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Risk-Based Energy Procurement via IGDT
Abstract
In this chapter, the power procurement problem of a large consumer under power price uncertainty is solved using information gap decision theory (IGDT). In contrast to other uncertainty modeling methods, the IGDT method makes it possible to model the positive and negative impacts of uncertainty through different strategies. To do so, the risk of the power procurement process of a large consumer is assessed considering the opportunity and robustness functions of the IGDT method, and three different strategies, risk-averse, risk-neutral, and risk-taker, are derived. It should be noted that the problem is formulated as mixed integer nonlinear programming and solved using GAMS programming software.
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This paper proposes a new formulation to speed up the security constraint unit commitment (SCUC) solution in large scale power systems. The number of variables and prevailing constraints grow drastically as the number of system buses and the credible contingencies increase. So, as the first stage, inessential variables and constraints are eliminated and necessary variables for a tighter formulation are defined. Some constraints and variables are removed and some constraints are modified based on the results of a small sub-problem at each iteration of Benders decomposition algorithm. By utilizing the proposed framework, especially in the case of large number of severe contingencies, a large number of variables and constraints will be eliminated. Up- and down-going reserves are considered at both generation- and demand-sides. The IEEE RTS1 and RTS2 systems are studied as illustrative examples. The SCUC results drawn using the proposed algorithm are compared with those obtained by a conventional MIP-based algorithm to show the effectiveness of the proposed algorithm.
A new strategy based on Takagi-Sugeno fuzzy controller is proposed in this paper for wide-area power system. In this strategy, the proposed fuzzy controller is optimized by a new hybrid metaheuristic algorithm and hyperplane clustering algorithm to partition the fuzzy space of the given input-output data. A global signal from the centralized controller is employed in wide area control (WAC) scheme to damp out the inter-area mode as well as local mode of oscillations. To demonstrate the capability of proposed strategy, three case studies have been used in this paper. The obtained results demonstrate the validity of proposed strategy through comparison with other techniques in this problem.
This paper deals with the Voltage Stability Constrained Optimal Power Flow (VSC-OPF) problem considering
the wind power generation uncertainty. An approach is proposed which determines the maximum tolerable
uncertainty of wind power generation for a given percentage of the increase in total cost. This maximum
uncertainty is determined in a way that a required loading margin (LM), is preserved. It is worth noting that
LM is the most important measure of voltage stability which reflects the distance from the current operating
point to the voltage collapse point. For this aim, Information Gap Decision Theory (IGDT) is utilized to
handle the uncertainty of wind power generation in the proposed VSC-OPF model. The main feature of the
proposed model is to handle the uncertainty of multiple wind farms (WFs) in a way that for a given worsening
of total cost, maximum tolerable uncertainty of wind power generation is achieved for all WFs. The proposed
model is implemented on IEEE 39-bus standard test system. In order to evaluate the effectiveness of the
proposed methodology for uncertainty handling of multiple WFs, the results obtained by IGDT technique are
compared with Monte Carlo simulations (MCS) and scenario based (SB) approach. The simulation results
imply that the uncertainty radius and the desired LM are inversely related, such that for a given tolerable
increase of cost, the radius of uncertainty decreases by increasing the desired LM.
This study presents a novel tractable mixed-integer linear programming model for multiyear transmission expansion planning (TEP) problem coping with the uncertain capital costs and uncertain electricity demands using the information-gap decision theory (IGDT). As the uncertain capital costs and electricity demands compete to occupy the permissible uncertainty budget, the proposed IGDT-based TEP (IGDT-TEP) framework employs the augmented ϵ-constraint method to solve a multiobjective optimisation problem maximising the robust regions against the uncertain variables (i.e. capital costs and electricity demands) centred on their forecasted values. This framework enables the system's planner to control the immunisation level of the optimal expansion plan regarding the enforced planning uncertainties using a certain uncertainty budget. Also, a Latin hypercube sampling-based post-optimisation procedure is introduced to evaluate the robustness of an expansion plan obtained from the proposed IGDT-TEP framework. Simulation results demonstrate the effectiveness of the IGDT-TEP model to handle the uncertain nature of capital costs and electricity demands.
