Outline • Basi Basics cs of a Pr Prac acti tica call AVR AVR • Cont ontrol rol Funct unctio ion ns • Per-Unitization • AVR AVR Cont Contro roll Con Confi figu gura rati tion onss
Outline • Basi Basics cs of a Pr Prac acti tica call AVR AVR • Cont ontrol rol Funct unctio ion ns • Per-Unitization • AVR AVR Cont Contro roll Con Confi figu gura rati tion onss
Basics of a Practical AVR AVR for small generators Microcontroller Microcontroller based Inputs – – – – –
Voltage sensing Current sensing Exter ternal voltage adjustme tment Auxiliary in 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 1 or 3 Ph Sensing
Voltage Adj
Microcontroller
UF Adj 1 or 5 A CT Input Stability Cap/Res External Volts Adj
Power Stage
Feedback
+/- 3 Vdc Aux Input Power Supply Droop Adj Firing Control Stability Adj
Output To Exciter
Input 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
t s
=
4 realpart
=
4
ζ wn
≥
6.4 sec .
Pure Gain Root Locus 0.8
0.6
0.4
0.2 s i x A y r a n i g a m I
0
-0.2
-0.4
-0.6
-0.8 -1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
Real Axis
-0.1
0
Lead / Lag Controller Design •
Lag/Lead controller, also known as transient gain reduction
K C ( s + G Lead G Lag ( s) = GC ( s) =
(s +
1 T 1
1
α * T 1
)( s +
)( s +
1 T 2 1
)
β * T 2
)
Lead / Lag Controller Design •
•
Parameters KC, T1 and alpha make up the lead portion
−π *ζ
M O
T2 and beta make up the lag portion t s
=
=
e
1−ζ 2
4 wn * ξ
< 10% ζ = .6
< 1sec .
wn
=
6.7
Lead / Lag Controller Design •
The desired closed loop poles are given by
s = −ζ * wn
± j * wn
1 − ζ 2
= −4 ± j 5.36
Lead / Lag Controller Design •
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:
G Lead ( s ) =
K C * ( s + 1)
( s + 7.75)
Lead / Lag Controller Design •
•
The magnitude condition is used to calculate gain, Kc
| G Lead GPlant ( s ) |s =−4+ j 5.36 = 1
The results are as follows: G Lead GP ( s ) =
171( s + 1) ( s + 7.75)( s + 1)(4 s + 1)
42.75
=
( s + 7.75)( s + .25)
Lead / Lag Controller Design •
Step response of rotary excited generator with lead compensator Step Response 1.4 System: G1cl Peak amplitude: 1.05 Overshoot (%): 9.54 At time (sec): 0.599
1.2
1 System: G1cl Settling Time (s ec): 0.889
0.8
e d u t i l p m A 0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Time (s ec)
5
Lead / Lag Controller Design •
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%
ess
=
1 1 + K P
1
=
1 + lim G Lead GP ( s) s →0
=
1 1 + 22
= .045 =
4.5%
Lead / Lag Controller Design • • •
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:
| G Lag ( s) |s = −4+ j 5.36 ≅ 1
− 3 < ∠G Lag ( s ) | s = −4 + j 5.36 <
0
Lead / Lag Controller Design •
The chosen lag compensator becomes:
G Lag ( s ) =
( s + .2) ( s + .02)
Lead / Lag Controller Design •
The resulting open G loop transfer function becomes: The steady state error is calculate by: e
= GC GP ( s ) = Lead G Lag GP ( s )
•
ss
=
1 1 + K P
42.75( s + .2) ( s + 7.75)( s + .02)( s + .25)
1
=
1 + lim GC GP ( s ) s →0
=
1 1 + 220
= .45%
Lead / Lag Controller Design Step Response 1.4 System: G12cl Peak amplitude: 1.08 Overshoot (%): 8.97 At time (sec): 0.6
1.2
1 System: G12cl Settling Time (sec): 0.874 e d u t i l p m A
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (sec)
4.5
5
PID Controller Design •
I
PID controller G (s ) = P + C s represented by:
+ Ds =
Ds 2
+
Ps + I
s
PID Controller Design •
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
PID Controller Design •
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
PID Controller Design •
Pole-Zero cancellation design results in the following PID values: P
= 1.25 D = 1.25 * 20 =
I = 0.25 D D
=
=
25
0.25 * 20 = 5
20
PID Controller Design •
The resulting peak overshoot and settling time will be as follows:
M o
t ss
=
=
0
4 * 0.2 = 0.8 sec
PID Controller Design Step Response 1 0.9 0.8 0.7 0.6 e d u t i l p m A
0.5 0.4 0.3 0.2 0.1 0
0
0.2
0.4
0.6
0.8
Time (sec)
1
1.2
Summary • Basics of a Practical AVR • Control Functions • Per-Unitization • AVR Control Configurations
