A new technique for solving the multi-objective optimization problem using hybrid approach

Energy efficiency, which consists of using less energy or improving the level of service to energy consumers, refers to an effective way to provide overall energy. But its increasing pressure on the energy sector to control greenhouse gases and to reduce CO₂ emissions forced the power system operators to consider the emission problem as a consequential matter besides the economic problems. The economic power dispatch problem has, therefore, become a multi-objective optimization problem. Fuel cost, pollutant emissions, and system loss should be minimized simultaneously while satisfying certain system constraints. To achieve a good design with different solutions in a multi-objective optimization problem, fuel cost and pollutant emissions are converted into single optimization problem by introducing penalty factor. Now the power dispatch is formulated into a bi-objective optimization problem, two objectives with two algorithms, firefly algorithm for optimization the fuel cost, pollutant emissions and the real genetic algorithm for minimization of the transmission losses. In this paper the new approach (firefly algorithm-real genetic algorithm, FFA-RGA) has been applied to the standard IEEE 30-bus 6-generator. The effectiveness of the proposed approach is demonstrated by comparing its performance with other evolutionary multi-objective optimization algorithms. Simulation results show the validity and feasibility of the proposed method.     

Tuned reactive power dispatch through modified differential evolution technique

This paper explores the capability of modified differential evolution (MDE) technique for solving the reactive power dispatch (RPD) problem. The proposed method is based on the basic differential evolution (DE) technique with a few modifications made into it. DE is one of the strongest optimization techniques though it suffers from the problem of slow convergence while global minima appear. The proposed modifications are tried to resolve the problem. The RPD problem mainly defines loss minimization with stable voltage profile. To solve the RPD problem, the generator bus voltage, transformer tap setting and shunt capacitor placements are controlled by the MDE approach. In this paper, IEEE 14-bus and IEEE 30-bus systems are chosen for MDE implementation. The applied modification show much improved result in comparison to normal DE technique. Comparative study with other soft-computing technique including DE validates the effectiveness of the proposed method.     

Multiobjective fuzzy dominance based bacterial foraging algorithm to solve economic emission dispatch problem

This paper proposes the bacterial foraging meta-heuristic algorithm for multiobjective optimization. In this multiobjective bacterial foraging optimization technique, the most recent bacterial locations are obtained by chemotaxis process. Next, Fuzzy dominance based sorting procedure is used here to select the Pareto optimal front (POF). To test the suitability of our proposed algorithm we have considered a highly constrained optimization problem namely economic/emission dispatch. Now-a-days environmental concern that arises due to the operation of fossil fuel fired electric generators and global warming, transforms the classical economic load dispatch problem into multiobjective environmental/economic dispatch (EED) problem. In the proposed work, we have considered the standard IEEE 30-bus six-generator test system and the results obtained by proposed algorithm are compared with the other recently reported results. Simulation results demonstrate that the proposed algorithm is a capable candidate in solving the multiobjective economic emission load dispatch problem.     

Artificial bee colony optimization for economic dispatch with valve point effect

In recent years, various heuristic optimization methods have been proposed to solve economic dispatch (ED) problem in power systems. This paper presents the well-known power system ED problem solution considering valve-point effect by a new optimization algorithm called artificial bee colony (ABC). The proposed approach has been applied to various test systems with incremental fuel cost function, taking into account the valve-point effects. The results show that the proposed approach is efficient and robust when compared with other optimization algorithms reported in literature.     

Reactive-power dispatch by successive quadratic programming

The reactive-power dispatch is formulated as the minimization of real-power losses in the system, utilizing a full set of control variables: generator voltages, switchable shunt susceptances, and transformer taps. The solution of the loss problem is obtained by successively solving quadratic programming problems. First- and second-order loss sensitivity coefficients are derived for the quadratic problem formulation. The derivations are based on the Jacobian method for sensitivity calculations. Sensitivity relations for the dependent constraints are based on the complete reactive-power model of the fast decoupled load flow method. The active-set projection method for quadratic programming is described and utilized as the solution algorithm for the quadratic reactive-power dispatch problems. Tests are conducted on the IEEE 30-bus and Mexican 253-bus systems. The computer results are discussed     

Joint economic and emission dispatch in energy markets: A multiobjective mathematical programming approach

