Strategic Bidding Research Articles

Solar Market Frictions: The Role of Platforms and Policies

Abstract This paper estimates a structural model of the solar photovoltaic (PV) installation market using detailed data from an online platform. The model incorporates households' solar installation choices and sellers' strategic bidding. Counterfactual simulations evaluate how equilibrium outcomes respond to changes in market structure and government subsidies, yielding two main results: (1) an increase from one to five bids through the platform reduces gross installation prices by $4,000 (15.5%), and (2) the U.S. Solar Investment Tax Credit increases total surplus on the platform by $1.35 per dollar of subsidy expenditure by mitigating market power and reducing pollution externalities.

Strategic behavior in TSO-DSO coordinated flexibility markets: A Nash equilibrium and efficiency analysis

This paper investigates the way in which the design of a TSO-DSO coordinated flexibility market can enable strategic behavior by flexibility service providers (FSPs). Multiple flexibility market models are considered for the procurement of flexibility services by transmission and distribution system operators, namely: a common (joint) market, a fragmented market, and a sequential multi-level market. Considering these market models, three non-cooperative games are introduced to investigate the strategic bidding and interaction between FSPs therein. Detailed conclusions are then drawn on the existence and uniqueness of Nash Equilibria (NEs) in the developed games, including derivations of closed-form expressions of the resulting NEs and corresponding price-of-anarchy, capturing the FSPs’ strategic bidding impact on the markets’ efficiency. The analysis considers – first in a duopoly setting, then with multiple players – three different use cases representing when: (1) a sufficient flexible capacity exists (sufficient flexibility offered from the FSPs and adequate interconnection/grid capacity between systems); (2) participants have a scarce flexibility capacity; and (3) a restrictive interface capacity exists between the systems. A case study considering an interconnected transmission–distribution system and multiple FSPs corroborates the analytical findings. The obtained results show that market participants have incentives to set bid prices greater than their marginal costs, thus decreasing the markets’ efficiency. This aspect is shown to be more pronounced when the available flexible capacity is limited, a restrictive line limit is present, or when the market is fragmented, thus supporting the need for additional network investments and the creation of joint flexibility market formats.

A bilevel programming approach to price decoupling in Pay-as-Clear markets, with application to day-ahead electricity markets

Motivated by the recent crisis of the European electricity markets, we propose the concept of Segmented Pay-as-Clear (SPaC) market, introducing a new family of market clearing problems that achieve a degree of decoupling between groups of participants. This requires a relatively straightforward modification of the standard PaC model and retains its crucial features by providing both long- and short-term sound price signals. The approach is based on dynamically partitioning demand across the segmented markets, where the partitioning is endogenous, i.e., controlled by the model variables, and is chosen to minimise the total system cost. The thusly modified model leads to solving Bilevel Programming problems, or more generally Mathematical Programs with Complementarity Constraints; these have a higher computational complexity than those corresponding to the standard PaC, but in the same ballpark as the models routinely used in real-world Day Ahead Markets (DAMs) to represent “nonstandard” requirements, e.g., the unique buying price in the Italian DAM. Thus, SPaC models should still be solvable in a time compatible with market operation with appropriate algorithmic tools. Like all market models, SPaC is not immune to strategic bidding techniques, but some theoretical results indicate that, under the right conditions, the effect of these could be limited. An initial experimental analysis of the proposed models, carried out through Agent Based simulations, seems to indicate a good potential for significant system cost reductions and an effective decoupling of the two markets.

