FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
As amended by the Patents (Amendment) Act, 2005
AND
The Patents Rules, 2003
As amended by the Patents (Amendment) Rules, 2005
COMPLETE SPECIFICATION
(See section 10 and rule 13)
TITLE OF THE INVENTION
A system for non-linear dynamic model of single phase PM BLDC motor.
APPLICANTS
Crompton Greaves Limited, CG House, Dr Annie Besant Road, Worli,
Mumbai 400 030, Maharashtra, India, an Indian Company.
INVENTOR
Fazil Mohammed of Crompton Greaves Ltd, Analytics Centre, CG Global
R&D Centre, Kanjur (E), Mumbai 400042, Maharashtra, India, an Indian
National.
PREAMBLE TO THE DESCRIPTION
The following specification particularly describes the nature of this invention and the manner in which it is to be performed:

Field of the Invention:
This invention relates to modeling of PM BLDC motors.
Particularly, this invention relates to a system for non-linear dynamic model of single phase PM BLDC motor.
Background of the Invention:
A Brushless PM BLDC motor uses permanent magnets on rotor for field excitation and electronically commutated winding on stator. The rare earth magnets helps to make these motors efficient and compact compared to induction motor and mechanically commutated dc motor. Single phase PM BLDC motors, though less efficient compared to three phase PM BLDC motors, is cost effective and easy to mass manufacture. It is used in applications which require output power ranges from fraction of watts to less than hundred watts.
Non-salient permanent magnet motors have two types of torque acting on the rotor, excitation and cogging torque. Excitation torque is generated due to interaction of winding current and permanent magnet field, whereas cogging torque is due to interaction of stator tooth and permanent magnet. The uniform air gap single-phase PM BLDC motors have coincident zero torque positions of excitation and cogging torque which makes them inherently non self starting. Asymmetric air gap is provided to shift the zero torque position of cogging torque from that of excitation torque and hence make them self starting.

Dynamic behaviour of SP PM BLDC motor can be modelled accurately in finite element softwares with transient solver. Very small time step is necessary because of irregular changes in back EMF, cogging torque and current waveform due to asymmetric air gap. Large simulation time required for transient finite element analysis (FEA) makes design variation studies difficult and modelling dynamic behaviour of motor with a control technique near impossible. Co-simulation technique using a circuit modeller and finite element software can address the modelling of control algorithm, but again FE machine model results in long simulation time.
Modelling of SP PM BLDC has been addressed in earlier literatures for showing the effects of either a modified control algorithm [l]-[3], [5], [12] or design changes in magnetic structure [8]-[10].
The dynamic model in these studies uses circuit coupled finite element method and has a long simulation time but produces accurate results. Reference [6] explains numerical modelling and simulation of a three phase brushless permanent-magnet dc (BLDC) motor using time-stepping FEM. The phase variable model for three phase BLDC motor explained in [13] and [15] has small simulation time, but neglects armature reaction and non linearity because of magnetic saturation. An accurate non linear model of doubly salient single phase permanent magnet motor is explained in [4]; non-linear data from finite element analysis is fitted as Fourier series and used in dynamic model.

Objects of the Invention:
An object of the invention is to provide an accurate non-linear model single phase PM BLDC motor.
Another object of the invention is to provide a modelling system which does not neglect armature reaction and non-linearity because of magnetic saturation
Yet another object of the invention is to consider non-linear flux linkage variation, armature reaction, and cogging torque for modelling of a motor.
Still another object of the invention is to reduce simulation time compared to finite element transient simulation.
Summary of the Invention:
According to this invention, there is provided a system for providing a non-linear dynamic model of single phase PM BLDC motor comprising rotor, stator and magnetic ring, said system comprises:
a. extraction means for extracting pre-defined non-linear quantities from said
motor;
b. finite element analysis means adapted to provide a finite element analysis of
said motor;
c. finite element modeling means for providing a Finite element modeling of
said motor with halbach magnetization;

d. first estimation means adapted to provide estimation of back EMF constant
and cogging torque variation with rotor position of said motor;
e. second estimation means for estimating the effect of armature reaction on
back EMF constant variation using finite element analysis;
f. motor modeling means adapted to provide a motor model by obtaining
voltage equation model and torque equation model in accordance with pre
defined equations;
g. power supply modeling means adapted to provide a power supply model;
and
h. load modeling means adapted to provide a load model
Typically, said extraction means includes tabulation means adapted to tabulate extracted Non linear quantities in the form of look up tables from parametric analysis of static 2D finite element model.
Typically, said Finite Element Modeling means includes means for modeling halbach magnet rings as segments with magnetization direction of segments belonging to a pole pair varies from 0 to 360 degrees
Typically, said first estimation means includes means to model two coils around tooth namely outer coil and inner coil having same number of turns per coil in order to provide, estimation of effect of armature reaction on EMF constant.
Typically, said second estimation means includes means to obtain Flux linkage variation with position of outer coil with armature reaction being modeled by

