Control Algorithms of Active Power Filters - piers

Progress In Electromagnetics Research Symposium Proceedings, Cambridge, USA, July 5–8, 2010

429

Control Algorithms of Active Power Filters P. Brandstetter, P. Chlebis, and P. Simonik Department of Electronics, VSB-Technical University of Ostrava, Czech Republic

Abstract— The paper deals with the control methods of the active power filter with voltage source which can be used for reduction of high harmonics in the supply current. For the correct function of the filter, it is necessary to determine magnitude of the currents, which have to be added to load current so as to eliminate high harmonics in the supply current. Several methods of the filter current control are described. Theoretical assumptions are confirmed by practical test on laboratory model of the active power filter which is controlled by modern digital signal processor. 1. INTRODUCTION

The power semiconductor converters are becoming to typical load in the distribution mains. Input circuits of these converters are often designed as a non-controlled rectifier, which consists of power semiconductor devices. Converter is non-linear load in the mains and its current consumption it is not only sinusoidal, but there are higher current harmonics, which unfortunately influence feed system. For reduction of the higher harmonics influence the filters compounded by inductors and capacitors are used. However these devices have many basic disadvantages, for example they and inner line impedance are making resonance circuit with sharp tuned resonances. All these undesirable properties it is possible to remove by using active power filters. For this purpose a semiconductor converter with current or voltage source shows as suitable. That converter is able to add or to take the theoretically any course of current in mains. The active filters with current source have more complicated structure and their purchase price is higher than price of the filters with voltage source. That is why the active power filters with voltage source are often used and we are interesting in them in our research [1, 2]. 2. ACTIVE POWER FILTER WITH VOLTAGE SOURCE

The active power filter (APF) consists of six a semiconductor switches (IGBT transistors), dc link capacitor as a voltage source and reactors for limitation of the current rate of rise (see Fig. 1). A fast microcomputer control system is needed of course. Principle of the filter is such, that a filter current is injected to mains by generation of output voltage out of converter. It can be achieved desired course of the current by suitable switching of converter’s switches. A voltage of the dc link capacitor (voltage source) has to be kept with desired value. It is achieved by means of an active power flow through the converter. For correct work of the filter it is necessary exactly and fast to determine a magnitude of the filter currents, which have to be added to load currents so as to be removed higher harmonics. usa LS isa

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Figure 1: Active power filter with voltage source.

It is effort to achieve as high rate of current rise as possible, because in this way the highest harmonics are filtered. At the same time the ripple of current increases if converter switching frequency is not high enough.

PIERS Proceedings, Cambridge, USA, July 5–8, 2010

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The real effect of the filtration depends on the performance of the filter and on the properties of the loads to be compensated as well. In the case of supply system with finally short circuit power the inner line impedance have to be taken into consideration. The filter currents are calculated from the measured load currents. There exist several ways how to solve the problem of determination of the filter currents. The next chapter will describe the control methods which were examined at the Department of Electronics. 3. CONTROL METHODS

For the correct function of the filter, it is necessary to determine magnitude of the currents, which have to be added to load current so as to eliminate high harmonics. This problem will be made easy very much by establishing a rotation axis system and by transformation load currents into this system. Rotation system forms two axes d, q, d-axis is in direction of supply voltage space vector. By the vector rotation with an angle θ, where θ is an angle between α-axis and d-axis, the two current components iLd and iLq are obtained. The component iLd is proportional to active power and the component iLq is proportional to reactive power. Vector rotation and inverse rotation are calculated by following equations: ¸ · ¸ ¸ · ¸ · ¸ · · ¸ · i cos θ − sin θ cos θ sin θ iLα iLα iLd · Ld = = · (1) sin θ cos θ iLq iLβ iLq − sin θ cos θ iLβ We can express the current components iLd and iLq as a sum of direct component and alternating component: · ¸ · ¸ ·¸ iLd iLd DC iLd AC l = · (2) iLq l iLq DC iLq AC The DC component iLd DC determines magnitude of fundamental harmonic of the active power and the AC component iLq AC is consisted of harmonics. The same is valid for reactive power in the q-axis. The purpose of the active power filtration is an elimination of alternating component in both axis, or direct component in q-axis for compensation of reactive power. For a calculation of reference filter currents there are several methods. We are intended on three of them — determination of reference currents by means of high band pass filter, mean value method and PI-controller method. Control structure of the active filter is shown in Fig. 2. For the correct function of the filter, it is necessary to determine magnitude of the currents, which have to be added to load current so as to eliminate high harmonics. 3.1. Method with High Band Pass Filter

A principle of the method is removing of the DC component iLd DC by a high band pass filter (HBPF). The load currents are transformed to two axis system [α, β] and then they are rotated to orientated system [d, q] by means of angle θ. The current component iLd is filtered by HBPF so as to obtain only alternating current component. The current, which is necessary to keep up the voltage of the capacitor, is taken from it. Then follows inverse vector rotation and after changing of sign of the reference filter currents are obtained. By that way it is compensated all reactive current and power factor cos ϕ is 1. If current component iLd is filtered then high harmonics of reactive current are only compensated and power factor cos ϕ is unchanged. We chose the 4th order Butterworth low pass filter as the HBPF with cut off frequency fc = 150 Hz.

Figure 2: Control structure of active power filter.

