- Email: [email protected]
Coupled Active and Reactive Power Dispatch Using Genetic Algorithms
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
14th World Congress ofIFAC
0-7c-09-1
Copyright (~) 1999 )FAC [4th Triennial World Congress, Beijing. P.R. China
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING GENETIC ALGORITHMS FLi
CHPeh
RDunn
Email: [Jj{@Jm.,ttutI2JJh Fax: (+44) 1225826305 Department ofElectronic & Electrical Engineering University of Bath, Claverton Down, Bath BA2 7AY. UK
ABSTRACT: The paper proposes a genetic algorithm (GA) based approach to solve the combined active and reactive power dispatch (CARD) problem, the aim of which is to minimise the fuel costs and maximise the security measure of power systems. The CARD problem is represented by a weighted sum of five objectives, namely fuel cost, reactive reserve margin, the load voltages, higher system load and avoidance of voltage collapse. The proposed approach utilises a Genetic Algorithm to simultaneously modiiY active and reactive power, outputs of compensating devices, transformer tap setting, and bus voltage levels, with the Newton-Raphson load flow algorithm embedded inside the GA performing the power f10w calculation. The effectiveness and simplicity of the approach to the CARD problem is verified on a 6-bus electric power system. Copynght © 1999 IFA C Keywords: Genetic Algorithms, Power Dispatch, Newton-Raphson load flow, Multi-objective optimisation
1. INTRODUCTION The economic operation of a power system is required to meet the system demand, whilst maintaining system security, at the minimum achievable cost. This objective can be further detailed as minimising the fuel costs and the system losses, and maximise the security measure of power systems in terms of limits on active and reactive power, outputs of compensating devices, transfonner tap setting, and bus voltage levels. The economic operation of slIch a system mainly consists of two aspects: active power regulation to minimise the fuel cost and reactive power dispatch to minimise network power losses and to maintain system security. Based on the fact that real and reactive power is only loosely coupled, and the large number of control variables involved in the solution to the problem, a common practice is to decouple the problem into the two separate P and Q sub-problems (Lee, et aI., 1985), and solve them sequentially.
Despite the simplicity having achieved, such practice cannot account for the impact of the reaJ power dispatch on voltage security. Nor can it easily handle the constraints which are dependent on hoth active and reactive powers, such as line flows and generator capability chart limitations. To better handle constraints, as well as to account for lhe interdependence of the real and reactive power, the fully coupled CARD problem has been approached by Chebbo and Irving with a Linear Algorithm (Chebbo, I 995a; 1995b), where five objectives have been optimised simultaneously, namely generation fuel cost, reactive power reserve margin, load voltage, higher system load and voltage collapse. Despite the success, the technique requires linearisation of the objective functions, and involves extensive iterations between linear programming and a Newton-Raphson load flow algorithm, hence overall computational effort can be high. In
7460
Copyright 1999 IF AC
ISBN: 008 0432484
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
addition, the solution result thus obtained is unlikely to be optimal. This paper investigates the application of Genetic Algorithms (GAs) for the CARD problem. GAs are selected as the solution methods due to their efficacy and efficiency in the search for the optimum in a multi-modal. multi-objective, highly non-linearly, and heavily constrained search space. This ability of GAs in power system optimisations has been verified by a number of researchers (Walters, and Sheble, 1993; Li, and Morgan, 1995). By using GAs to solve the CARD problem, the objectives are not restricted by linearity, but can come at any form, and therefore provides a more realistic problem domain. By trying various combination of the control variables, GAs cast a net across the entire search space, and therefore have more chance to attain a near global optimum operating point. Moreover, the inequality constraints impose on control variables, such as active and reactive power limits, ramping rate constraints bear no extra burden but can be handled by a GA inherently, The effectiveness and simplicity of GAs for the CARD problem are verified on a 6-bus system in this paper. The rest of the paper is organised as folJows: Section 2 details the mathematical formulation of the CARD problem. and Section 3 gives a brief introduction of GAs. In Section 4, the detailed procedure of how the GA is adopted to solve the CARD problem is outlined. Section 5 gives the information on the test system and discusses the test results. Finally, the conclusions arc summarised in Section 6.
2.
