KU ~~~ 3 HEALY 198KV neeeeeesseeeeeeeenes 4 GOLD HILL 69%KY a 1.1 1.0 0.7 @.5 1.8 324 1 TIME IN SECONDS USER.1:CAPAJAPA1BS.PLT;2 22-NOU-1983 ZEWNDER-GOLD HILL FAULT SUS TERMINAL VOLT (PU) Fig: iS 1 TEELAND 2 HEALY me ee eee 3 GOLD HILL wescesecceceveseeeens USER_1CAPAJAPAIBS .PLT;2 15.0 13.7 5.9 4.6 3.3 2.8 0.8 10% -1 213 22-NOV-1983 TIME IN SECONDS 1.5 2.0 TOM A-F/HEALY 0 ’ ZEHNDER-GOLD HILL FAULT SUS REACTOR OUTPUT (PU) 1 TEELAND a 2 MEALY ee ee 3 GOLD HILL caceccccececccseneoe » USER_1:CAPAIAPAIBS.PLT;2 213 @.5 22-NOU-1983 1.@ TIME IN SECONDS 1.5 2.8 44.0 38.8 1 TEELAND 2 HEALY 32.8 3 GOLD HILL -4.0 -10.0 1.5 @.5 TIME IN SECONDS 213 22-NOV-1983 USER_1 CAPAJAPAIBS.PLT;2 PORN A-F/HEALY ON/; TEMNDER-GOLD HILL FAULT HEALY GENERATOR 1 ANGLE (DEG) 2 SPEED (HZ) 3 EXC OUTPUT (PU) ............. 4 PM OUTPUT (PU) USER_1:LAPAJAPALBS.PLT;2 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.8 @.5 0.8 10% -1 4.8 3.6 3.2 2.8 2.4 2.8 1.2 0.4 @.8 3 612.8 609.6 607.2 604.8 620.8 597.6 S9S.2 592.8 590.4 588.@ 10% -1 48.0 36.0 24.0 12.8 -12.0 -24.8 @.5 22-N0U-1983 1.0 TIME IN SECONDS 1.5 2.0 TORU A-F/HEALY ON/2! ZEMNDER-GOLD HILL FAULT MACHINE ANGLES (DEG) Fig. '7 1 CHENA ce 2 WORTH POLE =— we nn 3 BELUGA 4 EKLUNTA S INTERNATIONAL USEP_1:CAPAJAPAILBS .PLT;2 30.0 15.0 0.04 715.0 -30.0 -45.0 -90.0 -105.0 -120.0 43215 8.5 22-NOV-1983 1.0 TIME IN SECONDS 1.5 2.8 TOMY A-F HEALY Ot ZEHNDER-GOLD HILL FAULT MACHINE SPEEDS (HZ) Fig-\ 1 CHENA 2 NORTH POLE S BELUGA vcesccscnsvecesevecm 4 EKLUNTA S INTERNATIONAL = _____ USER_1:CAPAJAPAIBS.PLT;2 604.8 603.6 602.4 601.2 596.4 $95.2 $94.0 0.8 10% -1 43215 0.5 22-NOV-1983 1.0 TIME IN SECONDS 1.5 2.8 TORU A-F/HEALY ON: @ CEHNDER-GOLD HILL FAULT MACH EXC OUT (PU) 1 e 3. N. POLE 4 0.0 @.5 1.0 1.5 2.8 gei4 TIME IN SECONDS USER_1:CAPAJAPAIBS .PLT;2 22-NOU-1983 TOMY A-F/HEALY ONY ZEHNDER-GOLD HILL FAULT RACH PM OUT (PU) Fig. 20 1 HEALY ee as) JON, POLE eaeeeesecseeseeeseee: 4 CHENA USER_1 SLAPAIAPALBS PLT 32 5.0 4.5 4.8 3.5 1.05). —— ee @.S 22-NOV-1983 1.0 TIME IN SECONDS 1.5 2.0 TOMY A-F/HEALY ON/E3OKY WACKENZ-UNIV FAULT INTERTIE P,V Fig. Z| 1 LINE 4-5 POXER @ TEELAND 138KN0 3 HEALY 138KU 4 GOLD HILL 6XKU eeeceececccscvorecees USER_1!CAPAJAPAIB4.PLT;1 1.4 i.1 @.7 324 @.1 28-NOU-1983 1.0 TIME IN SECONDS 7OMW A-F/HEALY ON/B3OKY MACKENZ-UNIV FAULT SUS TERMINAL VOLT (PU) Fi q: iE 1 TEELAND —E away 2 GOLD HELL sasessesnsesssennes . 213 TIME IN SECONDS USER.1!CAPAJAPAIB4.PLT;1 28-NOV-1983 7M A-F/HEALY ON/23@KU MACKENZ-UNIU FAULT SUS REACTOR OUTPUT (PU) Fig . 23 1 TEELAND ——— 2 WEALY Saree 3 GOLD HILL nan 6.0 6.5 1.0 1.5 2.0 ai3 TIME IN SECONDS USER.1:CAPAJAPALB4. PLT; 1 28-NOV-1983 PONY A-F/HEALY ON/23OKU MACKENZ-UNIV FAULT SVS OUTPUT (MUAR) Fig. L4 1 TEELAND ee B HEALY mt F GOLD WILL —saceeceseercrsesooees USER_11CAPAJAPA1B4.PLT;1 44.0 -10.0 @.0 @13 28-NOV-1983 TIME IN SECONDS TOMY A-F/HEALY ON/B30KY MACKENZ-UNIV FAULT HEALY GENERATOR 4.6 4.0 3.6 1.6 6.0 168 -1 USER.1sCAPAJAPALB4.PLT;1 40 2.4 28-NOU-1983 TINE 1.0 IN SECONDS 1.8 TOMY A=F/HEALY ON“ E3OKY MACKENZ-UNIV FAULT WACHINE ANGLES (DEG) : 30.0 ein Lo 15.0 1 CHENA a 0.03 Se aeetaenes @ NORTH POLE LE 3 BELUGA ee 4 EKLUNTA Teer ee te & INTERNATIONAL = —__ 30.0 -4.0 60.0 -78.0° -90.8 -106.0 120.0 , 0 10 43a16 TINE IN SECONDS USER_1SCAPAJAPAIB4.PLT;1 28-NOV-1983 TOMY A-F/HEALY ON7230KU WACKENZ-UNIV FAULT MACHINE SPEEDS (HZ) 604.8 1 CHENA —— 603.6 2 NORTH POLE ane 3 BELUGA sesotestusessvassese 4 EKLUNTA —___ = 5 INTERNATIONAL = 601.2 597.6 596.4 594.0 s @.6 6.6 1.0 1.56 2.0 ion -1 432816 TIME IN SECONDS USER.11CAPAJAPALB4.PLT;1 28-NOU-1983 7OMU A-F/HEALY ON/230KY NACKENZ-UNIV FAULT MACH EXC OUT (PU) Fig. 2& 4.0 evevccceccceccersons 2 a ai 0.e@ 6.6 1.0 1.6 2.0 3214 TIME IN SECONDS USER.1:CAPAJAPAIB4.PLT;1 28-NOV-1983 7ONU A-F/HEALY ON/230KY MACKEN2Z-UNIV FAULT MACH PH OUT (PU) 1.02 6.0 6.0 0.5 1.0 1.5 2.0 168 -1 3a14 TIME IN SECONDS USER_1!CAPAJAPALB4.PLT;1 28-NOV-1983 7OMY A-F/HEALY ON/23OKY UNIV=MACKEN2 FAULT INTERTIE P,U : 1S, 0.8 Fi q- 30 ak e3 1 LINE 4-8 POWER Lah os 2 TEELAND 13KU Le 9 WEALY 198KU caccssssssesccssnnen 4 GOLD WILL oY half “Ost 1b -0.9 1.0} 0.69 2 0.91 -0.7 oe -0.9 7b <a o.6 1 -1.3 0.6L -1.5 0.0 384 i TINE IN SECONDS USER.1CAPAJAPALB4.PLT;2 28-N0U-1983 TOM A-F/HEALY ON/230KY UNTU-NACKEN2 FAULT SUS TERMINAL VOLT (PU) Fig. 3l 1 TEELAND —_—— BQ HEALY ee ee 3D GOLD HILL —«——aeeeercerseecseees USER..11CAPAJAPAIB4. PLT) 2 28-NOU-1983 TIME IN SECONDS 1.6 POW A-F/HEALY ON/EIOKU UNIV-MACKENZ FAULT $US REACTOR OUTPUT (PU) Fig. 32 1 TEELAND a 2 MEALY ee eee 3 GOLD HILL cocccecevesssecensees USER.1 tCAPATAPA1B4.PLT;2 @.@ e13 28-NOV-1983 1.0 TIME IN SECONDS 7OMY A-FSHEALY ON/E30@KY UNTU-MACKEN2 FAULT SUS OUTPUT (MUARD Fiq: 33 50.0 44.0 1 TEELAND on 38.0 awAy ee 3 GCOLD HELL cassssescesesscsoes 7 “4.0 ~10.0 @.0 6.6 1.0 1.6 2.0 213 TIME IN SECONDS USER.1 SCAPAJAPALB4.PLT;2 28-NOV-1983 TOMY A=F/HEALY ON/23OKY UNTU-NACKENZ FAULT HEALY GENERATOR 4.5 1 2 3 EXC OUTPUT (PU) sreemvennennennesner gg 4m 3.0 0.0 108 -1 USER_11CAPAIAPAIB4.PLT;2 4.0 3.6 a.4 1.8 @.4 590.4 28-NOV-1983 1.0 TIME IN SECONDS TOMY A-F/HEALY ON/230KU UNIU-MACKEN2 FAULT MACHINE ANGLES (DEG) 180.0 Fig. 35 126.0 1 CHENA ene 72.0 @ NORTH POLE -————- 3 BELUGA secesncecsceseceeooes 4 EKLUTNA ned 5 INTERNATIONAL 144.0 198.0 252.0 306.0 4328156 TIME IN SECONDS USER_1sCAPAJAPAIB4.PLT;2 28-N0V~1983 POH A-F/HEALY ON/23OKY UNIV-MACKENZ FAULT MACHINE SPEEDS (HZ) Fig- 36 1 CHENA @ NORTH POLE -————- 3 BELUGA svveveccecsesccsores 4 EXLUTNA S INTERNATIONAL USER.11CAPAJAPAIB4.PLT;2 606.0 604.8 603.6 602.4 601.8 $97.6 594.0 6.0 168 -1 43815 28-NOU-1983 1.0 TIME IN SECONDS 1.5 2.0 7OMd A-F/HEALY ON/230KU UNTV=MACKENZ FAULT MACH EXC OUT (PU) 1 WEALY _——— @ ZEHNDER ee 3 NM. POLE ececveececceseecsooes 4 CHENA a USER.1!CAPAJAPAIB4.PLT;2 28-NOV-1983 1.0 TIME IN SECONDS 7OMU A-F/HEALY ON/B30KY UNIV=MACKEN2 FAULT RACH PM OUT (PU) Fig. 32 1 HEALY es @ ZEHNDER i i a a 3H. POLE silovmsvetsenensases 4. CHENA aes USER.1sCAPAJAPA1B4.PLT;2 4.5 4.0 6.0 6.0 ion -1 3814 88-NOV-1983 1.0 TIME IN SECONDS 1.6 TEELAND SUS FAILURE INTERTIE P,V 1 LINE 4-5 POVER 2 TEELAND 138KN ~~ 3 HEALY 138KV 4 GOLD HILL 69KU USER_1:CAPAIAPALB PLT; 10 eS 21-NOU-1983 TIME IN SECONDS 1.5 2.0 cONU A-F/HEALY CH2 TEELAND SUS FAILURE SUS REACTOR OUTPUT (PU) Fig. 40 1 TEELAND caer 2 MEANY ee ee 3 GOLD HILL cnn neeescceeecoseee “e.0 0.5 1.0 1.5 2.0 213 TIME IN SECONDS USER_1:CLAPAIAPALB.PLT;10 21-NOV-1983 TRAU A-F HEALY ON @ TEELAND SVS FAILURE SUS QUTPUT (MUAR) Fyq. 4 1 TEELAND en 2 HEALY ee 3 GOLD HILL eee eeeeeeeeeeee neers 0.0 0.5 1.0 1.5 2.0 213 TIME IN SECONDS USEP_13CAPAJAPAIB.PLT; 10 21-NOU-1983 TAN A-F HEALY ON/c TEELAND SUS FAILURE HEALY GENERATOR 1 ANGLE (DEG) @ SPEED (HZ) So 3 EXC OUTPUT (PUD .......ces00 4 PM OUTPUT (PU) USEP_1:CAPAWMPAIB.PLT; 10 S.0 4.5 4.8 3.5 3.8 2.5 2.8 1.5 1.0 @.5 0.0 0.0 LS88.