IEEE Std421.5-2005 IEEE STANDARD Ir Ip-jlo (2) Ip is the current component in-phase with the terminal voltage and therefore corresponds to the active power flowing from the machine to the system.Similarly,lo,corresponds to the reactive component of the current. When the current flowing from the generator lags the voltage,the reactive component of current,lo.and the associated reactive power,O,have positive values.For relatively constant terminal voltage (i.e.,changes of no more than a few percent from the nominal level),the amplitude of the active and reactive components of current will be equal to the active and reactive power output of the generator when expressed in pu. The original compensation equation can now be simplified,as shown in Equation (3): VcI (VT+Xcnlor+Xc12l02)+j(XcnlpI+XcI2Xp2) (3) (VT+Xcnlor+Xc12l02) The latter approximation is based on the fact that changes in the active component of current will have little effect on the compensated voltage amplitude.On newer systems,this algebraic equation is an exact representation of the AVR feedback signal,as the reactive component is resolved and multiplied by the compensation and then combined with the terminal voltage signal. Referring to Equation (3),when the selected compensation is positive and the reactive current lags the voltage,the compensated voltage,VCl,will be greater than the terminal voltage,V.When a larger value is presented to the AVR feedback input,the result is a reduction in excitation.Based on this,the type of compensation can be categorized as follows: Xc11>0,Xc12=0 Commonly referred to as reactive droop.The generator terminal voltage will exhibit a declining or drooping characteristic as reactive output increases. Xc11<0,Xc12=0 Commonly referred to as transformer-drop or line-drop compensation.The generator terminal voltage will exhibit a rising characteristic as reactive output increases Xc11≠0，Xc12≠0 Commonly referred to as cross-current compensation,although the preferred terminology is reactive differential compensation.Through careful selection of the two coefficients (e.g.,XC12=-XCI1),this form of compensation can be used to offset or eliminate the drooping voltage characteristic while enforcing reactive current sharing between synchronous machines sharing a common low-voltage connection. 5.Type DC-Direct current commutator exciters Few new synchronous machines are being equipped with Type DC exciters,which have been superseded by Type AC and ST systems.However many such systems are still in service.Considering the dwindling percentage and importance of units equipped with these exciters,the previously developed concept(see IEEE Committee Report [B18])of accounting for loading effects on the exciter by using the loaded saturation curve(see Annex C)is considered adequate. Digitally based voltage regulators feeding dc rotating main exciters can be represented with the AC Type AC8B model with the parameters Kc and Kp set to 0. The relationships between regulator limits and field voltage limits are developed in the IEEE Committee Report [B20]. 6 Copyright 2006 IEEE.All rights reserved
IEEE Std 421.5-2005 IEEE STANDARD 6 Copyright © 2006 IEEE. All rights reserved. (2) IP is the current component in-phase with the terminal voltage and therefore corresponds to the active power flowing from the machine to the system. Similarly, IQ, corresponds to the reactive component of the current. When the current flowing from the generator lags the voltage, the reactive component of current, IQ, and the associated reactive power, Q, have positive values. For relatively constant terminal voltage (i.e., changes of no more than a few percent from the nominal level), the amplitude of the active and reactive components of current will be equal to the active and reactive power output of the generator when expressed in pu. The original compensation equation can now be simplified, as shown in Equation (3): (3) The latter approximation is based on the fact that changes in the active component of current will have little effect on the compensated voltage amplitude. On newer systems, this algebraic equation is an exact representation of the AVR feedback signal, as the reactive component is resolved and multiplied by the compensation and then combined with the terminal voltage signal. Referring to Equation (3), when the selected compensation is positive and the reactive current lags the voltage, the compensated voltage, VC1, will be greater than the terminal voltage, VT. When a larger value is presented to the AVR feedback input, the result is a reduction in excitation. Based on this, the type of compensation can be categorized as follows: XC11 > 0, XC12 = 0 Commonly referred to as reactive droop. The generator terminal voltage will exhibit a declining or drooping characteristic as reactive output increases. XC11 < 0, XC12 = 0 Commonly referred to as transformer-drop or line-drop compensation. The generator terminal voltage will exhibit a rising characteristic as reactive output increases. XC11 ≠ 0, XC12 ≠ 0 Commonly referred to as cross-current compensation, although the preferred terminology is reactive differential compensation. Through careful selection of the two coefficients (e.g., XC12 = –XC11), this form of compensation can be used to offset or eliminate the drooping voltage characteristic while enforcing reactive current sharing between synchronous machines sharing a common low-voltage connection. 