Mitigation of Current Harmonics in Inverter-Fed Applications
Current harmonics are undesired in most applications. They cause additional losses, control loop instabilities, noise, vibrations and torque ripples in drive applications. A simple but effective method that allows online identification and compensation of the effects is presented in the following. It is exemplarily applied to an anisotropic permanent magnet synchronous machines with nonlinear magnetics. The method requires neither additional sensors nor extensive model parameterization. It can be implemented easily in existing inverter systems by software updates. Test bench measurements show significant improvements in the whole operational area. Measurements at nominal operation result in a motor current total harmonic distortion of 0.28 % which is less than a seventh of the uncompensated value. The functional principle is transferable to other machine types or grid applications enabling the mitigation of current harmonics in a wide field of applications.
Current harmonics are undesired in most applications. They cause additional losses, control loop instabilities, noise, vibrations and torque ripples in drive applications. A simple but effective method that allows online identification and compensation of the effects is presented in the following. It is exemplarily applied to an anisotropic permanent magnet synchronous machines with nonlinear magnetics. The method requires neither additional sensors nor extensive model parameterization. It can be implemented easily in existing inverter systems by software updates. Test bench measurements show significant improvements in the whole operational area. Measurements at nominal operation result in a motor current total harmonic distortion of 0.28 % which is less than a seventh of the uncompensated value. The functional principle is transferable to other machine types or grid applications enabling the mitigation of current harmonics in a wide field of applications.
Origins of Current Harmonics
The influences of motor current harmonics in inverter-fed drives are well known. They are caused by three effects: inverter switching, inverter nonlinearities and spatial harmonics of the machine. All three effects yield voltage harmonics that generate phase currents harmonics. Harmonics due to inverter switching are unavoidable since they follow the used working principle of the DC/AC inverter and the pulse-frequency related modulation scheme.
However, harmonics created by inverter nonlinearities can be mitigated. Most known approaches use an inverter model for that purpose. Model parameters are either obtained from product data sheets, characterization measurements or a combination of the two. Depending on model complexity the inverter dead-time, current zero-clamping and diode capacity effects are considered. Some methods partly work online to adapt parameters or to determine the current zero-crossing more precisely. Obviously, all inverter models contain errors and taking all physical effects into account results in complex models and extensive parameterization.
Other approaches mitigate current harmonics caused by machine spatial harmonics. It was shown that the sixth harmonic of the rotor-oriented dq-currents can be mitigated by including filters or by precise characterization measurements and feed-forward control. Both methods use offline parameterization and lookup tables. That is why usage of parameters obtained from one sample for multiple specimens in series production is questionable. Moreover, the methods only work for machines with equal inductances in the direct and quadrature axes and mitigate only one distinct frequency.
Current Harmonic Mitigation
To enable industrial application of current harmonic mitigation further improvements are necessary. Mitigation parameters have to be identified online during drive operation in a robust and fast way without additional sensors, little memory demand and low calculation effort. Additionally, current harmonic mitigation should be possible up to the physical limits of the total system given by the switching frequency and the voltage limit of the inverter. These requirements are fulfilled by the method illustrated in the graph. The mitigation scheme is integrated in a rotor-oriented current controller and based on two ideas:
- First, the interpretation of inverter nonlinearities and machine spatial harmonics as voltage errors that can be identified online using the controller reference voltages, the measured currents and the rotor angle.
- Second, the principle of repetitive control because the voltage errors are stored in dependence on the rotor angle that repeats periodically. Feed-forward control of the stored voltage errors yields remarkable mitigation.
Fig. 1: Scheme of the proposed method. The rotor-oriented dq-currents are closed loop controlled to their reference values. The essentials of the proposed method are marked blue. Voltage errors are identified online, stored in dependence on the rotor angle and feed-forward controlled.
Mitigation works best during stationary operation because then the total voltage errors are periodical. During transients the compensation of voltage errors is not a prior objective, because a good controller utilizes the maximal inverter output voltage anyway. The method works for any kind of permanent magnet synchronous machine because both nonlinear magnetics and magnetic anisotropy of the rotor are covered. All harmonics are mitigated, which is only restricted by the physical limits of the system given by the sampling frequency or rather the sampling theorem and the voltage limit of the inverter. Implementation on a micro-controller is simple as the number of calculations and the need of additional dynamic memory is limited.
Measurement Results
In order to evaluate the experimental performance of the described method three different controller setups and mitigation techniques are compared:
- (a) A PI-type controller with no compensation.
- (b) An advanced PI-type controller with compensation of the dead-time in the modulator which is a conventional compensation method.
- (c) The proposed method.
The behavior of nominal operation at a rotor speed of 4200 min-1 and a torque of 130 Nm is analyzed. The rotor-oriented currents in the dq-reference frame are shown in Fig. 2. Results of the proposed method are given in (c). The current ripples are significantly lower in comparison to the PI-type controller with compensation (b) and without compensation (a). In both (a) and (b) the current oscillates in a repetitive manner which is caused by the voltage errors of the machine and the inverter. In contrast, the proposed method (c) mitigates all harmonics. Due to the functional principle of the method any systematic oscillation of the current is removed which is why the current only contains noisy jittering besides the fundamental component. This is realized by feed-forward control of the online identified voltage errors. In order to compare the performance of the three methods the total harmonic distortion (THD) is calculated using the measured current samples for frequencies up to 4 kHz. The proposed method (c) significantly reduces the THD to 0.28 % which is less than a seventh of the value without compensation (a).
Fig. 2: Measured currents at nominal operationwitha direct current of -277.9 A and a quadrature current of 85.0 A. Results of the PI without compensation (a), of the PI with compensation (b) and of the proposed method (c) are shown. The THD of the proposed method is significantly lower in comparison to the conventional methods.
The absolute value of each harmonic of the measured dq-currents is calculated by Fourier transformation and given in the graph. The spectra of the conventional compensation and the no compensation method dominantly contain harmonics of the sextuple of the fundamental frequency. This is true because for example the -5th and 7th phase current harmonics are transformed to a 6th in the dq-reference frame. The proposed method reduces all harmonics regardless of their physical origin or frequency. Current harmonic mitigation is only limited by the sampling frequency and the inverter voltage limit.
Fig. 3: The Fourier transforms of the measured currents of Fig. 2 are shown in the plot. The harmonic content is significantly lower when the proposed method is used.
Conclusion
A control method is described that mitigates all current harmonics independent on their physical origin. Mitigation capability is only limited by the sampling frequency and the inverter voltage limit. The method is based on online identification, rotor angle dependent storage and precise feed-forward control of the voltage errors. It basically works without an inverter and machine model. The effectiveness of the proposed method is proven by measurements at nominal operation which show that the current harmonics are significantly reduced. Implementation of the method in existing inverters is easy. It can be realized by software updates because only the already available current and rotor angle sensors are needed. The method is micro-controller capable and extra need of calculation time and dynamic memory is very little. The used functional principle is transferable to other machine types and grid applications enabling the mitigation of current harmonics in a wide field of applications.
More background information, a detailed description of the working principle and additional measurement results that prove the effectiveness in the whole operational area of the machine are given in the full paper that was published at PCIM Europe in May 2015 in Nuremberg, Germany. A PDF version of the full paper can be downloaded free of charge here.