@ L-60.0 10% -1 4 b b [ k - 4.0 612.0 60.0 f 3.6 1609.6 | 48.0 1 3.2 eee L 36.0 | 2.8 ee } 24.0 4 2.4 (602.4 } 12.01 3 1.6 Aytn L-12.8 ; ; : 1 . . « ! 1.2 [595.2 |-24.0 | 0.8 [592.8 |-36.0 | 0.4 [590.4 |-48.0 | 0.0 0.5 1.0 1.5 2.0 10% -1 3 2 1 TIME IN SECONDS 21-NOV-1983 TORU A-F HEALY ON-2 TEELAND SUS FAILURE MACH EXC OUT (PU) 1 HEALY 2 ZEHNDER 3.°N. POLE 4 CHENA USEP_1CAPAJAPALB.PLT; 10 @.S 21-NOU-1983 1.0 TIME IN SECONDS 1.5 2.8 TORU A-F. HEALY ON TEELAND SVS FAILURE MACHINE SPEEDS (HZ) Fig. 44 1 CHENA eas 2 NORTH POLE ~~~. 2 BELUGA =—«_—aesessesssssseenaones 4 EKLUNTA S INTERNATIONAL USER_1:CAPAJAPAIB.PLT; 16 606.0 604.8 603.6 602.4 601.2 600. Og $98.8 $97.6 $96.4 $98.2 594.0 0.0 10% -1 43215 @.S 21-NOV-1983 1.8 TIME IN SECONDS 1.5 2.8 PONY A-F/HEALY ON”230KU HEALY SUS FAILURE INTERTIE P,V 1.5. @.5 Fig. 45° rab e3 1 LINE 4-5 POWER 1.3 8 2 TEELAND 13800 —~____. 3 HEALY 138KU 0 ceacsecceseeeeeeee. rl Leh 4 GOLD HILL 69KU ; y Lab -0.3 1.e | -@.sa 2 0.9 | -0.7 ' f oe) -¢.9 a7 b -164 @.6 | -1.3 esl -1.5 e.e 2.8 4.0 6.8 3.0 324 1 TIME IN SECONDS USER_1:CAPAJAPALB3.PLT;1 S-DEC-1983 7OMW A-F “HEALY ON/230KU HEALY SUS FAILURE SUS REACTOR OUTPUT (PU) Fig. 46 1 TEELAND en @ WEALY a 3 GOLD HILL wonssssscocereseaees 0.8 2.8 4.0 6.8 8.0 213 TIME IN SECONDS USER.1CAPAJAPAIB3.PLT;1 S-DEC-1983 7OMW A-F/HEALY ON/230KU HEALY SUS FAILURE SUS OUTPUT (MUAR) Fig Me a: 1 TEELAND SUE ELL 2 HEALY OE 3 GOLD HILL INL ctnaAe TALE USER_1:CAPAJAPALB3.PLT;1 50.0 44.0 38.0 32.0 26.6 20.0) 14.8 8.01 2.8 -4.0 2nd 2.8 S-DEC-1983 4.8 TIME IN SECONDS 6.8 POM A-F “HEALY ON/230KU HEALY $US FAILURE HEALY GENERATOR 5.0 Fig 4% 4.5 1 ANGLE (DEG) eet 0) 2 SPEED (H2) See 3 EXC OUTPUT (PU) 4 PM OUTPUT (PU) 2.5 2.8 1.5 @.$ e.8 10k -1 USER_1:CAPAJAPA1B3.PLT; 1 4.0 3.6 3.2 2.8 2.4 1.6 1597.6 |-12.8 1.2 @.4 3 612.8 609.6 } 4607.2 r +604.8 b 602.4 } 600.0} $95.2 | $92.8 S9e.4 Lsee.e 108 -1 2 36.8 LR acest ee ene me FZ 24.8 12.0 of 0.0, 1 -24.0 -36.@ ~48.8 ~60.0 2.0 2.0 4.8 6.0 8.e 1 TIME IN SECONDS S-DEC-1983 7OMW A-F. HEALY ON/230KU HEALY SUS FAILURE MACH EXC OUT (PU) Fig. 4Y 1 HEALY ee 2 ZEHNDER ee ee FM. POLE —vaceceesecneseccoce 4 CHENA —_——— yr) 2.0 2.0 6.8 8.8 3214 TIME IN SECONDS USER.1:CAPAJAPALBS.PLT;1 S-DEC-1983 POMU A-F/HEALY ON, 230KU HEALY SUS FAILURE MACHINE SPEEDS (HZ) Fig: SO CHENA NORTH POLE BELUGA EKLUTNA INTERNATIONAL Weaw wv tH USER_1tCAPAJAPA1B3.PLT;1 606.0 604.8 603.6 6@2.4 6@1.e 600. Og ee 598.8 597.6 596.4 595.2 $94.0 @.0 108 -1 43215 2.0 5-DEC-1983 TIME 4.0 IN SECONDS 6.0 TW A-F HEALY 0 @ GH SUS FAILURE INTERTIE P,V 15, 05 Fig. | Lal 03 1 LINE 4-5 POUR —__ nal et 2 TEELAND 138K0 3 HEALY 198K coccccecccccseceee i 4 GOLD HILL 69KY bree 1.11 -0.3 1.0 | -e.sae~ 0.9 | -0.7 0.8 | -0.9 0.7, -1.1 0.6 | -1.3 os L -1.5 0.8 @.5 1.8 1.5 2.8 324 1 TIME IN SECONDS USER_1tCAPAIAPALB.PLT;8 21-NOV-1983 TO A-F HEALY ( GH SUS FAILURE SUS REACTOR OUTPUT (PU) Fig: $2 1 TEELAND ee 2 HEALY ee eee 3 GOLD HILL oe eeeeneneeeneee = USER_1 SLAPAJAPALB.PLT;8 0.8 213 0.5 21-NOV-1983 1.0 TIME IN SECONDS 1.5 1 TEELAND ———— 2 HEALY 3 GOLD HILL USER_1 sCAPAJAPAIB.PLT;8 44.0 38.8 32.8 14.8 @.S 21-NOV-1983 TIME IN SECONDS 1.5 2.8 1 ANGLE (DEG) 2 SPEED (H2) 3 EXC OUTPUT (PU) ............ 4 PM OUTPUT (PU) USER_1SCAPAIAPALB.PLT;8 nn 3.5 5.@ 4.5 4.8 3.8 1.5 1.8 0.8 10% -1 4.0 3.6 3.2 2.4 1.2 0.4 3 612.6 607.2 604.8 602.4 597.6 $95.2 598.4 588.0 108 -1 48.0 36.8 24.0 6.5 21-N0V-1983 TIME IN SECONDS 1.5 2.8 ro AF AEALY @ GH SUS FAILURE MACH EXC OUT (PU) Fig aa 1 HEALY 2 ZEHNDER 3 N. POLE 4 CHENA 0.0 @.S 1.8 1.5 2.0 3214 TIME IN SECONDS USER.1:CAPAJAPAIB.PLT;8 21-NOV-1983 2ORU A-F HEALY e@ GH SUS FAILURE 604.8 603.6 602.4 601.2 $97.6 $96.4 $95.2 594.0 0.0 @.5 1.0 1.5 2.8 10% -1 43215 TIME IN SECONDS USER_1CAPAIAPAILB.PLT;8 21-N0U-1983 ANCHORAGE-FAIRBANKS INTERTIE STATIC VAR SYSTEMS (230 kV Pt. Mackenzie Area Transmission] CONTROL SYSTEM STUDY for ALASKA POWER AUTHORITY APA Contract No. APA-83-C-0051 Report by D.H. Baker ELECTRIC UTILITY SYSTEMS ENGINEERING DEPARTMENT GENERAL ELECTRIC COMPANY DECEMBER 1983 1.0 INTRODUCTION Control system studies have been performed for the Alaska Power Authority Anchorage to Fairbanks Intertie Static Var Systems. This study has been performed by the Electric Utility Systems Engineering Department of the General Electric Company in Schenectady, New York, to satisfy the requirements of Contract No. APA-83-C-0051. This study represents the power system in accordance with the specification; that is, the Pt. Mackenzie transmission area was represented as 230 kV and the Cantwell to Watana line was not in service. 2.0 SPECIFIED OBJECTIVES The requirements for the study were given in the specification and are restated below for convenience. “4.1.8 Perform control system studies to verify the specified control, parameters and functions. Investigate conditions of possible hunting among the three SVC installations and identify corrective or preventive measures taken to prevent such hunting.” 