Elsevier

Renewable Energy

Volume 86, February 2016, Pages 216-227
Renewable Energy

Impact of spatio-temporal correlation of wind production on clearing outcomes of a competitive pool market

https://doi.org/10.1016/j.renene.2015.07.104Get rights and content

Highlights

  • Spatio-temporal correlation of wind production affects market clearing outcomes.

  • Analysis of real-world wind data validates such a correlation among wind farms.

  • Dramatic change in slope of aggregate supply curve reinforces impact of the correlation.

  • Inter-temporal constraints of units increase price variability and its expected level.

  • Main concern on impact of inter-temporal constraints is in base- and average-load profiles.

Abstract

By the increase of wind power penetration in electricity markets, a relevant issue is how correlated power production of diverse wind farms may change market clearing outcomes. This paper uses real-world historical wind data to capture spatio-temporal correlation among diverse wind farms. In a simulation framework, we evaluate statistically impact of correlated wind production on clearing outcomes of a competitive pool market, while incorporating inter-temporal constraints of dispatchable generating units to market clearing model. This allows to address how such constraints and associated costs may change the impact of correlated wind production. The market clearing outcomes are statistically evaluated for different levels of spatio-temporal correlation of wind production in the cases with and without inter-temporal constraints. This numerical evaluation is run for different load profiles to examine how technological diversification of dispatchable generating units may change the impact of correlated wind production. An illustrative example and a case study show results and conclusions.

Introduction

By the increase of wind power penetration in electricity markets, a relevant issue is how correlated power production of diverse wind farms may change market clearing outcomes.

The interdependence structure of wind power production, in both time and space, is dynamic and complex [1]. The wind power production may temporally depend on time series of historical wind data. Moreover, the power productions of close wind farms may be spatially correlated. An important observation is that such a spatio-temporal correlation can affect the pattern of wind power production, and resulting consequences within electricity market.

As the pool market is an attractive choice for the wind producers, the market clearing outcomes are substantially coupled with dynamically changing wind production. In this condition, commitment status of some dispatchable generating units may change dynamically over time to accommodate the time-variant wind power production. In this respect, the working of the generating units is different due to technological diversification. The operational capability and flexibility of such units for handling the wind variability are mainly characterized by their inter-temporal constraints (ITCs) and associated costs. Within this context, a key issue is how the ITCs of generating units may change the impact of wind power production on the market clearing outcomes.

This paper aims to analyze the impact of correlated wind power production as well as the ITCs of dispatchable generating units on the clearing outcomes of a competitive pool-based day-ahead electricity market. To this end, the market clearing problem is mathematically modeled as Mixed-Integer Linear Programming (MILP) problem. This model accounts the ITCs and associated costs of dispatchable generating units. In addition, a statistical methodology is used to generate correlated scenarios of the wind power production considering the spatio-temporal correlation among diverse wind farms. The market clearing problem is solved for each correlated scenario. Finally, the clearing outcomes such as energy prices and operational behavior of dispatchable generating units are statistically evaluated.

As the wind power penetration is rapidly increasing in electricity industry, a variety of empirical studies have investigated different impacts of the wind power production on the outcomes of electricity markets. The interaction between wind energy sources and energy prices is analyzed in Dutch [2], Ontario [3], German–Austrian [4], and Texas [5]. In Ref. [6], robust econometric models and a statistical inference are used to assess benefits obtained from the wind power production in PJM day-ahead market. In Ref. [7], potential impact of the wind power production on the reduction of market prices and energy produced from gas and coal power plants in Australian national electricity market is examined. In Ref. [8], flexibility of dispatchable generating units to respond the variation of wind power production and load in German electricity market is assessed for a long-term horizon. In Ref. [9], performance of renewable electricity support schemes in Spanish electricity market is evaluated. In Ref. [10], technical challenges of large-scale wind integration in European electricity industry are reviewed. Furthermore, the efficiency of several possible options (e.g., increasing the spatial distribution of wind energy sources, deploying additional power reserve and expanding the power grid) to accommodate the wind power production is investigated.

While the empirical studies above can reveal ex-post impacts of the wind power production, simulation tools are required to carry out ex-ante analysis of the market outcomes before actual realization. Compared to the existing empirical reports, the simulation studies have rarely focused on this topic. To clarify the background of challenges and findings addressed in this paper, the technical literature of simulation studies can be categorized based on whether the correlation of wind power production is considered or not.

