Optimal Power Flow by Enhanced Genetic Algorithm
|
|
- Charlene Waters
- 5 years ago
- Views:
Transcription
1 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY Optimal Power Flow by Enhanced Genetic Algorithm Anastasios G. Bakirtzis, Senior Member, IEEE, Pandel N. Biskas, Student Member, IEEE, Christoforos E. Zoumas, Student Member, IEEE, and Vasilios Petridis, Member, IEEE Abstract This paper presents an enhanced genetic algorithm (EGA) for the solution of the optimal power flow (OPF) with both continuous and discrete control variables. The continuous control variables modeled are unit active power outputs and generator-bus voltage magnitudes, while the discrete ones are transformer-tap settings and switchable shunt devices. A number of functional operating constraints, such as branch flow limits, load bus voltage magnitude limits, and generator reactive capabilities, are included as penalties in the GA fitness function (FF). Advanced and problem-specific operators are introduced in order to enhance the algorithm s efficiency and accuracy. Numerical results on two test systems are presented and compared with results of other approaches. Index Terms Genetic algorithms (GAs), optimal power flow (OPF). NOMENCLATURE Bus voltage angle vector. Load (PQ) bus voltage magnitude vector. Unit active power output vector. Generation (PV) bus voltage magnitude vector. Transformer tap settings vector. Bus shunt admittance vector. System state vector. System control vector. A hat above vectors and denotes that the entry corresponding to the slack bus is missing. For simplicity of notation, it is assumed that there is only one generating unit connected on a bus. This assumption is relaxed in SectionV. I. INTRODUCTION SINCE its introduction as network constrained economic dispatch by Carpentier [1] and its definition as optimal power flow (OPF) by Dommel and Tinney [2], the OPF problem has been the subject of intensive research. The OPF optimizes a power system operating objective function (such as the operating cost of thermal resources) while satisfying a set of system operating constraints, including constraints dictated by the electric network. OPF has been widely used in power system operation and planning [3]. After the electricity sector restructuring, OPF has been used to assess the spatial variation of electricity prices and as a congestion management and pricing tool [4]. In its most general formulation, the OPF is a nonlinear, nonconvex, large-scale, static optimization problem with both Manuscript received October 9, 2000; revised August 20, The authors are with the Department of Electrical Engineering, Aristotle University of Thessaloniki, Thessaloniki 54006, Greece. Publisher Item Identifier S (02) continuous and discrete control variables. Even in the absence of nonconvex unit operating cost functions, unit prohibited operating zones, and discrete control variables, the OPF problem is nonconvex due to the existence of the nonlinear (AC) power flow equality constraints. The presence of discrete control variables, such as switchable shunt devices, transformer tap positions, and phase shifters, further complicates the problem solution. The literature on OPF is vast, and [5] presents the major contributions in this area. Mathematical programming approaches, such as nonlinear programming (NLP) [6] [9], quadratic programming (QP) [10], [11], and linear programming (LP) [12] [14], have been used for the solution of the OPF problem. Some methods, instead of solving the original problem, solve the problem s Karush Kuhn Tucker (KKT) optimality conditions. For equality-constrained optimization problems, the KKT conditions are a set of nonlinear equations, which can be solved using a Newton-type algorithm. In Newton OPF [15], the inequality constraints are added as quadratic penalty terms to the problem objective, multiplied by appropriate penalty multipliers. Interior point (IP) methods [16] [18], convert the inequality constraints to equalities by the introduction of nonnegative slack variables. A logarithmic barrier function of the slack variables is then added to the objective function, multiplied by a barrier parameter, which is gradually reduced to zero during the solution process. The unlimited point algorithm [19] uses a transformation of the slack and dual variables of the inequality constraints which converts the OPF problem KKT conditions to a set of nonlinear equations, thus avoiding the heuristic rules for barrier parameter reduction required by IP methods. OPF programs based on mathematical programming approaches are used daily to solve very large OPF problems. However, they are not guaranteed to converge to the global optimum of the general nonconvex OPF problem, although there exists some empirical evidence on the uniqueness of the OPF solution within the domain of interest [20]. To avoid the prohibitive computational requirements of mixed-integer programming, discrete control variables are initially treated as continuous, and post-processing discretization logic is subsequently applied [21], [22]. Whereas the effects of discretization on load tap changing transformers are small and usually negligible [20], the rounding of switchable shunt devices may lead to voltage infeasibility, especially when the discrete VAR steps are large, and requires special logic [22]. The handling of nonconvex OPF objective functions, as well as the unit prohibited operating zones, also present problems to mathematical programming OPF approaches /02$ IEEE
2 230 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002 Recent attempts to overcome the limitations of the mathematical programming approaches include the application of simulated annealing-type methods [23], [24], and genetic algorithms (GAs) [25], [26]. In [25], a simple genetic algorithm (SGA) is used for OPF solution. The control variables modeled are generator active power outputs and voltages, shunt devices, and transformer taps. Branch flow, reactive generation, and voltage magnitude constraints are treated as quadratic penalty terms in the GA fitness function (FF). To keep the GA chromosome size small, only a 4-bit chromosome area is used for the encoding of each control variable. A sequential GA solution scheme is employed to achieve acceptable control variable resolution. Test results on the IEEE 30-bus system, comprising 25 control variables, are presented. In [26], a GA is used to solve the optimal power dispatch problem for a multinode auction market. The GA maximizes the total participants welfare, subject to network flow and transport limitation constraints. The nodal real and reactive power injections that clear the market are selected as the problem control variables. A GA with two advanced operators, namely, elitism and hill climbing, is used. A 10-bit chromosome area is devoted to each control variable. Test results on a 17-node, 34-control variable system are presented. The GA-OPF approaches overcome the limitations of the conventional approaches in the modeling of nonconvex cost functions, discrete control variables, and prohibited unit operating zones. However, they do not scale easily to larger problems, since the solution deteriorates with the increase of the chromosome length, i.e., the number of control variables. Thus, the test results in the existing GA-OPF literature are limited to very small problems. This paper presents an enhanced genetic algorithm (EGA) for the solution of the OPF. The control variables and constraints included in the OPF and the penalty method treatment of the functional operating constraints are similar to the ones in [25] with the following improvements: switchable shunt devices and transformer taps are modeled as discrete control variables. Variable binary string length is used for different types of control variables, so as to achieve the desired resolution for each type of control variable, without unnecessarily increasing the size of the GA chromosome. In addition to the basic genetic operators of the SGA used in [25] and the advanced ones used in [26], problem-specific operators, inspired by the nature of the OPF problem, have been incorporated in our EGA. With the incorporation of the problem-specific operators, the GA can solve larger OPF problems. Test results on systems with up to 242 buses and 500 control variables demonstrate the improvement achieved with the aid of problem-specific operators. II. OPTIMAL POWER FLOW PROBLEM FORMULATION The OPF problem can be formulated as a mathematical optimization problem as follows: Min (1) S.t. (2) (3) (4) where The equality constraints (2) are the nonlinear power flow equations. The inequality constraints (3) are the functional operating constraints, such as branch flow limits (MVA, MW or A); load bus voltage magnitude limits; generator reactive capabilities; slack bus active power output limits. Constraints (4) define the feasibility region of the problem control variables such as unit active power output limits; generation bus voltage magnitude limits; transformer-tap setting limits (discrete values); bus shunt admittance limits (continuous or discrete control). III. GENETIC ALGORITHMS GAs are general purpose optimization algorithms based on the mechanics of natural selection and genetics. They operate on string structures (chromosomes), typically a concatenated list of binary digits representing a coding of the control parameters (phenotype) of a given problem. Chromosomes themselves are composed of genes. The real value of a control parameter, encoded in a gene, is called an allele [27]. GAs are an attractive alternative to other optimization methods because of their robustness. There are three major differences between GAs and conventional optimization algorithms. First, GAs operate on the encoded string of the problem parameters rather than the actual parameters of the problem. Each string can be thought of as a chromosome that completely describes one candidate solution to the problem. Second, GAs use a population of points rather than a single point in their search. This allows the GA to explore several areas of the search space simultaneously, reducing the probability of finding local optima. Third, GAs do not require any prior knowledge, space limitations, or special properties of the function to be optimized, such as smoothness, convexity, unimodality, or existence of derivatives. They only require the evaluation of the so-called fitness function (FF) to assign a quality value to every solution produced. Assuming an initial random population produced and evaluated, genetic evolution takes place by means of three basic genetic operators: 1) parent selection; 2) crossover; 3) mutation. Parent selection is a simple procedure whereby two chromosomes are selected from the parent population based on their fitness value. Solutions with high fitness values have a high probability of contributing new offspring to the next generation. The selection rule used in our approach is a simple roulette-wheel selection [27]. (5) (6)
