What is Space Vector Modulation? (Episode 10)

hi and welcome back to understanding motors last episode we proved that we can eliminate torque ripple while simultaneously minimizing the current in the d direction by having our three-phase currents be sinusoidal functions of our rotor angle however there are multiple ways of achieving this and it isn't immediately obvious which method is best by the end of this episode however we're going to have arrived at the industry standard method of optimized commutation so let's get into it [Music] so we're going to start today by talking about feedback control for some viewers feedback control may be a super familiar idea and for others it may be entirely foreign if you're in the latter category don't worry we're not going to take a deep dive into control theory here but i think it's a useful framework through which we can understand achieving our desired current in a lot of applications such as say fans or older washing machines motors are run in what is called an open loop fashion what this means is that the magnitude of the voltage applied across the leads of the motor is not necessarily a function of the current running through the motor at that time you can kind of think of this as having the voltage pattern being pre-scheduled however in cases where you care about the motor's angular position or if you want to dictate the velocity of the motor system and there are external forces being applied you would want to control it via what's called closed loop control i find that this is easiest to explain via an example so say that you want to control the angle of your motor you would come up with a position reference signal which you would then pass to your controller the controller would look at the error between the current orientation of the rotor and the position you specified you wanted it would then command a torque to the motor to turn it to the desired position as we talked about in episode 2 torque is proportional to current so really the controller is commanding a current to the motor however we don't have a way of just dictating an exact amount of current running through the motor instead we have to make a second nested controller here which looks at the current we want running through our motor as dictated by the first controller it then compares it to the current we have running through our motor and modulates the voltage being applied to our motor phases based on the error between the actual current and the desired current cool so that's a super basic overview of what closed loop current control is however this nested current controller has one issue that is fundamentally different than the position controller unlike rotor position which is a one-dimensional number both current and voltage are two-dimensional you can think of these dimensions in a rectangular cartesian plane as we did with the alpha beta axes however i find that for this conversation the most useful way to think of these is in a polar reference frame meaning that we're describing the vectors in terms of a rotation angle and a magnitude the reason i think this is useful is that while the magnitude of the current commanded and the voltage applied are functions of the error terms going into the controllers the angle at which they are applied is a function of the orientation of the dq axis and thus the rotor's position so i like to kind of think of these two variables as being separately controlled the magnitudes of the vectors will be determined by the feedback control loop meanwhile the angle of application will be a function of rotor angle and will be handled by the chosen method of commutation and pulse width modulation to the h-bridge we're going to talk more about designing the closed-loop controller which will dictate the magnitude of these signals in a later episode when we get a bit more into the system's analysis of motors but right now we're going to talk a bit more about commutation and the different ways you can modulate your voltage one of the simpler ways we can modulate our voltage has already been discussed here in fact it was the primary focus of episode six six block commutation here by using the signals from the hall effect sensors as a low resolution angular measurement we dictated the angle of application of our voltage vector and thus of the current flowing as a super discrete function of our rotor angle so if you were using six block commutation with your feedback controller your current controller would look at the current running through your motor it would then compare it to the reference you provide it and generate the magnitude of a voltage signal to be applied this voltage signal would then be divided by the supply voltage of the system to find the duty cycle which you would want to apply to the mosfets of the h-bridge if the commanded voltage was above your supply voltage you would simply saturate the duty cycle at one hundred percent finally these duty cycles would be supplied to the appropriate fets as dictated by your commutation scheme where a positive 100 duty cycle corresponds to the high side mosfet being active for 100 of the time and a negative 100 duty cycle corresponds to the low side mosfet being active 100 of the time note that this commutation pattern is for positive torques if we wanted to produce a negative torque we simply flip this commutation scheme about the x-axis for all the reasons we've talked about in the last couple episodes torque ripple unwanted d-axis current and such six block commutation leaves a lot to be desired however if you have a more resolute method of angular sensing like an encoder for example you can improve your method of commutation