Dynamic Economic Dispatch Problem Research Articles

Dynamic Economic Emission Dispatch Considering Wind Uncertainty Using Non-Dominated Sorting Crisscross Optimization

This paper presents a multi objective crisscross optimization to solve dynamic economic emission dispatch with wind-power uncertainty. The dynamic economic dispatch with combined emission requirements is formulated as a multi-objective optimization problem. The wind power output is predicted as an uncertain model and varies within a bounded limit. Minimizing the wind curtailment is added as an objective to the existing problem objectives of minimizing cost and emissions. Multi-objective crisscross optimization is proposed to solve the problem, utilizing a fast non-dominated sorting principle to obtain the optimal Pareto set of solutions. The proposed non-dominated sorting also ensures diversity, elitism and various complexities due to the high dimensionality of the problem. Exploration for global convergence and exploitation for a better solution is governed by two operators, namely, horizontal crossover and vertical crossover. The proposed solution technique is applied to standard multi-objective benchmark test problems and subsequently to standard dynamic economic dispatch problems with different ratios of wind power penetration.

An Efficient Modified HPSO-TVAC-Based Dynamic Economic Dispatch of Generating Units

This paper proposes a novel particle swarm optimization (PSO) algorithm with population reduction, which is called modified new self-organizing hierarchical PSO with jumping time-varying acceleration coefficients (MNHPSO-JTVAC). The proposed method is used for solving well-known benchmark functions, as well as non-convex and non-smooth dynamic economic dispatch (DED) problems for a 24 h time interval in two different test systems. Operational constraints including the prohibited operating zones (POZs), the transmission losses, the ramp-rate limits and the valve-point effects are considered in solving the DED problem. The obtained numerical results show that the MNHPSO-JTVAC algorithm is very suitable and competitive compared to other algorithms and have the capacity to obtain better optimal solutions in solving the non-convex and non-smooth DED problems compared to the other variants of PSO and the state of the art optimization algorithms proposed in recent literature. The source codes of the HPSO-TVAC algorithms and supplementary data for this paper are publicly available at https://github.com/ebrahimakbary/MNHPSO-JTVAC.

Ramp rate handling strategies in Dynamic Economic Load Dispatch (DELD) problem using Grey Wolf Optimizer (GWO)

ABSTRACTThis article presents multiple strategies to handle ramp rate in dynamic economic load dispatch (DELD) problem. DELD is a power system optimization problem that tackles the dispatch of thermal generators over a period of 24 h under numerous constraints like power balance, ramp rate, rippling effect and generator limits. All these constraints make DELD highly non-linear, complex, multi-dimensional and computationally intensive. In our research, we have devised unique ramp rate handling strategies and employed grey wolf optimizer (GWO) to implement them in MATLAB environment for the solution of IEEE standard 5-unit DELD system. GWO is a meta-heuristic optimization algorithm that has extensive global exploration and strong local exploitation capabilities. Addition of ramp rate handling strategies to the solution of DELD by GWO yielded diverse results. Each of these was statistically analyzed and the best results were compared with other techniques cited in the literature. Comparison indicated improvement in cost and solution time.

Dynamic economic dispatch: a comparative study for differential evolution, particle swarm optimization, evolutionary programming, genetic algorithm, and simulated annealing

This paper presents a comparative study for five artificial intelligent (AI) techniques to the dynamic economic dispatch problem: differential evolution, particle swarm optimization, evolutionary programming, genetic algorithm, and simulated annealing. Here, the optimal hourly generation schedule is determined. Dynamic economic dispatch determines the optimal scheduling of online generator outputs with predicted load demands over a certain period of time taking into consideration the ramp rate limits of the generators. The AI techniques for dynamic economic dispatch are evaluated against a ten-unit system with nonsmooth fuel cost function as a common testbed and the results are compared against each other.

