PowerPoint Presentation

12-Oct-15Load Frequency Control1EE 513Control Apps in Power SystemsLoad Frequency Control

Prof. Hossam Eldin TalaatProf. at Electrical Power Eng. Dept.Ain-Shams Univ.Power System Functions on Time Horizon12-Oct-15Load Frequency Control2

Why Load Frequency Control?System Frequency is the Power-System Health Indicator

12-Oct-15Load Frequency Control3North Americas 2003 Blackout12-Oct-15Load Frequency Control4

2003 Blackout Power/Frequency12-Oct-15Load Frequency Control5

Impact of Under/Over Frequency on Power System Components 1/2Turbine (very tight over/under frequency tolerance): vibrations arise in turbine blades when the generator is operating at off nominal frequencies. Resonant frequencies lie in the neighborhood of the fundamental base operating speed of the turbine. Running at these resonant freq. under load for any extended period, there is cumulative damage to the blades and an eventual failure of the turbine.12-Oct-15Load Frequency Control612-Oct-15Load Frequency Control7Generator (under frequency limit):Reduced frequency results in reduced ventilation -> overheating -> reduced kVA. Network Components: Transformers, Motors, Drives, Controllers, more tolerant frequency limits.Impact of Under/Over Frequency on Power System Components 2/2Steam Turbine Operating Limitations During Abnormal Frequency (IEEE C37.106 Standard)12-Oct-15Load Frequency Control8

Power/ Frequency Vs Time12-Oct-15Load Frequency Control9

System Frequency Response to a Disturbance12-Oct-15Load Frequency Control10

Evaluation of System Performance12-Oct-15Load Frequency Control11

Load Frequency Control (LFC)The highest priority in system operation is to ensure generation/load balance leading to maintaining system frequency.Each utility defines a CONTROL AREAControls its generation to help maintain SYSTEM frequencyControls its generation to meet load and interchange. 12-Oct-15Load Frequency Control12Interconnected Control Areas(Power Pool)12-Oct-15Load Frequency Control13Net Interchange from areaControl AreaObjectives of LFCMaintain(Regulate) System Frequency at steady stateEnhance transient response of frequencyMaintain Tie-Line Power interchanges.Minimize integration of frequency deviation

12-Oct-15Load Frequency Control14Levels of Generation ControlLocal Governor ControlResponds at generator level to correct frequency deviation. Does not attempt to restore all the way to nominal frequency 50/60 HzAutomatic generation Control Real-time control from Control centers controls generation to restore frequency to 50/60 Hz and interchanges to contracted amountEconomic dispatchReallocates generation to minimize cost

12-Oct-15Load Frequency Control15Generator Model12-Oct-15Load Frequency Control16Pm-Pe = M d/dtGeneration (Mechanical Power) Load (Electrical Power) Imbalance results in change in machine speed (frequency).Machine electro-mechanical dynamics are described by the swing equationFor a single machine serving a load ( in per unit)Generator Model (1/3)12-Oct-15Load Frequency Control17Pm= mechanical power IN Pe= electrical power OUT = speed(frequency) in p.u.M = 2 H (H is Inertia const.)Pm- Pe = M d/dtPmPeMGenerator Model (2/3)12-Oct-15Load Frequency Control18Majority of imbalances encountered in normal operation are small ( as compared to a fault)Customary to use small-signal linearized modelsPmo+ Pm- Peo - Pe = 2H d (o+ ) / dt Pm- Pe = 2H d ( ) / dtPmo, Peo and o represent the initial operation point where Pmo=PeoPm, Pe , (f) are (small) deviations from the operating point. Therefore, Generator Model (3/3)12-Oct-15Load Frequency Control19Apply Laplace transform: Pm(s)- Pe(s) = 2sH W (s) => W(s)= [ Pm(s) - Pe(s)]/ (2H s)A sustained load generation imbalanced would lead to a continuous change in frequency!!!!!!! Pm- Pe = 2H d ( ) / dt

Load Model12-Oct-15Load Frequency Control20 Pe = PL + D Where PL is the incipient demand increaseD represents the response the additional load causes freq to drop, all motors slow down=>load drops as D D = 0 for resistive loadsD = -ve for static inductive loadsD = +ve for induction motorsThe equivalent D of a system is often positiveGenerally, the P&Q absorbed by the load are functions of f&V.Assume D as the load dependency on frequency, thenGenerator + Load Model12-Oct-15Load Frequency Control21

System Behavior (gen+load)12-Oct-15Load Frequency Control22Lets say Pm=0 PL= P u(t) or PL(s) = P/s W(s) = - PL(s)/(Ms+D) = - P / s(MS+D) (t) = - (P/D) ( 1 e tM/D) Pm PL PeThe offsetting load change arrests frequency change frequency settles to = -P/DMATLAB Model: Inertia+Load12-Oct-15Load Frequency Control23

Governor Behavior12-Oct-15Load Frequency Control24Measures speed(frequency) and adjusts valves to change generation

Frequency drops => Raise generationSpeedDesired Generation Pm PL PeGovernorGenerator Turbine Governor Behavior

12-Oct-15Load Frequency Control25Generator Turbine Governor Behavior

12-Oct-15Load Frequency Control26Detailed and complex models for Governors exist and are used in long-term dynamic simulations

Simplest modelDroopMATLAB LFC Model 12-Oct-15Load Frequency Control27

12-Oct-15Load Frequency Control28

Generator Turbine Governor Behavior: Steady State Response12-Oct-15Load Frequency Control29Steady state errorUsing energy balance PL - D - (1/R) = 0

Load LoadGenerationChange Response Change from Governor = - PL /( D+1/R)

Typical R = 0.05 pu ( 5% factory set)

For P = 0.2 , D = 0.8, R=0.05 = -0.2/20.8 = - 0.0096 puGenerator Turbine Governor BehaviorSteady state response Role of Pref12-Oct-15Load Frequency Control30Pm = Pref (1/R) 0Pm Pref PrefAt nominal frequency (=0) unitwould generate Pref0+ Pref

Multiple Areas12-Oct-15Load Frequency Control31Pm1PLlPe1Pm2PL2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieNow look at two areas connected by a line or network

If load changes in any area how do frequencies and line power Ptie change?

