Optimal portfolio design of energy storage devices with financial and physical right market

Abstract

With the continuous development of the spot market, in the multi-stage power market environment with the day-ahead market and right market, the study associated with the portfolio of energy storage devices requires that attention should be paid to transmission congestion and power congestion. To maximize the profit of energy storage and avoid the imbalance of power supply and consumption and the risk of node price fluctuation caused by transmission congestion, this paper presents a portfolio strategy of energy storage devices with financial/physical contracts. First, the concepts of financial/physical transmission rights and financial/physical storage rights are proposed. Then, the portfolio models of financial contract and physical contract are established with the conditional value-at-risk to measure the risks. Finally, the portfolio models are verified through the test data of the Pennsylvania-New Jersey-Maryland (PJM) electric power spot market, and the comparison between the risk aversion of portfolios based on financial/physical contract with the portfolio of the market without rights. The simulation results show that the portfolio models proposed in this paper can effectively avoid the risk of market price fluctuations.

Graphical abstract

Keywords

portfolio / node price fluctuation / transmission right / energy storage right / risk aversion

1 Introduction

The electricity market can be described as an application of the cyber-physical-social system in energy (CPSSE), which emphasizes the interaction among the collection of market transaction information, the deployment of physical energy devices, and the gaming behaviors of various kinds of participants [1–5]. In recent years, storage owners are incentivized to participate in the electricity spot market for the sake of its profitability and flexibility [6,7].

In the spot market transaction, the information system and human participation have a remarkable impact on the coordination of the energy system and the maximization of social welfare [8]. Spot market can provide storage owners with the short-term value of energy storage derived from its ability to arbitrage energy across the area and forward in time, facilitating the reshaping of nodal supply and demand profiles over longer periods. The nodal supply and demand profiles, exhibited as locational marginal pricing (LMP) in spot market transactions, provide the opportunity for storage owners to predetermine portfolio strategies of storage arbitrage [9].

In the spot market, arbitrage is based on LMP differences over time: electricity is bought and stored as the LMP is lower, and is sold as the LMP rises. However, the challenge resides in the physical attributes of electricity transmission and constraints of the electricity system that may induce congestion in the spatial electricity transaction [10]. On the premise of omitting network loss, LMP will vary among locations or nodes in the system when the transmission network is congested [11]. Moreover, the increasing integration of various renewable energy sources may lead to temporary imbalances between the generation and consumption of electricity, intensifying the fluctuation of LMP among different nodes [12–15]. As the varied LMPs between different nodes represent extra congestion charges, the storage owner at low-priced generators should remunerate independent system operator (ISO) while supplying power to customers at high-priced locations. That leads to lost revenue for storage owners and eventually sizeable under-utilization relative to the social optimum [16,17]. Surely the conventional regulation on generation plants and transmission facilities would alleviate power congestion and avert the risk of LMP fluctuation, but such an approach entails a monopolistic energy operation system that contrasts to the original aim of the spot market [18–20]. Therefore, the reasonable congestion management mechanism is more important to hedge electricity price fluctuation in the spot market.

Numerous studies have been conducted to identify alternative mechanisms to support efficient congestion management and assuage the LMP fluctuation. To hedge inter-temporal price risk in the spot market, these studies are mainly focused on the collection of tradable market instruments capable of monetizing property rights to transmission and storage capacity. Financial transmission right (FTR) has become an important risk-hedging instrument of LMP-based electricity markets because of the role it plays in supporting the remuneration of merchant transmission investments to provide market participants with an effective hedge against transmission congestion costs for the long-term spatial energy transactions [21]. In Ref. [22], financial storage right (FSR) is proposed as a natural complement to FTR due to its ability to provide market participants with an effective hedge against storage congestion costs for the imbalance between generation and consumption. Physical transmission right (PTR) is deemed as a physical analog to FTR, which allows its holder to use congested transmission interface exclusively without additional congestion charges [23,24]. Similarly, physical storage right (PSR) also plays the same role of financial rights in hedging price variations in spot market [25].

In Fig. 1, both financial and physical rights can be auctioned in sequential auctions coordinated by the ISO, enabling the framework of the right market where storage owners can purchase property rights for their energy storage. Storage owners can simultaneously participate in the spot and right markets to maximize profits and mitigate inter-temporal price risks. Toward this end, the role of the right market can be added into the social field of the CPSSE model.

