 Open Access
 Total Downloads : 285
 Authors : Mohamed A. Metwally, Dr. Mohamed A. Ali, Dr. Said A. Kutb, Prof. Dr. Fahmy M. Bendary
 Paper ID : IJERTV5IS100194
 Volume & Issue : Volume 05, Issue 10 (October 2016)
 Published (First Online): 18102016
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Genetic Algorithm for Optimum Design of PID Controller in Multi Area Load Frequency Control for Egyptian Electrical Grid
Mohamed A. Metwally Suez Canal Authority, Cairo, Egypt
Dr. Mohamed A. Ali
Department of Electrical Engineering University of Benha
Egypt
Dr. Said A. Kutb Atomic Energy Authorit, Cairo, Egypt
Abstract This paper addresses the basic Load Frequency Control (LFC) model for the Egyptian electrical grid at 2024 after adding the first Nuclear Power Plant (NPP). The paper proposes a Genetic Algorithm (GA) technique used to determine the optimal tuning of the PID controllers parameters to improve the dynamic stability problem. Five types of energy sources transfer function block diagram models "thermal, hydraulic, gas, nuclear, wind" are simulated as a multi area power system by using MATLAB/SIMULINK to study the stability of the system. The performance of the proposed method is assessed compared to conventional PID controller in terms of Frequency response. A comparison with conventional PID controller shows that the proposed approach strategy can reduce the amplitude of oscillation and effectively enhance system stability.
Keywords–Egyptian grid; Load Frequency Control (LFC); PID controller; genetic algorithm.
I.INTRODUCTION
Large scale power systems are normally composed of control areas or regions representing coherent groups of generators. In a future combination of electricity in Egypt, the generation normally comprises of a mix of thermal, hydro, nuclear, gas and wind or renewable power generation. However, owing to their high efficiency, nuclear plants are usually kept at base load close to their maximum output with no participation in the system Automatic Generation Control (AGC). Gas power generation is ideal for meeting the varying load demand. Gas plants are used to meet peak demands only. Thus the natural choice for AGC falls on either thermal or hydro units [14]. Since the time of construction of the nuclear plant takes from six to seven years, so this was a study on 2024. According to the latest load forecast research results in Egypt for year 2024 is approximately 60 GW, were in line with expectations with loads of the company's Egyptian electricity holding the Egyptian ministry of electricity [5, 6]. This paper study the system performance of Egyptian grid at 2024 by tracking the change in system frequency values for each case mentioned above, and try to maintain the difference in the change
Prof. Dr. Fahmy M. Bendary
Department of Electrical Engineering University of Benha,
Egypt
within a reasonable values by adding PID controller. MATLAB/SIMULINK program tool has been used for simulate the Egyptian electrical grid model as a transfer function block diagram [7]. Genetic Algorithms (GAs) are global optimization techniques that utilize concurrent search from multiplepoints rather than from a singlepoint. GA is independent of the problem complexity. The main necessity of the GA is to specify the objective function and to place finite bounds on the parameters. GA is widely used for robust Power System Stabilization.
Optimization using GA techniques are widely applied in many real world problems such as image processing, pattern recognition, classifiers, machine learning. There are various forms of GA for different purposes. In this paper Genetic Algorithm techniques have been used to enhance the stabilization of the power systems by optimal tuning for the PID controller's parameters.

EGYPTIAN ELECTRICAL GRID DATA
Before the start in our study there important information about Egypt's current electrical grid and future expectations for the electrical grid in 2024 must be present and are as follows.

