Active Power Filter with Fast PI Controler

Active Power Filter with Fast PI Controler

International Journal of Engineering Research & Technology (IJERT)

ISSN: 2278-0181

Vol. 1 Issue 5, July – 2012

A.Bhaskar,Associate Prof.R.Sateesh kumar, QIS College of Engineering and Techology,Ongole.

JNTU Kakinada

Abstract

In a modern power system, due to broader applications of nonlinear loads such as power electronic equipment or arc furnaces, the degree of waveform distorted is increasingly serious now. These loads may cause poor power factors, lead to voltage notch, or result in a high degree of harmonics. The instantaneous response of the active power filter (APF) is very important while compensating rapidly varying balanced, unbalanced and nonlinear loads. Any change in the load affects the dc-link voltage directly. The proper operation of APF requires variation of the dc-link voltage within the prescribed limits. Conventionally, a proportional-integral (PI) controller is used to maintain the dc-link voltage to the reference value. It uses deviation of the capacitor voltage from its reference value as its input. However, the transient response of the conventional PI dc-link voltage controller is slow. In this paper, a fast-acting dc-link voltage controller based on the energy of a dc-link capacitor is proposed. Mathematical equations are given to compute the gains of the conventional controller based on fast-acting dc-link voltage controllers to achieve similar fast transient response. The detailed simulations are carried out on MATLAB environment to validate the proposed controller.

1. Introduction

   The proliferation of microelectronics processors in a wide range of equipments, from home VCRs and digital clocks to automated industrial assembly lines and hospital diagnostics systems, has increased the vulnerability of such equipment to power quality problems [1]. These problems include a variety of electrical disturbances, which may originate in several ways and have different effects on various kinds of sensitive loads.

   In a modern power system, increasing of loads and non-linear equipment's have been demanding the compensation of the disturbances caused for them. These nonlinear loads may cause poor power factor and high degree of harmonics.Active Power Filter (APF) can solve problems of harmonicand reactive power simultaneously. APFs consisting of voltage-source inverters and a DC capacitor have been researched

   and developed for improving the power factor and stability of transmission systems. APF have the ability to adjust the amplitude of the synthesized ac voltage of the inverters by means of pulse width modulation or by control of the dc-link voltage, thus drawing either leading or lagging reactive power from the supply. APFs are an up-to-date solution to power quality problems. Shunt APFs allow the compensation of current harmonics and unbalance, together with power factor correction, and can be a much better solution than conventional approach (capacitors and passive filters). The simplest method of eliminating line current harmonics and improving the system power factor is to use passive LC filters. However, bulk passive components, series and parallel resonance and a fixed compensation characteristic are the main drawbacks of passive LC filters.

   The shunt-connected custom power device, called the APF, injects current at the point of common coupling (PCC) so that harmonic filtering, power factor correction, and load balancing can be achieved. The APF consists of a current-controlled voltage-source inverter (VSI) which injects current at the PCC through the interface inductor. The operation of VSI is supported by a dc storage capacitor with proper dc voltage across it. One important aspect of the compensation is the extraction of reference currents. Various control algorithms are available in literature [7][9] to compute the reference compensator currents. However, instantaneous symmetrical component theory [9] is preferred. Based on this algorithm, the compensator reference currents are given as follows:

   where = tan / 3, and is the desired phase angle between the supply voltages and

   compensated source currents in the respective phases. The term Plavg is the dc or average value of the load power. The term Pdc accounts for the losses in the VSI without any dc loads in its dc link. To generate Pdc, a suitable closed-loop dc-link voltage controller should be used, which will regulate the dc voltage to the reference value. The transient performance of the compensator is decided by the computation time of average load power and losses in the compensator. In most APF applications, losses in the VSI are a fraction of the average load power. Therefore, the transient performance of the compensator mostly depends on the computation of Plavg. In this paper, Plavg is computed by using a moving average filter (MAF) to ensure fast dynamic response. The settling time of the MAF is a half-cycle period in case of odd harmonics and one cycle period in case of even harmonics presence in voltages and currents. Although the computation of Pdc is generally slow and updated once or twice in a cycle, being a small value compared Plavg to, it does not play a significant role in transient performance of the compensator. In some applications, such as the telecommunications industry uses several parallel-connected switch- mode rectifiers to support dc bus voltage. Such an arrangement draws nonlinear load currents from the utility. This causes poor power factor and, hence, more losses and less efficiency. Clearly, there are PQ issues, such as unbalance, poor power factor, and harmonics produced by telecom equipment in power distribution networks. Therefore, the functionalities of the conventional APF should be increased to mitigate the aforementioned PQ problems and to supply the dc loads from its dc link as well. The load sharing by the ac and dc bus depends upon the design and the rating of the VSI. Here, there are two important issues. The first one is the regulation of the dc-link voltage within prescribed limits under transient load conditions. The second one is the settling time of the dclink voltage controller. Conventionally, a PI controller is used to maintain the dc-link voltage. It uses the deviation of the capacitor voltage from its reference value as its input. However, the transient response of the conventional dc-link voltage controllers is slow, especially in applications where the load changes rapidly. Some work related to dc-link voltage controllers and their stability is reported in(2-5). In this paper, a fast-acting dc-link voltage controller based on the dc-link capacitor energy is

