How to understand DC motor inductor current?

[bittware]

motor inductor

Hello experts,
I am using PWM to control DMOS H-bridge to drive a brush DC motor. When PWM switches off, the current flowing through inductor can't be cut simultaneously. It will find a path through freewheeling diode. But the motor rotor is still spinning, the Back-EMF has a trend to force the current to inverse.
My question is:
Whether the current flowing through motor inductor would reverse or wouldn't reverse at all in a limited switch off time?
If yes, how to determine when the current flowing back?
I'll be very appreciated if you could provide a quantitative analysis based on physics formula.
Thanks in advance!

 

[nicleo]

reverse current dc motor

First of all, 'inductance' is a properties of an 'inductor'.
When switch is OFF, the current flowing through inductor could not reduce to ZERO instantaneously. The direction of the current flow will not reverse.

 

[bittware]

motor inductance vs speed

The current will not reverse, but the induced voltage across the motor will be reversed (Len's Law)

Assuming a extreme condition, if a rotor has been accelerated to a relative high speed and the driving power withdraws, the rotor will act as a generator. The kinetic energy will be converted into electric energy, meanwhile the current is reversed. How to explain this case?

 

[nicleo]

vemf = k!if

Assuming a extreme condition, if a rotor has been accelerated to a relative high speed and the driving power withdraws, the rotor will act as a generator. The kinetic energy will be converted into electric energy, meanwhile the current is reversed. How to explain this case?

No. The current will still in the same direction, i.e. not reversed. I assume that in your case, there is no 'external' torque to drive the motor (rotor) after the driving power is removed. The current flows through the motor winding, after the driving power is removed, will not change or reverse direction.

If you refer to the power supply (still attached to the system) terminals, the current will be in reversed direction when the switches are in OFF state.

If you have an external mechanical torque to maintain the kinetic energy and you have field current, then your dc motor will act as a generator.

 

[bittware]

load current motor inductance.

Assuming a extreme condition, if a rotor has been accelerated to a relative high speed and the driving power withdraws, the rotor will act as a generator. The kinetic energy will be converted into electric energy, meanwhile the current is reversed. How to explain this case?

No. The current will still in the same direction, i.e. not reversed. I assume that in your case, there is no 'external' torque to drive the motor (rotor) after the driving power is removed. The current flows through the motor winding, after the driving power is removed, will not change or reverse direction. According to Len's Law, the voltage across the motor winding must be reversed to (try to) 'maintain' the current, which will eventually reduce to zero.

If you have an external mechanical torque to maintain the kinetic energy and you have field current, then your dc motor will act as a generator.

Althogh after driving power is removed no external torque drives the motor, the residual kinetic energy instored in rotor itself will also be converted into electric energy. Right? So I believe a part of kinetic energy will cause revesed current eventually. What I am concerning is when the reversed current appears after the PWM switches off.

 

[nicleo]

inductor reverse current

Althogh after driving power is removed no external torque drives the motor, the residual kinetic energy instored in rotor itself will also be converted into electric energy. Right? So I believe a part of kinetic energy will cause revesed current eventually. What I am concerning is when the reversed current appears after the PWM switches off.

Well, we need to clarify whether we're discussing about the current flow direction in the motor winding or power supply terminal. Pls advise.

I think there are two stages after the switches are OFF:
1) The motor is running, and the current (not reversed) in motor decays to zero (providing there is a freewheeling path).
2) After the current decays to zero, the rotor still rotates due to its moment inertia.

Say in motoring mode, the rotor rotates 'clockwise'.

The current, when the switches (S1-S4) are ON, flows from the positive terminal of power supply (PS) to negative terminal of the PS:
Current path: +PS -> S1 -> motor winding -> S4 -> -PS

When the switches are OFF, the current in motor winding will be NOT change direction:
Current path: -PS -> D2 -> motor winding -> D3 -> +PS
The current direction at PS terminals reversed.

When Stage 2 (i.e. swtiches (S1, S2, S3, and S4) are OFF, just after motoring current decays to ZERO, and rotor still rotates), and if the stator has permanent magnet or the residual magnetic field on stator is strong enough:
Current path: -PS -> D4 -> motor winding -> D1 -> +PS
In this case, both the current at PS terminals and in motor winding are reversed (based on Fleming's rules) because the rotor is still in 'clockwise' direction.

Fleming’s rules give the direction of the magnetic field, motion, and current in electrical machines. The left hand is used for motors, and the right hand for generators and dynamos.

 

[usernam]

dc motor controller inductor

bittware are you refering to some sort of regeneration. If you are then yes eventually the current in the inductor will reverse. But not instantaneously. It will first decay to zero and if you are still in regenerative mode the current will go negative. Ofcourse you have to provide a path for the reverse current so you must be using a Hbridge or a Class C chopper. In the attachment which shows a Hbridge in various modes of motor operation (b) represents forward regenration.

