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Real Time Voltage Control using Genetic Algorithm
P. Thirusenthil kumaran, C. Kamalakannan
Department of EEE, Rajalakshmi Engineering College, Chennai, India
Abstract— An algorithm for control action selection for bus voltage and generator reactive power in electricity supply system is presented in this paper. To reduce the number of control actions, genetic algorithm (GA) with linear load flow equations and selection of participating controls are combined. Calculation time of GA is small and well suited for real time application in power system.
Keywords—Genetic algorithm (GA), reactive power control, voltage control.
I. INTRODUCTION
Normally in power system network parameters like bus voltage and reactive power should be maintained within the specified limits. When the operating limits are violated, control action is taken to correct this emergency state [1]. Voltage deviations are eliminated by secondary voltage control (SVC). The task of automatic SVC reduces to minimize the risk of reaching an emergency state which cannot be achieved by manual control. But in systems which don’t have automatic SVC, the operator in the dispatch center performs this task manually. The life of the electricity supply system is based on the talent and experience of the operator.
Without automatic SVC bus voltage and generator reactive power constraint violations are eliminated with control action selection is presented in this paper. Normally, bus voltages are allowed to deviate up to +5% of operational constraints around the nominal value. System instability occurs if the bus voltage values are further deviated. In such cases, necessary control action is to be taken. Line loads are disconnected automatically by under voltage protection. In the past many methods are developed for control action selection. An important problem that occurs in the past methods is that the calculations treat all variables are continuous. The solution for this problem is to round off the variables to a near discrete value. This leads to inadequate solutions [2]. Another problem is that the solutions require large number of actions.
Genetic algorithm (GA) brings solution to the above mentioned problems. GA has the ability to deal with continuous and discrete variables. It also has the ability to deal with wide range of optimization objectives.
II. SYSTEMMODELING
Using the following energy balance equation in every node k of a power system, the theoretical background of voltage control and reactive power control problem will be presented.
APK = PGK - PLK
(1) AQK = QGK - QLK
(2) Where
APK, AQK, active and reactive power energy balance of bus k;
PGK, QGK, generated active and reactive power at bus k;
PLK, QLK, active and reactive power of load at bus k;
E
k, E
j, voltage amplitudes at buses k and j;g
kj, b
kj, active and reactive parts of line admittance between buses k and j;k, j, voltage phase angles at bus k and j;
n number of buses.
To obtain the solution of load flow problem, the variables and constants mentioned above are classified as:
state variables (reactive power of generator and voltage phase angle, load voltage amplitude and phase angle);
control variables (active power of generator and voltage amplitude);
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disturbance variables (active and reactive power of load);
constants (admittance of line and transformer ratio).
In general for all buses the energy balance is represented by vector f. When ( , , , ) = , load flow solution is obtained where , are constants. By adjusting generator voltages, transformer ration and switching shunt devices. This indicates that the transformer ratio and reactive power of load are considered as controlled quantities. The aim of emergency control is to find a proper combination ( , ) such that
( , , , )= (3)
while enforcing the constraints to variables like generator loads, controlled quantities, bus voltage and line currents together represented by
( , , , )< (4)
In general, the number of possible solutions is large with the given various combinations of , , and an optimal choice of control actions is possible. In case of optimization problem, the equations become
Optimize ( , , , ) subject to
( , , , )=
( , , , )< (5)
III. SOLUTIONMETHODS
Linear programming [3] was the first published analytical method based on classic optimization methods in which load flow problem is presented by linear approximation of system equations around an initial solution such as
Δ =S (Δ ,Δ ,Δ ). (6)
where S is the sensitivity matrix which indicates the sensitivity of state variables to changes of controls. For n bus system, m generators, qVAr devices and t tap changing transformers, the model can be written as,
(7) where,
ΔE1,…..,ΔEm generator voltage amplitude changes;
ΔQG1,...,ΔQGm generator reactive power changes;
ΔEm+1,...ΔEn load bus voltage amplitude changes;
ΔQL1,....,ΔQLq reactive load changes;
ΔTap1,...,ΔTapt transformer taps changes;
S1 ….S6 sub matrices of sensitivity matrix S.