   proposed. The detailed modeling and simulation verifications are carried out by using MATLAB environment to prove the efficacy of this fast- acting dc-link voltage controller. There is no systematic procedure to design the gains of the conventional PI controller used to regulate the dc- link voltage of the APF. But some, mathematical equations are given to design the gains of the conventional controller based on the fast-acting dc- link voltage controllers to achieve similar fast transient response.

2. Design of APF

A.Principle of APF

A APF, which is schematically depicted in Figure-1, consists of a two-level Voltage Source Converter (VSC), a dc energy storage device, a coupling transformer connected in shunt to the distribution network through a coupling transformer. The VSC converts the dc voltage across the storage device into a set of three-phase ac output voltages. These voltages are in phase and coupled with the ac system thrugh the reactance of the coupling transformer. Suitable adjustment of the phase and magnitude of the APF output voltages allows effective control of active and reactive power exchanges between the APF and the ac system. Such configuration allows the device to absorb or generate controllable active and reactive power.

Figure 1 Schematic Diagram of a APF

The VSC connected in shunt with the ac system provides a multifunctional topology which can be used for up to three quite distinct purposes:

1. Voltage regulation and compensation of reactive power;

2. Correction of power factor

3. Elimination of current harmonics.

Here, such device is employed to provide continuous voltage regulation using an indirectly controlled converter. As shown in Figure-1 the shunt injected current Ish corrects the voltage sag by adjusting the voltage drop across the system impedance Zth. The value of Ish can be controlled by adjusting the output voltage of the converter. The shunt injected current Ish can be written as,

Ish = IL IS = IL ( Vth VL ) / Zth (1)

Ish /_ = IL /_-

(2)

The complex power injection of the APF can be expressed as,

Ssh = VL Ish*

(3)

It may be mentioned that the effectiveness of the APF in correcting voltage sag depends on the value of Zth or fault level of the load bus. When the shunt injected current Ish is kept in quadrature with VL, the desired voltage correction can be achieved without injecting any active power into the system. On the other hand, when the value of Ish is minimized, the same voltage correction can be achieved with minimum apparent power injection into the system.

B.Control for Harmonics Compensation

The Modified Synchronous Frame method is presented in [7]. It is called the instantaneous current component (id-iq) method. This is similar to the Synchrous Reference Frame theory (SRF) method. The transformation angle is now obtained with the voltages of the ac network. The major difference is that, due to voltage harmonics and imbalance, the speed of the reference frame is no longer constant. It varies instantaneously depending of the waveform of the 3-phase voltage system. In

this method the compensating currents are obtained from the instantaneous active and reactive current components of the nonlinear load. In the same way, the mains voltages V (a,b,c) and the available currents il (a,b,c) in – components must be calculated as given by (4), where C is Clarke Transformation Matrix. However, the load current components are derived from a SRF based on the Park transformation, where represents the instantaneous voltage vector angle (5).

(4)

(5)

Figure-2 Block diagram of SRF method

Figure-2 shows the block diagram SRF method. Under balanced and sinusoidal voltage conditions angle is a uniformly increasing function of time. This transformation angle is sensitive to voltage harmonics and unbalance; therefore d/dt may not be constant over a mains period. With transformation given below the direct voltage component .

1. DC-LINK VOLTAGE CONTROLLERS

   The sudden removal of load would result in an increase in the dc-link voltage above the reference value, whereas a sudden increase in load would reduce the dc-link voltage below its reference value. As mentioned before, the source supplies an unbalanced nonlinear ac load directly and a dc load through the dc link of the APF, as shown in figure-1. Due to transients on the load side, the dc bus voltage is significantly affected. To regulate this dc-link voltage, closed-loop controllers are used. The proportional-integral- derivative (PID) control provides a generic and efficient solution to many control problems. The control signal from PID controller to regulate dc link voltage is expressed as

   Uc = Kp (Vdc ref Vdc) +

   (7)

   In (7), Kp, Ki and Kd are proportional, integral, and derivative gains of the PID controller, respectively. The proportional term provides overall control action proportional to the error signal. An increase in proportional controller gain (Kp) reduces rise time and steady-state error but increases the overshoot and settling time. An increase in integral gain (Ki) reduces steady state error but increases overshoot and settling time. Increasing derivative gain (Kd) will lead to improved stability. However, practitioners have often found that the derivative term can behave against anticipatory action in case of transport delay. A cumbersome trial-and-error method to tune its parameters made many practitioners switch off or even exclude the derivative term [8], [9]. Therefore, the description of conventional and the proposed fast-acting dc-link voltage controllers using PI controllers are given in the following subsections.

