WO2015180558A1

WO2015180558A1 - Electric filter for motor system

Info

Publication number: WO2015180558A1
Application number: PCT/CN2015/078472
Authority: WO
Inventors: Shu Hung Henry Chung; Kuen-faat YUEN
Original assignee: City University Of Hong Kong
Priority date: 2014-05-30
Filing date: 2015-05-07
Publication date: 2015-12-03
Also published as: HK1201411A2

Abstract

An electric filter (202) for a motor system (204) is provided. The electric filter (202) comprises a first filter (206) arranged to connect with a controller (210) operable to control the motor system (204), and a second filter (208) arranged to connect with the motor system (204). The first filter (206) and the second filter (208) are in electrical communication so as to both filter an overvoltage spike formed by a voltage pulse generated by the controller (210).

Description

AN ELECTRIC FILTER FOR A MOTOR SYSTEM

TECHNICAL FIELD

The present invention relates to an electric filter for a motor system and particularly, although not exclusively, to a passive filter for overvoltage suppression in an inverter-fed motor drive system.

BACKGROUND

Electrical devices or systems such as electric motors, are powered by electrical power. The output of the motor may be controlled by altering an amount of electrical power fed to the motor. In turn, the total amount of electrical power may be altered by controlling the voltage and the current fed to the motor or by controlling the duty cycle of the electrical power transmitted to the motor with a pulse width modulation.

Inverter-fed drive systems have been widely used in residential, commercial, and industrial applications. Electrical filters are usually installed to avoid overvoltage spikes traveling along the cable and inside the motor when a long motor cable is used. Such overvoltage spikes would cause premature failure of the motor and cable insulation.

SUMMARY

In accordance with a first aspect of the present invention, there is provided an electric filter for a motor system, comprising a first filter arranged to connect with a controller operable to control the motor system, and a second filter arranged to connect with the motor system, wherein the first filter and the second filter are in electrical communication so as to both filter an overvoltage spike formed by a voltage pulse generated by the controller.

In an embodiment of the first aspect, the first filter is arranged to match a characteristic impedance value Z₀ of a cable connected between the controller and the motor system.

In an embodiment of the first aspect, the controller is a motor inverter.

In an embodiment of the first aspect, the first filter is an inverter-side suppression filter.

In an embodiment of the first aspect, the second filter is a motor-side suppression filter.

In an embodiment of the first aspect, the first filter includes a resister and an inductor arranged to connect to an output of the controller.

In an embodiment of the first aspect, the resister and the inductor are arranged to connect in parallel and form a resister-inductor network.

In an embodiment of the first aspect, the resister-inductor network is arranged to connect in series to the output of the controller.

In an embodiment of the first aspect, the resister has a resistance value of R_P equals to the characteristic impedance value Z₀ of the cable.

In an embodiment of the first aspect, the inductor has an inductance value of L_P, and the inductance value of L_P is related to a surge impedance value Z_M of the motor and a predetermined voltage overshoot value of the motor system.

In an embodiment of the first aspect, a high-frequency impedance value of the resister-inductor network is equal to the characteristic impedance Z₀ of the cable.

In an embodiment of the first aspect, the second filter is arranged to suppress a voltage overshoot in a motor winding of the motor system.

In an embodiment of the first aspect， the second filter is further arranged to reduce a common-mode current through a motor bearing of the motor system.

In an embodiment of the first aspect， the second filter includes a capacitor arranged to connect with the motor system.

In an embodiment of the first aspect， the capacitor is arranged to connect in parallel with the motor.

In an embodiment of the first aspect， the capacitor has a capacitance value CP equals to：

wherein t_r is a predetermined rise time of a voltage of the motor.

In an embodiment of the first aspect， the first filter and the second filter are arranged to alter a waveform of the voltage pulse generated by the controller.

In an embodiment of the first aspect， the first filter and the second filter are arranged to prolong a rise time of a voltage value of the voltage pulse transmitted to the motor system.

In an embodiment of the first aspect， the first filter and the second filter are arranged to reduce the voltage of the voltage pulse transmitted to the motor system.

In an embodiment of the first aspect， the electric filter is arranged to maintain a relatively constant power dissipation under different voltage overshoot conditions.

In an embodiment of the first aspect， the motor system is a multi-phase motor including a plurality of branches of input terminals with each of the plurality of branches of input terminals arranged to connect with the second filter， and the controller includes a plurality of branches of output terminals with each of the plurality of branches of output terminals arranged to connect with the first filter.

