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04/08/23 EE533F05Lecture4b.ppt 1

EE533 POWER OPERATIONSAutomatic Generation Control

Satish J. Ranade

Fall ‘05


Automatic Generation Control

• The first step in system operation is to ensure generation load balance

• This translates into maintaining system frequency• In classical operation (regulated)

– each utility defines a ‘control’ area– Controls its generation to help maintain SYSTEM

frequency– Controls its generation to meet load and interchange



Net Interchange from area

Control Area



General Objective ( Classical)Control MW Generation to• Maintain(Regulate) Frequency

-- assist entire system irrespective of cause

• Regulate Contractual Interchange• Technical Criteria set by National Electric

Reliability Council(NERC)



Local Governor Control-- responds at generator level to correct frequency deviation. Does not attempt to restore all the way to 60 Hz

Load Frequency Control --real-time control from Control centers controls generation to restore frequency to 60 Hz and interchange to contracted amount

Economic dispatch-- Reallocates generation to minimize cost


Automatic Generation ControlTo understand AGC we will look at

•Effect of small load-generation imbalances in terms of frequency and power flow changes•Governor action and how a governor controls frequency•Classical approach to restoring frequency and interchange using “Area Control Error “ concepts•Economics of generator scheduling and economic allocation of generation•Later we will look at changes brought about by restructuring


Generator Turbine Governor Behavior

Pm-Pe = M dω/dt

•Generation (Mechanical Power) – Load (Electrical Power) Imbalance results in change in machine speed, frequency and power flow•Machine electro-mechanical dynamics is described by swing equation•For a single machine serving a load ( in per unit)

Pm= mechanical power Pe= electrical power ω = speed(frequency)M = Inertia On time-scale of

electromechanical dynamicsPe = Pl where Pl is the load

Pm-Pl = M dω/dtPm

Pl



•We will look at how governors work and derive a model that shows how frequency changes because of load generation imbalance

•We will begin with a single generator and load and then generalize to large system


Generator Turbine Governor BehaviorPm-Pl = M dω/dt

Pm

Pl

Majority of imbalances encountered in normal operation are ‘small’( as compared to a fault at the terminals!)Customary to use small-signal linearized models

Pmo+ Δ Pm- Plo + Δ Pl = M d (ω o+Δ ω) / dt

Δ Pm- Δ Pl = M d (Δ ω) / dt

Pmo, Plo and ω o represent the initial operation point where Pmo=PloΔ Pm, Δ Pl ,Δ ωare (small) deviations from the operating point



Pm

PlΔ Pm- Δ Pl = M d (Δ ω) / dt

Pe

In modeling, analysis and simulation we often use Laplace domain block diagrams ( dF/dt=> sF(s) for zero initial conditions)Δ Pm(s)- Δ Pl(s) = sM Δ ω(s) =>

Δ ω(s)= [Δ Pm(s)- Δ Pl(s)]/ sM

1/(Ms)

A sustained load – generation imbalanced would lead to a continuouschange in frequency!!!!!!!

Δ Pm(s)

Δ Pl(s)Δ ω(s)



Pm

PlΔ Pm- Δ Pl = M d (Δ ω) / dt

Pe

In modeling, analysis and simulation we often use Laplace domain block diagrams ( dF/dt=> sF(s) for zero initial conditions)Δ Pm(s)- Δ Pl(s) = sM Δ ω(s) =>

Δ ω(s)= [Δ Pm(s)- Δ Pl(s)]/ sM

A sustained load – generation imbalanced would lead to a continuouschange in frequency!!!!!!!

