Dynamic Economic Dispatch Research Articles

Multi-objective fuzzy optimization model of power system dynamic environment economy based on coordinated dispatching of wind power and electric vehicles

In order to coordinate the impact of the integration of electric vehicles and wind power on the economic dispatch of power systems, a multi-objective dispatch model for the environmental economy of wind farms with PHEVs connected to the grid was constructed. The uncertain factors of wind power generation and load will increase the difficulty of dispatching. The fuzzy theory will be used to realize the fuzzy modelling of the coordinated connection of wind power and electric vehicles. The satisfaction index will be used to transform the multi-objective problems of deterministic environment and economy into single For the objective optimization problem, based on the improvement of the traditional particle swarm optimization algorithm using linear descent search ideas and the particle information sharing method considering boundary constraints, the improved PSO algorithm is used to solve the proposed dynamic environment and economic dispatch model. From the grid operation and vehicle owners from the perspective of demand, the constraints of the system’s rotation reserve and the daily travel of the owner are considered. The comparison and analysis of the simulation of algorithms and calculation examples and multiple scheduling schemes in different scenarios verify the rationality of the model and the superiority of the improved PSO algorithm for solving such dynamic scheduling problems.

Dynamic economic emission dispatch with wind power based on improved multi‐objective brain storm optimisation algorithm

Based on the non-parametric kernel density estimation technique, the probability distribution of wind power output and its forecast error are accurately modelled. The confidence interval and forecast error upper and lower bounds of wind power output are estimated to build a dynamic economic emission dispatch (DEED) model with wind power penetration. To effectively solve the DEED problem with multi-objective, high-dimensional, non-linear and strong constraints, based on the basic brainstorm optimisation (BSO) algorithm, three improvement mechanisms, namely random clustering centre, differential mutation operation and individual crossover operation are introduced to enhance the converging and diverging operation of BSO. Based on these improvements and external archive mechanism, an improved multi-objective BSO (IMOBSO) algorithm is proposed. Simulations on a classical test system with ten thermal units are performed, where two case studies are investigated carefully. The simulation results demonstrate that: (i) the proposed IMOBSO can optimise the cost and emission objectives simultaneously and have achieved better performance than other algorithms; (ii) the proposed DEED incorporating wind power model is reasonable and effective because it can achieve the optimal wind power output scheduling by adjusting the system's spinning reserve capacity and the confidence level of wind power prediction interval.

Assessment of Dynamic Economic and Emission Dispatch Problem using WOA in Networked Grids with Photovoltaic Power Injection

Since decades, the main aim for the researchers is to get reliable and inexpensive electricity out of available resources. Till now, different economic dispatch methods have been developed to meet the challenges of continuous and sustainable electricity production at optimized cost. Due to the increase of public awareness on environmental protection, the utilities have forced to use renewable energy sources to modify the operation strategies to reduce the pollution and atmospheric emissions produced due to power plants. This paper represents the allocation of dynamic economic emission dispatch (DEED) problem involving thermal and photovoltaic (PV) generation system as hybrid dynamic economic emission dispatch (HDEED) to meet the minimization of both the cost of fuel and emission simultaneously. Whale optimization algorithm (WOA) is used to minimize the total cost of operation and emission levels while dispatching power to committed generation units considering all operational constraints. To show the efficiency, the proposed technique is applied to solve the dynamic economic emission dispatch problem on 5- and 10-unit test systems. The technique is also used to solve the HDEED problem on IEEE 30-bus 6-unit and IEEE 57-bus 7-unit test system with and without renewable generation. The results obtained after injection of photovoltaic power into existing power systems show the effectiveness of the proposed techniques to reduce the cost of operation and emission levels.