Strategic bidding by predicting locational marginal price with aggregated supply curve

Price-makers in the generation sector can utilize offer data published by independent system operators (ISOs) for strategic bidding. Many research uses system-wide offer information for strategic bidding because individual offers are usually published with masked identifications. However, these methods are not applicable in markets with transmission congestion because the nodal information is not used. A research gap remains in using system-wide offer information and accessible nodal information for strategic bidding in markets with congestion. System-wide aggregated supply curves can be formed just with anonymous offers, and locational marginal price (LMP) is accessible nodal data containing the congestion information. This paper proposes a framework for price-makers to bid strategically by predicting LMPs with aggregated supply curves. A feature extraction method is proposed to make aggregated supply curves applicable for LMP prediction, and the maximal information coefficient is developed for feature selection. A convolutional neural network is combined with a long short-term memory network to model the impact of aggregated supply curves on LMPs. In this framework, price-makers can investigate the impact of their strategies on aggregated supply curves, predict LMPs with aggregated supply curves, and make the optimal bidding strategies. Numerical results based on the PJM-5 bus system and real data from the Midcontinent Independent System Operator validate the effectiveness of the proposed framework.

Distribution and transmission coordinated dispatch under joint electricity and carbon day-ahead markets

Worldwide efforts to attain a more renewable-based energy matrix have led to the creation of carbon emission-related markets. Simultaneously, the increasing penetration, mostly of renewable-based sources, in distribution networks may allow distribution system operators (DSOs) to change their traditional participation in wholesale markets as passive buyers. Over the last few years, many authors have investigated and proposed optimization models for the strategic participation of DSOs in electricity markets. Nonetheless, proposals regarding the DSO as a strategic agent in both electricity and carbon-related markets are rare. In this paper, we propose a stochastic bilevel formulation to address this gap. The economic and operational constraints of each stakeholder are considered in the model. Additionally, the problem is written in a convex formulation for which finite convergence to optimality is guaranteed. The formulation was tested for a 14-node transmission system and a 34-node distribution system in which dispatchable and non-dispatchable energy sources, energy storage systems, and demand response units are installed. The results show the DSO’s capacity to place strategic bids in both market environments to maximize its profit, which features intentionally taking financial losses in the carbon allowance market to maximize the overall profit due to the income maximization in the electricity market. Finally, an additional case study with a 123-node distribution system shows the proposed method’s scalability.

Strategic Behavior of Competitive Local Citizen Energy Communities in Liberalized Electricity Markets

The liberalization of energy retail markets empowered consumers with the ability to be part of new emerging entities, such as Citizen Energy Communities. With the increasing penetration of decentralized variable generation, communities have the advantage of incentive local carbon neutrality and sustainability. Local generation reduces transport grid usage and costs to consumers. Furthermore, worldwide legislation incentives energy communities by providing them discounts to other fee parts of the tariff apart from wholesale prices. This paper presents a model of strategic behavior, investment, and trading of energy communities. The model comprises the investment in local renewable generation, the design of competitive tariffs, and strategic bidding on wholesale markets. Consumers have an optimization model that selects the retail tariff that minimizes their costs with energy. These models are tested using data from Portuguese consumers and the Iberian electricity market. Results from the study indicate that inflexible consumers may reduce their costs by 29% by being part of the community. Furthermore, they have the potential to reduce their costs above 50% when using demand–response, adapting themselves to local production and wholesale prices.

Micro-grid tri-level EPEC based model for finding equilibria in the day-ahead and balancing markets

This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state.

Intelligent strategic bidding in competitive electricity markets using multi-agent simulation and deep reinforcement learning

Aiming at the lack of comprehension of agents in Multi-Agent Simulation (MAS) based on classic Reinforcement Learning algorithms of competitive electricity markets, an intelligent strategic bidding method using Deep Reinforcement Learning (DRL) and MAS is proposed in this paper, which not only can provide more intelligent strategies for market participants to maximize their profits, but can enhance the performance of simulation models dealing with high-dimensional continuous data in electricity markets. Firstly, a theoretical framework of intelligent strategic bidding in competitive electricity markets based on MAS and DRL is proposed, and the process of intelligent bidding in electricity markets based on MAS and DRL is described. Then, three MAS models of intelligent strategic bidding are built based on three classic DRL algorithms, including Deep Q-Network (DQN), Double Deep Q-Network (DDQN), and Asynchronous n-step Q-learning (Async n-step QL), and three algorithms’ convergence speed, computational efficiency, and response sensitivity are compared and analyzed. Finally, a novel Improved Async n-step QL (IAsync n-step QL) algorithm is proposed, the MAS model based on the IAsync n-step QL algorithm for intelligent strategic bidding is established. Simulation results show that the model using the novel DRL algorithm is more profitable and responsive than the classic DRL algorithms.