applying current to inner coil, said flux linkage variation being obtained for a pre-defined number of armature current values.
Typically, said second estimation means includes means to determine direction of current in the coil from unexcited EMF constant variation
Typically, said second estimation means includes means to pass current through outer coil in order to estimate effect of armature reaction on flux linkage variation of inner coil
Typically, said second estimation means includes averaging means to average flux linkage of inner and outer coil in order to obtain flux linkage variation of single coil.
Typically, said second estimation means includes calculation means adapted to calculate EMF constant from flux linkage using pre-defined equation.
Typically, said second estimation means includes calculation means to calculate the variation of flux linkage of coil and cogging torque with rotor position using series of simulations by shifting position of rotor over twice pole pitch in small steps.
Typically, said motor model includes implementation means in order to implement said motor model based on pre-define voltage and torque equations of DC motor.

Brief Description of the Accompanying Drawings:
The invention will now be described in relation to the accompanying drawings, in
which:
The specification and design details of SP PM BLDC (prototype) motor is given in
Table J.
Table 1: Specifications and Dimensions of SP PM BLDC (Prototype) motor

Sr. No Specifications Dimensions
1 Source Voltage 170 V
2 Power Output 20 W
3 Number of Pole 8
4 Rated Speed 360 rpm
5 Outer diameter 104 mm
6 Average radial air gap length 1.2 mm
7 Stator core length 11 mm
8 Magnet thickness 3.5 mm
9 Number of turns per coil f 1020 turns
Inverter states of full bridge inverter are given in Table 2; Table 2: Inverter states

State Tl T2 T3 T4
1 On Off Off On
2 On Off Off Off

3 Off On On Off
4 Off Off On Off
5 Off Off Off Off
Current limit control is implemented using modified operating states given in Table 3;
Table 3: Inverter states with current limit control

Source Current position limit;
68) If rotor position > position limit, then determine if coil current > current limit;
69) If rotor position < position limit, then shift the position of rotor and go to step 63;
70) If coil current > current limit, then determine flux linkage A = f(, i), if no, then, go to step 62;
71) End.
Similarly effect of armature reaction on flux linkage variation of inner coil is estimated by passing current through outer coil. The average flux linkage of inner and outer coil is taken as the flux linkage variation of single coil. EMF constant is calculated from flux linkage using equation (1) and its variation with armature current and position is shown in Figure 7. In Figure 7, X-axis (I) indicates EMF constant in Volt-Sec/Rad against Y axis (J) indicates rotor position (mechanical degree). Kl, K2, K3, K4, K5 and K6 indicate different current values which are used to calculate EMF constant.

Typically, the system for non-linear dynamic model of said single phase PM BLDC motor is disclosed.
Dynamic model of single phase PM BLDC motor consists of three parts, a power supply model which drives the motor model coupled to a load model based on position and current feed back.
In accordance with an additional embodiment of this invention, there is provided a Motor modeling means adapted to provide a motor model.
Motor model is implemented based on voltage and torque equations of DC motor. The back EMF of motor

Where, eh is back emf, keis EMF constant which is function of rotor position, 9 and winding current,/ and w is angular velocity. The voltage equation is

Where, v10 is inverter output voltage, R and Lare resistance and inductance winding.
Torque equation of single phase PM BLDC motor is

Where, Tm is motor torque and TCR is cogging toque obtained from FEA as function of rotor position θ. Model implementation of voltage and torque equation is shown

in Figures 8a and 8b. Inverter output voltage vm is having constant magnitude with
polarity depended on rotor position. The value of back EMF is calculated as product of angular velocity and EMF constant, which is obtained from look up table shown in Figure 7, based on rotor position and winding current.
Figures 8a and 8b illustrates Motor model considering non linear variations of EMF constant and cogging torque respectively.
In accordance with yet an additional embodiment of this invention there is provided a Power Supply modeling means adapted to provide a Power Supply model.
A single-phase drive with a full bridge inverter is used as drive as in Figure 9, each leg consists of two switches (TI & T2, or T3 & T4) and two anti-parallel diodes (D1 &D2, or D3 & D4). The gate drive signals are generated based on rotor position feedback. Inverter states of full bridge inverter are given in Table 2 and current limit control is implemented using modified operating states given in Table 3.
In accordance with still an additional embodiment of this invention, there is provided a Load modeling means adapted to provide a Load model.
The torque developed in motor has to work against load, inertia and moving friction. The load in current study is a ceiling fan. The equation governing the load behaviour can be written as


Where, kf is fan constant, is inertia motor including coupled load and b is viscous friction constant. Fan load model implementation is shown in Figure 10.
The system of this invention is explained with reference to a non-limiting exemplary embodiment, as discussed below.
A prototype motor with specification shown in Table 1 is made and inserted in to a ceiling fan casing with blades attached. The motor is driven by a variable DC source. Supply voltage, source current and input power are measured using Yokogawa WT210 single phase power analyzer and waveforms are captured by Yokogawa DL1640 digital oscilloscope,
The fan blades used requires 20watts at rated speed of 360 rpm; so value of fan constant can be derived using this data based on equ.5 and used for simulation of fan load. A comparison predicted and test waveform of voltage across the winding and winding current is shown in Figure 1 la and Figure l1b. Figure 11a illustrates plot of voltage (V) /Current (ma) as X-axis (L) against time in second as Y-axis (M), (N) indicates winding voltage and (O) indicates winding current. Similarly source current waveform for measured and predicted is plotted in Figure 12. Figure 12 illustrates Current .(mA) as X-axis (P) against Time in seconds as Y-axis (Q). (R) and (S) indicate the current measured and simulated respectively. The permanent magnet motors are having low value of core loss and is not considered in this study.