In accordance with a first aspect of the present invention, there is provided a motor driving system, comprising: an electric power inverter arranged to transmit electric power to a motor； and an electric filter in accordance with the first aspect, wherein the electric filter is arranged to connect between the motor and the electric power inverter.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will now be described, by way of example, with reference to the accompanying drawings in which:

Figure 1A is a schematic diagram of an equivalent circuit of a lossy transmission line；

Figure 1B is a schematic diagram of an equivalent circuit of a lossless transmission line；

Figure 2 is a schematic diagram of an inverter-cable-motor system with an electric filter for a motor system in accordance with an embodiment of the present invention；

Figure 3 is a schematic diagram of a Thévenin's equivalent circuit of a motor system；

Figure 4 is a schematic diagram of a canonical model for describing an inverter-cable-motor system with filters；

Figure 5 is a block diagram of a system model of the inverter-cable-motor system of Figure 4；

Figure 6A is a plot showing ideal impedance characteristics of Z_FM (s) ；

Figure 6B is a plot showing ideal impedance characteristics of Z_in (s) ；

Figure 7 is a schematic diagram of an inverter-cable-motor system with an RC filter；

Figure 8 is a plot showing impedance characteristics of Z_FM (s) of the inverter-cable-motor system of Figure 7；

Figure 9 is a schematic diagram of an inverter-cable-motor system with an RLC filter；

Figure 10A is a plot showing impedance characteristics of Z_in (s) of the inverter-cable-motor system of Figure 9 with large inductance；

Figure 10B is a plot showing impedance characteristics of Z_in (s) of the inverter-cable-motor system of Figure 9 with small inductance；

Figure 11A is a plot showing time-domain waveforms of v_th of the inverter-cable-motor system of Figure 9 with L_I＝100μH and different values of C_I；

Figure 11B is a plot showing time-domain waveforms of v_th of the inverter-cable-motor system of Figure 9 with L_I＝500μH and different values of C_I；

Figure 11C is a plot showing time-domain waveforms of v_th of the inverter-cable-motor system of Figure 9 with L_I＝1000μH and different values of C_I；

Figure 12 is a plot showing time-domain waveforms of i_RI of the inverter-cable-motor system of Figure 9 with different values of C_I；

Figure 13 is a schematic diagram of an inverter-cable-motor system with an electric filter for a motor system in accordance with an embodiment of the present invention for single-phase operation；

Figure 14 is a schematic diagram of an inverter-cable-motor system with an electric filter for a motor system in accordance with an embodiment of the present invention for three-phase operation；

Figure 15 is a plot showing impedance characteristics of Z_in (s) of the inverter-cable-motor system of Figure 13；

Figure 16 is a plot showing a voltage overshoot of v_M versus L_p with different R_p in the inverter-cable-motor system of Figure 13；

Figure 17 is a plot showing L_p versus percentage voltage overshoot of v_M under different Z_M in the inverter-cable-motor system of Figure 13；

Figure 18A is a photographic image of an electric filter for a motor system in accordance with an embodiment of the present invention；

Figure 18B is a schematic diagram of the electric filter for a motor system of Figure 18A；

Figure 19A is a plot showing a measured time-domain waveform of an inverter-cable-motor system without a filter；

Figure 19B is an enlarged plot of the measured time-domain waveform of Figure 19A；

Figure 20A is a plot showing a measured time-domain waveform of an inverter-cable-motor system with the electric filter for a motor system of Figure 18A；

Figure 20B is an enlarged plot of the measured time-domain waveform of Figure 20A；

Figure 21A is a plot showing a measured time-domain waveform of a voltage distribution of one phase of the motor windings without a filter；

Figure 21B is a plot showing a measured time-domain waveform of a voltage distribution of one phase of the motor windings with the electric filter for a motor system of Figure 18A；

Figure 22A is a plot showing a measured time-domain waveform of the motor terminal voltages and common-mode current of an inverter-cable-motor system without a filter；

Figure 22B is a plot showing a measured time-domain waveform of the motor terminal voltages and common-mode current of an inverter-cable-motor system with the electric filter for a motor system of Figure 18A；

Figure 23 is a plot showing a comparison of the power loss among the RLC filter, RC filter and an electric filter for a motor system in accordance with an embodiment of the present invention； and

Figure 24 is a plot showing a power loss versus rise time of the motor terminal voltage among the RLC filter, RC filter and an electric filter for a motor system in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The inventors have, through their own research, trials and experiments, devised that, pulse width-modulated (PWM) inverters that generate high-frequency voltage pulses of short rise time can establish destructive overvoltage spikes in motor drive systems with long motor cable. Such phenomenon can be expounded by using the long transmission line theory. When the motor surge impedance is different from the characteristic impedance of the cable (i.e., mismatched condition) , part of the voltage pulses sending from the inverter will be reflected back to the inverter at the motor terminal. The magnitude of the reflected pulses is determined by the ratio between the cable impedance and the motor impedance. Such ‘impedance mismatch’ between the motor and the cable occurs commonly as the motor impedance is generally greater than the characteristic impedance of the cable. Motors of power rating below 5-hp have impedances ranging from 500 Ω to 4000 Ω, while the cable impedance is much smaller, typically ranging from 35 Ω to 190 Ω. The reflected pulses are then superimposed onto the inverter output voltage pulses, forming pulses of higher voltage travelling along the cable. Theoretically, the magnitude of the superimposed voltage pulses could be double of the inverter output voltage. Furthermore, in systems with inverters having high carrier frequency and generating narrow-spaced pulses, the reflected pulse may not have fully decayed before the next pulse arriving. Charges trapped on the long cable will develop a voltage greater than twice the incident voltage at the motor terminals. In addition, voltage pulses with short rise time cause highly nonlinear inter-coil and inter-turn voltage distributions over the motor windings that generate common-mode current flowing through motor windings and bearings, accelerating the deterioration of the motor bearings. Hence, formation of the overvoltage spikes due to the long motor cable will cause premature failure of the motor and the cable.