3 BAKIRTZIS et al.: OPTIMAL POWER FLOW BY ENHANCED GENETIC ALGORITHM 231 Fig. 2. GA chromosome structure. Fig. 1. Simple genetic algorithm (SGA). Crossover is an extremely important operator for the GA. It is responsible for the structure recombination (information exchange between mating chromosomes) and the convergence speed of the GA and is usually applied with high probability ( ). The chromosomes of the two parents selected are combined to form new chromosomes that inherit segments of information stored in parent chromosomes. Until now, many crossover schemes, such as single point, multipoint, or uniform crossover have been proposed in the literature. Uniform crossover [28] has been used in our implementation. While crossover is the main genetic operator exploiting the information included in the current generation, it does not produce new information. Mutation is the operator responsible for the injection of new information. With a small probability, random bits of the offspring chromosomes flip from 0 to 1 and vice versa and give new characteristics that do not exist in the parent population [27]. In our approach, the mutation operator is applied with a relatively small probability ( ) to every bit of the chromosome. The FF evaluation and genetic evolution take part in an iterative procedure, which ends when a maximum number of generations is reached, as shown in Fig. 1. When applying GAs to solve a particular optimization problem (OPF in our case), two main issues must be addressed: 1) the encoding, i.e., how the problem physical decision variables are translated to a GA chromosome and its inverse operator, decoding; 2) the definition of the FF to be maximized by the GA (the GA FF is formed by an appropriate transformation of the initial problem objective function augmented by penalty terms that penalize the violation of the problem constraints [29]). IV. GENETIC ALGORITHM SOLUTION TO OPTIMAL POWER FLOW A. Encoding The chromosome is formed as shown in Fig. 2. There are four chromosome regions (one for each set of control variables), namely, 1) ; 2) ; 3) ; and 4). Encoding is performed using different gene-lengths for each set of control variables, depending on the desired accuracy. The decoding of a chromosome to the problem physical variables is performed as follows: 1) continuous controls taking values in the interval and 2) discrete controls taking values with (7) (8) where is the decimal number to which the binary number in a gene is decoded and is the gene length (number of bits) used for encoding control variable. B. Fitness Function (FF) GAs are usually designed so as to maximize the FF, which is a measure of the quality of each candidate solution. The objective of the OPF problem is to minimize the total operating cost (1). Therefore, a transformation is needed to convert the cost objective of the OPF problem to an appropriate FF to be maximized by the GA. The OPF functional operating constraints (3) are included in the GA solution by augmenting the GA FF by appropriate penalty terms for each violated functional constraint. Constraints on the control variables (4) are automatically satisfied by the selected GA encoding/decoding scheme (7) and (8). Therefore, the GA FF is formed as follows: (9) (10)
4 232 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002 where fitness function; constant; fuel cost function of unit (in our case, a quadratic function); weighting factor of functional operating constraint ; penalty function for functional operating constraint ; violation of th functional operating constraint, if positive; Heaviside (step) function; number of units; number of functional operating constraints. Given a candidate solution to the problem, represented by a chromosome, the FF is computed as follows. Step 1) Decode the chromosome to determine the actual control variables,, using (7) and (8). The computed control vector satisfies, by design, constraints (4). Step 2) Solve the power flow (2) to compute the state vector,. Step 3) Determine the violated functional constraints (3) and compute associated penalty functions (10). Step 4) Compute the FF using (9). In Step 2, a simple fast decoupled load flow (FDLF) [30] is used with no PV-PQ bus-type switching, since generator reactive capabilities are incorporated in the functional operating constraints and no local control adjustments, such as tap and switchable shunts [31], since the settings of these controls are determined by the GA. Therefore, only a few load flow iterations are required for convergence. The FDLF and matrices are formed and factorized only once in the beginning the effect of the changes of shunt admittances on the matrix is neglected. In case that, due to the random (yet within limits) initial selection of the control variables, the load flow does not converge within a predefined number of iterations (set to 8), large penalty terms, proportional to the maximum active/reactive power mismatch, are added to the FF. C. Advanced and Problem-Specific Genetic Operators One of the most important issues in the genetic evolution is the effective rearrangement of the genotype information. In the SGA crossover is the main genetic operator responsible for the exploitation of information while mutation brings new nonexistent bit structures. It is widely recognized that the SGA scheme is capable of locating the neighborhood of the optimal or near-optimal solutions, but, in general, requires a large number of generations to converge. This problem becomes more intense for large-scale optimization problems with difficult search spaces and lengthy chromosomes, where the possibility for the SGA to get trapped in local optima increases and the convergence speed of the SGA decreases. At this point, a suitable combination of the basic, advanced, and problem-specific genetic operators must be introduced in order to enhance the performance of the GA. Advanced Fig. 3. Gene swap operator. and problem-specific genetic operators usually combine local search techniques and expertise derived from the nature of the problem. A set of advanced and problem-specific genetic operators has been added to the SGA in order to increase its convergence speed and improve the quality of solutions. Our interest was focused on constructing simple yet powerful enhanced genetic operators that effectively explore the problem search space. The advanced features included in our GA implementation are as follows. 1) Fitness Scaling: In order to avoid early domination of extraordinary strings and to encourage a healthy competition among equals, a scaling of the fitness of the population is necessary [27]. In our approach, the fitness is scaled by a linear transformation. 2) Elitism: Elitism ensures that the best solution found thus far is never lost when moving from one generation to another. The best solution of each generation replaces a randomly selected chromosome in the new generation [32]. 3) Hill Climbing: In order to increase the GA search speed at smooth areas of the search space a hill-climbing operator is introduced, which perturbs a randomly selected control variable. The modified chromosome is accepted if there is an increase in FF value; otherwise, the old chromosome remains unchanged. This operator is applied only to the best chromosome (elite) of every generation [26], [29]. In addition to the above advanced features, which are called advanced despite their wide use in most recent GA implementations to distinguish between the SGA and our EGA, operators specific to the OPF problem have been added. All problem-specific operators introduce random modification to all chromosomes of a new generation. If the modified chromosome proves to have better fitness, it replaces the original one in the new population. Otherwise, the original chromosome is retained in the new population. All problem-specific operators are applied with a probability of 0.2. The following problem-specific operators have been used. 1) Gene Swap Operator (GSO): This operator randomly selects two genes in a chromosome and swaps their values, as shown in Fig. 3. This operator swaps the active power output of two units, the voltage magnitude of two generation buses, etc. Swapping among different types of control variables is not allowed. 2) Gene Cross-Swap Operator (GCSO): The GCSO is a variant of the GSO. It randomly selects two different chromosomes from the population and two genes, one from every selected chromosome, and swaps their values, as shown in Fig. 4. While crossover exchanges information between high-fit chromosomes, the GCSO searches for alternative alleles, exploiting information stored even in low-fit strings.
