[Paper Review] Complete results for a numerical evaluation of interior point solvers for large-scale optimal power flow problems

Juraj Kardoš, Drosos Kourounis+2 more|arXiv (Cornell University)|Jul 11, 2018

Optimal Power Flow DistributionEngineering19 references20 citations

TL;DR

This paper presents a comprehensive numerical evaluation of interior-point solvers for large-scale optimal power flow (OPF) problems using the MATPOWER framework. It evaluates performance across 1951- to 193,000-bus networks and introduces structure-exploiting methods like BELTISTOS-MP for multi-period OPF with energy storage, demonstrating up to 100x faster solution times and 10x lower memory use than black-box solvers like IPOPT and KNITRO.

ABSTRACT

Recent advances in open source interior-point optimization methods and power system related software have provided researchers and educators with the necessary platform for simulating and optimizing power networks with unprecedented convenience. Within the Matpower software platform a combination of several different interior point optimization methods are provided and four different optimal power flow (OPF) formulations are recently available: the Polar-Power, Polar-Current, Cartesian-Power, and Cartesian-Current. The robustness and reliability of interior-point methods for different OPF formulations for minimizing the generation cost starting from different initial guesses, for a wide range of networks provided in the Matpower library ranging from 1951 buses to 193000 buses, will be investigated. Performance profiles are presented for iteration counts, overall time, and memory consumption, revealing the most reliable optimization method for the particular metric.

Motivation & Objective

• To evaluate the robustness and performance of interior-point methods across diverse AC optimal power flow (OPF) formulations.
• To compare standard black-box solvers (IPOPT, KNITRO, FMINCON, MIPS) with structure-aware solvers for single- and multi-period OPF problems.
• To assess the scalability and efficiency of novel structure-exploiting algorithms, particularly BELTISTOS-MP, on large power systems with energy storage.
• To provide performance profiles for iteration count, runtime, and memory consumption to guide solver selection in power system optimization.

Proposed method

• Employs performance benchmarking profiles using MATPOWER’s OPF formulations, including polar and Cartesian voltage representations and current/power mismatch equations.
• Implements structure-exploiting linear algebra techniques in BELTISTOS-MP to efficiently solve the KKT systems arising in multi-period OPF with storage coupling.
• Uses a Schur complement-based factorization strategy that reuses and recomputes parts of the factorization to reduce memory usage, enabling the BELTISTOS-MEM variant.
• Applies the storage coupling model via linear inequality constraints involving the storage energy evolution equation (εn = εn−1 + BS Pgs^n) and bounds on energy levels.
• Evaluates solvers on real-world networks from the MATPOWER library, ranging from 1951 to 193,000 buses, with up to 10 storage devices and 4800 time periods.
• Compares numerical factorization and forward-backward substitution times, memory usage, and overall solution time across solvers under varying problem sizes and configurations.

Experimental results

Research questions

• RQ1 Which interior-point solver delivers the best performance in terms of solution time, iteration count, and memory usage for large-scale single-period AC OPF problems?
• RQ2 How do different OPF formulations (polar vs. Cartesian, current vs. power mismatch) affect solver performance and convergence?
• RQ3 To what extent do structure-exploiting solvers like BELTISTOS-MP outperform general-purpose black-box solvers (e.g., IPOPT, KNITRO) in multi-period OPF with energy storage?
• RQ4 How does the performance gap between solvers scale with increasing network size and number of time periods?
• RQ5 What is the trade-off between memory efficiency and computational time in the memory-optimized BELTISTOS-MEM variant compared to the full BELTISTOS-MP?

Key findings

• BELTISTOS-MP achieves approximately 1% of the solution time required by the best black-box competitor (IPOPT) on the smallest benchmark, with performance gap increasing significantly for larger problems.
• For N = 4800 time periods, black-box solvers like IPOPT failed due to memory or time limits, while BELTISTOS-MP succeeded and remained efficient.
• With 10-fold increase in storage devices (Ns), IPOPT’s solution time increased by 81x on the case1354pegase benchmark, while BELTISTOS-MP’s time increased only 3.7-fold.
• BELTISTOS-MP reduces memory requirements by more than one order of magnitude compared to black-box solvers by exploiting the KKT system’s block structure.
• The memory-optimized variant, BELTISTOS-MEM, reduces memory usage further by recomputing L factors during the Schur algorithm, though at the cost of increased computation time.
• Performance profiles show that BELTISTOS-MP consistently outperforms all other solvers in both runtime and memory efficiency across all tested networks and problem sizes.