An Elitist Multi-Objective Particle Swarm Optimization Algorithm for Sustainable Dynamic Economic Emission Dispatch Integrating Wind Farms

In recent years, wind energy has been widely used as an alternative energy source as it is a clean energy with a low running cost. However, the high penetration of wind power (WP) in power networks has created major challenges due to their intermittency. In this study, an elitist multi-objective evolutionary algorithm called non-dominated sorting particle swarm optimization (NSPSO) is proposed to solve the dynamic economic emission dispatch (DEED) problem with WP. The proposed optimization technique referred to as NSPSO uses the non-dominated sorting principle to rank the non-dominated solutions. A crowding distance calculation is added at the end of all iterations of the algorithm. In this study, WP is represented by a chance-constraint which describes the probability that the power balance cannot be met. The uncertainty of WP is described by the Weibull distribution function. In this study, the chance constraint DEED problem is converted into a deterministic problem. Then, the NSPSO is applied to simultaneously minimize the total generation cost and emission of harmful gases. To proof the performance of the proposed method, the ten-unit and forty-unit systems—including wind farms—are used. Simulation results obtained by the NSPSO method are compared with other optimization techniques that were presented recently in the literature. Moreover, the impact of the penetration ratio of WP is investigated.

A Fast LP-Based Approach for Robust Dynamic Economic Dispatch Problem: A Feasible Region Projection Method

The robust optimization based dynamic economic dispatch (DED) model has been extensively studied to address uncertainties of net loads induced by renewable energy resource variabilities and demand fluctuations. However, the robust DED model is computationally expensive, when solved by the column-and-constraint generation (CCG) approach that iterates between a master problem and a max-min subproblem. This letter proposes a feasible region projection-based approach to equivalently reformulate the robust DED as a single-level linear programming (LP) model that can be effectively solved while guaranteeing solution optimality. Numerical studies show the proposed approach is one order of magnitude faster than CCG.

Dynamic environmental‐economic load dispatch in grid‐connected microgrids with demand response programs considering the uncertainties of demand, renewable generation and market price

AbstractMicrogrids (MGs) as a key building block of smart grids have been emerged to address the proliferation of distributed energy resources. In grid‐connected MGs, dynamic economic load dispatch (DELD) module determines optimal schedule of distributed energy resources and adjustable loads and power to be exchanged with upstream grid, while all operational constraints of the MG are respected. DELD in MGs represents a constrained optimization problem with uncertain input data, as the forecasts of demand, renewable generation and market price are uncertain. In this research, particle swarm optimization (PSO) as a bio‐inspired optimization algorithm is used to solve DELD in grid‐connected MGs, while demand response program is integrated into MG and the uncertainties of demand, renewable power generation and market price are dealt with two‐point estimate method (TPEM). Load curtailment as a demand response program is used for reducing operation cost of microgrids. The performance of PSO is compared with two optimization algorithms including grey wolf optimization and backtracking search algorithm. As per the results, at times with low grid power price, microgrid imports power from upstream grid and at times with high power price it exports power to the upstream grid. The results show that the integration of demand response has significantly reduced the operation cost of the microgrid. The effect of change in maximum curtailable power on the operation cost of the MG has been investigated.

An Efficient Hybrid Approach to Solve Bi-objective Multi-area Dynamic Economic Emission Dispatch Problem

Single period economic dispatch cannot handle the intertemporal constraints in multi-period environment. To cope with this issue, the extension of economic dispatch over multiple time intervals (i.e., dynamic economic dispatch) has been introduced that considers the intertemporal constraints between different time intervals. Another issue is determining the most economical generation dispatch that could supply the area demand without violating the tie-line capacity, which cannot be solved by conventional economic dispatch problems. However, this study shows that the most economic schedule of power generation cannot satisfy echo-system expectation; therefore, making a compromise between fuel cost and environmental issues, a hot-button subject in industrialized nations, seems to be crucial. To reach the goals a bi-objective multi-area dynamic economic dispatch approach, which can handle intertemporal and multi-area constraints concurrently, is proposed to assist power system operators more and more. Finally, a hybrid algorithm, namely gray wolf optimizer-particle swarm optimization is introduced to solve the proposed problem and also a set of benchmark problems. By implementing the proposed approach on two small (10-unit, three areas) and large (40-unit, four areas) scale test systems, about 3.1% and 3.3% improvement in generation cost is obtained, respectively compare to the best reported results in the literature.