1/(Ms+D)

Δ Pm(s) +

Δ Pl(s) - Δ ω(s)



Pm

Pl

PeLoad response to frequency change For Rotating components of load thereal power increases withfrequency

Δ Pl(s) = Δ Pl(s)+ DΔ ω(s)

Δ Pl(s) now is an ‘incipient’ load change ( a motor starts)DΔ ω(s) represents the response that the additional load causes frequency to drop, all motors slow down, and so load drops as DΔ ω(s)



Pm

Pl


Δ Pm(s)- Δ Pl(s)-D Δ ω(s) = sM Δ ω(s) => Δ ω(s)= [Δ Pm(s)- Δ Pl(s)]/ (Ms+D)

1/(Ms+D)

Δ Pm(s) +

Δ Pl(s) - Δ ω(s)



Pm

Pl


1/(Ms+D)

Δ Pm(s) +

Δ Pl(s) - Δ ω(s)

Let’s say Δ Pm=0 Δ Pl= P u(t) or Δ Pl(s) = P/s

Δ ω(s) = - Δ PL(s)/(MS+D) = - P / [s(MS+D)

Δ ω(t) = - (P/D) ( 1 – e –tM/D)



Pm

Pl

PeLoad response to frequency changeFor Rotating components of load thereal power increases withfrequency

The offsetting load change arrests frequency change– frequency settles to Δ ω = -P/D

Could derive this through final value theorem or energy balance

P = original load increase = load drop due to frequency drop -D Δ ω


Generator Turbine Governor BehaviorModel with governor

For M= 6, D= 1 and Load change P=1 puSteady stae frequency dropΔω= -P/D = -1 pu



Measures speed(frequency) and adjusts valves to change generation

Frequency drops => Raise generation

The GovernorPm

PlPe

Speed

Governor Desired GenerationA 1 pu frequency drop is unrealistic and speed governing is needed!



Pm

Pl

Pe

Speed

Governor

Desired Generation


Generator Turbine Governor BehaviorEmphasis – A low tech gadget that isAutonomous


Generator Turbine Governor BehaviorDetailed and complex models for Governors exist and are used in long-term dynamic simulations

Simplest model

Droop


Generator Turbine Governor BehaviorResponse

Steady state error


Generator Turbine Governor BehaviorSteady State Response

Steady state error

Using energy balance

Δ Pl - D Δω - (1/R) Δω = 0

Load Load GenerationChange Response Change from

GovernorΔω = - Δ Pl /( D+1/R)

Typical R = 0.05 pu ( 5% factory set)

For ΔP = 1 , D = 1, R=0.05 Δω = 1/21 = - 0.0476 pu


Generator Turbine Governor BehaviorSteady state response – Role of Pref

ΔPm = Δ Pref – (1/R) Δ ω

Δ ω

0

ΔPmΔ Pref Δ Pref’

Δ Pref is used to change generation from the control center through SCADA

At nominal frequency (Δ ω=0) unitWould generate Pref0+ Δ Pref


Generator Turbine Governor Behavior-Isochronous governor

Uses Integral control and restoresFrequency error to zero

Use in standalone or islanded cases


Generator Turbine Governor SummaryNo Governor

Standard Governor

Isochronous

No– unacceptable deviation

Std – leaves small error

Iso – restores exactly


Multiple Generators and Areas

Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX

Area 1 or Gen 1 Tie Line Area 2 or Gen 2

Ptie

Now look at two generators or 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 reactance



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

A 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(δ1- δ2)

We also know that d δ1 /dt =ω1 d δ2 /dt = ω2

Combine these with swing equations



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

Pm1- Pl1 –D1Δ ω1-Ptie = M1d ω1/dt

Pm2- Pl2 –D2Δ ω2-Ptie = M2 d ω2/dt

Ptie= (1/X) sin(δ1- δ2)

d δ1 /dt =ω1 d δ2 /dt = ω2



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

Δ Pm1- Δ Pl1 –D1Δ ω1- Δ Ptie = M1d Δ ω1/dt

Δ Pm2- Δ Pl2 –D2Δ ω2- Δ Ptie = M2d Δ ω2/dt

Ptie= (1/X) (Δ δ1- Δ δ2) ; sin x~x for small x

d Δ δ1 /dt = Δ ω1 d Δ δ2 /dt = Δ ω2



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

In s domain with zero initial conditions

Δ Pm1(s)- Δ Pl1(s) –D1 Δ ω1(s)- Δ Ptie(s) = M1 sΔ ω1(s)

