Risk-based profit allocation to DERs integrated with a virtual power plant using cooperative Game theory

https://doi.org/10.1016/j.epsr.2014.11.025Get rights and content

Highlights

  • VPP trading under uncertainty in the day-ahead and balancing markets is evaluated.

  • Risk-aversion decreases/increases the expected total/surplus profit of VPP.

  • Integration into a VPP acts as a risk-hedging mechanism for DERs.

  • The role of each DER in covering the risks makes its share in the surplus profit.

Abstract

Distributed energy resources (DERs) play a key role in the deregulated power systems with environmental concerns. Their scales and the uncertainty pertaining to intermittent generation of renewable resources are the major challenges of participating in wholesale electricity markets. The concept of virtual power plant (VPP) makes their integration possible and also allows covering the risk due to uncertainties. It yields a surplus profit in comparison to profits made by uncoordinated DERs. In this paper, using a novel stochastic programming approach, the participation of a VPP in the day-ahead market (DAM) and the balancing (real-time) market (BM) is considered. The uncertainties involved in the electricity price, generation of renewables, consumption of loads, and the losses allocation are taken into account. The desired risk-aversion level of each independent DER owner is used to compute the conditional value-at-risk (CVaR) as a well-known risk measure. The role of each DER in covering the risk and making the total profit is evaluated. The Nucleolus and the Shapley value methods as the cooperative Game theory approaches are implemented to allocate VPP's profit to the DERs. The results of a numerical study are presented and concluded.

Introduction

Nowadays, distributed energy resources (DERs) including dispersed generation (DG), storage facilities (SFs), and demand response (DR) resources have a significant influence on the economic development of power systems. Although DGs and small- or medium-scale SFs seem highly successful in stimulating small investments, they face strong challenges of economic activities. Owners of these DERs will be limited to electricity price setting mechanisms considered by the distribution system operators (DSOs). Nodal pricing [1], locational marginal price (LMP) calculation [2], and contract pricing [3] are some of these mechanisms. On the other hand, small- or medium-scale consumers which are able to flexibly control their own loads are limited to DR programs offered by DSOs, and hence they are not at the advantage of competitive environment of wholesale electricity markets. Some of these programs are evaluated in [4], [5], [6], [7].

The concept of virtual power plant (VPP) is a practical way of eliminating aforementioned limitations. According to this concept, dispersed generation and consumption units can integrate into a single market agent to be large enough for participating in wholesale markets. So they can trade at the wholesale price similar to large-scale producers and consumers. Centralized and distributed dispatches of VPPs are analyzed in [8], [9]. In this paper, VPP is assumed to be centrally controlled. As smart grid infrastructure develops, the VPP concept becomes more practical, even for small DERs. Refs. [10], [11] compare the concepts of VPP and micro-grid. It is important to emphasize that, in comparison to micro-grids, VPPs concept is much broader. This is so because it is not limited to geographical location of DERs and the ownership of the grid.

However, participation in competitive markets poses the risk of profit variability. For instance, there is no subsidy or fixed tariff in competitive markets. DERs must compensate energy deviations in respect of their scheduled generations or consumptions in the day-ahead market (DAM). Ref. [12] presents the procedure of including risk measures such as the shortfall probability, the expected shortage, the value-at-risk (VaR), and the conditional value-at-risk (CVaR) in the formulation of the stochastic programming.

In some cases, an imbalance penalty must be paid [13], [14], [15], and in a wider context, energy deviations shall be traded in competitive markets, namely the balancing (real-time) market (BM). Trading in the BM at a single price is the common practice in the US [16]. In European electricity markets, there is a dual pricing system for the BM [17], i.e. the positive deviation (the generation surplus or consumption deficit) shall be sold to the BM+ and the negative deviation (the generation deficit or consumption surplus) shall be bought from the BM− [18], [19], [20]. The dual pricing system is considered in this paper.

The general mechanism for imbalance prices is described in [12], [20]. It is shown that, in competitive environments, the DAM price is hourly equal to or higher than the BM+ price, and equal to or lower than the BM−. The owners of the non-dispatchable sources must cope with the generation intermittency. Decision-making of large-scale wind power plants (WPPs) under uncertainty are presented in [20], [21]. These studies show that, as the risk aversion of non-dispatchable producers (NDPs) increases, the sale in the DAM decreases and in the BM increases at the expense of reducing the expected profit.

A joint configuration of a WPP and a pumped-hydro-storage plant (PHSP) is modeled in [13], [14], [15], [18], [19], and compared with an uncoordinated operation. These studies show that the joint operation results in a profit higher than the summation of profits uncoordinatedly obtained. In this paper, we call this added value “surplus profit”.

The price volatility in competitive electricity markets is the source of uncertainty from viewpoint of dispatchable units (DUs), such as conventional power plants (CPPs), SFs, and dispatchable loads (DLs). Decision-making of large producers under uncertainty is discussed in [22], [23], and energy procurement problem for large consumers is addressed in [24], [25]. These researches show that the energy trades through bilateral contracts and the futures market (FM) grow as the risk aversion becomes more significant. It often leads to a reduction in the expected profit of producers and the expected cost of consumers.