A current combination of the Egyptian electrical grid After reviewing the annual report for the year 2014 of the company's Egyptian Electricity Holding the Egyptian Ministry of Electricity show that the total production of electricity in Egypt for the year 2014 is almost 30 GW and the current combination of the sources of electricity production in Egypt as follows in Table I [5].
TABLE I. A CURRENT COMBINATION OF THE EGYPTIAN ELECTRICAL GRID.
Source type
Total production in GW
Total production in %
Thermal
20 GW
60%
Gas
7.5 GW
27%
Hydraulic
2.8 GW
10%
Wind and Renewable
GW 1
3%

The proposed combination of the Egyptian electricity grid at 2024
After study the current combination of the Egyptian grid, also review the future plans of the Ministry of Electricity in the construction of various types of plants for the production of electrical energy over the next ten year, and also predicted the total loads of the Egyptian grid in 2024 where it was almost 60 GW [6]. Taking into account all the circumstances and requirements for the production of electrical energy in 2024 from the fuel sources and construction time of a new different types of power plants, it has been found an urgent need to start building the first nuclear power plant in Egypt to overcome the increasing in the loads and decreasing in the fuel sources. Knowing that the construction of this station time about seven years, so our simulation must have been make at 2024. So the chart of the Egyptian electrical grid will be changed to become at 2024 as shown in Table II.
Source type
Total production in GW
Total production in %
Thermal
33 GW
55%
Gas
18 GW
30%
Hydraulic
3.2 GW
6%
Nuclear
1.2 GW
2%
Wind and Renewable
4.2 GW
7%
Source type
Total production in GW
Total production in %
Thermal
33 GW
55%
Gas
18 GW
30%
Hydraulic
3.2 GW
6%
Nuclear
1.2 GW
2%
Wind and Renewable
4.2 GW
7%
TABLE II. A PROPOSED COMBINATION OF THE EGYPTIAN ELECTRICAL GRID AT 2024.
Fig.1: Proposed combination energy sources of the Egyptian electrical grid at 2024.

thermal model
A single area thermal power system has two main parts that are speed governor and turbine. In starting it is assumed that this system is linear for simplicity. The transfer function block diagram model of thermal governor is shown as in Fig. 2 [79].
Fig. 2. Thermal power plant speed governor block diagram.
Where,
Ksg : Thermal speed governor gain.
RT : Thermal speed regulation of the governor.
Tsg : Thermal speed governor time constant.
The turbine transfer function is characterized by two time constants. For ease of analysis, it will be assumed here that turbine can be modeled to have a single equivalent time constant. Fig. 3 shows the transfer function model of a steam turbine without reheat and with reheat unit respectively. Typically the time constant T1 lies in the range 0.22.5 s [79].


MODELING OF POWER SYSTEM
Action will be design of the Egyptian electrical grid in year 2024 in the form of transfer function block diagrams as a one area power system, Electricity produced divided in the Table 2 proportions indicated in the table and illustrated in Fig.1 [8].
Fig. 3. Thermal power plant steam turbine block diagram.
Where,
Tt : Thermal turbine time constant.
Tr : Thermal reheater time constant.
Kr: Coefficient of thermal reheat steam turbine.

HYDRAULIC MODEL
As for the requirement of hydroelectric power system modeling for load frequency control, speed governor and turbine should be modeled. The model development of different components of single area hydro system is explained as in Fig. 4 [10, 11].
The Mathematical model considered for nuclear unit tandemcompound turbines, one HP section and two LP section with HP reheater as shown in Fig. 4.14. The HP exhausts Moisture Separator Reheater (MSR) before entering the LP turbine. The MSR reduces the moisture content of the steam entering the LP section, thereby reducing the moisture and erosion rates. High pressure steam is used to reheat the HP exhaust as show in Fig. 7.
Where,
Fig.4. Hydraulic power plant block diagram.
TRg : Hydraulic speed governor rest time.
TRH : Hydraulic transient droop time constant.
TGH : Main servo time constant.
Tw : Hydraulic water time constant.
Rhy : Hydraulic speed governor regulation parameter.

