Study of the Paper “Efficient AC Optimal Power Flow and Global

Optimizer Solutions”

Yuyang Chen

Presentation Agenda• Theoretical background Study

0. Background Introduction

1. SDP relaxation

2. D&C method ( angular cut + voltage magnitude cut)

3. Result comparison with MATPOWER

• Code package study

0. Parallel &distributed computing with openMP , case study.

• Suggestions On further work

0. Stop exploring a branch base on the distance between parent variable bisect points and parent SDP solution points. Instead of base on SDP solution on child nodes , ( potentially save 4 SDP calculation cycle at each generation that is about to branch in this study)

Theoretical background Study 0. Background Introduction

• OPF as a historical Non-Conex QCQP. (introduced by Carpenter in 1962)

• Currently , many approaches has been tried:

1) Bai propose Semidefinite Programming(SDP) relaxation for ACOPF. X. Bai, H. Wei, K. Fujisawa, and Y. Wang. “Semidefinite programming for optimal power flow problems.” Int J Elect Power Energy Syst, vol. 30, no. 6–7, pp. 383–392, 2008.

- Avoidance of NLP OPF ‘s Jacobian matrices and Hessian matrices computing and convergence problem.

- the method Itself does not guarantee rank-1 global solution. It’s been studied that If the result does not satisfied a low rank requirement , then it is physically meaningless in where the optimal global solution is.

- several studies followed, the only thing has been proven for SDP-OPF is that SDP’s relaxed Convex feasible region always cover the non convex feasible region of the original OPF.

Theoretical background Study 0. Background Introduction (continued)

2) Gopalakrishnan proposed Branched and Bound method combining with SDP

A. Gopalakrishnan, et. al., “Global optimization of optimal power flow using a branch and bound algorithm”, in Communication, Control, and Computing, Allerton, pp. 609–616, 2012

- Bisecting Voltage Magnitude , p,q in a non-convex quadratic constraint problem may not be the best way.

Theoretical background Study 0. Background Introduction (continued)

• 3) In this Paper “Efficient AC Optimal Power Flow and Global Optimizer Solutions” Zhe Hu, Gokturk Poyrazoglu, Student Member, IEEE, and HyungSeon Oh, Member, IEEE”

- Provided a solver that guarantee to find Global Optimum in OPF, if exists.

- Utilization of D&C method that includes angular cuts and Voltage magnitude cuts from the solution of SDP.

- It avoids including parent node solution in the child node to save time.

- It avoids further exploring unworthy nodes to improved efficiency.

- Recommended parallelism for algorithm implementation.

Theoretical background Study 1. SDP relaxation (general form)

Theoretical background Study 1. SDP relaxation (OPF)

Theoretical background Study 1. SDP relaxation (OPF)

Theoretical background Study 1. SDP relaxation (OPF) effect

Theoretical background Study 1. SDP relaxation (OPF) adds voltage angle

constrain

Theoretical background Study 2.D&C method ( angular cut + voltage magnitude cut)

Theoretical background Study 2.D&C method ( angular cut + voltage magnitude cut) effect

Theoretical background StudySummary & Programming Flow

Result comparison with MATPOWER• From IEEE case 14 study , this algorithm yields lower cost than

MATPOWER’s $8081.53/h

Code package study 0. Parrallel &distributed computing with

open-mpi , case study.

} Solve

Ideas On further work0.relative difference “D” contains information about the sub region.• The closer SDP point to Bisect

point, the more balance this region is relative to bisect point.

• The Further away SDP point to Bisect point , the less balance this region is relative to bisect point. At some D>=a , we can give up the feasible region to the right of Bisect point.

• “Point of Bisection is an Arbitrary reference”

• Is there a universal D that can be use to eliminate unworthy sub region?