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Two-stage stochastic power generation scheduling in microgrids
Abstract
In this study, the power scheduling problem in μ-grids is investigated taking the uncertainties in power demand and wind power into account. The problem is formulated as a stochastic mixed-integer linear optimization problem with the objective being minimizing the total μ-grid cost. The objective is subject to a set of operational constraints imposed on the generating units and the system itself. A two-stage stochastic programming method has been applied to find the optimal power generation schedule for a μ-grid. The developed approach was implemented in a General Algebraic Modeling System platform (GAMS). The developed method was tested on a μ-grid consisting of eight dispatchable units and a wind turbine. To demonstrate the necessity of uncertainty modeling, the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) were used to compare the stochastic power schedule obtained with the deterministic one.
... The micro-grid technical features, evidences its appropriateness for power providing in remote regions. Through designing a local small-scale unit, it is feasible to supply power in a small residential place possessing high reliability and also high security, by means of strict controlling and monitoring [12,13]. ...
... where, q max is a minute number near zero. Equation (12), if the condition (11) is met, is employed to represent new locations for the streams: ...
In recent years, the apprehensions about ecological pollution derived from the use of fossil fuels for electricity generation, as well as the concerns about using up all the reserved resources have been increased. On the other hand, the growth of electricity consumption has been noticeable in domestic and manufacturing parts. Therefore, employing renewable energy resources such as wind and solar can be an adequate substitution. Stochastic nature accompanied by the uncertainty existent in these renewable resources can be accounted as the issues which make planning and forecasting complex. In this study, the micro-grid optimal planning in presence of renewable energy resources is evaluated employing water cycle and grey wolf optimization algorithms. Actually, to control the load variations, in addition to the considered renewable resources, a diesel generator is employed. Battery energy storage is also considered in the micro-grid for charging and discharging operations in the demanded time. Besides, to model wind and solar renewable resources uncertainty, stochastic programming is used and probabilistic scenarios are defined, as well. Solar power intervals are anticipated to be between the hour 6th to the hour 19th. Additionally, utility grid is able to sell sufficient amount of power to the main grid so as to meet the load demand at hours 8th to 12th and also 19th to 22th. Lastly, the micro-grid operation cost gained via the proposed methods are compared against particle swarm optimization (PSO) and mixed-integer linear programming (MILP). The simulation results represent that, through application of the presented techniques, the operational cost of the system is lesser than PSO and MILP, which verifies the effectiveness of the methods.
... Technical characteristics of micro-grids make them appropriate for power supplying in remote rural areas. By designing a local small unit, it is possible to provide the power of a small residential area with high reliability and security using strict monitoring and control (Benz et al., 2003;Eajal, 2014). According to the characteristics, the loads can be divided into non-controllable loads and the loads that can be participated in demand response programs. ...
Nowadays, electricity consumption in industrial and domestic sectors is growing increasingly. In recent years, due to the expansion of consumption and increased concern about environmental pollution resulting from the use of fossil fuels to generate electricity and running out of the resources, using renewable energies such as wind and solar has been considered. One of the problems in these resources is the inherent uncertainty as well as accidental nature of these sources, which complicates planning and forecasting of resources. In this paper, optimal scheduling of micro-grid connected to the main grid with renewable energy resources is studied with the help of mixed-integer linear programming in general algebraic modeling system (GAMS) software. A diesel generator is used in cooperation with other renewable resources so as to control the load instability. Furthermore, stochastic programming and probabilistic scenarios are used in order to model the uncertainty of wind and solar resources. Solar power is predicted to be in the interval of hour 6th to hour 19th. At the outset and also at the end of day, power generation has the minimum amount, while the maximum amount of power generation can be found at hour 13th. Battery charging occurrence is in the case of low load, which is existent for the grid in all the scenarios (nights: at hours 2nd to 5th; days: at hours 13th to 15th). Selling the energy to the main grid is performed at the times in which the denoted price possesses the peak value (at hours 8th to 12th and 19th to 22th). Finally, operation cost of the micro-grid using the proposed method is compared with genetic algorithm, which confirms the efficiency of the method.