5 BAKIRTZIS et al.: OPTIMAL POWER FLOW BY ENHANCED GENETIC ALGORITHM 233 Fig. 4. Gene cross-swap operator. Fig. 5. Gene copy operator. Fig. 8. Enhanced genetic algorithm (EGA). Fig. 6. Fig. 7. Gene inverse operator. Gene max-min operator. 3) Gene Copy Operator (GCO): This operator randomly selects one gene in a chromosome and with equal probability copies its value to the predecessor or the successor gene of the same control type, as shown in Fig. 5. This operator has been introduced in order to force consecutive controls (e.g., identical units on the same bus) to operate at the same output level. 4) Gene Inverse Operator (GIO): This operator acts like a sophisticated mutation operator. It randomly selects one gene in a chromosome and inverses its bit-values from one to zero and vice versa, as shown in Fig. 6. The GIO searches for bit-structures of improved performance, exploits new areas of the search space far away from the current solution, and retains the diversity of the population. 5) Gene Max-Min Operator (GMMO): The GMMO tries to identify binding control variable upper/lower limit constraints. It selects a random gene in a chromosome and, with the same probability (0.5), fills its area with 1 s or 0 s, as shown in Fig. 7. D. Enhanced Genetic Algorithm (EGA) In the EGA, shown in Fig. 8, after the application of the basic genetic operators (parent selection, crossover, and mutation) the advanced and problem-specific operators are applied to produce the new generation. All chromosomes in the initial population are created at random (every bit in the chromosome has equal probability of being switched ON or OFF). Due to the decoding process selected [(7) and (8)], the corresponding control variables of the initial population satisfy their upper lower bound or discrete value constraints (4). However, the initial population candidate solutions may not satisfy the functional operating constraints (3) or even the load flow constraints (2) since the random, within limits, selection of the control variables may lead to load flow divergence (as already discussed in Section I V-B). Population statistics computed for the new generation include maximum, minimum, and average fitness values and the 90% percentile. Population statistics are then used to adaptively change the crossover and mutation probabilities [33]. If premature convergence is detected the mutation probability is increased and the crossover probability is decreased. The contrary happens in the case of high population diversity. V. TEST RESULTS In this section, the proposed EGA solution of the OPF is evaluated using two test systems: 1) the IEEE 30-bus system [6] and 2) the 3-area IEEE RTS96 [34]. The test examples have been run on a 1.4-GHz Pentium-IV PC. Twenty runs have been performed for each case examined. The results which follow are the best solution over these 20 runs. A. IEEE 30-Bus System The first test system is the IEEE 30-bus, 41-branch system [6]. It has a total of 24 control variables as follows: five unit active power outputs, six generator-bus voltage magnitudes, four transformer-tap settings, and nine bus shunt admittances. The gene length for unit power outputs is 12 bits and for generator voltage magnitudes is 8 bits. They are both treated as continuous controls. The transformer-tap settings can take 17 discrete values (each one is encoded using 5 bits): the lower and
6 234 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002 TABLE I IEEE 30-BUS SYSTEM RESULTS Fig. 9. FF comparison for IEEE 30-bus system. upper limits are 0.9 p.u. and 1.1 p.u., respectively, and the step size is p.u. The bus shunt admittances can take six discrete values (each one is encoded using 3 bits): the lower and upper limits are 0.0 p.u. and 0.05 p.u., respectively, and the step is 0.01 p.u. (on system MVA basis). The GA population size is taken equal to 80, the maximum number of generations is 200, and crossover and mutation are applied with initial probability 0.9 and 0.001, respectively. Two sets of 20 test runs were performed; the first (SGA) with only the basic GA operators and the second (EGA) with all operators, including advanced and problem-specific operators. The FF evolution of the best of these runs is shown in Fig. 9. The best and worst solutions of the second set of 20 runs (EGA) are shown in Table I. The operating costs of the best and worst solutions are $/h and $/h, respectively, (0.01% difference). The differences between the values of the control variables in the best and worst solutions are not significant. The operating cost of all EGA-OPF solutions is slightly less than the $/h figure reported in [6]. As shown in Table I, there is a slight difference in unit marginal costs (UMCs), attributed to network losses. Note that, in this case, the UMCs coincide with the nodal prices, since no unit limits are reached. Fig. 9 demonstrates the improvement achieved with the inclusion of the advanced and problem-specific operators. The SGA run took 18 s, while the EGA took 76 s to evaluate 200 generations. However, the EGA provides a far better solution than SGA even in the first 25 generations, or 10 s. B. IEEE 3-Area RTS96 The 3-area IEEE RTS-96 [34] is a 73-bus, 120-branch system. It consists of three areas connected through five tie lines. The area-a unit cost data are derived from the heat rate data provided in [34] and the fuel cost data listed in Table II. The value of water is zero, assuming excessive inflows. Area-B and area-c fuel costs are selected three times the area-a fuel costs, to impose exports from area A to areas B and C. A contingency case with tie lines and out of service, under 90% peak load conditions, is studied. To impose congestion, the ratings of tie lines and are reduced by 50% (to 250 MVA). This system has a total of 150 control variables as follows: 98 unit active power outputs, 33 generator-bus voltage magnitudes, 16 transformer tap-settings, and 3 bus shunt admittances. TABLE II FUEL COSTS FOR IEEE 3-AREA RTS-96 The lower and upper limits of voltage magnitude of all buses are 0.95 p.u. and 1.05 p.u., respectively, (except for PV buses where p.u.). Transformer taps take discrete values within 0.9 p.u. and 1.1 p.u. with a step size of p.u (17 discrete values). Similarly, bus shunt admittances take discrete values between 150 MVAR (inductor, at rated voltage) and 0 MVAR with a 50 MVAR step (four discrete values). The GA population size is taken equal to 180, the maximum number of generations is 600, and crossover and mutation are applied with initial probability 0.9 and 0.001, respectively. It was necessary to increase both the population size and the maximum number of generations to solve the larger problem. It was also necessary to increase the probability of application of problem-specific operators from 0.2 to 0.5. First, the unconstrained schedule is obtained by ignoring branch flow limits. Branch flow limits are ignored by selecting the corresponding penalty weight to zero in (9). The unconstrained schedule results in an 81.8 MVA overloading of tie line The corresponding operating cost is $/h. Next, the constrained schedule is calculated by activating the branch flow constraints. Tie line flow is now reduced to MVA (almost to the 250 MVA line rating). The operating cost is increased to $/h due to congestion. The FF evolution of both the SGA and the EGA, shown in Fig. 10, demonstrates the improvement achieved with the inclusion of the advanced and the problem-specific operators. The SGA run took 266 s, while the EGA took 1643 s to evaluate 600 generations. However, as shown in Fig. 10, a far better solution is provided by EGA during the same execution time as SGA.