Economic load dispatch is the method of determining the most efficient, low-cost and reliable operation of a power system by dispatching the available electricity generation resources to supply the load on the system. Environmental concerns that arise due to the operation of fossil fuel fired electric generators, change the classical problem into multiobjective emission/economic dispatch (MEED) which is formulated as a constrained nonlinear multiobjective mathematical programming (MMP). The proposed MEED formulation includes emission minimization objective, AC load flow constraints and security constraints of the power system which usually are found simultaneously in real-world power systems. The proposed model has a more accurate evaluation of transmission losses obtained from the load flow equations. The MMP approach based on ?-constraint algorithm has been proposed for generating Pareto-optimal solutions of power systems MEED problem. Moreover, fuzzy decision making process is employed to extract one of the Pareto-optimal solutions as the best compromise nondominated solution. The proposed approach is simulated on the IEEE 30-bus six-generator test system and obtained results have been comprehensively compared with some of the most recently published research in the area (from the both aspects of precision and execution tome) which confirms the potential and effectiveness of the proposed approach.     

Biobjective power dispatch using goal-attainment method and adaptive polynomial networks

This paper presents an integrated approach that combines goal-attainment (GA) and adaptive polynomial networks (APN) to real-time biobjective power dispatch. The goals considered are fuel cost and the environmental impact of multiple emissions. The complicated relationships between the input (power demand and operator's economic and emission preferences) and the output (power generated by each generator) can be efficiently modeled by the APN. Moreover, the APN can rapidly provide an accurate estimate of the real-time dispatch results for the power demand and the operator's preferences. The effectiveness of the proposed approach has been demonstrated by the IEEE 30-bus six-generator and the practical Taipower 388-bus 27-generator systems. Test results reveal that the proposed approach achieves significant savings in computation time and reduces the complexity of the real-time power dispatch. Furthermore, the proposed APN outperforms the artificial neural networks (ANNs) method, in both developing the model and estimating the power generated by each generator.     

Multiobjective power dispatch with line flow constraints using thefast Newton-Raphson method

The fast Newton-Raphson approach based on an alternative Jacobian matrix is proposed to solve the power system multiobjective power dispatch (MPD) problem with line flow constraints. Two conflicting objectives including minimization of fuel cost and environmental impact of emission are considered in this study. The Jacobian matrix is formulated by the incremental transmission loss in terms of the sensitivity factors, line flows and line resistances. The sensitivity factors are obtained from line flow solutions based on a DC load flow model. Moreover, the B-coefficients matrix and the Lagrange function can be shown as convex functions. Therefore, the existence and uniqueness of the solution for the nonlinear equation of the MPD problem can be proven. The proposed approach is tested on the IEEE 14- and 30-bus systems. Simulation results obtained from the proposed method confirm the advantage of computation rapidity and solution accuracy over that of the AC load flow method and the conventional B-coefficients method, respectively. The comparison confirms the capability of the proposed method in real-time implementation for the MPD problem     

Solution to economic dispatch problem with valve-point loading effect by using catfish PSO algorithm

This paper proposes application of a catfish particle swarm optimization (PSO) algorithm to economic dispatch (ED) problems. The ED problems considered in this paper include valve-point loading effect, power balance constraints, and generator limits. The conventional PSO and catfish PSO algorithms are applied to three different test systems and the solutions obtained are compared with each other and with those reported in literature. The comparison of solutions shows that catfish PSO outperforms the conventional PSO and other methods in terms of solution quality though there is a slight increase in computational time.     

Lift-and-project MVEE based convex hull for robust SCED with wind power integration using historical data-driven modeling approach

This paper presents an adjustable robust security constrained economic dispatch (SCED) model with wind power uncertainties. First, the scenario based adjustable robust SCED model is presented. It considers multiple scenarios from historical data as well as the spatial correlation among wind farms. Then, the proposed SCED model becomes an optimization problem with a large amount of constraints which is skillfully solved using a lift-and-project minimum volume enclosing ellipsoid (MVEE) based convex hull. Furthermore, the proposed model is transformed into a second order cone programming (SOCP) model by the use of participation factors to generate adjustable generation outputs and thus guarantee the energy balance. In order to further reduce the computational complexity, the inactive constraints reduction strategy is proposed to quickly eliminate inactive SOC security constraints before solving the model. Numerical results of IEEE 14-bus and 118-bus test systems as well as the practical Polish power systems with several wind farms show that the proposed model can achieve better economies. Moreover, more than 82% of security constraints are identified as inactive in various cases of the simulation, and the proposed inactive constraints reduction strategy is promising for improving the computational performance.     

