Stochastic Economic Dispatch Model Research Articles

Parallel Dual-DQAM for Multi-Scenario Stochastic Economic Dispatch Model by Temporal and Scenario Decompositions

Large-scale multi-scenario stochastic economic dispatch (SED) is hard to directly solve due to the huge number of variables and constraints. To reduce the computational burden, a nested dual-DQAM (Diagonal Quadratic Approximation Method) is proposed in this paper to decouple the SED problem in both scenarios and time periods, where each subproblem only contains one time period and one scenario. Moreover, these subproblems can be handled in parallel, such that the computational performance can be significantly improved. Besides, we have investigated the optimal policy to select the best parallel structure of the proposed dual-DQAM, and the theorical convergence performance is proved. Numerical results on several test systems show the effectiveness of the proposed dual-DQAM. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Nowadays, the safe operation and economic dispatch in power system are greatly challenged by the high penetration of renewable energy. Although the uncertainty of renewable energy can be well modeled by stochastic programming, the solution complexity will seriously increase due to the large number of typical scenarios. For this problem, the parallel solution using decomposition methods is the state-of-the-art strategy. In this paper, we propose an efficient solution to the multi-scenario SED problem by temporal and scenario decompositions. It realizes an important innovation in both reducing the computational burden and improving the solving efficiency, which greatly promotes the application of SED in large-scale systems. To better use this method, the following two properties should be highlighted: i) the proposed method has a convergence guarantee and works especially well on SED due to the sparsity property of linking constraint matrices. ii) the computational efficiency of the proposed method becomes more significant as the number of time periods and scenarios grows and can be further improved under a fast ramp rate.

Modeling the Reserve Capacity of Wind Power and the Inherent Decision-Dependent Uncertainty in the Power System Economic Dispatch

The ever-increasing penetration of renewable generation is demanding additional flexibility for the operation of power systems. In this sense, it has been proved that wind power generators (WPGs) can provide part of the required operating reserve through pitch angle control (PAC) under a deloaded strategy. Unlike conventional operating reserve sources, however, the operating reserve provided by WPGs can't always be considered reliable, which renders the power system dispatch more challenging. In this research, the reserve capacity of the WPGs is modeled considering the decision-dependent uncertainty (DDU). The random wind speed introduces uncertainty to the available reserve capacity of the WPGs while the decisions on the deloading degrees of the WPGs directly affect their coefficients between wind speed and usable wind power, making the uncertainty decision-dependent. Moreover, the operational technical limits of the WPGs and the multiple possible wind speed scenarios are also considered in the wind power reserve capacity modeling. Then, a two-stage reliability constrained stochastic economic dispatch model with WPGs' reserve provision (SED-WRP) is developed to jointly dispatch the generation and reserve. A group-based multi-cut Benders decomposition method is applied to improve the convergence performance of the solution algorithm. Case studies are solved to quantify the impact of considering the reserve provision of WPGs and the inherent DDU in power system dispatch decisions.

A Bayesian Approach for Estimating Uncertainty in Stochastic Economic Dispatch Considering Wind Power Penetration

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in the stochastic economic dispatch (SED) problem for the purpose of forecasting, the conventional Monte-Carlo (MC) method is prohibitively time-consuming for practical applications. To overcome this problem, we propose a novel Gaussian-process-emulator (GPE)-based approach to quantify the uncertainty in SED considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling (LHS) as the computer experimental design, a GPE is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated SED model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

Stochastic Economic Dispatch of Hydro-Thermal-Wind-Photovoltaic Power System Considering Mixed Coal-Blending Combustion