THE PROBLEM FORMULA nON
Mathematically, the CARD problem can bc well represented by the following five objectives fOf achieving the goal of minimising the fuel cost, and improving other system parameters: (1) Minimisation of generation fuel costs The cost of production "\lriJj be computed as the sum of the product of the power generated and the cost of production of that generator: NSTEP
FI
~
~,
NGA
of reactive power reserve margins In maximising the reactive power reserve margin, it is necessary to distribute the reserve power anlOng all the generators and SVC in proportion to ratjngs:
t:,
(3) Maximisation of the load voltages This is achieved by maximising the sum of the load voltages:
j= l
iEUJN
(4) Maximisation of bigher system load The higher system load is maintained by maximise the system load increment 0-,.; NCONTG
L "
+ J
J
a", ~1
(5) Avoidance of voltage collapse The voltage collapse can be minimised by maximising the voltage collapse proximity indicator lex for the whole system: NCONTO
1.:
K _ 1
where: NSTEP:
number of total time intervals number of contingency cases set of load voltages in the system number of generators number of controllable V AR sources
NCONTG!
LPN: NGP! NG:
These five objectives are subject to constraints imposed on both active and reactive power. Constraints specific to active power include: • generator active power upper and lower limits • generator active power reserve upper and lower limits • system active power reserve constraint • active power balance constraint Also, the following constraints are specific for reactive power: • generator reactive upper and Jower limits • network voltage limits • tap changer ranges • reactive power balance constraint • constfaint for avoiding voltage collapse • constraint for improving ability of system to maintain higher system load
j
.E, fiPi)
(2) Maximisation
F l
14th World Congress oflFAC
(Q Q
.D'
Constraints affect both active and reactive power are: • generator capability chart limits • branch current flow limits The problem of CARD for economic and secure operation of a power system is the weighted sum of tIle five objectives subject to constraints on both active and reactive power. Clearly, the problem is a multi-modal, multi-objectjve, highly constrained
i
7461
Copyright 1999 IFAC
ISBN: 0 08 043248 4
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
opnmlsation problem. Section 4 details how the problem is tackled by a simple genetic algorithm.
3.
AN INTRODUCTION TO GENETIC ALGORITHMS
14th World Congress ofIFAC
and two reactive power sources. The total active load for the system is 1,35MW and the reactive requirement is O.36MVARs. The detailed line and bus data are given in (Mamandur, and Chenoweth, 1981).
GAs are search algorithms based on the mechanics of natural genetics and natural selection (Goldberg, 19&9). They combine an artificial survival of the fittest concept with genetic operators abstracted from nature to fonn a surprisingly robust mechanism that is suitable for a variety of optimisation problems. GAs use stochastic operators instead of detenninistic rules to search a solution . GAs hop randomly from points to points, and have more chance of escaping local optimum and arriving at the global one. In addition, GA's search for the optimum does not depend on the linearity of the objectives, but al10w non-linearity and discontinuity to appear in the scarch space. Finally, the technique can inherent.ly handle inequality constraints imposed on the control variables.
4. GENETIC APPROACH TO THE CARD PROBLEM ON A SIX BUS SYSTEM
A genetic search for the optimum starts with randomly generating a group (population) of solutions to the CARD problem G(O), and thereafter: (1)
(2)
(3)
(4)
(5)
Each solution undergoes a Newton-Raphson Load Flow calculation Evaluation of an individual solution's fitness according to the load flow results, such as fuel costs, reactive reserve margin, and voltage profile for each bus. Select those solutions which have above a"'erage finless value, and reproduce them to form a temporary mating pool G(t) Apply crossover and mutation operators to those solutions O'(t) If the stop criterion is satisfied, then stop, otherwise t==t+l and Go back to (1)
The stopping rule can be the pre-defined maximum number of iteration (generation), or when the change of the best fitness is sufficiently small over a number of 2 generations. A flow chart for the GA implementation procedure is shown in Figure 1.
5.
