Bi-level Equilibrium Model Research Articles

The Economics of Demand-side Flexibility in Distribution Grids

To avoid unnecessary distribution network investments, distribution tariffs are expected to become more cost-reflective, and DSOs are expected to procure flexibility. This will provide an implicit and an explicit incentive to provide demand-side flexibility. In this paper, we develop a long-term bi-level equilibrium model. In the upper level, the DSO optimizes social welfare by deciding the level of investment in the distribution network and/or curtailing consumers. The regulated DSO also sets a network tariff to recover the network and flexibility costs. In the lower level, the consumers, active and passive, maximize their own welfare. We find that implicit and explicit incentives for demand-side flexibility are complementary regulatory tools, but there are limits. If network tariffs are too imperfect, the resulting consumption profiles can become too expensive to fix with curtailment. We also find that it is difficult to set an appropriate level of compensation because of the reaction by prosumers.

P2H Modeling and Operation in the Microgrid Under Coupled Electricity–Hydrogen Markets

The uncertainty and volatility of wind power have led to large-scale wind curtailment during grid connections. The adoption of power-to-hydrogen (P2H) system in a microgrid (MG) can mitigate the renewable curtailment by hydrogen conversion and storage. This paper conducts unified modeling for different types of P2H systems and considers the multi-energy trading in a hydrogen-coupled power market. The proposed bi-level equilibrium model is beneficial to minimize the energy cost of microgrids. Firstly, a microgrid operation model applied to different P2H systems including an alkaline electrolysis cell (AEC), a proton exchange membrane electrolysis cell (PEMEC), or a solid oxide electrolysis cell (SOEC) is proposed at the upper level. Secondly, an electricity market–clearing model and a hydrogen market model are constructed at the lower level. Then, the diagonalization algorithm is adopted to solve the multi-market equilibrium problem. Finally, case studies based on an IEEE 14-bus system are conducted to validate the proposed model, and the results show that the microgrid with a P2H system could gain more profits and help increase the renewable penetration.

Storage investment and network expansion in distribution networks: The impact of regulatory frameworks

In this paper we propose a bi-level equilibrium model that allows to analyze the impact of different regulatory frameworks on storage and network investment in distribution networks. In our model, a regulated distribution system operator decides on network investment and operation while he anticipates the decisions of private agents on storage investment and operation. Since, especially in distribution networks, voltage stability and network losses have a decisive influence on network expansion and operation, we use a linearized AC power flow formulation to adequately account for these aspects. As adjustments of the current regulatory framework, we consider curtailment of renewable production, the introduction of a network fee based on the maximum renewable feed-in, and a subsidy scheme for storage investment. The performance of the different alternative frameworks is compared to the performance under rules that are commonly applied in various countries today, as well as to a system-optimal (first-best) benchmark. To illustrate the economic effects, we calibrate our model with data from the field project Smart Grid Solar. Our results reveal that curtailment and a redesign of network fees both have the potential to significantly reduce total system costs. On the contrary, investment subsidization of storage capacity has only a limited impact as long as the distribution system operator is not allowed to intervene in storage operation.

Analysis of Market Equilibrium Based on Co-evolution in Electricity Spot Market

By solving the Nash equilibrium of the electricity market, it is possible to observe the game process of market entities under different boundary conditions and predict the future trend of the market. In order to study the state of market equilibrium in the power spot market, firstly we constructed a bi-level equilibrium model. The upper layer is the problem of maximizing the profit of power generation enterprises under the bidding constraint, and the lower layer is the security constraint economic dispatch with the goal of maximizing social welfare. The traditional solution transforms the bi-level model into MPEC or EPEC through optimal conditions, but they are generally non-convex and difficult to solve. In this regard, the coevolution algorithm is used to solve the bi-level model, and it is proved that the result of co-evolution under a limited strategy set is equivalent to the Nash equilibrium. Finally, an example of PJM 5 machine with 5 nodes is used to analyse the power market equilibrium in the spot market.

The Economics of Explicit Demand-Side Flexibility in Distribution Grids: The Case of Mandatory Curtailment for a Fixed Level of Compensation

Demand-side flexibility can be incentivised to reduce the need for investment in distribution grids either implicitly or explicitly. Implicit demand-side flexibility is when prosumers react to price signals triggered by network tariffs. Explicit demand-side flexibility is when the DSO can contract flexibility. In this paper, we focus on one contractual arrangement: mandatory curtailment by the DSO for a fixed level of compensation. We develop a long-term bi-level equilibrium model. The upper level (UL) is a regulated DSO deciding on the network investment and/or curtailing consumers for a fixed level of compensation. The lower level (LL) consists of consumers, which can be prosumers or passive consumers. Prosumers can invest in solar PV and battery systems. They react to the network tariffs and to the compensation provided by the DSO for curtailing them. The regulated DSO anticipates the reaction of the consumers when investing in the network and when setting the level of curtailment. Network tariffs are set to recover the network costs and the payments made to consumers that have been curtailed. We find that the economics of explicit demand-side flexibility in distribution grids are positive, and they are more positive when tariffs are cost-reflective. This implies that we cannot avoid redesigning tariffs by using explicit demand flexibility. We also find that setting an appropriate level of compensation is difficult in the presence of prosumers and passive consumers. A level of compensation that is high enough for passive consumers will be gamed by prosumers.