7 BAKIRTZIS et al.: OPTIMAL POWER FLOW BY ENHANCED GENETIC ALGORITHM 235 TABLE III COMPUTATIONAL REQUIREMENTS Fig. 10. FF comparison for IEEE 3-area RTS96. VI. COMPUTATIONAL REQUIREMENTS OF GENETIC ALGORITHM OPTIMAL POWER FLOW In an SGA, if a population of size PS is allowed to evolve for a total number of NG generations, the product PG NG determines the required number of FF evaluations (NFE) and hence the GA computational requirements. When problem-specific operators are used, the required number of fitness evaluations increases accordingly. In GA-OPF, the FF evaluation is synonymous with power flow solution in terms of computational requirements, since the latter is the computationally dominant task in the FF evaluation procedure (see Section IV-B). It is widely recognized among GA practitioners that the required NFE for a particular GA implementation depends on problem difficulty, which, in turn, depends on two factors: 1) the chromosome length and 2) the shape and characteristics of the fitness landscape. Problems with smooth fitness landscapes are easy to solve with GA. If the global optimum is located at the bottom of a steep gorge of the fitness landscape, the GA may require a large number of fitness evaluations to locate it. Thus, two optimization problems with the same chromosome length may require vastly different NFE to solve owing to the difference in their fitness landscapes. In GA-OPF, the chromosome length is determined by the number of control variables and the resolution required for each control type. The number of buses affects the fitness evaluation ( power flow solution) time. The fitness landscape of the GA-OPF is very hard to visualize, except for trivial problems employing at most two-decision variables. For the assessment of the GA-OPF computational requirements, an experiment is designed as follows. Four test systems of increasing size are created, based on the IEEE RTS96 [34] (1-, 3-, 5-, and 10-area configurations). The GA population size is 200, the probability of application of problem-specific operators is 0.5, and the maximum number of generations is 600 in all four cases. Table III summarizes the results of 20 test runs in all test systems. The last four columns report the average (over the 20 runs) computational requirements of the GA. The number of generations (NG) to arrive at a good quality OPF solution is reported in the 7th row. A good quality OPF solution is one with fitness value within 0.1% of the fitness obtained after allowing the GA to evolve for 600 generations (well within the flat portion of Fig. 10). The execution time to arrive at a good quality solution is reported in the 9th row. The results of Table III show that the difference of the best and worst solutions increases slightly and the execution time increases considerably as the system size increases. VII. CONCLUSIONS A GA solution to the OPF problem has been presented and applied to small and medium size power systems. The main advantage of the GA solution to the OPF problem is its modeling flexibility: nonconvex unit cost functions, prohibited unit operating zones, discrete control variables, and complex, nonlinear constraints can be easily modeled. Another advantage is that it can be easily coded to work on parallel computers. The main disadvantage of GAs is that they are stochastic algorithms and the solution they provide to the OPF problem is not guaranteed to be the optimum. Another disadvantage is that the execution time and the quality of the provided solution deteriorate with the increase of the chromosome length, i.e., the OPF problem size. The applicability of the GA solution to large-scale OPF problems of systems with several thousands of nodes, utilizing the strength of parallel computers, has yet to be demonstrated. REFERENCES [1] J. Carpentier, Contibution a. l etude du dispatching economique, Bull. Soc. Francaise Elect., vol. 3, pp , Aug [2] H. W. Dommel and W. F. Tinney, Optimal power flow solutions, IEEE Trans. Power Apparat. Syst., vol. PAS-87, pp , Oct [3] J. A. Momoh, R. J. Koessler, M. S. Bond, B. Stott, D. Sun, A. Papalexopoulos, and P. Ristanovic, Challenges to optimal power flow, IEEE Trans. Power Syst., vol. 12, pp , Feb [4] R. D. Christie, B. F. Wollenberg, and I. Wangensteen, Transmission management in the deregulated environment, Proc. IEEE, vol. 88, pp , Feb [5] J. A. Momoh, M. E. El-Hawary, and R. Adapa, A review of selected optimal power flow literature to 1993, IEEE Trans. Power Syst., pt. I and II, vol. 14, pp , Feb [6] O. Alsac and B. Stott, Optimal load flow with steady state security, IEEE Trans. Power Apparat. Syst., vol. PAS-93, pp , May/June [7] R. R. Shoults and D. T. Sun, Optimal power flow based on P-Q decomposition, IEEE Trans. Power Apparat. Syst., vol. PAS-101, pp , Feb [8] M. H. Bottero, F. D. Galiana, and A. R. Fahmideh-Vojdani, Economic dispatch using the reduced Hessian, IEEE Trans. Power Apparat. Syst., vol. PAS-101, pp , Oct [9] J. A. Momoh, A generalized quadratic-based model for optimal power flow, IEEE Trans. Syst., Man, Cybern., vol. SMC-16, [10] G. F. Reid and L. Hasdorf, Economic dispatch using quadratic programming, IEEE Trans. Power Apparat. Syst., vol. PAS-92, pp , 1973.
8 236 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 17, NO. 2, MAY 2002 [11] R. C. Burchett, H. H. Happ, and K. A. Wirgau, Large-scale optimal power flow, IEEE Trans. Power Apparat. Syst., vol. PAS-101, pp , Oct [12] B. Stott and E. Hobson, Power system security control calculation using linear programming, IEEE Trans. Power Apparat. Syst., pt. I and II, vol. PAS-97, pp , Sept./Oct [13] B. Stott and J. L. Marinho, Linear programming for power system network security applications, IEEE Trans. Power Apparat. Syst., vol. PAS-98, pp , May/June [14] R. Mota-Palomino and V. H. Quintana, A penalty function-linear programming method for solving power system constrained economic operation problems, IEEE Trans. Power Apparat. Syst., vol. PAS-103, pp , June [15] D. I. Sun, B. Ashley, B. Brewer, A. Hughes, and W. F. Tinney, Optimal power flow by Newton approach, IEEE Trans. Power Apparat. Syst., vol. PAS-103, pp , [16] H. Wei, H. Sasaki, J. Kubokawa, and R. Yokoyama, An interior point nonlinear programming for optimal power flow problems with a novel data structure, IEEE Trans. Power Syst., vol. 13, pp , Aug [17] G. L. Torres and V. H. Quintana, An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates, IEEE Trans. Power Syst., vol. 13, pp , Nov [18] J. A. Momoh and J. Z. Zhu, Improved interior point method for OPF problems, IEEE Trans. Power Syst., vol. 14, pp , Aug [19] G. Tognola and R. Bacher, Unlimited point algorithm for OPF problems, IEEE Trans. Power Syst., vol. 14, pp , Aug [20] A. D. Papalexopoulos, C. F. Imparato, and F. F. Wu, Large-scale optimal power flow: Effects of initialization decoupling and discretization, IEEE Trans. Power Syst., vol. 4, pp , May [21] W. F. Tinney, J. M. Bright, K. D. Demaree, and B. A. Hughes, Some deficiencies in optimal power flow, IEEE Trans. Power Syst., vol. 3, pp , May [22] E. Liu, A. D. Papalexopoulos, and W. F. Tinney, Discrete shunt controls in a Newton optimal power flow, IEEE Trans. Power Syst., vol. 7, pp , Nov [23] L. Chen, H. Suzuki, and K. Katou, Mean field theory for optimal power flow, IEEE Trans. Power Syst., vol. 12, pp , Nov [24] L. Chen, S. Matoba, H. Inabe, and T. Okabe, Surrogate constraint method for optimal power flow, IEEE Trans. Power Syst., vol. 13, pp , Aug [25] L. L. Lai, J. T. Ma, R. Yokoyama, and M. Zhao, Improved genetic algorithms for optimal power flow under both normal and contingent operation states, Elec. Power Energy Syst., vol. 19, no. 5, pp , [26] T. Numnonda and U. D. Annakkage, Optimal power dispatch in multinode electricity market using genetic algorithm, Elec. Power Syst. Res., vol. 49, pp , [27] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Reading. Reading, MA: Addison-Wesley, [28] L. J. Eshelman, R. A. Caruana, and J. D. Schaffer, Biases in the crossover landscape, in Proc. 3rd Int. Conf. Genetic Algorithms, 1989, pp [29] V. Petridis, S. Kazarlis, and A. Bakirtzis, Varying fitness functions in genetic algorithm constrained optimization: The cutting stock and unit commitment problems, IEEE Trans. Syst., Man, Cybern. B, vol. 28, pp , Oct [30] B. Stott and O. Alsac, Fast decoupled load flow, IEEE Trans. Power Apparat. Syst., vol. PAS-93, pp , May/June [31] S. K. Chang and V. Brandwajn, Adjusted solutions in fast decoupled load flow, IEEE Trans. Power Syst., vol. 3, pp , May [32] L. Davis, Handbook of Genetic Algorithms. New York: Van Nostrand, [33], Adapting operator probabilities in genetic algorithms, in Proc. 3rd Int. Conf. Genetic Algorithms Applications, J. Schaffer, Ed., San Mateo, CA, June 1989, pp [34] The IEEE reliability test system-1996, IEEE Trans. Power Syst., vol. 14, pp , Aug Anastasios G. Bakirtzis (S 77 M 79 SM 95) received the Dipl. Mech. & Electr. Eng. degree from the National Technical University of Athens, Athens, Greece, in 1979, and the M.S.E.E. and Ph.D. degrees from Georgia Institute of Technology, Atlanta, in 1981 and 1984, respectively. In 1984, he was a consultant to Southern Company, Atlanta, GA. Since 1986, he has been with the Department of Electrical Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece, where he is currently an Associate Professor. His research interests are in power system operation and control, reliability analysis, and alternative energy sources. Pandel N. Biskas (S 01) received the Dipl. Electr. Eng. degree from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1999, where he is currently pursuing the Ph.D. degree. His research interests are in power system operation and control and transmission pricing. Christoforos E. Zoumas (S 98) received the Dipl. Electr. Eng. degree from the Aristotle University of Thessaloniki, Thessaloniki, Greece, in 1996, where he is currently pursuing the Ph.D. degree. His research interest is in computer applications in power systems. Vasilios Petridis (M 77) received the B.S. degree in electrical engineering from the National Technical University, Athens, Greece, in 1969, and the M.Sc. and Ph.D. degrees in electronics and systems from King s College, University of London, London, U.K., in 1970 and 1974, respectively. He has been Consultant of the Naval Research Centre, Greece, and Director of the Department of Electronics and Computer Engineering and Vice-Chairman of the Faculty of Electrical and Computer Engineering at Aristotle University, Thessaloniki, Greece. He is currently Professor in the Department of Electronics and Computer Engineering in the Aristotle University of Thessaloniki, Thessaloniki, Greece. He is coauthor of the monograph Predictive Modular Neural Networks: Application to Time Series (Norwell, MA: Kluwer, 1998). He is also author of four books on control and measurement systems and approximately 110 research papers. His research interests include control systems, machine learning, intelligent and autonomous systems, artificial neural networks, evolutionary algorithms, fuzzy systems, modeling and identification, robotics, and industrial automation.