There are three example approaches to remedying the impacts of overvoltage pulses caused by the cable. The first approach is based on using oversized motors or inverter-duty motors having enhanced insulation system. However, this idea is less proactive as the root cause of the overvoltage spikes is not tackled.

The second approach is based on using a passive filter to match the cable impedance. Typical passive filters are line reactors and dv/dt filter on the inverter side, line reactor on the motor side, and line termination RC and RLC filters. Although their implementations are simple, cost-effective, and robust, they are counteracted by the following two main limitations:

1) High power loss–Since the overvoltage suppression is realized by using a resistor to match the cable impedance, the power dissipation in the resistor increases with the degree of overvoltage suppression. In addition, line reactors are usually large in size and carry the load current. They have high copper loss in the windings and core loss due to the high-frequency pulses.

2) Overvoltage distribution on the motor windings–As some filters, such as the termination RC filter, cannot alter the wavefront of the voltage pulses. There occur overvoltage distributions in the motor stator windings. Apart from causing insulation failure, the inter-coil and inter-turn overvoltage will also increase the high-frequency common-mode current to the ground through the motor bearings. This will accelerate the wear of the bearings.

The third approach is based on using an active circuit to match the cable impedance and convert the energy gained in the impedance matching process. An active low-loss motor terminal filter that clamps the maximum motor terminal voltage and alters the wavefront of the pulses at the motor terminal to improve the inter-coil and inter-turn voltage distributions in the motor has been proposed. To recover the energy gained in suppressing the overvoltage back to the system, one approach is to recover the energy through a separate cable, or in another approach, the energy is recycled through a synchronous modulation technique.

In terms of the technical, operational and economic merits, the second approach of remedying the impacts of overvoltage pulses caused by the cable may be the most attractive solution. However, there have been no significant enhancements in the structure and design in today’s overvoltage filters, as compared to the conventional ones. The power loss is still the main challenge. Accordingly, in accordance with one embodiment, there is provided a new perspective on the filter structure and design. A generalized model for characterizing the inverter-cable-motor system with the filter included is formulated to describe the interactions between the filter and the drive system. Based on the model, the characteristics of an ideal overvoltage filter will be derived. Furthermore, a low-loss filter, named as “RL-plus-C” filter that exhibits near ideal characteristics will be proposed. It consists of a parallel resistor-inductor network connected in series with the inverter output and a parallel capacitor connected in parallel with the motor. Its performance will be compared with that of the commonly-adopted RC and RLC filters, theoretically and experimentally on a 1-hp motor drive system.

A long motor cable in an inverter-fed drive system can be modelled by a long transmission line, as shown in Figure 1A, in which R_c represents the distributed resistance of the cable per unit length (Ω/m) . L_c represents the distributed inductance of the cable per unit length (H/m) . C_c represents the capacitance between two wires per unit length (F/m) . G_c represents the conductance of the dielectric material separating the two wires per unit length (S/m) . However, for the sake of simplicity in the analysis, a lossless transmission line with R_c＝0 and G_c＝∞ is considered. The model is shown in Figure 1B. The propagation delay of the cable τcan be expressed as

where l is the cable length.

The characteristic impedance of the cable Z_o is

With reference to Figure 2, there is shown an embodiment of an electric filter 202 for a motor system 204, comprising: a first filter 206 arranged to connect with a controller 210 operable to control the motor system 204； and a second filter 208 arranged to connect with the motor system 204； wherein the first filter 206 and the second filter 208 are in electrical communication so as to both filter an overvoltage spike formed by a voltage pulse generated by the controller 210.

In this embodiment, the controller 210 is a motor inverter operable to control or drive a motor 204 over a cable 212 between, such as a PWM controller 210 which may control the speed of the motor 204 by changing the duty cycle of the electric power transmitted to the motor 204. The first filter 206 is an inverter-side suppression filter, which is connected to the output of the controller 210, and the second filter 208 is a motor-side suppression filter connected to the input of the motor 204. As mentioned above, high-frequency voltage pulses of short rise time can establish destructive overvoltage spikes in motor drive systems with long motor cable 212, and these overvoltage spikes may be filtered or supressed by both the first and second filter 208 in the inverter-cable-motor system 200 such that the motor is protected from being damaged by these overvoltage spikes generated.

