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Optimal transmission switching based on probabilistic load flow in power system with large-scale renewable energy integration

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Abstract

High scale integration of renewable energies has led power system towards a new set of challenges that have increased the complexity of cost optimization problem. Moreover, forecast errors in the prediction of wind, PV and load affect the accuracy of optimization. Therefore, cumulants and Gram–Charlier method have been proposed for solving probabilistic load flow (PLF)-based optimal transmission switching (OTS) for large-scale integration of renewable energy. The cumulants method has been used for forecast error evaluation in order to improve the accuracy of the proposed method. Moreover, Gram–Charlier method has been utilized for PLF-based OTS evaluation due to its fast convergence. In this paper, the simultaneous optimization of generation dispatch and network topology for PLF-based OTS has been investigated. Wind farm along with PV has been considered for large-scale integration. The proposed approach has been applied on IEEE 118 bus system with renewable integration. The results depict that the proposed approach is quite useful for large-scale power systems.

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Abbreviations

\(\Omega _{{\text{B}}} ,\Omega _{{\text{D}}} ,\Omega _{{\text{W}}} ,\Omega _{{\text{G}}} ,\Omega _{{{\text{PV}}}} ,\Omega _{{{\text{reg}}}}\) :

Set of all buses, loads, wind farm units, thermal generator units, PV power system units, regulating units

\(i,d,g,l,t,w,pv\) :

Index for buses, loads, thermal units, transmission lines, time periods, wind farms, PV plants

\(P_{{pv}}^{{\text{r}}} (t),P_{w}^{{\text{r}}} (t),P_{d}^{{\text{r}}} (t)\) :

The real output power of the PV, wind farm and active load at time t

\(P_{w}^{{\text{f}}} (t),P_{{pv}}^{{\text{f}}} (t),P_{d}^{{\text{f}}} (t)\) :

Real forecasted output power of the PV, wind farm and forecasted active load at time t

\(\Delta P^{{\text{s}}} (t)\) :

The total imbalance power of the system triggered by wind, PV and load at time t

\(\Delta P_{{rg}}\) :

Real output power variation of the regulated unit g

\(\Delta P\) :

Vector of injection power variations of buses except for the slack bus

\(V_{w} ,V_{{pv}}\) :

The terminal voltage of wind farm, and PV

\(I_{l} (t)\) :

Current of the branch at time t

\(S_{{pv}}\) :

Apparent power of PV unit g

\(P_{g} ,Q_{g}\) :

Active and reactive \(\Delta e_{w} (t),\Delta e_{{pv}} (t),\Delta e_{d} (t)\) power of generator unit g

\(z_{i} (t)\) :

Binary variable (0 for an open line, 1 for the close line). Real forecasted error of output power of the wind farm, PV and load at time t

\(P_{l}^{{\max }}\) :

Maximum power flow limit of the branch

\(Q_{w} ,Q_{{pv}}^{{\text{r}}}\) :

The reactive power of wind farm, and PV system

\(I_{l}^{{\max }}\) :

Maximum current limit of the branch

\(P_{{rg}}\) :

Actual regulated power of regulating unit g

\(\Delta r_{{rg}}^{{\max }}\) :

Maximum ramp rate of the unit g

\(I_{{w \cdot {\text{stator}}}}^{{\max }} ,I_{{w \cdot {\text{rotor}}}}^{{\max }}\) :

A maximum current of the stator and rotor of the wind farm w

\(I_{{pv}}^{{\max }}\) :

A maximum current of PV converter system

\(X_{{w \cdot {\text{stator}}}} ,X_{{w \cdot {\text{excitation}}}}\) :

Stator reactance and excitation reactance of wind farm w

\(a_{g} ,b_{g} ,c_{g}\) :

Cost coefficients of conventional generators g

\(J\) :

Maximum no of lines allowed to be open

\(\alpha _{{rg}} ,\cos \theta _{{\max }}\) :

Regulated unit participation factor and allowable maximum power factor

\(M_{{{\text{D2B}}}} ,M_{{{\text{G2B}}}} ,M_{{{\text{P2B}}}} ,M_{{{\text{W2B}}}}\) :

Connectivity matrices between loads and buses, between regulated units and buses, between PV system and buses, between wind farms and buses in \(\Omega _{{\text{B}}}\)

\(P_{g}^{{\min }} \left( t \right),P_{g}^{{\max }} \left( t \right),Q_{g}^{{\min }} \left( t \right),Q_{g}^{{\max }} \left( t \right)\) :

Minimum and maximum real power, minimum and maximum reactive power limit of unit g

\(V_{i}^{{\min }} \left( t \right),V_{i}^{{\max }} \left( t \right),\theta _{i}^{{\min }} \left( t \right),\theta _{i}^{{\max }} \left( t \right)\) :

Minimum and maximum limit of the voltage magnitude and minimum and maximum voltage angle at bus i

\(P_{{rg}}^{{\max }}\) :

Maximum regulated power of the regulating unit

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Authors and Affiliations

  1. Shandong Xiaoya Group Company Ltd., Jinan, Shandong, China

    Rizwan Ahmed

  2. Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education, Shandong University, Jinan, 250000, China

    Aamir Nawaz, Aamer Abbas Shah & Orlando M. Valarezo

  3. Department of Electrical Engineering, Faculty of Engineering and Technology, Gomal University, Dera Ismail Khan, Pakistan

    Aamir Nawaz & Muhammad Yousaf Ali Khan

  4. Department of Electrical Engineering, The Hongkong Polytechnic University, Hung Hom, Hongkong

    Zahid Javid

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  1. Rizwan Ahmed
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  2. Aamir Nawaz
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  4. Muhammad Yousaf Ali Khan
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Correspondence to Aamir Nawaz.

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Ahmed, R., Nawaz, A., Javid, Z. et al. Optimal transmission switching based on probabilistic load flow in power system with large-scale renewable energy integration. Electr Eng 104, 883–898 (2022). https://doi.org/10.1007/s00202-021-01344-z

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  • DOI: https://doi.org/10.1007/s00202-021-01344-z

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