Hence, a portfolio strategy with financial and physical rights is of vital importance to the rational interests of storage owners and socially optimal operation of energy storage in the spot market. In the CPSSE system, the in-depth incorporation of human behavior is represented by the portfolio strategy with financial and physical rights. Few studies have investigated the extent to which the portfolio strategy with financial and physical rights might improve social welfare. This paper studies the impact of portfolio strategy with financial and physical rights on the wholesale electricity system respectively. It proposes the optimal portfolio model of financial and physical rights to balance revenue and risk.

This paper is contributive because it proposes an energy storage installation portfolio strategy taking into account the differences between financial and physical contracts, as the theoretical foundation of model establishment. In addition, the proposed portfolio strategy model encompassing financial and physical rights for calculating the benefits from the arbitrage of energy storage contributes to the risk avoidance of nodal price fluctuations caused by transmission congestion and power generation/consumption imbalance. Moreover, the separation of transmission rights and storage rights into financial contracts and physical contracts are considered in the proposed portfolio strategy, which balances profit and risk.

2 Financial/physical right contract

The power right market is divided into financial and physical right markets. The financial right market includes FTR and FSR, while the physical right market includes PTR and PSR. These rights are, in effect, an option contract that guarantees the right of contract holders to sell electricity in a given area. The physical contract is considered as a relatively ideal model based on the contract path or contract energy storage. In the case of using physical contracts, it is usually assumed that there exist few congestion paths or nodes, which greatly reduces the settlement calculation and ensures a strong market liquidity [26]. Thus, physical contracts are usually applied to decentralized markets based on bilateral trade. Although the decentralized market is mainly medium- and long-term markets and the spot market accounts for a small proportion, the congestion problem often occurs in the spot market [27]. Therefore, physical contracts are only considered in the spot market in this paper. The spot market is classified into centralized spot markets and decentralized spot markets [28]. Since there exist few congestion paths or nodes in the spot transactions of decentralized markets, the physical contract has a strong applicability. The financial contract will be registered between the adjacent nodes or the same node at different times, which are independent of transmission paths and common storage locations. As a option contract, the financial contract determines the congestion price through the difference of LMP [29]. Therefore, the financial contract can be applied to the centralized markets established by the pooling and pricing on the base of the node. The centralized spot market accounts for a large proportion, thus there exist many congestion paths or nodes, in which the financial contracts have a strong applicability.

2.1 Financial right contracts

2.1.1 FTR

In 1992, Hogan et al. proposed the concept of transmission rights to allocate congestion costs, which is the initial form of FTR [30]. FTR is the contract between the market participants and ISO. FTR gives the right for holders to obtain economic compensation in the case of transmission congestion to ensure the long-term stability of LMP.

FTR is regarded as the method of allocating the congestion earnings cost, whose holders can avoid the uncertain risk of transaction cost generated from the difference of LMP caused by transmission congestion. In power systems, market participants usually pay congestion charges based on the LMP of nodes. As the network loss is ignored, if the transmission network is congested, the congestion cost is expressed as

(1)c_C=P_{\mathrm{T}}(l_{\mathrm{T},j}-l_{\mathrm{T},i}),

where c_C is the congestion cost, P_{\mathrm{T}} is the electrical trading volume through the congestion branch, and l_{\mathrm{T}} is the locational marginal price for injection node.

When the network is not congested, the values of l_{\mathrm{T},i} and l_{\mathrm{T},j} are identical, and the congestion cost is zero. As the congestion occurs, the congestion cost is directly proportional to the difference in node price. If the market participant obtains the FTR with P_{\mathrm{T}} electricity transmission in the branch through auction, ISO will return the congestion cost to the holders of FTR in the settlement. Thus, the market surplus caused by congestion is distributed, and the loss of FTR holders is reduced.

