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Flexible line ratings in stochastic unit commitment for power systems with large-scale renewable generation

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Abstract

The thermal ratings of overhead transmission lines are typically conservative, which leads to underutilization of transmission assets. In this paper, we propose an optimization model that accounts for the inherent flexibility in line ratings of thermal restricted transmission lines. We determine, in a stochastic unit commitment framework, when and which line can and should adopt higher ratings (calculated based on anticipated weather conditions and loading) as part of the recourse actions. Such recourse decisions in the second stage models the capability of the transmission system to provide flexibility to mitigate the variability of renewable generation. Flexible line ratings in the recourse help improve first-stage commitment decisions. Numerical tests conducted on both IEEE 118 system and a network representing the Central European System demonstrate that with flexible line ratings recourse, the expected operation cost can be substantially reduced without degrading reliability.

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Abbreviations

T :

Set of time periods \(\{1,2,\ldots ,24\}\).

G :

Set of generators.

N :

Set of buses/nodes.

N(i):

Set of buses/nodes that have transmission lines connected to bus i.

GF :

Set of fast generators.

GS :

Set of slow generators.

RG :

Set of renewable generators.

S :

Set of scenarios.

Z :

Set of control zones.

t :

Time period indices; \(t\in T\).

i, j :

Bus/node indices; \(i,j\in N\).

g :

Generator indices; \(g\in G\).

s :

Scenario indices; \(s\in S\).

\(h_{g}\) :

Start-up cost of generator g.

\(k_{g}\) :

No-load cost of generator g.

\(c_{g}\) :

Fuel cost of generator g.

\(\rho _{i}\) :

Penalty cost of load shedding on bus i.

\(\hat{t}^{H}_{ij}\) :

Maximal consecutive time periods of high rating for line ij.

\(\hat{t}^{N}_{ij}\) :

Minimal normal rating time periods for line ij after adopting high rating.

\(F^{\max ,\text {normal}}_{ij}\) :

Normal flow capacity of line ij.

\(F^{\max ,\text {high}}_{ij}\) :

High flow capacity of line ij.

\(B_{ij}\) :

Susceptance of line ij.

\(\pi _{s}\) :

The probability of scenario s.

\(P^{\max }_{g}\) :

Maximal production level of generator g.

\(P^{\min }_{g}\) :

Minimal production level of generator g.

\(D_{i,t}\) :

Load on bus i at time t.

\(D^{net}_{i,t}\) :

Net load on bus i at time t.

\(u_{g,t(,s)}\) :

Commitment of generator g at time t (in scenario s).

\(\sigma _{g,t(,s)}\) :

Start-up indicator of generator g at time t (in scenario s).

\(P_{g,t(,s)}\) :

Production level of generator g at time t (in scenario s).

\(\gamma _{g,t}\) :

Reserve of generator g at time t.

\(F_{ij,t,s}\) :

Active power flow on line ij at time t in scenario s.

\(\theta _{ij,t,s}\) :

Voltage angle of bus i at time t in scenario s.

\(r_{ij,t,s}^{Off}\) :

Indicator of line ij being off at time t in scenario s.

\(r_{ij,t,s}^{N}\) :

Indicator of line ij adopting normal rating at time t in scenario s.

\(r_{ij,t,s}^{H}\) :

Indicator of line ij adopting higher rating at time t in scenario s.

\(L_{i,t,s}\) :

Load shedding on bus i at time t in scenario s.

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Acknowledgements

The authors would like to thank the Lawrence Livermore National Laboratory for granting computing resources on the Sierra and Cab cluster. This work was supported by NSF EAGER Grant ECCS 1549572, ARO grant W911NF-17-1-0555, and by TBSI, at UC Berkeley.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, The Tsinghua-Berkeley Shenzhen Institute, University of California, Berkeley, CA, 94709, USA

    Jiaying Shi & Shmuel S. Oren

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  1. Jiaying Shi
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  2. Shmuel S. Oren
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Correspondence to Shmuel S. Oren.

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This work is supported by the National Science Foundation under the EAGER program NSF Award no 1549572.

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Shi, J., Oren, S.S. Flexible line ratings in stochastic unit commitment for power systems with large-scale renewable generation. Energy Syst 11, 1–19 (2020). https://doi.org/10.1007/s12667-018-0306-8

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