Figure 2 also shows the architecture of an inverter-fed drive system 200. It consists of an inverter 210, inverter-side overvoltage suppression filter 206, motor cable 212, motor-side overvoltage suppression filter 208, and motor 204. The latter two components are lumped and represented by an impedance Z_L, named as “cable termination network” . v_in is the inverter output consisting of high-frequency voltage pulses, v_c is the inverter-side cable terminal voltage, and v_M is the motor-side cable terminal voltage.

By applying the Thévenin's theorem to the entire inverter-cable-motor system 200, Figure 3 shows the equivalent circuit of the inverter-cable-motor system 200 of Figure 2, in which v_th and Z_in are the Thévenin equivalent voltage source and Thévenin equivalent impedance, respectively, for modeling the inverter and the inverter-side overvoltage suppression filter. Thus, the canonical circuit model for representing the inverter-cable-motor system 200 with the filter included is shown in Figure 4, in which

is the reflected voltage from the motor-side cable terminal and

is the incident voltage at the inverter-side cable terminal. By transforming the system into s-domain, the following formulas are derived.

Consider the circuit on the inverter side,

V_th(s)＝H(s)V_in(s) (3)

where e^-sτ is the time delay function of the cable, H (s) is the transfer function of the filter, and G₁ (s) and G₂ (s) are expressed as

At the inverter-side cable terminal, the incident voltage

is

Consider the circuit on the motor side,

where D (s) is expressed as

At the motor-side cable terminal,

Substitute (7) into (8) ,

Substitute (4) into (11) ,

By putting (3) , (5) , (6) , and (9) into (12) , the motor terminal voltage V_M (s) is

With reference to Figure 5, there is shown a block diagram describing the equations from (3) to (13) . It depicts the entire inverter-cable-motor system 200 with the filter included. Thus, based on (13) , the effect of the reflected voltage

on the motor terminal voltage can be eliminated if the second term of the RHS of (13) is zero. Thus, the required condition is

As Z_L (s) ≠0, there are two possible techniques that make (14) fulfil. They are

and

Thus, by substituting (8) , (9) , and (10) into (15) ,

As

the first technique is

Z_L(s)＝Z_o (18)

Thus, the impedance of the cable termination network has to be resistive and is equal to the cable impedance. As Z_M＞Z_o, the motor-side overvoltage filter Z_FM (s) is typically connected in parallel with the motor and is dominant during the transient period. Thus,

Z_FM(s)≈Z_o (19)

The traditional RC termination filter is an example. By substituting (18) into (13) ,

Based on (16) , the second technique is

Z_in(s)＝Z_o (21)

that is, the Thévenin impedance of the inverter-side overvoltage filter is resistive and is the same as the cable impedance. By substituting (21) into (13) ,

Equations (19) and (21) give the required high-frequency impedance characteristics of the motor-side and inverter-side overvoltage filters. However, special emphasis should also be placed on the low-frequency impedance characteristics, as the motor voltage and current comprise major low-frequency components. First, for the motor-side filter, as it is connected across the motor, its low-frequency impedance should ideally be equal to infinity, in order to ensure zero low-frequency power dissipation in the filter. Second, for the inverter-side filter, as it is connected in series with the inverter output, its low-frequency impedance should ideally be equal to zero, in order to ensure zero low-frequency power dissipation in the filter.

Hence, based on the above considerations, the impedance characteristics of Z_FM (s) and Z_in (s) are expressed as follows:

where ω_c＝2πf_c and f_c is the cut-off frequency for determining the changes of the impedance.

With reference to Figure 6, there is shown a plot of ideal impedance characteristics of Z_FM (s) and Z_in (s) , in which f_c is equal to 50Hz, which is the maximum operation frequency of the motor under the variable-voltage-variable-frequency control.

The system model depicted in Figure 4 is used to study the reflected voltage at the motor terminal and power dissipation of two commonly-adopted RC and RLC filters in this section. The methodology is based on studying the effects of the first and second terms in (13) on v_M.

With reference to Figure 7, there is shown a structure of an RC filter 702, formed a resistor R_M and a capacitor C_M, connected to the motor 204 terminals in a inverter-cable-motor system 700. Thus, comparing the system 700 as shown in Figure 7 with the system 200 shown in Figure 3, the expressions of H (s) , Z_in (s) , Z_FM (s) , and Z_L (s) are

H(s)＝1 (25)

Z_in(s)＝0 (26)

Based on (18) , Z_L (s) is designed to be equal to Z_o, the effect of Z_L (s) on the first term on the RHS of (13) is negligible, while the second term is studied as follows. By using (8) - (10) and (28) , the reflected voltage

is

Thus, as Z_M＞Z_o,

The value of R_M is typically designed to be equal to Z_o. Thus,

Thus, the magnitude of the reflected voltage decreases as the value of C_M increases.

The current through R_M , I_FM (s) , can be expressed as

As

where V_dc is the amplitude of the inverter output voltage.