THE TEST SYSTEM AND THE TEST RESULTS
The test system is the Ward and Hale 6-bus system, shown in Figure 2. The test network has 6 buses, 2 power generators, 7 branches, 2 line transfonners
SS . D·j J J.O
1, ,=-3.&6
)O . O+-j l S.(l
2
~J~
Figure 2 The Basic System State Of The Ward And Hale 6-Bus Power System. The pre-processing of GA includes mapping the five objectives and constraints into a single fitness function, which is the only measure to guide the search towards the optimum; choosing control variables, which a GA can manipulate to achicve the least cost and the most security. In this paper, 9 control variables are selected for the GA to work with, they are: generator output level at bus 2 , SVCs at buses 4 & 6, Transfonner tapping settings at buses 1 & 2, Voltage levels at buses 1 & 2, System Load Increment, and Voltage Collapse Proximity Indicator. Each control variable has its own range of values, its maximum value, its minimum value, its lower limits and upper limits. Each of them is encoded in a 6 bits string length, and concatenated together. Figure 3 shows a solution encoded in a binary string fonnat consisting values for 9 control variables. Two CARD problems havc bcen examined. The first is the static CARD problem, where the total period of interest is just one time interval. The second is the dynamic CARD problem, where the problem is over 5 time intervals. The difference between the two problems not only lies in the different time durations, but also in the additional Ramping Rate constraint on the dynamic CARD problem, which restricts the search space severely. The solution rcsults for the static and dynamic CARD problems are summarised in Table 1 and Table 2 respectively, where different generations and populations are used to compare the end results and the associated computational expenses.
7462
Copyright 1999 IF AC
ISBN: 0 08 043248 4
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
It is clearly seen from the tables that the larger the population and generations, the better the result are. The computation time rises linearly with the number of generations and population size. With merely 10 population members and 10 generations, the GA obtain the results for the CARD problem with only 0.8 seconds for the 6-bus system. This is very encouraging for the technique to be applied to medium sized power systems. Although the results are better for the larger population and generations, they do not justiiY the extra computational effort needed. When comparing with conventional techniques, in theolY, GA solutions should offer more advantages. This is because they simultaneously manipulate control variables so that over the period of trial and error, GA is able to obtain a good overall solution . Furthennore, GA processes give optimal active and reactive power dispatch according to the past cost, and constraint "iolation, they learn fTOm the past experience and manipulate the variables so as not to fall into false optimum, or falling beyond the constrained space. Because of the learning ability, GAs should be able to give better results for the optimal load flow within the same computational effort as was conventional methods.
6.
CONCLUSION
The paper has proposed a genetic algorithm based method to solve the optimal power flow problem where the active and reactive power are fully coupled. TIle beauty of the genetic approach when applied to this problem is that the GA simultaneously manipulated various control variable, such as real power output, transfonner tape settings, SVC settings, bus voltage levels to attain an the overall better solution for the least operation cost and secure operation, while most of the conventional techniques nonnally change one control variable at a time. Five objectives have been used to represent the CARD problem in this study. These are fuel
14th World Congress ofIFAC
cost, reactive reserve margin, the load voltages, higher system load and avoidance of voltage collapse. The solution speed of 0.8 seconds for a 6bus system makes it feasible to apply the technique to medium sized systems. Future work wiII be directed to further scaling up the g enetic based optimal power flow for larger systems, and compare the results with that of Linear Programming.
REFERENCES Chebbo, A.M . and M.R. Irving (1995a). Combined Active and Reactive Disapatch: Part I . lEE Proc. Generation, Transmission and Distribution, VoI. 142, no 4, pp 393-400. Chebbo, A.M., M.R. Irving and N.H. Dandachi (l995b). Combined Active and Reactive Despatch, Part2: Test Results. lEE Proc. Generation, Transmission and Dis tribution, Vol. 142, no 4, pp 401-405.
Goldberg, D.E. (1989). Genetic Algorithms in Search Optimisation and Learning. Addison Wesley. Lee, K.Y. , YM Park and J.L. Ortiz (1985). A United Approach to Optimal Real and Reactive Power Dispatch, IEEE Transaction on Power Apparatus and Systems, Vol PAS-I04, NoS, pp 1147-1153. Li , F. and R. Morgan (1995). Genetic Approach to Economic - Environmental Dispatch. International Federation of Automatic Control - IFAC'95, Cancun, Mexico, pp 169-174. Mamandur, K .R.C. and R.D Chenoweth (1981).