   1. Conventional DC-Link Voltage Controller

      The conventional PI controller used for maintaining the dc-link voltage is shown in figure-

      6. To maintain the dc-link voltage at the reference value, the dc-link capacitor needs a certain amount of real power, which is proportional to the

      difference between the actual and reference voltages. The power required by the capacitor can be expressed as follows:

      Pdc = Kp (Vdc ref Vdc) +

      (8)

      Figure-6 Schematic diagram of the conventional dc-link voltage controller

      Figure-7 Schematic diagram of the fast-acting dc- link voltage controller

      The dc-link capacitor has slow dynamics compared to the compensator, since the capacitor

      voltage is sampled at every zero crossing of phase supply voltage. The sampling can also be performed at a quarter cycles depending upon the symmetry of the dc- link voltage waveform. The drawback of this conventional controller is that its transient response is slow, especially for fast-changing loads. Also, the design of PI controller parameters is quite difficult for a complex system and, hence, these parameters are chosen by trial and error. Moreover, the dynamic response during the transients is totally dependent on the

      values of Kp, and Ki, when Pdc is comparable to Plavg.

   2. Fast-Acting DC Link Voltage Controller

To overcome the disadvantages of the aforementioned controller, an energy-based dc-link voltage controller is proposed. The energy required by the dc-link capacitor (Wdc) to charge from actual voltage (Vdc) to the reference value (Vdc ref) can be computed as

Wdc = ½ Cdc

(9)

In general, the dc-link capacitor voltage has ripples with double frequency, that of the supply frequency. The dc power (Pdc) required by the dc- link capacitor is given as

(10)

where Tc is the ripple period of the dc-link capacitor voltage. However, due to the lack of integral term, there is a steady-state error while compensating the combined ac and dc loads. This is eliminated by including an integral term. The input to this controller is the error between the squares of reference and the actual capacitor voltages. This controller is shown in figure-7 and the total dc power required by the dc-link capacitor is computed as follows:

Pdc = Kpe

(11)

The coefficients Kpe and Kie are the proportional and integral gains of the proposed energy-based dc- link voltage controller. As an energy-based controller, it gives fast response compared to the conventional PI controller. Thus, it can be called a fast acting dc-link voltage controller. The ease in the calculation of the proportional and integral gains is an additional advantage. The value of the proportional controller gain (Kpe) can be given as

Kpe = Cdc / 2Tc

(12)

For example, if the value of dc-link capacitor is 2200 F and the capacitor voltage ripple period as

0.01 s, then Kpe is computed as 0.11 by using (12). The selection of Kie depends upon the tradeoff between the transient response and overshoot in the compensated source current. Once this proportional gain is selected, integral gain is tuned around and chosen to be 0.5. It is found that ifKie is greater than Kpe / 2, the response tends to be oscillatory and if Kie is less than Kpe / 2, then response tends to be sluggish. Hence, Kie is chosen to be Kpe / 2.

1. DESIGN OF CONVENTIONAL CONTROLLER BASED ON THE FAST- ACTING DC-LINK VOLTAGE CONTROLLER

   The conventional dc-link voltage controller can be designed based on equations given for the fast- acting dc-link voltage controller as in (11) and can be written as

   (13)

   It can also be written

   (14)

   Where

   (15)

   (16)

   It is observed from the aforementioned equations that the gains of proportional and integral controllers vary with respect to time. However, for small ripples in the dc-link voltage, Vdc Vdc ref, therefore, we can approximate the above gains to the following

   (17)

   (18)

   The relations (17)(18) give approximate gains for a conventional PI controller. This is due to the fact that Vdc ref + Vdc is not really equal to 2Vdc ref until variation in Vdc is small during transients. Hence, the designed conventional PI controller works only on approximation. The open-loop gains for the two cases are given by

   (19)

   Where Eer = and

   (20)

   where Er = Vdc ref – Vdc. Since is the same as Kie / Kpe,the higher gain in the conventional PI controller renders less stability than that of the proposed energy-based dc-link controller. For nearly the same performance, the conventional PI controller has gains which are 364 (40/0.11 from Table-III) times larger than that of that proposed one. Also, the amplifier units used to realize these gains need more design considerations and are likely to saturate when used with higher gains.