Identification of Joint Strategic Bidding Considering Spatial Correlation of Electricity Prices

Identification of Joint Strategic Bidding Considering Spatial Correlation of Electricity Prices

Dual-Sided Involvement of Energy Optimization and Strategic Bidding in Wind-PV System to Maximize Benefits for Customers and Power Providers

Dual-Sided Involvement of Energy Optimization and Strategic Bidding in Wind-PV System to Maximize Benefits for Customers and Power Providers

Econometric modeling of carbon price impacts on the bidding mechanism between different energy sources in the electricity market

Abstract Virtual power plants (VPPs) can aggregate different energy sources into a whole to participate in the electricity market and carbon trading market, and as the scale of VPPs continues to expand, they will also be transformed from the original price takers to price makers. The paper considers VPP as a price setter and suggests a two-tier bidding strategy for the VPP day-ahead electricity market that incorporates the impact of the carbon price. Among them, the upper-layer model aims to maximize the expected revenue of VPP, while the lower-layer model aims to minimize the system clearing cost. The dynamic carbon emission factor is used in the strategy to create a market incentive factor that corrects the offer price of each unit before clearing it again. Finally, the optimal bidding strategy, as well as the operation plan of the VPP, are given through an arithmetic example, and the impact of the uncertainty in the wind farm output forecast in the VPP on the expected return of the VPP is analyzed. The impact of carbon prices on power prices, output, and rates of energy demand change are further explored to provide a basis for the compensation mechanism for ecological protection of carbon values. The arithmetic example shows that VPP can influence the market price through strategic bidding decisions, and after considering the carbon price, the power market clearing price is 4.46 yuan/MWh, and the maximum gain is obtained as 225.54. The consumption rate of new energy units such as WT and PV is increased, the carbon emissions are reduced, and the total gain of VPP is increased. The increase in carbon prices and the offer of traditional generators increase the amount of electricity cleared by renewable energy units, while the increase in carbon quota ratio and the offer of new energy generators increase the average clearing price.

Auctions with Endogenous Initiation

ABSTRACTWe study initiation of takeover auctions by potential buyers and the seller. A bidder's indication of interest reveals that she is optimistic about the target. If bidders' values have a substantial common component, as in takeover battles between financial bidders, this effect disincentivizes bidders from indicating interest, and auctions are seller‐initiated. Conversely, in private‐value auctions, such as battles between strategic bidders, equilibria can feature both seller‐ and bidder‐initiated auctions, with the likelihood of the latter decreasing in commonality of values and the probability of a forced sale by the seller. We also relate initiation to bids and auction outcomes.

A reinforcement-probability Bayesian approach for strategic bidding and market clearing for renewable energy sources with uncertainty

With the participation of renewable energy sources (RESs) in the electricity market, the inherent uncertainty brings new challenges for strategic bidding and market clearing in the electricity market. In this paper, the market structure is formulated as a non-cooperative game among power suppliers, consumers, and the market operator. A reinforcement-probability Bayesian approach is proposed to obtain the optimal bidding strategy of RESs and achieve maximal social welfare at the market clearing, considering uncertain cost types of RESs and incomplete market information. First, a reinforcement-probability model is presented to obtain the optimal agent-type-strategy combination considering the uncertainty of cost type selection. A agent-type-probability algorithm is proposed for the model to update the mean of probability density function of cost types according to the expected profit. Second, an incremental-cost-based distributed algorithm is proposed to solve the market clearing problem, which accelerates the convergence rate without violating the system constraints via feedback from the scheduled power. Finally, a Bayesian probability model is proposed for RESs to learn the hidden information of the market and transform the incomplete information electricity market into a complete one. A Bayesian Nash equilibrium is reached in the model. To coordinate the information among market participants, the output of the Bayesian probability model is calculated by the Hysteretic Q-learning algorithm and used as the reward to update the agent-type-probability in the reinforcement-probability model. An illustrative example is presented to demonstrate the effectiveness of the proposed approach, which shows that the proposed approach has a better convergence performance and has a 2–6 times faster learning speed compared with the policy gradient and deep Q-network.