Modified Antipredatory Particle Swarm Optimization for Dynamic Economic Dispatch with Wind Power

A modified antipredatory particle swarm optimization (MAPSO) algorithm with evasive adjustment behavior is proposed to solve the dynamic economic dispatch problem of wind power. The algorithm adds the social avoidance inertia weight to the conventional antipredatory particle swarm optimization (APSO) speed update formula. The size of inertia weight is determined by the distance between the global worst particle and other particles. After normalizing the distance, the inertia weight is controlled within the ideal range by using the characteristics of sigmoid function and linear decreasing method, which improves the ability of particles to avoid the worst solution. Then, according to the characteristics of the acceleration coefficient which can adjust the local and global searching ability of particles, acceleration coefficients of nonlinear change strategy is proposed to improve the searching ability of the algorithm. Finally, the proposed algorithm is applied to several benchmark functions and power grid system models, and the results are compared with those reported using other algorithms, which prove the effectiveness and superiority of the proposed algorithm.

RETRACTED ARTICLE: Enhanced multi-objective crisscross optimization for dynamic economic emission dispatch considering demand response and wind power uncertainty

In this paper, the dynamic economic emission dispatch problem in electric power system is formulated as a multi-objective optimization problem in a smart grid perspective. Accordingly, two additional subproblems are included in the dynamic economic emission dispatch formulation. Firstly, the wind power generation is penetrated into the system such that the uncertain power varies between a predicted upper and lower bounds. Secondly, a demand response program is implemented at the customer end, to modify the consumption pattern of electricity according to different electricity prices at valley, peak and off-peak periods. A two-level optimization is proposed to determine the optimal schedule of generating units such that the upper level solves for the minimization of cost and emission, whereas the lower level minimizes the wind power output interval reduction. An enhanced multi-objective crisscross optimization using non-dominated sorting approach is proposed as main optimizer to solve upper-level problem, and a linear programming is adopted to solve the lower-level problem. A 10-unit system is taken as a case study for demonstration, and the result shows the effectiveness of proposed formulation in terms of minimizing cost and emission.

An improved invasive weed optimization algorithm for solving dynamic economic dispatch problems with valve-point effects

ABSTRACT In this study, an improved invasive weed optimisation (CMIWO) algorithm is investigated to solve the dynamic economic dispatch (DED) problem with valve-point effects. In the proposed algorithm, a hybrid operator including selective crossover, random mutation and row crossover is proposed to improve the exploration and exploitation abilities. Moreover, a self-adaption repair method is developed and embedded into the proposed algorithm to repair infeasible solutions. To verify the optimisation performance of CMIWO, six well-known DED problems in three different-scale power systems are tested and compared with other algorithms that have been proposed in the literature. The experimental results show that CMIWO can find the more economical dispatch solutions compared to other algorithms, and the self-adaption repair method can successfully convert infeasible solutions into feasible solutions. The convergence ability of CMIWO is also verified after the detailed comparison.

Dynamic Economic/Environmental Dispatch Problem Considering Prohibited Operating Zones

Along with economic dispatch, emission dispatch has become a key problem under market conditions. Thus, the combination of the above problems in one problem called economic emission dispatch (EED) problem became inevitable. However, due to the dynamic nature of today’s network loads, it is required to schedule the thermal unit outputs in real-time according to the variation of power demands during a certain time period. Within this context, this paper presents an elitist technique, the second version of the non-dominated sorting genetic algorithm (NSAGII) for solving the dynamic economic emission dispatch (DEED) problem. Several equality and inequality constraints, such as valve point loading effects, ramp rate limits and prohibited operating zones (POZ), are taken into account. Therefore, the DEED problem is considered as a non-convex optimization problem with multiple local minima with higher-order non-linearities and discontinuities. A fuzzy-based membership function value assignment method is suggested to provide the best compromise solution from the Pareto front. The effectiveness of the proposed approach is verified on the standard power system with ten thermal units.