... A scenarios generation approach based on a time-homogeneous Markov chain model is proposed to simulate time-series of renewable energy generation and load demand. Similar approaches are considered in [4] and [5], especially in [4] uncertainty is *Accepted for ECC 2016 1 Benjamin Heymann is a PhD student at the Ecole polytechnique, France. 2 J. Frédéric Bonnans is a researcher at Inria and Ecole polytechnique, France. 3 Francisco Silva is a professor at the University of Limoges. 4 Guillermo Jimenez is a researcher at the Universidad de Chile. ...
We propose a novel stochastic control formulation for the microgrid energy management problem and extend previous works on continuous time rolling horizon strategy to uncertain demand. We modelize the demand dynamics with a stochastic differential equation. We decompose this dynamics into three terms: an average drift, a time-dependent mean-reversion term and a Brownian noise. We use BocopHJB for the numerical simulations. This optimal control toolbox implements a semi-Lagrangian scheme and handle the optimization of switching times required for the discrete on/off modes of the diesel generator. The scheme allows for an accurate modelling and is computationally cheap as long as the state dimension is small. As described in previous works, we use a trick to reduce the search of the optimal control values to six points. This increases the computation speed by several orders. We compare this new formulation with the deterministic control approach introduced in [1] using data from an isolated microgrid located in northern Chile.
... A scenarios generation approach based on a time-homogeneous Markov chain model is proposed to simulate time-series of renewable energy generation and load demand. Similar approaches are considered in [63] and [32], especially in [63] uncertainty is characterized by a scenarios generation approach based on autoregressive moving average (ARMA) model according to the probability density function of each random variable. In [73], uncertainty is addressed using a two-stage decision process combined with a receding horizon approach. ...
We present our contribution on the optimization and regulation of electricity production.The first part deals with a microgrid Energy Management System (EMS). We formulate the EMS program as a continuous time optimal control problem and then solve this problem by dynamic programming using BocopHJB, a solver developed for this application. We show that an extension of this formulation to a stochastic setting is possible. The last section of this part introduces the adaptative weights dynamic programming algorithm, an algorithm for optimization problems with different time scales. We use the algorithm to integrate the battery aging in the EMS.The second part is dedicated to network markets, and in particular wholesale electricity markets. We introduce a mechanism to deal with the market power exercised by electricity producers, and thus increase the consumer welfare. Then we study some mathematical proper- ties of the agents’ optimization problems (producers and system operator). In the last chapter, we present some pure Nash equilibrium existence and uniqueness results for a class of Baye- sian games to which some networks markets belong. In addition we introduce an algorithm to compute the equilibrium for some specific cases.We provide additional information on BocopHJB (the numerical solver developed and used in the first part of the thesis) in the appendix.
This paper intends to analyze micro-grid energy management optimally with consideration of renewable resources, and taking into account the objectives such as pollution decrease and uncertainty, as well as economic objective. Accordingly, the micro-grid has been optimized with assumption of resources like solar and wind energy, and the use of fuel cells, micro turbines and storage batteries with the purpose of minimization of energy consumption price accompanied by reduction of the amounts of emitted pollutants in a micro-grid. The optimization process aims to determine how to charge and discharge storage elements by considering the type of load, and to determine the amount of micro turbine production, and fuel cell usage, as well as energy exchange with the upstream network according to the daily energy price. In this study, water cycle algorithm (WCA) utilization for energy consumption smart optimization has been considered, and besides, the use of probabilistic scenarios intended for modeling the renewable resources and the load uncertainty has been taken into account. From the derived results, it can be concluded that, once economic objective is considered, the optimizer effort is to deliver the load at the minimum cost, leading to increments in the pollution emission in this case. On the other hand, in the case of considering the emission function merely, the reverse will occur. If the mentioned functions are considered concurrently, a balance can be detected between in-network production and the upstream grid received energy with the aim of maintaining the pollutants emission and the costs at a reasonable amount. As a final point, the results derived from the presented method are analyzed against the operation costs of the micro-grid, acquired via mixed-integer linear programming(MILP), genetic algorithm(GA), and particle swarm optimization(PSO), authenticating the scheme precision.