It has been shown that non-dispatchable renewable energy resources such as a photovoltaic power plant (PVP) can be combined with a DP (e.g. a quick response CPP), or with a SF (e.g. a battery energy storage system (BSS) or a PHSP) to lower the risk of intermittent generation. Since VPP may have both generation and demand units (DERs), it may offer (to sell) or bid (to purchase) corresponding to the desired amount of power totally injected to the grid in a time period. Optimal offering problem of a VPP for participating in the DAM and the BM is presented in [26], [27], [28]. Optimal mid-term dispatch problem of a VPP is addressed in [29]. For taking uncertainties into account, Refs. [26], [29] use stochastic mixed-integer programming (MIP) approach, and Refs. [27], [28] use point-estimate method. Ref. [30] presents optimal bidding strategy of a VPP for participating in a joint market of energy and spinning reserve service. It takes no uncertainty into consideration and solves the proposed non-linear model via a genetic algorithm.

Refs. [27], [30] assume that VPP operates the distribution system, and so loss management is included in the proposed models. It is important to point out that, in general, VPPs are not equivalent to micro-grids, and so they have no control on all of DERs existing on the grid. Also they do not act as a DSO which is responsible for allocating electrical losses in deregulated distribution systems.

Non-cooperative and cooperative Game theories are widely used in power industry, e.g. for network cost allocation [31], [32], performance evaluation of thermal power plants [33], allocation of unit start-up costs [34], estimating the pricing of transmission [35], [36], LMP calculation [2], reactive control [37], making bid strategies [38], loss allocation [39], and profit allocation of independent power plants (IPPs) [40]. Since DERs integrated into a VPP play a cooperative Game in competitive electricity markets to earn the maximum economic profit, the procedure for using cooperative Game theory is presented in this paper to impartially share VPP's profit between the DERs. For this reason, the Nucleolus-based and the Shapley value-based methods which are two common ways to solve the problem of cooperative Games are implemented.

Since the owners of the DERs can be independent, a method based on the desired risk-aversion of each DER owner is proposed in this paper to determine the total risk-aversion degree of a VPP. Using stochastic programming approach, short-term market operations of a VPP under uncertainty are presented in detail.

To assess the impact of each DER on making the surplus profit, all possible states of DER combinations are taken into account via the concepts of the Nucleolus and the Shapley value. This study indicates that all of the possible coalitions of the following categories of the DERs can always yield a surplus profit:

  • NDUs (non-dispatchable units) including NDPs (e.g. WPP, PVP) and NDLs (non-dispatchable loads).

  • DUs including DPs (e.g. CPP), SFs (e.g. PHSP, BSS), and DLs (e.g. flexible DR).

Note that NDLs are considered similar to other NDUs in this paper. Also, for the reason explained in Section 1.3, allocated losses are considered in the profit allocation problem in a way similar to other uncertain parameters.

The rest of this paper is organized as follows. Section 2 provides a general view of the scope of this study. Market operations of a VPP are analyzed in detail in Section 3. Section 4 introduces the profit allocation mechanisms. An illustrative numerical study is presented in Section 5. Lastly, Section 6 concludes the paper.

Section snippets

Uncertainties

A typical VPP consisting of several DERs participates in wholesale electricity markets to turn the maximum profit. If the energy consumed by VPP is in the majority, the profit will be negative. In this case, the problem will be equivalent to the cost minimization. Whereas the DAM is cleared the day before in which the power delivery takes place, VPP needs to optimize offering/bidding curves, and so it needs to forecast all uncertain parameters. In this paper, the following uncertainties are

Optimal offering/bidding

The virtual offering curves pertaining to each combination of available DERs can be obtained by the following two-stage stochastic programming which is run by VPP.

The basis of cooperative Games

To recognize the role of each DER in covering the risks and earning the total profit, cooperative Game approach can be used. The Nucleolus-based and the Shapley value-based methods are implemented in this paper. All of the possible combinations of DERs are taken into consideration to form the basis of these methods. For this reason, virtual profits pertaining to all of the combinations of DERs should be obtained. Using state 1 and 0 to respectively represent the presence and absence of each DER

Description

For a comprehensive numerical study, all types of DERs described in Section 1.4 shall be taken into consideration. For this reason, DERs located in IEEE 30-bus test grid [46] are assumed as depicted in Fig. 2. The integrated units into a VPP are delineated. It is assumed that VPP exchanges the energy with upstream network via bus 2 in order to participate in wholesale markets. The rated capacities of the DERs are indicated in Fig. 2. The turbine and pump capacities of PHSP are 16 and 12 MW. The

Conclusions

After clearing markets by the MO and allocating losses by the independent DSO, the profit turned by a VPP should be allocated to the DERs. Since the risk-aversion level has a significant impact on this profit, the time horizon of the profit allocation problem begins with building the offering curves. For this reason, the optimal offering model of VPP under uncertainty should be run to obtain the scheduled powers, and then the optimal real-time dispatching model should be used to calculate

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