An optimization-based partial marginal pricing method to reduce excessive consumer payment in electricity markets

Among the pricing schemes, locational marginal pricing is the most widely adopted scheme in current electricity markets. Despite the nice properties, theoretical study and practical experience have shown that considering the strategic bidding behaviors of market participants, locational marginal pricing may result in excessive consumer payment and prejudices market efficiency. In this paper, we propose an optimization-based partial marginal pricing method to reduce consumer payment under strategic bidding. The advantages of the locational marginal pricing method are reserved to the best extent while the remaining problems are delicately handled. To achieve this, we first analyze the characteristics and problems of the locational marginal pricing scheme and present a partial marginal pricing structure. Second, we establish an optimization-based partial marginal pricing model, in which discriminatory price components are introduced in price formulation and the pricing properties including competitive equilibrium and revenue adequacy are formulated as constraints. Third, to verify the performance of the proposed pricing scheme considering the strategic bidding, a bi-level strategic bidding problem of the generator under the proposed pricing method is established and transformed into a mixed integer linear programming problem. The numerical results indicate that under the conventional pricing methods, the consumer payments under strategic bidding can be up to 16.67 times higher than those under truthful bidding, while the proposed method can effectively reduce excessive consumer payments by 92.1% while maintaining the desired pricing properties.

Stochastic bidding for VPPs enabled ancillary services: A case study

Strategic bidding which aims to optimally harvest the price difference in the wholesale electricity market can efficiently allocate VPPs’ aggregated resources to provide large flexibility for energy and frequency regulation (FR), aiding in the real-time rebalancing of supply and demand. However, the uncertainty of renewable energy results in substantial imbalances between supply and demand, which causes high randomness of system frequency deviation and significant price fluctuations in the electricity market, making bidding challenging. To tackle these issues, a risk-averse optimal bidding strategy is proposed for VPPs to participate in both energy and FR markets. Moreover, a payment recovery mechanism is designed to recover the cost of FR undersupply. Specifically, each VPP submits bids to maximize profit, while the market operator clears the market and penalizes undersupply through the payment recovery mechanism. The existence of Nash equilibrium is proved, and a distributed best response algorithm is implemented to calculate the risk-averse optimal bidding strategy, taking into account Denial-of-Service attacks. The mean-convergence and variance-convergence of our proposed algorithm are derived. A case study of Australian National Electricity Market (NEM) validates the effectiveness of the proposed method in reducing overbidding risk, strengthening FR service reliability and improving profits for VPPs.

A Nash–Stackelberg game approach to analyze strategic bidding for multiple DER aggregators in electricity markets

A Nash–Stackelberg game approach to analyze strategic bidding for multiple DER aggregators in electricity markets

A data-driven Stackelberg game approach applied to analysis of strategic bidding for distributed energy resource aggregator in electricity markets

In the context of the participation of distributed energy resource (DER) aggregators in day-ahead energy and reserve markets, most of the existing analysis models of strategic bidding behavior of DER aggregators ignore the consideration of the safe operation of distribution systems. To this end, this paper builds a one-leader multi-follower Stackelberg game model considering the safety checking of distribution systems with the discrete features of capacitor banks and tap ratio of the substation transformer in the lower level. Mathematically, this model constitutes a bi-level mixed-integer nonlinear programming (BMINLP) problem. We convert the BMINLP model to a bi-level mixed-integer linear programming (BMILP) model based on KKT conditions, strong duality theorem, and big-M approach, which is still difficult to be solved directly. As a result, we propose a customized data-driven algorithm based on sampling without tuning hyper-parameters and an improved linear surrogate function method, to accurately fit the corresponding constraints of the lower-level model of BMILP problem, and then transform the BMILP problem into a single-level mixed-integer linear programming (MILP) problem to solve. The simulation of data-driven algorithm and comparison with the particle swarm optimization algorithm shows the high practicability of the bi-level Stackelberg game model and the effectiveness of the data-driven algorithm.