 

[bittware]

driving motor understand reverse current

Althogh after driving power is removed no external torque drives the motor, the residual kinetic energy instored in rotor itself will also be converted into electric energy. Right? So I believe a part of kinetic energy will cause revesed current eventually. What I am concerning is when the reversed current appears after the PWM switches off.

Well, we need to clarify whether we're discussing about the current flow direction in the motor winding or power supply terminal. Pls advise.

I think there are two stages after the driving power is removed:
1) The motor is running, and the current (not reversed) in motor decays to zero.
2) After the current decays to zero, the rotor still rotates due to its moment inertia.

Say in motoring mode, the rotor rotates 'clockwise'.

The current, when the switch is ON, flows from the positive terminal of power supply (PS) to negative terminal of the PS:
Current path: +PS -> S1 -> motor winding -> S4 -> -PS

When the switch is OFF, the current in motor winding will be NOT change direction:
Current path: -PS -> D2 -> motor winding -> D3 -> +PS
The current direction at PS terminals reversed.

When Stage 2 (i.e. swtich is OFF, just after motoring current decays to ZERO, and rotor still rotates), and if the stator has permanent magnet or the residual magnetic field on stator is strong enough:
Current path: -PS -> D4 -> motor winding -> D1 -> +PS
In this case, both the current at PS terminals and in motor winding are reversed (based on Fleming's rules)

Fleming?s rules give the direction of the magnetic field, motion, and current in electrical machines. The left hand is used for motors, and the right hand for generators and dynamos.

I agree with your analysis for now.
But the key point is where is the boundary between "Stage 1" and "Stage 2". That is to say when the motor exits "Stage 1" and enter "Stage 2"? Is a quantitative calculation applicable? If yes, how to do that?

 

[nicleo]

dc inductor current

I agree with your analysis for now.
But the key point is boundary between "Stage 1" and "Stage 2". That is to say when the motor exits "Stage 1" and enter "Stage 2"? Is a quantitative calculation applicable? If yes, how to do that?

I think we can formulate equations to model the situation. The key (when State 1 -> State 2) is the current (in motor winding) changes 'direction'. So, in the simulation model, we can implement this by detecting the zero-crossing of the current waveform. Regarding the 'FULL' equation, I think usernam can find the equation (in the reference where the diagram in his post was copied from) that models the 'regenerative' operation mentioned in his post.

 

[bittware]

pwm switch motor reverse direction

nicleo,
Thanks for your suggestion.
usernam,
Could you provide more detail infomation regarding how to use formula to calculate out when the regenerative current comes up?
Thanks a lot.

 

[usernam]

regeneration of dc motor with pwm converter

We have to remember that this is a Hbridge. So the appropriate switches are constantly being switched on/off at the switching frequency.
I shall use nicleo's diagram as a reference.

Stage 1 The motor is running at some speed and current is being fed to the motor from source. This is normal motoring mode. While operating in this mode S1 will always be on. The switch S4 will be turned on/off according to the duty cycle D. When S4 is on current flows from source through S1 then through DC motor and finally through S4 and back to source again. When S4 is off current flows from S1 through DC motor through D3 and then back to S1 again. This is equivalent to a buck converter mode. While S1 and S4 are conducting voltage across the inductor is positive therefore the inductor current rises. When S1 and D3 conduct the voltage across the inductor is negative therefore the current through the inductor falls. This repeats with every switching cycle. Note that the average current remains positive but there is some slight variation during switching.

Stage 1 - Stage 2 transition Motor is rotating in the same direction as above. Initially current will be in the positive direction i.e. as in the above Stage 1 case. Suppose we wish to begin regeneration.While curent is positive we will use the same switching procedure as above. However we will reduce the switching duty cycle D. So now suppose S1 and S4 are conducting. Voltage across the inductor is positive. So current through the inductor rises. Now suppose S4 is turned off and the current is still positive. S1 and D3 will conduct. Here voltage across inductor is negative so the current through the inductor will fall. However since S4 is on for a lesser interval of time than before (we reduce the D) there will be a net current decrease. So average inductor current is falling with each succesive switching cycle. Now suppose inductor current has finally come to zero while motor is still rotating in the same direction. We turn S2 on and S1 and S4 off. Voltage across the inductor becomes negative (using previous refernce directions) so current through the inductor falls i.e it becomes negative. Current flow is D4 Dc motor and then S2 then back to D4. Now regenerative process has begun. Now we are using the Hbridge in boost converter mode. Now turn S2 off and D1 begins conducting. Voltage across the inductor is positive so the inductor current rises i.e becomes less negative. Current flow is D4 then DC motor then D1 then source and back to D4. So now the average inductor current is negative. Average power flow is from motor (now a generator) to the source. So you are now in stage 2.

