POWER SYSTEM OPERATION AND CONTROL
CONTENTS CHAPTER ECONOMIC ASPECTS INTRODUCTION LOAD CURVE LOAD–DURATION CURVE INTEGRATED LOAD–DURATION CURVE USES OF INTEGRATED LOAD–DURATION CURVE DE? NITION OF TERMS AND FACTORS CONNECTED LOAD MAXIMUM DEMAND DEMAND FACTOR AVERAGE LOAD LOAD FACTOR DIVERSITY FACTOR PLANT CAPACITY PLANT CAPACITY FACTOR UTILIZATION FACTOR (OR PLANT-USE FACTOR) FIRM POWER PRIME POWER DUMP POWER SPILL POWER COLD RESERVE HOT RESERVE SPINNING RESERVE BASE LOAD AND PEAK LOAD ON A POWER STATION LOAD FORECASTING PURPOSE OF LOAD FORECASTING CLASSI? CATION OF LOAD FORECASTING FORECASTING PROCEDURE KEY NOTES SHORT QUESTIONS AND ANSWERS MULTIPLE-CHOICE QUESTIONS REVIEW QUESTIONS PROBLEMS CHAPTER ECONOMIC LOAD DISPATCH-I CHARACTERISTICS OF POWER GENERATION (STEAM) UNIT SYSTEM VARIABLES CONTROL VARIABLES (PG AND QG ) DISTURBANCE VARIABLES (PD AND QD ) STATE VARIABLES (V AND ?) PROBLEM OF OPTIMUM DISPATCH—FORMULATION INPUT–OUTPUT CHARACTERISTICS UNITS OF TURBINE INPUT COST CURVES INCREMENTAL FUEL COST CURVE HEAT RATE CURVE INCREMENTAL EF? CIENCY 2 10 NON-SMOOTH COST FUNCTIONS WITH MULTIVALVE EFFECT 2 11 NON-SMOOTH COST FUNCTIONS WITH MULTIPLE FUELS 2 12 CHARACTERISTICS OF A HYDRO-POWER UNIT EFFECT OF THE WATER HEAD ON DISCHARGE OF WATER FOR A HYDRO-UNIT INCREMENTAL WATER RATE CHARACTERISTICS OF HYDRO-UNITS INCREMENTAL COST CHARACTERISTIC OF A HYDRO-UNIT CONSTRAINTS OF HYDRO-POWER PLANTS 2 13 INCREMENTAL PRODUCTION COSTS 2 14 CLASSICAL METHODS FOR ECONOMIC OPERATION OF SYSTEM PLANTS 2 15 OPTIMIZATION PROBLEM—MATHEMATICAL FORMULATION (NEGLECTING THE TRANSMISSION LOSSES) OBJECTIVE FUNCTION CONSTRAINT EQUATIONS 2 16 MATHEMATICAL DETERMINATION OF OPTIMAL ALLOCATION OF TOTAL LOAD AMONG DIFFERENT UNITS 2 17 COMPUTATIONAL METHODS ANALYTICAL METHOD GRAPHICAL METHOD SOLUTION BY USING A DIGITAL COMPUTER 2 18 ECONOMIC DISPATCH NEGLECTING LOSSES AND INCLUDING GENERATOR LIMITS 2 19 FLOWCHART FOR OBTAINING OPTIMAL SCHEDULING OF GENERATING UNITS BY NEGLECTING THE TRANSMISSION LOSSES 2 20 ECONOMICAL LOAD DISPATCH—IN OTHER UNITS NUCLEAR UNITS PUMPED STORAGE HYDRO-UNITS HYDRO-PLANTS INCLUDING REACTIVE-POWER ? OWS ECONOMIC LOAD DISPATCH-II OPTIMAL GENERATION SCHEDULING PROBLEM: CONSIDERATION OF TRANSMISSION LOSSES MATHEMATICAL MODELING TRANSMISSION LOSS EXPRESSION IN TERMS OF REAL-POWER