In domestic sector, robust scheduling of energy usage under various uncertainties is an important factor for any smart home energy management systems (EMS). In this paper, information gap decision theory (IGDT) is proposed for robust scheduling of apartment smart building (ASB) in the presence of price uncertainty and solar thermal storage system (STS). The proposed sample ASB contains combined heat and power (CHP) generator, boiler, battery storage system (BSS), STS system and smart appliances. IGDT approach doesn't depend on the size of the model. So, the EMS of ASB which is known as small scale loads can use IGDT to make more informed decisions against the price uncertainty. IGDT contains two functions namely robustness and opportunity functions. Risk-averse perspective of optimal scheduling of ASB is modeled by robustness function and opportunity function is used to model risk-taker perspective of optimal scheduling of ASB. Also, to assess the effect of STS system on proposed problem, two case studies are studied, and significant results were obtained, which indicate the validity of proposed model.
One of the big challenging issues for the operators of smart home is optimal scheduling of these homes within various uncertainties that can lead to increase or decrease of the operation cost of smart home. In this paper, information gap decision theory (IGDT) is proposed for robust scheduling of apartment smart building in the presence of price uncertainty. IGDT approach doesn't depend on the size of model. So, the operators of apartment smart building which are known as small scale loads can use IGDT to make more informed decisions against the price uncertainty. IGDT method contains two functions i.e. robustness function and opportunity functions. Robustness function is used to model the negative impacts of market price uncertainty while the opportunity function is used to model positive effects of market price uncertainty. By comparing the obtained results from robustness function of IGDT, it can be found that by taking risk-averse strategy and analyzing one of the obtained strategies, operation cost of apartment smart building is increased 26.18% while robustness of apartment smart building against increase of market price is increased up to 51.87% which means that the apartment smart building has become robust against increase of market price. On the other hand, according to the obtained results from opportunity function of IGDT, by taking risk-seeking strategy and analyzing one of the obtained strategies, due to 56.92% reduction of market price, the operation cost of smart home is reduced 3 £ which is 26.18% of total operation cost of apartment smart building. In fact, these strategies obtained from robustness and opportunity functions help home energy management system to take appropriate decisions to handle various possible outcomes of uncertainty. The proposed IGDT-based sample model is solved using General Algebraic Modeling System (GAMS).
This paper proposes the application of information gap decision theory (IGDT) to the design of robust wide-area power system stabilizers (WPSSs) with consideration of wind farm (WF) power outputs variations and transmission line outages. According to IGDT, an optimization problem is constructed to tune WPSS parameters. Then, the derived optimal WPSSs can achieve explicit and favorable robustness to ensure the required damping control effects on the inter-area oscillations over a maximum variation range of WF steady-state power outputs in normal and emergent operating conditions. Moreover, with the intent of using the excellent global searching capability of particle swarm optimization (PSO), a customized PSO algorithm is proposed to efficiently solve the resulting highly nonlinear programming problem. Finally, simulations are carried out on a modified New England (10-Machine 39-Bus) system to validate the efficiency of the IGDT-based design method. The derived WPSSs exhibit expected robustness with respect to the wind power variations and transmission line outages.
This paper presents a novel framework for designing and optimal scheduling of an air source heat pump based industrial continuous heat treatment furnace (ICHTF) which is driven by a solar Stirling engine and a wind turbine. The proposed flame-making process equipped with two inside and outside fans, an expansion valve, compressor, condenser and an evaporator to supply the heating demand with the high-temperature more than 900 K over a 24-h time interval. Use of solar, wind and the proposed heating cycle in an industrial furnace with no need to fossil fuels reduce the greenhouse gas emissions and increase the economic saving in the consumption of petroleum products, significantly. Moreover, an information gap decision theory (IGDT) is implemented in order to find the optimal scheduling strategies taking into account the heating demand uncertainty. The IGDT technique assesses the robustness and opportunistic aspects of the optimal scheduling scenarios in the presence of heating load uncertainty to make the risk-averse or risk-taker decisions, respectively. The proposed ICHTF is simulated as a nonlinear programming (NLP) problem on a benchmark small-scale industrial sector to minimize total energy procurement cost considering the operational constraints of Stirling cycle and air source heat pump. Simulation results confirm that the risk-aversion or risk-taking decisions affect the output mechanical power of Stirling engine and total electrical power purchased from the upstream grid.
