Power System Economic Dispatch Research Articles

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.

Efficient method for the optimal economic operation problem in point-to-point VSC-HVDC connected AC grids based on Lagrange multipliers

This paper describes a method based on Lagrange multipliers for efficiently solving the economic dispatch in power systems including point-to-point VSC-HVDC links. The proposed formulation bases on linear models of the AC systems and HVDC links where power losses are properly considered through incremental transmission loss factors.This timely formulation preserves suitable outcome accuracy while showing a greater computational efficiency than what is achieved with classical, nonlinear OPF methods. Its main features are demonstrated using two compelling test cases: a system accommodating one point-to-point VSC-HVDC link and another comprising multi-infeed HVDC connected AC power grids. Results of this approach are compared with those calculated by the nonlinear interior point method. It is confirmed that both fundamentally different approaches are in good agreement since errors smaller than 0.5% were obtained for generation costs, whereas the computational time was reduced by more than 60% with the introduced method.To show the method applicability in realistic power systems, the 10-generator New England Test system incorporating a VSC-HVDC link is studied. The DC link effect on system operation is examined for a 24-hour period dispatch thus demonstrating its usefulness, unrivalled modelling versatility and numerical efficiency with respect to existing approaches.

Hybrid Particle Swarm Optimization and Gravitational Search Algorithm for Economic Dispatch in Power System

Hybrid Particle Swarm Optimization and Gravitational Search Algorithm for Economic Dispatch in Power System

Solving Power System Economic Dispatch Problem Based on Genetic Algorithm

With the rapid development of the world economy, the demand for power load is also growing rapidly. The power system economic dispatch problem studied in this paper is to reduce the fuel cost of generator units on the premise of satisfying some series of constraints of power system. In this paper, genetic algorithm is adopted as the solution strategy for power system economic dispatch problem, and the penalty function is used to deal with the equality constraint condition in the power system economic dispatch problem. Finally, we use the genetic algorithm to solve the IEEE-9 notes power system economic dispatch problem and give the corresponding simulation results. The simulation results show that the genetic algorithm can solve the power system economic dispatch problem effectively.

ADMM-based distributed algorithm for economic dispatch in power systems with both packet drops and communication delays

By virtue of alternating direction method of multipliers (ADMM), Newton-Raphson method, ratio consensus approach and running sum method, two distributed iterative strategies are presented in this paper to address the economic dispatch problem (EDP) in power systems. Different from most of the existing distributed ED approaches which neglect the effects of packet drops or/and time delays, this paper takes into account both packet drops and time delays which frequently occur in communication networks. Moreover, directed and possibly unbalanced graphs are considered in our algorithms, over which many distributed approaches fail to converge. Furthermore, the proposed schemes can address the EDP with local constraints of generators and nonquadratic convex cost functions, not just quadratic ones required in some existing ED approaches. Both theoretical analyses and simulation studies are provided to demonstrate the effectiveness of the proposed schemes.

An Efficient New Hybrid ICA-PSO Approach for Solving Large Scale Non-convex Multi Area Economic Dispatch Problems

Multi-area economic dispatch (MAED) is one of the vital problems in economic operation of interconnected power systems. This paper proposes a novel hybrid approach based on combined imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) methods in order to determine the feasible optimal solution of the non-convex economic dispatch (ED) problem considering valve loading effects. In the proposed algorithm we have defined new type of countries in ICA algorithm, namely independent countries. These types of countries improve their position using a PSO based search strategy. The proposed method benefits from the advantage of the both algorithms. The proposed hybrid approach based on ICA-PSO is applied on different test systems and compared with most of the recent methodologies. Also, a large scale multi-area economic dispatch (MAED) problem is solved using the proposed hybrid approach to minimize total fuel cost in all areas while satisfying power balance constraints, generating limits and tie-line capacity constraints. The results show the effectiveness of the proposed approach and prove that ICA-PSO is applicable for solving the power system economic load dispatch problem, especially in large scale power systems.