OPTIMAL POWER FLOW EVALUATION OF POWER SYSTEM USING GENETIC ALGORITHM
OPTIMAL POWER FLOW EVALUATION OF POWER SYSTEM USING GENETIC ALGORITHM C. M. WANKHADE, 2 A. P. VAIDYA Department of Electrical Engineering, Lokmanya Tilak College of Engineering, Koparkhairane, Navi Mumbai,
More informationNetwork-Constrained Economic Dispatch Using Real-Coded Genetic Algorithm
198 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 1, FEBRUARY 2003 Network-Constrained Economic Dispatch Using Real-Coded Genetic Algorithm Ioannis G. Damousis, Student Member, IEEE, Anastasios G. Bakirtzis,
More informationSwarm intelligence approach to the solution of optimal power flow
J. Indian Inst. Sci., Sept. Oct. 2006, 86, 439 455 Indian Institute of Science. Swarm intelligence approach to the solution of optimal power flow Department of Electrical Engineering, Indian Institute
More informationPowerApps Optimal Power Flow Formulation
PowerApps Optimal Power Flow Formulation Page1 Table of Contents 1 OPF Problem Statement... 3 1.1 Vector u... 3 1.1.1 Costs Associated with Vector [u] for Economic Dispatch... 4 1.1.2 Costs Associated
More informationReal Time Voltage Control using Genetic Algorithm
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
More informationEvolutionary Computation
Evolutionary Computation - Computational procedures patterned after biological evolution. - Search procedure that probabilistically applies search operators to set of points in the search space. - Lamarck
More informationA GENETIC ALGORITHM APPROACH FOR SOLVING AC-DC OPTIMAL POWER FLOW PROBLEM
A GENETIC ALGORITHM APPROACH FOR SOLVING AC-DC OPTIMAL POWER FLOW PROBLEM 1 S. B. WARKAD, 2 DR. M. K. KHEDKAR, 3 DR. G. M. DHOLE 1 Department of Electrical Engineering, Visvesvaraya National Institute
More informationOPTIMAL POWER FLOW SOLUTIONS USING FIREFLY ALGORITHM C.N. Ravi 1, D.B.G. Reddy 2 1,2
OPTIMAL POWER FLOW SOLUTIONS USI FIREFLY ALGORITHM C.N. Ravi 1, D.B.G. Reddy 2 1,2 Professor, Department of Electrical & Electronics Eng., Vidya Jyothi Institute of Technology, Hyderabad Abstract Optimal
More informationCSC 4510 Machine Learning
10: Gene(c Algorithms CSC 4510 Machine Learning Dr. Mary Angela Papalaskari Department of CompuBng Sciences Villanova University Course website: www.csc.villanova.edu/~map/4510/ Slides of this presenta(on
More informationAn Efficient Decoupled Power Flow Control Method by use of Phase Shifting Transformers
FACTA UNIVERSITATIS (NIŠ) SER.: ELEC. ENERG. vol. 17, April 2004, 111-119 An Efficient Decoupled Power Flow Control Method by use of Phase Shifting Transformers Dragan P. Popović Abstract: This paper presents
More informationMulti-objective Emission constrained Economic Power Dispatch Using Differential Evolution Algorithm
Multi-objective Emission constrained Economic Power Dispatch Using Differential Evolution Algorithm Sunil Kumar Soni, Vijay Bhuria Abstract The main aim of power utilities is to provide high quality power
More informationLecture 9 Evolutionary Computation: Genetic algorithms
Lecture 9 Evolutionary Computation: Genetic algorithms Introduction, or can evolution be intelligent? Simulation of natural evolution Genetic algorithms Case study: maintenance scheduling with genetic
More informationJ. Electrical Systems 10-1 (2014): Regular paper. Optimal Power Flow and Reactive Compensation Using a Particle Swarm Optimization Algorithm
Ahmed Elsheikh 1, Yahya Helmy 1, Yasmine Abouelseoud 1,*, Ahmed Elsherif 1 J. Electrical Systems 10-1 (2014): 63-77 Regular paper Optimal Power Flow and Reactive Compensation Using a Particle Swarm Optimization
More informationRegular paper. Particle Swarm Optimization Applied to the Economic Dispatch Problem
Rafik Labdani Linda Slimani Tarek Bouktir Electrical Engineering Department, Oum El Bouaghi University, 04000 Algeria. rlabdani@yahoo.fr J. Electrical Systems 2-2 (2006): 95-102 Regular paper Particle
More informationEvolutionary computation
Evolutionary computation Andrea Roli andrea.roli@unibo.it DEIS Alma Mater Studiorum Università di Bologna Evolutionary computation p. 1 Evolutionary Computation Evolutionary computation p. 2 Evolutionary
More informationGenetic Algorithm for Solving the Economic Load Dispatch
International Journal of Electronic and Electrical Engineering. ISSN 0974-2174, Volume 7, Number 5 (2014), pp. 523-528 International Research Publication House http://www.irphouse.com Genetic Algorithm
More informationGA BASED OPTIMAL POWER FLOW SOLUTIONS
GA BASED OPTIMAL POWER FLOW SOLUTIONS Thesis submitted in partial fulfillment of the requirements for the award of degree of Master of Engineering in Power Systems & Electric Drives Thapar University,
More informationLoadability Enhancement by Optimal Load Dispatch in Subtransmission Substations: A Genetic Algorithm
Loadability Enhancement by Optimal Load Dispatch in Subtransmission Substations: A Genetic Algorithm M.R. Haghifam A.Ghanbarnezhad H.Lavaee G.Khoshkholg Tarbait Modarres University Tehran Regional Electric
More informationOptimal Operation of Large Power System by GA Method
Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) (1): 1-7 Scholarlink Research Institute Journals, 01 (ISSN: 11-7016) jeteas.scholarlinkresearch.org Journal of Emerging Trends in
More informationOPTIMAL POWER FLOW BASED ON PARTICLE SWARM OPTIMIZATION
U.P.B. Sci. Bull., Series C, Vol. 78, Iss. 3, 2016 ISSN 2286-3540 OPTIMAL POWER FLOW BASED ON PARTICLE SWARM OPTIMIZATION Layth AL-BAHRANI 1, Virgil DUMBRAVA 2 Optimal Power Flow (OPF) is one of the most
More informationReal power-system economic dispatch using a variable weights linear programming method
Open Access Journal Journal of Power Technologies 95 (1) (2015) 34 39 journal homepage:papers.itc.pw.edu.pl Real power-system economic dispatch using a variable weights linear programming method M. Rahli,
More informationAnalyzing the Effect of Loadability in the
Analyzing the Effect of Loadability in the Presence of TCSC &SVC M. Lakshmikantha Reddy 1, V. C. Veera Reddy 2, Research Scholar, Department of Electrical Engineering, SV University, Tirupathi, India 1
More informationState Estimation and Power Flow Analysis of Power Systems
JOURNAL OF COMPUTERS, VOL. 7, NO. 3, MARCH 01 685 State Estimation and Power Flow Analysis of Power Systems Jiaxiong Chen University of Kentucky, Lexington, Kentucky 40508 U.S.A. Email: jch@g.uky.edu Yuan
More informationECONOMIC OPERATION OF POWER SYSTEMS USING HYBRID OPTIMIZATION TECHNIQUES
SYNOPSIS OF ECONOMIC OPERATION OF POWER SYSTEMS USING HYBRID OPTIMIZATION TECHNIQUES A THESIS to be submitted by S. SIVASUBRAMANI for the award of the degree of DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL
More informationMohd Jamil Khan and 2 Yogesh Kumar. Churu, Raj., India.