GAS MODEL
As for the requirement of gas power system modeling for load frequency control, speed governor, valve positioner, fuel system and turbine should be modeled These are modeled as shown in Fig. 5 [12, 13].
Fig. 5. Gas power plant block diagram.
Fig. 7. Nuclear power plant turbine block diagram.
Where,
PCN : Change in speed changer setting of nuclear system.
Rn : Speed regulation of nuclear governor.
Tgn : Governor time constant of nuclear system.
T1 : HP nuclear turbine time constant.
Kh : Coefficient of HP reheat nuclear steam turbine. Kg1 : Coefficient of LP reheat nuclear steam turbine. Trh : LP nuclear turbine time constant.
E. Wind model
As for the requirement of wind power system modeling for load frequency control, speed governor, and turbine should be modeled. These are modeled as shown in Fig. 8 [14, 15].
Where,
X and Y : Gas speed governor lead and lag time constants.
a, b and c : Gas valve positioner constants.
TF : Gas fuel time constant.
TCR : Gas combustion reaction time delay.
TCD : Gas compressor discharge volume time constant.
Rg : Gas speed governor regulation parameter.
D. Nuclear model
As for the requirement of nuclear power system modeling for load frequency control, speed governor
Where,
Fig. 8. Wind power plant block diagram.
and turbine should be modeled. The transfer function block diagram model of governor is shown as in Fig. 6 [11].
Kgw : Wind speed governor gain.
Tgw : Wind speed governor time constant.
Ttw : Wind turbine time constant.
Kgw : Wind turbine gain.
Rw : Wind governor speed regulation.
F. Load and generator model
The generator dynamics is modeled by swing equation and given in equation (1):
= Pe (1)
Fig.6. Nuclear Power Plant Speed Governor block diagram.
For small perturbation the above relation can be represented by a block diagram as shown in Fig. 9 [7].
Fig. 9. Generator and load power system block diagram.
Where,
Fr : Nominal system frequency.
Pr : Rated power of the system MW.
: change in power angle.
Pm : Change in mechanical power.
Pe : Change in electrical power.
H : inertia constant of the generator MWs/MVA .
D : System damping load frequency characteristic pu MW/Hz.
Kps: Power system gain =1/D Hz/pu MW.
Tps : Power system time constant = 2H/(Fr*D) sec.
can put an initial vision or suppose block diagram model for the Egyptian electrical grid as a five area power system at 2024 as shown in Fig. 10 and Fig. 11 [16].
To apply this model will be classified our power system load generation to five parts for the five areas as follow:
Thermal area power system:
Fr = 50 Hz, Pr = 33000 MW, H = 6 MWs/MVA
Hydraulic area power system:
Fr = 50 Hz, Pr = 3600 MW, H = 3 MWs/MVA
Gas area power system:
Fr = 50 Hz, Pr = 18000 MW, H = 3 MWs/MVA
Nuclear area power system:
Fr = 50 Hz, Pr = 1200 MW, H = 6 MWs/MVA
Wind area power system:
Fr = 50 Hz, Pr = 4200 MW, H = 5 MWs/MVA
AREA 1
Thermal
The dynamic performance of LFC has been made based upon a linearized analysis. The simple LFC model does not consider the effects of the physical constraints. Although considering all dynamics in frequency control synthesis and analysis may be difficult and not useful, it should be noted that to get an accurate perception of the LFC subject it is necessary to consider the important inherent requirement and the basic constraints imposed by the physical system dynamics, and model them for the sake of performance evaluation [7].


THE BLOCK DIAGRAM MODEL FOR THE EGYPTIAN ELECTRICAL GRID AT 2024
From the previous study of the different types of energy sources to produce the electricity and how to simulate in a transfer function block diagram models, now we
and the change in the system frequency will be seen in the results section before and after PID controller.
VI. PID CONTROLLER
In this study PID controller is used as a supplementary control for LFC and AVR. The PID controllers are widely used in industry because of its clear functionality, easy implementation, applicability, robust performance and simplicity. The transfer function of PID controller is
() = + + (2)
Where () is the controller output and tracking error signals in sdomain. is the proportional gain, is the integral gain and is the derivative gain. In PID controller, proportional part reduces the error responses to disturbances, the integral part minimizes the steadystate error and the derivative term improves the transient response and stability of the system. To
AREA 5
Wind
AREA 4
Nuclear
AREA 2
Hydraulic
AREA 3
Gas
get the optimum performance from the considered system, the gains of the PID controller must be tuned in such a way that the close loop system produces desired result. The desired result should have minimum settling time, no overshoot and zero steady state error. These parameters of the PID controller can be designed by some methods like try and error, and ZieglerNichols method, that called conventional methods. The parameters of the PID controller can be
Fig. 10. Egyptian electrical grid as a multi area flow chart.