This paper presents a chance constrained information gap decision model for multi-period microgrid expansion planning (MMEP) considering two categories of uncertainties, namely random and non-random uncertainties. The main task of MMEP is to determine the optimal sizing, type selection, and installation time of distributed energy resources (DER) in microgrid. In the proposed formulation, information gap decision theory (IGDT) is applied to hedge against non-random uncertainties of long-term demand growth. Then, chance constraints are imposed in the operational stage to address the random uncertainties of hourly renewable energy generation and load variation. The objective of chance constrained information gap decision model is to maximize the robustness level of DER investment meanwhile satisfying a set of operational constraints with a high probability. The integration of IGDT and chance constrained program, however, makes it very challenging to compute. To address this challenge, we propose and implement a strengthened bilinear Benders decomposition method. Finally, the effectiveness of proposed planning model is verified through the numerical studies on both the simple and practical complex microgrid. Also, our new computational method demonstrates a superior solution capacity and scalability. Compared to directly using a professional mixed integer programming solver, it could reduce the computational time by orders of magnitude.
Electricity price forecasts are imperfect. Therefore, a merchant energy storage facility requires a bidding and offering strategy for purchasing and selling the electricity to manage the risk associated with price forecast errors. This paper proposes an information gap decision theory (IGDT)-based risk-constrained bidding/offering strategy for a merchant compressed air energy storage (CAES) plant that participates in the day-ahead energy markets considering price forecasting errors. Price uncertainty is modeled using IGDT. The IGDT-based self-scheduling formulation is then used to construct separate hourly bidding and offering curves. The theoretical approach to develop the proposed strategy is presented and validated using numerical simulations.
This paper presents an optimal bidding strategy for industrial consumers with cogeneration facilities, power-only and heat-only units to participate in day-ahead electricity market. A information gap decision theory (IGDT) technique is implemented for determining the optimal bidding strategies considering market price uncertainty. IGDT evaluates the robustness/opportunity of optimal bidding strategy under market price uncertainty considering the consumer choice of taking risk-averse or risk-taking decisions. It is confirmed that the risk-averse or risk-taking decisions might affect the expected profit and bidding curve of the consumers.
This paper presents a novel modified interactive honey bee mating optimization (IHBMO) base fuzzy stochastic long-term approach for determining optimum location and size of distributed energy resources (DERs). The Monte Carlo simulation method is used to model the uncertainties associated with long-term load forecasting. A proper combination of several objectives is considered in the objective function. Reduction of loss and power purchased from the electricity market, loss reduction in peak load level and reduction in voltage deviation are considered simultaneously as the objective functions. First, these objectives are fuzzified and designed to be comparable with each other. Then, they are introduced into an IHBMO algorithm in order to obtain the solution which maximizes the value of integrated objective function. The output power of DERs is scheduled for each load level. An enhanced economic model is also proposed to justify investment on DER. An IEEE 30-bus radial distribution test system is used to illustrate the effectiveness of the proposed method. © Higher Education Press and Springer-Verlag Berlin Heidelberg 2014.
In the context of electricity market and smart grid, the uncertainty of electricity prices due to the high complexities involved in market operation would significantly affect the profit and behavior of electric vehicle (EV) aggregators. An information gap decision theory-based approach is proposed in this paper to manage the revenue risk of the EV aggregator caused by the information gap between the forecasted and actual electricity prices. The proposed decision-making framework can offer effective strategies to either guarantee the predefined profit for risk-averse decision-makers or pursue the windfall return for risk-seeking decision-makers. Day-ahead charging and discharging scheduling strategies of the EV aggregators are arranged using the proposed model considering the risks introduced by the electricity price uncertainty. The results of case studies validate the effectiveness of the proposed framework under various price uncertainties.
In restructured electricity market, the consumers have various procurement strategies to supply their electricity demand from alternative resources. An approach to cost reduction and risk management for a large consumer is participation in demand response programs (DRP). Due to uncertain nature of pool prices and price fluctuations in pool market, uncertainty modeling is inevitable. For evaluation of different procurement strategies of large consumer, a technique based on information gap decision theory (IGDT) is proposed. This paper develops an energy acquisition model for large consumer with multiple procurement options including distributed generation (DG), bilateral contracts and pool market purchase with participating in DRP. This paper is focused to study the effect of DRP on the procurement strategy problem. Also, the time-of-use (TOU) rates of demand response programs have been modeled and consequently its influence on load profile and procurement strategy has been discussed. The proposed method does not minimize the procurement cost, but allows deriving robust decision with respect to price volatility. The robustness of procurement strategies for high procurement costs is optimized and related procurement strategy is proposed. The proposed method either deals with optimizing the opportunities to take advantage from low procurement costs or low pool prices. Finally, a case study is studied to show the advantages of proposed method.