Thus, the current through R_M, i_FM (t) , and the power dissipation P_loss, _RC in R_M are

The characteristics of Z_FM (s) is shown in Figure 8. If the value of C_M is large, the characteristics will be close to the ideal one. However, the power loss will also increase.

With reference to Figure 9, there is shown a structure of the RLC filter 902, formed a resistor R_I, an inductor L_I, and a capacitor C_I, connected at the inverter 210 output in a inverter-cable-motor system 900. Thus, comparing the system 900 as shown in Figure 9 with the system 200 shown in Figure 3, the expressions of H (s) , Z_in (s) , and Z_L (S) are

Z_L(S)＝Z_M (39)

By substituting (37) - (39) into (13) ,

According to (40) , V_M is determined by two voltage components. The first one is the reflected voltage

and the second one is the Thévenin voltage source V_th. Their effects are discussed as follows.

In order to eliminate the effect of

the high-frequency value of Z_in should be equal to Z_o. The required value of R_I is

R_I＝Z_o (41)

Thus, the characteristic of Z_in is determined by the values of L_I and C_I. Figures 10A and 10B show the characteristics with L_I＝1000μH and L_I＝100μH, respectively. The value of C_I varies from 10nF to 1000nF. The characteristic is getting closer to the ideal characteristic [i.e., eq. (24) ] with large L_I and C_I. In general, with small L_I, the corner frequency will move to the high-frequency range. With small C_I, the filter is in underdamped condition having a resonant peak that will does not match the cable impedance. Thus, large values of L_I and C_I can help alleviate the effects of

.

Based on (3) , Figure 11 shows the time-domain waveforms of V_th with different combinations of L_I and C_I, when the filter is subject to a unit step. The results reveal that the overshoot increases with an increase in L_I and decreases with an increase in C_I.

Based on the above observations, it can be concluded that a large value of C_I can alleviate the effects of the two voltage components in (40) . This can be visualized by considering that Z_in is always equal to Z_o if C_I＝∞. However, this will cause a concern on the power dissipation in R_I. As shown in Figure 9, the current through R_I, I_RI, is

By applying inverse Laplace transformation,

The power loss in R_I, P_loss, _RLC, is

With reference to Figure 12, there is shown the waveforms of i_RI (t) with different values of C_I. Thus, the rms value of i_RI, and thus the power loss, will increase with C_I.

Therefore, the model described in Figure 4 can give a new perspective on the filter performance on overvoltage suppression and power dissipation in the filter. It can be used to explain the effectiveness of the filters connected to the inverter side and motor side.

In an exemplary embodiment, with reference to Figure 13, there is shown an electric filter 1302 for a motor system 204, which may be considered as a “RL-plus-C” filter 1302 that can resemble the characteristics in Figure 6B.

In this embodiment, the first filter 1306, or the inverter-side suppression filter includes a resister and an inductor arranged to connect to an output of the controller 210. Preferably, the first filter 1306 is a parallel resistor-inductor network, formed by the resistor R_p and the inductor L_p, is connected in series with the inverter output. The second filter 1308, or the motor-side suppression filter, includes a capacitor arranged to connect with the motor system 204. Preferably, the second filter 1308 is a capacitor C_p is connected across the motor terminals.

In another example embodiment, the motor system is a multi-phase motor 1404 including a plurality of branches 1414 of input terminals with each of the plurality of branches 1414 of input terminals arranged to connect with the second filter 1408, and the controller 1410 includes a plurality of branches 1414 of output terminals with each of the plurality of branches 1414 of output terminals arranged to connect with the first filter 1406. With reference to Figure 14, the inverter-cable-motor system 1400 inclues a three-phase motor system 1404 with each of the branches 1414 connected with both a first filter 1406 and a second filter 1408.

Preferably, the impedance of the RL network 1306 is small at low frequency and is equal to Z_o at high frequency, so as to satisfy (23) , and the capacitor C_p is arranged to alter the wavefront of the voltage pulses, in order to suppress overvoltage on the motor windings. Preferably, the first filter (206, 1306) and the second filter (208, 1308) are arranged to prolong a rise time of a voltage value of the voltage pulse transmitted to the motor system 204, and to reduce the voltage of the voltage pulse transmitted to the motor system 204.

By comparing the inverter-cable-motor system 1300 as shown in Figure 13 with the system 200 shown in Figure 3, it can be shown that

H(s)＝1 (45)

Figure 15 shows the characteristics of Z_in (s) . If the value of L_p is large, the characteristics will be close to the ideal one. By putting (45) into (3) , (4) , (7) , (8) and (10) , the cable terminal voltage on the inverter side V_c is

The voltage across the RL network, V_RL, is

By substituting (45) into (3) , (8) , (10) and (12) , the cable terminal voltage on the motor size V_M is

As τ is significantly smaller than the switching period of the voltage pulses, a first-order approximation to e^-sτ is taken,