Optimal bidding strategies of advanced adiabatic compressed air energy storage based energy hub in electricity and heating markets

Integration of power and heating systems can not only improve energy efficiency but also reduce the peak generation capacity by narrowing the gap between peak and valley demands. Advanced adiabatic compressed air energy storage (AA-CAES) is a large-scale and environmental-friendly storage technology that can supply heat and power. It can be adopted as an energy hub that integrates electricity and heating systems. This paper studies the strategic behavior of an AA-CAES based energy hub in deregulated electricity and heat markets. Firstly, a heat market clearing model with elastic thermal demands is developed, and the impact of demand elasticity on the stability of the heat market is analyzed. Secondly, based on the proposed heat market model, a bi-level optimization model is established to explore the strategic bidding and scheduling of the merchant AA-CAES based energy hub in both markets. Through exploiting the weakly coupling structure of the bi-level problem, a special decomposition method is proposed to compute the market equilibrium. The optimal response of the lower-level power/heat market clearing problem is analytically expressed by multi-parametric programming techniques, where the bidding strategies are parameters. With the lower-level parameterized solution, the original complex joint optimization problem is transformed into a small-scale mixed integer quadratic program with only a few binary variables, and thus can be solved efficiently. Case studies verify the proposed model and method. Results show that the AA-CAES based energy hub/heat market is conducive to an 8.6%/22.5% reduction in the operation cost of the heat market/energy hub.

Analysis of strategic bidding of a DER aggregator in energy markets through the Stackelberg game model with the mixed-integer lower-level problem

An open electricity market environment provides sufficient conditions for a distributed energy resource (DER) aggregator to participate in the day-ahead electricity market. Therefore, a one-leader multi-follower Stackelberg game model is developed to analyze the strategic bidding behavior of a DER aggregator and one of the lower-level problems is to check the security of the distribution system (DS), which is elaborated by the mixed-integer second-order cone programming (MISOCP) model considering the active power loss and discrete controls in the DS. Moreover, we first use the Karush–Kuhn–Tucker (KKT)-based reformulation approach to transform the model into a one-leader one-follower model. However, the objective function of the upper-level model cannot be completely linearized by using the strong dual theorem because the active power loss of the DS is considered in the lower-level security check problem. Therefore, we propose a piecewise linear approximation approach based on the data-driven algorithm to linearize the upper-level objective function. Moreover, we apply multivariate linear surrogation to transform this one-leader one-follower model into a single-level MISOCP model. Finally, we verify the correctness of the proposed algorithm by comparing it with the particle swarm optimization (PSO) algorithm in a small integrated transmission and distribution (T&D) system and validate the effectiveness of the proposed algorithm in a practical integrated T&D system.

Learning Active Constraints to Efficiently Solve Linear Bilevel Problems: Application to the Generator Strategic Bidding Problem

Bilevel programming can be used to formulate many problems in the field of power systems, such as strategic bidding. However, common reformulations of bilevel problems to mixed-integer linear programs make solving such problems hard, which impedes their implementation in real-life. In this paper, we significantly improve solution speed and tractability by introducing decision trees to learn the active constraints of the lower-level problem, while avoiding to introduce binaries and big-M constants. The application of machine learning reduces the online solving time, by moving the selection of active constraints to an offline process, and becomes particularly beneficial when the same problem has to be solved multiple times. We apply our approach to the strategic bidding of generators in electricity markets, where generators solve the same problem many times for varying load demand or renewable production. Three methods are developed and applied to the problem of a strategic generator, with a DCOPF in the lower-level. These methods are heuristic and as so, do not provide guarantees of optimality or solution quality. Yet, we show that for networks of varying sizes, the computational burden is significantly reduced, while we also manage to find solutions for strategic bidding problems that were previously intractable.