generator control and protection automatic voltage regulators

GENERATOR CONTROL AND PROTECTION

Automatic Voltage Regulators


Outline

• Basics of a Practical AVR

• Control Functions

• Per-Unitization

• AVR Control Configurations


Basics of a Practical AVR

AVR for small generators

Microcontroller based

Inputs

– Voltage sensing

– Current sensing

– External voltage adjustment

– Auxiliary input (+/- 3Vdc)

– Operating Power


Basics of a Practical AVR

Internal Adjustments

– Voltage

– Droop

– Stability

– Under frequency knee / slope

Outputs

– Exciter field voltage


AVR Block Diagram

Power Stage

Microcontroller1 or 3 Ph Voltage AdjSensing

UF Adj1 or 5 A CT Input

Stability Cap/ResExternal

Volts AdjFeedback

+/- 3 VdcAux Input

Power Supply

Droop AdjFiring Control

Stability Adj

Output Input

To Exciter Shunt / PMG


Control Functions

• Voltage Control

• Droop Compensation

• V/Hz Compensation

• Over Excitation Shutdown

• Loss of Sensing Protection

• Build up from Residual

• Internal Adjustments


Control Functions

• External Adjustments

• Auxiliary Input

• Regulation Accuracy

• Temperature Drift

• Operating Temperature Range


Per-Unitization

• Goal is to set the gain for each block to “1” except the controller block

• The gain of each block is determined by dividing the output by the input for that block

• The gains for the blocks are combined together and the result appears in the controller block


Per-Unitization


DC Gain Adjustment


New Per-Unit Model


Algorithm

• Once we determine the overall loop gain,

we compensate for it by introducing Kg,

with the inverse of the loop gain

• Once we have done this, now the PID

controller gains reflect what is really

happening in the loop


AVR Control Configurations• Control configurations are different for static

excited versus rotary excited generators

• Static excited generators use:– Pure gain

– Lag/lead network

– PI controller

• Rotary excited generators use:– Lag/lead and lead/lag networks

– Rate feedback controller

– PID controller


AVR Control Configurations

• Design of a rotary excited generator

controller

– Tg = 4s, Te = 1s

– Mo < 10%

– ts < 1s

– ess < 0.5%


AVR Control Configurations

• Pure gain will not achieve our goal

.sec4.644

≥==n

swrealpart

tζ


Pure Gain

-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Root Locus

Real Axis

Imagin

ary

Axis


Lead / Lag Controller Design

• Lag/Lead controller, also known as transient gain

reduction

)*

1)(

*

1(

)1

)(1

(

)()(

21

21

Ts

Ts

Ts

TsK

sGsGG

C

CLagLead

βα++

++

==



• Parameters KC, T1

and alpha make up

the lead portion

• T2 and beta make up

the lag portion

6.%1021

*

=⇒<= −

−

ζζ

ζπ

eM O

7.6.sec1*

4=⇒<= n

n

s ww

tξ



• The desired closed

loop poles are given

by

36.541** 2jwjws nn ±−=−±−= ζζ



• We place the lead

compensator zero to

cancel the exciter

pole and use the

angle condition for

the overall system to

determine the lead

controller as:

)75.7(

)1(*)(

+

+=

s

sKsG C

Lead



• The magnitude

condition is used to

calculate gain, Kc

• The results are as

follows:

1|)(| 36.54 =+−= jsPlantLead sGG

)25.)(75.7(

75.42

)14)(1)(75.7(

)1(171)(

++=

+++

+=

sssss

ssGG PLead


Lead / Lag Controller Design• Step response of rotary excited generator with

lead compensatorStep Response

Time (sec)

Am

plit

ude

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

1.4

System: G1cl

Peak amplitude: 1.05

Overshoot (%): 9.54

At time (sec): 0.599

System: G1cl

Settling Time (sec): 0.889



• Some observations:

– Response shows a significant steady state error

– Transient spec of < 10% overshoot and <1s settling time are met

• Steady state error is approx 5%

%5.4045.221

1

)(lim1

1

1

1

0

==+

=+

=+

=

→sGGK

ePLead

sP

ss



• Spec requires steady state error <0.5%

• We will use the lag controller, with a beta of 10 to achieve the steady state error spec.

• The value of T2 is chosen based on the following conditions:

1|)(| 36.54 ≅+−= jsLag sG oo 0|)(3 36.54 <∠<− +−= jsLag sG



• The chosen lag compensator becomes: )02.(

)2.()(

+

+=

s

ssGLag



• The resulting open loop transfer function becomes:

• The steady state error is calculate by:

)25.)(02.)(75.7(

)2.(75.42)()(

+++

+==

sss

ssGGsGGG PCPLagLead

%45.2201

1

)(lim1

1

1

1

0

=+

=+

=+

=

→sGGK

ePC

sP

ss



Step Response

Time (sec)

Am

plit

ude

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2

1.4

System: G12cl

Peak amplitude: 1.08

Overshoot (%): 8.97

At time (sec): 0.6

System: G12cl

Settling Time (sec): 0.874


PID Controller Design

• PID controller

represented by:( )

s

IPsDsDs

s

IPsGC

++=++=

2



• Plant described by:

• 1/(4s + 1)(s +1)

• Denominator rewritten as:

• (4s + 1)(s +1) = 4s2+5s +1 = 4 * [s2+1.25s +0.25]

• PID controller numerator re-written as:

• Ds2 + Ps + I = D * [s2 + (P/D)s + (I/D)]

• For pole-zero cancellation we set:

• P/D = 1.25; I/D = 0.25



• We can now choose the value of D to set the loop

gain. It is easy to see that D = 20 will place the

third closed-loop pole at s=-5 as shown by the

following:

• G(s) Gc(s) =

• D[s2+1.25s +0.25] / 4s[s2+1.25s +0.25] = -1

• D/4s = -1

• s=-5 for D=20



• Pole-Zero cancellation design results in the

following PID values:

20

520*25.025.0

2520*25.125.1

=

===

===

D

DI

DP



• The resulting peak overshoot and settling time

will be as follows:

0=oM

sec8.02.0*4 ==sst



0 0.2 0.4 0.6 0.8 1 1.20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Step Response

Time (sec)

Am

plit

ude


Summary

• Basics of a Practical AVR

• Control Functions

• Per-Unitization

• AVR Control Configurations


QUESTIONS?

generator control and protection automatic voltage regulators

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