Amplifier / power supply
(Amplifier)


Model description

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: $$P_{use}=P_{dmd}$$

Inputs

ParameterSymbolUnitDescription
State\(s\)noneOperational state of the component (0=OFF, 1=ON)
PDmd\(P_{dmd}\)WElectric energy demand of the connected drives

Outputs

ParameterSymbolUnitDescription
PSupply\(P_{supp}\)WElectric power demand on the upstream power supply
PLoss\(\dot{Q}_{loss}\)WAccounting (thermal) losses in the device
PTotal\(P_{tot}\)WTotal electric power demand of the component
PUse\(P_{use}\)WElectric power supplied to the downstream components
Efficiency\(\eta\)noneEfficiency of the operational point (PUse/PTotal)

Parameters

ParameterSymbolUnitDescription
Efficiency\(\underline\eta_s\)noneVector of the efficiencies corresponding to the power samples
PowerCtrl\(P_{ctrl}\)WElectric power demand of the integrated control unit if the component in ON
PowerSamples\(\underline P_s\)WSample vector of power demands supplied by the component to the downstream drives