Handbook of Distributed Generation pp 285-316 | Cite as

# Steady-State Analysis of Unbalanced Distribution Networks with High Penetration of Photovoltaic Generation

## Abstract

Thrust for clean energy has led to increasing penetration of Photovoltaic (PV) generation in distribution networks . Multiple factors affecting the steady-state operations of unbalanced distribution networks in the presence of PV generation necessitates detailed modelling of all network components in order to assess the impact of Distributed Generation (DGs) . This chapter provides an overview of phase-domain modelling of distribution networks, need and application of sequential time simulations (STS) in determining feeder response characteristics in the presence of PVDGs and factors affecting their response characteristics. Parameters such as hosting capacity of feeder, voltage profile , active and reactive power demand , reverse power flow , power factor and performance of voltage regulating equipment are discussed. Necessity and role of energy storage systems is also discussed for the distribution networks with PVDGs. Several case studies are presented to elaborate the effect of PVDGs on steady-state operations of unbalanced distribution networks.

## Keywords

Reactive Power Power Flow Battery Energy Storage System Node Voltage Substation Node## Nomenclature

## Transformer and Voltage Regulator Modelling

- \({\text{CT}}_{\text{P}} ,{\text{CT}}_{\text{S}}\)
Respectively, primary and secondary side current rating (A) of Current Transformer (CT);

- \(I_{An} ,I_{Bn} ,I_{Cn}\)
Phase currents (A) on primary side of Voltage Regulator (VR) in phase

*a*,*b*and*c*, respectively;- \(I_{an} ,I_{bn} ,I_{cn}\)
Phase currents (A) on secondary side of VR in phase

*a*,*b*and*c*, respectively;- \(N_{1} ,N_{2}\)
Number of turns in shunt and series winding, respectively, in VR;

- \(N_{\text{PT}}\)
Turns ratio of potential transformer;

- \(R_{{{\text{comp-}}\varOmega }} ,X_{{{\text{comp-}}\varOmega }}\)
Resistance and reactance (Ω) obtained for VR setting;

- \(R_{{{\text{line-}}\varOmega }} ,X_{{{\text{line-}}\varOmega }}\)
Resistance and reactance (Ω) for line to be compensated;

- \(R_{\text{pu}} ,X_{\text{pu}}\)
Resistance and reactance in per unit for VR setting;

- \(R_{\text{pu}}^{\prime} ,X_{\text{pu}}^{\prime}\)
Resistance and reactance (V) for VR setting;

- \(V_{An} ,V_{Bn} ,V_{Cn}\)
Phase to neutral voltage (V) on primary side of VR for phase

*a*,*b*and*c*, respectively;- \(V_{\text{L}} ,I_{\text{L}}\)
Load side voltage (V) and current (A), respectively, in VR;

- \(V_{\text{LN}}\).
Line to neutral voltage (V) in VR;

- \(V_{an} ,V_{bn} ,V_{cn}\)
Phase to neutral voltage (V) on secondary side of VR for phase

*a*,*b*and*c*, respectively;- \(a_{\text{r}} ,a_{\text{R}}\)
Voltage regulator ratio and effective voltage regulator ratio, respectively;

- \(a_{ra} ,a_{rb} ,a_{rc}\)
VR ratio in phase

*a*,*b*and*c*, respectively.

## PV Array Modelling

- \(\Delta_{\text{T}}\)
Difference in module temperature with respect to Standard Temperature Conditions (STC) in Kelvin

- \(G_{n}\)
Global irradiance under STC (W/m

^{2})- \(I_{0, n}\)
Diode saturation current (A) under STC

- \(I_{0}\)
Diode saturation current (A) under normal temperature

- \(I_{\text{mp}}\)
Module current (A) when PV module operates at MPP

- \(I_{\text{pv}}\)
PV Module current (A) due to photovoltaic effect

- \(I_{{{\text{sc}},n}}\)
PV module short circuit current (A) under STC

- \(K_{\text{I}}\)
Coefficient of temperature for current in %/K

- \(K_{\text{V}}\)
Coefficient of temperature for voltage in %/K

- \(N_{\text{s}}\)
Number of PV cells connected in series in a PV module

- \(P_{{{ \hbox{max} },{\text{e}}}}\)
Maximum power (W) produced by module under STC

- \({\text{PV}}_{\text{area}}\)
Gross area of photovoltaic modules receiving solar insolation, m

^{2}- \(R_{\text{p}}\)
Equivalent parallel resistance in Ω

- \(R_{\text{s}}\)
Equivalent series resistance in Ω

- \(V_{\text{mp}}\)
PV Module voltage (V) operating at maximum power point

- \(V_{{{\text{oc}},n}}\)
PV module open circuit voltage (V) under STC

- \(V_{\text{t}}\)
Thermal voltage (V) of PV module at temperature \(T\)

*G*Global irradiance in W/m

^{2}- \(I\)
PV Module current (A) at given temperature and irradiance

- \(T\)
Temperature of PN junction in Kelvin

- \(V\)
PV module voltage (V) at given temperature and irradiance

*a, k*Diode ideality factor, Boltzmann’s constant

- \(q\)
Electron charge

- \(\eta\)
Overall gross efficiency of photovoltaic plant

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