Equivalent circuit of photovoltaic generator using Newton‐Raphson algorithm

Abstract

Purpose

The purpose of this paper is to develop a linearized equivalent electrical circuit of a photovoltaic generator. This circuit is appropriate to confront problems such as numerical instability, increased computational time and nonlinear/non‐canonical form of system equations that arise when a photovoltaic system is modelled, either with differential equations or with equivalent resistive circuits that are generated by electromagnetic transient software packages for power systems studies.

Design/methodology/approach

The proposed technique is based on nonlinear and well‐tested i_pv−v_pv equations which are however used in an alternative mathematical manner. The application of the Newton‐Raphson algorithm on the i_pv−v_pv equations leads to uncoupling of the i_pv and v_pv quantities in each time step of a digital simulation. This uncoupling is represented by a linearized equivalent electrical circuit.

Findings

The application of nodal analysis equivalent resistive circuits using the proposed equivalent photovoltaic generator circuit leads to a system model based on linear algebraic equations. This is in opposition to the nonlinear models that normally result when a nonlinear i_pv−v_pv equation is used. In addition, using the proposed scheme, the regular systematic methods of circuit analysis are fully capable of deriving the differential equations of a photovoltaic system in standard form, thus avoiding the time‐consuming solution process of nonlinear models.

Originality/value

In this paper, a new method of using the i_pv−v_pv characteristic equations is proposed which remarkably simplifies photovoltaic systems modeling. Moreover, a very important practical application is that by using this methodology one can develop a photovoltaic generator element in electromagnetic transient programs for power systems analysis, of great value to power engineers who are involved in photovoltaic systems modeling.

Citation

Theocharis, A.D., Charalampakos, V.P., Drosopoulos, A. and Milias‐Argitis, J. (2012), "Equivalent circuit of photovoltaic generator using Newton‐Raphson algorithm", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 31 No. 4, pp. 1224-1245. https://doi.org/10.1108/03321641211227492