Abstract

The paper addresses the inadequacy of traditional generation expansion planning (GEP) methods in competitive electricity markets. While conventional approaches minimized system-wide costs, the new framework emphasizes profit-maximization for privatized generation firms. A game-theoretic model is proposed to account for firms' independent decision-making under competitive conditions.

Key Points

Traditional GEP Challenges

• Traditional GEP minimizes costs considering:
  • Construction and operating costs.
  • Reliability criteria such as Loss-of-Load Probability (LOLP).
  • Constraints on fuel mix, capacity additions, and reserve margins.
    Formulated as:
    $\min \sum_{t=1}^{T} \left[ f_1(U_t) + f_2(X_t) - f_3(U_t) \right]$
    Subject to:

Where:

Market-Based GEP Model

• Shifts focus to profit-maximization for individual firms in a competitive environment.
• Modeled as a non-cooperative game with Nash equilibrium.
• Profit Function For firm 𝑖 the objective is:
  $\max \sum_{t=1}^{T} \left[ f_t(X_t) - g_t(U_t) - h_t(X_t) - k_t(U_t) \right]$

Where:

• Nash Equilibrium
  Firms interact under constraints, and Nash equilibrium is defined as:

Numerical Simulation

• Example with two firms (A and B) operating oil and coal plants.
• Decision variables include plant size, type, and timing.
• Results:
  Firm A's strategy: Add two 50 MW coal plants.
  Firm B's strategy: Add one 40 MW and one 20 MW oil plant.
  Profits at Nash equilibrium:
  $\text{Firm A:} \quad \Pi_A = 39,089 \, [\text{k\$}], \\ \text{Firm B:} \quad \Pi_B = 58,117 \, [\text{k\$}].$

Conclusion

• The paper proposes a novel framework for addressing generation expansion planning (GEP) in the context of competitive electricity markets, where the traditional centralized, cost-minimization approach is no longer effective. The competitive environment introduced by deregulation has shifted the focus from system-wide cost efficiency to profit maximization for individual generation firms. These firms must now make strategic decisions independently, based on their own financial goals, market conditions, and expectations for future energy prices.

• The key contribution of the study lies in the development of a game-theoretic model that effectively captures the interactions among competing firms in the electricity market. Unlike conventional GEP models, which rely on centralized planning to minimize costs, the proposed model treats GEP as a non-cooperative game where firms aim to maximize their individual payoffs. The model incorporates essential market dynamics, including constraints on reliability (e.g., reserve margins and Loss-of-Load Probability) and technical limitations (e.g., construction capacity and fuel diversity).

• The study demonstrates the practicality of the model through a numerical example based on realistic data. By solving the GEP problem under Nash equilibrium conditions, the model determines optimal expansion strategies for firms, ensuring that their decisions align with both profitability and power system reliability. The simulation results reveal that the proposed method can guide firms to achieve profitable outcomes while adhering to system-wide reliability constraints, such as maintaining adequate reserve margins and LOLP thresholds.

• The study also highlights the computational efficiency of the proposed model. By reducing the solution space through firm-specific constraints, the model avoids the combinatorial explosion typical of traditional GEP methods. This makes it more suitable for real-world applications in competitive market environments.

Practical Implications

• The proposed model has significant implications for policy-makers, regulators, and generation firms. For policy-makers, the study emphasizes the importance of creating market structures that incentivize firms to invest in new generation capacity while maintaining system reliability. For generation firms, the model offers a strategic tool to evaluate investment decisions under competitive conditions, helping them balance profitability with compliance to reliability standards.