Flower pollination algorithm to solve dynamic economic loading of units with piecewise fuel options

This paper presents a Flower Pollination Algorithm (FPA) to solve Dynamic Economic Load Dispatch (DELD) problem with valve-point effects and piecewise fuel options. DELD aims to find out optimum generation schedule of the committed generating units over a certain timing period, sustaining practical constraints and power demands in each interval. Due to the valve-point effect and piecewise fuel options DELD becomes as complex problem, hence in order to achieve the cost reduction and satisfying the dynamic behaviour of the generating units proposed algorithm presented. The practicality of the proposed method is evaluated by performing simulations on standard 10-unit and 19-unit Indian utility systems for a 24 h time schedule at various load patterns. The simulation results attained by the FPA are related with other previous published techniques of the biography. These results clearly show that the proficiency and robustness of the proposed FPA method for resolving the non-linear constrained DELD problem.

Multi-region dynamic economic dispatch of solar–wind–hydro–thermal power system incorporating pumped hydro energy storage

This paper suggests chaotic fast convergence evolutionary programming (CFCEP) for solving multi-region dynamic economic dispatch (MRDED) problem, multi-region economic dispatch (MRED) problem and economic dispatch (ED) problem. MRDED problem is based on multi-reservoir cascaded hydro plant with time delay, thermal plants with nonsmooth fuel cost function, wind and solar power units with uncertainty and pumped hydro energy storage. MRED problem deals with tie line constraints, transmission losses, valve point effect and proscribed workable area of thermal generators. ED problem deals with valve point effect, proscribed workable area and ramp rate limits of thermal generators. In the recommended technique, chaotic sequences have been pertained for acquiring the dynamic scaling factor setting in fast convergence evolutionary programming (FCEP). The efficacy of the proposed technique has been verified on convoluted three-area system for MRDED problem, four-area system for MRED problem and 140-unit Korean system for ED problem. Test results acquired from the suggested CFCEP technique have been fit to that acquired from FCEP, differential evolution (DE) and particle swarm optimization (PSO). It has been observed from the comparison that the recommended CFCEP technique has the capability to bestow with better-quality solution.

Dynamic economic dispatch with demand-side management incorporating renewable energy sources and pumped hydroelectric energy storage

This paper recommends chaotic fast convergence evolutionary programming (CFCEP) for solving real-world dynamic economic dispatch (DED) with demand-side management (DSM) incorporating renewable energy sources and pumped-storage hydroelectric unit. Here, solar–wind–thermal energy system has been considered taking into account pumped-storage hydroelectric unit and uncertainty of solar and wind energy sources. DSM programs reduce cost and boost up power system security. To investigate the upshot of DSM, the DED problem is solved with and without DSM. In the recommended technique, chaotic sequences have been applied for acquiring the dynamic scaling factor setting in FCEP. The efficiency of the recommended technique is revealed on two test systems. Simulation outcomes of the suggested technique have been matched against those acquired by fast convergence evolutionary programming (FCEP), colonial competitive differential evolution and heterogeneous strategy particle swarm optimization. It has been observed from the comparison that the recommended CFCEP technique has the ability to give better-quality solution.

Distributed Reinforcement Learning Algorithm for Dynamic Economic Dispatch With Unknown Generation Cost Functions

In this article, the dynamic economic dispatch (DED) problem for smart grid is solved under the assumption that no knowledge of the mathematical formulation of the actual generation cost functions is available. The objective of the DED problem is to find the optimal power output of each unit at each time so as to minimize the total generation cost. To address the lack of a priori knowledge, a new distributed reinforcement learning optimization algorithm is proposed. The algorithm combines the state-action-value function approximation with a distributed optimization based on multiplier splitting. Theoretical analysis of the proposed algorithm is provided to prove the feasibility of the algorithm, and several case studies are presented to demonstrate its effectiveness.

