Research Article  Open Access
A DiscreteTime Decoupled Current Control Scheme Applied to VSCBased ThreePhase ThreeLine Systems
Abstract
Accurate current control of the voltage source converters (VSCs) is one of the key research subjects in modern power electronics. To achieve a preferable solution to current coupling effect in the VSCbased threephase threeline system, a discretetime decoupled current control strategy is proposed in the paper. With integration of the ฮฑฮฒ transform and two independent current controllers, the proposed methodology can effectively implement decoupled control of the threephase currents, which can thereby eliminate the impact from the neutralpoint voltage especially under asymmetrical loading conditions. Control performance under digital realization was characterized with extensive tests on a shunt active power filter (SAPF) platform. Both the simulative and experimental results have demonstrated that the SAPF could function well and thereby verified the feasibility and effectiveness of the proposed current control methodology.
1. Introduction
Based on fully controlled power semiconductors, voltage source converters (VSCs), such as DCDC, DCAC, and ACDC converters, are being more widely used than current source converters (CSCs), as the DC side capacitor used for energy storage in a VSC is much superior to an inductor in a CSC in terms of weight, cost, and efficiency, especially suitable for the nowadays switching semiconductors. For concrete applications with VSCs, such as active power filters (APF), PWM rectifiers, power factor correction (PFC), HVDC light and gridconnected inverters, an accurate current control methodology with preferable dynamic performance is indispensible and critical [1โ7]. Current control is normally used for the inner closed loop in a VSCbased system, in which PWM signals are directly generated to track the current reference accurately as well as ameliorate controllability and dynamic response of the system.
For a threephase fourline circuitry of a VSC, the current control strategy makes no difference at all from that for a singlephase system since the phase currents are independent of each other in the circuitry. However, in a threephase threeline system, the threephase currents are interactional and electromagnetically coupled. As a result, only two circuit equations are independent accordingly. In addition, the neutral point voltage of the threeline circuitry will also affect the behavior of current tracking control in the VSC, especially when the threephase voltages or loads are not symmetrically presented. Hence, it is a pending issue to be properly tackled of the current control strategy in a VSCbased threephase threeline circuitry.
Most of the nowadays current control strategies are based on the dq synchronous rotating frame as to decouple the active currents and the reactive currents in a threephase VSC system [7โ12], in which the physical concepts of the adopted variables are unique and clear; however, the instant value of the angular power frequency and the output inductance of the VSC should be known in advance. Also, the sensible impact of the neutral point voltage was not incorporated [9, 10, 12]. References [13, 14] advised using an ฮฑฮฒ stationary frame to transform the mathematical model of an APF, and the VSC topology was designed in the ฮฑฮฒ stationary frame so as to achieve current decoupling, which did facilitate the control strategy but the corresponding hardware design became much more complicated than before.
To cope with the abovementioned issues, based on a general mathematical model of the threephase threeline VSC system, the impact of the neutral point voltage on current control scheme was fully elucidated in this paper. Further, a discretetime mathematical model in the ฮฑฮฒ coordinate system was established through orthogonal transform, with a view to developing a decoupled current control strategy as to eliminate the impact of the neutral point voltage and finally achieve decoupling of the threephase currents. Simulation and experimental results on an APF prototype under nonlinear loading conditions were also presented for verification purpose.
2. Impact of Current Coupling in a ThreeLine VSC System
For a typical VSC configuration in the threeline system as shown in Figure 1, several assumptions are made as follows in establishing a mathematical model: (1) the sources and loads are in Y connection (ฮ connection can be transferred into Y connection); (2) the threeline inductance is ignored due to its very small value and little effect; (3) the threeline resistances and the output Inductor of the VSC unit are symmetrical; (4) the mathematical model of the VSC unit is described in the continuoustime system for convenience.
Given asymmetrical sources or loads in the threephase system, the phase voltages , , and can be expressed as follows:
If the sources and loads are symmetrical in the threephase system, then will be fulfilled. For the threeline voltages , , and in the AC side, one gets
Based on Kirchhoffโs Voltage Law, the circuit equation of phase A is governed by
If the switching states of , , and are expressed by , , and , then , where logic 1 represents that the upperleg switch is turned on while the lowerleg switch is turned off. Similarly, logic 0 represents the lowerleg switch is turned on while the upperleg switch is turned off. If is turned on and is turned off, then and . If is turned on and is turned off, then and . Hence, we get and (3) can be changed to
In the same way, the governing equations of phase B and phase C are obtained as follows: where , , and denote the threeline currents, , , and represent the phase voltages relative to point N, expresses the DC side voltage and denotes the voltage difference between point N and the neutral point.
