Exploring how to incentivize power plant construction in the face of uncertainty, market power, and regulations.
Ensuring a reliable supply of electricity is crucial for modern society. But how do we make sure enough power plants are built to meet demand, especially when the future is uncertain and companies might act strategically? This article explores the challenges of resource adequacy in electricity markets and delves into the ideas presented in the paper "Identifying optimal capacity expansion and differentiated capacity payments under risk aversion and market power: A financial Stackelberg game approach" by Bichuch, Hobbs, and Song.
We'll use interactive visualizations to understand the core concepts, aiming for intuition rather than getting lost in complex mathematics right away.
In a perfect, theoretical electricity market, the price of energy ($/MWh) fluctuates based on supply and demand. During times of scarcity (high demand, low supply), prices should rise significantly. These high prices are supposed to signal the need for new power plants and provide the revenue to build them, especially for peaking power plants (or "peakers") that only run during these high-demand periods.
However, real-world markets often have price caps ($M$) imposed by regulators to protect consumers from extremely high prices. While well-intentioned, these caps can prevent peaker plants from earning enough revenue during scarce hours to cover their large investment costs ($F$). This is known as the missing money problem.
Imagine a simple peaking power plant. It has an annual investment cost that needs to be recovered. It only makes money when the electricity price is high, but there's a cap on how high the price can go.
With the current settings, the price cap prevents the peaker from recovering its investment cost. No rational investor would build it!
To address the missing money problem, many electricity markets introduce capacity payments ($C$). These are payments made to generators simply for being available, measured in $/MW/year, regardless of how much energy they actually produce. The idea is to provide an additional revenue stream to cover investment costs.
The System Operator (SO) - the entity managing the grid and market - typically sets or oversees these payments.
Let's add a capacity payment to our previous example. Can the SO set a payment ($C$) that makes the peaker plant viable?
(Investment Cost, Price Cap, and Scarcity Hours are carried over from the previous section.)
Adjust the capacity payment slider. Try to find the minimum payment needed for the plant to break even (Profit ≥ 0).
Okay, so capacity payments can fill the revenue gap. Problem solved? Not quite.
Power plant owners aren't just passive recipients of payments. They are businesses aiming to maximize profits. They might realize that if *everyone* builds less capacity, scarcity will be more frequent, driving up energy prices (even with a cap, prices might hit the cap more often or stay high just below it longer) and potentially leading the SO to offer higher capacity payments in the future. This strategic interaction, where firms anticipate each other's actions, is often modeled as a Nash Equilibrium.
The paper models this as a game in the *investment stage*: given the SO's capacity payment rules, suppliers strategically decide *how much* capacity ($K$) of each type to build.
Building and operating power plants involves uncertainty. Future demand, fuel prices, energy prices, and even the capacity payments themselves might fluctuate. Investors and companies are often risk-averse – they prefer a more certain outcome over a risky one, even if the average expected payoff is the same.
This is typically modeled using a utility function, which represents satisfaction or preference. For risk-averse entities, the utility gained from an extra dollar decreases as wealth increases. A common form is the negative exponential utility function: $U(x) = -e^{-\gamma x}$, where $x$ is the monetary outcome (e.g., profit) and $\gamma$ is the coefficient of risk aversion. Higher $\gamma$ means higher risk aversion.
Consider an investment choice: Option A gives a certain profit of $50K. Option B gives a 50% chance of $0K profit and a 50% chance of $110K profit. The *expected* profit of Option B is (0.5 * 0) + (0.5 * 110) = $55K, which is higher than Option A.
How does risk aversion affect the choice? We calculate the *expected utility*.
Utility Function: $U(x) = 1 - e^{-\gamma x}$ (scaled for plotting)
Adjust the risk aversion slider. Notice how higher risk aversion makes the uncertain (but higher expected profit) Option B less attractive compared to the certain Option A.
In electricity markets, higher risk aversion might lead suppliers to demand higher capacity payments to compensate for uncertainty, or favor investments with more predictable revenue streams, potentially distorting the optimal generation mix.
The System Operator (SO) faces a complex task. It wants to ensure reliability and keep costs low for consumers, but it must account for the strategic behavior (market power) and risk preferences of the suppliers.
The paper models this interaction as a Stackelberg game, a type of leader-follower game:
This structure is mathematically formulated as a Mathematical Program with Equilibrium Constraints (MPEC). The SO's optimization problem has a constraint that requires the suppliers' decisions ($K$) to be a Nash Equilibrium of *their* game, given the SO's choice of $C$.
A key question the paper explores is whether the SO should set a *uniform* capacity payment for all technologies or *differentiate* payments based on technology type (e.g., pay more for nuclear than for gas).
Let's simulate a simplified version of this market. We have three generator types: Baseload (high investment cost $F$, low operating cost $G$), Peaker (low $F$, high $G$), and Renewable (medium $F$, near-zero $G$, but maybe less reliable or needing specific conditions - simplified here). The SO sets capacity payments ($C_{base}, C_{peak}, C_{ren}$). Suppliers decide how much capacity ($K_{base}, K_{peak}, K_{ren}$) to build.
Adjust the SO's strategy and market conditions. Observe the impact on built capacity, costs, and reliability. (Note: This is a highly simplified model for illustration).
(LOLE = Loss of Load Expectation, hours per year demand might exceed supply. Lower is better.)
The paper, through its more complex mathematical model and analysis, provides several key insights, some of which you might observe in the simplified simulation above:
Designing electricity markets to ensure resource adequacy is a complex balancing act. Simple energy prices are often insufficient due to price caps (the missing money problem). While capacity payments can help, their optimal design must consider the realities of market power (strategic supplier behavior) and risk aversion.
The research suggests that sophisticated approaches, like the Stackelberg game model allowing for differentiated capacity payments, can provide valuable insights. By understanding these interactions, policymakers and regulators can design smarter market rules that better navigate the trade-offs between reliability, cost, and the strategic incentives of market participants, ultimately helping to keep the lights on affordably and reliably.