International Journal of Mathematics Research. ISSN 0976-5840 Volume 8, Number 3 (2016), pp. 251-263 International Research Publication House http://www.irphouse.com Optimal Power Flow (OPF) formulation
More informationMinimization of Energy Loss using Integrated Evolutionary Approaches
Minimization of Energy Loss using Integrated Evolutionary Approaches Attia A. El-Fergany, Member, IEEE, Mahdi El-Arini, Senior Member, IEEE Paper Number: 1569614661 Presentation's Outline Aim of this work,
More informationA Study of the Factors Influencing the Optimal Size and Site of Distributed Generations
Journal of Clean Energy Technologies, Vol. 2, No. 1, January 2014 A Study of the Factors Influencing the Optimal Size and Site of Distributed Generations Soma Biswas, S. K. Goswami, and A. Chatterjee system
More informationBranch Outage Simulation for Contingency Studies
Branch Outage Simulation for Contingency Studies Dr.Aydogan OZDEMIR, Visiting Associate Professor Department of Electrical Engineering, exas A&M University, College Station X 77843 el : (979) 862 88 97,
More informationApplication of Teaching Learning Based Optimization for Size and Location Determination of Distributed Generation in Radial Distribution System.
Application of Teaching Learning Based Optimization for Size and Location Determination of Distributed Generation in Radial Distribution System. Khyati Mistry Electrical Engineering Department. Sardar
More informationGENETIC ALGORITHM FOR CELL DESIGN UNDER SINGLE AND MULTIPLE PERIODS
GENETIC ALGORITHM FOR CELL DESIGN UNDER SINGLE AND MULTIPLE PERIODS A genetic algorithm is a random search technique for global optimisation in a complex search space. It was originally inspired by an
More informationEnhanced Newton Method Based Radial Distribution System Load Flow Analysis with Extrapolation Techniques
Enhanced Newton Method Based Radial Distribution System Load Flow Analysis with Extrapolation Techniques Asst. Prof. Dr. Hassan Kuhba Electrical Engineering Department, Engineering College/Baghdad University,
More informationUnderstanding Load Flow Studies by using PSAT
Understanding Load Flow Studies by using PSAT Vijay Kumar Shukla 1, Ashutosh Bhadoria 2 1,2 Department of Electrical Engineering, Lovely Professional University, Jalandhar, India Abstract: Load Flow Study
More informationA Decomposition Based Approach for Solving a General Bilevel Linear Programming
A Decomposition Based Approach for Solving a General Bilevel Linear Programming Xuan Liu, Member, IEEE, Zuyi Li, Senior Member, IEEE Abstract Bilevel optimization has been widely used in decisionmaking
More informationChapter 8: Introduction to Evolutionary Computation
Computational Intelligence: Second Edition Contents Some Theories about Evolution Evolution is an optimization process: the aim is to improve the ability of an organism to survive in dynamically changing
More informationThe Role of Crossover in Genetic Algorithms to Solve Optimization of a Function Problem Falih Hassan
The Role of Crossover in Genetic Algorithms to Solve Optimization of a Function Problem Falih Hassan ABSTRACT The genetic algorithm is an adaptive search method that has the ability for a smart search
More informationContents Economic dispatch of thermal units
Contents 2 Economic dispatch of thermal units 2 2.1 Introduction................................... 2 2.2 Economic dispatch problem (neglecting transmission losses)......... 3 2.2.1 Fuel cost characteristics........................
More informationOPTIMAL CAPACITORS PLACEMENT IN DISTRIBUTION NETWORKS USING GENETIC ALGORITHM: A DIMENSION REDUCING APPROACH
OPTIMAL CAPACITORS PLACEMENT IN DISTRIBUTION NETWORKS USING GENETIC ALGORITHM: A DIMENSION REDUCING APPROACH S.NEELIMA #1, DR. P.S.SUBRAMANYAM *2 #1 Associate Professor, Department of Electrical and Electronics
More informationCHAPTER 3 FUZZIFIED PARTICLE SWARM OPTIMIZATION BASED DC- OPF OF INTERCONNECTED POWER SYSTEMS
51 CHAPTER 3 FUZZIFIED PARTICLE SWARM OPTIMIZATION BASED DC- OPF OF INTERCONNECTED POWER SYSTEMS 3.1 INTRODUCTION Optimal Power Flow (OPF) is one of the most important operational functions of the modern
More information2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes
2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or
More informationQuasi-Newton Power Flow Using Partial Jacobian Updates
332 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 16, NO. 3, AUGUST 2001 Quasi-Newton Power Flow Using Partial Jacobian Updates Adam Semlyen, Life Fellow, IEEE and Francisco de León Abstract We present a quasi-newton
More informationInterior-point based algorithms for the solution of optimal power flow problems
Electric Power Systems Research 77 (2007) 508 517 Interior-point based algorithms for the solution of optimal power flow problems Florin Capitanescu, Mevludin Glavic, Damien Ernst, Louis Wehenkel Department
More informationMinimization of load shedding by sequential use of linear programming and particle swarm optimization
Turk J Elec Eng & Comp Sci, Vol.19, No.4, 2011, c TÜBİTAK doi:10.3906/elk-1003-31 Minimization of load shedding by sequential use of linear programming and particle swarm optimization Mehrdad TARAFDAR
More informationEvolutionary Computation. DEIS-Cesena Alma Mater Studiorum Università di Bologna Cesena (Italia)
Evolutionary Computation DEIS-Cesena Alma Mater Studiorum Università di Bologna Cesena (Italia) andrea.roli@unibo.it Evolutionary Computation Inspiring principle: theory of natural selection Species face
More informationEVOLUTIONARY ALGORITHM FOR CALCULATING AVAILABLE TRANSFER CAPABILITY
Journal of ELECTRICAL ENGINEERING, VOL. 64, NO. 5, 2013, 291 297 EVOLUTIONARY ALGORITHM FOR CALCULATING AVAILABLE TRANSFER CAPABILITY Darko Šošić Ivan Škokljev The paper presents an evolutionary algorithm
More informationAnalyzing the Optimal Reactive Power Dispatch in the Presence of Series and Shunt Facts Controllers
Analyzing the Optimal Reactive Power Dispatch in the Presence of Series and Shunt Facts Controllers M. Lakshmikantha Reddy 1, M. Ramprasad Reddy 2, V. C. Veera Reddy 3 Research Scholar, Department of Electrical
More informationMulti Objective Economic Load Dispatch problem using A-Loss Coefficients
Volume 114 No. 8 2017, 143-153 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Multi Objective Economic Load Dispatch problem using A-Loss Coefficients
More informationJournal of Artificial Intelligence in Electrical Engineering, Vol. 1, No. 2, September 2012
Multi-objective Based Optimization Using Tap Setting Transformer, DG and Capacitor Placement in Distribution Networks Abdolreza Sadighmanesh 1, Mehran Sabahi 2, Kazem Zare 2, and Babak Taghavi 3 1 Department
More informationLinear Programming: Simplex
Linear Programming: Simplex Stephen J. Wright 1 2 Computer Sciences Department, University of Wisconsin-Madison. IMA, August 2016 Stephen Wright (UW-Madison) Linear Programming: Simplex IMA, August 2016
More informationOPTIMAL DISPATCH OF REAL POWER GENERATION USING PARTICLE SWARM OPTIMIZATION: A CASE STUDY OF EGBIN THERMAL STATION
OPTIMAL DISPATCH OF REAL POWER GENERATION USING PARTICLE SWARM OPTIMIZATION: A CASE STUDY OF EGBIN THERMAL STATION Onah C. O. 1, Agber J. U. 2 and Ikule F. T. 3 1, 2, 3 Department of Electrical and Electronics
More informationA three-level MILP model for generation and transmission expansion planning
A three-level MILP model for generation and transmission expansion planning David Pozo Cámara (UCLM) Enzo E. Sauma Santís (PUC) Javier Contreras Sanz (UCLM) Contents 1. Introduction 2. Aims and contributions
More informationCHAPTER 4 INTRODUCTION TO DISCRETE VARIABLE OPTIMIZATION
CHAPTER 4 INTRODUCTION TO DISCRETE VARIABLE OPTIMIZATION. Introduction.. Examples of Discrete Variables One often encounters problems in which design variables must be selected from among a set of discrete
More informationCoordinated Design of Power System Stabilizers and Static VAR Compensators in a Multimachine Power System using Genetic Algorithms
Helwan University From the SelectedWorks of Omar H. Abdalla May, 2008 Coordinated Design of Power System Stabilizers and Static VAR Compensators in a Multimachine Power System using Genetic Algorithms