2.1.2 FSR

FSR is a concept proposed by Munoz-Alvarez et al. in 2014 [31]. Together with FTR, it is used to share the unbalanced costs generated in power transactions. FTR is used to avoid the LMP fluctuation of different nodes at the same time, and FSR is used to avoid the LMP fluctuation risk of the same node at different times. FSR is a market mechanism based on tradable financial instruments, which entitles holders to the right to receive financial compensation when the power is congested. Each node in the power system is equipped with a common energy storage device, which is managed by ISO. It can be used by market participants to balance the temporary surplus or shortage of power in the power system. FSR is the financial contract based on the capacity of public energy storage devices, which can be apportioned and settled according to the amount held by the holders.

FSR is a financial payment contract established by the holders to avoid the risk of price fluctuation. The surplus settlement of FSR depends on the matching degree of supply and demand in the spot electricity market. When the power is insufficient or excess in the power system, the public energy storage will be used to balance the power supply and demand. The power congestion brought by the excess power will cause the LMP fluctuation of the power system and generate the power congestion cost. In this case, FSR can compensate for the loss caused by excess or shortage of power, so that the holders can avoid the risk caused by price changes at different times in specific nodes.

(2)c_P=l_{\mathrm{S},j}(P_{\mathrm{S},j}-P_{\mathrm{S},i}),

where c_P is the power congestion cost, P_{\mathrm{S}} is the power generation and consumption, and l_{\mathrm{S}} is the locational marginal price for load node.

When there is no congestion in the power network, the generation and consumption are alike, and the congestion charge is zero. When congestion occurs, congestion charges increase as the excess power increases. If the market participant obtains the right of common energy storage capacity P_{\mathrm{S},j}-P_{\mathrm{S},i} at this node, the system operator will return the congestion charge to FSR holders in the settlement. Thus, the market surplus caused by congestion is shared and the loss of FSR holders is declined.

2.2 Physical right contracts

2.2.1 PTR

PTR entitles its holders the right to use the capacity of transmission port in priority, which is used in the actual transmission of power system or sold in the electricity market. If the market participant does not purchase the PTR and uses the line to transmit electrical energy, PTR holders will receive the corresponding compensation. Due to the constraint of Kirchhoff’s law in the transmission process, the electric energy will not flow according to the path of specified physical contract. Therefore, PTR is usually difficult to be implemented in engineering [32].

PTR holders have an absolute exclusivity in transmission capacity. Even in the event of transmission congestion, no other electricity transaction can occupy the vacant capacity. PTR plays the same role as FTR in avoiding congestion price fluctuations, which means its holders do not have to pay additional congestion charges. As PTR is adopted by ISO to avoid congestion, the calculation method of congestion cost is the same as that of FTR. However, in the event of congestion, ISO will not give PTR holders congestion compensation.

2.2.2 PSR

The PSR allocates the right to use the common energy storage capacity of the nodes. Its holders can take advantage of the charging and discharging characteristics of the common energy storage to relieve the power congestion of the system.

PSR holders are similar to PTR holders, who have an absolute exclusive ownership of public storage capacity. The sum of the amount of electricity charged into the storage by PSR holders and that of electricity discharged is equivalent. PSR holders do not need to pay an extra fee if there exists congestion caused by excess power.

PSR holders use the physical rights of PSR to arbitrage the prices or reduce the cost of the existing contract. However, there are two important constraints. On the one hand, the ability of market participants to take advantage of PSR depends on their position in the network relative to energy storage facilities, and this restriction may limit market access. On the other hand, the final physical dispatch of energy storage is determined by a series of auctions, and the results of the auctions are likely to deviate from the grid dispatch.

When PSR is adopted by ISO to avoid congestion, congestion charges are calculated in the same way as FSR. However, in the case of electricity congestion, ISO does not give PSR holders congestion compensation.

3 Mathematical formulation

3.1 Market environment

The portfolio strategy for energy storage devices is divided into two components: a portion of the capital is invested in the risk-free right market to ensure the minimum value of the portfolio, a portion of the capital is allocated to the risky day-ahead market and adjusts the proportion of the day-ahead market and the right market according to the variation of the risk aversion [33,34].

This paper focuses on the portfolio strategy of energy storage devices in the day-ahead market and the right market. Energy storage implements price arbitrage in the day-ahead market based on the LMP mechanism, but it may be exposed to the volatility risk of settlement price. Considering the right market as the trading financial derivative, energy storage can accomplish the insurance of portfolio by participating in the right market.