By substituting (5) , (6) , (9) , (46) , (47) and (51) into (49) and (50) , it can be shown that

and

where

b_RL,4＝L_pR_pC_pZ_MZ_oτ²,

b_RL,1＝2L_pR_p,

a_RL,4＝L_pC_pZ_MZ_oτ²(R_p+Z_o)，

a_RL,3＝{R_pC_pZ_MZ_o ²τ+L_p(R_p+Z_o)[2C_pZ_MZ_o+(Z_M+Z_o)τ]}τ,

b_M,1＝2Z_MZ_o(L_p+R_pτ),b_M,0＝2R_pZ_MZ_o,a_RL,4＝L_pC_pZ_MZ_oτ²(R_p+Z_o),

a_RL,3＝{R_pC_pZ_MZ_o ²τ+L_p(R_p+Z_o)[2C_pZ_MZ_o+(Z_M+Z_o)τ]}τ，

By applying inverse Laplace transform to (52) , the high-frequency power loss in the resistor R_p, P_loss, _H, is

where f_s is the switching frequency of the inverter.

The low-frequency power loss in R_p, P_loss, _L, caused by the fundamental frequency of the inverter output current is

where I_RL, _rms is the rms value of the fundamental frequency current flowing through R_p, and I_M, _rms is the rms value of the motor current.

Thus, the total power loss in R_p , P_loss is,

P_loss, _L is usually very small as the inductor has a low reactance at low-frequency. Thus,

The values of the components used in the “RL-plus-C” filter 1302 are designed by considering the following parameters:

1. V_max : Maximum voltage at the motor terminal

2. V_dc : DC-link voltage of the inverter 210

3. Z_o : The cable 212 characteristic impedance

4. Z_M : The motor 204 surge impedance

5. t_r : Designed rise time of the motor terminal voltage

6. τ : Propagation delay of the motor cable 212

Preferably, the first filter (206, 1306) is arranged to match a characteristic impedance value Z₀ of a cable connected between the controller 210 and the motor system 204. Based on (24) , the high-frequency impedance of the RL network 1306 is Z_o. The value of R_p is

R_p＝Z_o (58)

Such condition is confirmed by the analysis shown in Figure 16, in which the relationships between the percentage voltage overshoot and the value of L_p for a given value of R_p are illustrated. The percentage voltage overshoot is minimum, when (58) is taken.

By substituting (45) and (47) into (22) and neglecting the cable delay time,

By performing inverse Laplace transformation with V_in(s)＝V_dc/s,

Let

v_M(t_r)＝0.9V_dc (61)

By substituting (60) and (61) , it can be shown that

With the chosen values for R_p and C_p, the value of L_p is designed by considering the voltage overshoot at the motor terminal voltage V_M. By considering a range of values for L_p, such as between 100 μH and 2000 μH, the overshoot is calculated by (53) with a value L_p. For example, a Matlab program may be used for calculating L_p:

clear all；

Vmax＝310；

Vdc＝300；

Overshoot＝Vmax/Vdc；％ Nominated maximum motor terminal voltage

Zo＝74；

Zm＝2e3；

R＝74；

c＝5e-9；

T＝6.6e-7；

L＝1e-4:1e-5:2e-3；％L∈[100μH,2000μH]

t＝0:1e-9:3e-5；

for i＝1:1:191

b2(i)＝2*L(i)*Zm*Zo*T；

b1(i)＝2*Zm*Zo*(L(i)+R*T)；

b0(i)＝2*R*Zm*Zo；

a4(i)＝L(i)*c*Zm*Zo*(R+Zo)*T^2；

a3(i)＝(R*c*Zm*Zo*T^2+L(i)*(R+Zo)*(2*c*Zm*Zo+(Zm+Zo)*T))*T；

a2(i)＝R*Zo*T*(2*c*Zm*Zo+T*(Zm+Zo))+2*L(i)*(Zo*(Zm+Zo)*T+R*(c*Zm*Zo+(Zm+Zo)*T))；

a1(i)＝2*Zo*(L(i)*(R+Zm)+R*(Zm+Zo)*T)；

a0(i)＝2*R*Zm*Zo；

num＝[b2(i)b1(i)b0(i)]；

den＝[a4(i)a3(i)a2(i)a1(i)a0(i)]；

y＝step(num,den,t)；

m＝max(y)；％Use step response function to find the maximum value

if m<Overshoot ％search for the required inductance for the maximum overshoot

Inductance＝L(i)

Overshoot＝m

break；

end

Figure 17 shows an example of the relationships between L_p and percentage voltage overshoot with different Z_M. The value of L_p is chosen by considering the value of Z_M and the designed voltage overshoot.

By including the electric filter for motor system with long cable between the motor and the controller, the motor can be protected from being damaged by overvoltage spikes generated by the high frequency electrical power switching of the PWM controller, such that the motor system is more stable and robust.

These embodiments are advantageous in that the electric filter are low-loss and has low power dissipation. The electric filter can perform with near-ideal electrical characteristics. Apart from suppressing overvoltage at the motor terminal, it is able to prolong the rise time of the motor terminal voltage to suppress the voltages overshoot inside the motor windings and reduce the common-mode current through the motor bearings.