Dynamic economic dispatch of islanded water-energy microgrids with smart building thermal energy management system

In this paper, a mixed integer nonlinear programming formulation is proposed to intelligently dispatch the distributed generators, manage buildings’ thermal energy, and support the water demand in an islanded water-energy microgrid. To optimize the demand of water distribution system, pump’s nonlinear scheduling and hydraulic factors, and daily water usage of buildings are added to the formulation. In addition, thermal management of electric chillers considering customers’ comfort level and outside temperature forecast was formulated. For a summer cooling schedule, it is shown that adjusting the indoor temperature settings at 20–25 °C for both occupied and unoccupied hours offers the lowest daily operation cost and peak demand charges. A fixed temperature setting of 25 °C during the occupied and unoccupied hours results in a lower daily cost and demand charges than a wide temperature setting of 15–30 °C. Lowest daily costs and electricity demand can be achieved within the proposed integrated water-energy microgrid with optimal water demand and building thermal energy management. By incorporating the water system constraints in the optimization model, hourly cost savings up to $150 can be achieved. In addition, incorporating building’s thermal management in the proposed economic dispatch model can result in up to $20 hourly energy saving in the water-energy system.

Dynamic programming for scalable just-in-time economic dispatch with non-convex constraints and anytime participation

This paper considers two classes of dynamic programming frameworks for economic dispatch in power systems. The first framework is of classical continuous convex economic dispatch. We present recursive formulae for computing the parameters of value functions and show that the value functions are generalized quadratic and generalized piecewise quadratic for unconstrained and generation-capacity constrained convex economic dispatch, respectively. The second framework is of discrete dynamic programming for economic dispatch with non-convex cost functions and constraints. The discrete dynamic programming framework is computationally scalable and decentralized. The computations of the value table are scalable in the sense that any newcomers and seceders of generation units can be numerically efficiently taken care of, by not redoing the entire backward induction process but only computing the value tables of the successors. Extension of the discrete dynamic programming framework to dynamic economic dispatch with ramp constraints is also presented. We demonstrate the proposed algorithms by three numerical case studies. One is for non-convex economic dispatch with 15 generation units and prohibited operating zones. Another example of a larger scale system of 53 units with consideration of transmission losses is also studied. For a dynamic case, the proposed method is applied to a dynamic economic dispatch problem with non-convex ramp constraints.

Dynamic Economic Dispatch with Wind Power Penetration Based on Non-Parametric Kernel Density Estimation

In order to analyze the randomness of wind power in dynamic economic dispatch (DED) with wind power, based on non-parametric kernel density estimation (KDE) technology, the probability distribution of wind power output and wind power forecast error is accurately modeled. A segmented statistical method on wind power forecast data is adopted to construct the confidence interval of the wind power output, the upper and lower bounds of the forecast errors. According to the established wind power output probability model, forecast confidence interval and forecast error upper and lower bounds, a DED model with wind power is formulated in this paper. A hybrid algorithm combining the evolutionary advantages of bat algorithm (BA) and particle swarm optimization (PSO) algorithm is designed to solve the proposed model. A crossover mechanism, which can solve the problem of falling into local optimum easily existed in BA and PSO, is introduced in the evolution of the algorithm. Finally, the effectiveness of the proposed model and algorithm is verified by simulation examples.

Strength Pareto Evolutionary Algorithm for the Dynamic Economic Emission Dispatch Problem incorporating Wind Farms and Energy Storage Systems

Intermittent and stochastic characteristics of wind energy sources cause many challenges for the existing power networks. One of these challenges is the violation of the energy balance constraint due to the high penetration of wind power. The use of Energy Storage Systems (ESS) can facilitate the high penetration of wind power and mitigate the effect of its intermittency. Within this context, ESS incorporate the Dynamic Economic Emission Dispatch (DEED) problem. The problem is formulated as a multi-objective problem and the Strength Pareto Evolutionary Algorithm (SPEA) is used for its resolution. Simulations were carried out on a well-known ten-unit system and the results show the importance of using ESS in reducing the total production cost of electricity and total emissions.

