The realization of an improved predictive current controller based on a trapezoidal model is described, and the impact of this technique is assessed on the performance of a 2 kW, 21.6 kHz, fourwire, Active Power Filter for utility equipment of Metro Railway, PowerLand Substations. The operation of the trapezoidal predictive current controller is contrasted with that of a typical predictive control technique, based on a single Euler approximation, which has demonstrated generation of highquality line currents, each using a 400 V DC link to improve the power quality of an unbalanced nonlinear load of Metro Railway. The results show that the supply current waveforms become virtually sinusoidal waves, reducing the current ripple by 50% and improving its power factor from 0.8 to 0.989 when the active filter is operated with a 1.6 kW load. The principle of operation of the trapezoidal predictive controller is analysed together with a description of its practical development, showing experimental results obtained with a 2 kW prototype.
The use of Active Power Filters (APFs) in the electrical grid is critical for onland transportation applications, such as Metropolitan Railway Substations, which reduce the flowing of current harmonics caused by the increased utilization of nonlinear loads, whilst improving the power quality of the supply. APFs are an attractive solution to comply with the national and international power quality standards at every level of the network infrastructure, [
Fourwire shunt APFs are a commonplace strategy that exhibit attractive characteristics to inject currents and reshape the line currents drawn by unbalanced nonlinear loads, whilst providing a path to cancel the neutral current by using either an additional switching limb or a split DC link [
This paper presents the realization and experimental verification of a trapezoidal predictive current controller for a fourwire shunt APF that improves the power quality of unbalanced AC loads in contrast to the typical predictive Euler control strategy. The trapezoidal strategy relies its operation on a discrete trapezoidal linear approximation that more accurately determines the switching of the active filter for the onestep ahead current sample, such that three significant advantages are potentially exhibited: first, the trapezoidal predictive controller slightly increments the processing time without affecting the switching of the power converter; second, in contrast to the typical Euler approximation used in other works [
The fourwire shunt APF is connected in parallel to the unbalanced nonlinear load as shown at the righthand side of Figure
Fourwire shunt active filter and its corresponding control block diagram.
The principle of operation of the APF of Figure
The APF requires a fixed DClink capacitor voltage
Since the split DClink node
A space vector ACside model of the APF threephase converter is derived calculating the filter inductor voltage vector as shown in
A discrete time model of (
Normalized converter voltage space vectors with respect to the transistor switching states.
Transistor state combination 

Normalized converter voltages  











0  1  0  1  0  1 

0  0 

1  1  0  0  0  1 


0 

1  1  1  0  0  0 




0  1  1  1  0  0 




0  0  1  1  1  0 


0 

0  0  0  1  1  1 




1  0  0  0  1  1 




1  0  1  0  1  0 

0  0 

Trapezoidal approximation of the voltseconds integral of (
Onestep ahead current samples,
An error current vector,
Following the description given above, a flow diagram of the APF control algorithm of Figure
Algorithm flow diagram of the predictive current controller.
A 2 kVA, fourwire shunt APF prototype rig was built to evaluate the operation of the APF of Figure
Operating parameters and components of the fourwire APF prototype.
Electrical parameters  

Variable  Value  
Prototype power rating (laboratory design)  2 kW  
Threephase supply 

127 V, 60 Hz 
DClink voltage reference 

400 V 
Sampling frequency 

21.6 kHz 
ADC resolution  12 bits  


Prototype components  


Line filters inductors 

10 mH 
DClink capacitors 

10 mF 
Power IGBTs  BSM100GD60DLC, 1200 V, 30 A  
IGBT drivers  Infineon 2ED300CL7s  
AC/DC voltage sensors  LEM LV 25P  
AC/DC current sensors  Honeywell CSNA111  
DClink 
 
DClink voltage balance controller 

A 150 MHz TMS320F28335 Digital Signal Processor (DSP) was used to implement the control strategy of Figures
The 2 kVA APF prototype was verified with the Euler and trapezoidal predictive current controllers and a 127 V, 60 Hz linetoneutral supply voltage and under three nonlinear load conditions: a 1.6 kW, naturally controlled threephase rectifier with a
Nonlinear loads used to experimentally verify the APF and predictive current controller of Figure
Figure
Experimental verification of the APF prototype with the 1.6 kW balanced load of (a). (a) Measured waveforms
Figure
(a) Measured supply current waveforms
Figure
A power analyser was used to measure the supply active power,
Bar plot of the power quality results for the AC load circuits of Figure
Closer inspection of the microprocessor operation revealed that the total period to perform the algorithm of Figure
The presented trapezoidal predictive controller is slightly more complex than the typical predictive strategy to perform the current reference tracking and generates a slight increase of power losses, which could make it inadequate for implementation in lowrated rigs; nevertheless, the ripple current reduction, closer current tracking, and power quality improvement are important advantages to consider over the traditional predictive controller technique. Furthermore, the digital implementation is acceptable for fast microcontrollers, such as a DSPs and hybrid digital controllers, and will be used once the trapezoidal control strategy is implemented to control other power converter systems, which would be suitable to obtain high power quality results.
The utilization of a trapezoidal predictive technique to generate the filter currents of a fourwire, shunt APF allows the power quality improvement of using unbalanced nonlinear loads for onland utility applications, such that the supply currents become virtual sinusoidal waves. The latter makes the current control strategy attractive for easy and straight implementation on future power converters that require highperformance power quality; nevertheless, the control technique is suitable for a wide range of power converter applications. In this work, the trapezoidal predictive controller was experimentally verified and evaluated with the fourwire APF under three load conditions; in the first, the load was set up with a threewire, balanced nonlinear circuit to preliminary check the basic operation of the control technique, such that sinusoidal supply current waves were generated and the power quality was improved. A current THD of 10% and a power factor of 0.989 were measured in the first experiment showing a noticeable improvement in contrast to the traditional predictive technique.
In the second and third load conditions, the load was fourwire, unbalanced nonlinear load, with the load currents being much distorted and producing a neutral current path in both load conditions. The supply current waveforms were all improved and balanced when the APF and the trapezoidal predictive controller were activated, with the neutral current being mitigated; the current THD was 15% and 18%, respectively, and the power factor was 0.98 in both experiments with a 127 V, 60 Hz threephase supply voltage. The shape of the supply current waveforms and the power quality were significantly improved in comparison with the original load currents and power quality, with the active power being slightly increased, due to the highfrequency switching losses of the APF power transistors.
The practical realization of the presented trapezoidal predictive controller could consider the use of an extended sampleddata horizon, either forward or backward, to achieve a faster convergence and reduce the current ripple amplitude. This would be convenient for developing power converters with new generation of switching power devices for other applications.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors are grateful to the National Council of Science and Technology (CONACyT), the Instituto Politécnico Nacional (IPN) of Mexico, the Institute of Science and Technology of Mexico City (ICyT), and the Universidad de Talca, Chile, for their encouragement and the realization of the prototype. Additionally, the authors acknowledge the Metropolitan Railway Transportation System of Mexico City (SCT Metro) for the support offered to obtain power quality measurements at Line B installations.