Equivalent circuit of photovoltaic generator using Newton-Raphson algorithm
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.
circuits circuit analysis electric power generation mathematical modeling nonlineatity newton-raphson method solar power