Figure 13a show comparison of predicted and measured value of speed and input power variation with voltage. In figure 13a X-axis (T) illustrates Speed in RPM and Y-axis (U) illustrates Voltage. (Tl) and (T2) indicate the speed measured and predicted respectively. Figure 13b show comparison of predicted and measured value of source current variation with voltage. In figure 13b X-axis (V) illustrates source current in "A" and Y-axis (W) illustrates Voltage. (VI) and (V2) indicate the source current in "A" and predicted respectively, Figure 13c show comparison of predicted and measured value of input power variation with voltage. In figure 13a X-axis (X) illustrates input power in RPM and Y-axis (Y) illustrates Voltage. (XI) and (X2) indicate the input power measured and predicted respectively. There is a minor oscillation present in the proto-type motor, reflecting in variation of time period of current waveform; this along with the core loss can be attributed to the difference between the predicted and test values. The performance deterioration by armature reaction is shown in Figure 14, where efficiency as X-axis (Z) is plotted against voltage as Y-axis (Zl). Z2, Z3 and Z4 are efficiency measured with armature reaction, efficiency predicted with armature reaction and efficiency measured without armature reaction respectively.
A non-linear model of single phase PM BLDC motor has been described and validated using a proto-type ceiling fan. Simple step-by-step approach has been followed starting from extraction of non-linear quantities (flux linkage variation and cogging torque) in the form data table from 2D static finite element analysis to its implementation in dynamic model.

The system of this invention presents accurate modelling of armature reaction and its effect on performance of single phase PM BLDC motor. The model drastically reduces simulation time compared to finite element transient simulation and can be used for developing of control strategy of motor drives, studies related to torque ripple reduction and transient behaviour of motor and the like.

We claim,
1. A system for providing a non-linear dynamic model of single phase PM BLDC motor comprising rotor, stator and magnetic ring, said system comprising:
a. extraction means for extracting pre-defined non-linear quantities from said
motor;
b. finite element analysis means adapted to provide a finite element analysis of
said motor;
c. finite element modeling means for providing a Finite element modeling of
said motor with halbach magnetization;
d. first estimation means adapted to provide estimation of back EMF constant
and cogging torque variation with rotor position of said motor;
e. second estimation means for estimating the effect of armature reaction on
back EMF constant variation using finite element analvsis;
f. motor modeling means adapted to provide a motor model by obtaining
voltage equation model and torque equation model in accordance with pre
defined equations;
g. power supply modeling means adapted to provide a power supply model;
and
h. load modeling means adapted to provide a load model
2. A system as claimed in claim 1 wherein, said extraction means includes tabulation means adapted to tabulate extracted Non linear quantities in the form of look up tables from parametric analysis of static 2D finite element model.

3. A system as claimed in claim 1 wherein, said Finite Element Modeling means includes means for modeling halbach magnet rings as segments with magnetization direction of segments belonging to a pole pair varies from 0 to 360 degrees
4. A system as claimed in claim 1 wherein, said first estimation means includes means to model two coils around tooth namely outer coil and inner coil having same number of turns per coil in order to provide estimation of effect of armature reaction on EMF constant.
5. A system as claimed in claim 1 wherein, said second estimation means includes means to obtain Flux linkage variation with position of outer coil with armature reaction being modeled by applying current to inner coil, said flux linkage variation being obtained for a pre-defined number of armature current values.
6. A system as claimed in claim 1 wherein, said second estimation means includes means to determine direction of current in the coil from unexcited EMF constant variation
7. A system as claimed in claim 1 wherein, said second estimation means includes means to pass current through outer coil in order to estimate effect of armature reaction on flux linkage variation of inner coil

8. A system as claimed in claim 1 wherein, said second estimation means includes averaging means to average flux linkage of inner and outer coil in order to obtain flux linkage variation of single coil.
9. A system as claimed in claim 1 wherein, said second estimation means includes calculation means adapted to calculate EMF constant from flux linkage using pre-defined equation.
10.A system as claimed in claim 1 wherein, said second estimation means includes calculation means to calculate the variation of flux linkage of coil and cogging torque with rotor position using series of simulations by shifting position of rotor over twice pole pitch in small steps.
11.A system as claimed in claim 1 wherein, said motor model includes implementation means in order to implement said motor model based on predefine voltage and torque equations of DC motor.