5. Type DC—Direct current commutator exciters Few new synchronous machines are being equipped with Type DC exciters, which have been superseded by Type AC and ST systems. However many such systems are still in service. Considering the dwindling percentage and importance of units equipped with these exciters, the previously developed concept (see IEEE Committee Report [B18]) of accounting for loading effects on the exciter by using the loaded saturation curve (see Annex C) is considered adequate. Digitally based voltage regulators feeding dc rotating main exciters can be represented with the AC Type AC8B model with the parameters KC and KD set to 0. The relationships between regulator limits and field voltage limits are developed in the IEEE Committee Report [B20]. IT IP jIQ = – VC1 VT XC11IQ1 XC12I + + Q2 ( ) j XC11IP1 + XC12XP2 = + ( ) VT XC11IQ1 XC12I + + Q2 ≈ ( )
IEEE FOR EXCITATION SYSTEM MODELS FOR POWER SYSTEM STABILITY STUDIES Std421.5-2005 5.1 Type DC1A excitation system model This model,described by the block diagram of Figure 5-1,is used to represent field-controlled dc commutator exciters with continuously acting voltage regulators (especially the direct-acting rheostatic, rotating amplifier,and magnetic amplifier types).Because this model has been widely implemented by the industry,it is sometimes used to represent other types of systems when detailed data for them are not available or when a simplified model is required. The principal input to this model is the output,Vc,from the terminal voltage transducer and load compensator model previously described.At the summing junction,terminal voltage transducer output,VC, is subtracted from the set point reference,VREF.The stabilizing feedback,Ve,is subtracted and the power system stabilizing signal,Vs is added to produce an error voltage.In the steady state,these last two signals are zero,leaving only the terminal voltage error signal.The resulting signal is amplified in the regulator.The major time constant,T,and gain,K4,associated with the voltage regulator are shown incorporating non- windup limits typical of saturation or amplifier power supply limitations.A discussion of windup and non- windup limits is provided in Annex E.These voltage regulators utilize power sources that are essentially unaffected by brief transients on the synchronous machine or auxiliary buses.The time constants,TB and TC. may be used to model equivalent time constants inherent in the voltage regulator,but these time constants are frequently small enough to be neglected and provision should be made for zero input data. VUEL VRMAX (ALTERNATE) 1+sTc HV Ka VR EFQ 1+STB GATE 1+STA VREF VE VRMIN Vx=EFDSE[EFD] SKF 1+STF Figure 5-1-Type DC1A-DC commutator exciter The voltage regulator output,VR,is used to control the exciter,which may be either separately excited or self-excited as discussed in the IEEE Committee Report [B20].When a self-excited shunt field is used,the value of Ke reflects the setting of the shunt field rheostat.In some instances,the resulting value of Kg can be negative and allowance should be made for this. Most of these exciters utilize self-excited shunt fields with the voltage regulator operating in a mode commonly termed buck-boost.The majority of station operators manually track the voltage regulator by periodically trimming the rheostat set point so as to zero the voltage regulator output.This may be simulated by selecting the value of Ke so that initial conditions are satisfied with Ve =0,as described in the IEEE Committee Report [B20].In some programs,if Kg is entered as zero,it is automatically calculated by the program for self-excitation. If a nonzero value for Ke is provided,the program should not recalculate Ke,as a fixed rheostat setting is implied.For such systems,the rheostat is frequently fixed at a value that would produce self-excitation near 5Examples of excitation systems represented by this model will be made available on the IEEE Web site.Annex I lists examples avail- able at the time of writing this standard. Copyright 2006 IEEE.All rights reserved. 7
IEEE FOR EXCITATION SYSTEM MODELS FOR POWER SYSTEM STABILITY STUDIES Std 421.5-2005 Copyright © 2006 IEEE. All rights reserved. 