Optimal Control of Reactive Power Flow for Improvements in Voltage Profiles and for Real Power Loss Minimisation. IEEE Transaction on Power Apparatus and Systems, Vol PAS-100, No 7 , pp 3J85-3193.
Waiters, D.e. and B. ShebJe (1993 ). Genetic Algoritlun Solution of Economic Dispatch with Valve Point Loading. IEEE Transaction on Power Systems, VoJ. 8, No 3, pp 1325-1332, 1993 .
7463
Copyright 1999 IF AC
ISBN: 0 08 043248 4
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
14th World Congress ofIFAC
population of initial solutions
each undergoes a Newton Raphson load
evaluate fitness value for each solution
genetic modification of control variables
Figure 1. The flow chart ofintegrated GA and NR
[ P2 1 SVC4 1 SVC61 Tl 1 T2 1 VI I V2 I a. ! le [01001011 01001/100011/101100100 11001010 101/01111011100111111000]
Figure 3.
The CARD solution representation in a binal)' string format
T a ble 1 The so uUon resut tstoth e CARD pro bI em over single tIme mterval
Population Size Generations
10
Cost lO
1.4368 1.4374 1.4106 1.4117
20 50 100
50
30
Time
Time (s)
Cost
0.88 1.81 4.39 8.79
1.4262 1.4165 1.4086 1.4025
Cost
80
Time
Cost
Time
1.3848
7 .03 14.06 35.11 69.45
(sl
(s)
(s)
2.63 5.27
1.3937 1.4089 1.4015 1.4022
13.13 26.04
3.96 8.84 21.87 43.41
1.4031 1.3954 1.4017
. T a ble 2 Th e so uUon resu ts to the CARD pro bI em over 5 hme mterv a1 s Population Size Generations
10 30 50 100
30
10
50
Cost
Time
Cost
Cost
Time
7.6165 7 .5545 7 .5721 7.5242
(s) 3.95 11.81 11.86 39.39
Time (s)
7.5745 7.5545 7.5418 7.5169
11.81
7.5775 7 .5567 7.5086 7.5132
(s) 19.72 59.17 99.56 197.03
35.49 6 0.00 118.24
7464
Copyright 1999 IF AC
ISBN: 0 08 043248 4
14th World Congress ofIFAC
0-7c-09-1
Copyright (~) 1999 )FAC [4th Triennial World Congress, Beijing. P.R. China
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING GENETIC ALGORITHMS FLi
CHPeh
RDunn
Email: [Jj{@Jm.,ttutI2JJh Fax: (+44) 1225826305 Department ofElectronic & Electrical Engineering University of Bath, Claverton Down, Bath BA2 7AY. UK
ABSTRACT: The paper proposes a genetic algorithm (GA) based approach to solve the combined active and reactive power dispatch (CARD) problem, the aim of which is to minimise the fuel costs and maximise the security measure of power systems. The CARD problem is represented by a weighted sum of five objectives, namely fuel cost, reactive reserve margin, the load voltages, higher system load and avoidance of voltage collapse. The proposed approach utilises a Genetic Algorithm to simultaneously modiiY active and reactive power, outputs of compensating devices, transformer tap setting, and bus voltage levels, with the Newton-Raphson load flow algorithm embedded inside the GA performing the power f10w calculation. The effectiveness and simplicity of the approach to the CARD problem is verified on a 6-bus electric power system. Copynght © 1999 IFA C Keywords: Genetic Algorithms, Power Dispatch, Newton-Raphson load flow, Multi-objective optimisation
1. INTRODUCTION The economic operation of a power system is required to meet the system demand, whilst maintaining system security, at the minimum achievable cost. This objective can be further detailed as minimising the fuel costs and the system losses, and maximise the security measure of power systems in terms of limits on active and reactive power, outputs of compensating devices, transfonner tap setting, and bus voltage levels. The economic operation of slIch a system mainly consists of two aspects: active power regulation to minimise the fuel cost and reactive power dispatch to minimise network power losses and to maintain system security. Based on the fact that real and reactive power is only loosely coupled, and the large number of control variables involved in the solution to the problem, a common practice is to decouple the problem into the two separate P and Q sub-problems (Lee, et aI., 1985), and solve them sequentially.
