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Optimal participation of demand response aggregators in reconfigurable distribution system considering photovoltaic and storage units

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Abstract

Feeder reconfiguration is an important operational process in power distribution grids, which is implemented to enhance the system’s performance by managing the switches. Given variations of the electricity price and load pattern in smart distribution networks, the operational problems of the distribution system are largely time-dependent and very complex. To deal with these temporal dependencies, it is important to extend the problem across different time intervals. Toward this end, a multi-objective optimization model is presented in this study for dynamic feeder reconfiguration problem in the distribution system over multiple time intervals considering distributed generators, energy storage systems, and solar photovoltaic units. The demand response program including interruptible/curtailable service is proposed to enable energy consumers to rethink their energy consumption patterns based on incentive and punitive policies. The common objectives considered in the feeder reconfiguration problem are power loss and voltage deviation which are important objectives for traditional distribution systems, but less attention has been paid to distribution network voltage security. This study considers operational cost, energy loss and voltage stability index as objective functions that can meet operational and voltage security expectations. Dynamic feeder reconfiguration problem is a complex integer nonlinear program problem and hence it is difficult to solve which requires the use of appropriate optimization algorithms to converge to global optima or find close to global optima. In this paper, a modified honey bee matting optimization algorithm based on the new mating mechanism is presented to solve the multi-objective dynamic feeder reconfiguration problem. The proposed approach uses an eliminating zone concept to finds a set of non-dominated solutions during the search process. Furthermore, a fuzzy decision-maker is adopted to select the best compromise solution among the non-dominated solutions. The suggested approach is tested on the IEEE 33-node and 136-node test systems and its superiorities are shown through comparison with other evolutionary algorithms.

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Abbreviations

\(\varvec{f}_{\varvec{b}} \left( \varvec{s} \right)\) :

Beta distribution function

\(\alpha ,\beta\) :

Parameters of the beta distribution function

\(Rad^{t}\) :

Predicted solar radiation

\(\varvec{Rad}_{{\varvec{std}}}\) :

Solar radiation

\(\varvec{P}_{{\varvec{sn}}}\) :

Nominal power of PV units

\(\partial_{c}\) :

Certain radiation point

\(\mu\) :

Mean value

\(\sigma\) :

Standard deviation

\(N_{Sw}\) :

Number of sectionalizing switches

\(P_{Dg}^{k}\) :

Output power of the \(k^{th}\) DG

\(P_{{ES_{k} }}\) :

Output power of the \(k^{th}\) ES unit

\(P_{Dg,i}^{t}\) :

Active power of the \(i^{th}\) DG at the \(it^{th}\) h

\(P_{Sub,k}^{t}\) :

Active power of the \(k^{th}\) sub-station at the \(t^{th}\) h

\(\begin{aligned} a_{DG,i} ,b_{DG,i} \hfill \\ c_{DG,i} \hfill \\ \end{aligned}\) :

Cost coefficients of the \(i^{th}\) DG

\(\Pr ice_{Sw,j}^{t}\) :

Switching cost of the \(j^{th}\) switch at the \(t^{th}\) h

\(\Pr ice_{Sub,k}^{t}\) :

Price of the \(k^{th}\) sub-station at the \(t^{th}\) h

\(N_{Sub}\) :

Number of sub-stations

\(SW_{j}^{t}\) :

State of \(j^{th}\) switch at the \(t^{th}\) h

\(SW_{j}^{t - 1}\) :

State of \(j^{th}\) switch at the \(t - 1^{th}\) h

\(N_{Dg }\) :

Number of DGs

\(N_{Bus }\) :

Number of buses

\(S_{i,h}\) :

Complex power of the \(i^{th}\) bus at the \(h^{th}\) h

\(V_{i,h}\) :

Voltage magnitude of the \(i^{th}\) bus at the \(h^{th}\) h

\(\delta_{i,h}\) :

Voltage angle of the \(i^{th}\) bus at the \(h^{th}\) h

\(Y_{ij}\) :

Magnitude of admittance between \(i^{th}\) and \(j^{th}\) buses

\(E(i,i)\) :

Self-elasticity

\(E(i,j)\) :

Cross-elasticity

\(TP\left( {CC\left( i \right) - CC_{0} \left( i \right)} \right)\) :

Total payment for incentive

\(pen \left( {{\text{CC}}\left( {\text{i}} \right) - {\text{CC}}_{0} \left( {\text{i}} \right)} \right)\) :

Total payment for the penalty

\(prob \left( D \right)\) :

