Application of SDDP to SOCP and SDP relaxations of distribution networks

Details

Supervisors

Papavasiliou, Anthony

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées

Abstract

The growing influence of power generation in the distribution network poses an important challenge to power system operation. The environmental context and the recent developments in solar generation and power storage are profoundly changing the structure of power systems, adding distributed uncertain generation along with storage devices that could be capable of mitigate the variability of renewable resources. In addition to this, the modern communication infrastructure makes it possible to decentralize the operation of the network, relying on a hierarchical organization. The advantage of a decentralized approach is that, if possible, it is scalable to systems of arbitrary size. The resulting optimization problem covers multiple time stages and must deal with the uncertainty brought by renewables. This is typically the class of problems tackled by the Stochastic Dual Dynamic Programming (SDDP) algorithm, developed in the framework of linear programming and which has found great commercial success. However, distribution networks are governed by a set of nonconvex constraints, Kirchhoff’s laws, which render the problem challenging to solve efficiently. Under the ideal assumption of a balanced network, the problem can be relaxed into a second-order cone program (SOCP). Otherwise, if the network is unbalanced like in practical low-voltage distribution networks, we must resort to a semi-definite program (SDP). The goal of this thesis is first to try to extend the SDDP algorithm to convex programming, i.e. the SOCP and SDP relaxations. To this end, these relaxations are first formally derived, and theoretical tightness conditions are provided. After that, the next chapter introduces the SDDP algorithm and argues that it can be extended to convex programming. Then, tightness and efficiency are experimentally tested, discussed and compared to commercial solvers on a 15-bus network. At last, we will study the influence of network imbalance, and try to understand its consequences on the solution and the computational effort required.