Despite the simplicity having achieved, such practice cannot account for the impact of the reaJ power dispatch on voltage security. Nor can it easily handle the constraints which are dependent on hoth active and reactive powers, such as line flows and generator capability chart limitations. To better handle constraints, as well as to account for lhe interdependence of the real and reactive power, the fully coupled CARD problem has been approached by Chebbo and Irving with a Linear Algorithm (Chebbo, I 995a; 1995b), where five objectives have been optimised simultaneously, namely generation fuel cost, reactive power reserve margin, load voltage, higher system load and voltage collapse. Despite the success, the technique requires linearisation of the objective functions, and involves extensive iterations between linear programming and a Newton-Raphson load flow algorithm, hence overall computational effort can be high. In
7460
Copyright 1999 IF AC
ISBN: 008 0432484
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
addition, the solution result thus obtained is unlikely to be optimal. This paper investigates the application of Genetic Algorithms (GAs) for the CARD problem. GAs are selected as the solution methods due to their efficacy and efficiency in the search for the optimum in a multi-modal. multi-objective, highly non-linearly, and heavily constrained search space. This ability of GAs in power system optimisations has been verified by a number of researchers (Walters, and Sheble, 1993; Li, and Morgan, 1995). By using GAs to solve the CARD problem, the objectives are not restricted by linearity, but can come at any form, and therefore provides a more realistic problem domain. By trying various combination of the control variables, GAs cast a net across the entire search space, and therefore have more chance to attain a near global optimum operating point. Moreover, the inequality constraints impose on control variables, such as active and reactive power limits, ramping rate constraints bear no extra burden but can be handled by a GA inherently, The effectiveness and simplicity of GAs for the CARD problem are verified on a 6-bus system in this paper. The rest of the paper is organised as folJows: Section 2 details the mathematical formulation of the CARD problem. and Section 3 gives a brief introduction of GAs. In Section 4, the detailed procedure of how the GA is adopted to solve the CARD problem is outlined. Section 5 gives the information on the test system and discusses the test results. Finally, the conclusions arc summarised in Section 6.
2.
THE PROBLEM FORMULA nON
Mathematically, the CARD problem can bc well represented by the following five objectives fOf achieving the goal of minimising the fuel cost, and improving other system parameters: (1) Minimisation of generation fuel costs The cost of production "\lriJj be computed as the sum of the product of the power generated and the cost of production of that generator: NSTEP
FI
~
~,
NGA
of reactive power reserve margins In maximising the reactive power reserve margin, it is necessary to distribute the reserve power anlOng all the generators and SVC in proportion to ratjngs:
t:,
(3) Maximisation of the load voltages This is achieved by maximising the sum of the load voltages:
j= l
iEUJN
(4) Maximisation of bigher system load The higher system load is maintained by maximise the system load increment 0-,.; NCONTG
L "
+ J
J
a", ~1
(5) Avoidance of voltage collapse The voltage collapse can be minimised by maximising the voltage collapse proximity indicator lex for the whole system: NCONTO
1.:
K _ 1
where: NSTEP:
number of total time intervals number of contingency cases set of load voltages in the system number of generators number of controllable V AR sources
NCONTG!
LPN: NGP! NG:
These five objectives are subject to constraints imposed on both active and reactive power. Constraints specific to active power include: • generator active power upper and lower limits • generator active power reserve upper and lower limits • system active power reserve constraint • active power balance constraint Also, the following constraints are specific for reactive power: • generator reactive upper and Jower limits • network voltage limits • tap changer ranges • reactive power balance constraint • constfaint for avoiding voltage collapse • constraint for improving ability of system to maintain higher system load
j
.E, fiPi)
(2) Maximisation
F l
14th World Congress oflFAC
(Q Q
.D'
Constraints affect both active and reactive power are: • generator capability chart limits • branch current flow limits The problem of CARD for economic and secure operation of a power system is the weighted sum of tIle five objectives subject to constraints on both active and reactive power. Clearly, the problem is a multi-modal, multi-objectjve, highly constrained
i
7461
Copyright 1999 IFAC
ISBN: 0 08 043248 4
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
opnmlsation problem. Section 4 details how the problem is tackled by a simple genetic algorithm.
3.
