2.4 Modeling on reactive power or voltage control. Saadat s Chapters Kundur s Chapters 5.4, 8 and 11.2 EPRI Tutorial s Chapter 5

Transcription

1 2.4 Modeling on reactive power or voltage control Saadat s Chapters Kundur s Chapters 5.4, 8 and 11.2 EPRI Tutorial s Chapter 5 1

2 Objectives of Reactive Power and Voltage Control Equipment security: Voltages at terminals of all equipment (of either utility and customers) in the system are within acceptable limits to avoid damage System stability: System stability is enhanced to maximize utilization of the transmission system. (Voltage and reactive power control have a significant impact on system stability.) Transmission efficiency: The reactive power flow is minimized so as to reduce RI 2 and XI 2 losses to improve transmission system efficiency, i.e. leaving the room mainly for real power transfer 2

3 Methods of Reactive Power and Voltage Control Equipment Supply Q Absorb Q Synchronous generator Overhead lines Underground cables Transformers Loads Compensating devices Y (Over excited) Y Mostly Y Y (Under excited) Y Y Mostly Y Generators: Excitation control systems with automatic voltage regulators (AVRs) Other control devices Sources or sinks of var, e.g. shunt capacitors, shunt reactors, synchronous condensers, static var compensators (SVC) Line reactance compensators, e.g. series capacitors Regulating transformers, e.g. tapchanging transformers and boosters. 3

4 Excitation Systems of Generators The basic function of an excitation system is to provide direct current to the synchronous machine field winding. In addition, the automatic voltage regulator (AVR) with an excitation system performs control and protective functions essential to the satisfactory performance of the power system by controlling the field voltage and thereby the field current Field current 4

5 Performance Requirements of Excitation Systems Generator considerations: Under steady state conditions, the excitation system should supply and automatically adjust the field current of the synchronous generator to maintain the terminal voltage as the output varies continuously within the capacity of the generator Under disturbances, the excitation system must be able to respond to transient disturbances with field forcing consistent with the generator instantaneous and short term capacities In either case, heating limits (e.g. due to resistances that carry I t or i fd ) should be concerned Power system considerations The excitation system should contribute to effective control of voltage and enhancement of system stability under both large and small disturbances 5

6 Reactive Capacity of a Generator (Supplying Q, Lagging p.f.) 2 Overexcited Underexcited (Absorbing Q, Leading p.f.) 1 Under-excited Limit End region heating limit (due to heating caused by end-turn flux in under-excited conditions) 1 I t <I t,max : Armature current heating limit 2 i fd <i fd, max : Field current heating limit Always >0 Ignore R a >0 (over-excited) or <0 (under-excited) 6

7 Elements of an Excitation Control System 1. Exciter provides dc power to the generator field winding 2. Regulator (AVR) processes and amplifies input control signals for control of the exciter 3. Terminal voltage transducer and load compensator helps maintain the terminal voltage and the voltage at a remote point at desired levels 4. Power system stabilizer (PSS) provides an additional input signal to the regulator to damp system oscillations 5. Limiters and protective circuits ensure that the capability limits of the exciter and generator are not exceeded. 7

8 Excitation Control System/AVR Model Simplified linear model (ignoring saturations with the amplifier and exciter and other nonlinearities Rectifier/Sensor model: R is very small, e.g to 0.06s Amplifier model: K A =10 to 400, A =0.02 to 0.1s Exciter model: E is very small for modern exciters Generator model: K G =0.7 to 1.0, G =1.0 to 2.0s from full load to no load What is G? ~ () s e d fd () s 8

9 Simplified Linear Model Open and closed loop transfer functions: KKKK A E G R KG() s H () s = (1 + t s)(1 + t s)(1 + t s)(1 + t s) A E G R Vt() s KAKEKG(1 Rs) V ( s) = + t (1 + t s)(1 + t s)(1 + t s)(1 + t s) + K K K K ref A E G R A E G R (K E K G K R 1) 1 For a step input Vref () s, using the final value theorem, the steady-state response is s V tss K AK EK G K A = lim svt ( s) =» s 0 1+ K K K K 1+ K A E G R A If K A, V tss =V ref 9

10 Saadat s Example

11 Root Locus K A =12.16 K A =10, V tss =0.909V ref 1.8 Terminal voltage step response Imaginary Axis (seconds -1 ) / R -1/ A -1/ E -1/ G Real Axis (seconds -1 ) t, s K A =5, V tss =0.833V ref K A =12.16, V tss =0.924V ref 1.4 Terminal voltage step response 2 Terminal voltage step response t, s t, s 11

12 Excitation System Stabilizers K A =10 Rate feedback K F =0.2 T F =0.02 PID control (sim12ex8.mdl) Terminal voltage step response K P =1 K I =0.25 K D =0.28 t, s 12

13 Stability Analysis on AVR See Example 7.8 in Anderson s Power System Control and Stability for details on choosing K F and F 13

14 F >1 0.05< F <1 F <

15 Non reciprocal per unit system L ad -base Reciprocal per unit system: armature terminal voltage E t is around 1.0 pu under normal operating conditions, but exciter output voltage e fd (i.e. field voltage) in pu is very small (~0.001 pu) Non-reciprocal per unit system: 1 pu field voltage E fd produces rated armature terminal voltage E t on the air-gap line 1 pu field current I fd corresponds to rated field current i fd See Example 8.1: R fd = pu, L adu =1.66 pu i fd =1.565 pu, e fd = pu I fd =2.598 pu, E fd =2.598 pu 15

16 Detailed excitation system model with load compensation V R E fd With positive (or negative) R C and X C, the voltage at a point within (or outside) the generator is regulated. 16

17 DC Exciter Separately excited DC Exciter (DC generator) Main generator V R =E ef V R =E ef -E X 17

18 IEEE Type DC2A Excitation System Model: ESDC2A Voltage transducer (V UEL - Under-excitation limiter output) From PSS (Taking the bigger input) 18

19 AC Exciter (Brushless Excitation) Electronic rectifiers replace the commutator, slip rings and brushes AC exciter Main generator 19

20 IEEE Type AC2A Excitation System Model: ESAC2A Rectifier regulation model 20