I am attaching the calculations and also the inductor current waveforms for motoring and regenerative mode.
In the calculations I have assumed that the effect of armature resistance is negligible and that initially in the motoring mode Do was the duty cycle. Then the duty cycle was reduced to D1<Do. The initial average inductor current is Iavg. Obviously the time taken for inductor current to go to zero depends on exactly at which point of the switching cyle you decided to change the duty cycle but the value given in the calculations is approximately right.

 

[bittware]

reverse current in inductor

Hello usernam,
I can't understand why you introduce an extra D1 duty PWM phase. For extreme condition, take D1=0, I can't get significative result from your equation.
If you don't take winding resistance into account, how the electric energy stored in inductor dies out to zero eventually?(you know the kinetic energy of rotator dies out because of friction) I think the quation should at least include integral and differential characteristics. If I am wrong, please correct me.

 

[usernam]

voltage current dc inductor

If you don't take winding resistance into account

I was only neglecting its effect while equating Do*Vs = Back EMF. Since usually Back EMF is in the order of a 100 V and Ia*Ra drop is around 4 or 5V it can be neglected.

I can't understand why you introduce an extra D1 duty PWM phase. For extreme condition, take D1=0, I can't get significative result from your equation.

Yes for an extreme condition you will take D1=0. I was just giving a general case. Perhaps you may not want a high (di/dt) for a sustained period time. In that case you will not resort to the extreme condition.

 

[bittware]

inverse current dc motor pwm

Hello usernam,
I am using a small brush DC motor(35W, 24V). What I care about is the current variation in inductor when PWM swithes off. Based on common sense, the motor resistor will consume up the energy stored in indutor during recirculation phase. And as for PWM off time is enough long, the current will alternate its direction finally. Bigger the motor resister is, quicker the current changes its flowing direction. How to calculation this crucial timing point(when the current changes direction) is my concern. And I deem only take motor resistor part in the result could make sense.
If I am wrong, please correct me.

 

[nicleo]

dc motor regeneration mode

Model:

Vs = Vemf + L di/dt + Ri ....... (1)

Vs = driving voltage supply (also = voltage across motor winding terminals if the voltage drops across switches are negligible)
Vemf = back emf voltage
L = inductance of motor winding
R = resistance of motor winding

After switches are OFF (hard switching), the mathematical model of the system should reduce to

[correction] -Vs = Vemf + L di/dt + Ri ....... (2)

After entering stage (2) and if all switches are kept OFF until the rotor stops, the Vemf will be reduced as the rotor speed reduces.

To bittware:
The stator of the DC motor has permanent magnet or field winding?

 

[usernam]

are motors inductors

bittware I need to get a few things clear. What do you mean by PWM switches off? Do you mean S4 is off and current is free wheeling from S1 to DC Motor to D3.

 

[nicleo]

solving for vemf chopper

bittware I need to get a few things clear. What do you mean by PWM switches off? Do you mean S4 is off and current is free wheeling from S1 to DC Motor to D3.

To usernam and bittware, what do you think we just focus our discussion on 'hard switching' first so we won't be confused?

 

[bittware]

vemf chopper

Model:

Vs = Vemf + L di/dt + Ri ....... (1)

Vs = driving voltage supply
Vemf = back emf voltage
L = inductance of motor winding
R = resistance of motor winding

After entering stage 2, the mathematical model of the system should reduce to

0 = Vemf + L di/dt + Ri ....... (2)

To bittware:
The stator of the DC motor has permanent magnet or field winding?

Hello nicleo,
In my case, I am using PM DC motor and also know the formula you mentioned above. But it can't directly help calculate the timing point I wanted.

 

[bittware]

motor inductors

bittware I need to get a few things clear. What do you mean by PWM switches off? Do you mean S4 is off and current is free wheeling from S1 to DC Motor to D3.

Hello usernam,
I mean when PWM switches on the S1 and S4 are close simultaneously and when PWM switches off the S1 and S4 are opened simultaneously.
To simlify this case, assume all these operation has nothing relationship with S2 and S3. They are always set opened.
I understand the current path illustrated in nicleo's diagram. The red one represents the driving current when PWM switches on. The blue one represents the unleashed current from inductor when PWM switches off. But from the diagram can't see the reversed current path which generated by BEMF.

 

[bittware]

motor is an inductor

bittware I need to get a few things clear. What do you mean by PWM switches off? Do you mean S4 is off and current is free wheeling from S1 to DC Motor to D3.

To usernam and bittware, what do you think we just focus our discussion on 'hard switching' first so we won't be confused?

I agree. However, regardless of what switching style is, I think the phenomenas are the same.