We will want to restore both to nominal value

A simple model for the line is just a series inductive reactanceMultiple Generators and Areas12-Oct-15Load Frequency Control32Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieA simple model for the line is just a series inductive reactance.Let us also assume voltage magnitudes are ~nominal ( 1pu)

From simplified transmission line models Ptie~ (1/X) sin(1- 2)

We also know that d 1 /dt =1 d 2 /dt = 2

Combine these with swing equationsMultiple Generators and Areas12-Oct-15Load Frequency Control33Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtiePm1- Pl1 D1 1-Ptie = M1 d1/dtPm2- Pl2 D2 2+Ptie = M2 d2/dt

Ptie= (1/X) sin(1- 2)

d 1 /dt =1 d 2 /dt = 2Multiple Generators and Areas12-Oct-15Load Frequency Control34Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2Ptie Pm1- Pl1 D1 1- Ptie = M1d 1/dt Pm2- Pl2 D2 2+ Ptie = M2d 2/dt

Ptie= Ps( 1- 2) ;sin x~x for small x

d 1 /dt = 1 d 2 /dt = 2Multiple Generators and Areas12-Oct-15Load Frequency Control35Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieIn s domain with zero initial conditions

Pm1(s)- Pl1(s) D1 1(s)- Ptie(s) = M1 s 1(s) Pm2(s)- Pl2(s) D2 2(s)+ Ptie(s) = M2 s 2(s)

Ptie(s)= Ps ( 1(s)- 2(s))

1(s) = 1(s)/s 2 (s) = 2(s)/sMultiple Generators and Areas12-Oct-15Load Frequency Control36Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2Ptie1/(M1s+D1) Pm2(s) + Pl2(s) - 1(s)1/s+-1/X1/(M2s+D2) 2(s)1/s Pm1(s) + Pl1(s) --+GovernorGovernor Ptie(s) 1(s) 2(s)Multiple Generators and Areas12-Oct-15Load Frequency Control37Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieQualitative Response

Load increase in area 1Area 1 frequency dropsArea 1 voltage phase angle fall behind area 2Ptie decreases (stabilizes Area 1 frequency, drags down area 2)Area 2 frequency dropsBoth governors raise generationSteady state achieved at a lower frequency and PtieArea 1 assists Area 2 in meeting the load increase; frequency drop is lowerMultiple Generators and Areas12-Oct-15Load Frequency Control38

Multiple Generators and Areas12-Oct-15Load Frequency Control39

ptie decreases from 1 to 2 1 2Frequency ErrorInterchange ErrorMultiple Generators and Areas12-Oct-15Load Frequency Control40

ptie decreases from 1 to 2Phase angle differenceCombined effects: Inertia+ Governor + AGC12-Oct-15Load Frequency Control41

Multiple Generators and Areas12-Oct-15Load Frequency Control42Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieSteady state => return to synchronism at some frequency = 1 = 2

Pl1 - D1 - (1/R1) + Ptie = 0

Load LoadGenerationInterchangeChange Response Change from Governor Pl2 - D2 - (1/R2) - Ptie = 0Multiple Generators and Areas12-Oct-15Load Frequency Control43Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieSteady state => return to synchronism at some frequency

= -( Pl1 + Pl2)/( D1+D2 + 1/R1 + 1/R2)

Ptie = - Pl1 + (D1+1/R1)( Pl1 + Pl2)/( D1+D2 + 1/R1 + 1/R2) Pm1 = - (1/R1)( Pl1 + Pl2)/( D1+D2 + 1/R1 + 1/R2)

Pm2 = - (1/R2)( Pl1 + Pl2)/( D1+D2 + 1/R1 + 1/R2)

Multiple Generators and Areas12-Oct-15Load Frequency Control44Pm1P1lPe1Pm2Pl2Pe2jXArea 1 or Gen 1Tie LineArea 2 or Gen 2PtieIdentical Areas R1=R2=0.05 D1=D2=1 Pl1 = 1 Pl2=0

= -( Pl1 + Pl2)/( D1+D2 + 1/R1 + 1/R2) = -0.0238 puCorrected!Ptie = -0.5 pu Pm1 = 0.5pu

Pm2 = .5 pu --------- Concept of Assist

Multiple Generators and Areas12-Oct-15Load Frequency Control45Coherent generators

The oscillation in frequency/angle represent synchronizing swingsAs generators exchange Kinetic energy trying to synchronize or find a common frequency

The swing is large and slow when systems are separated by long lines

Within an area generators synchronize quickly and swing as one large unit against other areas.

An area can be modeled as one large unit.

Multiple Generators and Areas12-Oct-15Load Frequency Control46Regulation R cannot be made too small

-- System becomes oscillatory and/or unstable

Governor-Turbine Generator SummaryLoad-generation imbalance produces frequency changes as well as power flow (interchange) changesTurbine generator dynamics is described by the swing equationGovernors achieve load-generation balance by changing generation based on frequency deviationRegulation/droop permits proper load sharingAll generators(areas) assist in the load balancing processGovernors do not restore frequency error to zero

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