There are some restrictions in applying linear programming to solve equation (5).
(i) Since the variables obtained are continuous it must be round off to their nearest discrete values.
(ii) The number of control actions and calculation time is more.
For optimization problem, previous publications shows a wide range of objective functions like cost minimization of control action [4], control deviation from initial operating point [4]. Use of the number of controls and time for control actions to complete [4].
To save cost and to eliminate constraint violations, one or more of the control actions in a set are needed. Less number of control actions is suitable for manual control actions. Mixed integer programming [5] deals with both discrete and continuous variables and applied to voltage control problem. But this method involves long calculation time. Based on the experience of the supervisors,
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expert systems have been developed in recent years [6], [7]. But it does not optimize any objective function. Linearity and continuity of objective function is not required for GA. Hence GA is more effective in dealing with discrete control devices and with objectives. For voltage and reactive power problem, many GA applications exist for planning and optimal allocation of reactive power sources [8] and also for voltage security enhancement by preventive control [9]. In many publications, optimal power flow (OPF) problem also been involved [10], [11]. But in OPF solution, control actions leads to loss or cost optimization.
The main aim of this paper is to eliminate constraint violations. Through a preselection of control devices the number of control actions are minimized is included in the paper [11], [12]. The continuation of paper published [13] with improvements in algorithm and results are presented in the paper.
IV. ALGORITHM
In case of immediate control problem, for improving the calculation time of GA the first step is the proper selection of control devices. In power system many control devices are available in which most of them have only a marginal influence on the reactive loads of generator and distributed bus voltages. The algorithm here gives the advantages of both the model of linear system and GA.
(i) Sensitivity coefficients are calculated for all control devices.
(ii) To minimize the constraint violations based on the ability of control devices, first select the set of number of controls involved in the next calculation stage.
(iii) To find a proper set of control action GA is used. The number of controls used and the remaining constraint violations determines the fitness of a solution.
No
Yes
No Yes
Figure 1 Flowchart of Genetic Algorithm
This algorithm shows the ability of GA to deal with discrete variables and noncontinuous objective function. The flowchart of GA shown in figure 1 presents the calculation scheme. Three steps are involved:
Step (i): For a initial values of controlling devices like generator voltages and transformer ratio, sensitivity coefficients are calculated which has the influence of all controls devices on load bus voltage and reactive power of generator.
Step (ii): With the operation range of controls, sensitivity coefficients give the fast estimation of the improvement of bus voltages and reactive power of generator. For each out of limit variable k how much the constraint violation k - gk can be reduced is
Start
Check load flow for violation of bus voltage &
reaction power
If violation exit
Calculate the sensitivity matrix of controls
Choose first set of controls
Choose initial population of solutions For all populated strings find the remaining
violations
All constraint violation solved
End
With genetic operator create new population End
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calculated. This makes to rank the controls based on the decreasing value of their effectiveness and make a selection of set of candidates to eliminate the constraint violation k. Based on the ranking, the most effective controls for violation of constraints,
k - gk are first selected. For each individual out of limit variable, to find the set of controller candidates this rule is applied.
If more constraint violations exist, the control is effective in decreasing constraint violation c while increasing constraint violation d (c d). It is seen that few control actions cause some new constraint violations. In such case, the set of candidate controls for each violated constraint k > gk is enlarged so that it eliminates twice the value of constraint violation k - gk.
Step (iii): GA finds the control devices which are included in are to be activated. In every generation this algorithm is created with many sets of possible control actions Δ and their fitness is checked. Control actions are represented as binary values and continuous variables are represented by discrete values. The function of changes in load flow is the fitness of a set of controls. For each string that represent the set of control actions Δ , the approximated resulting system state
’= +S (8) and new constraint violations are
( 0 + S , + ) > ) (9)
Here and represent the previous values of state variables and control. Fitness f of a solution is given as,
f = P – n1 - n2 (10) where the number of violated constraints are represented by k = 1,…..,m and the set of controls included in is represented by j = 1,…..,p. Also Xj = 0 for Δxj = 0 and Xj = 1 for Δxj 0 .