Policy implications for achieving the carbon emission reduction target by 2030 in Japan-Analysis based on a bilevel equilibrium model

In Japan, the National Intended Determined Contributions (INDCs) towards post-2020 GHG emission reductions indicates a reduction of 26.0% is expected by the fiscal year 2030. However, regional emissions allowances have not been fully discussed based on Japan's INDCs target, which considers the regional socio-economic features. Given this, this study points out a soft-path for a fair and efficient quota allocation by proposing an integrated bilevel equilibrium model within a hierarchical structure consisting of the national government and 47 prefectural governments. This proposed model can be changed into a single level solvable equilibrium model, which can be solved by Particle Swarm Optimization (PSO) method. The major findings show that Hokkaido, Tokyo and Osaka were allowed the largest emissions quotas, while Tottori, Saga and Okinawa had the lowest emissions quotas. And the equity is necessary to be considered along with improving the emissions efficiency when reallocating carbon emission quotas, otherwise, the initiative to reduce emissions will not take place in prefectures with higher efficiency performance. Based on the findings, energy policy implications can be generated based on the above quantitative analysis to form a fair and efficient emission quota system at a sub-national level.

Electricity wholesale market equilibrium analysis integrating individual risk-averse features of generation companies

With the deregulation of world power markets, the importance of power market equilibrium analysis tools becomes more prominent. Due to the increasing uncertainty in the power markets, the influences of risk attitudes on the participants’ strategic bidding behaviors and market equilibrium become more significant, which makes risk feature formulation more necessary in the market bidding decision-making process. This paper fully considers the risk-averse features of power generation companies based on the concept of the conditional value at risk and proposes a bilevel equilibrium model to practically simulate market behaviors. The mathematical model is essentially a modified equilibrium problem with equilibrium constraints. The upper-level problem of the model maximizes the profits minus the risks of each generation company, while the lower-level problem represents the market clearing processes of day-ahead markets by the independent system operator. A linearization method is proposed to transform the proposed model into a mixed-integer linear model. An illustrative example and a numerical example are performed to show the effectiveness, validity and adaptability of the proposed model. The comparisons with other equilibrium models demonstrate the better performances of the proposed method to simulate the market equilibrium with several oligopolies. The sensitivity analysis is proposed to analyze the phenomenon where different risk-averse levels and market ownership structures would result in different market equilibrium.

Mechanisms to Coordinate Storage Investment and Network Expansion in Distribution Networks

In this paper we propose a bi-level equilibrium model that allows to analyze the impact of different regulatory frameworks on storage and network investment in distribution networks. In our model, a regulated distribution system operator decides on network investment and operation while he anticipates the decisions of private agents on storage investment and operation. As adjustments of the current regulatory framework, we consider curtailment of renewable production, the introduction of a network fee based on the maximum renewable feed-in, and a subsidy scheme for storage investment. The performance of the different alternative frameworks is compared to the performance under rules that are commonly applied in various countries today, as well as to a system-optimal (first-best) benchmark. To illustrate the economic effects, we calibrate our model with data from the field project Smart Grid Solar. Our results reveal that curtailment and a redesign of network fees both have the potential to significantly reduce total system costs. On the contrary, investment subsidization of storage capacity has only a limited impact as long as the distribution system operator is not allowed to intervene in storage operation.

Market equilibria and interactions between strategic generation, wind, and storage

Rising wind penetrations can suppress wholesale energy prices by displacing higher-cost conventional generation from the merit order. Wind suffers disproportionately from this price suppression, because the price is most suppressed when wind availability is high, hindering wind-investment incentives. One way to mitigate this price suppression is by wind exercising market power, which introduces efficiency losses. An alternative is to use energy storage, which allows energy to be stored when wind availability is high. This stored energy is later discharged when wind availability is lower and prices are higher.This paper proposes a bilevel equilibrium model to study market equilibrium interactions between energy storage and wind and conventional generators. We represent the market interaction using an equilibrium problem with equilibrium constraints. An illustrative case study is used to demonstrate the social welfare and profit benefits of using energy storage in this manner.

Evaluating the Contribution of Energy Storages to Support Large-Scale Renewable Generation in Joint Energy and Ancillary Service Markets

Energy storage systems (ESSs) are of great value to realize energy management and to support large-scale renewable generation. The combined operation of ESSs and renewables is one way to achieve output levelling and to improve the integration of sustainable energy. However, in a market-based environment, ESSs would make strategic decisions on self-schedules and arbitrage in energy and ancillary service markets, maximizing the overall profits. Will the strategic operation of ESSs promote renewable generation integration? To explicitly answer this question, this paper proposes a multi-period Nash-Cournot equilibrium model for joint energy and ancillary service markets to evaluate the contribution of the ESSs for supporting renewable generation. Then, a reformulation approach based on the potential function is proposed, which can transform the bi-level equilibrium model into an integrated single-level optimization problem to enhance the computation efficiency. Numerical examples are implemented to validate the effectiveness of the reformulation technique. The results of the case study indicate that the ESSs indirectly but substantially provide improved flexibilities while pursuing individual profit maximization.

Capacity Expansion Equilibria in Liberalized Electricity Markets: An EPEC Approach

This paper presents a novel way to model the generation capacity expansion problem in a liberalized framework via a multi-year bilevel equilibrium model. In the upper level the competing generation companies maximize their individual profits, while the lower level represents the market using a conjectured-price response approach, which allows us to vary the strategic spot market behavior, to see how much the reigning competitive behavior impacts investment decisions. The bilevel equilibrium model is formulated as an equilibrium problem with equilibrium constraints, transformed into a mixed integer linear program and solved as such using diagonalization in order to verify equilibria. We present a case study to apply this new modeling approach and to demonstrate that the proposed equilibrium problem with equilibrium constraints can have multiple solutions whose respective investments can vary.