Δ Pm2(s)- Δ Pl2(s) –D2 Δ ω2(s)- Δ Ptie(s) = M2 sΔ ω2(s)

Ptie(s)= (1/X) (Δ δ1(s)- Δ δ2(s))

Δ δ1(s) = Δ ω1(s)/s δ2 (s) = Δ ω2(s)/s



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

1/(M1s+D1)

Δ Pm1(s) +

Δ Pl1(s) -

Δ ω1(s) 1/s

+

-1/X

1/(M1s+D1) Δ ω1(s) 1/s

Δ Pm1(s) +

Δ Pl1(s) - +

-

Governor

Governor

Δ Ptie(s)

Δ δ1(s)

Δ δ2(s)



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

Qualitative Response

Load increase in area 1Area 1 frequency dropsArea 1 voltage phase angle fall behind are 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 lower



Δptie decreases from 1 to 2

Δω1

Δω2

Frequency Error

Interchange Error



Δptie decreases from 1 to 2

Phase angle difference



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

Steady state => return to synchronism at some frequency Δω = Δω1 = Δω2Δ Pl1 - D1 Δω - (1/R1) Δω + ΔPtie = 0

Load Load Generation InterchangeChange Response Change from

GovernorΔ Pl2 - D2 Δω - (1/R2) Δω - ΔPtie = 0



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

Steady state => return to synchronism at some frequency

Δω = -( ΔPl1 + ΔPl2)/( D1+D2 + 1/R1 + 1/R2)

ΔPtie = -Δ Pl1 + (D1+1/R1)( ΔPl1 + ΔPl2)/( D1+D2 + 1/R1 + 1/R2) ΔPm1 = - (1/R1)( ΔPl1 + ΔPl2)/( D1+D2 + 1/R1 + 1/R2)

ΔPm2 = - (1/R2)( ΔPl1 + ΔPl2)/( D1+D2 + 1/R1 + 1/R2)



Pm1

P1l

Pe1

Pm2

Pl2

Pe2jX


Ptie

Identical Areas R1=R2=0.05 D1=D2=1 ΔPl1 = 1 ΔPl2=0

Δω = -( ΔPl1 + ΔPl2)/( D1+D2 + 1/R1 + 1/R2) = -0.0238 puCorrected!

ΔPtie = -0.5 pu ΔPm1 = 0.5pu

ΔPm2 = .5 pu --------- Concept of Assist


Multiple Generators and AreasLoad sharing (also see Example 11.2 Glover and Sarma)Area 1 R1=0.05 1000 MVA BaseArea 2 R2= 0.05 500 MVA baseD1=D2=0 ΔPl1 = 1 ΔPl2=0

On 1000 MVA Base R2= R2*Sbase new/Sbase old=0.1Δω = -( ΔPl1 + ΔPl2)/( D1+D2 + 1/R1 + 1/R2) = .03333 pu

ΔPtie = -0.5 pu ΔPm1 = 0.666 pu 2/3 of load changeΔPm2 = 0.333 pu 1/3 of load change

If droop is same on own area( or machine) base areas raise generation in proportion to their capacities


Multiple Generators and AreasCoherent generators

The oscillation in frequency/angle represent ‘synchronizing swings’As 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.



Regulation R cannot be made too small

-- System becomes oscillatory and/or unstable


Multiple Generators and AreasIsochronous governors cannot be used with multiple generators

-- Difficult to supply identical reference frequency to each generators

Pm1

Pm2


Governor-Turbine Generator Summary• Load-generation imbalance produces frequency

changes as well as power flow (interchange) changes• Turbine generator dynamics is described by the swing

equation• Governors achieve load-generation balance by

changing generation based on frequency deviation• Regulation/droop permits proper load sharing• All generators(areas) assist in the load balancing

process• Governors do not restore frequency error to zero


Load Frequency Control- Restoring Frequency and Interchange

load

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