Multi-Area Reserve Dimensioning Using Chance-Constrained Optimization

Abstract

We propose a chance-constrained formulation for the problem of dimensioning frequency restoration reserves on a power transmission network. We cast our problem as a two-stage stochastic mixed integer linear program, and propose a heuristic algorithm for solving the problem. Our model accounts for the simultaneous sizing of both upward and downward reserves, and uncertainty driven by imbalances, contingencies and available transmission capacity. Our core methodology is further adapted in order to minimize inter-zonal flows and in order to split reserve requirements between automatic and manual frequency restoration reserves. We apply our methodology to the problem of sizing reserves in the four load frequency control areas of the Swedish power system. We demonstrate the benefits of our method in terms of decreasing reserve requirements in the absence of reserve sharing, we analyze the spatial allocation of reserves, and we perform various sensitivity analyses.

Investigating Reserve Dimensioning Approaches for Multi-Area Reserve Capacity Markets: A Nordic Case Study

“…In the Nordic region, FRR is not procured in co-optimization with the DA market and hence these approaches are not compliant with the market setup studied in this paper. The work most related to ours is the work in [21], where FRR is dimensioned and allocated for the Swedish LFC areas with a certain reliability criterion. The problem is formulated as a chance-constrained optimization problem, where the chance constraints represent the probability of reserves not being adequate.…”

“…The problem is formulated as a chance-constrained optimization problem, where the chance constraints represent the probability of reserves not being adequate. In [21], the problem is solved with a heuristic method, but a branch-and-cut algorithm was later presented in [22] to ensure a global optimum is found. However, the method in [21] does not follow the proposed methodology in [4], as FRR for RIs and NIs is not dimensioned sequentially.…”

“…In [21], the problem is solved with a heuristic method, but a branch-and-cut algorithm was later presented in [22] to ensure a global optimum is found. However, the method in [21] does not follow the proposed methodology in [4], as FRR for RIs and NIs is not dimensioned sequentially. Additionally, the method in [21] does not take short-term operating conditions into consideration by dimensioning FRR statically for one year, while existing literature points towards the benefits of dynamic FRR dimensioning.…”

“…The framework is based on simulating imbalance scenarios and using these as input to chanceconstrained optimization problems. The framework is compliant with the proposed methodology in [4] and is applied to a case study of the Nordic LFC block in this paper, compared to the Swedish case study in [21]. Contribution 2: We provide a new methodology named Modified Constant Conservative Approximation (MCCA) to solve the chance-constrained MILP optimization problem with a large number of binary variables in a computationally reasonable time.…”

“…Table II compares FRR-RI dimensioning for one day with the Dynamic Pre-DA approach when using the MCCA method, a conventional Big-M chance constraint reformulation with binary variables, and the heuristics suggested in [21]. The MCCA method is computationally fast and provides a result closer to the global optimum compared to the heuristics approach.…”