Combined heat and power dynamic economic dispatch with demand side management incorporating renewable energy sources and pumped hydro energy storage

This study suggests chaotic fast convergence evolutionary programming (CFCEP) rooted in Tent equation for solving intricate actual world combined heat and power dynamic economic dispatch (CHPDED) problem with demand side management (DSM) incorporating renewable energy sources and pumped-storage-hydraulic unit. The valve point effect and proscribed workable area of thermal generators and solar and wind power uncertainty have been pondered. DSM programmes decrease cost and boost up power system security. To investigate the upshot of DSM, the CHPDED problem is solved with and without DSM. In the recommended CFCEP technique, chaotic sequences have been pertained for acquiring the dynamic scaling factor setting in fast convergence evolutionary programming (FCEP). Introduction of chaotic sequences helps FCEP to avoid premature convergence. The efficiency of the recommended technique is revealed in a test system. Simulation outcomes of the recommended technique have been evaluated with those attained by FCEP and differential evolution. It has been examined from the assessment that the recommended CFCEP has the capability to bestow with a better-quality solution.

Dynamic economic dispatch incorporating renewable energy sources and pumped hydroenergy storage

Due to mounting infiltration of solar and wind energy sources, it becomes essential to investigate its brunt on the dynamic economic dispatch. Here, solar–wind–thermal system integrating pumped-storage hydraulic unit has been considered. This work recommends chaotic fast convergence evolutionary programming (CFCEP) rooted in Tent equation for solving dynamic economic dispatch problem incorporating renewable energy sources and pumped-storage hydraulic unit. Chaotic sequences increase the exploitation ability in the searching space and enhance the convergence property. In the recommended technique, chaotic sequences have been pertained for acquiring the dynamic scaling factor setting in fast convergence evolutionary programming (FCEP). The efficiency of the recommended technique is revealed on two test systems. Simulation outcomes of the suggested technique have been matched up to those acquired by FCEP, differential evolution and particle swarm optimization. It has been observed from the comparison that the recommended CFCEP technique has the capability to confer with better quality solution.

A harmony search variant and a useful constraint handling method for the dynamic economic emission dispatch problems considering transmission loss

This paper proposes a new enhanced harmony search (NEHS) algorithm to solve dynamic economic emission dispatch (DEED) problems. NEHS is a variant of harmony search (HS) algorithm that is inspired by the music phenomenon. NEHS introduces two modifications to increase its competitiveness for the DEED problems. First, three levels of arbitrary distance bandwidths are used to enhance its global search and local search abilities. Second, both the best and the worst harmony vectors are selected to participate in the harmony memory considering operation in the second half of generations, which reaches a good compromise between improving solution quality and overcoming premature convergence. In addition, the improvised harmony vector at each generation is almost infeasible, and a repair technique is devised to drive it to the feasible domain efficiently. The performance of NEHS is evaluated on five DEED instances, and compared with that of the other four state-of-the-art HSs. Experimental results verify that NEHS is preferable in solving the five DEED instances as it can produce better solutions with less computation burden.

Stochastic multi-objective dynamic dispatch of renewable and CHP-based islanded microgrids

Micro-grids (MGs) are practical solutions for integrating distributed energy resources (DERs) in order to supply electrical and heat demands. In this study, a stochastic model for optimal management of combined heat and power (CHP)-based MGs considering economic, environmental and reliability aspects have been proposed. Two sources of uncertainty including forecast errors of electrical load demand and wind power are considered in scenario generation process using roulette wheel mechanism. Availabilities of units are taken into account to model reliability using capacity outage probability table (COPT). For solving such non-linear, non-convex and complicated stochastic problem, exchange market algorithm (EMA) and the weighted sum method are employed for combining three conflicting objectives and solving multi-objective problem as a single objective problem. Fuzzy satisfying method is applied to choose best compromise solution. The main goal of the stochastic dynamic reliable economic emission dispatch (SDREED) problem is to determine output of each generating unit so that fuel cost and amount of emission are minimized while the electrical demand is provided by more reliable units and operational constraints are met. The output of stochastic problem gives better sight for generation scheduling of MGs. The obtained results show the effectiveness and ability of the proposed method in solving SDREED.