we know that the resistor inductor circuit that is a motor acts as a relatively fast low-pass filter between voltage and current so at low to medium rotation rates you can produce a sinusoidal current vector which rotates with the motor's angle by inputting voltage vectors which rotate at the same rate with the motor's angle but how do you actually do that in the real world well just like with block commutation the output of your current control loop would specify a voltage magnitude to be applied again you would then divide this by your supply voltage and saturate it 100 now however instead of applying this duty cycle full blast to whichever fet would be dictated by the block commutation you would multiply this duty cycle by your a b and c sinusoids which are functions of theta this produces three duty cycles between negative 100 and positive 100 which you can then output accordingly to your h bridge however while this commutation scheme will allow for you to better control your current to the q axis and by phase shifting your sinusoids forwards or backwards by some angular offset you could modulate current in the d direction if you wanted to say field weaken there is one nuanced downside to sinusoidal commutation at no point during sinusoidal commutation are you taking full advantage of your voltage range but what do i mean when i say this well when we're applying quote a voltage really what that means is applying a voltage differential so the absolute magnitude of the voltage being applied to phase a doesn't really matter what matters is the difference in magnitude of the voltage applied to a versus that to b and c kind of like how if you jumped from a platform that was 100 feet in the air onto another platform that was 99 feet in the air gravity was only accelerating you for that one foot but if we plot the sinusoidal functions of voltage being applied to phases a b and c we notice that at no point our phase is spanning the full range of supply voltage possible in fact if we plot the voltage differential so the highest voltage minus the lowest voltage for each angle on this plot we see that the maximum differential we're using is only 86.6 percent of what our system could do and this brings us to the industry standard way of modulating our voltage space vector modulation just like with sinusoidal modulation space vector modulation maintains a voltage differential which rotates with the motor angle to stay in line with the q axis however through some clever math it takes full advantage of your supply voltage i personally find that the easiest way to show how it works is just to demonstrate the transformations that take the voltage curve from the sinusoidal commutation waveforms and transform them into the space vector modulation voltage signals because we know that our voltage differential could theoretically be increased by 1 over 0.866 or 15.47 percent we're going to start by multiplying our voltage signals by 1.1547 however this obviously creates a new problem while we would now be applying the maximum voltage differential our supply voltage could provide we would also be required to command a duty cycle of 115 which is by definition impossible but here is where we get creative to start with i want to remind you again that it's not the absolute value of the voltage that matters it's the voltage differential so if we look at one of these places where we would need to command the voltage to high for 115 percent of the time well what's being applied on the other side of the circuit here we're only commanding the other two phases to ground at a 58 duty cycle so accounting for the fact that the circuit dynamics will filter the pwm voltage into a pseudo-continuous voltage signal the ability of the voltage differential to drive current would be the exact same for this location if instead of having the impossible 115 duty cycle and 58 duty cycle we shifted all three phases down by 28.8 percent such that one was connected to high 86.6 percent of the time and the other two were connected to low six point six percent of the time in the same way we see that the points when the low side would be required to connect to ground with a hundred and fifteen percent duty cycle we could shift the common voltage of the three up by twenty eight point eight percent such that the three duty cycles were again 86.6 percent so in order to bring the negative 115 sections up and the positive 115 sections down we will add a triangle wave with peaks at these locations to all three of our sinusoids now using this modulation scheme we're taking full advantage of the voltage range made available to us while keeping our required duty cycles at or below 100 percent so that's space vector modulation which is generally regarded as one of the best ways to perform motor commutation however like we discussed in episode 7 with block commutation there are still many different ways you can perform your actual pwm switching for any given commutation scheme so next episode we're going to look at the best way to perform space vector modulation in the real world

Channel: Jantzen Lee

Views: 16,510

Rating: 4.9096045 out of 5

Keywords: Voltage Modulation, Sinusoidal Modulation, Motor Commutation, brushless motor, brushless motor commutation, BLDC, Jantzen Lee, understanding motors, how does space vector, space vector modulation, brushed motors, learn from home, physics of motors, optimal motor control, field weakening, mechanical engineering, engineering of motors, power electronics, space vector, pulse width modulation, space vector pwm, space vector inverter, Simulink, SVM

Id: hSXSY4LRizg

Length: 10min 53sec (653 seconds)

Published: Thu Sep 10 2020