Risk constrained self-scheduling of hydro/wind units for short term electricity markets considering intermittency and uncertainty
Introduction
Emergence of electric utility deregulation issues, recent liberalization of the electricity markets in several countries and striking growth of wind power application has increased the need for risk measurement and management tools. Risk in economic theory is defined as an option where the profit is not known because of different uncertain parameters, such as market price and generating units' uncertainties, but for which an array of alternative outcomes and associated probabilities are known [1]. The price uncertainty is one key factor which can change the value of energy trades in different market conditions. A firm's portfolio risk is discussed by evaluating the risk venture from changes in any of the variables that affect existing contracts or the firm's projections from demand, supply and prices [2]. Value at-Risk (VaR) is a well-known measure which is applied in many risk-management studies, especially the electricity market activities with varying objectives, including [3]: (i) avoiding great profit losses due to the price fluctuations or energy consumption uncertainty which their risks are not accurately reported or have not been properly controlled; (ii) proper modeling and risk quantification for intermittency of traditional generating units as well as the uncertainty of renewable energy resources, e.g. wind power, solar energy, and biomass; and (iii) identifying optimal hedging strategies or assessing hybrid hedging opportunities in order to control the financial risks of GENCOs as cost effectively as possible. With the use of VaR method, a market operator and participants can then determine the best use of the physical and financial capital costs in order to maximize their earnings [4] or perform comprehensive risk management in view of both the portfolio and operational risk [5].
An integrated risk management cost is proposed in [6] for simultaneous analysis on both uncertainties of spot prices and production. This work presents an efficient market model which allows power producers to identify a benchmark value for a forward contract. This value is equal to the sum of the expected production marginal cost and the spread option embedded in the spot selling. Another risk management model is introduced and carried out in [7] to provide the proper trade-off between the maximum profit and the minimum risk of electricity price and the technical features of hydrothermal units for GENCOs in for day-ahead competitive market. Ref. [8] has proposed a stochastic mid-term risk-constrained hydrothermal scheduling algorithm to maximize the profit of GENCO. In this work, the profit shortfall of each scenario is defined as the risk of scenario. In [9] the financial risk is considered in the stochastic Price-Based Unit Commitment (PBUC) problem.
Under deregulation, there are many uncertainties in the power system related to, e.g., electrical demand and price variations and generator and branch outages. In [10], [11], a Unit Commitment (UC) problem is implemented for the stochastic security-constrained electricity market clearing problem to determine reserve services considering the expected load not served. Ref. [12] considers two modeling approaches for the reduction of computational effort of the stochastic UC. In these studies, the generation outages considered as a load increments. A multi-stage stochastic program has been proposed in [13] for self-scheduling of a thermal unit considering the price uncertainty.
It is noted that the intermittency of traditional generation unit and uncertainty of renewable resources as well as demand side uncertainty have been investigated apart from the market price risk in several surveys. For instance, in [14] the stochastic SCUC and Monte Carlo simulation method has been used for contingencies of generation units and transmission lines and load forecasting inaccuracies. Also, [15] has considered the effects of the stochastic wind speed and load on the UC and economic dispatch of power systems with high levels of wind power. Results of this stochastic optimization problem show less costly and better scheduling of resources than the deterministic optimization.
This paper addresses a risk constrained market model for the hybrid wind-hydro power scheduling (WHPS) problem by a GENCO. This risk constrained short-term operation model is applied by GENCO to determine the commitment status and power generation of each hydro unit and achieve optimal trade-off between the maximum profit and risks of the price as well as wind power behavior uncertainties. The proposed model is formulated as a stochastic optimization problem wherein the expected profit is maximized using the mixed integer programming (MIP) technique. The price uncertainty is modeled based on the price forecast error using the roulette wheel mechanism to generate price of energy and spinning and non-spinning reserves for each hour of the scheduling period. The contributions of this paper with respect to the previous works in the area can be briefly summarized as follows:
- (i)
Risk of generating units' intermittency as well as the price and wind power generation uncertainties is modeled in the stochastic optimization framework.
- (ii)
New multi-risk index is presented to quantify maximum expected downside risk of the electricity market and system uncertainties.
The remainder of this paper is organized as follows: Section 2 describes the stochastic formulation of hybrid wind-hydro scheduling. The ARIMA method for modeling of wind power generation uncertainty is explained in Section 3. Section 4 introduces the concept of VaR in risk measurement and presents the proposed risk management model for WHPS problem. Section 5 addresses the case studies, simulation assumptions and provides results with detailed discussions. In Section 6, some relevant conclusions are addressed.
Section snippets
MIP formulation of WHPS
In the following subsections, the optimization problem of WHPS is introduced in the form of MIP formulation.
Uncertainties characterization
In order to have a profitable participation in the electricity markets, the GENCOs are inevitably supposed to consider different types of uncertainty sources in their self-scheduling. The sources of uncertainty for short term WHPS problem are generating units' contingency, specially wind power generation, and price variations. To solve the stochastic WHPS problem, a two-stage solution method is proposed in this paper. In the first stage the multiperiod scenarios are generated. In this stage,
Risk model for HWPS integration
Considering uncertain parameters of restructured power systems and their competitive market such as traditional generation units intermittencies, uncertainty of renewable DG, uncertain market price and demand side uncertainty, electricity market participants especially GENCOs are encountered with different risks. Hence, GENCOs need to reformulate the portfolio formulations as the risk-constrained optimization problem in order to trade-off between the maximum profit and minimum risk of the
Numerical results
The risk constrained HWPS model developed in Section 3 is applied to a GENCO considering both hydro and wind energy application during day-ahead energy trading market. To model hydro units, eight hydro units are considered. The required data of hydro units are taken from [18]. In addition to hydro units, two wind farms are assumed which are supervised financially under GENCO operating scheme. Random behavior of wind power generation is modeled by ARIMA(0,1,1) time series model as described in
Conclusions
This paper considered a practical methodology of risk measurement and management model for hybrid wind/hydro generation scheduling that allows GENCO to manage the risk of wind generation and market price uncertainties in the day-ahead energy/reserve market. The proposed risk constrained market model is based on the optimization procedure for the maximization of the expected profits in the presence of risk constraints considering novel weighted risk coefficients as maximum expected downside
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