3.0 METHOD OF INVESTIGATION The control system study was performed using the MANSTAB (Machine And Network STABility) digital computer program where system equations are linearized around an operating point and eigenvalues calculated. This program has been used extensively to predict generator, HVDC and SVS control behavior. For the Intertie system, control stability was determined by varying the SVS control gain and time constant. The resulting root locus is then used to determine the limits on gain and time constant to make the system stable under the most restrictive case. 4.0 POWER SYSTEM REPRESENTATION The entire 138 kV Intertie including the three static var systems were modeled. The Anchorage and Fairbanks networks were represented using equivalents at Pt. Mackenzie and Gold Hill. The Gold Hill 69 kV equivalent is chosen corresponding to the weak system (low generation) case. A lumped capacitance at Pt. Mackenzie was used to represent the cable charging there and an inductive equivalent was used for the system beyond. The transformer impedances of the Healy, Teeland and Gold Hill SVS transformers were modified to reflect recent information. The Gold Hill to Ft. Wainright 138 kV line was assumed to be not in service. The three static var systems were modeled using the TCR (Thyristor Controlled Reactor) model. This is a dynamic model using differential equations for the inductive and capacitive elements. The block diagram of the SVS regulator model is like that used in the stability studies. The gains and time constants of the three static var systems were chosen to be the same. 5.0 CASE RESULTS Cases analyzed were selected on two criteria: i) Select cases in which the system is weaker so that the gain and time constant stability limitations are the most restrictive. ii) Select cases which covered the extremes of SVS operation, capacitive and inductive. The summary of the cases analyzed is given in Table 1. Except for PFTS1, the Healy generator was assumed to be out of service thus increasing system impedance. Table 1 SYSTEM DESCRIPTION Case Power Flow Senseo Intertie Open SVS Off PFTS1 70 MW Anchorage to Fairbanks On No No PFTS2 70 MW Anchorage to Fairbanks orf No No TSIN19 70 MW Anchorage to Fairbanks orf No Teeland TSIN14 70 MW Anchorage to Fairbanks orf No Gold Hill TSIN18 70 MW Anchorage to Fairbanks off No Healy PFTS10 Light Load orf No No TSIN3 - off Gold Hill 138 kV No TSIN4 - off Teeland 138 kV No TSINGA - off Teeland 230 kV No TSIN4AHO - off Teeland 230 kV Healy For each case, as both the control gains and time constants are varied in the analysis, a cross-plot of gain versus time constant for the stability boundary was developed. These stability limits in control gain and time constant are included in Figure 1. The stability boundary shown is where there is zero damping of an oscillation. The area to the right of each curve is the region of control stability. Choosing gain and time constants further to the right of the stability boundary increases the damping of the oscillations. Normally, a 3 to 1 gain margin or having the actual gain set to 1/3 of the instability gain provides sufficient damping of the oscillations. Since the gain needs to be 20 (5% control slope) for steady-state regulation, it is desirable to look at what the time constant needs to be for different cases for adequate stability. The restricting case is TSINSA where the Pt. Mackenzie to Teeland 230 kV tie is open. The Teeland SVS is left looking at a very high impedance and contributes most significantly to the instability. The Healy SVS also participates. To have a 3 to 1 gain margin over the 20 pu gain, the time constant should be approximately 0.15 seconds. This is determined by looking at where the instability gain is about 60. A typical root locus plot for the restrictive case TSIN4A is shown in Figure 2. This plot has the time constant of the SVS controller fixed at .1 seconds and the control gain is varied. It is instructive to point out in the root locus that if the static var systems are operating capacitive then a mode that is above 60 Hz moves and goes unstable. If the static var system is operating inductive as case TSINSA, then a mode that is between zero and 60 Hz (377 rad/sec) moves and goes unstable. CONCLUSIONS i. Of the system conditions studied, the Intertie open at the Teeland 230 kV breaker with the Healy generator off is the decisive condition in establishing the SVS time constant. A time constant of 150 ms is recommended for an SVS gain of 20 (5% voltage slope). 2. With the above gain and time constant, no hunting or instabilities among the SVS installations are expected. pu Control Gain 10@ 40 38 Fig. 1 TSIN3 ~ (Fete TSIN4 TSINI4 TSINI9 TSIN4AHO 20 40 10@ 200 400 1000 Control Time Constant in milliseconds Instability boundary in Control Gain vs. Time Constant Fig. 2 400.8 84.0 180.8 bs 10b.0 SIGMA (1/SEC) Root Locus Plot for Case TSIN4A Teeland Open at 230 kV Variation in Gain With Time Constant of @.1 sec. VWNODA <OamMoormkh MANSTAB/POSSIM POWER SYSTEM DYNAMIC ANALYSIS PROGRAMS - A NEW APPROACH COMBINING NONLINEAR SIMULATION AND LINEARIZED STATE-SPACE/FREQUENCY DOMAIN CAPABILITIES E.V. Larsen W.W. Price General Electric Company Schenectady, New York ABSTRACT A new and highly flexible approach to perform- ing state-space and frequency domain analysis of multimachine power systern dynamics is described, The fundamental feature of this approach is a tech- nique of linearizing a system about its operating point and constructing the state matrix equations of this linearized system directly from a nonlinear time sim- ulation program which models the system. These state matrix equations are then used to obtain eigen- values and mode shapes of the system, and frequency response, or Bode, plots of selected transfer func- tions. This technique has been applied to two highly flexible power system simulation programs, one with algebraic network representation and one with elec- trical transmission network dynamics included. These programs are described and applications tothe analy- sis of subsynchronous resonance and to power system dynamic stability are presented, It is felt that this set of programs provides an extremely powerful tool for the analysis of power system dynamics, and that the technique described can be applied to many exist- ing simulation programs, including simulation pro- grams for other than power system applications. INTRODUCTION In recent years it has been found advantageous to apply frequency domain analysis techniques developed in the control system field to the analysis of power system stability anddynamic performance, For small disturbance analysis, the power system canbe treated as a generalized, linear dynamic system which canbe represented by the following vector state equations: x: Ax+Bu (la) y = Cx+Du (1b) Presented at the IEEE PICA Conference, May 1977, Toronto, Canada. where x = vector of state variables (n) y = vector of output variables (2) u = vector of input variables (m) A = state matrix (nxn) B = input matrix (nxm) _C = output matrix (fxn) D = algebraic connection matrix (fxm) The power systemincludes