Power Quality Enhancement for Nonlinear Unbalanced Loads through Improved Active Power Filter Control Tarek A. Youssef, Ahmed T. Elsayed, Alberto Berzoy and Osama A. Mohammed Energy Systems Research Laboratory Florida International University Miami, Florida, USA
[email protected]. Abstract—This paper presents a modified synchronous reference frame for Active Power Filter control (APF) to compensate for harmonics and reactive power for both balanced and unbalanced non-linear loads. The proposed controller autonomously detects different power quality problems, filters out load created harmonics and compensates for unbalances and/or DC offsets resulting from non-linear loads connected at the point of common coupling (PCC). The main objective of the controller is to force the AC grid currents at the PCC to be balanced three-phase currents with minor harmonics regardless of the characteristics of the local AC load. In addition, the developed controller uses only current measurements which reduces the cost and complexity of system implementation. The performance of the developed controller was examined under several extreme cases, including: non-linear loads, distorted load currents, unbalanced loads, loss of one supply phase and existence of DC current component conditions. The results show that the developed controller succeeds to improve power quality at the PCC under various loading conditions.
usually used in the three phase four wire unbalanced systems. The disadvantage of this method that it requires measuring the voltage and current for the three phases and requires more computations which is reflected on the costs of implementation. The proposed controller reduces the computational burden as it uses modified SRF to support three phase unbalanced system with only current measurements and utilizes a second order low pass filter which makes it suitable for implementation on low end digital processors. This paper is organized as follows; in section II, some of the most common active filtering techniques adopted in the literature are discussed. In section III: a description of the system under study and the proposed control technique is presented. In section IV: several case studies are presented and investigated to validate the developed controller. Finally, in section V, conclusion that can be deducted from this work is listed.
Index Terms—Active filter, power quality, non-linear loads.
II. INVERTER CONTROL AND ACTIVE FILTERING TECHNIQUES
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I. INTRODUCTION
OWER electronics converters are widely used in industrial applications. These converters cause current distortion, harmonic pollution and low power factor. Consequently, to improve power quality, it is necessary to eliminate harmonic components and compensate for reactive current by injecting negative harmonics and reactive current into the power network. Many approaches were developed and utilized to improve power factor and reduce harmonics [1]-[6]. APF can be connected in shunt or series, shunt APF provides the capability to compensate for harmonics and reactive power problems simultaneously [7]. Moreover, the active power filter can also compensate for unbalanced loads and regulate voltage at the point of coupling. The APF controller analyzes the load current in real-time to extract reference current that represents the harmonics and reactive current components and inject opposite current to cancel unwanted components from the source current. The performance of the active filter is mainly dependent on the accuracy of the used method to extract undesired current. The Synchronous Reference Frame (SRF) method is used in three phase balanced systems, but it fails with unbalanced system. While instantaneous power theory
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In order to clarify the contribution of this work, a brief overview of the various techniques adopted for inverter control and active power filtering will be presented. A. Inverter Control Techniques The first stage in the APF control is to generate reference current represent harmonics and reactive current contents. Calculating the reference current is either based on frequency or time domain. The frequency domain compensation is based on Fourier analysis of the distorted signal to extract the harmonics, which leads to high computation burden and slow response. The time domain compensations are based on the instantaneous derivation of the compensating signals from the distorted ones. Most of the time domain compensation techniques are based on synchronous reference frame and instantaneous power theory. Synchronous Reference Frame The synchronous reference frame compensation method uses the Park’s transform to represent the distorted signal in dq plane as depicted in (1). With this transformation, the fundamental component will be represented by a DC value in the d-q plane. The harmonic component will be represented by
an AC component with a frequency of 100 Hz and/or other multiples of 50 Hz. The active power in this case corresponds to the component of the current in the d-axis (in one of the notations) while the reactive power corresponds to the other component. Hence, bi-directional control of the flow of P and Q can be done separately. Moreover, the harmonic compensation current can be extracted from the d-axis current using a high pass filter. In case of three-phase unbalanced system, when applying park’s transform, an AC component appears in the d-q plane with a frequency of 100 Hz in 50 Hz networks due to unbalancing. This AC component is equal to the AC component produced by the third harmonics [8] which leads to injection of 3rd harmonic to the grid. ͳ
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B. Active Power Filter configuration Active power filters may take one of several possible configurations to meet different loads compensation requirements. These active power filter configurations can be classified based on: Converter type The proposed APF uses voltage source inverter works in current control mode to inject the harmonic and reactive current required by the nonlinear load. The voltage source inverter used in APF has a self-supporting DC bus with a large capacitor. For proper operation of the voltage source inverter, it is necessary to maintain its DC bus voltage greater than the peak of the line voltage. Therefore, the DC bus voltage is dependent only on the rated voltage of APF. APF with voltage source inverter configuration became more dominant because it is lighter in weight and cheaper, in addition to the fact that the DC link characteristics are independent on the load characteristic compared to current source inverter in which the DC link characteristics are dependent on the load current. To enhance the performance, a multilevel inverter can be used to operate at lower switching frequency and better efficiency.
Fig. 1. Block diagram of instantenous power theory APF control.
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applied to three-phase four-wire balanced and unbalanced systems. It can also be applied to system with voltage harmonics [11]. However, there are some disadvantages of the instantaneous power theory technique; they involve complex hardware implementation due to the requirement of measuring voltages and line currents, and extra calculations to transform voltage and current to Įȕ0 coordinates. Figure 1 shows the block diagram for instantaneous power theory.
iFb
iLb iLc
Fig. 2. A layout of the system under study.