AN INTRODUCTION TO GENETIC ALGORITHMS
14th World Congress ofIFAC
and two reactive power sources. The total active load for the system is 1,35MW and the reactive requirement is O.36MVARs. The detailed line and bus data are given in (Mamandur, and Chenoweth, 1981).
GAs are search algorithms based on the mechanics of natural genetics and natural selection (Goldberg, 19&9). They combine an artificial survival of the fittest concept with genetic operators abstracted from nature to fonn a surprisingly robust mechanism that is suitable for a variety of optimisation problems. GAs use stochastic operators instead of detenninistic rules to search a solution . GAs hop randomly from points to points, and have more chance of escaping local optimum and arriving at the global one. In addition, GA's search for the optimum does not depend on the linearity of the objectives, but al10w non-linearity and discontinuity to appear in the scarch space. Finally, the technique can inherent.ly handle inequality constraints imposed on the control variables.
4. GENETIC APPROACH TO THE CARD PROBLEM ON A SIX BUS SYSTEM
A genetic search for the optimum starts with randomly generating a group (population) of solutions to the CARD problem G(O), and thereafter: (1)
(2)
(3)
(4)
(5)
Each solution undergoes a Newton-Raphson Load Flow calculation Evaluation of an individual solution's fitness according to the load flow results, such as fuel costs, reactive reserve margin, and voltage profile for each bus. Select those solutions which have above a"'erage finless value, and reproduce them to form a temporary mating pool G(t) Apply crossover and mutation operators to those solutions O'(t) If the stop criterion is satisfied, then stop, otherwise t==t+l and Go back to (1)
The stopping rule can be the pre-defined maximum number of iteration (generation), or when the change of the best fitness is sufficiently small over a number of 2 generations. A flow chart for the GA implementation procedure is shown in Figure 1.
5.
THE TEST SYSTEM AND THE TEST RESULTS
The test system is the Ward and Hale 6-bus system, shown in Figure 2. The test network has 6 buses, 2 power generators, 7 branches, 2 line transfonners
SS . D·j J J.O
1, ,=-3.&6
)O . O+-j l S.(l
2
~J~
Figure 2 The Basic System State Of The Ward And Hale 6-Bus Power System. The pre-processing of GA includes mapping the five objectives and constraints into a single fitness function, which is the only measure to guide the search towards the optimum; choosing control variables, which a GA can manipulate to achicve the least cost and the most security. In this paper, 9 control variables are selected for the GA to work with, they are: generator output level at bus 2 , SVCs at buses 4 & 6, Transfonner tapping settings at buses 1 & 2, Voltage levels at buses 1 & 2, System Load Increment, and Voltage Collapse Proximity Indicator. Each control variable has its own range of values, its maximum value, its minimum value, its lower limits and upper limits. Each of them is encoded in a 6 bits string length, and concatenated together. Figure 3 shows a solution encoded in a binary string fonnat consisting values for 9 control variables. Two CARD problems havc bcen examined. The first is the static CARD problem, where the total period of interest is just one time interval. The second is the dynamic CARD problem, where the problem is over 5 time intervals. The difference between the two problems not only lies in the different time durations, but also in the additional Ramping Rate constraint on the dynamic CARD problem, which restricts the search space severely. The solution rcsults for the static and dynamic CARD problems are summarised in Table 1 and Table 2 respectively, where different generations and populations are used to compare the end results and the associated computational expenses.
7462
Copyright 1999 IF AC
ISBN: 0 08 043248 4
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
It is clearly seen from the tables that the larger the population and generations, the better the result are. The computation time rises linearly with the number of generations and population size. With merely 10 population members and 10 generations, the GA obtain the results for the CARD problem with only 0.8 seconds for the 6-bus system. This is very encouraging for the technique to be applied to medium sized power systems. Although the results are better for the larger population and generations, they do not justiiY the extra computational effort needed. When comparing with conventional techniques, in theolY, GA solutions should offer more advantages. This is because they simultaneously manipulate control variables so that over the period of trial and error, GA is able to obtain a good overall solution . Furthennore, GA processes give optimal active and reactive power dispatch according to the past cost, and constraint "iolation, they learn fTOm the past experience and manipulate the variables so as not to fall into false optimum, or falling beyond the constrained space. Because of the learning ability, GAs should be able to give better results for the optimal load flow within the same computational effort as was conventional methods.