Privacy-preserving decentralized power system economic dispatch considering carbon capture power plants and carbon emission trading scheme via over-relaxed ADMM

This paper proposes a decentralized power system economic dispatch (DPSED) model considering carbon capture power plants (CCPPs) and carbon emission trading scheme (CETS) under a low-carbon economy. First, CETS is introduced and analyzed, and a time-varying carbon emission quota allocation method is proposed. The centralized power system economic dispatch model (CPSED) under a low-carbon economy is established with the objective function to minimize the total operation cost in which CCPPs are introduced that can capture CO2 to reduce carbon emission trading cost. Then, the centralized economic dispatch problem is reformulated into a decentralized model. It is composed of a set of sub-problems in individual areas that can preserve privacy and be solved independently. The alternating direction method of multipliers (ADMM) algorithm is employed to solve the decentralized optimization model, reducing the amount of exchanged information and preserving the privacy of information shared among participating areas. Moreover, the over-relaxed ADMM algorithm is further adopted to accelerate the convergence. Finally, case studies are performed on a 6-bus system and an IEEE 118-bus system to validate the effectiveness of the proposed model and algorithm. Numerical results demonstrate that CCPPs could reduce carbon emissions, help wind power utilization, and achieve economic operation.

Combined heat and power system intelligent economic dispatch: A deep reinforcement learning approach

This paper proposed a Deep Reinforcement learning (DRL) approach for Combined Heat and Power (CHP) system economic dispatch which obtain adaptability for different operating scenarios and significantly decrease the computational complexity without affecting accuracy. In the respect of problem description, a vast of Combined Heat and Power (CHP) economic dispatch problems are modeled as a high-dimensional and non-smooth objective function with a large number of non-linear constraints for which powerful optimization algorithms and considerable time are required to solve it. In order to reduce the solution time, most engineering applications choose to linearize the optimization target and devices model. To avoid complicated linearization process, this paper models CHP economic dispatch problems as Markov Decision Process (MDP) that making the model highly encapsulated to preserve the input and output characteristics of various devices. Furthermore, we improve an advanced deep reinforcement learning algorithm: distributed proximal policy optimization (DPPO), to make it applicable to CHP economic dispatch problem. Based on this algorithm, the agent will be trained to explore optimal dispatch strategies for different operation scenarios and respond to system emergencies efficiently. In the utility phase, the trained agent will generate optimal control strategy in real time based on current system state. Compared with existing optimization methods, advantages of DRL methods are mainly reflected in the following three aspects: 1) Adaptability: under the premise of the same network topology, the trained agent can handle the economic scheduling problem in various operating scenarios without recalculation. 2) High encapsulation: The user only needs to input the operating state to get the control strategy, while the optimization algorithm needs to re-write the constraints and other formulas for different situations. 3) Time scale flexibility: It can be applied to both the day-ahead optimized scheduling and the real-time control. The proposed method is applied to two test system with different characteristics. The results demonstrate that the DRL method could handle with varieties of operating situations while get better optimization performance than most of other algorithms.

Scenario-Set-Based Economic Dispatch of Power System With Wind Power and Energy Storage System

In view of uncertainties caused by large-scale wind power integration, energy storage system (ESS) is being considered to stabilize the fluctuation of wind power. In this paper, the influence of ESS on power system operation with wind power is analyzed in detail, and an economic dispatch (ED) model with wind power and ESS is proposed based on scenario set. First, the initial scenario set of wind power output is generated by the Monte Carlo sampling. To overcome the shortcoming of heavy dependence on the initial clustering centers, which usually leads to unstable clustering results, the k-means clustering is improved by combining self-organizing feature map neural network and particle swarm optimization (PSO). Then, the initial scenario set is reduced based on this improved k-means clustering method. Finally, an ED model solved by PSO is used to minimize the comprehensive power generation cost based on the reduced scenario set. Taking IEEE-39 bus system as an example, the scenario-set-based ED model is implemented in this paper. The simulation results show that, when solving the ED problem with wind power and ESS, the proposed method considering scenario reduction makes not only the clustering index better, but also the results of ED more reasonable.

