A Mixed Integer Conic Model for Distribution Expansion Planning: Matheuristic Approach

Abstract

This paper presents a mixed-integer conic programming model (MICP) and a hybrid solution approach based on classical and heuristic optimization techniques, namely matheuristic, to handle long-term distribution systems expansion planning (DSEP) problems. The model considers conventional planning actions as well as sizing and allocation of dispatchable/renewable distributed generation (DG) and energy storage devices (ESD). The existing uncertainties in the behavior of renewable sources and demands are characterized by grouping the historical data via the k-means. Since the resulting stochastic MICP is a convex-based formulation, finding the global solution of the problem using a commercial solver is guaranteed while the computational efficiency in simulating the planning problem of medium-or large-scale systems might not be satisfactory. To tackle this issue, the subproblems of the proposed mathematical model are solved iteratively via a specialized optimization technique based on variable neighborhood descent (VND) algorithm. To show the effectiveness of the proposed model and solution technique, the 24-node distribution system is profoundly analyzed, while the applicability of the model is tested on a 182node distribution system. The results reveal the essential requirement of developing specialized solution techniques for large-scale systems where classical optimization techniques are no longer an alternative to solve such planning problems.Index Terms-Distribution systems expansion planning, energy storage devices, VND-based matheuristic algorithm, mixed-integer conic programming, stochastic programming.

Multi-stage Co-planning Model for Power Distribution System and Hydrogen Energy System Under Uncertainties

“…In general, the planning problems of PDS and HES have been widely studied in the existing literature in a separate manner. For the former, the planning strategies for PDS with high RES penetration have been well investigated such as [10]- [15]. Generally, the PDS planning is to upgrade the system assets to satisfy the growing demand while responding to the technical and security constraints, which is a complex mixed-integer non-linear problem.…”

“…In [14], a security-constrained AC/DC hybrid PDS expansion planning model is established to accommodate the high penetration of RES in weak grids, and the overall problem is formulated as a mixed-integer second-order cone programming (MISOCP) model. Reviewed from the aspect of solution techniques, the commonly-used methods in existing literature can be divided into three groups: mathematical optimization methods [10], [11], [14], heuristic methods [12], and hybrid algorithms [15]. As for mathematical optimization methods, it can formulate PDS planning problems into tractable models and solve them with efficient off-the-shelf software.…”

Hybrid PSO-TS Based Distribution System Expansion Planning for System Performance Improvement Considering Energy Management

“…Where for individual and collective DERs can be calculate using equation (11)- (15) and can be calculated using equation (29). For dispatchable DGs, and ℎ will be equal to 1.…”

“…In this stage, the collective integration of DGs, RSs, ESSs, and EVs are performed and the operational costs are investigated as shown in (15).…”

“…Multiple types of RESs, along with RSs, and ESS are installed in the PDS by considering fourth-stages genetic optimization algorithm in order to minimize the system operational costs which is discussed in [14]. A stochastic multi-period mixed integer conic problem has been proposed in [15] for the distribution system expansion purposes using RESs and ESSs in order to access the system emissions and operational costs over a predefined time horizon. The authors in [2] present a model to analyze the impacts of RSs on system performance in terms of voltage profile improvement, and stability index enhancement.…”