PID controller learning

1. Modeling and simulation
Voltage and Frequency
Variations

2. Out line:
• Introduction.
• Automatic Voltage Regulator (AVR).
• Load Frequency Controller (LFC).
• LFC Model for Two Areas Power System.
• LFC for Three Areas Power System.
• Combining AVR with LFC system.
• Conclusion.

3. Introduction:
• An electrical power system consists of
many elements connected to form
complex system capable of generating,
transmitting and distributing electrical
energy over a large geographical area.

4. Introduction:
• Power system stability requires a well
designed controllers to regulate system
variations.
• Voltage and frequency control actions needed
to maintain system operating conditions.
• Automatic Generation Control actions take
effect.

5. Introduction:
• Automatic Generation Control (AGC)
is the name given to a control system
having three major objectives:
1.Hold system frequency at a specified
value (50Hz in UAE).
2. To maintain the correct value of
interchange power between control
areas.
3. To maintain each unit's generation at
the most economic value.

6. Introduction:
• Automatic Generation Control has
more advantages, such as:
• Increase Generation Ability by
connecting two or more areas
together.
• Improve ability of load variation
recovery.
• More efficient for detecting and fixing
power faults.

7. Power Generation Mechanism:
• Mechanical energy provide the needed
motion (rotational) to produce
electrical power.
• Generated using thermal energy such
as steam, natural gas and nuclear and
the little rest by hydro-mechanical such
as water falls energy or wind.

8. Elements Of AGC efficiency:
• Load Frequency Controller (LFC).
• The Automatic Voltage Regulator
(AVR).

9. Aims of the project:
• Design and simulate AVR.
• Design and simulate LFC.
• Design and simulate LFC for two areas power
system.
• Design and simulate LFC for three areas
power system.
• Combining AVR with LFC.
• Control the power of different areas.

10. Automatic Voltage
Regulator (AVR)

11. Introduction for the AVR system:
• What is the AVR system?
• Why we need the AVR system?
• Where its connect in the power system?
• What elements its consist of?

12. The AVR system:
• Make the system efficient.
• Consist of sensor, amplifier, exciter and
generator.
• Deals with the reactive power.

13. The AVR system:
• This is diagram for AVR system and it shows where it is
connected in the generation system

14. Modeling and Simulation:
Simple AVR System:

15. Transfer function relating the generator terminal voltage
Vt(s) to the reference voltage Vref(s) is:

16. What is Happening in the AVR
system?
• The amplifier comes first in the AVR system
to amplify the error signal.
• Then the error signals alter the exciter and
consequently the generator.
• The sensor sense the voltage output and
send it to the transducer and the transducer
send in the signal after comparing it to the
amplifier.

17. PID (proportional-integral-derivative):
The transfer function of a PID controller is:

18. Advantages of PID:
-Fast response and small error (due to the proportional gain).
- Reduced steady-state error (due to the integral gain).
- Reduced overshoot (due to the derivative gain).
Disadvantages of PID:
- There is no formal way to determine the best PID gains.

19. Simple AVR Model Simulink:
Input signal (Step Function) Output response from model
Time (s) Time (s)
Delta
V
Delta
V

20. Steady State error = 1 – 0.96 = 0.04.
Overshoot = 1.09 – 1 = 0.09.
Settling Time = 4s.

21. AVR with PID Controller:

22. Case 4( Kd=1,Ki=3,Kp=4).
Case 3( Kd=0.2,Ki=0.5,Kp= 3).
Case 2( Kd=0.5,Ki =0.5,Kp=0.5).
Case 1( Kd=0.1,Ki=0.1,Kp=1).
Time (s)
Time (s)
Time (s) Time (s)
Delta
V
Delta
V
Delta
V
Delta
V

23. The case 1 is the best case because it has less time
settling, less overshoot and less steady state error.
Steady State
Error
Settling Time (s)
Overshoot
Kp
Ki
Kd
Cases
0.001
3
0.003
1
0.1
0.1
1
0.4
10
0.4
0.5
0.5
0.5
2
0.01
4
0.4
3
0.5
0.2
3
0.01
5
0.17
4
3
1
4

24. Load Frequency
Control (LFC)

25. Load Frequency Control (LFC):
• The main problems of control in the
large power system are:
• Active Power.
• Reactive Power.
• Active power control is closely related
to frequency control.
• The frequency has an inverse
relationship with the load that is
changing continually.

26. Load Frequency Control (LFC):
• Feedback.
• Sensor.
• Frequency fixed.
• Frequency of UAE power system = 50 Hz

27. Load Frequency Control (LFC):
• Analysis of LFC :
High load (Air conditions, machines)  High pressure on
system  Decreasing in frequency of the load (< 50 + 0.05Hz) 
System is unstable.
To return the value of load frequency to its normal:
1) The output will multiply with the value of KG (speed regulation)
then, multiply it with governor delay.
2) There will be a command which tells control valve to control the
pushing of fuel.
3) More mechanical power to turbine  More electrical power 
Frequency of the load will increase to its normal value 
System is stable.