Joint market clearing in a stochastic framework considering power system security

This paper presents a new stochastic framework for provision of reserve requirements (spinning and non-spinning reserves) as well as energy in day-ahead simultaneous auctions by pool-based aggregated market scheme. The uncertainty of generating units in the form of system contingencies are considered in the market clearing procedure by the stochastic model. The solution methodology consists of two stages, which firstly, employs Monte–Carlo Simulation (MCS) for random scenario generation. Then, the stochastic market clearing procedure is implemented as a series of deterministic optimization problems (scenarios) including non-contingent scenario and different post-contingency states. The objective function of each of these deterministic optimization problems consists of offered cost function (including both energy and reserves offer costs), Lost Opportunity Cost (LOC) and Expected Interruption Cost (EIC). Each optimization problem is solved considering AC power flow and security constraints of the power system. The model is applied to the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS) and simulation studies are carried out to examine the effectiveness of the proposed method.     

An effortless hybrid method to solve economic load dispatch problem in power systems

This paper proposes a new approach and coding scheme for solving economic dispatch problems (ED) in power systems through an effortless hybrid method (EHM). This novel coding scheme can effectively prevent futile searching and also prevents obtaining infeasible solutions through the application of stochastic search methods, consequently dramatically improves search efficiency and solution quality. The dominant constraint of an economic dispatch problem is power balance. The operational constraints, such as generation limitations, ramp rate limits, prohibited operating zones (POZ), network loss are considered for practical operation. Firstly, in the EHM procedure, the output of generator is obtained with a lambda iteration method and without considering POZ and later in a genetic based algorithm this constraint is satisfied. To demonstrate its efficiency, feasibility and fastness, the EHM algorithm was applied to solve constrained ED problems of power systems with 6 and 15 units. The simulation results obtained from the EHM were compared to those achieved from previous literature in terms of solution quality and computational efficiency. Results reveal that the superiority of this method in both aspects of financial and CPU time.     

Genetic single objective optimisation for sizing and allocation of renewable DG systems

The optimal design of renewable-based distributed generations (DGs) is a challenging issue in order to maximise their benefits and to overcome power quality problems. Therefore, this paper proposes a methodology for optimal allocation and sizing of renewable DG units to minimise total power losses over radial distribution systems. The planning problem is formulated as a single objective nonlinear mixed integer-constrained optimisation problem and is solved by using the augmented Lagrangian genetic algorithm (ALGA) by combining the objective function and the nonlinear constraints. In that case, the ALGA solves a sequence of sub-problems where the objective function penalises the constraints violation in order to obtain the best solution. The proposed technique is applied to IEEE radial test systems including 33-bus, 69-bus and 119-bus and is implemented with different scenarios including all possible combinations and various types of renewable DG units to prove the effectiveness of the proposed methodology.     

Economic dispatch using particle swarm optimization: A review

Electrical power industry restructuring has created highly vibrant and competitive market that altered many aspects of the power industry. In this changed scenario, scarcity of energy resources, increasing power generation cost, environment concern, ever growing demand for electrical energy necessitate optimal economic dispatch. Practical economic dispatch (ED) problems have nonlinear, non-convex type objective function with intense equality and inequality constraints. The conventional optimization methods are not able to solve such problems as due to local optimum solution convergence. Meta-heuristic optimization techniques especially particle swarm optimization (PSO) has gained an incredible recognition as the solution algorithm for such type of ED problems in last decade. The application of PSO in ED problem, which is considered as one of the most complex optimization problem has been summarized in present paper.     

基于改进的多目标差分演化算法求解电力系统清洁经济优化调度问题

利用改进的多目标差分演化算法求解考虑安全运行约束的电力系统清洁经济优化调度问题,对相互冲突的发电费用函数和污染气体排放量函数同时进行优化,采用非支配排序和拥挤距离排序对种群进行选择操作,并引入基于平均熵的种群初始化和基于混沌Logistic映射的控制参数调整策略来改善算法收敛性能。在IEEE 30节点6机系统上获得的仿真结果验证了该算法的优越性。     

A novel evolutionary algorithm for dynamic economic dispatch with energy saving and emission reduction in power system integrated wind power

An optimization algorithm is proposed in this paper to solve the economic dispatch problem that includes wind farm using the Chaotic Quantum Genetic Algorithm (CQGA). In addition to the detailed models of economic dispatch introduction and their associated constraints, the wind power effect is also included in this paper. The chaotic quantum genetic algorithm used to solve the economic dispatch process and discussed with real scenarios used for the simulation tests. After comparing the proposed algorithm with several other algorithms commonly used to solve optimization problems, the results show that the proposed algorithm is able to find the optimal solution quickly and accurately (i.e. to obtain the minimum cost for power generation in the shortest time). At the end, the impact to the total cost savings for power generation after adding (or not adding) wind power generation is also discussed. The actual implementation results prove that the proposed algorithm is economical, fast and practical. They are quite valuable for further research.     

