Optimal Power Flow and Global Optimizer Solutions part2, The - - PowerPoint PPT Presentation

Study of the Paper “Efficient AC Optimal Power Flow and Global Optimizer Solutions” part2, The Angular Cut

Yuyang Chen

Presentation Agenda

I. Background introduction , review of part 1’s theory II. Primary theoretical studies: how does the angular cut in D&C work, Detail explanations

• III. Secondary theoretical studies: the effects of

additional constraints.

• IV. Conclusions

• I. Background introduction , review of part 1’s

theory

• In Bai’s paper , SDP relaxation of OPF gives some promising results. But it
• ffers no help when the rank of SDP solution matrix is larger than 2, which

is physically meaningless.

• In Mitsubishi's B&B method it attempts to address such problem by D&C

algorithm type approach.

• This paper’s 1st contribution is the introduction of a Novel angular cut,

which increase the effectiveness of D&C method.

• This paper’s 2nd contribution is to guarantee the infeasibility of original OPF

if no solution is feasible from GO method.

• This paper ‘s method does not required CONOPF , a Non-Linear solver.

Note: for simplicity we will refer to the (SDP, D&C , angular cut )method used in this paper as “GO method”

• I. Background introduction , review of part 1’s

theory

• Previously , we gave a frame work of GO method :

through SDP relaxation of OPF and Divide and Conquer method we can find the Global Optimizer.

• Let’s take a closer look at how a efficient branching

from parent problem into child problems is achieve through a novel angular cut introduced in this paper

• II. Primary theoretical studies:

What is the effect of applying D&C , its visualization on OPF feasible region and SDP solution space.

𝜄𝑗

∗ = tan−1 𝑧𝑗

∗

𝑦𝑗

∗ = tan−1 𝑦𝑗 ∗𝑧𝑗 ∗

𝑦𝑗

∗2 = tan−1 𝑋 𝑗,𝑗+𝑂 ∗

𝑋

𝑗,𝑗 ∗

but Also , 𝜄𝑗

∗ = tan−1 𝑧𝑗

∗2

𝑦𝑗

∗𝑧𝑗 ∗ = tan−1 𝑋 𝑗+𝑂,𝑗+𝑂 ∗

𝑋

𝑗,𝑗+𝑂 ∗

if rank W >1 tan−1 𝑋

𝑗+𝑂,𝑗+𝑂 ∗

𝑋

𝑗,𝑗+𝑂 ∗

≠ tan−1 𝑋

𝑗,𝑗+𝑂 ∗

𝑋

𝑗,𝑗 ∗

• GO method can be more efficient because it exploit the SDP solution when dividing parent problem but B&B did not.
• In D&C type approach ( this include both B&B and Go method) ,If parent node solution overlap with child node solution then such

algorithm is less efficient and can be improved:

• In B&B method parent node solution and child node solutions over lap. In GO method they do not.
• Go method do not use CONOPF , a non-linear solver.

• Adding more constrains to the same set of variables makes the SDP

relaxation tighter and therefore easier to compute.

III . Secondary theoretical studies:

Effects of adding additional constraints without adding additional variables

Conclusions & ending remarks