Mean-tracking model based stochastic economic dispatch for power systems with high penetration of wind power

The random wind power that accounts for a growing proportion in power systems imposes higher challenge on the reliable operation of power system under uncertain circumstances. Since forecasted values of wind speed are accessible to system operators in advance, the corresponding calculated pre-schedule can be regarded as a reference for the stochastic economic dispatch (SED) problem. Existing methods seldom take the pre-schedule into account when determining an optimal dispatch solution, and the resulting dispatch solutions generally differ greatly from the pre-schedule. In this paper, aiming to readjust from the reference schedule as little as possible, the mean-tracking model is proposed for the first time to search for optimal dispatch solutions with the minimal expectation of generation cost and the minimal tracking errors, among which the tracking errors is implemented to each generator unit in terms of minimizing the deviation in generation cost between the trial solution and the pre-schedule. Moreover, the affine decision rule is applied in this paper to distribute the uncertain wind power proportionally to each generator unit. To guarantee the stable operation of power systems, the voltage operating limits are considered to ensure the voltage on each bus remains within the security margins of voltage. Numerical experiments are carried out on a modified IEEE-30 bus system, and simulation results demonstrate the effectiveness of the proposed mean-tracking model for the SED problem.

Prediction short-term photovoltaic power using improved chicken swarm optimizer - Extreme learning machine model

Photovoltaic power generation is greatly affected by weather conditions while the photovoltaic power has a certain negative impact on the power grid. The power sector takes certain measures to abandon photovoltaic power generation, thus limiting the development of clean energy power generation. This study is to propose an accurate short-term photovoltaic power prediction method. A new short-term photovoltaic power output prediction model is proposed Based on extreme learning machine and intelligent optimizer. Firstly, the input of the model is determined by correlation coefficient method. Then the chicken swarm optimizer is improved to strengthen the convergence. Secondly, the improved chicken swarm optimizer is used to optimize the weights and the extreme learning machine thresholds to improve the prediction effect. Finally, the improved chicken swarm optimizer extreme learning machine model is used to predict the photovoltaic power under different weather conditions. The testing results show that the average mean absolute percentage error and root mean square error of improved chicken swarm optimizer - extreme learning machine model are 5.54% and 3.08%. The proposed method is of great significance for the economic dispatch of power systems and the development of clean energy.

Lightning Search Algorithm (LSA) Technique For Solving Economic Dispatch (ED) Problem

Economic Dispatch problem involves the scheduling of generating unit outputs that can satisfy load demand at minimum operating cost. This paper proposes a Lightning Search Algorithm (LSA) to optimize the economic dispatch in power system. LSA has three main steps which are transition projectile, space projectile and lead projectile. The proposed method has been applied to solve 3 unit and 6-unit generation system of economic dispatch problem. The objective of this problem is to minimize a total generation cost and to consider the losses. The propose method has been compared with other techniques such as GA, PSO, ABC, and GWO. The comparative result shows that the LSA can provide better solution with a convergence and robustness for solving economic dispatch.

Economic Dispatch of Power System with Wind Power and Energy Storage Based on Discrete Particle Swarm Optimization

Economic Dispatch of Power System with Wind Power and Energy Storage Based on Discrete Particle Swarm Optimization

Particle Swarm Optimization with Compression Factor for Solving the Power Systems Economic Dispatch Problem

With the rapid development of economy, the demand for electricity is increasing rapidly. Therefore, how to effectively realize power scheduling becomes very important. In this paper, we first introduced the basic principle of particle swarm optimization, then discuss the influence of parameter selection on the efficiency of particle swarm optimization. After that, we use the compression factor method to set the parameters of the particle swarm optimization algorithm. The experimental results show that the parameter selection method based on compression factor is effective and feasible.

