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Frequency-constrained unit commitment problem with considering dynamic ramp rate limits in the presence of wind power generation

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Abstract

An increased use of variable generation technologies such as wind power generation can have important effects on system frequency performance during normal operation as well as contingencies. This has led to new challenges for system operators in terms of improving frequency characteristics during contingencies. This subject is stated within the framework of frequency-constrained unit commitment problem (FCUCP) in this study by augmenting the frequency characteristic in the multi-thermal units. The ramp rate is proposed as dynamic constraint, and FCUCP is solved efficiently by binary particle swarm optimization (BPSO) based heuristic optimization algorithms. The influence of the proposed ramping on FCUCP is simulated, and it can be shown that the costs of the system under considering practical limitations that are solved by BPSO are minimized.

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Acknowledgements

This work is supported by the Azarbaijan Shahid Madani University through the Grant: ASMU/1093-17/18947.

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Authors and Affiliations

  1. Department of Electrical Engineering, Azarbaijan Shahid Madani University, Kilometer 35, Tabriz/Azarshahr Road, P.O. Box: 53714-161, Tabriz, Iran

    Amin Safari & Hossein Shahsavari

Authors
  1. Amin Safari
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  2. Hossein Shahsavari
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Correspondence to Amin Safari.

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Appendices

Appendix 1

Min up/down

$$ \sum\limits_{m = 1}^{{T_{i}^{\text{Up}} - T_{i,0}^{\text{Up}} }} {[1 - u_{i}^{m} ] = 0} \quad \left( {{\text{if}}\,u_{i}^{0} = 1\quad {\text{and}}\quad T_{i}^{\text{Up}} > T_{i,0}^{\text{Up}} } \right) $$
(47)
$$ \begin{aligned} & \sum\limits_{m = k}^{{k + T_{i}^{Up} - 1}} {u_{i,m} } \ge T_{i}^{\text{Up}} \left[ {u_{i}^{k} - u_{i}^{k - 1} } \right] \\ & k = G_{i} + 1, \ldots ,T - T_{i}^{Up} + 1. \\ & G_{i} = \left\{ {\begin{array}{*{20}l} {u_{i}^{0} (T_{i}^{\text{Up}} - T_{i,0}^{\text{Up}} ),} \hfill & {T_{i}^{\text{Up}} > T_{i,0}^{\text{Up}} } \hfill \\ 0 \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right. \\ \end{aligned} $$
(48)
$$ \sum\limits_{m = k}^{T} {[u_{i}^{m} - u_{i}^{k} + u_{i}^{k - 1} ] \ge 0} ,\quad k = T - T_{i}^{\text{Up}} + 2, \ldots ,T $$
(49)
$$ \sum\limits_{m = 1}^{{T_{i}^{\text{Dn}} - T_{i,0}^{\text{Dn}} }} {u_{i}^{m} = 0} \quad \left( {{\text{if}}\,u_{i}^{0} = 0\quad {\text{and}}\quad T_{i}^{\text{Dn}} > T_{i,0}^{\text{Dn}} } \right) $$
(50)
$$ \begin{aligned} & \sum\limits_{m = k}^{{k + T_{i}^{\text{Dn}} - 1}} {[1 - u_{i}^{m} ]} \ge T_{i}^{\text{Dn}} \left[ {u_{i}^{k - 1} - u_{i}^{k} } \right] \\ & k = W_{i} + 1, \ldots ,T - T_{i}^{\text{Dn}} + 1. \\ & W_{i} = \left\{ {\begin{array}{*{20}l} {\left( {1 - u_{i}^{0} } \right)\left( {T_{i}^{\text{Dn}} - T_{i,0}^{\text{Dn}} } \right),} \hfill & {T_{i}^{\text{Dn}} > T_{i,0}^{\text{Dn}} } \hfill \\ 0 \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right. \\ \end{aligned} $$
(51)
$$ \sum\limits_{m = k}^{T} {[1 - u_{i}^{m} - u_{i}^{k - 1} + u_{i}^{k} ] \ge 0} ,\quad k = T - T_{i}^{\text{Dn}} + 2, \ldots ,T $$
(52)

where TUp and TDn are the generator minimum up/down time, respectively, and T0 is the generator initial time.

Appendix 2

IEEE 30 Bus Test System Data

See Tables 7, 8, 9 and 10.

Table 7 Unit data
Full size table
Table 8 Hour load demand
Full size table
Table 9 Bus load factors
Full size table
Table 10 Dynamic data of generators
Full size table

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Safari, A., Shahsavari, H. Frequency-constrained unit commitment problem with considering dynamic ramp rate limits in the presence of wind power generation. Neural Comput & Applic 31, 5241–5254 (2019). https://doi.org/10.1007/s00521-018-3363-y

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