ADMM for Nonconvex AC Optimal Power Flow - Engineering Assignment Help

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Abstract—The objective of the paper is to implement al- ternative direction method of multipliers (ADMM) to solve a nonconvex alternating current optimal power flow (AC OPF) problem. There is no guarantee of convergence for ADMM when it is applied to a nonconvex optimization problem. In this article, we not only present the procedure of consensus ADMM implementation on an AC OPF problem for IEEE 14-bus system but also present the results related to ADMM parameters and convergence. The solutions from MATPOWER and ADMM implementation are also compared.
Index Terms—AC OPF; ADMM; Fmincon

I. INTRODUCTION

AC OPF is a nonlinear and nonconvex optimization prob- lem. The decision variables include generators’ real and reactive power outputs and voltage magnitude and angle at each bus. The objective function is usually the generation cost and the constraints include equality constraints that describe power injection relationship with voltage phasor and inequality constraints that describe generator limits, voltage limits, and line flow limits.

Alternating direction method of multipliers (ADMM) is a simple powerful technique suited to solve distributed convexoptimization. In ADMM, we divide the main system into different sub-system called as area, and each area is coor- dinated to find the final optimized solution. It is a attempt to blend the benefits of Dual Decomposition method and Augmented Lagrangian Methods for constraints optimization in ADMM algorithm. The detail description on dual decom- position and Augmented Lagrangian is discussed in [1]. InADMM, there are different algorithms, e.g., Gauss-Seidal,consensus ADMM, and proximal Jacobian ADMM.

ADMM Implementation

The IEEE 14-Bus network is shown in Fig. 1. It has 5 generator buses and 9 load buses. The network is partitioned into 2 areas: Area A and Area B. In the figure, the area enclosed with red dotted line is the intersection area called as consensus area or overlapping area. Area A includes buses 1-5, the branches inside this area as well as the branches in the consensus area (4-7, 4-9, and 5-6). Area B includes buses 6-14, branches inside Area B as well as the branches 6-5, 7-4, and 9- 4. Each area decides its own buses’ voltage magnitudes, phase angles as well as real and reactive power of its generators inside the area. Area A treats the buses belonging to Area B in the overlapping area as voltage sources and decides their voltage magnitudes and phase angles. Power injection equality of those buses (Bus 6, 7, 9) will not be considered. Area B treats the buses inside the overlapping area but belonging to Area A as the boundary buses (Bus 4 and Bus 5). For its own buses, power injection equations will be imposed as equality constraints while considering Bus 4 and 5 as two voltage sources.

CONCLUSION

ADMM is implemented in this paper for a nonconvex AC OPF. The consensus ADMM algorithm is applied to IEEE 14- Bus system to solve an AC OPF problem. Different scenarios are carried out to test our methodology. Based on the output of the case studies, we can conclude that a nonconvex opti- mization problem will not always present a stable converged output. Ability to achieve a converged solution depends on the tuning penalty parameter ρ.

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