many dissimilar com- ponents, including transmission lines,transformers, loads, and synchronous turbine-generators with their excitation and speed controls. Many of these com- ponents, when analyzed in detail, are characterized by nonlinear differential equations. Certain of these nonlinearities are routinely represented in simula- tions of power systems. These nonlinearities include generator saturation, control limits, the sinusoidal transformation of reference frames, speed effects of synchronous generators, and rectifier and thyristor bridge characteristics. More detailed transmission system studies may also include transformer satura- tion, corona losses,and nonlinear shunt reactor and lightning arrestor characteristics, Often these de- tailed simulation models involve extensive develop- ment and validation effort. While detailed models including nonlinear effects are required to obtain the correct time response to a system disturbance, a small-signal linearized analy- sis of often useful for evaluating the stability of the system abouta particular operating point. Manytech- niques for stability analysis from linear contro] theory have been successfully applied to power systems. These have included Routh-Hurwitz!, Nyquist2, 3-4, and root locus>*©techniques. Inthe past severalyears much interest has focused on the linear state equation formulation of the power system equations which per- mits the application of useful frequency domain analy- sis techniques. The application of linearized state equation methods to power systems has involved the develop- ment of specialized computer programs?~1!1 separate from the nonlinear simulation programs more famil- iar to many power system engineers. The procedure for developing these programs has been to start with the nonlinear differential equations for the various power system components, linearize the equations about an operating point, develop formulas for each of the elements of the state equation matrices, and write a program to calculate these elements for par- ticular values of system parameters. Any change in the modeling of the systern or in the input or output variables requires a repetition of the above process. The method describedinthis paper permits direct construction of the power system state equations from asimulation program, Any program inwhich the inputs and outputs of the integrating elements are explicitly available could be readily adapted to this procedure, Basically, this procedure involves first initializing the simulation to the desired operating point, and then perturbing, in turn, the output of each integrator and each input variable. The relative amount of change of the integrator inputs and of the output variables gives directly the elements for the system state equation matrices. This technique is more fully described in Section Il, together with the way in which these ma- trices are used for eigenvalue, root locus, and fre- quency response analysis. . This technique has been applied to two programs. One of these programs is POSSIM (for POwer System SiMulator), a 50 machine transient stability program adapted from the FACE Multi-Machine Program!2, which uses algebraic representation of the network equations. The MANSTAB program (for MAchine and Network STABility) is a similar multi-machine pro- gram which includes the differential equations of the electrical transmission network. MANSTAB was recently developed to provide a tool for the analysis of phenomena involving the electrical dynamics of the transmission network, such as subsynchronous reso- mance, in the frequency domain, The state matrix building technique described in this paper is a key element of MANSTAB, and was first implemented and refinedonthis program;thus, thistechnique is closely associated with the MANSTAB program. These pro- grams are described in more detail in Section I of this paper. The motivation for the development of this fre- quency domain analysis approach came from the need for stability analysis in two areas: 1) Turbine-generator rotor torsional instability due to subsynchronous resonance, 2) Power system dynamic stability. The MANSTAB and POSSIM programs have been ex- tensively used to analyze these and other aspects of power system dynamic performance. Examples of the application of these programs are described in Section IV. I. COMPUTATIONAL TECHNIQUES There are two separate computational tasks re- quired for frequency domain analysis: construction of the state matrices, and calculation of eigenvalues, mode shapes, and transfer functions, The first step, construction of the state matrices, is included in the simulation programs themselves. The second step is performed by a general purpose frequency domain analysis program. State Matrix Construction As mentioned previously, the state equation ma- trices, A, B, C, and D of equation (1), are con- structed directly from the nonlinear differential equa- tions of the power system simulation programs, An explicit integration algorithm is used in these pro- grams, and both integrator inputs and integrator outputs are readily available. The integrator outputs (state variables) are eachincremented a small amount in turn. Then one pass is made through the simulation equations and the effect ofeach state variable uponthe rates of change of all of the state variables, plus the effect upon the variables designated as output vari- ables, is determined. The changes in these variables, normalized by the change inthe perturbed variable, give directly the elements of the Aand C matrices. column by column. Input variables to the system are treated the same way, building the B and Dmatrices column by column, Nonlinearities require special attention when utilizing this technique. Continuous nonlinearities, such as sinusoidal axis transformations and generator saturation, require input perturbations small enough that the true slope at the operating point is obtained. Experience has indicated the proper perturbation sizes forthe integrator outputs of the MANSTAB and POSSIM programs, although the effect of arbitrary system input to nonlinearities must be considered for each such input variable and appropriate perturbation sizes chosen if the nominal sizes are too large. In addition to keeping perturbation