The value of constant p is chosen large enough to get a positive value for the fitness function. In equation (10), second term represents the penalty for violation of constraints and third term represents the penalty added to reduce the number of controls used.
n1 and n2 are the weight factors which is constant. The value of n1 chosen to be large compared to n2 so as to find the set of control actions which removes all constraint violations.
If the control problem solution is identified the constraint violations will be reduced to zero in the first generations created by GA.
Since the main aim of the process is reached the algorithm may be stopped at this stage. This process can be continued and based on the last term of fitness which indicates the number of controls used, the population of solutions will develop. Constraints in GA avoid unacceptable changes of control variables.
Random selection of initial population of solutions is done. Efficiency is improved with the proper selection of initial population.
Solution containing less number of control actions is preferred and a part of initial population is selected to present the solution of one control action.
V. SIMULATIONRESULTS 5.1 CASE STUDIES FOR IEEE 14 BUS SYSTEM:
The simulation of the proposed Genetic Algorithm was conducted using MATLAB software. Real time voltage control using Genetic Algorithm has been carried out for IEEE 14 bus system. Figure 2 shows the one-line diagram of IEEE 14 bus system. Bus data and Line data for IEEE 14 bus system is given in table 1 and table 2. Algorithms are coded using Matlab programming. Load flow studies are carried out for the system and real power loss before correction and after correction is found out. It is also seen that the number of control actions is also minimized. The bus voltage before correction and after correction is also carried out.
Figure 2 ONE-LINE DIAGRAM OF IEEE 14 BUS SYSTEM:
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Bus Data
Table 1 below displays the bus data for IEEE 14 bus system. Column 1 of Table 1 outlines the bus number and column 2 contains the bus code. Columns 3 and 4 show the voltage magnitudes in p.u. and phase angle in degrees. Columns 5 and 6 outline the size of the active and reactive loads connected to the corresponding buses in MW and MVAr. Columns 7 through to 10 are MW, MVAr, minimum MVAr and maximum MVA of generation, in that order. The last column is the injected MVAr of capacitance into the system. The bus code entered in column 2 is used for identifying load, voltage-controlled, and slack buses as outlined below;
1 – This code is used for the slack bus.
0 – This code is used for load buses.
2 – This code is used for the voltage controlled buses.
Line Data
Table 2 below displays the line data for IEEE 14 bus system. Columns 1 and 2 of Table 2 outline the corresponding line bus numbers. Columns 3 through to 5 contain the line resistance, reactance, and one-half of the total line charging susceptance in per unit on the MVA base of 100MVA. The last column details the transformer tap setting. The bus and line data was structured in such a way so that the MATLAB load flow program could be used for the simulation.
TABLE 1 BUS DATA FOR IEEE 14 BUS SYSTEM:
TABLE 2 LINE DATA FOR IEEE 14 BUS SYSTEM:
Bus nl
Bus nr
R p.u
X p.u
½ B p.u
Line Code or Tap Setting
1 2 0.01938 0.05917 0.0264 1
2 3 0.04669 0.19797 0.0219 1
2 6 0.05811 0.17632 0.0187 1
1 7 0.05403 0.22304 0.0246 1
2 7 0.05695 0.17388 0.0170 1
3 6 0.06701 0.17103 0.0173 1
6 7 0.01335 0.04211 0.0064 1
7 4 0.0 0.25202 0.0 0.932 6 8 0.0 0.20912 0.0 0.978 8 5 0.0 0.17615 0.0 1
6 9 0.0 0.55618 0.0 0.969 8 9 0.0 0.11001 0.0 1
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9 10 0.03181 0.08450 0.0 1
4 11 0.09498 0.19890 0.0 1
4 12 0.12291 0.25581 0.0 1
4 13 0.06615 0.13027 0.0 1
9 14 0.12711 0.27038 0.0 1
10 11 0.08205 0.19207 0.0 1
12 13 0.22092 0.19988 0.0 1
13 14 0.17093 0.34902 0.0 1
5.2 RESULTS FOR IEEE 14 BUS SYSTEM:
Due to the stochastic nature of GA, results may change slightly for different calculation runs. The results for a single calculation run is shown below.
