        There are many companies that make Permanent Magnet Brush less Motors and all have there own variety of variables they use to for the analyse of the motor. I reviewed many of these sites and took the variables that made the most sense and came up with the set in Table 1.0.

For simplicity an in order to help present the analytical sections of this TDA we are going to present the following naming convention along with a set of symbols that define specific parameters of the PMB DC motor. We will reference these parameters throughout the analysis. The analysis that we will present will be in two states, Steady State or Static performance and Commutating or Dynamic performance. Our main objective is to use the data collected for proof of concept in order to develop a reliable test criteria for the Hybrid Power Modules Test System as defined in the Bridge Test System TDA. Characterising a motor However, would require the addition of a dynamometer along with a few other parameters.  As stated previously we will cover this in another TDA.

 Symbol Description Units Terminal Resistance Ohms or (impedance Z) Inductance of he phase coils ABC Henry Torque Constant Ounce-Inches / Amp Torque Output of Motor Ounce-Inches / Amp Motor Current Amps Most Efficient Motor Current Amps @ RPM Motor Efficiency Percent % {0 to 100} No Load Motor Current Amps @ RPM Input Motor Power Watts Motor Mechanical Output Power Watts Motor Voltage Generator Constant Volts / 1000RPM Generator Constant in radian format Volts / Radians / Sec Voltage at Motor terminals Volts Revolutions Per Minute RPM Battery Supply Voltage Volts Line A to Line B Generator Voltage Volts Line B to Line C Generator Voltage Volts Line C to Line A Generator Voltage Volts Applied Voltage to terminals A-B volts Applied Voltage to terminals B-C volts Applied Voltage to terminals C-A volts Number of steps of the motor for 2 integer rotational position index 0,1..n integer The following shows relationship between DELTA (Line to Line) and WYE (Line to Neutral) vectors. In the WYE configuration the coil and line currents are equal and the line voltage is times the coil voltage. In the Delta configuration the coil voltages are equal and the line currents are times the line current. The equation sets derived here are for the purpose of characterizing system block functions. The actual losses within the motor are not covered here except where they have direct connections to the equation set. The manufacturing efficiency and design parameters of the motor are usually supplied by the manufacture. We will discuss motor efficiency and characterizing in a later article.   Top

# Line to Line and Line to NeutralDelta to Wye Vectors Phase ab was selected as the 0º reference which we will explain later in the analysis. The voltage equations for both line to line and line to neutral as follows.
The Line to Neutral voltage is The Line to Line voltage is # 4 Wire Line to Neutral "WYE"      # The applications of Faraday's Law states that an EMF will be generated due to the magnetic field (Flux) and the field windings passing in proximity to each other. This EMF is the Motor Voltage Generator Constant and for a typical 6 pole motor is in the range of 1 to 6 volts / 1000 RPM, where the average is around 2.5 volts/1000 RPM. The motor manufacturer will give this constant in the motor specifications. The contributing factors of this constant are the magnetic field strength, the coil size and the number poles. Since this is in a rotating environment, then in order to use this in our analysis we have to transform this to an angular or polar domain, hence; Volts /Radians/Seconds relating to electrical revolutions. Converting this to seconds is a preference and does not matter in the final analysis as long as the labels are in domain order. First rule of analysis if the labels do not make sense neither will the results. Hence: Keeping the terms in the proper domains, the conversion to electrical rotation radians/seconds (Rotational Position per Second) is also required. From the previous page,the Electrical revolutions with relation to the mechanical revolutions is defined as . Therefore the Electrical Radian/Seconds to mechanical rotation is defined as: Hence: This now satisfies the domain changes and labeling.

The 3Ø Motor Generator equations that define the EMF generated Line to Line , , and Line to Neutral ,  using phase ab as the 0º reference are as follows. Plotting these equations gives us a better perspective of the voltage levels of the two systems.  For those who want to research this further, these equations are derived from applications of poly-phase systems and phasor geometry.

# Voltage equation set for 3 wire DELTA system, Line to Line   # Voltage equation set for 4 wire WYE system, Line to Neutral   # Generator Voltage developed at 100 RPM6 pole permanent magnet brushless motor Page 2 covers the creation of the applied voltage equation set to commutate the motor.
Page 3 covers the application  analysis of the Bridge Test System data comparisons.