A hybrid technique for solving the congestion management problem in an electricity market based on harmony search algorithm (HAS) and Fuzzy mechanism is presented in this article. This algorithm does not require initial value setting for the variables and does not require differential gradients, thus it can consider discontinuous functions as well as continuous functions. The HAS is a recently developed powerful evolutionary algorithm, inspired by the improvisation process of musicians, for solving single/multiobjective optimization problems. In the proposed technique, each musician plays a note for finding a best harmony all together. Transmission pricing and congestion management are the key elements of a competitive electricity market based on direct access. They also focus of much of the debate concerning alternative approaches to the market design and the implementation of a common carrier electricity system. This article focuses on the tradeoffs between simplicity and economic efficiency in meeting the objectives of a transmission pricing and congestion management scheme. The effectiveness of the proposed technique is applied on 30 and 118 bus IEEE standard power system in comparison with CPSO, PSO-TVAC, and PSO-TVIW. The numerical results demonstrate that the proposed technique is better and superior than other compared methods. © 2015 Wiley Periodicals, Inc. Complexity, 2015
This paper evaluates the real-time price-based demand response (DR) management for residential appliances via stochastic optimization and robust optimization approaches. The proposed real-time price-based DR management application can be imbedded into smart meters and automatically executed on-line for determining the optimal operation of residential appliances within 5-minute time slots while considering uncertainties in real-time electricity prices. Operation tasks of residential appliances are categorized into deferrable/non-deferrable and interruptible/non-interruptible ones based on appliances' DR preferences as well as their distinct spatial and temporal operation characteristics. The stochastic optimization adopts the scenario-based approach via Monte Carlo (MC) simulation for minimizing the expected electricity payment for the entire day, while controlling the financial risks associated with real-time electricity price uncertainties via the expected downside risks formulation. Price uncertainty intervals are considered in the robust optimization for minimizing the worst-case electricity payment while flexibly adjusting the solution robustness. Both approaches are formulated as mixed-integer linear programming (MILP) problems and solved by state-of-the-art MILP solvers. The numerical results show attributes of the two approaches for solving the real-time optimal DR management problem for residential appliances.
This paper considers a profit-maximizing thermal unit producer that participates in a day-ahead market. The producer behaves as a price-taker in the day-ahead electricity market. This paper provides the information gap decision theory for determining the optimal bidding strategies for the day-ahead market. While making bidding strategy, factors such as characteristics of the generator and market price uncertainty need to be considered as they have direct impact on the expected profit and bidding curve. In this paper, a method of building an optimal bidding strategy is presented under market price uncertainty using information gap decision theory (IGDT). Information gap decision theory is a non-probabilistic decision theory that seeks to optimize robustness to failure – or opportunity to windfall – under severe uncertainty. It is shown that risk-aversion and risk-taker may influence the expected profit and bidding curve of a producer. The proposed method is illustrated through a realistic case study.
This paper provides a technique to derive the bidding strategy in the day-ahead market for a large consumer that procures its electricity demand in both day-ahead market and a subsequent adjustment market. It is considered that hourly market prices are normally distributed and this correlation is modeled by variance–covariance matrix. The uncertainty of procurement cost is modeled using concepts derived from information gap decision theory which allows deriving robust bidding strategies with respect to price volatility. First Order Reliability Method is applied to construct the robust bidding curve. The proposed technique is illustrated through a realistic case study.
In the competitive electricity market, consumers seek strategies to meet their electricity needs at minimum cost and risk. This paper provides a technique based on Information Gap Decision Theory (IGDT) to assess different procurement strategies for large consumers. Supply sources include bilateral contracts, a limited self-generating facility, and the pool. It is considered that the pool price is uncertain and its volatility around the estimated value is modeled using an IGDT model. The proposed method does not minimize the procurement cost but assesses the risk aversion or risk-taking nature of some procurement strategies with regard to the minimum cost. Using this method, the robustness of experiencing costs higher than the expected one is optimized and the related strategy is determined. The proposed method deals with optimizing the opportunities to take advantage of low procurement costs or low pool prices. A case study is used to illustrate the proposed technique.