Energy storage users submit power offer information (including the total amount of power traded, the start and end times) to the day-ahead market. The power is purchased to charge energy storage at a lower clearing price and sold at a higher bidding price in the day-ahead market. The profit of energy storage power trading is derived from the arbitrage of low storage and high generation in the day-ahead market.

The right market involved in this paper comprises transmission rights and storage rights. Specifically, in Fig. 2, the right market is subdivided into a financial right market and a physical right market for energy storage users to hedge the risk of trading price fluctuations. Energy storage users submit right offer information (including the number of rights purchased, the starting and ending times) before the day-ahead market is started. The financial rights are purchased in the financial right market and the physical rights are bought in the physical right market as shown in Fig. 2.

3.2 Model formulation

3.2.1 Portfolio model of energy storage devices considering financial contracts

Due to the uncertainty of market prices, actual profits may fluctuate. Therefore, the expected profit as an important indicator aims to assess the reasonableness of the selected portfolio. Energy storage users mainly utilize the peak-valley spread to achieve price arbitrage in the electricity market. The bigger the peak-valley spread, the larger the arbitrage margin. However, when the peak-to-valley price spread in the spot market is smaller, the extreme situation of negative arbitrage profit may occur. Thus, the portfolio strategy of energy storage users in the multi-market environment should confront the impact of this extreme situation.

In the Markowitz portfolio theory, the minimum variance is the benchmark objective and the risk is expressed as the standard deviation of portfolio revenue. But the standard deviation reflects less likely large unascertainable and expected losses in the portfolio [35]. CVaR (conditional value at risk) can provide a better control of excess losses than VaR (value at risk, VaR) by optimizing the proportion of risky assets in the portfolio to reduce extreme risk. If the CVaR is added to constrain the portfolio and pre-limit the potential risk of the portfolio, it can play a risk-averse role by optimizing the portfolio. In this paper, CVaR, as a risk metric, is presented for confronting the problem of portfolio management with energy storage.

The goal of the portfolio strategy for energy storage installations maximizes the profitability of energy storage. However, high profits are usually accompanied by high risks. To address this issue, energy storage users apply a weighted average approach to balance profit and risk when users design their portfolios, which can be formulated as

(3)\max (\mathrm{1}-\phi )\mathrm{Exp}(F)+\phi CVa{R}_{\alpha }(F),

where \phi is the risk weighting parameter, F is the expected profit set of energy storage in some power trading days, and CVa{R}_{\alpha }(F) is the CVaR of profits.

It is assumed that the probability of obtaining each profit is the same for each trading day. Therefore, the average of the expected profit F is calculated as

(4)CVa{R}_{\alpha }(X)=\mathrm{Exp}(F)={\displaystyle \frac{\mathrm{1}}{N}}{\displaystyle \sum _{i=\mathrm{1}}^{N}F},

where CVa{R}_{\alpha }(X) is the CVaR of expected profits. The CVaR of a random variable X is calculated as

(5)CVa{R}_{\alpha }(X)=\mathrm{Exp}(X|X\le Va{R}_{\alpha }(X)),

where \alpha is the confidence level which ranges from 0.9 to 0.99 [36], VaR is the expected profit with a quantile of 1−α in the experimental scenario, i.e., the expected profit probability for energy storage that is smaller or equal to VaR is 1−α.

The Kolmogorov–Smirnov test proves that the probability density function (PDF) of the expected profit F of energy storage at each trading day follows the normal distribution. µ is the mean, σ is the standard deviation, \epsilon is the normal distribution parameter, VaR is µ− \gamma \sigma, CVaR is µ−\epsilon \sigma, and the confidence level is 1 − α.

(6)CVa{R}_{\alpha }(F)={\displaystyle \frac{\mathrm{1}}{N}}{\displaystyle \sum _{i=\mathrm{1}}^{N}F}-\epsilon \sqrt{{\displaystyle \frac{\mathrm{1}}{N-\mathrm{1}}}{\sum _{i=\mathrm{1}}^N\left|F-{\displaystyle \frac{\mathrm{1}}{N}}{\displaystyle \sum _{i=\mathrm{1}}^{N}F}\right|}^{\mathrm{2}}}.