Nash-Q learning-based collaborative dispatch strategy for interconnected power systems

The large-scale utilization and sharing of renewable energy in interconnected systems is crucial for realizing “instrumented, interconnected, and intelligent” power grids. The traditional optimal dispatch method can not coordinate the economic benefits of all the stakeholders from multiple regions of the transmission network, comprehensively. Hence, this study proposes a large-scale wind-power coordinated consumption strategy based on the Nash-Q method and establishes an economic dispatch model for interconnected systems considering the uncertainty of wind power, with optimal wind- power consumption as the objective for redistributing the shared benefits between regions. Initially, based on the equivalent cost of the interests of stakeholders from different regions, the state decision models are respectively constructed, and the noncooperative game Nash equilibrium model is established. The Q-learning algorithm is then introduced for high-dimension decision variables in the game model, and the dispatch solution methods for interconnected systems are presented, integrating the noncooperative game Nash equilibrium and Q-learning algorithm. Finally, the proposed method is verified through the modified IEEE 39-bus interconnection system, and it is established that this method achieves reasonable distribution of interests between regions and promotes large-scale consumption of wind power.     

Interactive DE for solving combined security environmental economic dispatch considering FACTS technology

This paper presents an efficient interactive differential evolution (IDE) to solve the multi-objective security environmental/economic dispatch (SEED) problem considering multi shunt flexible AC transmission system (FACTS) devices. Two sub problems are proposed.The first one is related to the active power planning to minimize the combined total fuel cost and emissions, while the second is a reactive power planning (RPP) using multi shunt FACTS device based static VAR compensator (SVC) installed at specified buses to make fine corrections to the voltage deviation, voltage phase profiles and reactive power violation. The migration operation inspired from biogeography-based optimization (BBO) algorithm is newly introduced in the proposed approach, thereby effectively exploring and exploiting promising regions in a space search by creating dynamically new efficient partitions. This new mechanism based migration between individuals from different subsystems makes the initial partitions to react more by changing experiences. To validate the robustness of the proposed approach, the proposed algorithm is tested on the Algerian 59-bus electrical network and on a large system, 40 generating units considering valve-point loading effect. Comparison of the results with recent global optimization methods show the superiority of the proposed IDE approach and confirm its potential for solving practical optimal power flow in terms of solution quality and convergence characteristics.     

An improved PSO for dynamic load dispatch of generators with valve-point effects

Dynamic load economic dispatch problem (DLED) is important in power systems operation, which is a complicated nonlinear constrained optimization problem. It has nonsmooth and nonconvex characteristics when generator valve-point effects are taken into account. This paper proposes an improved particle swarm optimization (IPSO) to solve DLED with valve-point effects. In the proposed IPSO method, feasibility-based rules and heuristic strategies with priority list based on probability are devised to handle constraints effectively. In contrast to the penalty function method, the constraint-handling method does not require penalty factors or any extra parameters and can guide the population to the feasible region quickly. Especially, equality constraints of DLED can be satisfied precisely. Furthermore, the effects of two crucial parameters on the performance of the IPSO for DLED are also studied. The feasibility and the effectiveness of the proposed method are demonstrated applying it to some examples and the test results are compared with those of other methods reported in the literature. It is shown that the proposed method is capable of yielding higher-quality solutions.     

A genetic evolving ant direction DE for OPF with non-smooth cost functions and statistical analysis

This paper proposes an evolving ant direction differential evolution (EADDE) algorithm for solving the optimal power flow problem with non-smooth and non-convex generator fuel cost characteristics. The EADDE employs ant colony search to find a suitable mutation operator for differential evolution (DE) whereas the ant colony parameters are evolved using genetic algorithm approach. The Newton–Raphson method solves the power flow problem. The feasibility of the proposed approach was tested on IEEE 30-bus system with three different cost characteristics. Several cases were investigated to test and validate the robustness of the proposed method in finding the optimal solution. Simulation results demonstrate that the EADDE provides superior results compared to a classical DE and other methods recently reported in the literature. An innovative statistical analysis based on central tendency measures and dispersion measures was carried out on the bus voltage profiles and voltage stability indices.