0 100 200 300 400 500 600 700 800 900 1000 0
2 4 6 8 10 12 14 16 18 20
Generations
Fitness Value
Figure 3 Average Fitness of the Population of Solution
0 100 200 300 400 500 600 700 800 900 1000 0
2 4 6 8 10 12 14
Generations
Number of Control Actions
Figure 4 Number of Controls used in Best Solution
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Figure 5 Bus Voltages Before and After Execution of Control Actions
From figure 3, during the first generations, the average fitness of the population of solutions increased rapidly indicating a decrease of constraint violations. Normalized fitness values are shown here and a value of 18 presents the theoretical case that no constraints are violated and the number of control actions is zero. In the population the best fitness solution increased considerably faster. The number of controls used in this solution was 14, as shown in figure 4. Further generations produces solution with less control actions, a sufficient solution was found based on eleven controls. A population size of 20 was applied. Of the initial population, 20 strings were selected as a single step up or step down of the control devices. Crossover rate was 0.800 and mutation rate was 0.04. Figure 5 Bus voltages before and after the execution of control actions. It is seen that the final values of all voltages are within limits (5% margin around nominal value, indicated by dashed line).
Using Newton–Raphson load flow calculation, the control actions found were checked. These results show that no constraint violations (0.95 and 1.05 p.u.) exist after the control actions application. It is also seen that reactive power of all generators was brought within the limits (not shown in graphs). Due to the absence of control devices at the network ends, the control actions effect on buses with correct voltage in the system center cannot be avoided but does not causes any new constraint violations.
Here minimum possible number of control actions that is eleven controls are used with an overall computation time of 19 s.
According to the requirement of VAR source in each bus, the compensation will be carried by the capacitor as shown in the following table 1. Table 2 shows the real power loss before and after corrective control and table 3 shows the bus voltage before and after corrective action.
Table 3 Requirement of VAR sources in each bus Bus Requirement of VAR Sources in p.u
1 0.0300
2 0
3 0.0400
4 0.0300
5 0.0400
6 0.0900
7 0.0500
8 0.0500
9 0
10 0.0900
11 0
12 0.0100
13 0.0400
14 0.0600
Table 4 Real Power Loss before and After Correction
Table 5 Bus Voltage Before and After Corrective Action Bus Bus Voltage Before
Correction in p.u
Bus Voltage After Correction in p.u
1 1.0600 1.0600
Real Power Loss Before Correction p.u
Real Power Loss After Correction p.u
0.193229 0.185634
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2 0.9950 0.9950
3 0.9600 0.9600
4 1.0200 1.0200
5 1.0400 1.0400
6 0.9471 0.9558
7 0.9586 0.9655
8 0.9696 0.9837
9 0.9312 0.9511
10 0.9327 0.9560
11 0.9660 0.9779
12 0.9991 1.0052
13 0.9879 0.9973
14 0.9357 0.9610
VI. CONCLUSION
The bus voltage was brought within the limits (0.95 p.u. and 1.05 p.u.). Hence, the proposed genetic algorithm is capable of determining the near global solution. From table 4 and table 5, it is seen that genetic algorithm results in improved voltage profile and greater power loss reductions. From figure 4, the number of control actions is minimized. Based on the requirement of VAR sources in each bus shown in table 1, system losses are reduced and results in greater economic savings. As a result, the proposed Genetic Algorithm for capacitor placement escapes local optima and converges to the near global solution.
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