Progress In Electromagnetics Research Symposium Proceedings, Cambridge, USA, July 5–8, 2010

431

3.2. Mean Value Method

For right compensation dynamic, it is necessary to determinate magnitude of the DC component iLd DC . The equation, that is suitable for calculating of mean value, is: 1 iLd DC (t) = T

Zt iLd (t)dt

i00fd = iLd − iLd DC

i0fd = iLd

(3)

t−T

T = T0 is fundamental period. In digital form: k 1 X iLd DC (k) = iLd (kTS ) N

or

k−N

N = T /TS , TS is sampling period.

1 iLd DC (k) = N

"

k X

# iLd (k) − iLd (k − N )

k−N

(4)

N is a element number of a circular buffer.

We can calculate in one period of fundamental harmonic this way. Power difference between actual and calculated direct component is compensated from storage energy of the condenser. So the speed of active power determination influences voltage magnitude of the voltage source and with faster determination of mean value, the condenser capacity may be smaller. The mean value determination inserted in control structure is shown in Fig. 3. 3.3. PI-controller Method

The method uses the PI-controller of dc link capacitor voltage (see Fig. 4). It presents very simple way of control active filter being sufficient for non-linear loads with slower current changes. Direct current component in d-axis is removed by PI-controller which lets only active current flow needed for keeping condenser voltage through filter converter. The current components are described by following equations: i0fd = iLd − iDC

i0fd = iLq

(5)

4. CURRENT CONTROL OF THE ACTIVE POWER FILTER

The current control can be performed by two-level hysteresis controllers or PI-controllers with vector pulse-width modulation (PWM) [3, 5]. The two-level hysteresis controller is classical controller which is very simple and fast, but requires fast sampling frequency in the case of digital signal processor (DSP) implementation (see Fig. 5). The filter currents in axes d, q can be controlled by PI-controllers (see Fig. 6). The outputs of the controllers are reference voltages u∗fdh and u∗fqh . However the current in d-axis is not only affected by voltage in this axis, but also by voltage in q-axis. That means, there is mutual coupling between d-axis and q-axis and must be cancelled in block of decoupling. The voltages u∗fdh and u∗fqh are afterwards transformed to α, β-components and enter to PWM modulator of the converter. There is used vector PWM technique. 5. EXPERIMENTAL RESULTS

The active power filter was practically performed according to Fig. 1. The IGBT switches of converter are for frequency up to 20 kHz, maximum current is 78 A and maximum collectoremitter voltage is 1200 V. The filter is controlled by control system based on the Texas Instruments

Figure 3: Mean value method.

Figure 4: PI-controller method.

PIERS Proceedings, Cambridge, USA, July 5–8, 2010

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TMS320F2812 Digital Signal Processor (see Fig. 7). Generation of TMS320C28xTM . digital signal controllers are the industry’s first 32-bit DSP-based controllers with on-board Flash memory and performance up to 150 MIPS [4]. Figures 8 and 9 show time courses of important quantities of the APF. Fig. 8 shows current waveforms in steady state. Fig. 9 shows current waveforms in case of load change from 0% to 100%. There we can see the right and quick filtration. The first trace in both figures is the input current of the non-linear load (three phase noncontrolled rectifier loaded by resistor R = 20 Ω and inductor L = 60 mH). The second trace is output current of the proposed APF which is injected to the power supply line by the APF. The third trace is line current compensated by proposed APF. The current scale is 10 A per division. The current control of the APF was performed by two-level hysteresis controllers.

Figure 5: Two-level hysteresis current controllers.

Figure 6: PI-controllers with vector PWM.

Figure 7: Laboratory workplace with active power filter.

Figure 8: Time courses of important quantities of the APF in steady state.

Figure 9: Time courses of important quantities of the APF at load change from 0% to 100%.

Progress In Electromagnetics Research Symposium Proceedings, Cambridge, USA, July 5–8, 2010

433

6. CONCLUSION

Power quality problems are important in most commercial, industrial and utility networks. In the paper there is described active power filter which uses the rotating axis system enabling simple separate active and reactive current components. Some control algorithms for removing of high harmonics and current control of active power filter are described here. The practical results, which show the dynamic state system performances, are presented. ACKNOWLEDGMENT

Research described in the paper was financially supported by the Czech Grant Agency (grant 102/09/P665). REFERENCES

1. Brandstetter, P., “Research of active power filters,” Research Report of Project GA CR 102/99/0193, VSB, Technical University of Ostrava, 2001. 2. Brandstetter, P., P. Chlebis, P. Palacky, and P. Simonik, “Unconventional soft switched parallel active power filter,” Proceedings of 10th International Scientific Conference Electric Power Engineering, 347–351, ISBN 978-80-248-1947-1, Kouty nad Desnou, Czech Republic, 2009. 3. Chlebis, P., P. Moravcik, and P. Simonik, “New method of direct torque control for threelevel voltage inverter,” Proceedings of 13th European Conference on Power Electronics and Applications, ISBN 978-1-4244-4432-8, Barcelona, Spain, 2009. 4. Osmancik, L., M. Polak, P. Simonik, L. Hrdina, P. Skotnica, and P. Palacky, “Digital signal processor TMS320F2812 and its application in electric drives,” Proceedings of International Conference on Applied Electronics, 129–132, ISBN 978-80-7043-442-0, Pilsen, Czech Republic, 2006. 5. Lettl, J., “Matrix converter induction motor drive,” Proceedings of 12th International Power Electronics and Motion Control Conference, 787–792, ISBN 1-4244-0121-6, Maribor, 2006.