Synthesis of the output voltage control loop of a nonlinear Solid State Transformer

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 filter capacitor, which is connected to the output of the secondary winding. The factors hindering the technical implementation of the control of this object are analyzed. The nonlinearity of the transformer's magnetic system is approximated by a power series along with odd exponents. 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 local region of state space is defined in which a nonlinearity can be transformed to a form that allows the fulfillment of the conditions of the Poincaré-Lyapunov theorem for a nonlinear system of differential equations. A system of lower-order differential equations is obtained that is equivalent in some region to the original nonlinear singularly perturbed system. The possibility of replacing a nonlinear system of a reduced order by its first approximation for the construction of a control law is substantiated. The control law is synthesized using the Lyapunov function method for the first-approximation system of equations. The control law is a linear combination of the variables of the reduced system of equations. The choice of the Lyapunov function in the form allowing to establish an unambiguous relationship between the coefficients of this function and the scale coefficients of the control law equation is proposed. Analytical expressions for calculating these scale factors are obtained. 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 law.Bibl.10, Fig.2