Advantageously, the electric filter includes only simple passive components, which is more robust, and cost effective when compared with active filters for a motor system, which may include active controllers and the structures are usually higher complexity and have larger sizes than passive filters.

With reference to Figures 18A and 18B, there is shown an embodiment of an electric filter 1402 for a motor system 1404 in accordance with an embodiment of the present invention. The electric filter 1402 has been evaluated on a three-phase inverter drive system N700E-022SF (1410) manufactured by HYUNDAI. The inverter 1410 is used to drive a 1-hp induction motor 1404 -Type DEM II No 9572380007 manufactured by Degem Systems. The motor 1404 has a surge impedance of 2kΩ. The induction motor 1404 is mechanically coupled to a dc generator 1816 , Type DEM 4 No 9572380019 manufactured by Degem Systems, with its output connecting to the Agilent 6050A electronic load 1818 for controlling the loading on the induction motor 1404. The switching frequency of the inverter drive 1410 is 10 kHz, the dc link voltage, V_dc is 300V and the rise/fall time of the output voltage pulses is 100ns. The motor cable 212 constants are L_c＝0.49μH/m, C_c＝89pF/m and Z_o＝74Ω. The cable length is 100m. The electric filter 1402 is designed with a maximum overshoot 3.3％of the motor terminal voltage (i.e., V_max＝310V) and 1μs rise/fall time of the motor terminal voltage (t_r＝1μs) . Based on the procedure given above, the values of the components used in the filter 1402 are shown in the following table:

Parameter	Value
Parameter	Value	2/3R_p	49Ω
2/3L_p	670μH	2/3R_p	49Ω

3/2C_p

7.5nF

Figures 19A and 19B show the waveforms of the inverter output voltage (v_in) , voltage in the middle of the cable 1412 (i.e., at 50m) (v_mid) , and the motor terminal voltage (v_M) without any filter. There are voltage peaks of magnitude 570V, about 190％of the dc link voltage at the motor terminal, and of magnitude 530V in the middle of the cable 1412.

Figures 20A and 20B show the waveforms of v_in, v_mid, v_M and the motor side-cable terminal voltage v_c with the electric filter 1402 when the motor 1404 is in full-load operation. The peak voltages of v_mid and v_M are both 310V (3.3％voltage overshoot) and the peak voltages of v_c is 307V. With reference to Figure 19B, the rise time of the voltage pulses is extended from 100ns in v_in into 1μs in v_M. Hence it is shown that, the first filter 1406 and the second filter 1408 are arranged to prolong a rise time of a voltage value of the voltage pulse transmitted to the motor system 1404. It is shown that the voltages across the motor terminal and in the cable 1412 can be significantly reduced with the electric filter 1402.

To study the voltage distribution inside the motor windings, one of the motor windings was rewound with several taps on it. The voltage waveforms at the motor terminal, 90％, 50％and 10％of one of the motor windings are shown in Figures 21A and 21B, which show the results without and with the electric filter 1402, respectively. Results show that the electric filter 1402 does not only reduce the motor terminal voltage from 560V to 310V, but is also able to reduce the voltage stress inside the motor winding, for examples, the voltage across 90％of one phase of the motor winding is reduced from 545V to 270V, the voltage across 50％of one phase of the motor winding is reduced from 360V to 160V and that across 10％of the winding is reduced from 120V to 50V.

Figures 22A and 22B show the waveforms of the motor terminal voltage and the common mode current without and with the electric filter 1402, respectively. The results reveal that the common-mode current flowing from motor to the earth is reduced from the maximum value 0.75A to 0.25A by using the electric filter 1402.

The power losses of three filters, including the RLC filter 902, RC filter 702, and electric filter 1402 in accordance with an embodiment of the present invention, are compared. The results are shown in Figure 23. The results show that the electric filter 1402 has the lowest power loss under the same motor terminal voltage overshoot. For example, when the voltage overshoot level is set at 3.3％, the electric filter 1402 consumes 36W, while the RLC filter 902 consumes 335W and the RC filter 702 consumes 275W. Preferably, the electric filter 1402 is arranged to maintain a relatively constant power dissipation under different voltage overshoot conditions. As shown in Figure 23, the power loss of electric filter 1402 keeps at a relatively constant power dissipation of 36W under different voltage overshoots.