GENERATION—DERIVATION MATHEMATICAL DETERMINATION OF OPTIMUM ALLOCATION OF TOTAL LOAD WHEN TRANSMISSION LOSSES ARE TAKEN INTO CONSIDERATION DETERMINATION OF ITL FORMULA PENALTY FACTOR FLOWCHART FOR THE SOLUTION OF AN OPTIMIZATION PROBLEM WHEN TRANSMISSION LOSSES ARE CONSIDERED OPTIMAL UNIT COMMITMENT COMPARISON WITH ECONOMIC LOAD DISPATCH NEED FOR UC CONSTRAINTS IN UC THERMAL UNIT CONSTRAINTS HYDRO-CONSTRAINTS MUST RUN FUEL CONSTRAINTS COST FUNCTION FORMULATION START-UP COST CONSIDERATION SHUT-DOWN COST CONSIDERATION CONSTRAINTS FOR PLANT COMMITMENT SCHEDULES UNIT COMMITMENT—SOLUTION METHODS ENUMERATION SCHEME PRIORITY-LIST METHOD DYNAMIC PROGRAMMING CONSIDERATION OF RELIABILITY IN OPTIMAL UC PROBLEM PATTON’S SECURITY FUNCTION OPTIMAL UC WITH SECURITY CONSTRAINT 4 10 START-UP CONSIDERATION OPTIMAL POWER-FLOW PROBLEM—SOLUTION TECHNIQUE OPTIMAL POWER-FLOW PROBLEM WITHOUT INEQUALITY CONSTRAINTS ALGORITHM FOR COMPUTATIONAL PROCEDURE OPTIMAL POWER-FLOW PROBLEM WITH INEQUALITY CONSTRAINTS INEQUALITY CONSTRAINTS ON CONTROL VARIABLES INEQUALITY CONSTRAINTS ON DEPENDENT VARIABLES—PENALTY FUNCTION METHOD HYDRO-THERMAL SCHEDULING HYDRO-THERMAL CO-ORDINATION SCHEDULING OF HYDRO-UNITS IN A HYDRO-THERMAL SYSTEM CO-ORDINATION OF RUN-OFF RIVER PLANT AND STEAM PLANT LONG-TERM CO-ORDINATION SHORT-TERM CO-ORDINATION CONSTANT HYDRO-GENERATION METHOD CONSTANT THERMAL GENERATION METHOD MAXIMUM HYDRO-EF? CIENCY METHOD GENERAL MATHEMATICAL FORMULATION OF LONG-TERM HYDRO-THERMAL SCHEDULING SOLUTION OF PROBLEM-DISCRETIZATION PRINCIPLE SOLUTION TECHNIQUE ALGORITHM SOLUTION OF SHORT-TERM HYDRO-THERMAL SCHEDULING PROBLEMS—KIRCHMAYER’S METHOD ADVANTAGES OF OPERATION OF HYDRO-THERMAL COMBINATIONS FLEXIBILITY GREATER ECONOMY SECURITY OF SUPPLY BETTER ENERGY CONSERVATION RESERVE CAPACITY MAINTENANCE LOAD FREQUENCY CONTROL-I NECESSITY OF MAINTAINING FREQUENCY CONSTANT LOAD FREQUENCY CONTROL GOVERNOR CHARACTERISTICS OF A SINGLE GENERATOR ADJUSTMENT OF GOVERNOR CHARACTERISTIC OF PARALLEL OPERATING UNITS LFC: (P–F CONTROL) Q–V CONTROL GENERATOR CONTROLLERS (P–F AND Q–V CONTROLLERS) P–F CONTROL VERSUS Q–V CONTROL 7 10 DYNAMIC INTERACTION BETWEEN P–F AND Q–V LOOPS 7 11 SPEED-GOVERNING SYSTEM SPEED-GOVERNING SYSTEM MODEL 7 12 TURBINE MODEL NON-REHEAT-TYPE STEAM TURBINES INCREMENTAL OR SMALL SIGNAL FOR A