This model implements the energetic behaviour of an amplifier or power supply control for electric drives based on a Willan's approach. Given the input $P_{dmd}$ as the sum of the power demands of all umpstream component. The model will compute the required electric power \(P_{tot}\) to be supplied to the amplifier or power control in order to meet this demand as follows:
$$P_{tot}= \left\lbrace \begin{matrix}P_{ctrl}+ \frac{P_{dmd}}{\eta\left(P_{dmd}\right)} & \text{if }s=1\\0&\text{else}\end{matrix} \right .$$
\(s\) indicates the value of the state-input (0=OFF, 1=ON) and \(P_{ctrl}\) is the constant control power required by the device.
The load specific efficiency is calculated based on liner interpolation using the efficiency samples \(\underline\eta_s\) and power samples \(\underline P_s\), both with \(N\) elements:
$$\eta\left(P_{dmd}\right)=\left\lbrace\begin{matrix}\eta_{s,1}&\forall\,P_{dmd}\leq P_{s,1}\\\eta_{s,N}&\forall\,P_{dmd}\geq P_{s,N}\\\eta_{s,i}+\frac{\eta_{s,i+1}-\eta_{s,i}}{P_{s,i+1}-P_{s,i}} \cdot \left(P_{dmd}-P_{s,i}\right)&\text{else}\end{matrix}\right .$$
Important: \(P_{s,i}\lt P_{s,i+1}\) must hold \(\forall\,i\in\lbrace 1,2,\ldots,N-1\rbrace\).
The difference electric power input and output power are assumed to be thermal losses, thus:
$$\dot{Q}_{loss}=P_{tot}-P_{dmd}$$
Two different supplies of electric power to the amplifier or power supply are considered: First the control power required to oeprated the MC of the device (usually 12/24 VDC supply); second, the supply by the net or intermediated DC circuit. The second one is called the supply power and denoted as \(P_{supp}\):
$$P_{supp}=P_{tot}-P_{ctrl}$$
The useable power of this component type is equal to the power demand of the down-stream components:
$$P_{use}=P_{dmd}$$