One category studies the market impacts of wind power production without considering such correlation [11], [12], [13]. It is worthy to note that the main contribution of these references lies on the modeling of energy markets with wind power integration, however the wind power uncertainty is simply modeled. In Ref. [11], the behavior of UK electricity market is simulated in target year 2020. Energy prices and revenues are analyzed with respect to penetration level and variability of the wind production. In Ref. [12], a pricing scheme is proposed for a pool market that includes a significant number of wind producers. Moreover, the potential benefits that can be obtained from it are numerically analyzed. In Ref. [13], the equilibrium of an oligopolistic pool market in presence of large-scale wind integration is modeled as equilibrium problem with equilibrium constraints. The simulation results reveal that wind spillage and profit gained by dispatchable units may increase in higher levels of wind penetration.

Another category models correlated wind power production based on 1) temporal correlation structure [14], [15], [16], [17], [18], [19], [20], 2) spatial correlation structure [21], [22], [23], [24], [25], and 3) spatio-temporal correlation structure [26], [27]. In this vein, we find that the technical reports address the market impact of correlated wind production from two prevailing perspectives. One view focuses on modeling wind correlation in wind power forecast and assessing the market impacts of forecast accuracy. Another one focuses on developing probabilistic models which allow to characterize inherent variability of correlated wind power production, and to quantify statistically its resulting consequences within the electricity market.

Temporal correlation studies: In Ref. [14], performance of persistent and Grey predictors for short-term forecast of the wind power production is compared, and impact of the wind power volatility and the forecast accuracy on market prices is evaluated. The results demonstrate that improvement of the wind forecast accuracy does not necessarily result in more accurate market prices. In Ref. [15], an agent-based modeling approach is adopted to simulate day-ahead electricity market. Within this computational laboratory, impact of short-term wind forecast accuracy as well as wind penetration level on market prices and net revenues of the wind producers is assessed. The results show that the application of more accurate wind forecast method is effectively beneficial to increase the net revenues of the wind producers. In Ref. [16], Northern European day-ahead and regulating power markets are modeled to evaluate the impact of large-scale wind power production on system imbalance, while the wind power production is forecasted by using high resolution numerical weather prediction models. In Ref. [17], a probabilistic model is developed to analyze long-term effects of the wind power production on market prices and revenues of the wind producers. In this simulation, a combination of time series models and Weibull distribution is used to model variability of the wind power production. The simulation concludes that the variability of energy prices can be decreased by the increase of geographical dispersion of wind farms. In Ref. [18], the performance of different alternative schemes of system cost minimization within day-ahead energy market is studied. In this reference, the wind variability is modeled using autoregressive moving average (ARMA) models. In Ref. [19], time series models are used to examine medium- and long-term effects of large-scale wind penetration on market prices, reliability of supply and revenues of dispatchable generating units. The findings show that the increase of wind penetration level can reduce the market prices, and promote the reliability of supply in medium-term, while in long-term horizon such effects may not be necessarily realized. In Ref. [20], an out-of-sample chronological simulation is run to compare two families of offering strategies (i.e., deterministic and stochastic programming methods) for a wind producer in a pool market. In this study, ARMA models are fitted to real-world wind data and used to prepare single-point forecast and temporally correlated scenarios of the wind production for both deterministic and stochastic programming methods, respectively.

Spatial correlation studies: In Ref. [21], a simulation framework is developed to evaluate impact of wind penetration level and spatial correlation among wind farms on locational marginal prices in a fully competitive pool market. The results show that the spatial correlation has a small/significant effect on expectation (EXP)/standard deviation (STD) of the locational marginal prices. In Ref. [22], an extended point-estimate method is proposed for probabilistic power flow with dependent input variables such as wind power productions and loads. The simulation results validate the proposed method is computationally efficient compared to Monte Carlo method, while providing negligible small relative errors. The numerical results show the impact of spatial correlation among wind farms on the variability of power flow outcomes, e.g., bus voltages and active powers. In Ref. [23], an improved dispatch model for the electricity market with large-scale wind penetration is proposed, and compared with two alternative schemes of conventional and stochastic dispatch models. The comparative analysis for different levels of wind power penetration as well as spatial correlation among wind farms clarifies that the proposed model is much more efficient than the conventional one. In Ref. [24], the wind power production of diverse wind farms is modeled through a joint Normal distribution and impact of the wind variability on market prices is evaluated. In Ref. [25], a statistical cognitive model is proposed to simulate oligopolistic pool market in presence of the wind power production. The results indicate that the market power exercised by diverse power producers may significantly reinforce potential impact of the wind penetration level as well as the spatial correlation on market clearing outcomes.