The daily profit of energy storage consists of three components, corresponding to three types of markets. The profit for the trading dayi is calculated as

(7)F_i=F_i^{\mathrm{DA}}+F_i^{\mathrm{FTR}}+F_i^{\mathrm{FSR}},

(8)F_i^{\mathrm{DA}}=l_{j,\mathrm{gen}}^{\mathrm{DA}}(P_{j,\mathrm{out}}-P_{j,\mathrm{in}})t-c_{\mathrm{0}}(P_{j,\mathrm{out}}+P_{j,\mathrm{in}})t,

(9)F_i^{\mathrm{FTR}}=[(l_{j,\mathrm{load}}^{\mathrm{RT}}-l_{j,\mathrm{gen}}^{\mathrm{RT}})-(l_{j,\mathrm{load}}^{\mathrm{DA}}-l_{j,\mathrm{gen}}^{\mathrm{DA}})]P_j^{\mathrm{FTR}}t,

(10)F_i^{\mathrm{FSR}}=(l_{j,\mathrm{load}}^{\mathrm{RT}}-l_{j,\mathrm{load}}^{\mathrm{DA}})P_j^{\mathrm{FSR}}t,

where “DA” is the superscript for the day-ahead market risk weighting parameter, “RT” is the superscript for real-time market, “gen” is the superscript for the clearing price at the source node, “out” is the superscript for discharge, “t” is the set of simulation time slots, “in” is the superscript for discharge, c₀ is the operation cost per, and “load” is the superscript for the clearing price at the load node.

Input/output power constraint: the trading power in each market should not exceed the maximum input/output power of energy storage.

(11)\mathrm{0}\le P_{j,\mathrm{out}}\le P_{\max },

(12)\mathrm{0}\le P_{j,\mathrm{in}}\le P_{\max },

(13)\mathrm{0}\le P_j^{\mathrm{FTR}}\le P_{\max }^{\mathrm{FTR}},

(14)\mathrm{0}\le P_j^{\mathrm{FSR}}\le P_{\max }^{\mathrm{FSR}},

where P_{\max } is the maximum input/output power.

In each time slot, the total power of energy storage charging/discharging should not exceed its maximum input/output power.

(15)P_{j,\mathrm{out}}-P_{j,\mathrm{in}}\ge -P_{\max },

(16)P_{j,\mathrm{out}}-P_{j,\mathrm{in}}\le P_{\max }.

Energy storage capacity constraint: the energy storage device cannot exceed its maximum capacity. Equations (18) and (19) describe the capacity constraint of energy storage considering the energy loss in the current period. Equation (20) is the calculation of the energy storage capacity in the next period.

(17)\mathrm{0}\le E_j\le E_{\max },

(18)E_j\ge {\displaystyle \frac{(P_{j,\mathrm{out}}-P_{j,\mathrm{in}})t}{\lambda }},

(19)E_j\le E_{\max }+\lambda (P_{j,\mathrm{out}}-P_{j,\mathrm{in}})t,

(20)E_{j+\mathrm{1}}=E_j-{\displaystyle \frac{P_{j,\mathrm{out}}t}{\lambda }}+\lambda P_{j,\mathrm{in}}t,

where E_{\max } is the maximum storage capacity and \lambda is the charging and discharging efficiency of storage.

It is assumed that the energy storage device will remain at a constant level at the beginning and end of each day. Thus, the initial and final electrical energy of the energy storage device in a working day are equal.

(21)E_{\mathrm{0}}=E_{\mathrm{24}+\mathrm{1}}=E_{\mathrm{initial}},

where E_{\mathrm{0}} is the initial storage capacity, E_{\mathrm{24}+\mathrm{1}}is the storage capacity at the beginning of the next operation day, and E_{\mathrm{initial}} is the initial state of energy storage capacity.

3.2.2 Portfolio model of energy storage devices considering physical contracts

The portfolio model of energy storage devices considering physical contracts has similarities with that of financial contracts. The objective function, as well as the expected profit in the day-ahead market, is calculated in the same way.

In this section, using physical right risk aversion, energy storage users participate in the physical right market, and the expected profit of PTR purchased in the day-ahead market can be defined as

(22)F_i^{\mathrm{PTR}}=-[(l_{j,\mathrm{in}}^{\mathrm{DA}}-l_{j,\mathrm{out}}^{\mathrm{DA}})]P_j^{\mathrm{PTR}}t,

The expected profit of PSR can be calculated as

(23)F_i^{\mathrm{PSR}}=-l_{j,\mathrm{in}}^{\mathrm{DA}}{P}_j^{\mathrm{PSR}}t.