sizes small, the MANSTAB and POSSIM state matrix building routines also in- crement the variables both up and down, then average to obtain the best linearization about the operating point. Discrete nonlinearities, such as limits and deadbands, must have special logic added to provide a representation of their dynamic characteristics forthe signal sizes of interest. Such characteristics can generally be determined bya describing function analy- sis of the nonlinearity. This state matrix building technique should be generally applicable to any simulation program which utilizes an explicit integration technique. Implemen- tation is relatively straightforward on simulation programs such as MANSTAB and POSSIM where the numerical integration of all state variables is per- formed in one location and the integrator inputs and outputs are all available as arrays in common, but more difficult on programs where the numerical inte- grationis performedthroughout the program andinte- grationinputs and outputs are notin acommon storage block. As indicated above, careful consideration must be givento perturbation sizes to ensure good lineariza- tion of continuous nonlinearities, and discrete non- linearities must be represented by a model yielding the equivalent dynamic performance at the signal sizes of concern, Frequency Domain Computations Expressing a linearized set of dynamic equations in a state variable format makes possible the use of a single general analysis program to perform the fre- quency domain calculations. Such a program, called FREQRESP (for FREQuency RESPonse), has been developed around the EISPACK)3 routines, developed by Argonne National Laboratories to calculate the eigenvalues and eigenvectors of a system. The FREQRESP program calculates the frequency depen- dent transfer functions between the system inputs and outputs using a modal technique described below, and also performs input-output control functions for ob- taining eigenvalues aud mode shapes from the EISPACK routines, Taking the Laplace transform of equations (la) and (1b) and solving for the output vector as a function of the input vector yields: ¥(s) = {c (st - a)" B+ D} U(s) (2) Defining T(s) as an xm matrix whose elements are the Laplace transforms of the relationships between the elements of Y(s) and the elemenis of U(s), it is seen that Tis) = C(sI- A)") B+D (3) Setting s = jwin Eq. (3) yields the desired frequency dependent transfer functions; however, this process requires the inversion of a complex matrix for each desired value of frequency. This is avoided by apply- ing the following modal technique. Note that, by defi- nition, A=MAM? (4) where A = state matrix A = diagonal eigenvalue matrix M = eigenvector matrix Substituting (4) into (3) and performing some matrix manipulation results in a -) T(s) = CM (sI - A)") M™ (5) Since the matrix to be inverted is now diagonal, the inversionis very simple and equation (5) is much more computationally efficient than equation (3), This com- putationally efficient form is obtained at the expense of calculating eigenvalues and eigenvectors of the system, but if more than a few frequency points are desired, this form leads to greater overallefficiency. In addition to simplifying the frequency response cal- culations, eigenvalues and mode shapes provide con- siderable useful information about the system and itis therefore desirable to calculate these anyway. A point worth noting is that, since the eigenvalues are known, frequency response calculations can be performed pre- cisely about resonance points, thus ensuring determi- nation of peaks associated with lightly damped roots. -3- Il, PROGRAM DESCRIPTION The two simulation programs being discussed here, POSSIM and MANSTAB, are basically very simi- lar in structure. POSSIM is a direct outgrowth of the earlier FACE Multi-Machine Program described in reference 12, with improved capabilities, and MANSTAB is an extension of POSSIM to include the dynamics of the electrical transmission network, as indicated in Figure 1. The flexible modular structure used in the FACE Multi-Machine Program for coupling models of various power systerm components has been retained as a fundamental feature, and user con- veniences, primarily a self-initialization feature, have been added to minimize user set up time and to im- prove reliability and efficiency. The state matrix building feature has been incorporated into the pro- gramsin a manner which allows the user to select the required inputs and outputs with a minimum of input data. POSSIM and MANSTAB are generally used to study different aspects of power system performance, and hence only one or the other is used at one time. The additional programs indicatedin Figure 2, LOFYR and FREQRESP, provide the initialization and fre- quency domain analysis functions for the POSSIM and MANSTAB programs. LOFYR (for LOad Flow and Y-matrix Reduction) performs the load flow calculation toinitialize the system for either simulation program, and in addition calculates the system matrix usedwith POSSIM_MO. NETWORK Y= finde HL-i%efT wer" H{E-_ (1-9 ois) NETWORK xis): fimiestie Lert Wwe E_(- @ onis) POSSIM and MANSTAB Modular Power System Representation Figure 1. the POSSIM program. Due to the different type of net- work representation, the MANSTAB program performs its own matrix construction and the network data is entered directly. FREQ RESP uses the state matrices built by POSSIM or MANSTAB to perform frequency domain computations. All data is transferred via tape or disc files, so manual data handling is eliminated. Program Structure and Flow The simulation programs have an executive routine which handles input/output functions, calls the state matrix building routine if requested, and loops through the time simulation. At each time step, an"APARAT" subroutine is called to define integrator inputs, then the integration routine is called to update the integrator outputs, and the time clock is advanced. APARAT is auser written subroutine which places calls to library subroutines containing the simulation equations of various equipment models, thereby interconnecting all of the apparatus being modeled, Input and output vari- ables for the equipment model subroutines are passed through a common block, so the