With the increasing influence of new energy power system, the prediction of Photovoltaic (PV) output power becomes more and more important In this paper, it is the first time to put forward a hybrid modeling method combining long-short term memory recurrent neural network (LSTM) and stochastic differential equation (SDE). This method realizes the prediction of PV output power in different seasons and overcomes the uncertainty of PV power generation. Wavelet analysis and automatic encoder are used to decompose data and extract important features. According to the detailed signal sequence and the approximate signal sequence, the LSTM prediction model is established. Meanwhile, the mathematical model of SDE is established according to the detailed signal sequence. Finally, the output sequences of the two models are reconstructed by wavelet transform. This hybrid model can not only realize the point prediction of PV output power according to the predicted mean value, but also achieve the interval prediction under different confidence levels according to the randomness. In this paper, the proposed method is applied to predict the PV output power of CHINT photovoltaic power generation system with installed capacity of 10MW in different seasons, and the weather forecast data with errors of ±10%, ±20% and ±30% are used. Experimental results prove the effectiveness of the method. In the summer model considering forecast errors within ±20% of weather forecast data, the RMSEs of BP neural network, LSTM and convolutional neural network (CNN) are 5.9468, 5.6762 and 5.8004 respectively. However, the RMSE of the mean prediction with the confidence level of 90% under the proposed method is 4.4647. With this method, the results of interval prediction and point prediction of PV output power can provide better decision support for the stable and safe operation of PV grid connection. They have higher reference value for energy dispatching departments.
Average household electricity use and industrial branches electrical energy consumptions are on a rising trend these days. Actually, utilization of fossil fuels for electricity generation purposes, results in contamination of the environment. Besides, loss of resources may be encountered owning to the persistent consumption of the energy produced through this process. Hence, the mentioned concerns necessitate the existent generations substitution by renewable resources obtained energies, for instance wind and solar, which can be accounted as a reasonable approach. However, one of the complications ahead is modeling of the uncertainty for these resources, accompanied by their random nature aggravating the resultant planning and prediction. Accordingly, micro-grid optimal scheduling in presence of renewable resources for energy production and storage systems is assessed in this study, assuming the case in which micro-grid is connected to the main grid. The simulations are devoted to mixed-integer linear programming (MILP), which are performed via GAMS software. With the help of scheduling a central control system in the studied micro-grid, a virtual power producer (VPP) is capable of controlling the load as well as managing optimal production of the energy. According to the load variable and unpredictable behavior, in addition to the diesel generator, some other renewable resources are employed for load management and control. Again, for uncertainty modeling associated with solar and wind resources, probabilistic schemes are evaluated, and besides, stochastic programming is designated. Moreover, the generated pollution of the units is also modeled. As a final step, a comparison is made between the operation cost results achieved by the proposed technique and those derived from genetic algorithm (GA) in the studied micro-grid, validating the correctness of the scheme.
In order to support the increasing penetration of plug-in electric vehicle (PEV) users, a novel regional PEV charging station system with DC level 3 fast charging is proposed in this paper. To promote sustainable development, the proposed system is designed to be equipped with a distributed energy storage system charged by wind generation, solar PV generation, and electricity from the power grid, which can simultaneously charge multiple PEVs. The objective of the proposed system is to minimize operational cost. Wind/solar PV generation and electricity market price are input state variables in this problem and are predicted by support vector regression (SVR). The uncertainties of the SVR models are analyzed using a Martingale Model Forecast Evolution (MMFE). Finally, bounds of the optimal operational cost in this problem are evaluated with two stochastic measures, which can be solved using the expected value problem and the wait-and-see solution. Bounds from experiments simulating models of the Dallas-Fort Worth metroplex show that the largest uncertainty in the system occurs during weekdays in the summer.