7 5.1 Type DC1A excitation system model This model, described by the block diagram of Figure 5-1, is used to represent field-controlled dc commutator exciters with continuously acting voltage regulators (especially the direct-acting rheostatic, rotating amplifier, and magnetic amplifier types).5 Because this model has been widely implemented by the industry, it is sometimes used to represent other types of systems when detailed data for them are not available or when a simplified model is required. The principal input to this model is the output, VC, from the terminal voltage transducer and load compensator model previously described. At the summing junction, terminal voltage transducer output, VC, is subtracted from the set point reference, VREF. The stabilizing feedback, VF, is subtracted and the power system stabilizing signal, VS, is added to produce an error voltage. In the steady state, these last two signals are zero, leaving only the terminal voltage error signal. The resulting signal is amplified in the regulator. The major time constant, TA, and gain, KA, associated with the voltage regulator are shown incorporating nonwindup limits typical of saturation or amplifier power supply limitations. A discussion of windup and nonwindup limits is provided in Annex E. These voltage regulators utilize power sources that are essentially unaffected by brief transients on the synchronous machine or auxiliary buses. The time constants, TB and TC, may be used to model equivalent time constants inherent in the voltage regulator, but these time constants are frequently small enough to be neglected and provision should be made for zero input data. The voltage regulator output, VR, is used to control the exciter, which may be either separately excited or self-excited as discussed in the IEEE Committee Report [B20]. When a self-excited shunt field is used, the value of KE reflects the setting of the shunt field rheostat. In some instances, the resulting value of KE can be negative and allowance should be made for this. Most of these exciters utilize self-excited shunt fields with the voltage regulator operating in a mode commonly termed buck-boost. The majority of station operators manually track the voltage regulator by periodically trimming the rheostat set point so as to zero the voltage regulator output. This may be simulated by selecting the value of KE so that initial conditions are satisfied with VR = 0, as described in the IEEE Committee Report [B20]. In some programs, if KE is entered as zero, it is automatically calculated by the program for self-excitation. If a nonzero value for KE is provided, the program should not recalculate KE, as a fixed rheostat setting is implied. For such systems, the rheostat is frequently fixed at a value that would produce self-excitation near 5 Examples of excitation systems represented by this model will be made available on the IEEE Web site. Annex I lists examples available at the time of writing this standard. Figure 5-1—Type DC1A—DC commutator exciter
IEEE Std421.5-2005 IEEE STANDARD rated conditions.Systems with fixed field rheostat settings are in widespread use on units that are remotely controlled.A value for Kg=1 is used to represent a separately excited exciter. The term Se[EFp]is a nonlinear function with values defined at two or more chosen values of EFp,as described in Annex C.The output of this saturation block,Vx is the product of the input,EFp,and the value of the nonlinear function Se[Epp]at this exciter voltage. A signal derived from field voltage is normally used to provide excitation system stabilization,Ve,via the rate feedback with gain,Ke,and time constant,TF. 5.2 Type DC2A excitation system model The model shown in Figure 5-2 is used to represent field-controlled dc commutator exciters with continuously acting voltage regulators having supplies obtained from the generator or auxiliary bus.It differs from the Type DCIA model only in the voltage regulator output limits,which are now proportional to terminal voltage /r. It is representative of solid-state replacements for various forms of older mechanical and rotating amplifier regulating equipment connected to dc commutator exciters. VUEL (ALTERNATE) VTVRMAX 1+sTc HV KA VR 1+STB GATE 1+STA VFE VTVRMIN KE Vx=EFDSE[EFD] SKF 1+STE Figure 5-2Type DC2A-DC commutator exciter with bus-fed regulator 5.3 Type DC3A excitation system model The systems discussed in the previous subclauses are representative of the first generation of high gain,fast- acting excitation sources.The Type DC3A model is used to represent older systems,in particular those dc commutator exciters with non-continuously acting regulators that were commonly used before the development of the continuously acting varieties. These systems respond at basically two different rates,depending upon the magnitude of voltage error.For small errors,adjustment is made periodically with a signal to a motor-operated rheostat.Larger errors cause resistors to be quickly shorted or inserted and a strong forcing signal applied to the exciter.Continuous motion of the motor-operated rheostat occurs for these larger error signals,even though it is bypassed by contactor action.Figure 5-3 illustrates this control action. The exciter representation is similar to that of systems described previously.Note that no excitation system stabilizer is represented. 8 Copyright 2006 IEEE.All rights reserved