CASE STUDIES ON THE OUR MODEL
To complete study the dynamic stability and reliability on the system after adding the first NPP to the Egyptian grid, three cases of study. To do sensitivity analysis or study the effect of varying various parameters on the dynamic responses of the Egyptian electrical grid, 1%, 5% and 10% step load perturbation in the thermal model has been done as shown in Fig

PID controller has been added to the system in the two cases to overcome the effect of this disturbance,
designed using developed Genetic Algorithm (GA) [17, 18].

GENET1C ALGORITHM
Genetic Algorithms (GAs) are based on Darwins theory of natural selection and survival of the fittest. It is a heuristic optimization technique for the most optimal solution (fittest individual) from a global perspective but more importantly, it provides a mechanism by which solutions can be found to complex optimization problems firly quickly and reliably. The GA is an optimization and stochastic global search
technique based on the principles of genetics and natural selection. A GA allows a population composed of many individuals to evolve under specified selection rules to a state that maximizes the fitness (i.e., minimizes the cost function). The method was developed by John Holland (1975) over the course of the 1960s and 1970s and finally popularized by one of his student, David Goldberg (1989). Generally in GA, there are three basic operations like reproduction, crossover and mutation. A proposed GA technique flow chart that shows these operations see in Fig. 12.

Reproduction: It is a process in which a new generation of population is formed by selecting the fittest individuals in the current population. This is the survival of the fittest mechanism. Strings selected for reproduction are copied and entered to the mating pool.

Crossover: Mating is the creation of one or more offspring from the parents selected in the pairing process. The current members of the population limit the genetic makeup of the population. The most common form of mating involves two parents that produce two offspring. The new offspring may replace the weaker individuals in the population. With the cross over operation, GA is able to acquire more information with the generated individuals and the search space is thus extended and more complete.

Mutation: Random mutations alter a certain percentage of the bits in the list of chromosomes. Mutation is the second way a GA explore a cost surface. It can introduce traits not in the original population and keeps the GA from converging too fast before sampling the entire cost surface.
Fig. 11. Egyptian grid at 2024 as a multi area block diagram model with thermal disturbances.
GA based minimization approach to determine the values of , , has been developed in this paper. The parameter of PID controller has been tuned according to GA based performance indices [19, 20].


SIMULATION AND RESULTS
The simulation of LFC was done for two cases "1%, and 10%" step load perturbation in the thermal area, and will see the results in the following paragraphs.

The frequency response for 1% load perturbation
After five second 1% load perturbation happen on the thermal area in our model the frequency response for the five area power system Shown in Fig. 6.13 (a, b, c, d, e), where the change in frequency 'delta F' curve don't return to zero again in each area its mean system not stable. Five PID controllers have been added to the system one for each area to overcome the effect of this disturbance, and the change in the system frequency will be seen in Fig, 6.13 (a, b, c, d, e) after putting the PID controller. The controller parameters tuned by two methods conventional method and AI method "GA technique" to get the best results for the system stability, the PID controller parameters used shown in Table III.
Fig. 12. Genetic algorithm technique flow chart
PID no.
PID parameters
Conventional values
GA
values
PID1
1
0.58
0.72
1
1.60
1.61
1
4.11
2.53
PID2
2
0.25
0.25
2
1.60
1.58
2
0.012
0.03
PID3
3
0.20
0.20
3
1.66
1.66
3
0.61
0.61
PID4
4
1.34
1.34
4
1.50
1.50
4
0.92
0.92
PID5
5
1.16
1.16
5
1.55
1.56
5
0.90
1.28
PID no.
PID parameters
Conventional values
GA
values
PID1
1
0.58
0.72
1
1.60
1.61
1
4.11
2.53
PID2
2
0.25
0.25
2
1.60
1.58
2
0.012
0.03
PID3
3
0.20
0.20
3
1.66
1.66
3
0.61
0.61
PID4
4
1.34
1.34
4
1.50
1.50
4
0.92
0.92
PID5
5
1.16
1.16
5
1.55
1.56
5
0.90
1.28
TABLE III. PID CONTROLLERS' PARAMETERS FOR 1% THERMAL LOAD PERTURBATION.