Probability of adding drone sperm to the queen spermatheca

\(\Delta f\) :

Absolute difference between the drone’s fitness and queen’s fitness

\(\vartheta\) :

Speed reduction value

\(X_{brood,j}\) :

Selected queen vector

\(Sp_{f}\) :

\(f^{th}\) individual in the queen’s spermatheca

\(I_{rand,Sp}\) :

Random integer between 1 and \(N_{Sp}\)

\(E^{pr}\) :

Distribution function parameter

\(R_{i}\) :

Resistance of the \(i^{th}\) line at the \(t^{th}\) h

\(I_{i}^{t}\) :

Current of the \(i^{th}\) line at the \(t^{th}\) h

\(N_{branch}\) :

Number of lines

\(X\) :

Decision variables vector

\(Sw_{j}\) :

State of the \(j^{th}\) sectionalizing switch

\(Tie_{j}\) :

State of the \(j^{th}\) tie switch

\(N_{tie}\) :

Number of tie switches

\(\theta_{ij}\) :

Angle of admittance between \(i^{th}\) and \(j^{th}\) buses

\(V_{min} ,V_{max}\) :

Minimum and maximum limits voltage magnitude of the \(i^{th}\) node

\(V_{i,h}\) :

Voltage magnitude of the \(i^{th}\) bus at the \(h^{th}\) h

\(I_{fdr,i,h} ,I_{fdr,i}^{Max}\) :

Current amplitude of the \(i^{th}\) feeder at the \(h^{th}\) h and its maximum current

\(P_{dg}^{min} ,P_{dg}^{max}\) :

Minimum and maximum limits active power value of \(i^{th}\) DG at the \(h^{th}\) h

\(N_{feeder}\) :

Number of feeders

\(I_{fdr,i,h} ,I_{fdr,i}^{Max}\) :

Charge and discharge allowed rates of the \(i^{th}\) ES unit at the \(h^{th}\) h

\(\partial_{ch,i}\) :

Efficiency of the \(i^{th}\) ES unit during charge

\(\partial_{dis,i}\) :

Efficiency of the \(i^{th}\) ES unit during discharge

\(E_{i}^{max} ,E_{i}^{min}\) :

Maximum and minimum energy amounts of the \(i^{th}\) ES unit

\(P_{ch,i}^{\hbox{max} } ,P_{dis,i}^{\hbox{max} }\) :

Maximum charge and discharge rates of the \(i^{th}\) ES unit at the \(h^{th}\) h

\(\rho \left( i \right)\) :

Spot electricity price at the \(i^{th}\) h

\(\rho_{0} \left( i \right)\) :

Initial electricity price at the \(i^{th}\) h

\(CC\left( i \right)\) :

Consumption of customer in the \(i^{th}\) h

\(CC_{0} \left( i \right)\) :

Initial demand of customer at the \(i^{th}\) h

\(inc\left( i \right),pen\left( i \right)\) :

Incentive cost and penalty value at the \(i^{th}\) h

\(CI\left( {CC\left( i \right)} \right)\) :

Customer’s income at the \(i^{th}\) h when the demand value is \(CC_{0}\)

\(CI_{0} \left( i \right)\) :

Initial customer’s income at the \(i^{th}\) h when the demand value is \(CC_{0}\)

\(IC \left( i \right)\) :

Demand value that the consumer is committed to reducing or transfer it

\(f_{i}^{min} ,f_{i}^{max}\) :

Lower and upper boundaries of the \(i^{th}\) objective function

\(N_{nds}\) :

Number of non-dominant solutions

\(\sigma_{k}\) :

Weight of \(k^{th}\) objective function

\(S\left( t \right)\) :

Queen’s speed

\(\xi , \delta\) :

Random number between zero and one

\(N_{Sp}\) :

Size of the queen’s spermathecal

\(\varphi_{2} ,\varphi_{3} , \varphi_{4}\) :

Random numbers between zero and one

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Authors and Affiliations

  1. Department of Electrical Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran

    Hossein Lotfi

  2. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Reza Ghazi

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  1. Hossein Lotfi
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  2. Reza Ghazi
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Correspondence to Hossein Lotfi.

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Lotfi, H., Ghazi, R. Optimal participation of demand response aggregators in reconfigurable distribution system considering photovoltaic and storage units. J Ambient Intell Human Comput 12, 2233–2255 (2021). https://doi.org/10.1007/s12652-020-02322-2

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  • DOI: https://doi.org/10.1007/s12652-020-02322-2

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