This paper proposes a stochastic economic dispatch (SED) model for hydro-thermal-wind-photovoltaic power system (HTWPPS) considering mixed coal-blending combustion (MCBC) to improve the operational efficiencies of thermal power units (TPUs) with deep peak-regulating operation (DPRO). Firstly, the rations for different types of coal can be acquired by meeting the operational requirements of boilers. Three functions including the cost of coal consumption, polluting gas emission, and the life loss cost for TPUs could be obtained by fitting coal quality. Besides, they would be strictly piecewise linearized, respectively. Consequently, the objective function involving the above three kinds of costs as well as the cost of oil injection can be presented. Secondly, there is a two-stage framework for reducing the coupling of HTWPPS and improving the solving efficiency. In the first stage, the Monarch Butterfly Optimization (MBO) algorithm is employed for obtaining the power outputs of hydro-power units (HPUs) taking the minimum water consumption as the objective. In the second stage, the load curve can be updated according to the results from the first stage. Besides, the Latin Hypercube Sampling method and the backward scene reduction technique are utilized to acquire a set of scenarios of wind power. In this way, the SED model considering MCBC can be achieved. The case studies have been carried out on a simplified provincial power system in China with the help of MATPOWER and CPLEX. The results show that the proposed model can effectively increase the economic and environmental benefits for TPUs.

Day-ahead stochastic economic dispatch of wind integrated power system considering demand response of residential hybrid energy system

As the installed capacity of wind power is growing, the stochastic variability of wind power leads to the mismatch of demand and generated power. Employing the regulating capability of demand to improve the utilization of wind power has become a new research direction. Meanwhile, the micro combined heat and power (micro-CHP) allows residential consumers to choose whether generating electricity by themselves or purchasing from the utility company, which forms a residential hybrid energy system. However, the impact of the demand response with hybrid energy system contained micro-CHP on the large-scale wind power utilization has not been analyzed quantitatively. This paper proposes an operation optimization model of the residential hybrid energy system based on price response, integrating micro-CHP and smart appliances intelligently. Moreover, a novel load aggregation method is adopted to centralize scattered response capability of residential load. At the power grid level, a day-ahead stochastic economic dispatch model considering demand response and wind power is constructed. Furthermore, simulation is conducted respectively on the modified 6-bus system and IEEE 118-bus system. The results show that with the method proposed, the wind power curtailment of the system decreases by 78% in 6-bus system. In the meantime, the energy costs of residential consumers and the operating costs of the power system reduced by 10.7% and 11.7% in 118-bus system, respectively.

Research on Power System Stochastic Economic Dispatch Considering Interruptible Load and Wind Power

Interruptible load was an important measure for demand response which can effectively implement the interaction between grid side and demand side. It’s also the important feature and component of smart grid. This paper established a stochastic economic dispatch model which brought both interruptible load and stochastic wind generation models into scheduling, and took the active and reactive power constraint of generator, the adjustable capacity constraint of interruptible load and the constraint of branch power flow into account. On the basis of Monte Carlo simulation and modified interior point method, a comprehensive optimization algorithm is proposed to tackle the above stochastic economic dispatch model. The result of IEEE 118-bus system illustrated that the proposed method can effectively curtail system’s operational cost and, to some extent, boost grid’s adaptability to wind power.

A Frequency-Constrained Stochastic Economic Dispatch Model

In this paper, we formulate the economic dispatch problem as a two-stage stochastic convex program for operational decision making under uncertainty. Post-contingency minimum frequency constraints are formulated as convex sets using a simplified model of frequency dynamics. The L-shaped method is used to decompose the large stochastic program into smaller sub-problems. Large-scale system examples are provided to demonstrate the computational efficiency of the proposed model formulation. Numerical results show the value of the proposed model and indicate that the proposed model is especially useful under a higher level of wind penetration.

Power System Stochastic Economic Dispatch Considering Uncertain Discharge Capacity from V2G

V2G technology achieves a two-way interaction of the grid and electric vehicles (EVs), it makes plug-in hybrid electric vehicle (PHEV) be able to access grid and participate in grid scheduling. By V2G technology, PHEVs can provide FM and spinning reserve ancillary services such as economic dispatch. With the extensive use of plug-in hybrid electric vehicles (PHEVs), its important impact on charge and discharge process will be the grid safe and economic operation. Firstly, the article proves the V2G discharge capacity of a normal distribution from the theory, and based on which to establish a stochastic economic dispatch model. The results which obtain by using the IEEE 14 node system simulation show that this conclusion of the constructed model is feasible and effective, and the conclusions that the V2G node optimal active output power and minimum scheduling cost expectations are proportional to the the V2G discharge capacity expectations are also obtained.