Dual-Layer Model Improves Energy Market Welfare

The study, published in the journal Energy Informatics, introduces a co-optimised structure that integrates physical energy dispatch with financial market participation, aiming to resolve the structural dislocation between operational energy flows and financial risk management. By treating these two aspects as a unified system rather than independent problems, the model seeks to capture the strategic behaviour of participants who simultaneously manage operational exposure and financial hedge positions.

The motivation for this research stems from the rapid transformation of global electricity systems, where the increasing share of wind and solar generation challenges traditional merit-order dispatch models. As renewable energy integration progresses, the variability of generation creates significant price volatility and revenue risks for generators. Existing trading models often treat physical and financial markets separately, overlooking the interdependence where forward positions influence physical offering incentives and clearing prices affect financial contract demand. This new framework aims to close that gap by formally linking the two layers through specific constraints and pricing signals.

The DLETM architecture organises the market into two interacting layers governed by a System Operator. The Physical Layer handles day-ahead and real-time energy exchange among renewable generators, prosumers, storage operators, and retailers. The Financial Layer facilitates forward contracts, green energy certificate trading, and risk hedging instruments. These layers are connected by the Cross-Layer Volume Consistency Constraint, which limits discrepancies between physical offers and forward positions, and the Dual-Layer Pricing Signal, which overlays prices from both layers into a single coordination signal broadcast by the System Operator at each stage transition.

To analyse the equilibrium of this complex market structure, the authors formulated the problem as a Generalized Nash Equilibrium Problem and reformulated it as a Variational Inequality. The study demonstrates that at least one Variational Equilibrium exists, providing a theoretical foundation for the stability of the proposed market design. The equilibrium conditions reveal how the dual variable associated with the consistency constraint acts as an endogenous interlinkage price, coordinating behaviour between the physical and financial layers without the need for centralised planning.

For computational tractability, the researchers developed the Augmented Lagrangian Decomposition with Primal-Dual Coupling algorithm, which enables decentralised computation of the market equilibrium. This algorithm incorporates a momentum acceleration term in the dual updates, which empirically reduces the number of iterations required for convergence by approximately 35% compared to standard Alternating Direction Method of Multipliers approaches. The decentralised nature of the algorithm is crucial for scalability, as it allows individual participants to solve their local subproblems in parallel while coupling them through dual variable updates, reflecting the practical constraints of real-world market operations.

Simulation experiments were conducted on a stylised market comprising 12 participants, including renewable generators, prosumer communities, storage operators, retailers, and a financial trader. The base case scenario assumed a 40% renewable penetration level, with 20 equiprobable scenarios used to represent renewable output uncertainty. The results indicated that the DLETM improved social welfare by 8.3% compared to single-layer benchmark models. Additionally, the model achieved a 21.7% reduction in physical price volatility and a 16.2% increase in renewable energy utilisation, demonstrating significant efficiency gains over existing market structures.

Sensitivity analyses further explored the impact of renewable penetration levels on market performance. The welfare benefit of the dual-layer architecture was found to increase as renewable penetration rose, reaching 14.2% at a 70% penetration level. This suggests that the value of integrating financial hedging into market design grows with the progression of the energy transition and the associated increase in renewable volatility. The analysis also identified an optimal range for the consistency constraint tolerance parameter, suggesting that regulators could tune this parameter to balance price stabilisation against operational flexibility for generators.

At the participant level, the model showed distinct benefits for different market actors. Risk-averse renewable generators experienced reduced revenue volatility and lower Conditional Value-at-Risk, as financial hedging allowed them to commit to higher physical outputs without bearing the full burden of price uncertainty. Prosumers benefited from additional revenue through green energy certificate trading, which complemented their peer-to-peer physical trading income. Storage operators captured intertemporal price spreads in the financial layer, increasing their daily profits compared to physical-only markets. Retailers achieved lower procurement costs and reduced tail risk, indicating that the dual-layer structure enhances efficiency for end-users as well.

The study acknowledges several limitations, including the absence of transmission network constraints, which would introduce locational marginal prices and alter the pricing signals. The renewable output scenarios were generated independently, ignoring spatial correlations between wind and solar resources that could affect risk structures. Furthermore, the financial instrument set was limited to forward contracts and green energy certificates, excluding options and other non-linear derivatives that might introduce non-convexities. The retailer demand was assumed to be price-inelastic, which may not reflect the behaviour of industrial consumers who can adjust consumption in response to price signals.

Despite these limitations, the findings suggest that formally coupling financial market infrastructure with physical dispatch mechanisms is becoming increasingly important for efficient market operation under high renewable penetration. The proposed model provides a principled mechanism for internalising the coordination externality between physical and financial layers, offering a potential pathway for market designers to enhance stability and welfare. Future research will focus on extending the model to include network constraints, multi-period capacity planning, and empirical validation using real-world market data from European or Australian electricity markets.