The power system and transportation sector are our planet's main sources of greenhouse gas emissions. Renewable energy sources (RESs), mainly wind and solar, can reduce emissions from the electric energy sector; however, they are very intermittent. Likewise, next generation plug-in vehicles, which include plug-in hybrid electric vehicles and electric vehicles with vehicle-to-grid capability, referred to as gridable vehicles (GVs) by the authors, can reduce emissions from the transportation sector. GVs can be used as loads, energy sources (small portable power plants) and energy storage units in a smart grid integrated with renewable energy sources. However, uncertainty surrounds the controllability of GVs. Forecasted load is used in unit commitment (UC); however, the actual load usually differs from the forecasted one. Thus, UC with plug-in vehicles under uncertainty in a smart grid is very complex considering smart charging and discharging to and from various energy sources and loads to reduce both cost and emissions. A set of valid scenarios is considered for the uncertainties of wind and solar energy sources, load and GVs. In this paper, an optimization algorithm is used to minimize the expected cost and emissions of the UC schedule for the set of scenarios. Results are presented indicating that the smart grid has the potential to maximally utilize RESs and GVs to reduce cost and emissions from the power system and transportation sector.
It is widely accepted that renewable energy sources are the key to a sustainable energy supply infrastructure since they are both inexhaustible and nonpolluting. A number of renewable energy technologies are now commercially available, the most notable being wind power, photovoltaic, solar thermal systems, biomass, and various forms of hydraulic power. In this paper, a methodology has been proposed for optimally allocating different types of renewable distributed generation (DG) units in the distribution system so as to minimize annual energy loss. The methodology is based on generating a probabilistic generation-load model that combines all possible operating conditions of the renewable DG units with their probabilities, hence accommodating this model in a deterministic planning problem. The planning problem is formulated as mixed integer nonlinear programming (MINLP), with an objective function for minimizing the system's annual energy losses. The constraints include the voltage limits, the feeders' capacity, the maximum penetration limit, and the discrete size of the available DG units. This proposed technique has been applied to a typical rural distribution system with different scenarios, including all possible combinations of the renewable DG units. The results show that a significant reduction in annual energy losses is achieved for all the proposed scenarios.
This paper presents a new method based on the cost-benefit analysis for optimal sizing of an energy storage system in a microgrid (MG). The unit commitment problem with spinning reserve for MG is considered in this method. Time series and feed-forward neural network techniques are used for forecasting the wind speed and solar radiations respectively and the forecasting errors are also considered in this paper. Two mathematical models have been built for both the islanded and grid-connected modes of MGs. The main problem is formulated as a mixed linear integer problem (MLIP), which is solved in AMPL (A Modeling Language for Mathematical Programming). The effectiveness of the approach is validated by case studies where the optimal system energy storage ratings for the islanded and grid-connected MGs are determined. Quantitative results show that the optimal size of BESS exists and differs for both the grid-connected and islanded MGs in this paper.
Third edition. "Since publication of the second edition, there have been extensive changes in the algorithms, methods, and assumptions in energy management systems that analyze and control power generation. This edition is updated to acquaint electrical engineering students and professionals with current power generation systems. Algorithms and methods for solving integrated economic, network, and generating system analysis are provided. Also included are the state-of-the-art topics undergoing evolutionary change, including market simulation, multiple market analysis, multiple interchange contract analysis, contract and market bidding, and asset valuation under various portfolio combinations"-- "Online video course with powerpoint slides for each chapter at www.cusp.umn.edu; site also contains links to important research reports, an entire set of student programs in MATLAB, and sets of power system sample data sets for use in student exercises"-- Preface to the third edition -- Preface to the second edition -- Preface to the first edition -- Acknowledgment -- Introduction -- Industrial organization, managerial economics, and finance -- Economic dispatch of thermal units and methods of solution -- Unit commitment -- Generation with limited energy supply --Transmission system effects -- Power system security -- Optimal power flow -- Introduction to state estimation in power systems -- Control of generation -- Interchange, pooling, brokers, and auctions -- Short-term demand forecasting -- Index.