Spatio-temporal correlation studies: In Ref. [26], the wind power production obtained from a spatio-temporal forecast method is used as input data for unit-commitment model, and the value of accurate forecast is assessed in Dutch power system. The results indicate that if large enough capacity of combined heat and power plant is installed, the limited predictability of the wind power production has not significant influence on the operating cost savings. Note that in this study, the case of minimum load profile is identified to be problematic. In Ref. [27], the accuracy of spatio-temporal wind power forecast is compared with temporal-only wind forecast models (e.g., autoregressive and persistent forecast models). In addition, an advanced robust look-ahead dispatch framework is used to exploit economic benefits of the spatio-temporal forecast. Compared to the temporal-only forecast methods, the wind forecast accuracy and the system operation cost can be increased and reduced, respectively, by the application of the spatio-temporal forecast method. Note that these two references study the market impact of spatio-temporal correlation by focusing on the wind power forecast accuracy.

In the above simulation studies, a problematic issue is the lack of a probabilistic model that is capable of simulating the market clearing outcomes statistically, considering spatio-temporal correlation of the wind production and the ITCs of dispatchable generating units.

This paper follows up on the branch of spatio-temporal correlation studies, while coupling the market clearing outcomes with the ITCs of dispatchable generating units in a short-term horizon. Within this context, the contributions of this paper are threefold:

  • 1.

    To develop a simulation framework which allows to statistically analyze impact of the spatio-temporal correlation of wind production and the ITCs of dispatchable generating units on the clearing outcomes of competitive pool market.

  • 2.

    To evaluate how the technological diversification of the generating units may change the impact of wind power production in different load profiles.

  • 3.

    To simulate a realistic case study in which the spatio-temporal correlation among wind farms is modeled based on real-world historical wind data.

In Section 2, the clearing problem of a day-ahead electricity market is mathematically modeled. Moreover, the methodology used to generate the correlated scenarios of wind speed is explained and implemented based on real-world data. In Section 3, the simulation for an illustrative example and a case study is run, and the results are presented. In Section 4, relevant policy implications and critical issues are explained and discussed. In Section 5, conclusions are drawn.

Section snippets

Market clearing model

With the aim of analyzing the impact of wind production and ITCs, the clearing model of a day-ahead electricity market is formulated as a MILP below [28]:Minimizeh=1NH[i(vsuci(h)+vsdci(h)+jpijG(h)fijG(h))+kpkW(h)fkW(h)]subject toiΩbGpiG(h)+kΩbWpkW(h)(b,m)ΩLpbmL(h)+(n,b)ΩLpnbL(h)=pbD(h),bΩB,hpnmL(h)=bnm(δn(h)δm(h)),(n,m)ΩL,hpnmL,maxpnmL(h)pnmL,max,(n,m)ΩL,h0pijG(h)pijG,max(h),i,j,hpiG(h)=jpijG(h),i,hui(h)piG,min(h)piG(h)piG,max(h)ui(h),i,h(ui(h)ui(h1))sucivsu

Illustrative example

In this subsection, we study the impact of correlated wind power production on the market outcomes in a 5-bus power system as an illustrative example.

Discussion

This section is intended to address policy implications drawn from the results and critical issues for future researches.

Conclusions

The numerical framework in this paper allows to evaluate the short-term impact of spatio-temporal correlation among diverse wind farms considering inter-temporal constraints of dispatchable generating units. The main conclusions obtained from the comprehensive analysis of the results are as follows:

  • 1.

    Analysis of real-world historical wind data validates the spatio-temporal correlation among wind farms. We observe that the cross-correlation among close wind farms may be significant.

  • 2.

    The increase of

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