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

  • Kalpesh JoshiEmail author
  • Naran Pindoriya


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.


Reactive Power Power Flow Battery Energy Storage System Node Voltage Substation Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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;


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;


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


Difference in module temperature with respect to Standard Temperature Conditions (STC) in Kelvin


Global irradiance under STC (W/m2)

\(I_{0, n}\)

Diode saturation current (A) under STC


Diode saturation current (A) under normal temperature


Module current (A) when PV module operates at MPP


PV Module current (A) due to photovoltaic effect


PV module short circuit current (A) under STC


Coefficient of temperature for current in %/K


Coefficient of temperature for voltage in %/K


Number of PV cells connected in series in a PV module

\(P_{{{ \hbox{max} },{\text{e}}}}\)

Maximum power (W) produced by module under STC


Gross area of photovoltaic modules receiving solar insolation, m2


Equivalent parallel resistance in Ω


Equivalent series resistance in Ω


PV Module voltage (V) operating at maximum power point


PV module open circuit voltage (V) under STC


Thermal voltage (V) of PV module at temperature \(T\)


Global irradiance in W/m2


PV Module current (A) at given temperature and irradiance


Temperature of PN junction in Kelvin


PV module voltage (V) at given temperature and irradiance

a, k

Diode ideality factor, Boltzmann’s constant


Electron charge


Overall gross efficiency of photovoltaic plant


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IIT GandhinagarGandhinagarIndia

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