Optimal linear control of the output voltage of a grid-connected single-phase photovoltaic power source
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Abstract
The object of the study is an autonomous source of sinusoidal voltage, which consists of a bridge frequency converter with PWM, equipped with an output LC filter and a single-phase nonlinear output transformer with an additional output filter, which is connected to the non-autonomous grid. The nonlinearity of the magnetic system of the transformer is approximated by an odd function of the arctg type. The substitution of variables made possible to develop a mathematical description of the circuit in the form of a nonlinear singularly perturbed system of differential equations. It is assumed that there is an attractive invariant surface, which makes it possible to reduce the order of the original system of equations. An analytical form of the equations of this surface in the form of a series in powers of a small parameter is obtained. A system of lower-order differential equations is obtained that is equivalent in some region to the original nonlinear singularly perturbed system. The non-linear reduced system is transformed to a form that has made it possible to apply the linear feedback control strategies. The Lyapunov function is obtained as a quadratic form, the coefficients of which are solutions of the matrix algebraic Riccati equation. A condition is set out in which the use of these coefficients guarantees the local asymptotic stability of this nonlinear system. The results of digital simulation are presented. The simulation was performed taking into account the limitations inherent in the real object of power electronics and affecting the possibility of technical implementation of the obtained control strategy. Local equivalency and isomorphism in the control strategies of full-length and reduced systems avoids the need to measure all variables in the space of states, which facilitates practical implementation. The possibility of reducing the impact of load jumps on the form of the output voltage has been checked, taking into account the constraints specific to real systems, has been verified using digital simulation.
Ref. 11, fig. 2.
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