Distributed event‐triggered scheme for economic dispatch in power systems with uncoordinated step‐sizes

Considering potential applications in power systems, economic dispatch problem (EDP) in time-varying balanced communication networks is studied, aiming to minimise the total cost of generating electricity. This is equivalent to dealing with the problem of optimising the sum of local functions while a single generator possesses only its local function. The variables of generators, satisfying some local constraints, are coupled by a linear constraint. In order to resolve the EDP, the authors design a fully distributed primal-dual optimisation algorithm with time-varying uncoordinated step-sizes. In consideration of saving computation and communication resources, an event-triggered scheme is introduced into the algorithm, based on which each generator is only allowed to interact with their neighbouring generators at some independent event-triggered sampling time instants. The proposed algorithm is able to achieve a linear convergence rate under the strong convexity and smoothness of the local objective functions. The Zeno-like behaviour is rigorously excluded, which means that the interval between any two consecutive sampling time instants of each generator is not less than two. Effectiveness of the algorithm and correctness of the theoretical analysis are verified by numerical experiments.

A new hybrid gravitational search-teaching-learning-based optimization method for the solution of economic dispatch of power systems

A new hybrid gravitational search-teaching-learning-based optimization method for the solution of economic dispatch of power systems

Combined Emission Economic Dispatch of Power System in Presence of Solar and Wind Using Flower Pollination Algorithm

ED (Economic Dispatch) problem is one of the vital step in operational planning. It is a nonconvex constrained optimization problem. However, it is solved as convex problem by approximation of machine input/output characteristics, thus resulting in an inaccurate result. Reliable, secure and cheapest supply of electrical energy to the consumers is the prime objective in power system operational planning. Increase in fuel cost, reduction in fossil-fuel assets and ecological concerns have forced to integrate renewable energy resources in the generation mix. However, the instability of wind and solar power output affects the power network. For solution of such solar and wind integrated economic dispatch problems, evolutionary approaches are considered potential solution methodologies. These approaches are considered as potential solution methodologies for nonconvex ED problem. This paper presents CEED (Combined Emission Economic Dispatch) of a power system comprising of multiple solar, wind and thermal units using continuous and binary FPA (Flower Pollination Algorithm). Proposed algorithm is applied on 5, 6, 15, 26 and 40 thermal generators by integrating several solar and wind plants, for both convex and non-convex ED problems. Proposed algorithm is simulated in MATLAB 2014b. Results of simulations, when compared with other approaches, show promise of the approach.

Distributed model predictive control for economic dispatch of power systems with high penetration of renewable energy resources

Distributed generation entities such as renewable energy sources have posed great challenges on power system economic dispatch because of their output variability and stochasticity. Accordingly, operators need to lessen unpredictable changes in scheduled generation settings by fully utilizing available forecast information in the decision-making process. This paper proposes a closed-loop algorithm for solving economic dispatch at runtime while reducing potential deviations of generation schedules. At first, a traditional centralized approach that addresses the economic dispatch problem is presented with discussions on potential enhancement enabled by model predictive control (MPC) techniques. The MPC application makes it possible for operators to address the concern of variability and stochasticity. This paper develops a dual decomposition-based distributed model predictive control (DDMPC) strategy that is compatible with consensus techniques. Different advantages of the proposed DDMPC are highlighted throughout the paper and are analyzed through simulations. The simulation results validate the advantages of the proposed DDMPC approach by comparing it with traditional techniques for economic dispatch and by another distributed method based on MPC.

SR‐based chance‐constrained economic dispatch for power systems with wind power

In this study, the authors present a chance-constrained economic dispatch model for power systems with the integration of wind power. In the proposed model, the automatic generation control (AGC) regulation is adopted to compensate for the power variations caused by the forecast errors of wind power and load. Moreover, the power flow limits and the transient stability constraints under contingencies are formulated as chance constraints through the security region (SR) approach. On the basis of the hyper-plane characteristics of the boundaries of SR, the chance constraints of power flow limits and transient stability limits are converted to equivalent deterministic linear inequalities. The proposed method can assure that there is enough reserve capacity in the dispatch solution to accommodate the power variations caused by wind power and load, and the branch power flow limits and the transient stability constraints under uncertain power injections and contingencies are satisfied with a high probability. Numerical tests show that the proposed method has well-convergence property and computational efficiency and it serves as a useful tool for power dispatchers to identify a balance between economics and robustness of power system operation.

Economic dispatch of power system containing UHVDC with direct power purchase by large consumers

Economic dispatch of power system containing UHVDC with direct power purchase by large consumers