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Active power loss allocation in radial distribution networks with power factor variation

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Abstract

The consumers of power distribution networks are usually advised to maintain improved load power factor (LPF) as it affects power loss of a feeder network which has a significant impact on electrical tariff structure. Hence, a judicious loss allocation procedure should incorporate an adequate rewarding/penalising policy for improved/poor power factor consumers, respectively. Keeping this in view, this paper introduces a new active power loss allocation (APLA) scheme which assigns losses to the network participants with due consideration to their load demands, geographical locations and power factors. The proposed methodology awards incentives/penalties only to the concerned consumers against variation in LPFs, which is validated through a proper mathematical and statistical analysis. It allocates losses by simplifying the impact of cross-terms mathematically from loss formulation without any assumptions and approximations. The effectiveness of the proposed APLA method is investigated at two different scenarios of LPFs using 30-bus and 33-bus radial distribution networks (RDNs). The performance with regard to variations in distributed generator power factor is also verified with the considered 30-bus RDN. The comparison results obtained highlight the novelty of the present procedure against other established methods.

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Abbreviations

\(n\) :

Node Number

\(nb\) :

Total number of buses in the RDN

\(^{ * }\) :

Represents the symbol for getting conjugate of a complex number

\(V_{n{\rm vlt}}^{n}\) :

Voltage at node ‘\(n\)’

\(P_{\rm load}^{n}\) :

Load active power at node ‘\(n\)’

\(P_{\rm dg}^{n}\) :

DG injected active power at node ‘\(n\)’

\(P_{\rm inj}^{n}\) :

Total active power at node ‘\(n\)’

\(I_{b{\rm crt}}^{bc}\) :

Current of branch ‘\(bc\)’

\(P_{\rm inj}^{bc,n}\) :

Total active power at the subsequent node ‘\(n\)’ of branch ‘\(bc\)’

\(V_{n{\rm vlt}}^{bc,n}\) :

Voltage at the subsequent node ‘\(n\)’ of branch ‘\(bc\)’

\(V_{n{\rm vlt}}^{bc,{\rm re}}\) :

Receiving end voltage of branch ‘\(bc\)’

\(S_{b{\rm loss}}^{bc}\) :

Apparent power loss of branch ‘\(bc\)’

\(Q_{b{\rm loss}}^{bc}\) :

Reactive power loss of branch ‘\(bc\)’

\(B_{n{\rm img}}^{bc,n}\) :

Imaginary part associated with the subsequent node ‘\(n\)’ of branch ‘\(bc\)’

\(P_{n{\rm loss}}^{n}\) :

Total active power loss of node ‘\(n\)’

\(PF_{\rm conj}^{n}\) :

Power factor of the consumer connected at node-\(n\)

\(bc\) :

Branch number

\(\Re\) :

Represents the symbol for getting real value of a complex number

\(\varepsilon\) :

Represents the symbol for ‘belongs to’

\(SN(bc)\) :

Array which stores the subsequent nodes of a branch ‘\(bc\)’

\(Q_{\rm load}^{n}\) :

Load reactive power at node ‘\(n\)’

\(Q_{\rm dg}^{n}\) :

DG injected reactive power at node ‘\(n\)’

\(Q_{\rm inj}^{n}\) :

Total reactive power at node ‘\(n\)’

\(I_{\rm neci}^{n}\) :

Equivalent current injection at node ‘\(n\)’

\(Q_{\rm inj}^{bc,n}\) :

Total reactive power at the subsequent node ‘\(n\)’ of branch ‘\(bc\)’

\(V_{n{\rm vlt}}^{bc,{\rm se}}\) :

Sending end voltage of branch ‘\(bc\)’

\(Z_{\rm bimp}^{bc}\) :

Impedance of branch ‘\(bc\)’

\(P_{\rm bloss}^{bc}\) :

Active power loss of branch ‘\(bc\)’

\(A_{n{\rm rel}}^{bc,n}\) :

Real part associated with the subsequent node ‘\(n\)’ of branch ‘\(bc\)’

\(P_{n{\rm loss}}^{bc,n}\) :

Active power loss associated with the subsequent node ‘\(n\)’ of branch ‘\(bc\)’

\(P_{t{\rm loss}}^{\rm RDN}\) :

Total active power loss of the RDN

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Authors and Affiliations

  1. Department of Electrical Engineering, IIIT Bhubaneswar, Bhubaneswar, Odisha, India

    Ambika Prasad Hota & Debani Prasad Mishra

  2. Department of Electrical Engineering, CAPGS, BPUT, Rourkela, Odisha, India

    Sivkumar Mishra

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  1. Ambika Prasad Hota
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  2. Sivkumar Mishra
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  3. Debani Prasad Mishra
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Correspondence to Sivkumar Mishra.

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Hota, A.P., Mishra, S. & Mishra, D.P. Active power loss allocation in radial distribution networks with power factor variation. Electr Eng 104, 1289–1304 (2022). https://doi.org/10.1007/s00202-021-01385-4

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