Reaction Wheel Array Power Model

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Description

The Reaction Wheel Array Power Model is a Power Node Model that attaches to a Reaction Wheel Array to model the electrical load from driving BLDC motors. The model implements standard DC motor equations to compute current draw, mechanical power, and copper losses based on commanded voltages and wheel speeds. When the sum of commanded voltages exceeds available bus voltage, output commands are scaled proportionally.

Unlike constant power loads, reaction wheel motors are classical resistive loads where the resistance can be computed directly from the commanded voltages and wheel speeds without quasi-static iteration.

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Example Use Cases

• Power-Limited Actuation: Simulate realistic wheel behavior when battery voltage drops, automatically scaling voltage commands.
• Power Budget Analysis: Evaluate power consumption during slew maneuvers and momentum management operations.
• Current Spike Analysis: Determine peak current draw during high-torque commands for power system sizing.

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Module Implementation

DC Motor Equations

Reaction wheels use BLDC motors driven by inverter electronics. The model implements the following motor equations for each wheel.

Back-EMF: The rotating motor generates a voltage proportional to speed:

$$V_{\text{emf}}=K_e\cdot \omega$$

where $K_e$ is the back-EMF constant and $\omega$ is the wheel angular velocity.

Motor Current: The current drawn depends on the voltage applied minus back-EMF:

$$I=\frac{V_{\text{cmd}}-V_{\text{emf}}}{R_{\text{winding}}}$$

If the back-EMF exceeds the applied voltage (regenerative braking condition), the current is clamped to zero as the model does not simulate power return to the bus.

Motor Torque: The torque produced is proportional to current:

$$\tau =K_t\cdot I$$

where $K_t$ is the torque constant. For an ideal motor in SI units, $K_t=K_e$.

Power Consumption

The total DC power draw per wheel includes mechanical power, copper losses, and overhead:

$$P_{\text{DC}}=\frac{P_{\text{mech}}+P_{\text{copper}}}{\eta }+I_{\text{no-load}}\cdot V_{\text{in}}+P_{\text{standby}}$$

where:

• $P_{\text{mech}}=|\tau \cdot \omega |$ is the mechanical power delivered to the wheel
• $P_{\text{copper}}=I^2\cdot R_{\text{winding}}$ is the winding resistive loss
• $\eta$ is the drive inverter efficiency
• $I_{\text{no-load}}$ accounts for bearing friction, windage, and iron losses
• $P_{\text{standby}}$ is the quiescent power of the drive electronics

Voltage Limiting

If the sum of commanded voltages exceeds the available input voltage, all output voltage commands are scaled:

$$s=\frac{V_{\text{in}}}{\sum |V_{\text{cmd}}|}$$ $$V_{\text{out}}=s\cdot V_{\text{cmd}}$$

Resistance Calculation

The equivalent resistance presented to the power bus is:

$$R=\frac{V_{\text{in}}^2}{\sum P_{\text{DC}}}$$

When no power is being drawn, the resistance defaults to a large value ($10^{12}\Omega$).

Parameters

Parameter	Description	Default
TorqueConstant_Kt	Motor torque constant (N·m/A)	0.02
BackEmfConstant_Ke	Motor back-EMF constant (V/(rad/s))	0.02
WindingResistance	Motor winding resistance (Ω)	1.5
NoLoadCurrent	No-load current for friction/windage (A)	0.05
DriveEfficiency	Inverter efficiency (0–1)	0.85
DriveStandbyPowerPerWheel	Quiescent power per wheel (W)	0.5

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Assumptions/Limitations

• All wheels in the array share the same motor and drive parameters.
• Regenerative braking is not modeled; negative current is clamped to zero.
• The model assumes ideal inverter behavior with constant efficiency across the operating range.
• When disabled or input voltage is zero, output voltage commands are set to zero.
• Thermal effects on winding resistance and motor constants are not modeled.