Application of the Average Circuit Method to the Modelling of AC to DC Converters

The state-space averaging technique i s currently used for modelling DC-DC converters in constant frequency conventional "duty ratio programmed mode" as well as "current programmed mode". It consists in averaging the different exact descriptions of the switched models over a cycle, to obtain a continuous model. At the sampling instants corresponding to the beginning of each cycle, the state vector of the simplified model is identical to the real state vector, to the first order and partly to the second order. With this simplified model, one ccm associate either on equivalent electric circuit for large or small signals, or a sampled or continuous transfer function between a state variable (or the output) and the control variable. In this paper, we propose to generalize the method to AC-DC converters (half or full controlled bridge) working in fully continuous conduction mode and driving a DC machine or a system (converter-AC machine) modelled as a DC machine. We can then take into account the defaults of the source (transformer with its leakage inductance and resistance seen from the secondary winding) and model their consequences : for example average voltage drop due to the overlap phenomena and depending on the current amplitude, influence of a supplementary inductance or resistance on the dynamic behaviour of the state vector. With this average model, one enn associate an equivalent electric circuit or a transfer function between a state variable (or the output : the speed, generally) and the phase shift angle with regard to the natural commuta tion instant. When the source can be considered as perfect we show that the sampled transfer function corresponds to a sampler, with period equal to the duty cycle, a gain block (linear or not), a zero order hold system plus the transfer function of the continuous DC system. It is this model we get when we split the variable input voltage into a continuous term corresponding to the average voltage, and an alternative term, the effect of which on the state variable or output is neglected, an the system can be considered a low-pass filter.