The purchase constraints for PTR and PSR are expressed as

(24)\mathrm{0}\le P_j^{\mathrm{PTR}}\le P_{\max }^{\mathrm{PTR}},

(25)\mathrm{0}\le P_j^{\mathrm{PSR}}\le P_{\max }^{\mathrm{PSR}}.

4 Results and discussion

This section demonstrates the functioning of the portfolio model in the case study. The latest Pennsylvania-New Jersey-Maryland (PJM) market data are used for the case study. First, the input data simulated from the energy market is described. After that, the simulation results are presented and analyzed. The proposed model can be tested in the MATLAB environment on a desktop with an Intel Core i5-6650 CPU at 3.2 GHz and 8 GB RAM. The YALMIP toolbox and Gurobi solver are used for portfolio optimization.

The input variables include the price of energy storage input and output, FTR, and FSR. The decision variables are composed of the maximum input/output power, maximum purchase quantity, operation cost per, risk weighting parameter, confidential level, maximum storage capacity, the initial state of energy storage capacity, and charging and discharging efficiency of storage.

The representative days are chosen by performing cluster analysis. The decision is made: ① on the day-ahead basis, for each representative day, the portfolio design predetermines how much energy to purchase in the day-ahead market; ② on a right market basis, the portfolio design calculates how much financial or physical right to purchase in the right market; and ③ in the last stage, the portfolio design decides on the time which the storage owners sell the stored energy.

4.1 Data and scenario setup

To start with, the market data and scenarios used in the simulations are specified. For market prices, publicly available historical data of LMP in the PJM are used. From these data, one node is chosen and 30 typical scenarios are defined based on day-ahead and real-time conditions. For each manually defined day-cluster, the average prices per hour are obtained, which are depicted in Fig. 3. Similarly, congestion price scenarios from day-ahead and real-time markets are obtained from the same source as above, as shown in Fig. 4.

4.2 Performance and comparison

The results of the energy storage device portfolio strategy considering financial and physical contracts are demonstrated in Figs. 5 and 6. In Fig. 5, energy storage users buy energy when market prices are low from 4:00 to 7:00, sell electric energy to the market at high prices from 14:00 to 18:00. Energy storage users buy FTR from 20:00 to 21:00. Figure 4 indicates that during these periods, the day-hour and day-ahead congestion prices are high, and the purchase of FTR in these periods can avoid the risk of electricity price fluctuation caused by transmission congestion. From 24:00 to 12:00, the day-hour and day-ahead congestion prices are low, less likely to be congested. Therefore, in this period energy storage users do not purchase FTR. As illustrated in Fig. 5, energy storage users buy FSR from 14:00 to 21:00. Figure 3 suggests that during this period, the day-hour and day-ahead market prices are higher, and during these periods, the purchase of FSR can avoid the risk of electricity price fluctuation caused by the imbalance. From 0:00 to 6:00, the day-hour and day-ahead market prices are lower, and the risk aversion is unnecessary. Therefore, there is no purchase of FSR during these periods.

Figure 6 manifests that energy storage users buy electricity from 5:00 and sell electricity from 12:00 to 15:00. Low storage and high generation make them avoid buying electricity among the highest eight hours of price in the day-ahead market but buy PTR from 18:00 to 22:00. It is observed from Fig. 3 that the day-ahead electricity price is higher than day-hour electricity prices, the occurrence possibility of transmission congestion and power congestion is higher, and participation in the right market can avoid the risk of price volatility.

To further analyze the energy storage portfolio effects of financial/physical contracts, this paper analyzes and compares the monthly portfolio of a year. The monthly portfolio strategy for energy storage is exhibited in Figs. 7 and 8. Figure 7 shows, the real profits of the portfolio considering financial contracts are higher than the real profits without right market, and the real profits of the porfolio considering physical contracts are lower than the real profits without the right market in a few months, but the difference is not significant. In Fig. 8, CVaR of the portfolio considering financial/physical contract is significantly better than those in the rights-free market. Energy storage devices may make higher profits in a non-privileged market environment, but the risk is higher. To sum up, financial/physical contracts can effectively avoid the price risks, and can better balance the income and risk.

