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Seeking Cost--Effective Incentive for Merchant MTDC Investment in an AC Grid: A Parametric MISOCP Model to VSC Siting and Sizing
Haixiao Li, Jure Lokar, Leopold Herman, Aleksandra Lekić
TL;DR
MTDC networks can help address transmission congestion, but merchant investors need an incentive that supports investment while preserving benefits for the TSO. The paper jointly optimizes VSC siting, sizing, and system operation in a parametric MISOCP, then searches for a suitable benefit-sharing rate. In the case study, MTDC integration reduced annual generation costs by $6,016,437, or 2.85%.
Problem
The planning problem must identify an incentive that makes merchant investment viable while preserving sufficient economic benefits for the TSO.
Source: §1.1 · p. 1, §1.2 · p. 2Method
A parametric MISOCP jointly optimizes VSC siting, sizing, and operation at a prescribed benefit-sharing rate, with a search procedure to determine the rate.
Source: §1.3 · p. 2, §2.4 · p. 5Results
$6,016,437 in annual generation costs, a 2.85% reduction, resulted from integrating the optimally configured MTDC network.
Source: §4.2 · p. 7Takeaways & Limitations
The case-study results demonstrate the proposed model and solution method’s effectiveness for MTDC planning and benefit-sharing-rate selection.
Source: §5 · p. 7The model provides only a preliminary representation of investor–TSO interaction; future work will examine richer strategic and market behaviors.
Source: §5 · p. 8
Abstract
from arXiv · showhide
Deploying voltage source converter (VSC)-based multi-terminal DC (MTDC) networks in existing AC grids offers a promising solution for alleviating transmission congestion, enhancing power-transfer capability, and improving operational economy. However, constructing an MTDC network requires participation from merchant investors. Therefore, the transmission system operator (TSO) responsible for the AC grid must provide an adequate economic incentive that enables merchant investors not only to recover the MTDC investment cost but also to earn a reasonable return commensurate with their risk and expectations. An insufficient incentive may fail to attract merchant investment, whereas an excessive incentive may unnecessarily reduce the economic benefits retained by the TSO. Determining an appropriate incentive that balances these competing interests therefore becomes a critical issue. To address this issue, this paper formulates a sharing-rate-parameterized mixed-integer second-order cone programming (MISOCP) model that jointly optimizes VSC siting and sizing while coordinating AC/DC system operation. A straightforward search procedure is then employed to identify the benefit-sharing rate that meets the investor's expectations while preserving sufficient benefits for the TSO. Case studies demonstrate the operating-cost benefits of MTDC integration and validate the proposed search strategy for seeking such a benefit-sharing rate.
1 Introduction
The introduction frames VSC siting and sizing as central to MTDC’s technical and economic value, while identifying investor incentives as a gap in OPF-based planning. It proposes a benefit-sharing-rate model that jointly optimizes converter planning and seeks a balance between investor viability and TSO benefits.
1.1 Background and Motivation
- Jointly optimizing VSC locations and capacities is essential because poor siting limits congestion relief, undersizing restricts transfer capability, and oversizing leaves investment underused.Source: §1.1 · p. 1
- A cost-effective incentive must support merchant investors’ viable siting and sizing decisions while leaving the TSO sufficient economic benefits.Investors fund the project, while much of its benefits accrue to the power system; a low sharing rate may not attract investment, and an unnecessarily high rate may reduce TSO benefits.Source: §1.1 · p. 1, §1.2 · p. 2
1.2 Literature Review
- Prior AC/DC OPF studies jointly optimize converter locations and capacities, but planning may not yield implementable projects if it overlooks investor returns.The introduction identifies benefit-sharing as a way to link investor revenue to MTDC project benefits.Source: §1.2 · pp. 1–2
1.3 Contributions and Outlines
- The paper develops a parametric MISOCP and search procedure to determine a benefit-sharing rate while jointly optimizing VSC siting and sizing.Binary variables represent candidate connection points, and convexified AC/DC power-flow equations form the MISOCP.Source: §1.3 · p. 2
2 Model Formulation
The model combines AC/DC operating constraints with VSC siting and sizing decisions, then evaluates investment incentives through annual operating-cost savings and investor participation. A parametric MISOCP selects a sharing rate to maximize TSO benefit while meeting the investor’s minimum profit requirement.