More informationMEASUREMENTS that are telemetered to the control
2006 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 4, NOVEMBER 2004 Auto Tuning of Measurement Weights in WLS State Estimation Shan Zhong, Student Member, IEEE, and Ali Abur, Fellow, IEEE Abstract This
More informationYIELD curves represent the relationship between market
Smoothing Yield Curve Data by Least Squares and Concavity or Convexity I. P. Kandylas and I. C. Demetriou Abstract A yield curve represents the relationship between market interest rates and time to maturity
More informationEvolutionary computation
Evolutionary computation Andrea Roli andrea.roli@unibo.it Dept. of Computer Science and Engineering (DISI) Campus of Cesena Alma Mater Studiorum Università di Bologna Outline 1 Basic principles 2 Genetic
More informationAn Effective Chromosome Representation for Evolving Flexible Job Shop Schedules
An Effective Chromosome Representation for Evolving Flexible Job Shop Schedules Joc Cing Tay and Djoko Wibowo Intelligent Systems Lab Nanyang Technological University asjctay@ntuedusg Abstract As the Flexible
More informationSIGNIFICANT increase in amount of private distributed
1 Distributed DC Optimal Power Flow for Radial Networks Through Partial Primal Dual Algorithm Vahid Rasouli Disfani, Student Member, IEEE, Lingling Fan, Senior Member, IEEE, Zhixin Miao, Senior Member,
More informationEvolutionary Functional Link Interval Type-2 Fuzzy Neural System for Exchange Rate Prediction
Evolutionary Functional Link Interval Type-2 Fuzzy Neural System for Exchange Rate Prediction 3. Introduction Currency exchange rate is an important element in international finance. It is one of the chaotic,
More informationDevelopment. biologically-inspired computing. lecture 16. Informatics luis rocha x x x. Syntactic Operations. biologically Inspired computing
lecture 16 -inspired S S2 n p!!! 1 S Syntactic Operations al Code:N Development x x x 1 2 n p S Sections I485/H400 course outlook Assignments: 35% Students will complete 4/5 assignments based on algorithms
More informationA DC Power Flow Extension
2013 4th IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe), October 6-9, Copenhagen 1 A DC Power Flow Extension Theodoros Kyriakidis, Rachid Cherkaoui, Maher Kayal Electronics Laboratory
More informationRepresentation and Hidden Bias II: Eliminating Defining Length Bias in Genetic Search via Shuffle Crossover
Representation and Hidden Bias II: Eliminating Defining Length Bias in Genetic Search via Shuffle Crossover Abstract The traditional crossover operator used in genetic search exhibits a position-dependent
More informationTwo-Layer Network Equivalent for Electromagnetic Transients
1328 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 18, NO. 4, OCTOBER 2003 Two-Layer Network Equivalent for Electromagnetic Transients Mohamed Abdel-Rahman, Member, IEEE, Adam Semlyen, Life Fellow, IEEE, and
More informationStructure Design of Neural Networks Using Genetic Algorithms
Structure Design of Neural Networks Using Genetic Algorithms Satoshi Mizuta Takashi Sato Demelo Lao Masami Ikeda Toshio Shimizu Department of Electronic and Information System Engineering, Faculty of Science
More information796 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 24, NO. 2, MAY /$ IEEE
796 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 24, NO. 2, MAY 2009 Coupling Optimization and Dynamic Simulation for Preventive-Corrective Control of Voltage Instability Florin Capitanescu, Thierry Van Cutsem,
More informationHaploid-Diploid Algorithms
Haploid-Diploid Algorithms Larry Bull Department of Computer Science & Creative Technologies University of the West of England Bristol BS16 1QY, U.K. +44 (0)117 3283161 Larry.Bull@uwe.ac.uk LETTER Abstract
More informationCAPACITOR PLACEMENT IN UNBALANCED POWER SYSTEMS
CAPACITOR PLACEMET I UBALACED POWER SSTEMS P. Varilone and G. Carpinelli A. Abur Dipartimento di Ingegneria Industriale Department of Electrical Engineering Universita degli Studi di Cassino Texas A&M
More informationCourse notes for EE394V Restructured Electricity Markets: Locational Marginal Pricing
Course notes for EE394V Restructured Electricity Markets: Locational Marginal Pricing Ross Baldick Copyright c 2013 Ross Baldick www.ece.utexas.edu/ baldick/classes/394v/ee394v.html Title Page 1 of 132
More information1348 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY /$ IEEE
1348 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 3, JULY 2010 Optimal Coordination of Directional Overcurrent Relays Considering Different Network Topologies Using Interval Linear Programming Abbas
More informationIncorporation of Asynchronous Generators as PQ Model in Load Flow Analysis for Power Systems with Wind Generation
Incorporation of Asynchronous Generators as PQ Model in Load Flow Analysis for Power Systems with Wind Generation James Ranjith Kumar. R, Member, IEEE, Amit Jain, Member, IEEE, Power Systems Division,
More informationComparison between Interval and Fuzzy Load Flow Methods Considering Uncertainty
Comparison between Interval and Fuzzy Load Flow Methods Considering Uncertainty T.Srinivasarao, 2 P.Mallikarajunarao Department of Electrical Engineering, College of Engineering (A), Andhra University,
More informationOPTIMAL POWER FLOW (OPF) is a tool that has been
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 2, MAY 2005 773 Cumulant-Based Probabilistic Optimal Power Flow (P-OPF) With Gaussian and Gamma Distributions Antony Schellenberg, William Rosehart, and
More informationIN order to provide system operators (SOs) with useful
1 Redispatching active and reactive powers using a limited number of control actions Florin Capitanescu and Louis Wehenkel, Member, IEEE Abstract This paper deals with some essential open questions in
More informationOptimal Locating and Sizing of TCPST for Congestion Management in Deregulated Electricity Markets
Optimal Locating and Sizing of TCPST for Congestion Management in Deregulated Electricity Markets M. Joorabian Shahid Chamran University, Ahwaz, Iran mjoorabian@yahoo.com M. Saniei Shahid Chamran University,
More informationModule 6 : Preventive, Emergency and Restorative Control. Lecture 27 : Normal and Alert State in a Power System. Objectives
Module 6 : Preventive, Emergency and Restorative Control Lecture 27 : Normal and Alert State in a Power System Objectives In this lecture you will learn the following Different states in a power system
More informationOptimal Power Flow. S. Bose, M. Chandy, M. Farivar, D. Gayme S. Low. C. Clarke. Southern California Edison. Caltech. March 2012
Optimal Power Flow over Radial Networks S. Bose, M. Chandy, M. Farivar, D. Gayme S. Low Caltech C. Clarke Southern California Edison March 2012 Outline Motivation Semidefinite relaxation Bus injection
More informationProbabilistic Assessment of Atc in the Deregulated Network
Australian Journal of Basic and Applied Sciences, 5(6): 882-890, 2011 ISSN 1991-8178 Probabilistic Assessment of Atc in the Deregulated Network Mojtaba Najafi and Mohsen Simab Department of Engineering,
More informationA Modular Approach to Power Flow Regulation Solution
Send Orders for Reprints to reprints@benthamscience.ae The Open Electrical & Electronic Engineering Journal, 25, 9, 9-98 9 A Modular Approach to Power Flow Regulation Solution Open Access Yang Liu-Lin,*,
More informationPower System Security Analysis. B. Rajanarayan Prusty, Bhagabati Prasad Pattnaik, Prakash Kumar Pandey, A. Sai Santosh
849 Power System Security Analysis B. Rajanarayan Prusty, Bhagabati Prasad Pattnaik, Prakash Kumar Pandey, A. Sai Santosh Abstract: In this paper real time security analysis is carried out. First contingency
More informationIEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 24, NO. 3, AUGUST
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 24, NO. 3, AUGUST 2009 1435 DCOPF-Based Marginal Loss Pricing With Enhanced Power Flow Accuracy by Using Matrix Loss Distribution V. Sarkar, Student Member, IEEE,
More informationData Warehousing & Data Mining
13. Meta-Algorithms for Classification Data Warehousing & Data Mining Wolf-Tilo Balke Silviu Homoceanu Institut für Informationssysteme Technische Universität Braunschweig http://www.ifis.cs.tu-bs.de 13.