As far as the attitude of energy storage users to risk changes is concerned, the portfolio strategy will change. Figure 9 analyzes the sensitivity of risk aversion, which shows that the expected profit decreases with the increase of risk aversion, while CVaR increases with the increase of risk aversion. When the degree of risk aversion is less than 0.2, CVaR increases rapidly but when the degree of risk aversion is higher than 0.2, CVaR increases slowly. When the degree of risk aversion is less than 0.2, the expected profit decreases rapidly but when the degree of risk aversion is higher than 0.2 and less than 0.6, the expected profit decreases slowly. When the degree of risk aversion is higher than 0.6, the expected profit decline becomes faster. When the expected profit decreases, CVaR increases, indicating that the proportion of energy storage users participating in the day-ahead market decreases but the proportion of participation in the right market increases.

5 Conclusions

In this paper, a portfolio model of energy storage participation in the day-ahead market and the right market is proposed. CVaR is used as the risk measure of the bidding strategy optimization problem. FTR and FSR are introduced to form the financial contract, while PTR and PSR form the physical contract. The simulation results show that the expected profit of energy storage mainly comes from the day-ahead market, and the right market can effectively avoid risk, i.e., the financial contract and physical contract can effectively avoid price risk and balance risk and income. The proposed portfolio can obtain the expected profit and has a high CVaR. The CVaR of the portfolio increases with the increase of the share of the right market.

References

[1] Chinmoy L, Iniyan S, Goic R. Modeling wind power investments, policies and social benefits for deregulated electricity market—a review. Applied Energy, 2019, 242: 364–377

[2] Ghorani R, Fotuhi-Firuzabad M, Moeini-Aghtaie M. Main challenges of implementing penalty mechanisms in transactive electricity markets. IEEE Transactions on Power Systems, 2019, 34(5): 3954–3956

[3] Tudu B, Mandal K K, Chakraborty N. Optimal design and development of PV-wind-battery based nano-grid system: a field-on-laboratory demonstration. Frontiers in Energy, 2019, 13(2): 269–283

[4] Gupta A R, Kumar A. Reactive power deployment and cost benefit analysis in DNO operated distribution electricity markets with D-STATCOM. Frontiers in Energy, 2019, 13(1): 86–98

[5] Li P, Cai G, Zhang Y, . Multi-objective optimal allocation strategy for the energy internet in Huangpu District, Guangzhou, China. Frontiers in Energy, 2020, 14(2): 241–253

[6] Vespermann N, Hamacher T, Kazempour J. Access economy for storage in energy communities. IEEE Transactions on Power Systems, 2021, 36(3): 2234–2250

[7] Tenti P, Caldognetto T. A general approach to select location and ratings of energy storage systems in local area energy networks. IEEE Transactions on Industry Applications, 2019, 55(6): 6203–6210

[8] Aguado J A, Quintana V H, Madrigal M, . Coordinated spot market for congestion management of inter-regional electricity markets. IEEE Transactions on Power Systems, 2004, 19(1): 180–187

[9] Deng L, Li Z, Sun H, . Generalized locational marginal pricing in a heat-and-electricity-integrated market. IEEE Transactions on Smart Grid, 2019, 10(6): 6414–6425

[10] Asrari A, Ansari M, Khazaei J, . A market framework for decentralized congestion management in smart distribution grids considering collaboration among electric vehicle aggregators. IEEE Transactions on Smart Grid, 2020, 11(2): 1147–1158

[11] Huang S, Wu Q, Shahidehpour M, . Dynamic power tariff for congestion management in distribution networks. IEEE Transactions on Smart Grid, 2019, 10(2): 2148–2157

[12] Han D, Zhang C, Ping J, . Smart contract architecture for decentralized energy trading and management based on blockchains. Energy, 2020, 199: 117417

[13] Weibelzahl M. Nodal, zonal, or uniform electricity pricing: how to deal with network congestion. Frontiers in Energy, 2017, 11(2): 210–232

[14] Mahesh A, Sandhu K S. A genetic algorithm based improved optimal sizing strategy for solar-wind-battery hybrid system using energy filter algorithm. Frontiers in Energy, 2020, 14(1): 139–151