calls from APARAT contain only indices indicating the variable locations. All of the simulation models are called twice in each time step; first to calculate output variables based on updated integrator outputs, then to calculate rates of changes of states based upon these updated output variables. In MANSTAB, the transmission network model is called first, and then the network model outputs are used for computing variables in the ma- chine and load models. Rotor torsional models, ex- citation system models, governor models, prime mover models, etc., are then called to update their outputs. Based upon these updated outputs, rates of changes for all the state variables are obtained by calling all of the simulation models again, Transmission Network Modeling Both POSSIM and MANSTAB have the same modular structure for the equipment models, but differ in the modeling of the electrical transmiséion network. POSSIM uses a reduced, complexhybrid matrix (Y for generator nodes, Z for nonlinear load nodes) and solves the network equations algebraically, as indi- cated by equation (6), This hybrid matrix is more fully described in reference 14. A basic assumption of this procedure is that speed deviations are small. However, flux - current relationships are used rather than voltage current relationships, i.e., 4) . Tm H | - so that for a system witha high X:R ratio,the solution is accurate over a reasonable range of speed devi- ations!2, r ve = (6) a. MANSTAB retains the dynamic properties of the electrical network by transforming the basic network differential equations, per phase, to a rotating refer- LOAD FLOW INITIALIZATION TIME RESPONSE TIME RESPONSE STATE MATRICES FREQRESP EIGENVALUES, MODE SHAPES INPUT-OUTPUT FREQUENCY RESPONSE Figure 2. Simulation Flow Diagram ence frame, These transformed network equations include speed voltage terms as well as rate of change of flux (py) terms,and thus a voltage-current relation- ship is completely valid. Hence, MANSTAB utilizes a voltage-current relationship rather than a flux- current relationship as in POSSIM. The assumption of balanced three-pnase operation reduces the three differential equations totwo; on the d and q axes of the rotating reference frame. A brief derivation of these differential equations is given in Appendix A. The transmission network equations for both POSSIM and MANSTAB are calculated on the d-q axes of a rotating reference frame, This can be a rated speed reference or the rotor of a reference machine. All machine models have their simulation equations written on their own d-q axes, and the resulting sub- transient fluxes of POSSIMor subtransient voltages of MANSTAB are rotated to the reference axes before use. Resulting currents fromthe network solution are then rotated back to the axes of the individual ma- chines, Special non-machine loads are modeled on the reference axes, and may be current output, flux input, rather than flux output, current input, neces- sitating the hybrid matrix rather than a pure Y-matrix in POSSIM. As indicated, subtransient generator fluxes or voltages are usedas sources for the network solutions, and subtransient impedances are included in the net- work as sourceimpedances, Implicitinthis procedure is the assumption that subtransient saliency can be neglected, It has been shown!2 that neglecting sub- transient saliency and using X"'= X¥ results in good accuracy regarding the stability margins associated with rigid body oscillations of the rotor. Further, cylindrical rotor machines have very low subtransient saliency and represent an increasing percentage of units on today's power systems. Hence, this assump- tion is very reasonable. ’ Apparatus Models Several options are available for modeling the various power system components, as indicated below: @ Synchronous machines can be represented with any degree of detail from a simple equivalent react- ance to a solid iron rotor model with seven rotor circuits and airgap saturation!5, An induction motor representation is also available. e@ Excitation system representations are available for the standard IEEE models! 6, as well as de- tailed models of certain specific systems. Sup- plementary control devices, i.e., power system stabilizers and torsional dampers, can also be represented in any degree of detail. e@ Turbine-generator torsional systems can be re- presented with a classical spring-mass model, or in a modal decoupled form. e@ Power filter dynamics for a subsynchronous series blocking filter]? with coupled stages can be modeled within the MANSTAB program. @ Governor controls and prime mover dynamics have several representations, e Leads are representedas S(V, £) =P(V,f£) + jQ(v,£), with polynomial relationships to voltage and fre- quency!4, Additional models are easily implemented within the modular structure, Power filter dynamics exist only inthe MANSTAB program since network dynamics are ignored in POSSIM. Generally, MANSTAB is used for studying relatively high speed dynamics, and con- sequently governor models, prime mover models, and S(V,f) load models exist only in the POSSIM library. IV. APPLICATION EXAMPLES Examples are givenhere indicating the usefulness of the frequency domain capabilities of the MANSTAB and POSSIM programs in analyzing two areas of prime concern to power system stability and control: sub- synchronous resonance, and dynamic stability (rigid body oscillation modes). Subsynchronous Resonance The MANSTAB program is an excellent tool for analyzing the stability of a system under subsynchro- mous resonance conditions, The real parts of the eigenvalues calculated by MANSTAB for particular values of series compensation tell not only whether instability will occur, but also give a direct measure of the amount of additional damping required to stabi- lize the system. A root locus of the eigenvalues calculated by MANSTAB for the system of Figure 3 is shown in Figure 4. X_ was varied from 0. to .85 per unit. The roots associated with the torsional modes of the HP and LP turbine generators are identified on the -5- HP x, 0.04 0.8 ¢ Lp CROSS-COMPOUND UNIT AT NO LOAD Figure 3. System for SSR Example root locus plot as HP1, HP2, HP3, and LPl, LP2, LP3, respectively, The two lowest frequency roots are associated withthe rigid body modes of oscillation of the machines against each other and against the system. These are identified on the plot asHP <«—»> LP and HP + LP, respectively. The widely migrating root is that associated with the inductance and series capacitance of the network. With no series capaci- tance, it consists of a coruplex pair of roots at -16 + j377 sec-1, Since the state equations of the system are constructed with respect to a synchronously rotat- ing reference frame, the electrical resonant frequency of the network is actually 377 rad/sec minus the fre- quency of the electrical root. Hence, this root is equivalent toa real root at -16 secml ona stationary reference frame resulting fromthe series R-L circuit. 