Strength Pareto Evolutionary Algorithm for the Dynamic Economic Emission Dispatch Problem incorporating Wind Farms and Energy Storage Systems

Strength Pareto Evolutionary Algorithm for the Dynamic Economic Emission Dispatch Problem incorporating Wind Farms and Energy Storage Systems

A T-cell algorithm for solving dynamic economic power dispatch problems

This paper presents the artificial immune system IA_DED (Immune Algorithm Dynamic Economic Dispatch)
 to solve the Dynamic Economic Dispatch (DED) problem and the Dynamic Economic Emission Dispatch (DEED) problem.
 Our approach considers these as dynamic problems whose constraints change over time. 
 IA\DED is inspired on the activation process that T cells suffer in order to find partial solutions.
 The proposed approach is validated using several DED problems taken from specialized literature and 
 one DEED problem. The latter is addressed by transforming a multi-objective
 problem into a single-objective problem by using a linear aggregating function that combines the
 (weighted) values of the objectives into a single scalar value.
 Our results are compared with respect to those obtained by 
 other approaches taken from the specialized literature. We also provide some 
 statistical analysis in order to determine the sensitivity
 of the performance of our proposed approach to its parameters. Part of this work was presented at the XXV 
 Argentine Congress of Computer Science (CACIC), 2019.
 

Hybrid PSOGSA technique for solving dynamic economic emission dispatch problem

In this paper, a new hybrid population-based algorithm is proposed with the combining of particle swarm optimization (PSO) and gravitational search algorithm (GSA) techniques. The main idea is to integrate the ability of exploration in PSO with the ability of exploration in the GSA to synthesize both algorithms’ strength. The new algorithm is implemented to the dynamic economic emission dispatch (DEED) problem to minimize both fuel cost and emission simultaneously under a set of constraints. To demonstrate the efficiency of the proposed algorithm, a 5-unit test system is used. The results show the effectiveness and superiority of the proposed method when compared to the results of other optimization algorithms reported in the literature.

The Economic Dispatch of Wind Integrated Power System based on an Improved Differential Evolution Algorithm

Background: As more and more renewable energy such as wind energy is connected to the power grid, the static economic dispatch in the past cannot meet its needs, so the dynamic economic dispatch of the power grid is imperative. Methods: Hence, in this paper, we proposed an Improved Differential Evolution algorithm (IDE) based on Differential Evolution algorithm (DE) and Artificial Bee Colony algorithm (ABC). Firstly, establish the dynamic economic dispatch model of wind integrated power system, in which we consider the power balance constraints as well as the generation limits of thermal units and wind farm. The minimum power generation costs are taken as the objectives of the model and the wind speed is considered to obey the Weibull distribution. After sampling from the probability distribution, the wind speed sample is converted into wind power. Secondly, we proposed the IDE algorithm which adds the local search and global search thoughts of ABC algorithm. The algorithm provides more local search opportunities for individuals with better evolution performance according to the thought of artificial bee colony algorithm to reduce the population size and improve the search performance. Results: Finally, simulations are performed by the IEEE-30 bus example containing 6 generations. By comparing the IDE with the other optimization model like ABC, DE, Particle Swarm Optimization (PSO), the experimental results show that obtained optimal objective function value and power loss are smaller than the other algorithms while the time-consuming difference is minor. The validity of the proposed method and model is also demonstrated. Conclusion: The validity of the proposed method and the proposed dispatch model is also demonstrated. The paper also provides a reference for economic dispatch integrated with wind power at the same time.

A spatiotemporal decomposition algorithm for fully decentralized dynamic economic dispatch in a microgrid

In this paper, we present a spatiotemporal decomposition solution approach to the fully decentralized dynamic economic dispatch (DED) problem in a microgrid. Our approach divides the centralized DED problem into a series of sub-problems in the spatiotemporal dimensions and relies on multiple agents to solve those sub-problems. The proposed method requires no central operator intervention, preserving the decision independence and information privacy of each unit. Approximate value functions are used to describe the interaction among those sub-problems. With the approximate value functions, one agent not only knows the impact of its decision on the decisions of other agents in the same period, but also knows the impact of this decision on the decisions of its subsequent periods. Unlike the existing value function update strategy, which updates the state variables and value functions in one direction, we update the state variables and value functions in two directions based on a forward-push-back strategy. In this manner, the time-delayed problem can be solved, and the iteration speed of the algorithm is greatly improved. Moreover, the proposed algorithm does not require parameter tuning and has good accuracy and adaptability. Numerical simulations for multiple cases demonstrate the effectiveness of the proposed algorithm.