Obviously, the threeline currents will meet
Based on (4) to (7), the following relationship can be derived:
Further, we can get
If (9) is substituted into (4) to (6), the mathematical model of the VSC unit can be obtained when the sources or loads are in asymmetrical conditions: where
For the symmetrical conditions of the sources or loads in the threephase system, will be met, which directly results in the corresponding mathematical model of the VSC shown below:
Only two governing equations are outstandingly independent since the summation of the threephase currents always is equal to zero as shown in (7). With regard to the asymmetrical system, (10) shows that the neutral point voltage will impose direct impact on the tracking control performance of output currents in the VSC system. For an example shown in Figure 2, where a VSC unit is utilised in a shunt APF topology with nonlinear loads, simulations are carried out with the PSIM software. The source frequency of the APF system is 50โHz and the source voltage is 220โV (RMS). The nonlinear load is represented by a threephase rectifier in a symmetrical system, and the threephase rectifier connected with an asymmetrical RLC circuitry denotes the loads within the asymmetrical system. Referential command currents are calculated by the instantaneous reactive power theory, while the APF output currents are controlled by a classical PID controller. Without considering the affection of current coupling under the symmetrical or asymmetrical condition, Figure 3 shows the load and source currents in phase A after compensation of the shunt APF, while Figure 4 typically shows that under asymmetrical conditions including source or loads asymmetry. By comparison of the simulated results it can be seen that the current tracking error in the asymmetric system is much larger than that in the symmetric system. Hence, proper measures must be taken to counteract the current tracking errors that resulted from current coupling as well as the neutral point voltage.
(a) Asymmetrical source system
(b) Asymmetrical loads system
3. DiscreteTime Mathematical Model of the ThreePhase ThreeLine VSC in ฮฑฮฒ Domain
The discretetime expression of the mathematical model of a threephase threeline VSC can be derived from (10) as follows: where T is the sampling interval, .
Based on ฮฑฮฒ transform of the instantaneous reactive power theory, (13) can be transformed into the ฮฑฮฒ domain through the orthogonal transform matrix C, which transforms the threephase system to a twophase system, as shown in (17):
The expressions in (17) clearly indicate that the items associated with the neutral point voltage have disappeared in the ฮฑฮฒ domain, which means the same current tracking control behavior of an asymmetrical system as that of a symmetrical system. Therefore, if the current control scheme of the threeline VSC is implemented directly in the ฮฑฮฒ domain, it would be unnecessary to consider the impact any more from the neutral point voltage, and only two controllers are thereby required. As a result, there comes the discretetime mathematical model of the threephase threeline VSC in the ฮฑฮฒ domain, based on which decoupled current control will be achieved accordingly:
4. Implementation of the Decoupled Current Control Scheme
Here a classical PID controller is combined with the decoupled current control scheme of the VSC in the ฮฑฮฒ domain, the diagram of which is shown in Figure 5. The input of the controller is defined as where and denotes the referential command currents of the VSC in the ฮฑฮฒ domain. The current control loop is realized using a DSP hardware controller, in which the current references are calculated and given by the instantaneous reactive power theory. The output currents of the VSC are sampled by the DSP element as to be the current feedback.
Since the sampling interval T is small, then . From (18) and (19), one can get
The incremental form of the discretetime PID algorithm is applied, namely, where , and represent the PID controller parameters. Combination of (20) and (21) gives the expression of the prosed control strategy:
Firstly, the controller output is calculated according to (22). Then, based on the relationship between the output and the switching logic, the states of the switches , , and can be determined. Finally, the controlling signals of the threephase PWM are generated accordingly.
With substitution of (11), (17) corresponding to the control strategy can be changed into
According to (22) and (23), the following relationship can be obtained.If , ; if , .If , and ; if , and .If and , and ; if and , and .
The true values of the threephase PWM switching signals are consequently given in Table 1 for the discretetime decoupled current control methodology.

The switching states in the three legs can be determined by collating the true value table according to the output of the discretetime controller acquired from (23). The threephase PWM switching signals will be generated as to subsequently realize decoupled control of the threecurrent , , and .
5. Simulation and Experiment
Performance verification of the proposed decoupled current control methodology is carried out on a developed VSCbased shunt APF system, as shown in Figure 2.
5.1. Simulation Results
The available program PSIM is adopted to establish simulation models as to verify the effectiveness and validity of the new algorithm proposed above. This simulation topology is the same as the shunt APF system shown in Figure 2, and the nonlinear load is also represented by a threephase rectifier connected with an asymmetrical RLC circuitry. The whole system is simulated in the discretetime domain while the sampling frequency is set to 12โkHz. The current reference signals to be tracked are acquired by the instantaneous reactive power theory, in which lowpass digital filters (LPFs) of the secondorder Butterworth IIR type are incorporated [15]. The circuits for twophase current controller are established, as well as the logic circuits to implement the decoupled control scheme. Here, the maximum switching frequency is set to 20โkHz in the simulations.