28. Load Frequency Control (LFC):
• Model of LFC:

29. Load Frequency Control (LFC):
• Modeling & Simulation:
Typical LFC Model
Name TCV TT K D
Value 0.2 sec 0.5 sec 0.8 20
constant values in LFC

30. Load Frequency Control (LFC):
• Frequency response of LFC:
• It is not stable.
Delta
f
(Hz)
Time (sec)

31. Load Frequency Control (LFC)
• Improvement of LFC:
• Adding PID controller to the LFC.
PID Controller. PID parameters effects (Ki, Kd, Kp)

32. Load Frequency Control (LFC):
• Model of LFC after adding PID Controller:
Simulink diagram for LFC with PID control system

33. Load Frequency Control (LFC):
• LFC response with different values of PID
parameters:
LFC response for (Kp = 1, Ki = 1, Kd = 1) LFC response for (Kp = 1, Ki = 0.3, Kd = 1)
Time (sec) Time (sec)
Delta
f
(Hz)
Delta
f
(Hz)

34. Load Frequency Control (LFC):
• LFC response with different values of PID
parameters:
LFC response for (Kp = 1, Ki = 0.3, Kd = 0.6) LFC response for (Kp = 2, Ki = 0.8, Kd = 1.1)
Delta
f
(Hz)
Delta
f
(Hz)
Time (sec) Time (sec)

35. Load Frequency Control (LFC):
• The output result of undershoot, settling time and
steady- state error for different values of PID
parameters:
Kp Ki Kd Undershoot Settling time Steady- state error
1 1 1 -0.012 >10 -0.002
1 0.3 1 -0.014 11 -0.0015
1 0.3 0.6 -0.015 10 -0.0011
2 0.8 1.1 -0.009 6 -0.0001
- Last value of PID controller parameter is the best one.

36. LFC Model for Two Areas Power System:
Area 1 Area 2
Two areas power system
∆Pd1
∆Pd2
∆Pt12
∆f2
∆f1
∆Pt21
∆Pt12
∆f1 ∆f2
∆f1 = f1 – fo ∆f2 = f2 – fo
∆Pd2
∆Pd1

37. LFC Model for Two Areas Power System:
LFC Model for two areas without integral controller

38. LFC Model for Two Areas Power System:
∆f1 ∆f2
∆Pt12
Outputs figures (∆f1, ∆f2, ∆Pt12):
The system is not stable.
Time (sec) Time (sec)
Time (sec)
Delta
f
(Hz)
Delta
f
(Hz)
Delta
f
(Hz)

39. LFC Model for Two Areas Power System :
LFC Model for two areas with Integral Controller

40. Figures for outputs (∆f1, ∆f2, ∆Pt12) with Integral Controller:
For (ki1 = 0.02 & ki2 = 0.01):
∆f1 ∆f2
∆Pt12
LFC Model for Two Areas Power System
:
Delta
f
(Hz)
Delta
f
(Hz)
Delta
f
(Hz)
Time (sec)
Time (sec)
Time (sec)

41. LFC Model for Two areas
For (ki1 = 0.1 & ki2 = 0.02):
∆f1 ∆f2
∆Pt12
LFC Model for Two Areas Power System
:
Time (sec) Time (sec)
Time (sec)
Delta
f
(Hz)
Delta
f
(Hz)
Delta
f
(Hz)

42. For (ki1 = 0.42 & ki2 = 0.019):
∆f1 ∆f2
∆Pt12
The system is stable because output results go to the reference point.
LFC Model for Two Areas Power System
:
Delta
f
(Hz)
Delta
f
(Hz)
Delta
f
(Hz)
Time (sec)
Time (sec)
Time (sec)

43. Two Areas with Um Al Naar Substation:

44. Two Areas with Um Al Naar Substation :
• Studying cases of LFC system of two area:
- Case 1: Area 1 and 2 are in the normal situation. (∆P1=0 & ∆P2=0) .
- Case 2: Area 1 is overloaded to more than 10% of the normal limit, i.e. a
step load disturbance of 0.1. Area 2 is in the normal situation. (∆P1 = 0.1&
∆P2 = 0) .
- Case 3: Areas 1 and 2 are overloaded to more than 10% of the normal limit,
i.e. load disturbances of 0.1 for each area. (∆P1 = 0.1& ∆P2 = 0.1) .
- Case 4: Area 1 and 2 are overloaded to more than 10% and 20% of the
normal limit, i.e. load disturbances of 0.1 and 0.2 respectively. (∆P1 = 0.1&
∆P2 = 0.2) .

