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Renewable resources are starting to constitute a growing portion of the total generation mix of the power system. A key difference between renewables and traditional generators is that many renewable resources are managed by individuals, especially in the distribution system. In this paper, we study the capacity investment and pricing problem, wher...
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Context 1
... Suppose that the investment price is the same for all players, i.e., γ = 0.25, then following the analysis in Section 4, we know that the optimal capacity satisfies C * 1 = C * 2 . Assuming that the demand is normalized to 1, we solve the social optimization in (5) with equal investment price γ . The optimal solution leads to a total capacity of Fig. 3. To verify that C * 1 = C * 2 = 0.855 is indeed a symmetric Nash equilibrium, we vary the capacity from C * 1 and study how player 1's profit changes. The analysis for player 2 proceeds in the same way because of symmetry. We show the result of optimality for player 1 in Fig. 4 in terms of profit, with a fixed capacity for player 2 ...
Context 2
... us assume that the generation distribution is uniform, i.e., Z i ∼ unif(0, 1). Suppose that the investment price is the same for all players, i.e., γ = 0.25, then following the analysis in Section 4, we know that the optimal capacity satisfies C * 1 = C * 2 . Assuming that the demand is normalized to 1, we solve the social optimization in (5) with equal investment price γ . The optimal solution leads to a total capacity of Fig. 3. To verify that C * 1 = C * 2 = 0.855 is indeed a symmetric Nash equilibrium, we vary the capacity from C * 1 and study how player 1's profit changes. The analysis for player 2 proceeds in the same way because of symmetry. We show the result of optimality for player 1 in Fig. 4 in terms of profit, with a fixed capacity for player 2 where C 2 = C * 2 = 0.855. As can be seen from Fig. 4, the profit for player 1-when the other player's capacity is fixed at C * 2 -peaks at C 1 = C * 1 . By symmetry, we can argue that player 2's profit is maximized at C * 2 when player 1's capacity remains fixed. Therefore, (C * 1 , C * 2 ) is indeed a Nash equilibrium as neither player has any incentive to deviate from its investment strategy. In other words, the socially optimal capacity is also a Nash equilibrium for the game shown in (1). ...
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Citations
... STEP II: Calculation with Uncertainties in the Energy Market The middle management of Company 2 incorporates the gathered information into the energy market model to calculate NPV and other parameters for the evaluation of investment with respect to each strategy. Although there have been several previous studies of the energy market of RE [40,41], this study assumes that the energy market is competitive and not dominated by Company 1. The hourly spot price of electricity (Yen per kWh) is decided based on the supply curve generated by the energy supply capability of both companies and the demand obtained from the input of STEP I. Furthermore, the spot price is applied to all supply capacities of technology that are below the demand. ...
With respect to decision making by companies, normative approaches such as the net present value (NPV) method are widely applied, even though it is known that investors may make non-normative decisions. This study aimed to obtain new information on the decision-making behavior of renewable energy (RE) companies under uncertainty in the energy market, which is not provided by the conventional normative approach. In this study, we designed a novel framework that expressed both normative and non-normative perspectives of decision making, and developed a behavioral decision-making model of a power generation company investing in large-scale RE (RE company). We also examined the decisions of the RE company under uncertainty in the energy market using the developed model, considering the Kansai region in Japan as an example study area. As a result, compared to the conventional NPV method, we obtained the following information: (i) heavy investments in either photovoltaics (PV) or wind resulted in decreased variable renewable energy (VRE) capacity, even though financial support was sufficient; (ii) balanced investments in both PV and wind yielded a larger VRE capacity in cases where financial support was sufficient; and (iii) co-worker’s suggestions that lowered the decision-makers’ reference point (RFP) encouraged VRE investments despite insufficient financial support.
... L. Marshall et al. [87] proved that, under the current market environment, zero-marginal-cost generators gain more advantage when competing with other generators using collusive shadow prices, which illustrates the inefficiency of the existing market mechanisms towards high renewable penetration. Some other works focus on distribution market designs, including the capacity-price game for renewable investors [88] and the average pricing market with abundant renewables [89]. -Systems reliability. ...
With the accelerating penetration of solar energy in energy systems, market operations concerning the solar associated intermittency are widely discussed. How to correctly model the solar generation in the market and solve the uncertainty-based operation problems call for solutions. Unlike other renewable resources, solar power can be more easily applied to the demand side through behind-the-meter installations in a distributed manner with significant future extensibility. The corresponding operational rules in the markets are largely being revised. Over the past two decades, with the development of deregulated power markets, numerous studies related to uncertainty-based market operations tend to transform the market from a deterministic and centralized framework to a stochastic and decentralized one. As the relevant literature is most recent, this paper reviews their contributions to electricity market operations with solar integration and
underlines the research directions of this topic and ongoing industry practices. A thorough review of the electricity markets worldwide with solar energy is provided. A variety of proposed mathematical solutions to the problem are also discussed.