IEEE Std 421.5-2005 IEEE STANDARD 8 Copyright © 2006 IEEE. All rights reserved. rated conditions. Systems with fixed field rheostat settings are in widespread use on units that are remotely controlled. A value for KE = 1 is used to represent a separately excited exciter. The term SE[EFD] is a nonlinear function with values defined at two or more chosen values of EFD, as described in Annex C. The output of this saturation block, VX, is the product of the input, EFD, and the value of the nonlinear function SE[EFD] at this exciter voltage. A signal derived from field voltage is normally used to provide excitation system stabilization, VF, via the rate feedback with gain, KF, and time constant, TF. 5.2 Type DC2A excitation system model The model shown in Figure 5-2 is used to represent field-controlled dc commutator exciters with continuously acting voltage regulators having supplies obtained from the generator or auxiliary bus. It differs from the Type DC1A model only in the voltage regulator output limits, which are now proportional to terminal voltage VT. It is representative of solid-state replacements for various forms of older mechanical and rotating amplifier regulating equipment connected to dc commutator exciters. 5.3 Type DC3A excitation system model The systems discussed in the previous subclauses are representative of the first generation of high gain, fastacting excitation sources. The Type DC3A model is used to represent older systems, in particular those dc commutator exciters with non-continuously acting regulators that were commonly used before the development of the continuously acting varieties. These systems respond at basically two different rates, depending upon the magnitude of voltage error. For small errors, adjustment is made periodically with a signal to a motor-operated rheostat. Larger errors cause resistors to be quickly shorted or inserted and a strong forcing signal applied to the exciter. Continuous motion of the motor-operated rheostat occurs for these larger error signals, even though it is bypassed by contactor action. Figure 5-3 illustrates this control action. The exciter representation is similar to that of systems described previously. Note that no excitation system stabilizer is represented. Figure 5-2Type DC2A—DC commutator exciter with bus-fed regulator
IEEE FOR EXCITATION SYSTEM MODELS FOR POWER SYSTEM STABILITY STUDIES td421.5-2005 Depending upon the magnitude of voltage error,VREF-Vc,different regulator modes come into play.If the voltage error is larger than the fast raise/lower contact setting,Ky(typically 5%),VRMAx or VRMIN is applied to the exciter,depending upon the sign of the voltage error.For an absolute value of voltage error less than Ky,the exciter input equals the rheostat setting VRH.The rheostat setting is notched up or down,depending upon the sign of the error.The travel time representing continuous motion of the rheostat drive motor is TRH. A non-windup limit(see Annex E)is shown around this block,to represent the fact that when the rheostat reaches either limit,it is ready to come off the limit immediately when the input signal reverses.Additional refinements,such as dead band for small errors,have been considered,but were not deemed justified for the relatively few older machines using these voltage regulators. Kv VRMAX VERR VRMAX VRMIN VRH S KV TRH -Kv VRMIN VRE IF VERR>KV,VR=VRMAX IF VERR<KV,VR=VRH VR- IF VERR<-KV,VR=VRMIN STE Vx=EFDSE[EFD] Figure 5-3-Type DC3A-DC commutator exciter with non-continuously acting regulators The model assumes that the quick raise/lower limits are the same as the rheostat limits.It does not account for time constant changes in the exciter field as a result of changes in field resistance(as a result of rheostat movement and operation of quick action contacts). 5.4 Type DC4B excitation system model These excitation systems utilize a field-controlled dc commutator exciter with a continuously acting voltage regulator having supplies obtained from the generator or auxiliary bus.The replacement of the controls only as an upgrade(retaining the dc commutator exciter)has resulted in a new model.The block diagram of this model is shown in Figure 5-4.This excitation system typically includes a proportional,integral,and differential (PID)generator voltage regulator (AVR).An alternative rate feedback loop (KF,T)for stabilization is also shown in the model if the AVR does not include a derivative term.If a PSS control is supplied,the appropriate model is the Type PSS2B model. Copyright 2006 IEEE.All rights reserved. 9
IEEE FOR EXCITATION SYSTEM MODELS FOR POWER SYSTEM STABILITY STUDIES Std 421.5-2005 Copyright © 2006 IEEE. All rights reserved. 9 Depending upon the magnitude of voltage error, VREF – VC, different regulator modes come into play. If the voltage error is larger than the fast raise/lower contact setting, KV (typically 5%), VRMAX or VRMIN is applied to the exciter, depending upon the sign of the voltage error. For an absolute value of voltage error less than KV, the exciter input equals the rheostat setting VRH. The rheostat setting is notched up or down, depending upon the sign of the error. The travel time representing continuous motion of the rheostat drive motor is TRH. A non-windup limit (see Annex E) is shown around this block, to represent the fact that when the rheostat reaches either limit, it is ready to come off the limit immediately when the input signal reverses. Additional refinements, such as dead band for small errors, have been considered, but were not deemed justified for the relatively few older machines using these voltage regulators. The model assumes that the quick raise/lower limits are the same as the rheostat limits. It does not account for time constant changes in the exciter field as a result of changes in field resistance (as a result of rheostat movement and operation of quick action contacts). 