# Optimal allocation of unified power quality conditioner in the smart distribution grids

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## Abstract

The optimal operation of current distribution networks has a great importance due to growing electrical demand and significant power losses. In this paper, the optimal allocation of unified power quality conditioner (UPQC) in smart grid with responsive loads is investigated as an appropriate solution to reduce power losses. Also, in order to consider different consumption patterns and to predict the demand with the lowest error, different linear and nonlinear models of responsive loads are taken into account. New pricing method in demand response programs (DRPs) is another concept which is developed in the paper by which optimal electricity prices in DRP during peak, off-peak, and valley periods are determined. Moreover, DRPs are prioritized by the Topsis method based on the different Utility’s policies. The final proposed model has been applied on the IEEE 12-bus, IEEE 33-bus, and the practical 94-bus Portuguese RDS distribution system. The results show that the UPQC allocation in the presence of DRPs is a win–win game both for the Utility and for customers.

## Keywords

Demand response Smart grid Electricity pricing Unified power quality conditioner (UPQC)## List of symbols

*CL*_{i}Proximity to the ideal option

*D*Decision matrix

*E*(.)Element of the price elasticity matrix

*H*Harmonic order

*I*_{j}^{h}*j*th bus current in the*h*th harmonic*I*^{h}Buses injected current for the

*h*th harmonic*I*_{L}Load current

*I*_{L}(.)Load current of each bus

*I*_{L}^{f}Main components of the load current

*I*_{lk}Current in each branch

*I*_{Sh}Injected current of the shunt inverter

*I*_{s}Current source

*N*_{Branch}Number of the network branches

*N*_{Bus}Number of buses

- Nh
Number of harmonic order

*N*_{line}Number of lines

*N*_{load}Number of loads

- \( {\text{NSI}}_{a} \)
Network security index

*P*_{Se}Active power of series inverter

*P*_{sh}Active power of shunt inverter

*Q*_{Se}Reactive power of series inverter

*Q*_{sh}Reactive power of shunt inverter

- \( Q_{\text{L}}^{ '} \left( i \right) \)
Reactive power demand for the

*i*th bus*Q*_{Se}^{i}Injected reactive power of the series inverter in the

*i*th bus- RP
_{Loss} Real loss

*S*_{Sh}Steady-state capacity of the shunt inverter

*S*_{se}Series inverter’s capacity

*T*Total time period

- THD
_{L} Total harmonic distortion of the load current

*V*_{se}Voltage of the series inverter

*V*_{S}Voltage source

*V*_{DL}Appropriate load voltage

*V*_{L}Load voltage

*V*_{S}Source voltage

*V*_{j}^{h}*j*th bus voltage in the*h*th harmonic*V*^{h}Buses voltage vectors for the

*h*th harmonic- LODF
Line outage distribution factor

*V*_{j}^{1}Magnitude of the

*j*th bus in the main frequency*V*_{j}^{h}Voltage magnitude of the

*j*th bus in the*h*th harmonic- \( {\text{VSF}}_{a} \)
Voltage stability index

*Y*^{h}Admittance matrix for the

*h*th harmonic*α*_{i}Phase angle before the UPQC allocation

*d*^{max}(.)Maximum demand during

*T**d*^{min}(.)Minimum demand during

*T**d*_{0}^{max}(.)Maximum initial demand during

*T**d*_{0}^{min}(.)Minimum initial demand during

*T**d*^{lin}(.)Linear load model

*d*^{pot}(.)Potential load model

*d*^{exp}(.)Exponential load model

*d*^{log}(.)Logarithmic load model

*d*_{0}(.)Initial demand before DRPs implementation

*d*_{i}^{−}Distance between the option

*i*and the negative ideal option*d*_{i}^{+}Distance between the option

*i*and the positive ideal option- \( {\text{inc}}\left( {t^{{\prime }} } \right) \)
Incentive at the

*t*th hour*k*Index of the transfer bus for the

*lk*th bus- loss
_{0}(.) Initial loss

- loss(.)
Loss after DRPs

*l*Index of the receiver bus for the

*lk*th bus*n*_{ij}*j*th element of the matrix*D*- \( {\text{pen}}\left( {t^{{\prime }} } \right) \)
Penalty at the

*t*th hour*r*(*lk*)Resistance of the

*lk*th branch*r*_{ij}Gain obtained by the option

*i*in the criterion*Z*(*lk*)Impedance of the

*lk*th branch*ρ*(.)Electricity price after the optimal pricing

*ρ*_{0}(.)Initial electricity price

*θ*_{se}Angle between the source voltage and series inverter

*θ*_{sh}Angle between the source voltage and shunt inverter

*δ*_{i}Angle between the load voltage the source voltage in the

*i*th bus*φ*Angle between the voltage and the load current

*δ*Angle between the load voltage and the voltage source

## Abbreviations

- A/S
Ancillary services market

- CAP
Capacity market

- CPP
Critical peak pricing

- CSA
Cuckoo search algorithm

- DB
Demand bidding

- DE
Differential evolution

- DED
Dynamic economic dispatch

- DFACTS
Distributed flexible AC transmission system

- DGs
Distributed generations

- DLC
Direct load control

- DPTV
Deviation of peak to valley

- DRPs
Demand response programs

- DSM
Demand-side management

- DSTATCOM
Distribution static compensator

- DVR
Dynamic voltage restorer

- EDRP
Emergency demand response program

- ESSs
Energy storage systems

- GLODF
Generalized line outage distribution factor

- ICA
Imperialist competitive algorithm

- I/C
Interruptible/curtailable service

- LF
Load factor

- ISO
Independent system operator

- MCDM
Multi-criteria decision-making

- MIP
Mixed integer programming

- MOSOA
Multi-objective seeker-optimization-algorithm

- PC
Peak compensate

- PDR/PTR
Peak day rebates/peak time rebates

- PEM
Price elasticity matrix

- PLP
Peak load pricing

- PQ
Power quality

- PSO
Particle swarm optimization

- PTV
Peak to valley

- RESs
Renewable energy sources

- RTP
Real-time pricing

- SG
Smart grid

- TCPST
Thyristor-controlled phase shifting transformer

- TCSC
Thyristor-controlled series capacitor

- THD
Total harmonic distortion

- TOU
Time of use

- UPQC
Unified power quality conditioner

- VGC
Vickrey–Clarke–Groves

## Notes

## References

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