... However, this work considered zero cost related to the production (i.e., no production cost or possible penalty cost). In electricity markets, the works in [18] and [19] also used Bertrand-Edgeworth model to analyze the competition among renewable energy suppliers with random generations. However, both [18] and [19] considered the suppliers' electricity-selling competition in a single-settlement energy market, and suppliers deliver random generations in real time. ...
... In electricity markets, the works in [18] and [19] also used Bertrand-Edgeworth model to analyze the competition among renewable energy suppliers with random generations. However, both [18] and [19] considered the suppliers' electricity-selling competition in a single-settlement energy market, and suppliers deliver random generations in real time. These studies did not consider day-ahead bidding strategies and any deviation penalty cost. ...
... The distribution of wind or solar power can be characterized using the historical data, which is known to the renewable energy suppliers. 1 As renewables usually have extremely low marginal production costs compared with traditional generators, we assume zero marginal production costs for the suppliers [18] [19]. ...
Renewable energy generations and energy storage are playing increasingly important roles in serving consumers in power systems. This paper studies the market competition between renewable energy suppliers with or without energy storage in a local energy market. The storage investment brings the benefits of stabilizing renewable energy suppliers’ outputs, but it also leads to substantial investment costs as well as some surprising changes in the market outcome. To study the equilibrium decisions of storage investment in the renewable energy suppliers’ competition, we model the interactions between suppliers and consumers using a three-stage game-theoretic model. In Stage I, at the beginning of the investment horizon (containing many days), suppliers decide whether to invest in storage. Once such decisions have been made (once), in the day-ahead market of each day, suppliers decide on their bidding prices and quantities in Stage II, based on which consumers decide the electricity quantity purchased from each supplier in Stage III. In the real-time market, a supplier is penalized if his actual generation falls short of his commitment. We characterize a price-quantity competition equilibrium of Stage II in the local energy market, and we further characterize a storage-investment equilibrium in Stage I incorporating electricity-selling revenue and storage cost. Counter-intuitively, we show that the uncertainty of renewable energy without storage investment can lead to higher supplier profits compared with the stable generations with storage investment due to the reduced market competition under random energy generation. Simulations further illustrate results due to the market competition. For example, a higher penalty for not meeting the commitment, a higher storage cost, or a lower consumer demand can sometimes increase a supplier’s profit. We also show that although storage investment can increase a supplier ’s profit, the first-mover supplier who invests in storage may benefit less than the free-rider competitor who chooses not to invest.
... However, this work considered zero cost related to the production (i.e., no production cost or possible penalty cost). In electricity markets, the works in [18] and [19] also used Bertrand-Edgeworth model to analyze the competition among renewable energy suppliers with random generations. However, both [18] and [19] considered the suppliers' electricity-selling competition in a single-settlement energy market, and suppliers deliver random generations in real time. ...
... In electricity markets, the works in [18] and [19] also used Bertrand-Edgeworth model to analyze the competition among renewable energy suppliers with random generations. However, both [18] and [19] considered the suppliers' electricity-selling competition in a single-settlement energy market, and suppliers deliver random generations in real time. These studies did not consider day-ahead bidding strategies and any deviation penalty cost. ...
... The distribution of wind or solar power can be characterized using the historical data, which is known to the renewable energy suppliers. 1 As renewables usually have extremely low marginal production costs compared with traditional generators, we assume zero marginal production costs for the suppliers [18] [19]. ...
This paper studies the duopoly competition between renewable energy suppliers with or without energy storage in a local energy market. The storage investment brings the benefits of stabilizing renewable energy suppliers' outputs, but it also leads to substantial investment costs as well as some surprising changes in the market outcome. To study the equilibrium decisions of storage investment in the renewable energy suppliers' competition, we model the interactions between suppliers and consumers using a three-stage game-theoretic model. In Stage I, at the beginning of the investment horizon, suppliers decide whether to invest in storage. Once such decisions have been made, in the day-ahead market of each day, suppliers decide on their bidding prices and quantities in Stage II, based on which consumers decide the electricity quantity purchased from each supplier in Stage III. In the real-time market, a supplier is penalized if his actual generation falls short of his commitment. We characterize a price-quantity competition equilibrium of Stage II, and we further characterize a storage-investment equilibrium in Stage I incorporating electricity-selling revenue and storage cost. Counter-intuitively, we show that the uncertainty of renewable energy without storage investment can lead to higher supplier profits compared with the stable generations with storage investment due to the reduced market competition under random energy generation. Simulations further illustrate results due to the market competition. For example, a higher penalty for not meeting the commitment, a higher storage cost, or a lower consumer demand can sometimes increase a supplier's profit. We also show that although storage investment can increase a supplier 's profit, the first-mover supplier who invests in storage may benefit less than the free-rider competitor who chooses not to invest.