2.1 AC/DC Power Flow Constraints
- Convex relaxation of the AC/DC power-flow constraints is used to improve tractability when VSC siting decisions are binary.The constraints are first formulated for a given MTDC topology.Source: §2.1 · p. 2
- AC-grid constraints cover branch active and reactive flows, apparent-power limits, nodal injections and balances, and voltage and generator-output limits.The original AC equality is relaxed to an SOCP constraint.Source: §2.1 · p. 2
- MTDC constraints include DC-branch losses, voltage drops and power-transfer limits, nodal power balance, bus-voltage limits, and an SOCP relaxation.The DC branch-end powers sum to the resistive branch loss.Source: §2.1 · p. 2
- VSC-station constraints represent a two-bus equivalent and enforce transformer power flows, converter-side voltage and capability limits, power balance, losses, and current limits.The converter capability region is approximated by an N-side polygon.Source: §2.1 · pp. 2–3
2.2 VSC Siting and Sizing Constraints
- The merchant investor preselects the MTDC configuration, while the planning model chooses each VSC’s AC connection and capacity.Binary siting variables select a candidate AC bus; unselected connections have zero exchanged active and reactive power.Source: §2.2 · pp. 3–4
- VSC capacity becomes a decision variable, and investment costing uses the capacity rounded up to an integer MVA rating.The optimized capacity represents the minimum required by system operation, and investment cost increases with rated capacity.Source: §2.2 · pp. 4–5
2.3 Investment Incentive Constraints and Objective Function
- For a sharing rate β, the investor receives a fraction of annual operating-cost savings that must cover annualized investment costs and minimum acceptable profit.Savings compare annual generation costs with and without MTDC over representative scenarios whose hours sum to 8,760.Source: §2.3 · p. 5
2.4 Parametric Optimization Formulation
- The parametric MISOCP chooses β and the VSC plan to maximize retained TSO benefit while meeting the investor’s profit requirement.For each prescribed β, F(β) is the maximum annual TSO benefit after optimizing siting, sizing, and operation; ties select the smallest β.Source: §2.4 · p. 5
3 Problem Solving
The procedure searches for a benefit-sharing rate by repeatedly solving a fixed-rate MISOCP and selecting the rate that yields the highest feasible TSO benefit.
3 Problem Solving
- The fixed-rate inner problem is solved as a standard MISOCP, and its resulting TSO benefit is recorded.Source: §3 · pp. 5–6
- The search tests sharing rates across [0, 1], then evaluates progressively finer rates near the rate producing the highest feasible TSO benefit.The search continues until the prescribed resolution is reached, returning the selected rate and its VSC configuration.Source: §3 · p. 6
- The search begins with step Δβ(0), reduces the step by γ after each round, and stops after a round with Δβ ≤ εβ.Previously evaluated rates are reused; if none is feasible, the full interval [0, 1] is retained for the next round until the stopping threshold is reached.Source: §3 · p. 6
4 Case Study and Discussion
The case study searches for a benefit-sharing rate and evaluates MTDC integration under seasonal operation. It reports annual generation-cost savings and minor SOCP–NLP gaps in a customized AC/DC system.
4 Case Study and Discussion
- The customized test system uses a 9-bus AC network based on a simplified Slovenian 400-kV system and considers a 3-terminal MTDC, with VSC connection points and capacities determined by the parametric model.Annual operation is simplified into four seasonal operating states, each comprising 2,190 hours, with load assumed constant throughout each seasonal scenario.Source: §4 · p. 6, Figure 2 · p. 6
4.1 Seeking Cost-Effective Incentive with Benefit-Sharing
- Across the three-round search, the selected sharing rate stays at β = 0.500 in the first two rounds and changes to β = 0.492 after final refinement, yielding a TSO benefit of $3.056 × 10^6/yr.When candidate values of β reappear in later rounds, their previously obtained solutions are reused rather than recomputed.Source: §4.1 · pp. 6–7
4.2 Benefits of MTDC Integration
- $6,016,437/year in annual generation-cost savings (2.85%) accompanies the selected β = 0.492, with the investor’s minimum-profit requirement met and considerable TSO benefits retained.The annual generation-cost comparison is presented in Table 7; the selected VSC siting and sizing are presented in Table 6.Source: §4.2 · p. 7, Table 7 · p. 7, Table 6 · p. 7
4.3 Gap Between SOCP- and NLP-Based Optimal Power Flow Model
- Generation-cost and total-generation gaps relative to NLP results are minor, supporting the SOCP relaxation for system-wide power-flow and VSC operating constraints.The comparison is reported in Table 8.Source: §4.3 · p. 7, Table 8 · p. 7
5 Conclusion
The paper develops a parametric MISOCP and search procedure for benefit-sharing that jointly optimizes VSC siting and sizing. Numerical experiments demonstrate the approach, while the investor–TSO interaction remains preliminary.
5 Conclusion
- The proposed parametric MISOCP and associated search procedure seek a cost-effective benefit-sharing rate while jointly optimizing VSC siting and sizing.Numerical experiments on a customized AC/DC case system demonstrate the effectiveness of the model and solution method.Source: §5 · p. 7
- The planning approach allocates MTDC-related system benefits between the TSO and merchant investor to address investment incentives.The conclusion identifies attracting merchant investment through benefit-sharing as part of the planning problem.Source: §5 · p. 7
- The model offers only a preliminary representation of investor–TSO interaction; future work will examine richer strategic and market behaviors.The authors also propose extending the optimization framework to better reflect practical investment decisions.Source: §5 · p. 8