5.4 Type DC4B excitation system model These excitation systems utilize a field-controlled dc commutator exciter with a continuously acting voltage regulator having supplies obtained from the generator or auxiliary bus. The replacement of the controls only as an upgrade (retaining the dc commutator exciter) has resulted in a new model. The block diagram of this model is shown in Figure 5-4. This excitation system typically includes a proportional, integral, and differential (PID) generator voltage regulator (AVR). An alternative rate feedback loop (KF, TF) for stabilization is also shown in the model if the AVR does not include a derivative term. If a PSS control is supplied, the appropriate model is the Type PSS2B model. Figure 5-3—Type DC3A—DC commutator exciter with non-continuously acting regulators
IEEE Std421.5-2005 IEEE STANDARD ALTERNATE VoEL4- OEL INPUTS-VOEL ALTERNATE UEL INPUTS V V"VRMAX Vs VRMAXKA LV HV GATE Ero 1+sT K。+ GATE 1+sTp VVRMIN EMIN V K Vx-VESe(Erp) V: SKr (1+sT) Figure 5-4-Type DC4B-DC commutator exciter with PID style regulator 6.Type AC-Alternator-supplied rectifier excitation systems These excitation systems use an ac alternator and either stationary or rotating rectifiers to produce the dc field requirements.Loading effects on such exciters are significant,and the use of generator field current as an input to the models allows these effects to be represented accurately.These systems do not allow the supply of negative field current,and only the Type AC4A model allows negative field voltage forcing. Modeling considerations for induced negative field currents are discussed in Annex G.If these models are being used to design phase lead networks for PSSs,and the local mode is close to 3 Hz or higher,a more detailed treatment of the ac machine may be needed.However,the models will be satisfactory for large- scale simulations. In these models,a signal,VFE,proportional to exciter field current is derived from the summation of signals from exciter output voltage,Ve,multiplied by Ke+SelVe],(where Se[Ve]represents saturation as described in Annex C)and IFp multiplied by the demagnetization term,Kp.In some of the models,the exciter field current signal,VFE.is used as the input to the excitation system stabilizing block with output,Ve. 6.1 Type AC1A excitation system model The model shown in Figure 6-1 represents the field-controlled alternator-rectifier excitation systems designated Type AC1A.These excitation systems consist of an alternator main exciter with non-controlled rectifiers.The exciter does not employ self-excitation,and the voltage regulator power is taken from a source that is not affected by external transients.The diode characteristic in the exciter output imposes a lower limit of zero on the exciter output voltage,as shown in Figure 6-1. 10 Copyright 2006 IEEE.All rights reserved
IEEE Std 421.5-2005 IEEE STANDARD 10 Copyright © 2006 IEEE. All rights reserved. 6. Type AC—Alternator-supplied rectifier excitation systems These excitation systems use an ac alternator and either stationary or rotating rectifiers to produce the dc field requirements. Loading effects on such exciters are significant, and the use of generator field current as an input to the models allows these effects to be represented accurately. These systems do not allow the supply of negative field current, and only the Type AC4A model allows negative field voltage forcing. Modeling considerations for induced negative field currents are discussed in Annex G. If these models are being used to design phase lead networks for PSSs, and the local mode is close to 3 Hz or higher, a more detailed treatment of the ac machine may be needed. However, the models will be satisfactory for largescale simulations. In these models, a signal, VFE, proportional to exciter field current is derived from the summation of signals from exciter output voltage, VE, multiplied by KE + SE[VE], (where SE[VE] represents saturation as described in Annex C) and IFD multiplied by the demagnetization term, KD. In some of the models, the exciter field current signal, VFE, is used as the input to the excitation system stabilizing block with output, VF. 6.1 Type AC1A excitation system model The model shown in Figure 6-1 represents the field-controlled alternator-rectifier excitation systems designated Type AC1A. These excitation systems consist of an alternator main exciter with non-controlled rectifiers. The exciter does not employ self-excitation, and the voltage regulator power is taken from a source that is not affected by external transients. The diode characteristic in the exciter output imposes a lower limit of zero on the exciter output voltage, as shown in Figure 6-1. Figure 5-4—Type DC4B—DC commutator exciter with PID style regulator