[15] Sharma R, Suhag S. Feedback linearization based control for weak grid connected PV system under normal and abnormal conditions. Frontiers in Energy, 2020, 14(2): 400–409

[16] Hartwig K, Kockar I. Impact of strategic behavior and ownership of energy storage on provision of flexibility. IEEE Transactions on Sustainable Energy, 2016, 7(2): 744–754

[17] Paterakis N G, de la Nieta A A S, Bakirtzis A G, . Effect of risk aversion on reserve procurement with flexible demand side resources from the ISO point of view. IEEE Transactions on Sustainable Energy, 2017, 8(3): 1040–1050

[18] Saber H, Heidarabadi H, Moeini-Aghtaie M, . Expansion planning studies of independent-locally operated battery energy storage systems (BESSs): a CVaR-based study. IEEE Transactions on Sustainable Energy, 2020, 11(4): 2109–2118

[19] Liu X, Yan Z, Wu J. Optimal coordinated operation of a multi-energy community considering interactions between energy storage and conversion devices. Applied Energy, 2019, 248: 256–273

[20] Naderi M, Hashemi F, Bekker A, . Modeling right-skewed financial data streams: a likelihood inference based on the generalized Birnbaum-Saunders mixture model. Applied Mathematics and Computation, 2020, 376: 125109

[21] Lo Prete C, Guo N, Shanbhag U V. Virtual bidding and financial transmission rights: an equilibrium model for cross-product manipulation in electricity markets. IEEE Transactions on Power Systems, 2019, 34(2): 953–967

[22] Taylor J A. Financial storage rights. IEEE Transactions on Power Systems, 2015, 30(2): 997–1005

[23] Gribik P R, Shirmohammadi D, Graves J S, . Transmission rights and transmission expansions. IEEE Transactions on Power Systems, 2005, 20(4): 1728–1737

[24] Baldick R. Border flow rights and contracts for differences of differences: models for electric transmission property rights. IEEE Transactions on Power Systems, 2007, 22(4): 1495–1506

[25] Thomas D, Kazempour J, Papakonstantinou A, . A local market mechanism for physical storage rights. IEEE Transactions on Power Systems, 2020, 35(4): 3087–3099

[26] Budworth L, Prestwich A, Sykes-Muskett B, . A feasibility study to assess the individual and combined effects of financial incentives and monetary contingency contracts on physical activity. Psychology of Sport and Exercise, 2019, 44: 42–50

[27] Leshno J D, Pradelski B S R. The importance of memory for price discovery in decentralized markets. Games and Economic Behavior, 2021, 125: 62–78

[28] Madrigal M, Flores M. Integrated software platform to teach different electricity spot market architectures. IEEE Transactions on Power Systems, 2004, 19(1): 88–95

[29] Gui Z, von Thadden E L, Zhao X. Incentive-compatibility, limited liability and costly liquidation in financial contracting. Games and Economic Behavior, 2019, 118: 412–433

[30] Hogan W W. Contract networks for electric power transmission. Journal of Regulatory Economics, 1992, 4(3): 211–242

[31] Muñoz-Álvarez D, Bitar E. Financial storage rights: definition and basic properties. In: 2014 North American Power Symposium (NAPS), Pullman, WA, USA, 2014: 1–6

[32] Quintela F R, Redondo R C, Melchor N R, . A general approach to Kirchhoff’s laws. IEEE Transactions on Education, 2009, 52(2): 273–278

[33] Sioshansi R. Using storage-capacity rights to overcome the cost-recovery hurdle for energy storage. IEEE Transactions on Power Systems, 2017, 32(3): 2028–2040

[34] Cui S, Wang Y, Li C, . Prosumer community: a risk aversion energy sharing model. IEEE Transactions on Sustainable Energy, 2020, 11(2): 828–838

[35] Palomba G, Riccetti L. Portfolio frontiers with restrictions to tracking error volatility and value at risk. Journal of Banking & Finance, 2012, 36(9): 2604–2615

[36] Catalao J P S, Pousinho H M I, Mendes V M F. Optimal offering strategies for wind power producers considering uncertainty and risk. IEEE Systems Journal, 2012, 6(2): 270–277

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