Frequency response of thermal area.

Frequency response of hydraulic area.

Frequency response of gas area.

Frequency response of nuclear area.

Frequency response of wind area.
Fig. 13. Frequency response of five areas for 1% load perturbation on thermal area.
Table IV show the maximum over shot and settling time for each area in our model after 1% load perturbation on thermal area happen and adding PID controller in each area.
TABLE IV. FREQUENCY RESPONSE RESULTS FOR EACH AREA FOR 1% LOAD PERTURBATION
Area
Results
F
F (Hz)
Thermal
Max. over shot
0.0057
49.71 Hz
Settling time
10 sec
Hydraulic
Max. over shot
0.005
49.7 Hz
Settling time
10 sec
Gas
Max. over shot
0.0033
49.8 Hz
Settling time
10 sec
Nuclear
Max. over shot
0.0022
49.9 Hz
Settling time
10 sec
Wind
Max. over shot
0.0025
49.87 Hz
Settling time
10 ec


The frequency response for 10% load perturbation


After five second 10% load perturbation happen on the thermal area in our model the frequency response for the five area power system Shown in Fig. 6.14 (a, b, c, d, e), where the change in frequency 'delta F' curve don't return to zero again in each area its mean system not stable. Five PID controllers have been added to the system one for each area to overcome the effect of this disturbance, and the change in the system frequency willbe seen in Fig, 6.14 (a, b, c, d, e) after putting the PID controller. The controller parameters tuned by two methods conventional method and AI method "GA technique" to get the best results for the system stability, the PID controller parameters used shown in Table VI.
TABLE VI. PID CONTROLLER'S PARAMETERS FOR 10% THERMAL LOAD PERTURBATION.
PID no.
PID
parameters
Conventional values
GA
values
PID1
1
1.95
6.95
1
3.95
8.47
1
6.45
19.45
PID2
2
0.21
0.12
2
1.58
1.42
2
0.012
0.02
PID3
3
0.20
1.59
3
1.66
1.56
3
0.61
0.11
PID4
4
1.34
1.08
4
1.50
0.91
4
0.92
0.30
PID5
5
1.16
1.37
5
1.56
1.53
5
0.90
0.91

Frequency response of thermal area.

Frequency response of hydraulic area.

Frequency response of gas area.

Frequency response of nuclear area.

Frequency response of wind area.
Fig. 14. Frequency response of five areas for 10% load perturbation on thermal area.
Table VII show the maximum over shot and settling time for each area in our model after 10% load perturbation on thermal area happen and adding PID controller in each area.
TABLE VII. FREQUENCY RESPONSE RESULTS FOR EACH AREA FOR 10% LOAD PERTURBATION.
Area
Results
F
F (Hz)
Thermal
Max. over shot
0.018
49.1 Hz
Settling time
15 sec
Hydraulic
Max. over shot
0.008
49.6 Hz
Settling time
15 sec
Gas
Max. over shot
0.005
49.75 Hz
Settling time
10 sec
Nuclear
Max. over shot
0.004
49.8 Hz
Settling time
15 sec
Wind
Max. over shot
0.005
49.75 Hz
Settling time
15 sec

CONCLUSION

After finish this analysis by make different load perturbation '1%, and 10%' on the thermal area in our model, it's clear that as increasing in the load perturbation as increasing in the maximum over shot and settling time for all areas of our model, also the PID controllers remain the system stay stable after that disturbances because the maximum overshot frequency and the settling time do not exceed "1 Hz" and "15 sec" for each area of our model and it is in the allowable range.
It's clear that when GA technique used for tuned PID controllers increase the accuracy of the frequency response results than the conventional tuning methods. Moreover, GA technique is faster than the conventional method and highly complex, dynamic behavior and nonlinearity for power systems, together with their almost continuously time varying nature, have posed a great challenge to power system control engineers for decades.
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