State Space Average Modeling of Buck-Boost Converter

Combining the buck and boost converters produces a new converter called the buck-boost converter, also known as a buck-boost converter.

This form of converter output voltage is in anti-phase with the input voltage. In buck and boost converters, there is a time when energy flows directly from the power supply to the load. In a buck-boost converter, energy is first stored in the inductor and then flows to the load, which is their main difference.

The basic working principle of the circuit: When the controllable switch V is in the on state, the power supply E supplies power to the inductor L via V to store energy, and the current is i1. At the same time, capacitor C maintains the output voltage substantially constant and supplies power to the load. Thereafter, V is turned off, and the energy stored by the inductor L is released to the load, and the current is i2. When V is in the on state, uL=E; and when V is in the off state, uL=uo. So, Eton=U0toff, so the output voltage is

The output current is obtained by EI1=U0I2

The state space averaging method is a first-order approximation of the averaging method. Its essence is: according to the original network composed of linear RLC components, independent power supplies and periodic switches, the capacitor voltage and the inductor current are used as state variables, according to the "ON" of the power switching device. And "OFF" two states, using the time averaging technique, get the average state variable in a cycle, transform a nonlinear circuit into an equivalent linear circuit, and establish a state space average model.

For an ideal PWM converter that does not consider parasitic parameters, the equation of state corresponding to two switching states in a continuous switching mode (CCM) is:

Where d is the duty cycle of the power switch, d=ton/T, ton is the on time, T is the switching period; x=[iL uC], x is the state variable, x is the derivative of the state variable, iL Is the inductor current, uc is the capacitor voltage, E is the input voltage of the switching converter; A1, A2, B1, B2 are the coefficient matrix, which is related to the structural parameters of the circuit.

The average equation for the above equation is x=Ax+Bvi, A=dA1+(1-d)A2, B=dBq+(1-d)B2, which is the famous state space averaging method. It can be seen that the time-varying circuit becomes a non-time-varying circuit. If d is a constant, the system described by this equation is a linear system, so the contribution of the state space averaging method is to replace a switching circuit with a linear circuit.