6.
CONCLUSION
The paper has proposed a genetic algorithm based method to solve the optimal power flow problem where the active and reactive power are fully coupled. TIle beauty of the genetic approach when applied to this problem is that the GA simultaneously manipulated various control variable, such as real power output, transfonner tape settings, SVC settings, bus voltage levels to attain an the overall better solution for the least operation cost and secure operation, while most of the conventional techniques nonnally change one control variable at a time. Five objectives have been used to represent the CARD problem in this study. These are fuel
14th World Congress ofIFAC
cost, reactive reserve margin, the load voltages, higher system load and avoidance of voltage collapse. The solution speed of 0.8 seconds for a 6bus system makes it feasible to apply the technique to medium sized systems. Future work wiII be directed to further scaling up the g enetic based optimal power flow for larger systems, and compare the results with that of Linear Programming.
REFERENCES Chebbo, A.M . and M.R. Irving (1995a). Combined Active and Reactive Disapatch: Part I . lEE Proc. Generation, Transmission and Distribution, VoI. 142, no 4, pp 393-400. Chebbo, A.M., M.R. Irving and N.H. Dandachi (l995b). Combined Active and Reactive Despatch, Part2: Test Results. lEE Proc. Generation, Transmission and Dis tribution, Vol. 142, no 4, pp 401-405.
Goldberg, D.E. (1989). Genetic Algorithms in Search Optimisation and Learning. Addison Wesley. Lee, K.Y. , YM Park and J.L. Ortiz (1985). A United Approach to Optimal Real and Reactive Power Dispatch, IEEE Transaction on Power Apparatus and Systems, Vol PAS-I04, NoS, pp 1147-1153. Li , F. and R. Morgan (1995). Genetic Approach to Economic - Environmental Dispatch. International Federation of Automatic Control - IFAC'95, Cancun, Mexico, pp 169-174. Mamandur, K .R.C. and R.D Chenoweth (1981).
Optimal Control of Reactive Power Flow for Improvements in Voltage Profiles and for Real Power Loss Minimisation. IEEE Transaction on Power Apparatus and Systems, Vol PAS-100, No 7 , pp 3J85-3193.
Waiters, D.e. and B. ShebJe (1993 ). Genetic Algoritlun Solution of Economic Dispatch with Valve Point Loading. IEEE Transaction on Power Systems, VoJ. 8, No 3, pp 1325-1332, 1993 .
7463
Copyright 1999 IF AC
ISBN: 0 08 043248 4
COUPLED ACTIVE AND REACTIVE POWER DISPATCH USING G ...
14th World Congress ofIFAC
population of initial solutions
each undergoes a Newton Raphson load
evaluate fitness value for each solution
genetic modification of control variables
Figure 1. The flow chart ofintegrated GA and NR
[ P2 1 SVC4 1 SVC61 Tl 1 T2 1 VI I V2 I a. ! le [01001011 01001/100011/101100100 11001010 101/01111011100111111000]
Figure 3.
The CARD solution representation in a binal)' string format
T a ble 1 The so uUon resut tstoth e CARD pro bI em over single tIme mterval
Population Size Generations
10
Cost lO
1.4368 1.4374 1.4106 1.4117
20 50 100
50
30
Time
Time (s)
Cost
0.88 1.81 4.39 8.79
1.4262 1.4165 1.4086 1.4025
Cost
80
Time
Cost
Time
1.3848
7 .03 14.06 35.11 69.45
(sl
(s)
(s)
2.63 5.27
1.3937 1.4089 1.4015 1.4022
13.13 26.04
3.96 8.84 21.87 43.41
1.4031 1.3954 1.4017
. T a ble 2 Th e so uUon resu ts to the CARD pro bI em over 5 hme mterv a1 s Population Size Generations
10 30 50 100
30
10
50
Cost
Time
Cost
Cost
Time
7.6165 7 .5545 7 .5721 7.5242
(s) 3.95 11.81 11.86 39.39
Time (s)
7.5745 7.5545 7.5418 7.5169
11.81
7.5775 7 .5567 7.5086 7.5132
(s) 19.72 59.17 99.56 197.03
35.49 6 0.00 118.24
7464
Copyright 1999 IF AC
ISBN: 0 08 043248 4