The penetration of renewable sources (particularly wind power) in to the power system network has been increasing in the recent years. As a result of this, there have been serious concerns over reliable and satisfactory operation of the power systems. One of the solutions being proposed to improve the reliability and performance of these systems is to integrate energy storage devices into the power system network. Further, in the present deregulated markets these storage devices could also be used to increase the profit margins of wind farm owners and even provide arbitrage. This paper discusses the present status of battery energy storage technology and methods of assessing their economic viability and impact on power system operation. Further, a discussion on the role of battery storage systems of electric hybrid vehicles in power system storage technologies had been made. Finally, the paper suggests a likely future outlook for the battery technologies and the electric hybrid vehicles in the context of power system applications.
Uncertainty in power systems operations has been traditionally managed by multistage decision making and operating reserve requirements. A familiar example of multistage decisions is day-ahead unit commitment and real-time economic dispatch. An alternate approach for managing uncertainty is a stochastic formulation, which allows the explicit modeling of the sources of uncertainty. This paper compares stochastic and reserve methods and evaluates the benefits of a combined approach for the efficient management of uncertainty in the unit commitment problem. Numerical studies show that unit commitment solutions obtained for the combined approach are robust and superior with respect to the traditional approach in terms of both economics and reliability metrics.
Microgrids are low voltage intelligent distribution networks comprising various distributed generators, storage devices and controllable loads which can be operated as interconnected or as islanded system. The optimal generation scheduling is one of the important functions for the Microgrid operation. This paper describes a three-step efficient method for the optimal generation scheduling of a Microgrid in island operation. The first step of the method is to set up an initial feasible solution for thermal unit commitment and the next step is to solve the thermal unit commitment problem. The final step is to optimize the renewable-thermal dispatch based on thermal unit commitment results. Solving the thermal unit commitment problem has more opportunity to minimize the operating cost. Therefore, few algorithms such as Lagrangian relaxation, genetic algorithm and a hybrid algorithm of Lagrangian relaxation and genetic algorithm have been used to find the least operating cost. Microgrid which is considered in the case study, consists of a PV system, a wind plant, 10 thermal units and a battery bank.
This article develops a linear programming cost minimisation model for the high level system design and corresponding unit commitment of generators and storage within a microgrid; a set of energy resources working co-operatively to create a cost effective, reliable and environmentally friendly energy provision system. Previous work in this area is used as a basis for formulation of a new approach to this problem, with particular emphasis on why a microgrid is different to centralised generation or other grid-connected decentralised energy resources. Specifically, the model explicitly defines the amount of time that the microgrid would be expected to operate autonomously, and restricts flow of heat between microgrid participants to defined cases. The model developed is applied to a set of United Kingdom commercial load profiles, under best current estimates of energy prices and technology capital costs, to determine investment attractiveness of the microgrid. Sensitivity analysis of results to variations in energy prices is performed. The results broadly indicate that a microgrid can offer an economic proposition, although it is necessarily slightly more expensive than regular grid-connected decentralised generation. The analysis results have raised important questions regarding a fair method for settlement between microgrid participants, and game theory has been identified as a suitable tool to analyse aspects of this situation.
293 pages Provider Notes: gams.com * User Guide * McCarl's guide (much longer, more examples)* CPLEX/GAMS manual * GAMS mailing list (not very active, but sometimes searching helps). General things users should understand for debugging and development. Related Documents:WS62a
Microgrids are low-voltage (LV) distribution networks comprising various distributed generators (DGs), storage devices, and controllable loads that can operate either interconnected or isolated from the main distribution grid as a controlled entity. This paper describes the operation of a central controller for microgrids. The controller aims to optimize the operation of the microgrid during interconnected operation, i.e., maximize its value by optimizing the production of the local DGs and power exchanges with the main distribution grid. Two market policies are assumed including demand-side bidding options for controllable loads. The developed optimization algorithms are applied on a typical LV study case network operating under various market policies and assuming realistic spot market prices and DG bids reflecting realistic operational costs. The effects on the microgrid and the distribution network operation are presented and discussed.
Resource scheduling under uncertainty in a smart grid with renewables and plug-in vehicles
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