45. Two Areas with Um Al Naar Substation :
Case 1: Area 1 and 2 are in the normal situation. (∆P1=0 & ∆P2=0)
0 5 10 15 20 25 30 35 40 45 50
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Two-area system ( Area 1 )
Time (s)
Delta
f
(Hz)
0 5 10 15 20 25 30 35 40 45 50
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Two-area system ( Area 2 )
Time (s)
Delta
f
(Hz)
Response for area 1 when ∆P1 = 0 and ∆P2 = 0. Response for area 2 when ∆P1 = 0 and ∆P2 = 0.

46. Two Areas with Um Al Naar Substation :
Case 2: (∆P1=0.1 & ∆P2=0)
0 5 10 15 20 25 30 35 40 45 50
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
x 10
-3
Two areas system (Area 1)
Time (sec)
w(t)
(Hz)
0 5 10 15 20 25 30 35 40 45 50
-10
-8
-6
-4
-2
0
2
x 10
-3
Two areas system (Area 2)
Time (sec)
w(t)
(Hz)
Response for area 1 when ∆P1 = 0.1 and ∆P2 = 0. Response for area 2 when ∆P1 = 0.1 and ∆P2 = 0.

47. Two Areas with Um Al Naar Substation :
Case 3: (∆P1=0.1 & ∆P2=0.1)
0 5 10 15 20 25 30 35 40 45 50
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
Two-area system ( Area 1 )
Time (s)
Delta
f
(Hz)
0 5 10 15 20 25 30 35 40 45 50
-0.012
-0.01
-0.008
-0.006
-0.004
-0.002
0
Two-area system ( Area 2 )
Time (s)
Delta
f
(Hz)
Response for area 1 when ∆P1 = 0.1 and ∆P2 = 0.1. Response for area 2 when ∆P1 = 0.1 and ∆P2 = 0.1.

48. Two Areas with Um Al Naar Substation :
Case 4: (∆P1=0.1 & ∆P2=0.2)
0 5 10 15 20 25 30 35 40 45 50
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
Two-area system ( Area 1 )
Time (s)
Delta
f
(Hz)
0 5 10 15 20 25 30 35 40 45 50
-0.025
-0.02
-0.015
-0.01
-0.005
0
Two-area system ( Area 2 )
Time (s)
Delta
f
(Hz)
Response for area 1 when ∆P1 = 0.1 and ∆P2 = 0.2. Response for area 2 when ∆P1 = 0.1 and ∆P2 = 0.2.

49. LFC Three Areas
Power System

50. Three-Area Power System:
Area1
Area2 Area3
ΔPt23
ΔPt32
ΔPt12
ΔPt21
ΔPt13
ΔPt31

51. Simple Block Diagram for 3-area
Power System:
3 Area Power System
ΔPd1
ΔPd2
ΔPd3
Δf1
Δf2
Δf3
ΔPt12
ΔPt23
ΔPt13
Inputs Variables Outputs

52. Three Area LFC system:

53. Output from LFC Three Area System:
Time (sec)
Δf1 (Hz)
Output from Area-1

54. Output from LFC Three Area System:
Time (sec)
Δf2 (Hz)
Output from Area-2

55. Output from LFC Three Area System:
Time (sec)
Δf3 (Hz)
Output from Area-3

56. Combining AVR with
LFC System

57. Combining AVR with LFC System:
• The connection between the AVR and the
LFC systems only represented in some
constants K1, K2…etc.
• The main concentration in AGC system is
the LFC part more than the AVR system.
• If the LFC system wasn’t stable the AGC
system will not be stable

58. Simulation of the AGC system:

59. Simulation:

60. Result by using MATLAB:
The response of the AGC the LFC part The response of the AGC the AVR part
Kp=0.1, Ki=0.2 and Kd=0.009
Overshoot = 0.16
Response Time = 12 s
Steady state error = 0
Overshoot = 0.185
Response Time = 3.5 s
Steady state error = 0

61. The response of the AVR and LFC
system separately:
AVR LFC

62. From the previous example:
• If the LFC system is not stable the
AGC system is stable.
• If the AVR system wasn’t stable it
not meant to be that the AGC
system isn’t stable.

63. Conclusion:
• The purpose of AGC is the tracking of load
variations while maintaining system frequency,
net tie-line interchanges, and optimal
generation levels close to specified values.
• AGC has more advantages than the previous
technique such as, increasing generation
ability, improve ability of load increase
recovery, more efficient for detecting and fixing
power faults, saving time.

64. Conclusion:
• LFC is used to regulate the output power of
each generator at prescribed levels while
keeping the frequency fluctuations within pre-
specified limits.
• The study of AVR
• show what is the important of the
proportional-integral-derivative action (PID)
controller.
• The LFC system is much slower than the AVR
due to the mechanical inertia constant in LFC.

65. Conclusion:
• If the LFC system is not stable the
AGC system is not stable.
• If the AVR system wasn’t stable it not
mean that the AGC system isn’t
stable.

66. Thank You For Your Listening
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Questions