31400 Xcr0 ee alt) +s Xc20 (-1637 os 4 {50 0.8 075 Xcr0 pirat oS HP.LP os 085 07: 75054 X20 aye — my 46-0 -9 8-7 6 5-4 3 2 -- 0 1 2 3 4 @ (seen!) Figure 4. Root Locus Varying Series Compensation x, For extremely small values of X_ this "electrical" root migrates to the right and a second "electrical" complex root migrates to the left from 377 rad/sec on the imaginary axis. At a very small value of X_,, these roots meet and then separate, one moving into the supersynchronous range and the other into the sub- synchronous range. As X_is increased, the frequency of the electrical subsynchronous root passes the fre- quency of each of the torsional roots and these roots, depending on the degree of coupling, migrate into the unstable right-half-plane by a certain amount. For sufficiently high values of X., the electrical root itself becomes unstable, indicating that self-excitation, or classical subsynchronous resonance, has occurred, Figure 5 presents these results in a form more useful for analyzing torsional interaction instability. The real parts of the torsional roots are plotted as functions of X,. This shows the range of X, over which instability would occur and the amount of ad- ditional damping required for stability, The above analysis was performed with no mechanical damping represented in the torsional models, This damping is typically on the order of .05 sec}, and, as can be seen from Figure 5, would not be sufficient for sta- bility except for the third mode of the HP turbine generator, 20 15 = '0 ¢ 2 = . 05 0 3 _-___ = 5o>-—or 02.03 04 05. 06 Oo” Xp (pu) Figure 5. Torsional Mode Undamping vs. Series Compensation x. Dynamic Stability Effects of a voltage regulator, system reactance, and generator loading for a one machine-infinite bus system areillustratedinthis example. Figure 6 shows two root locus plots, obtained from the POSSIM/ FREQRESP programs, of the rotor oscillation mode as reactance and loading are varied (unity power factor, x,/R, = 10, S= apparent power = real power since pf = 1.0). One plot is with a dc regulator gain of 200 and one with a gain of 100, both with transient gain reductions of 10 sec:] sec, It is seen by comparing the two plots that increases in loading and/or reactance tend to increase the negative damping effect due to regulator action. This is due to the small-signal gain ofthe path from rotor angle to terminal voltage in- creasing with load and external reactance! 9, thereby increasing the negative damping component voltage regulator action. due aa RX O— (Xp /Re#10) = ith +0.5 “1.0 -05 0 +405 o(sec*) Kreg *200 Figure 6. and Line Reactance Upon Frequency and Damping of Rotor Oscillation Mode Effect of Regulator Gain, Loading, Itis shownin reference 19that the negative damp- ing components of torque caused by high gain voltage regulators increase with regulator gain, but that the synchronizing components of torque are relatively in- sensitive to changes in regulator gain, if the initial gain is high. The root locus plots indicate this effect, as damping changes significantly while frequency re- mains nearly constant. This effect can be illustrated more clearly with the frequency response plots of Figure 7, where the real and imaginary parts of the open loop transfer function from rotor angle to elec- trical torque (with P= 1,0, X, = 0.7, and for both values of regulator gain) are plotted vs. frequency. Note that in the range of 3 rad/sec to 12 rad/sec (approximately 0.5 Hz to 2 Hz), where typical rotor oscillation frequencies lie, regulator gain has little effect upon the real (synchronizing) component of torque, but has a relatively large effect upon the imaginary (damping) component of torque, in a nega- tive damping direction. The benefit of higher regula- tor gain in steady-state is also indicated by the in- creased synchronizing component at very low fre- quencies, ! 4 0.1 1.0 ols) 10 wo Figure 7. Effect of Regulator Gain Upon Frequency Response Characteristics of Angle-Torque Loop SUMMARY This paper has described a straightforward tech- nique for obtaining a linearized state variable matrix description of a general nonlinear dynamic system which has been modeled with atime domain simulation program including allof the nonlinear effects and utili- zing an explicit integration technique. The use of this technique with twohighly flexible power system simu- lation programs has been extensively discussed, in- cluding descriptions of these programs and examples of their application to the analysis of subsynchronous resonance due to series compensation and dynamic stability involving rigid body modes of rotor oscilla- tion. These programs derive their flexibility from a modular structure which allows for the modeling of a wide variety of power system components intercon- nected by an electrical transmission network. As such,these programs provide an excellent and valuable tool for the analysis of power system stability and dynamic performance characteristics, and for evalu- ating the influence of various pieces of equipment and contro] strategies upon these characteristics, Exten- sive usehas been and is being made of these programs forthe analysis of power system dynamic performance in such areas as subsynchronous resonance, dynamic stability, system voltage control, and power plant control. ACKNOWLEDGEMENTS The authors wish to acknowledge the fine program- ming efforts of Mrs. J.B. Randallandthe contributions of D. H. House to the initial program development work on the FREQRESP and MANSTAB programs, Their efforts have resultedin a setof prograrns which are highly reliable and relatively simple to use. The digital computer programs referred tointhis paper,i.e. MANSTAB, POSSIM, FREQRESP, LOFYR, and the FACE Multi-Machine Program, have all been developed by the Electric Utility Systerms Engineering Department of the General Electric Company. APPENDIX A - Derivation of Electrical Network Differential Equations on a Rotating Reference Frame Consider a balanced 3-phase line with series capacitors, The differential equations describing this network are, in matrix form: 1 -1 Sabe ~ {R} dave * *{L} Sine ts {c} dane (2) where rele vector of phase source voltages dpe = vector of phase currents {R}, {1}, and {c}7 = balanced "impedance" matrices of the form {z}=/z z 2z z Z 2 | _“m “m s and s = differential operator, Z. Using Park's transform?! , 2 cos ce 2 cos e 7 2 cos % 1 Te 3 -2 sin 6, -2 sin 6 -2 sin 9! 