Figure 6 shows the threephase load currents. The compensated currents of the shunt APF can be acquired by adjusting the parameters of the two PID controllers. As an example, both the supply voltage and current of phase A are given in Figure 7, which indicates that the supply current can be effectively compensated to be in phase with the supply voltage. A transition process as well as a little steady error may exist due to the dynamic characteristics of the lowpass digital filters being adopted; however, they can be easily avoided if the physical compensating operation starts from some instant within the steady status of the digital filters. The threephase PWM signals shown in Figure 8 for decoupled current control can be acquired according to Table 1. It can be seen that the spectrum of phase A is deferent from that of the other two phases, which is mainly due to the decoupled process being carried out between phase B and phase C.
5.2. Experimental Results
An experimental platform for the VSCbased shunt APF system has been established, in which the proposed decoupled current control scheme is incorporated. The converter is controlled within a closed loop by a 32bit 150โMHz DSP element. Figure 9 shows the schematic diagram of the 400โV shunt APF circuitry for experimental setup. Here the source voltage is in 50โHz and rated at 220โV (RMS). In the experiments, a threephase rectifier being connected with an asymmetrical RLC circuitry is used to act as the loads which are similar to that in the above simulations.
The experimental platform, consisting of a converter and a control circuit, functions well to realize data acquisition, signal driver, generation of the compensated current, and so on. Three HALL voltage sensors as well as six HALL current sensors are used to pick up the threephase supply voltages, supply currents, and load currents. The detected signals are amplified and isolated by the signal modulating unit before being sent into the DSP module. The most important component of the shunt APF converter is an IGBTbased intelligent power module (IPM). Also, several DC sources are designed with sufficient isolation to output +5โV, +3.3โV, and +1.9โV for experimental usage. An executive program is written into the DSP module to complete signal sampling, calculation of the harmonic and reactive currents, output current control of the shunt APF and the DC side voltage with a PID controller, and so forth.
All the waveforms are captured with a digital oscilloscope Agilent DOS5034A. In spite of the supply current fed by the current clamp directly into the oscilloscope, the rest waveforms are taken from the entry of the DSP module.
Figure 10 shows the asymmetrical load currents, while Figure 11 shows the threephase output currents of the shunt APF unit. In Figures 12, 13, and 14, the experimental results for the voltages and currents of phase A, B, and C after compensation are presented, the four waveforms of which in turn from upward to downward denote the supply voltage, the compensation current of the shunt APF, the supply current, and the load current.
Figure 15 shows the measured voltages and currents of phase C when the shunt APF starts running with a load step, the four waveforms of which in turn denote the supply voltage, the compensation current, the supply current, and the load current.
It can be seen from the experimental waveforms that, with a fast control loop based on the decoupled current control methodology, the supply current will be approximately compensated into a powerfrequency sine wave, in which the lowfrequency harmonics are significantly reduced. Also, the supply current can be compensated to be exactly in phase with the supply voltage of basefrequency. The experimental studies demonstrate that the new control algorithm proposed in this paper can effectively and correctly realize instantaneous compensation of the harmonics and the reactive power. The decoupled current control algorithm presents a significant strategy to counteract the impact from either the current coupling or the nonlinear and asymmetrical loading conditions, which also helps to extend the application of VSCbased shunt APF technology in power systems.
6. Conclusion
The coupling effect of the threephase currents in a threeline VSCbased system increases the difficulty of current tracking control. The paper proposed an effective decoupled current control scheme which was verified by both simulative and experimental studies.
Only two governing equations are independent in the mathematical model of a threephase threeline VSCbased system since the summation of the threephase currents is always zero. Further, for asymmetrical conditions, the neutral point voltage will directly affect the tracking control behavior of the VSC output currents. Simulations verified that the current tracking control error would be enlarged if the coupling effect was ignored.
A discretetime mathematical model in the ฮฑฮฒ domain for the threephase threeline VSC is derived through orthogonal transform, in which the impact from the neutral point voltage on current tracking control is eliminated. The decoupling of the threephase currents can be achieved in the ฮฑฮฒ coordinate system.
Combined with the instantaneous harmonic and reactive currents detection and the PID controller, an integrated decoupled current control scheme has been established. Simulations and experiments have verified the feasibility and effectiveness of the proposed control strategy.
Acknowledgments
This research work was supported by the National Science Foundation of China (50807033) and the Shandong Provincial Natural Science Foundation (ZR2009FQ025, ZR2009FM013).
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Copyright
Copyright © 2011 Hui Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.