Apparatus and method for determining impedance characteristics of an electrical load
Apparatus ( 103 ) suitable for determining the resistance and inductance of an electric motor ( 101 ) estimates the phase shift between a voltage applied to the motor and motor current. Estimation of the phase shift employs a heterodyne technique. The measured motor current is conditioned prior to heterodyning in a mixer 203 in order to reduce the effects of nonlinearities introduced by a voltage source inverter ( 102 ) which supplies the motor ( 101 ) with a voltage. A value for impedance may be calculated as a ratio of a voltage applied to the motor and the motor current. The resistance and inductance may then be calculated from the impedance and phase shift calculations. In cases where the voltage applied to the motor cannot be directly measured but only the voltage supply to the voltage source inverter 102 is known, a value for impedance may be determined based on a ratio of a reconstructed voltage signal having a phase angle equal to that of the motor current and the motor current.
1. A method for determining impedance characteristics of an electrical load, the method comprising; applying a test voltage signal to the load, receiving a load current which flows in the load, differentiating the load current and an auxiliary voltage signal, said auxiliary voltage signal having the same frequency as the test voltage signal and zero phase shift, to produce derivative signals, heterodyning the derivative signals to produce heterodyned output signals, and extracting from the heterodyned output signals a phase angle between the derivative of the load current and the derivative of the auxiliary voltage signal which is equivalent to a phase shift between the test voltage signal applied to the load and the load current flowing in the load.
2. The method of claim 1 wherein the auxiliary voltage signal comprises sine and cosine components of equal magnitude and wherein the method comprises heterodyning a derivative of each of the sine and cosine components with the derivative of the load current.
3. The method of claim 1 wherein extracting the phase angle comprises determining an arctangent function of components of the heterodyned output signals.
4. The method of claim 1 further comprising determining an impedance value by dividing the test voltage applied to the load by the load current and determining real and imaginary parts of the impedance value from the determined impedance value and from the extracted phase angle.
5. The method of claim 1 further comprising generating a reconstructed voltage signal having the same phase angle and frequency as the test voltage signal and the load current, differentiating the reconstructed voltage signal and the load current to produce derivative signals, determining an impedance value by dividing the derivative of the reconstructed voltage signal by the derivative of the load current, determining real and imaginary parts of the impedance value from the determined impedance value and from the extracted phase angle.
6. The method of claim 5 further comprising determining the impedance value during a period when non-linear effects due to application of a voltage to the load are at a minimum.
7. An apparatus for determining impedance characteristics of an electrical load, the apparatus comprising; a first module arranged to apply a test voltage signal to the load and to generate an auxiliary voltage signal, said auxiliary voltage signal having the same frequency as the test voltage signal and zero phase shift, a second module arranged to receive a load current which flows in the load and to differentiate the load current and the auxiliary voltage signal to produce derivative signals, and to mix the derivative signals to produce heterodyned output signals, and to extract from the heterodyned output signals, a phase angle between the derivative of the load current and the derivative of the auxiliary voltage signal which is equivalent to a phase shift between the test voltage signal applied to the load and the load current flowing in the load.
8. The apparatus of claim 7 further comprising a second order low pass filter arranged to filter the extracted phase angle.
9. The apparatus of claim 7 wherein the second module is arranged to extract a phase angle by determining an arctangent function of components of the heterodyned output signals.
10. The apparatus of claim 7 comprising a first arithmetic module arranged to determine an impedance value from the test voltage signal applied to the load and the load current, and a second arithmetic module arranged to determine real and imaginary parts of the impedance value from the determined impedance value and from the extracted phase angle.
11. The apparatus of claim 7 wherein the first module is arranged to generate a reconstructed voltage signal having the same phase angle and frequency as the test voltage signal and the load current, and wherein the apparatus comprises a third module arranged to differentiate the reconstructed voltage signal and the load current to produce derivative signals and to determine an impedance value by dividing the derivative of the reconstructed voltage signal by the derivative of the load current, and an arithmetic module arranged to determine real and imaginary parts of the impedance value from the determined impedance value and from the extracted phase angle.
12. The apparatus of claim 11 further comprising a first order low pass filter for filtering the determined impedance value.
13. The apparatus of claim 11 wherein the third module is arranged to determine the impedance value during a period when non-linear effects due to application of a voltage to the load are at a minimum.
14. The apparatus of claim 7 wherein the apparatus is implemented in an integrated circuit.
15. A tangible computer program product having code executable by a computer system and stored in non-transitory media therein to perform a method for determining impedance characteristics of an electrical load in accordance with claim 1 , wherein the impedance characteristics are determined only from a measurement of the load current.