1 1 1 5 equation (Al) will be transformed to an arbitary dgo reference frame: ago * Tape = 7 [i= bane * 9 {UL} Lee +d tert s,,,] -1 -1 7 = (T{R}T) Ti + (Ts {L}T VTi. etfs ryra. -1 “1, = (T{R}T Viggo + (Ts {L} T ) Sago +r {c}™ Th... (A2) Performing the matrix multiplications indicated in (A2), with due regard for the effect of the operator 5 upon the transformation matrix T, the following results are obtained: For the resistive term: “Rago [ , ii R,,) Sago i (A3) =dqo For the inductive term: Stage = Ug - Ln! [ {e6) +s | Sago (a4) where {I} = identity matrix oll iene) 0) and{se} =| se 0 0 Lo 0 0 | 66 = w= speed of reference frame. For the capacitive term: Taal Cant [tse + +] Yeago (A5) (Note that (Z_ - Z_) is the positive sequence value of impedance for a balanced 3-phase line.) Equations (A3), (A4), and (A5) can be used to simulate the electrical dynamics of a balanced, 3- phase, series R-L-C transmission line from a refer- ence frame rotating at speed s9. These equations can be expanded to simulate an entire transmission network by describing the network in loop impedance form20, This involves building a connection matrix relating all brances of the network to a minimum set of independ- dent loops, and using this matrix together witha primi- tive impedance matrix to obtain a loop impedance ma- trix. The connection matrix is also used to relate branch currents and voltages to the loop currents and voltages used in the network simulation. Since balanced operation is assumed for the ma- chine and network stability program, zero sequence currents do not interact with currents in the dor q axes,nordothey produce torques on generator rotors; hence, the zero sequence components are neglected and only the equations for the d and q axes are simu- lated. The fina] form of the network simulation equa- tions is given in equations (A6). “1 “1,47 {t,} [Eee Vega t 00) {Le yh ly, - {R,} X44| (Aéa) -1f "leq° {L,} | Eta ~ Yctq- (86) {L,} loa ] [ {R,} Leal (A6b) 1 Lyte 4 Yera® {ee} [24a {Cel Neag ase eae a y=3 ; "Ye ta* {c,} ites ~ (se) {c,} Yera| (asa) where the subscript ¢ denotes variables and matrices associated with the loop impedance formulation of the network equations. References 1, C. Concordia, "Steady-state Stability of Synchro- nous Machines as Affected by Voltage Regulator Characteristics,"" Trans. AIEE, vol. 63, pp. 215-220, May 1944, 2. D.N. Ewart and F.P. deMello, "A Digital Com- puter Program for the Automatic Determination of Dynamic Stability Limits,"' IEEE Trans., Vol. PAS-86, pp. 867-875, July 1967. 3. A. Aldred and G, Shackshaft, "A Frequency Re- sponse Method for Predetermination of Synchro- nous Machine Stability,"’ Proc. IEEE, vol. 107, p. 2, 1960. 4. J. M, Undrill and T.E. Kostyniak, "Subsynchro- nous Oscillations, Part 1: Comprehensive Sys- tem Stability Analysis,"' Paper No. F76 114-9, IEEE 1976 Winter Power Meeting. 5. C.A. Stapleton, "Root-locus Study of Synchro- nous Machine Regulation," Proc. IEE, vol. 111, p. 761-768, 1964. 6. J.M. Undrill, "Dynamic Stability Calculations for an Arbitrary Number of Interconnected Synchro- * nous Machines," IEEE Trans., vol. PAS-87, pp. 835-844, March 1968. 7. J.M. Undrill and A.E. Turner, "Construction of Power System Electromechanical Equivalents by Modal Analysis," IEEE Trans., vol. PAS-90, pp. 2049-2059, Sep/Oct. 1971. 8. J.H. Anderson, "Matrix Methods for the Study of a Regulated Synchronous Machine," Proc. IEEE, vol. 57, pp. 2122-2136, Dec. 1969. 9. J.E. VanNess and W.F. Goddard, "Formationof the Coefficient Matrix of a Large Dynamic System," IEEE Trans., vol. PAS-87, pp. 80-83, Jan.1968. 10. M.K. Pal, "State Space Representation of Multi- machine Power Systems,"" IEEE Paper No. C74 396-8, 1974 Summer Power Meeting. 11, R.T.H. Alden and H. M. Zein El-Din. "Multi- Machine Dynamic Stability Calculations,"' IEEE Paper No. F76 153 7, 1976 Winter Power Meet- ing. 13. 14. 16. 17, 18, 19. 20. 21. D.N. Ewart and R.P. Schulz, "FACE Multi- Machine Power System Simulator Program," IEEE PICA Proc. 1969, pp. 133-153. B.T. Smith, et.al., Matrix Eigensystem Routines - EISPACK Guide, Lecture Notes in Computer Science, Vol. 6, Springer - Verlag, Berlin, Heidel- berg, New York, 1974. P.L. Dandeno and P. Kundur, "A Non-lIterative Transient Stability Program Including Effects of Variable Load-Voltage Characteristics, “IEEE Trans., vol. PAS-92, pp. 1478-1484, Sept/Oct1973. R.P. Schulz,W.D. Jones,D.N. Ewart, "Dynamic Models of Turbine Generators Derived from Solid Rotor Equivalent Circuits, "IEEE Trans., vol. PAS-92, pp. 926-933, May/June 1973. IEEE Committee Report, "Computer Represen- tation of Excitation Systems, "IEEE Trans., vol. PAS-88, pp. 1248-1258, Aug. 1969. C. Concordia, J.B. Tice, C.E.J. Bowler, "Sub- synchronous Torques on Generating Units Feeding Series Capacitor Compensated Lines,'' Amer, Power Conf. Proc., May 8-10, 1973, Chicago, i. C.E.J. Bowler, D.N. Ewart, C. Concordia, "'Self- Excited Torsional Frequency Oscillations with Series Capacitors," IEEE Trans., vol. PAS-92, pp. 1688-1695, Sep/Oct 1973. F.P. DeMello, C. Concordia, "Concepts of Syn- chronous Machine Stability as Affected by Exci- tation Control, '' IEEE Trans., vol. PAS-88,No. 4, pp. 316-329, Apr. 1969. E.A. Guillemin, Introductory Circuit Theory, 1953,J. Wiley & Sons, Inc., New Yorkand London, R.H. Park, 'Two-Reaction Theory of Synchronous Machines, PartI, Generalized Method of Analysis," A.1.E.E. Trans, ,Vol.48, pp.716-730, July 1929.