Second Order Sliding Mode Control of the Output Voltage of an Alternative Power Source in a Single-Phase Grid
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Abstract
The object of the study is an alternative power source of sinusoidal voltage, consisting of a PWM bridge frequency converter, a single-phase linear output transformer with an additional output LC-filter, which is connected to a non-autonomous grid. An additional inductance is inserted into the primary winding of the transformer to reduce current ripples. The mathematical model of this system, which is described by ordinary differential equations, is constructed. Usual assumptions are used that the system of equations is linear, and the current of the magnetization of the transformer can be neglected. Therefore, a transition to a simplified circuit for replacing a single-phase transformer is possible. The synthesis of the control law by means of the forced introduction of the traditional sliding mode for minimizing the influence of perturbations on the source output voltage is carried out. Conditions of the existence of a sliding mode with the use of the known method of equivalent control are obtained. In the formation of a sliding surface, a sliding mode of the second order was used, which made it possible to reduce the number of quantities of electric variables that require direct measurement. The proposed strategy allows achieving more robustness, acceptable steady state error, exponential convergence, and good matching of the output voltage of the source for the autonomous consumer network. This strategy eliminates the need to use an accurate current sensor, which reduces the cost of the frequency converter and facilitates practical implementation. The features of the functioning of an alternative energy source with this type of sliding mode in a system with real parameters of electric circuits are investigated. The comparisons are presented as simulations among conventional sliding mode (first order) control and second order sliding mode in a sliding surface at different test conditions, such as stationary state, grid voltage perturbations and output load disturbances.
The results of digital simulation are presented. Simulation was performed taking into account the constraints inherent in the real object of power electronics and influencing the possibility of technical implementation of the developed control strategy. In the mode of minimum dissipation there is a very slight deterioration of the spectral composition of the voltage, which can be neglected. The possibility of reducing the effect of load changes on the form of the output voltage has been considered, taking into account the constraints specific to real systems, and has been verified using digital simulation.
Ref. 14, fig. 4
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