More informationPower System Security. S. Chakrabarti
Power System Security S. Chakrabarti Outline Introduction Major components of security assessment On-line security assessment Tools for contingency analysis DC power flow Linear sensitivity factors Line
More informationA Statistical Genetic Algorithm
A Statistical Genetic Algorithm Angel Kuri M. akm@pollux.cic.ipn.mx Centro de Investigación en Computación Instituto Politécnico Nacional Zacatenco México 07738, D.F. Abstract A Genetic Algorithm which
More informationThe Existence of Multiple Power Flow Solutions in Unbalanced Three-Phase Circuits
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003 605 The Existence of Multiple Power Flow Solutions in Unbalanced Three-Phase Circuits Yuanning Wang, Student Member, IEEE, and Wilsun Xu, Senior
More informationNONLINEAR. (Hillier & Lieberman Introduction to Operations Research, 8 th edition)
NONLINEAR PROGRAMMING (Hillier & Lieberman Introduction to Operations Research, 8 th edition) Nonlinear Programming g Linear programming has a fundamental role in OR. In linear programming all its functions
More informationPROPOSED STRATEGY FOR CAPACITOR ALLOCATION IN RADIAL DISTRIBUTION FEEDERS
IMPACT: International ournal of Research in Engineering & Technology (IMPACT: IRET) ISSN 2321-8843 Vol. 1, Issue 3, Aug 2013, 85-92 Impact ournals PROPOSED STRATEGY FOR CAPACITOR ALLOCATION IN RADIAL DISTRIBUTION
More informationAnalysis of Coupling Dynamics for Power Systems with Iterative Discrete Decision Making Architectures
Analysis of Coupling Dynamics for Power Systems with Iterative Discrete Decision Making Architectures Zhixin Miao Department of Electrical Engineering, University of South Florida, Tampa FL USA 3362. Email:
More informationAN EVOLUTIONARY ALGORITHM TO ESTIMATE UNKNOWN HEAT FLUX IN A ONE- DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM
Proceedings of the 5 th International Conference on Inverse Problems in Engineering: Theory and Practice, Cambridge, UK, 11-15 th July 005. AN EVOLUTIONARY ALGORITHM TO ESTIMATE UNKNOWN HEAT FLUX IN A
More informationINSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous)
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 ELECTRICAL AND ELECTRONICS ENGINEERING QUESTION BANK Course Name : Computer Methods in Power Systems Course Code : A60222
More informationTotal Transfer Capability Enhancement Using Hybrid Evolutionary Algorithm
CMU. J. Nat. Sci. (2007) Vol. 6(2) 301 Total Transfer Capability Enhancement Using Hybrid Evolutionary Algorithm Peerapol Jirapong* Department of Electrical Engineering, Faculty of Engineering, Chiang
More informationReactive Power and Voltage Control of Power Systems Using Modified PSO
J. Energy Power Sources Vol. 2, No. 5, 2015, pp. 182-188 Received: March 29, 2015, Published: May 30, 2015 Journal of Energy and Power Sources www.ethanpublishing.com Reactive Power and Voltage Control
More informationA Benders Decomposition Approach to Corrective Security Constrained OPF with Power Flow Control Devices
A Benders Decomposition Approach to Corrective Security Constrained OPF with Power Flow Control Devices Javad Mohammadi, Gabriela Hug, Soummya Kar Department of Electrical and Computer Engineering Carnegie
More informationLocal Search & Optimization
Local Search & Optimization CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2017 Soleymani Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 4 Outline
More informationDetermination of Optimal Tightened Normal Tightened Plan Using a Genetic Algorithm
Journal of Modern Applied Statistical Methods Volume 15 Issue 1 Article 47 5-1-2016 Determination of Optimal Tightened Normal Tightened Plan Using a Genetic Algorithm Sampath Sundaram University of Madras,
More informationARTIFICIAL NEURAL NETWORK WITH HYBRID TAGUCHI-GENETIC ALGORITHM FOR NONLINEAR MIMO MODEL OF MACHINING PROCESSES
International Journal of Innovative Computing, Information and Control ICIC International c 2013 ISSN 1349-4198 Volume 9, Number 4, April 2013 pp. 1455 1475 ARTIFICIAL NEURAL NETWORK WITH HYBRID TAGUCHI-GENETIC
More informationAn Equivalent Circuit Formulation of the Power Flow Problem with Current and Voltage State Variables
An Equivalent Circuit Formulation of the Power Flow Problem with Current and Voltage State Variables David M. Bromberg, Marko Jereminov, Xin Li, Gabriela Hug, Larry Pileggi Dept. of Electrical and Computer
More informationPOWER SYSTEMS in general are currently operating
TO APPEAR IN IEEE TRANSACTIONS ON POWER SYSTEMS 1 Robust Optimal Power Flow Solution Using Trust Region and Interior-Point Methods Andréa A. Sousa, Geraldo L. Torres, Member IEEE, Claudio A. Cañizares,
More informationSlack Bus Treatment in Load Flow Solutions with Uncertain Nodal Powers
8 th International Conference on Probabilistic Methods Applied to Power Systems, Iowa State University, Ames, Iowa, September 12-16, 2004 Slack Bus reatment in Load Flow Solutions with Uncertain Nodal
More informationCoordinated Multilateral Trades for Electric Power Networks: Theory and Implementation. Felix F. Wu and Pravin Varaiya
PWP-031 Coordinated Multilateral Trades for Electric Power Networks: Theory and Implementation Felix F. Wu and Pravin Varaiya June 1995 This paper is part of the working papers series of the Program on
More informationIN RECENT years, an instability, usually termed a voltage
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I: REGULAR PAPERS, VOL. 52, NO. 3, MARCH 2005 625 Toward a CPFLOW-Based Algorithm to Compute all the Type-1 Load-Flow Solutions in Electric Power Systems Chih-Wen
More informationA PROPOSED STRATEGY FOR CAPACITOR ALLOCATION IN RADIAL DISTRIBUTION FEEDERS
A PROPOSED STRATEGY FOR CAPACITOR ALLOCATION IN RADIAL DISTRIBUTION FEEDERS 1 P.DIVYA, 2 PROF. G.V.SIVA KRISHNA RAO A.U.College of Engineering, Andhra University, Visakhapatnam Abstract: Capacitors in
More information