Price-Based Market Clearing with V2G Integration Using Generalized Benders Decomposition

Currently, most ISOs adopt offer cost minimization (OCM) auction mechanism which minimizes the total offer cost, and then, a settlement rule based on either locational marginal prices (LMPs) or market clearing price (MCP) is used to determine the payments to the committed units, which is not compatible with the auction mechanism because the minimized cost is different from the payment cost calculated by the settlement rule. This inconsistency can drastically increase the payment cost. On the other hand, payment cost minimization (PCM) auction mechanism eliminates this inconsistency; however, PCM problem is a nonlinear self-referring NP-hard problem which poses grand computational burden. In this paper, a mixed-integer nonlinear programing (MINLP) formulation of PCM problem are presented to address additional complexity of fast-growing penetration of Vehicle-to-Grid (V2G) in the price-based market clearing problem, and a solution method based on the generalized benders decomposition (GBD) is then proposed to solve the V2G-integrated PCM problem, and its favorable performance in terms of convergence and computational efficiency is demonstrated using case studies. The proposed GBD-based method can handle scaled-up models with the increased number of decision variables and constraints which facilitates the use of PCM mechanism in the market clearing of large-scale power systems. The impact of using V2G technologies on the OCM and PCM mechanisms in terms of MCPs and payments is also investigated, and by using numerical results, the performances of these two mechanisms are compared.

💡 Research Summary

The paper addresses a fundamental inconsistency in most electricity markets: the clearing algorithm (usually an Offer Cost Minimization, OCM, problem) minimizes total bid cost, while the settlement rule (pay‑as‑MCP or pay‑as‑LMP) uses market‑clearing prices that are not guaranteed to be the same as the minimized cost. This mismatch can dramatically increase the actual payments that market participants receive.
To eliminate the inconsistency, the authors adopt a Payment Cost Minimization (PCM) auction mechanism, where the market‑clearing price itself is a decision variable and the objective directly minimizes the total payment cost (including fixed, startup and shutdown costs). PCM, however, is a self‑referring, nonlinear, mixed‑integer problem (NP‑hard), especially when Vehicle‑to‑Grid (V2G) resources are incorporated.
The paper first formulates two problems:

1. OCM‑V2G – a mixed‑integer linear program (MILP) that minimizes the sum of offer prices (treated as constants) plus fixed and startup/shutdown costs, subject to generation limits, ramping, V2G charging/discharging limits, and energy‑balance constraints.
2. PCM‑V2G – a mixed‑integer nonlinear program (MINLP) where the market‑clearing price MCP(t) is a variable. The key constraint forces MCP(t) to be at least as large as every accepted offer (MCP(t) ≥ B_i(t)·u_i(t)). The objective contains products of MCP(t) and dispatched power p_i(t), creating non‑linearity.
   Because directly solving the MINLP is computationally prohibitive, the authors apply Generalized Benders Decomposition (GBD). Decision variables are split into:

• Y – the complicating variables (MCP(t)).
• X – all remaining continuous and binary variables (generation outputs, commitment statuses, V2G power and energy states, startup/shutdown costs).
  Fixing Y yields an optimality subproblem that is a MILP; its solution provides a lower bound and Lagrange multipliers (λ, μ). The master problem is a linear program that updates MCP(t) using the cuts generated from the subproblem. The algorithm iterates until the gap between the lower and upper bounds falls below a preset tolerance.
  The methodology is tested on two systems: a small 6‑generator/2‑V2G fleet case and a larger 30‑generator/10‑V2G fleet case (both without transmission constraints, so a uniform MCP is used). Results show:
• PCM consistently yields lower MCP values (4 %–9 % reduction) and total payment costs (5 %–12 % reduction) compared with OCM. The benefit grows with higher V2G penetration because V2G can shift energy to low‑price periods, reducing the maximum accepted offer.
• The GBD‑based algorithm converges rapidly. Compared with solving the MINLP directly using commercial global solvers, GBD reduces solution time by a factor of 3 or more, and remains stable even when the number of variables and constraints roughly doubles.
• The approach scales to larger systems, demonstrating that PCM with V2G can be implemented in realistic market‑clearing horizons.
  The paper’s contributions are threefold: (i) it quantifies the economic advantage of PCM over OCM in the presence of V2G, (ii) it provides a tractable GBD‑based solution framework for the resulting MINLP, and (iii) it validates the scalability of the method for medium‑size power systems.
  Future work suggested includes extending the model to incorporate transmission constraints (yielding LMP‑based PCM), integrating additional flexible resources such as stationary batteries and renewable generation, and accelerating the GBD process through parallelization or approximation techniques for real‑time market applications.
  Overall, the study offers a solid theoretical and computational foundation for adopting payment‑cost‑oriented market clearing with V2G integration, paving the way for more efficient and consistent electricity market designs in the era of high‑penetration electric vehicles and distributed storage.