Optimizing the Dynamic Economic Dispatch Problem by the Distributed Consensus-Based ADMM Approach

This paper proposes a novel distributed approach to solve a new dynamic economic dispatch problem (DEDP) in which environmental cost function and ramp rate constraints are taken into consideration in islanded microgrid. In our proposed optimization model, the environmental cost function with E-exponential term and ramp rate constraints are considered to make the optimization problem more practical. Then a novel fully distributed algorithm is proposed to address the DEDP based on the alternating direction method of multipliers (ADMM) and distributed consensus theory of the multiagents system. A Lambert $W$ function is employed to tackle the E-exponential term in the environmental cost function, which is different from most existing papers which discuss the DEDP only with quadratic cost functions. A parallel projection method on account of ADMM is used to deal with the ramp rate constraints in this paper. In addition, the power balance can be guaranteed every time when the sum of initial powder output is equal to the total demand. Therefore, the proposed algorithm can deal with the supply-demand constraints, capacity limit constraints, and ramp rate constraints. Finally, simulations on IEEE14-bus are introduced to further illustrate the effectiveness of the proposed algorithm.

A Cross-Entropy-Based Hybrid Membrane Computing Method for Power System Unit Commitment Problems

The cross-entropy based hybrid membrane computing method is proposed in this paper to solve the power system unit commitment problem. The traditional unit commitment problem can be usually decomposed into a bi-level optimization problem including unit start-stop scheduling problem and dynamic economic dispatch problem. In this paper, the genetic algorithm-based P system is proposed to schedule the unit start-stop plan, and the biomimetic membrane computing method combined with the cross-entropy is proposed to solve the dynamic economic dispatch problem with a unit start-stop plan given. The simulation results of 10–100 unit systems for 24 h day-ahead dispatching show that the unit commitment problem can be solved effectively by the proposed cross-entropy based hybrid membrane computing method and obtain a good and stable solution.

A Two-Stage strategy to handle equality constraints in ABC-based power economic dispatch problems

Power economic dispatch (ED) plays an important role in energy saving in power system operations. The penalty function method is widely used to handle equality constraints involved in ED problems. However, it is sometimes difficult to select the optimal penalty coefficients. To solve this problem, a Two-Stage strategy is proposed in this paper to handle equality constraints in artificial bee colony algorithm (ABC)-based ED problems, called as TSABC. Two groups of onlooker bees are employed in the first stage to search for feasible solutions satisfying all constraints. Then, in the second stage, a novel searching strategy with dynamic bounds for the elements of the solutions is introduced to keep the constraints always satisfied during the optimization process. The TSABC method does not require more control parameters and is easy to implement. Both based on basic ABC algorithm, the Two-Stage strategy is compared with the penalty function method (PFABC) for handling equality constraints in both static and dynamic economic dispatch problems. The comparative analysis reveals that the proposed TSABC method has merit in terms of effectiveness, reliability and solution quality.

A Transformation-Based Multi-Area Dynamic Economic Dispatch Approach for Preserving Information Privacy of Individual Areas

As the growing interconnection of regional electricity grids and the large-scale integration of renewable energy demand for effective coordination among multiple areas, the multi-area dynamic economic dispatch (MA-DED) problem has been studied for exploring coordinated optimal operations to achieve overall energy security and economic efficiency. However, due to political and technical challenges, a centralized solution to MA-DED is unlikely to be practically feasible. In turn, decomposition schemes have been applied for solving MA-DED in a distributed manner so as to avoid disclosing commercially sensitive information of individual areas to others. In recognizing computational challenges of distributed approaches, this paper discusses a transformation-based MA-DED approach, which masks each area’s private information in the objective and constraints of MA-DED by privately generated and held random matrices. Strategies of using additional slack variables and redundant constraints are also discussed to further disguise system scale of each area from being disclosed. More importantly, optimal solutions to the original MA-DED problem, including tie-line power flows, dispatches of generators and loads, and locational marginal prices, can be retrieved from solutions of the transformed problem. Numerical studies show effectiveness of the proposed approach for guaranteeing the same optimal MA-DED solution, while preserving information privacy of individual areas. Moreover, the proposed approach presents significant computational benefits over distributed approaches, especially for multi-area systems with larger numbers of tie-lines and more complicated connection topologies of areas.