Voluntary Renewable Programs: Optimal Pricing and Revenue Allocation

Abstract

This paper develops a multi-period optimization framework to design a voluntary renewable program (VRP) for an electric utility company, aiming to maximize total renewable energy deployments. In the business model of VRP, the utility must ensure it generates renewable energy up to the total amount of contract during each market episode (i.e., a year), while all the revenue collected from the VRP must either be used to invest in procuring renewable capacities or to maintain the current renewable fleet and infrastructure. We thus formulate the problem as an optimal pricing problem coupled with revenue allocation and renewable deployment decisions. We model the demand function of voluntary renewable contracts as an exponential decay function based on survey data. We analytically derive the optimal pricing policy of the VRP as a function of the current grid carbon intensity. We prove that a myopic policy is conditionally optimal, which maximizes renewable capacity in each period, attains the long-run optimum due to the utility's revenue-neutral constraint. We show different binding conditions and marginal values of decision variables correspond to different phases of the energy transition, and that the utility should strategically design its revenue-sharing decisions, balancing investments in renewable expansion and subsidizing existing renewable fleets. Finally, we show that voluntary renewable programs can only extend renewable penetration but cannot achieve net-zero emissions or a fully renewable grid. This pricing-allocation-expansion framework highlights both the potential and limitations of voluntary renewable demand, providing analytical insight into optimal policy design and the qualitative shifts occurring during the energy transition process.

Figures (2)

• Figure 1: Multi-period simulation under baseline demand. The figure summarizes system evolution across multiple decision periods: (1) cumulative renewable capacity $Q_t$, (2) modeled renewable (wind) generation percentage, (3) grid emissions intensity $e(Q_t)$, (4) optimal renewable program price $p_t^*$, (5) renewable capacity expansion $q_t^*$, and (6) revenue-sharing ratio $\gamma_t^*$ between the program operator and renewable generators. Together, these panels illustrate how VRP revenues can sustain continued renewable deployment while ensuring financial feasibility and declining grid emissions intensity.
• Figure 2: Grid-property visualization for the ISO-NE test system. Subfigure 1 shows the carbon intensity of the grid when operational prediction error and uncertainty are incorporated, while Subfigure 2 shows the corresponding relationship under perfect prediction for comparison. Subfigure 3 reports effective renewable output as a function of installed wind capacity, accounting for curtailment, and exhibits the broadly concave pattern assumed in the model. Subfigure 4 shows the wholesale market price received by renewable generation (wind) as wind capacity increases. This relationship is monotonically decreasing but neither globally convex nor concave, highlighting the nonlinear effects of uncertainty and market-clearing dynamics in the power system.

Theorems & Definitions (21)

• Theorem 1: Single-Period Optimal Pricing
• Corollary 1: Single-period expansion under the optimal price
• Corollary 2: Optimal Price Decreases with Renewable Capacity
• Proposition 1: General Pricing Reduction
• Theorem 2: Existence and uniqueness of the long-run capacity limit
• Proposition 2: Non-vanishing emissions at the long-run limit
• Corollary 3: Market-driven nature of the long-run capacity limit
• Remark 1: Markovian structure and profit-neutral regulation
• Theorem 3: Myopic policy optimality under monotone reachability
• Corollary 4: Minimum hitting time