TURBINE-GOVERNOR SYSTEM REHEAT TYPE OF STEAM TURBINES 7 13 GENERATOR-LOAD MODEL 7 14 CONTROL AREA CONCEPT 7 15 INCREMENTAL POWER BALANCE OF CONTROL AREA 7 16 SINGLE AREA IDENTI? CATION BLOCK DIAGRAM REPRESENTATION OF A SINGLE AREA 7 17 SINGLE AREA—STEADY-STATE ANALYSIS SPEED-CHANGER POSITION IS CONSTANT (UNCONTROLLED CASE) LOAD DEMAND IS CONSTANT (CONTROLLED CASE) SPEED CHANGER AND LOAD DEMAND ARE VARIABLES 7 18 STATIC LOAD FREQUENCY CURVES 7 19 DYNAMIC ANALYSIS 7 20 REQUIREMENTS OF THE CONTROL STRATEGY INTEGRAL CONTROL 7 21 ANALYSIS OF THE INTEGRAL CONTROL 7 22 ROLE OF INTEGRAL CONTROLLER GAIN (KI) SETTING 7 23 CONTROL OF GENERATOR UNIT POWER OUTPUT LOAD FREQUENCY CONTROL-II COMPOSITE BLOCK DIAGRAM OF A TWO-AREA CASE RESPONSE OF A TWO-AREA SYSTEM—UNCONTROLLED CASE STATIC RESPONSE DYNAMIC RESPONSE AREA CONTROL ERROR —TWO-AREA CASE COMPOSITE BLOCK DIAGRAM OF A TWO-AREA SYSTEM (CONTROLLED CASE) TIE-LINE BIAS CONTROL STEADY-STATE RESPONSE OPTIMUM PARAMETER ADJUSTMENT LOAD FREQUENCY AND ECONOMIC DISPATCH CONTROLS DESIGN OF AUTOMATIC GENERATION CONTROL USING THE KALMAN METHOD DYNAMIC-STATE-VARIABLE MODEL MODEL OF SINGLE-AREA DYNAMIC SYSTEM IN A STATE-VARIABLE FORM OPTIMUM CONTROL INDEX (I) OPTIMUM CONTROL PROBLEM AND STRATEGY DYNAMIC EQUATIONS OF A TWO-AREA SYSTEM STATE-VARIABLE MODEL FOR A THREE-AREA POWER SYSTEM ADVANTAGES OF STATE-VARIABLE MODEL REACTIVE POWER COMPENSATION OBJECTIVES OF LOAD COMPENSATION P F CORRECTION VOLTAGE REGULATION IMPROVEMENT LOAD BALANCING IDEAL COMPENSATOR SPECI? CATIONS OF LOAD COMPENSATION THEORY OF LOAD COMPENSATION VOLTAGE REGULATION LOAD BALANCING AND P F IMPROVEMENT OF UNSYMMETRICAL THREE-PHASE LOADS UNCOMPENSATED TRANSMISSION LINES FUNDAMENTAL TRANSMISSION LINE EQUATION CHARACTERISTIC IMPEDANCE SURGE IMPEDANCE OR NATURAL LOADING UNCOMPENSATED LINE WITH OPEN-CIRCUIT VOLTAGE AND CURRENT PRO? LES THE SYMMETRICAL LINE AT NO-LOAD UNDEREXCITED OPERATION OF GENERATORS DUE TO LINE-CHARGING THE UNCOMPENSATED LINE UNDER LOAD RADIAL LINE WITH ? XED SENDING-END VOLTAGE REACTIVE POWER REQUIREMENTS THE UNCOMPENSATED LINE UNDER LOAD WITH CONSIDERATION OF MAXIMUM POWER AND STABILITY 9 10 COMPENSATED TRANSMISSION LINES 9 11 SUB-SYNCHRONOUS RESONANCE EFFECTS OF SERIES AND SHUNT COMPENSATION OF LINES CONCEPT OF SSR IN LINES 9 12 SHUNT COMPENSATOR THYRISTOR-CONTROLLED