   TABLE -III: SIMULATION PARAMETERS

2. Matlab/Simulink Modeling and simulation results

   capacitance 1550e-6 F, Inverter series inductance

   10 mH, Source resistance of 0.1 ohm and inductance of 0.9 mH. Load resistance and inductance are chosen as 30mH and 60 ohms respectively.

   Figure-8 Matlab/Simulink power circuit model of APF

   Figure-9 shows the three phase source voltages, three phase source currents and load currents respectively without APF. It is clear that without APF load current and source currents are same.

   Figure-8 shows the Matab/Simulink power circuit model of APF. It consists of five blocks named as source block, non linear load block, control block, APF block and measurements block. The system parameters for simulation study are source voltage of 11kv, 50 hz AC supply, DC bus

   Figure-9 Source voltage, current and load current without APF

   Figure-10 shows the three phase source voltages, three phase source currents and load currents respectively with APF. It is clear that with APF even though load current is non sinusoidal source currents are sinusoidal.

   Figure-12 DC Bus Voltage with fast PI controller

   Figure-10 Source voltage, current and load current with APF

   Figure-11 shows the DC bus voltage. The DC bus voltage is regulated to 11kv by using PI regulator.

   Figure-12 shows the DC bus voltage with fast PI controller. Form the figure it is clear that with fast PI controller DC link voltage controlled with less time.

   Figure-13 shows the phase-A source voltage and current, even though the load is non linear RL load the source power factor is unity.

   Figure-13 Phase-A source voltage and

   current

   Figure-14 shows the harmonic spectrum of Phase A Source current without APF. The THD of source current without APF is 36.89%.

   Figure-11 DC Bus Voltage with PI controller

   Figure-14 Harmonic spectrum of Phase-A Source current without APF

   Figure-15 shows the harmonic spectrum of Phase A Source current with APF. The THD of source current with APF is 5.05%

   Figure-15 Harmonic spectrum of Phase-A Source current with APF

3. Conclusion

A VSI topology for APF compensating ac unbalanced and nonlinear loads and a dc load supplied by the dc link of the compensator is presented. The state-space modeling of the APF is discussed for carrying out the simulation studies. An energy-based fast-acting dc-link voltage controller is suggested to ensure the fast transient response of the compensator. Mathematical equations are developed to compute the gains of this controller.Finally Matlab/Simulink based model is developed and simulation results are presented.

References

1. K.A Corzine, and Y.L Familiant, A New Cascaded Multi-level H-Bridge Drive, IEEE Trans. Power.Electron., vol.17, no.1, pp.125-131. Jan 2002.

2. J.S.Lai, and F.Z.Peng Multilevel converters A new bread of converters, IEEE Trans. Ind.Appli., vol.32, no.3, pp.509-517. May/ Jun. 1996.

3. T.A.Maynard, M.Fadel and N.Aouda, Modelling of multilevel converter, IEEE Trans. Ind.Electron., vol.44, pp.356-364. Jun.1997.

4. P.Bhagwat, and V.R.Stefanovic, Generalized structure of a multilevel PWM Inverter, IEEE Trans. Ind. Appln, Vol.1A-19, no.6, pp.1057-1069,

   Nov./Dec..1983.

5. J.Rodriguez, Jih-sheng Lai, and F Zheng peng, Multilevel Inverters; A Survey of Topologies, Controls, and Applications, IEEE Trans. Ind. Electron., vol.49 , no4., pp.724-738. Aug.2002.

6. Roozbeh Naderi, and Abdolreza rahmati, Phase- shifted carrier PWM technique for general cascaded inverters, IEEE Trans. Power.Electron., vol.23, no.3, pp.1257-1269. May.2008.

7. Bhim Singh, Kamal AlHaddad & Ambrish Chandra, 1999, A Review of Active Filter for Power Quality Improvements, IEEE Trans on Industrial Electronics, 46(5), pp.960970

8. Mauricio Angulo, Pablo Lezana, Samir Kouro, Jos´e Rodr´guez and Bin Wu,Level-shifted PWM for Cascaded

   Multilevel Inverters with Even Power Distribution IEEE Power Electronics specialist conference, 17-21 june 2007, pp.2373-2378.

9. B. P. McGrath and D. G. Holmes, Multicarrier PWM strategies for

multilevel inverters, IEEE Trans. Ind. Electron., vol. 49, no. 4, pp. 858

867, August 2002.