.

Motivation

Conclusions This study proves that TS finds a more optimal topology than the original one.

The switching process decreases the number of available lines, but the losses over the reduced number of

lines may increase.

Our TS algorithm finds a more optimal configuration that guarantees the reduction in cost without

sacrificing reliability and network resiliency.

Operating cost of the system after transmission switching ALWAYS yields lower cost.

May increase the real power losses of the system, but will ALWAYS provide the lowest operating cost.

LESS COST

Results

The 5th trading period, as magnified in above, illustrates how the

results differ with and without N-1 contingency condition.

Our experiments indicated that transmission switching ALWAYS

returned a better solution than the original network.

The analysis of the 5th trading period deserves careful attention as

opposed to our expectation that real power loss will decrease, higher

real power losses were observed.

Electricity Price Variance

Gokturk Poyrazoglu, Charles Hashem, HyungSeon Oh Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, NY 14260

Toward Global Optimization

Before

Transmission Switching

PGen1 : 74.7 MW

PGen2 : 127.1 MW

Operating Cost :$ 3,289

Real Power Loss : 1.08 MW

LMP at Bus 1: $10/MWh

LMP @ Bus 2 : $20/MWh

LMP @ Bus 3: $31.15/MWh

After

Transmission Switching

PGen1 : 206.5MW

PGen2 : 0.00 MW

Operating Cost :$ 2,065

Real Power Loss : 6.55 MW

LMP at Bus 1: $10/MWh

LMP @ Bus 2 : $10.29/MWh

LMP @ Bus 3: $10.62/MWh

Solut ion to SDP is the lower bound of the original case

Optimal Switching Problem Nomenclature

𝑪𝒐𝒔𝒕𝒍𝒐𝒄𝒂𝒍 𝒐𝒑𝒕𝒏𝒆𝒘 𝒕𝒐𝒑𝒐𝒍𝒐𝒈𝒚

< 𝐶𝑜𝑠𝑡𝑆𝐷𝑃𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙

≤ 𝐶𝑜𝑠𝑡𝑔𝑙𝑜𝑏𝑎𝑙 𝑜𝑝𝑡𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙

≤ 𝑪𝒐𝒔𝒕𝒍𝒐𝒄𝒂𝒍 𝒐𝒑𝒕𝒐𝒓𝒊𝒈𝒊𝒏𝒂𝒍

Control variables

𝑧 :Binary variable for state of line

𝑃𝑔, 𝑄𝑔: real and reactive power generations

𝑉, 𝑆 ∶ magnitudes of voltage and power flow

𝜃: voltage angle

𝑣: voltage in the Cartesian coordinate system

𝑊 = 𝑣𝑣𝑇

Parameters

𝑧′: line contingency to meet FERC’s criterion

𝑃𝐺, 𝑄𝐺: generation limits

𝑃𝐷, 𝑄𝐷 : real and reactive demand

PY, QY: matrices associated with Kirchhoff's laws

𝑀𝑘 =𝑒𝑘𝑒𝑘𝑇 0

0 𝑒𝑘𝑒𝑘𝑇

𝑉𝑚𝑎𝑥, 𝑆𝑚𝑎𝑥 : limits of voltage and power flow

𝑌: Admittance matrix, 𝑌 ≔ 𝐺 + 𝑗𝐵

min𝑘 ∈ 𝒢𝑧

𝑓(𝑃𝑔𝑘)

𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜

𝑃𝑔𝑘 − 𝑃𝐷𝑘 = 𝑉𝑘 𝑉𝓁 ∗ 𝑌𝑘𝑙(𝑧, 𝑧′) ∗ cos 𝜃𝑙 − 𝜃𝑘 , ∀𝑘 ∈ 𝒦𝓁 ∈𝒦

𝑄𝑔𝑘 − 𝑄𝐷𝑘 = −𝑉𝑘 𝑉𝓁 ∗ 𝑌𝑘𝑙(𝑧, 𝑧′) ∗ sin 𝜃𝑙 − 𝜃𝑘 ∀𝑘 ∈ 𝒦𝓁 ∈𝒦

𝑃𝐺𝑘𝑚𝑖𝑛 ≤ 𝑃𝑔𝑘 ≤ 𝑃𝐺𝑘

𝑚𝑎𝑥, ∀𝑘 ∈ 𝒢

𝑄𝐺𝑘𝑚𝑖𝑛 ≤ 𝑄𝑔𝑘 ≤ 𝑄𝐺𝑘

𝑚𝑎𝑥 ∀𝑘 ∈ 𝒢

𝑉𝑘𝑚𝑖𝑛 ≤ 𝑉𝑘 ≤ 𝑉𝑘

𝑚𝑎𝑥 ∀𝑘 ∈ 𝒦

𝑆𝑘𝓁 ≤ 𝑆𝑘𝓁𝑚𝑎𝑥 ∀ 𝑘, 𝓁 ∈ 𝒩

Mixed Integer Nonlinear Programming