REACTOR THYRISTOR-SWITCHED CAPACITOR 9 13 SERIES COMPENSATOR 9 14 UNI? ED POWER-FLOW CONTROLLER 9 15 BASIC RELATIONSHIP FOR POWER-FLOW CONTROL WITHOUT LINE COMPENSATION WITH SERIES CAPACITIVE COMPENSATION WITH SHUNT COMPENSATION WITH PHASE ANGLE CONTROL 9 16 COMPARISON OF DIFFERENT TYPES OF COMPENSATING EQUIPMENT FOR TRANSMISSION SYSTEMS 9 17 VOLTAGE STABILITY—WHAT IS IT? VOLTAGE STABILITY VOLTAGE COLLAPSE VOLTAGE-STABILITY ANALYSIS P–V CURVES CONCEPT OF VOLTAGE COLLAPSE PROXIMATE INDICATOR VOLTAGE-STABILITY ANALYSIS: Q–V CURVES DERIVATION FOR VOLTAGE-STABILITY INDEX VOLTAGE CONTROL 10 1 INTRODUCTION 10 2 NECESSITY OF VOLTAGE CONTROL 10 3 GENERATION AND ABSORPTION OF REACTIVE POWER 10 4 LOCATION OF VOLTAGE-CONTROL EQUIPMENT 10 5 METHODS OF VOLTAGE CONTROL EXCITATION CONTROL SHUNT CAPACITORS AND REACTORS SERIES CAPACITORS TAP-CHANGING TRANSFORMERS BOOSTER TRANSFORMERS SYNCHRONOUS CONDENSERS 10 6 RATING OF SYNCHRONOUS PHASE MODI? ER MODELING OF PRIME MOVERS AND GENERATORS 11 1 INTRODUCTION HYDRAULIC TURBINE SYSTEM MODELING OF HYDRAULIC TURBINE STEAM TURBINE MODELING NON-REHEAT TYPE REHEAT TYPE SYNCHRONOUS MACHINES SALIENT-POLE-TYPE ROTOR NON-SALIENT-POLE-TYPE ROTOR SIMPLI? ED MODEL OF SYNCHRONOUS MACHINE (NEGLECTING SALIENCY AND CHANGES IN FLUX LINKAGES) EFFECT OF SALIENCY GENERAL EQUATION OF SYNCHRONOUS MACHINE DETERMINATION OF SYNCHRONOUS MACHINE INDUCTANCES ASSUMPTIONS ROTOR INDUCTANCES ROTOR SELF-INDUCTANCE STATOR TO ROTOR MUTUAL INDUCTANCES 11 10 STATOR SELF-INDUCTANCES 11 11 STATOR MUTUAL INDUCTANCES 11 12 DEVELOPMENT OF GENERAL MACHINE EQUATIONS—MATRIX FORM 11 13 BLONDEL’S TRANSFORMATION (OR) PARK’S TRANSFORMATION TO ‘DQO’ COMPONENTS 11 14 INVERSE PARK’S TRANSFORMATION 11 15 POWER-INVARIANT TRANSFORMATION IN ‘F-D-Q-O’ AXES 11 16 FLUX LINKAGE EQUATIONS 11 17 VOLTAGE EQUATIONS 11 18 PHYSICAL INTERPRETATION OF EQUATIONS (11 62) AND (11 68) 11 19 GENERALIZED IMPEDANCE MATRIX (VOLTAGE–CURRENT RELATIONS) 11 20 TORQUE EQUATION 11 21 SYNCHRONOUS MACHINE—STEADY-STATE ANALYSIS SALIENT-POLE SYNCHRONOUS MACHINE NON-SALIENT-POLE SYNCHRONOUS (CYLINDRICAL ROTOR) MACHINE 11 22 DYNAMIC MODEL OF SYNCHRONOUS MACHINE SALIENT-POLE SYNCHRONOUS GENERATOR—SUB-TRANSIENT EFFECT DYNAMIC MODEL OF SYNCHRONOUS MACHINE INCLUDING DAMPER WINDING EQUIVALENT CIRCUIT OF SYNCHRONOUS