An integrated solution for optimal generation operation efficiency through dynamic economic dispatch

We propose a total and intelligent solution for optimal demand management for energy efficiency under the new framework of true dynamic economic dispatch (DED) which integrates advanced metering, new modelling for demand, dynamic load dispatch and bidding strategy together. It involves the following essential modules. (i) Dynamic economic dispatch is a true dynamic optimization formulation. With real time measurements and both supply and demand modelling, the optimization will produce the optimal plant operation modes and settings which give the highest efficiency of the overall system and are fed back to the plants for execution. (ii) Dynamic sensing is real time sensing and data acquisition system to access the real operating status of the generation plant with measurement of relevant variables. The big data technology is adopted for construction of the overall hardware and software to store huge volume of plant and market data and perform fast off line modelling and design as well as on line real time control. (iii) Dynamic modelling is model building to forecast energy demands and generation over time. Under the DED, these modules are well integrated to work together and achieve an optimal demand management for maximum energy efficiency. Its solution, verification and field implementation are reported.

SOLVING WIND INTEGRATED DYNAMIC ECONOMIC LOAD DISPATCH USING DYNAMIC NEIGHBORHOOD BASED DIFFERENTIAL EVOLUTION

Economically satisfying the power demand of various consumers in dynamic mode becomes a prime challenge nowadays. Unbalanced load variation makes the power demand and power loss vibrant which leads to the rough load curve. To deal with differential power requirement, dynamic economic (DELD) load dispatch is witnessed as major one in consideration with unauthorized operating zone, economic load dispatch in valve pointed loading, etc. On considering the surplus power demand it is mandatory to find an alternate way to satisfy it economically, hence renewable energy support is crucial. The discontinuous power generation of wind energy with respect to the availability of wind source makes the DELD problem non smooth and non convex in practical. Hence an evolutionary computational technique is prominent to find a better solution. In proposed topology, Neighborhood based Differential Evolution Algorithm has been evaluated for resolving the wind integrated DELD problem including various constraints. To check out values attained from proposed method, 15 unit and 10 unit system test data is optimized for various power demand including the wind support and evaluated with the results from the literature.

Optimization of power dispatching strategies integrating management attitudes with low carbon factors

With the rapid development of low-carbon electricity, wind power and carbon prices serving as low carbon factors have drawn significant attention. Owing to the wind power uncertainties, the carbon price fluctuations and the immeasurability of management attitudes towards these two factors, the traditional dynamic economic emission dispatch (DEED) models are no longer completely practicable for low-carbon power dispatching problem. Aiming at these difficulties, this paper establishes a stochastic DEED model concentrating on low carbon factors. After discussing the wind power’s statistical characteristics, a scenario-based deterministic form for the proposed model is set up. Furthermore, a sequence of nondominated sorting genetic algorithm-II (NSGA-II) program steps with constraints-handling techniques is designed to solve this model, and an auxiliary decision-making method is developed for the selection of optimal power dispatching strategies. According to carbon prices, wind power uncertainties and satisfaction degrees, the optimal power dispatching strategies integrating management attitudes with low carbon factors could be achieved through the proposed model and method. The simulation results finally prove that carbon emissions could be controlled by carbon trading without significantly increasing generation costs, and carbon trading will further contribute to improvement of energy efficiency.

Power Dispatching Considering Copula Correlation of Multiple Wind Farms Generation

The dynamic economic dispatching of power system connected with multiple wind farms is a typical stochastic programming problem. How to model the randomness of wind power and how to solve this complex stochastic optimization problem are the key points. In this paper, copula theory is used to formulate the correlation of multi-wind farms generation. Then, the dynamic economic dispatching model is founded with the fuel consumption, gas pollution emission fees and purchase costs as the optimized objective. The two-stage compensation algorithm is then introduced to solve the dispatching problem. In this algorithm, the conventional (nonstochastic) decision variables and stochastic variables are decoupled, which separate the dynamic dispatching model into two stage modes. The optimal dispatching result is worked out by iteration between the two stage models. Case studies on IEEE118-bus system shows that the proposed algorithm can drastically reduce computational burden, and satisfy the actual requirements of engineering practice.