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Behavioral model of power converter
The DC-DC Converter block represents a behavioral model of a power converter. This power converter regulates voltage on the load side, and the required amount of power is drawn from the supply side so as to balance input power, output power, and losses. Optionally the converter can support regenerative power flow from load to supply.
The following circuit illustrates the behavior of the converter.
The P_{fixed} component draws a constant power, and corresponds to converter losses that are independent of load current. The power drawn is set by the Fixed converter losses independent of loading parameter value. The resistor R_{out} corresponds to losses that increase with load current, and is determined from the value you specify for the Percentage efficiency at rated output power parameter.
The voltage source is defined by the following equation:
v = v_{ref} – i_{load}D + i_{load}R_{out}
where:
v_{ref} is the load side voltage set point, as defined by the value you specify for the Output voltage reference demand parameter.
D is the value you specify for the Output voltage droop with output current parameter. Having a separate value for droop makes control of how output voltage varies with load independent of load-dependent losses.
The current source value i is calculated so that the power flowing in to the converter equals the sum of the power flowing out plus the converter losses.
If the voltage presented by the load is higher than the converter output voltage reference demand, then power will flow from the load to the converter. If you set the Power direction parameter to Unidirectional power flow from supply to regulated side, then the power is absorbed by the converter, and the current source current i is zero. If you set the Power direction parameter to Bidirectional power flow, then the power is transmitted to the supply side, and i becomes negative.
Optionally the block can include voltage regulation dynamics. If you select Specify voltage regulation time constant for the Dynamics parameter, then a first-order lag is added to the equation defining the voltage source value. With the dynamics enabled, a step change in load results in a transient change in output voltage, the time constant being defined by the Voltage regulation time constant parameter.
The model is based on the following assumptions:
The two electrical networks connected to the supply-side and regulated-side terminals must each have their own Electrical Reference block.
The supply-side equation defines a power constraint on the product of the voltage (v_{s}) and the current (i_{s}). For simulation, the solver must be able to uniquely determine v_{s}. To ensure that the solution is unique, the block implements two assertions:
v_{s} > 0
i_{s} < i_{max}
The first assertion ensures that the sign of v_{s} is uniquely defined. The second deals with the case when the voltage supply to the block has a series resistance. When there is a series resistance, there are two possible steady-state solutions for i_{s} that satisfy the power constraint, the one with the smaller magnitude being the desired one. You should set the value for the Maximum expected supply-side current parameter (i_{max}) to be larger than the expected maximum current. This will ensure that when the model is initialized the initial current does not start at the undesired solution.
The set point for the voltage regulator, and the output voltage value when there is no output current. The default value is 10 V.
The number of volts that the output voltage will drop from the set point for an output current of 1 A. The default value is 0.1 V/A.
Select one of the following methods for the direction of power conversion:
Unidirectional power flow from supply to regulated side — Most small power regulators are unidirectional. This is the default option.
Bidirectional power flow — Larger power converters can be bidirectional, for example, converters used in electric vehicles to allow regenerative braking
Set this value to a value greater than the maximum expected supply-side current in your model. Using twice the expected maximum current is generally sufficient. For more information, see Basic Assumptions and Limitations. The default value is 2 A.
The output power for which the percentage efficiency value is given. The default value is 10 W.
The efficiency as defined by 100 times the output load power divided by the input supply power. The default value is 80 percent.
The power drawn by the P_{fixed} component in the equivalent circuit diagram, which corresponds to converter losses that are independent of load current. The default value is 1 W.
Specify whether to include voltage regulation dynamics:
No dynamics — Do not consider the voltage regulation dynamics. This is the default option.
Specify voltage regulation time constant — Add a first-order lag to the equation defining the voltage source value. With the dynamics enabled, a step change in load results in a transient change in output voltage.
The time constant associated with voltage transients when the load current is stepped. This parameter is only visible when you select Specify voltage regulation time constant for the Dynamics parameter. The default value is 0.02 s.
This is the value of v_{ref} at time zero. Normally, v_{ref} is defined by the Output voltage reference demand parameter. However, if you want to initialize the model with no transients when delivering a steady-state load current, you can set the initial v_{ref} value by using this parameter, and increase it accordingly to take account of output resistance and droop. This parameter is only visible when you select Specify voltage regulation time constant for the Dynamics parameter. The default value is 10 V.