GENERATOR—INCLUDING DAMPER WINDING EFFECT 11 23 MODELING OF SYNCHRONOUS MACHINE—SWING EQUATION MODELING OF SPEED GOVERNING AND EXCITATION SYSTEMS MODELING OF SPEED-GOVERNING SYSTEMS FOR STEAM TURBINES MECHANICAL–HYDRAULIC-CONTROLLED SPEED- GOVERNING SYSTEMS ELECTRO–HYDRAULIC-CONTROLLED SPEED- GOVERNING SYSTEMS GENERAL MODEL FOR SPEED-GOVERNING SYSTEMS FOR HYDRO-TURBINES ELECTRIC–HYDRAULIC-CONTROLLED SPEED- GOVERNING SYSTEM MODELING WITH LIMITS WIND-UP LIMITER NON-WIND-UP LIMITER MODELING OF A STEAM-GOVERNOR TURBINE SYSTEM REHEAT SYSTEM UNIT BLOCK DIAGRAM REPRESENTATION TRANSFER FUNCTION OF THE STEAM-GOVERNOR TURBINE MODELING MODELING OF A HYDRO-TURBINE-SPEED GOVERNOR EXCITATION SYSTEMS EFFECT OF VARYING EXCITATION OF A SYNCHRONOUS GENERATOR EXPLANATION LIMITATIONS OF INCREASE IN EXCITATION 12 10 METHODS OF PROVIDING EXCITATION COMMON EXCITATION BUS METHOD INDIVIDUAL EXCITATION METHOD BLOCK DIAGRAM REPRESENTATION STRUCTURE OF A GENERAL EXCITATION SYSTEM 12 11 EXCITATION CONTROL SCHEME 12 12 EXCITATION SYSTEMS—CLASSI? CATION DC EXCITATION SYSTEM AC EXCITATION SYSTEM STATIC EXCITATION SYSTEM 12 13 VARIOUS COMPONENTS AND THEIR TRANSFER FUNCTIONS OF EXCITATION SYSTEMS PT AND RECTI? ER VOLTAGE COMPARATOR AMPLI? ERS 12 14 SELF-EXCITED EXCITER AND AMPLIDYNE 12 15 DEVELOPMENT OF EXCITATION SYSTEM BLOCK DIAGRAM TRANSFER FUNCTION OF THE STABILIZING TRANSFORMER TRANSFER FUNCTION OF SYNCHRONOUS GENERATOR IEEE TYPE-1 EXCITATION SYSTEM TRANSFER FUNCTION OF OVERALL EXCITATION SYSTEM 12 16 GENERAL FUNCTIONAL BLOCK DIAGRAM OF AN EXCITATION SYSTEM TERMINAL VOLTAGE TRANSDUCER AND LOAD COMPENSATION EXCITERS AND VOLTAGE REGULATORS EXCITATION SYSTEM STABILIZER AND TRANSIENT GAIN REDUCTION POWER SYSTEM STABILIZER 12 17 STANDARD BLOCK DIAGRAM REPRESENTATIONS OF DIFFERENT EXCITATION SYSTEMS POWER SYSTEM SECURITY AND STATE ESTIMATION THE CONCEPT OF SYSTEM SECURITY LONG-TERM PLANNING OPERATIONAL PLANNING ON-LINE OPERATION SECURITY ANALYSIS DIGITAL SIMULATION HYBRID COMPUTER SIMULATION LYAPUNOV METHODS PATTERN RECOGNITION SECURITY ENHANCEMENT SSS ANALYSIS REQUIREMENTS OF AN SSS ASSESSOR TRANSIENT SECURITY ANALYSIS LYAPUNOV METHOD STATE ESTIMATION STATE ESTIMATOR STATIC-STATE ESTIMATION MODELING OF UNCERTAINTY SOME BASIC FACTS OF STATE ESTIMATION LEAST SQUARES ESTIMATION APPLICATIONS OF STATE ESTIMATION