The mathematical formulation of the DLETM incorporates risk management directly into the objective functions of specific participant types. Renewable generators and retailers maximize expected profit while subtracting a penalty based on Conditional Value-at-Risk, a metric that quantifies the severity of potential losses in the worst-case scenarios. This approach reflects the reality that these actors face both quantity uncertainty from variable renewable output and price uncertainty from market fluctuations. In contrast, storage operators, financial traders, and the System Operator are modeled as risk-neutral in the base-case parameterisation, focusing instead on arbitrage opportunities and market clearing. The model also enforces a Truthful Offer Requirement, which audits reported costs against actual delivery patterns to prevent strategic capacity withholding in the physical layer, thereby ensuring that forward hedging does not coincide with artificial supply constraints.

The computational performance of the proposed ALD-PDC algorithm is sensitive to several structural parameters within the simulated market. The study identifies renewable penetration as the dominant factor influencing computational time, with an increase from 30% to 70% penetration resulting in an approximately 78% increase in total computation time. This occurs because higher penetration levels introduce greater scenario variability, which enlarges the feasible region for each participant’s stochastic subproblem and necessitates more solver iterations. Additionally, the tightness of the Cross-Layer Volume Consistency Constraint affects convergence speed; a tighter tolerance of 0.05 requires 112 iterations for convergence, compared to 87 iterations at a looser tolerance of 0.40. The momentum parameter in the dual update also plays a critical role, with a value of 0.3 reducing the required iterations from 142 to 92 in the base case, confirming the efficiency gains attributed to the accelerated update rule.

Specific participant outcomes in the base case illustrate the distribution of benefits across the market. Generator G2, identified as the most risk-averse wind generator with a coefficient of 0.5, experienced a 12.1% increase in revenue and a 31% reduction in Conditional Value-at-Risk compared to the physical-only benchmark. This improvement is attributed to a 65% forward hedge ratio, which converts uncertain spot sales into contractually certain forward sales. Prosumer communities P1 and P3 generated approximately 1,840 per day in green energy certificate revenue, representing about 18% of their total net revenue and providing a significant financial incentive for community photovoltaic investment. Storage operator S1 increased its daily profit by 12.0% to 4,120, a gain traced to the capture of intertemporal forward price spreads in the financial layer. Meanwhile, retailer R1 reduced its average procurement cost by 7.3% to 48.6 per MWh and lowered its procurement cost Conditional Value-at-Risk by 31%, demonstrating that the dual-layer structure benefits end-users by reducing both expected costs and tail risk.

The interlinkage price, represented by the dual variable of the consistency constraint, ranges between 2.1 and 8.7 per MWh across the 24-hour period in the base case. This price is highest during evening demand peaks, indicating that the constraint is binding when the incentive to deviate between physical and financial layers is greatest. The existence of this non-zero price confirms that the Cross-Layer Volume Consistency Constraint actively organizes behavior between the layers, internalizing the coordination externality that is absent in single-layer models. In the theoretical limit where the tolerance parameter approaches infinity, the layers decouple, and the interlinkage price approaches zero, recovering the independent equilibria of traditional market designs. Conversely, as the tolerance approaches zero, full volume consistency is imposed, and the financial price converges to the expected spot price under risk-neutrality, aligning with classical two-settlement market theory.

The study’s simulation design relies on specific assumptions that define the scope of its findings. The market comprises 12 participants, including four renewable generators with capacities of 200 MW each, three prosumer communities with a total of 120 MW of photovoltaic capacity, and two storage operators with capacities of 200 MWh and 80 MWh. Renewable uncertainty is represented by 20 equiprobable scenarios, with wind generation modeled using Beta distributions fitted to specific capacity factors and solar generation modeled using deterministic diurnal profiles disturbed by cloud-cover factors. The simulations were conducted on a workstation with an Intel Core i7-12700 processor and 32 GB of RAM, using CVXPY and Gurobi for optimization. While the results demonstrate significant efficiency gains in this stylised environment, the authors note that empirical validation using actual market data is required to confirm the generalisability of the findings, particularly given the exclusion of transmission network constraints and spatial correlations in renewable output.

Subject of Research: Dual-Layer Energy Trading Model for Renewable-Integrated Electricity Markets

Article Title: Energy financial market equilibrium analysis based on a new energy trading model

Article References: Zhao, S. (2026). Energy financial market equilibrium analysis based on a new energy trading model. Energy Informatics, 9(1), Article 68. https://doi.org/10.1186/s42162-026-00671-4

Image Credits: AI Generated

DOI: 10.1186/s42162-026-00671-4

Keywords: Energy Informatics, Electricity Markets, Renewable Energy, Financial Hedging, Market Equilibrium, Generalized Nash Equilibrium, Variational Inequality, Price Volatility, Green Energy Certificates, Storage Operators, Energy, financial