Luis Badesa

Alireza Zabihi, Luis Badesa, Araceli Hernandez

The increasing penetration of single-phase loads and distributed generation exacerbates voltage unbalance (VU) in distribution grids, raising concerns about power quality and complicating network operation. However, most market-clearing models and price-based coordination frameworks do not enforce VU limits within a three-phase AC representation, so the implications for grid-code compliance, numerical scalability, and economic signals remain unclear. This paper embeds VU in a three-phase AC optimal power flow market-clearing model and benchmarks two treatments: strict VU limit enforcement and objective function penalization. Building on these insights, an Improved Hybrid Limits (IHL) formulation is proposed that preserves compliance while using a smooth unbalance proxy in the objective to guide the optimization solver. Case studies on a European low-voltage feeder show that IHL maintains feasible operating points, yields price and curtailment signals consistent with conventional hybrid formulations, and converges substantially faster and more reliably than a penalization based on the exact unbalance metric. These results support IHL as a practical and scalable mechanism for VU mitigation in market-based operation of unbalanced distribution systems.

Peng Wang, Luis Badesa

An important limitation of Inverter-Based Resources (IBR) is their reduced contribution to Short-Circuit Current (SCC), as compared to that of Synchronous Generators (SGs). With increasing penetration of IBR in most power systems, the reducing SCC poses challenges to a secure system operation, as line protections may not trip when required. In order to address this issue, the SCC ancillary service could be procured via an economic mechanism, aiming at securing adequate SCC on all buses. However, the suitability of markets for SCC services is not well understood, given that these could be prone to market power issues: since the SCC contributions from various SGs to a certain bus are determined by the electrical topology of the grid, this is a highly local service. It is necessary to understand if SGs at advantageous electrical locations could exert market power and, if so, how it could be mitigated. In order to fill this gap, this paper, for the first time, adopts an SCC-constrained bilevel model to investigate strategic behaviors of SGs. To address the non-convexity due to unit commitment variables, the model is restructured through a primal-dual formulation. Based on a modified IEEE 30-bus system, cases with strategic SGs placed at different buses are analyzed. These studies demonstrate that strategic agents exerting market power by manipulating service prices and extending operating periods could achieve up to triple revenues from SCC provision, which reduces market efficiency and would increase the financial burden on consumers. These findings highlight the need for careful market design, for which potential measures to mitigate these market power issues are also discussed.

Alireza Zabihi, Luis Badesa, Araceli Hernandez

Finding clear economic signals for distribution-network operation and expansion is increasingly important as single-phase loads and distributed energy resources escalate. These devices create phase-to-phase imbalances that manifest as voltage unbalance, a power quality issue that accelerates insulation aging in machines and increases network losses, thereby raising costs for operators and consumers. Traditional grid codes address unbalance via disparate hard limits on various indices thresholds that differ across standards, offer no dynamic economic incentive and undermine optimality. This paper proposes instead to treat voltage unbalance as a `soft limit' by adding penalty terms to grid operation costs within a three-phase optimal power flow to reflect the cost of the decrease in lifetime of assets due to being subject to voltage unbalance. This unified approach yields dynamic economic signals unbalance-aware Distribution Locational Marginal Prices (DLMP) that reflect the cost of power quality deviations. A novel mathematical decomposition of DLMP is developed, isolating the energy, loss, congestion, and unbalance components. Case studies conducted on two benchmark networks demonstrate the effectiveness and practical value of the proposed method. The results indicate that unbalance penalties reshape nodal prices, produce unexpected phase-level effects, and even allow scenarios where added load reduces unbalance and lowers costs, while providing planners and market designers with actionable insights to balance investment, operation, and power quality in modern distribution systems.

Peng Wang, Luis Badesa

Synchronous Generators (SGs) currently provide important levels of Short-Circuit Current (SCC), a critical ancillary service that ensures line protections trip during short-circuit faults. Given the ongoing replacement of SGs by power-electronics-based generation, which have a hard limit for current injection, it has become relevant to optimize the procurement of SCC provided by remaining SGs. Pricing this service is however challenging due to the integrality constraints in Unit Commitment (UC). Existing methods, e.g., dispatchable pricing and restricted pricing, attempt to address this issue but exhibit limitations in handling binary variables, resulting in SCC prices that either fail to cover the operating costs of units or lack interpretability. To overcome these pitfalls, we adopt a primal-dual formulation of the SCC-constrained dispatch that preserves the binary UC while effectively computing shadow prices of SCC services. Using a modified IEEE 30-bus system, a comparison is carried out between the proposed approach and the previously developed pricing schemes. It demonstrates that, under the proposed pricing method, adequate and intuitive service prices can be computed without the need for uplift payments, an advantage that cannot be achieved by other pricing approaches.