Figure 24 reveals the relationships among the overshoot of the motor terminal voltage, rise time of the motor terminal voltage pulses, and power loss of the three filters. The power loss of the RC filter 702 increases with the decrease in the voltage overshoot. It is important to note that only the RLC filter 902 and the electric filter 1402 can vary the rise time of the voltage pulses. This is a distinct advantage as compared with the RC filter 702, as increasing the rise time of the voltage pulses can reduce the inter-turn voltage stress and common-mode current. With the same rise time of the voltage pulses, the electric filter 1402 gives a smaller voltage overshoot than the RLC filter 902. For example, with the rise time of 1μs, the RLC filter 902 gives a voltage overshoot of 41％while the electric filter 1402 gives a voltage overshoot of 3.3％only. The results also reveal that the voltage overshoot increases with an increase in the rise time of the voltage pulses if the value of the inductor is unchanged. For example, the voltage overshoot is 3.3％with the rise time of 1μs and is 6.2％with the rise time of 2.5μs. The voltage overshoot can be reduced by increasing the inductor value if the rise time of the voltage pulses is increased. The change of the inductance does not cause additional power loss in the resistors. For example, with the rise time of 2.5μs, the voltage overshoot is kept at 3.3％by increasing the inductance from 670 μH to 1000 μH and its power loss is still 55W.

Without deviating from the spirit of the invention, the electric filter may also be used for other electrical devices or systems. In some embodiments, the electric filter can be arranged for filtering electrical power transmitted to, such as but not limited to, an electromagnetic device or a lighting device, a heating device or any other electrical or electronic devices which may be controllable by a PWM controller as known by a per skilled in the art.

It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

Any reference to prior art contained herein is not to be taken as an admission that the information is common general knowledge, unless otherwise indicated.

Claims

An electric filter for a motor system, comprising:

a first filter arranged to connect with a controller operable to control the motor system； and

a second filter arranged to connect with the motor system；

wherein the first filter and the second filter are in electrical communication so as to both filter an overvoltage spike formed by a voltage pulse generated by the controller.
An electric filter for a motor system in accordance with claim 1, wherein the first filter is arranged to match a characteristic impedance value Z₀ of a cable connected between the controller and the motor system.
An electric filter for a motor system in accordance with any one of claims 1 or 2, wherein the controller is a motor inverter.
An electric filter for a motor system in accordance with any one of claims 1 to 3, wherein the first filter is an inverter-side suppression filter.
An electric filter for a motor system in accordance with any one of claims 1 to 4, wherein the second filter is a motor-side suppression filter.
An electric filter for a motor system in accordance with any one of claims 1 to 5, wherein the first filter includes a resister and an inductor arranged to connect to an output of the controller.
An electric filter for a motor system in accordance with claim 6, wherein the resister and the inductor are arranged to connect in parallel and form a resister-inductor network.
An electric filter for a motor system in accordance with claim 7, wherein the resister-inductor network is arranged to connect in series to the output of the controller.
An electric filter for a motor system in accordance with any one of claims 6 to 8, wherein the resister has a resistance value of R_P equals to the characteristic impedance value Z₀ of the cable.
An electric filter for a motor system in accordance with any one of claims 6 to 9, wherein the inductor has an inductance value of L_P, and the inductance value of L_P is related to a surge impedance value Z_M of the motor and a predetermined voltage overshoot value of the motor system.
An electric filter for a motor system in accordance with any one of claims 7 to 10, wherein a high-frequency impedance value of the resister-inductor network is equal to the characteristic impedance Z₀ of the cable.
An electric filter for a motor system in accordance with any one of claims 1 to 11, wherein the second filter is arranged to suppress a voltage overshoot in a motor winding of the motor system.
An electric filter for a motor system in accordance with any one of claims 1 to 12, wherein the second filter is further arranged to reduce a common-mode current through a motor bearing of the motor system.
An electric filter for a motor system in accordance with any one of claims 1 to 13, wherein the second filter includes a capacitor arranged to connect with the motor system.
An electric filter for a motor system in accordance with claim 14, wherein the capacitor is arranged to connect in parallel with the motor.
An electric filter for a motor system in accordance with any one of claims 14 to 15，wherein the capacitor has a capacitance value C_P equals to：
wherein t_r is a predetermined rise time of a voltage of the motor.
An electric filter for a motor system in accordance with any one of claims 1 to 16，wherein the first filter and the second filter are arranged to alter a waveform of the voltage pulse generated by the controller.
An electric filter for a motor system in accordance with claim 17， wherein the first filter and the second filter are arranged to prolong a rise time of a voltage value of the voltage pulse transmitted to the motor system.
An electric filter for a motor system in accordance with any one of claims 17 or 18，wherein the first filter and the second filter are arranged to reduce the voltage of the voltage pulse transmitted to the motor system.
An electric filter for a motor system in accordance with any one of claims 1 to 19，wherein the electric filter is arranged to maintain a relatively constant power dissipation under different voltage overshoot conditions.
An electric filter for a motor system in accordance with any one of claims 1 to 20，wherein the motor system is a multi-phase motor including a plurality of branches of input terminals with each of the plurality of branches of input terminals arranged to connect with the second filter， and the controller includes a plurality of branches of output terminals with each of the plurality of branches of output terminals arranged to connect with the first filter.
A motor driving system， comprising：

an electric power inverter arranged to transmit electric power to a motor； and an electric filter in accordance with any one of claims 1 to 21, wherein the electric filter is arranged to connect between the motor and the electric power inverter.