Instantaneous Power Theory Another control method uses the instantaneous power theory proposed by Akagi [9],[10]. It is based on Clark’s transformation of the three phase voltages and currents from the abc coordinates to the Įȕ0 Coordinates. The AC and DC components of the power can be obtained from the instantaneous power equations using high-pass and low-pass filters respectively. The instantaneous power theory can be
Supply System An active power filter can be classified according to the supply system and load type to: single-phase APF, three-phase three-wire APF and three-phase four-wire APF. A singlephase or three-phase active power filter can be series, shunt or unified power quality conditioner, operating with either a current source or a voltage source converter. For three-phase four-wire system with unbalanced load, APFs can be designed as three independent single-phase filters with isolation transformers for independent phase control, or as a four-wire filter to compensate neutral current and balance the load [11]. There are two configurations for three-phase four-wire active filters; the first configuration is known as capacitor mid-point type. In this configuration the entire neutral current flows through DC bus capacitors. The second configuration is known as the four-arm converter type. The fourth converterarm is used to compensate the neutral current. III. CONTROLLER DESCRIPTION A. Description of Proposed Current Controller The system under study is shown in Fig. 2, consisting of a six step hysteresis current-controlled voltage source inverter
(VSI) and 220V, 50 Hz AC source. Loads are connected directly to the point of common coupling. L and C are 15 mH and 2.2 mF respectively. The reference current generator is the most important block in the shunt active power filter. The shunt active power filter performance relies on the accuracy of the reference current generator. Moreover, the hardware implementation complexity depends on the complexity of the reference current generator. In this simulation, the reference current signal is obtained from the measured load current through the use of a modified synchronous -reference framebased method. The synchronous reference frame method requires measuring the three-phase load currents only rather than the three-phase currents and voltages in the instantaneous power theory-based method. The disadvantage of the synchronous reference frame based method is that it is only suitable for a three-phase balanced system. Accordingly, some manipulations will be presented herein to make it suitable for three-phase, four wires, balanced and unbalanced systems.
fundamental component existing in the load current, hence it is being subtracted from the load current to obtain the distorted component instead of calculating it directly. To calculate the Park’s transform, sin(ș) and cos(ș) should be known. A phase locked loop (PLL) is used to obtain the supply voltage phase angle in order to calculate sin(ș) and cos(ș) [12]. In some cases a frequency drift of the fundamental component can happen, the adopted PLL has the capability to accurately track the frequency and compensate for this drift. The developed controller detects the power quality problems resulting from the load and automatically generates the needed compensating currents. Hence, it prevents power quality issues from propagating to the network of the grid as the harmonics or distorted current are not seen beyond the PCC. The general idea of typical APF is to measure the source current and subtract it from the load current in order to get the content of current harmonics that needs to be compensated. The single line schematic shows this practical issue in Fig. 4.
iS
PARK TRANSFORMATION
DC VOLTAGE REGULATOR
REFERENCE CURRENT
iL
+ +
id +
Fig. 4. A block digram showing the effect of APF in load current compensation.
SIN & COS
LPF
iF
Iq,i0=0
INVERSE PARK TRANSFORMATION
Fig. 3. A block diagram of the reference current generator.
Fig. 3 shows the block-diagram of the modified synchronous reference current generator. It is shown that id is being calculated from the three phase currents using Park’s transformation. The calculated id contains a DC component that represents the fundamental active component current, while the AC component represents the harmonic components. The AC component frequency will be 100 Hz in an AC 50 Hz network. To obtain the DC component, id passes through a low pass filter with a cut-off frequency of 75 Hz. The output of the low pass filter will be used to obtain the sinusoidal fundamental component existing in the load current by using inverse Park’s transform, iq and i0 will be set to zero since we need to obtain the active fundamental component only. Consequently, the calculated sinusoidal component is subtracted from the load current. The obtained component is a reference current that represents all harmonics and reactive components existing in the load current. By this method, we can manage to overcome the problem of AC component that exists in the id current due to the unbalanced load, since calculations in this scheme depend on calculating the
From Fig. 4, it can be deduced: (1) ଓҧ ൌ ଓҧௌ ଓҧி Where ଓҧ is the current vector in the load that is a function of current in phase A, B and C ଓҧ ሺ݅ ǡ ݅ ǡ ݅ ሻ ൌ ଓҧ̴ , ଓҧௌ ൌ ଓҧ ሺ݅ௌ ǡ ݅ௌ ǡ ݅ௌ ሻ ൌ ଓҧௌ̴ is the current vector in the source and ଓҧி ൌ ଓҧ ሺ݅ி ǡ ݅ி ǡ ݅ி ሻ ൌ ଓҧி̴ is the current vector in the power active filter. Then, the reference for the control in APF will be: (2) ଓҧி ൌ ଓҧ െ ଓҧௌ The last equation gives the current reference for the APF ଓҧி ൌ ଓҧி̴̴ . That means it is necessary to measure 6 currents, 3 currents for the source and 3 currents for the load. This paper proposes to just measure the current in the load ଓҧ , to make the power active filtering and also power factor correction. The load current contains the information of the fundamental current (50Hz) that can be extracted by filtering high order harmonics. After filtering the fundamental current waveform will be ଓҧௌ called current source replacement vector. The methodology to find the reference will be to create the ଓҧௌ and subtract with the current load ଓҧ . (3) ଓҧி̴ ൌ ଓҧௌ െ ଓҧ B. APF Current Reference Computation For the construction of the reference, the load current has to be transformed through Park transformation as shown in Fig. 3.
Detailed procedure of the transformation and current reference computation is shown in Fig. 5: (4) ଓҧ ሺ̴݅ௗ ǡ ̴݅ ሻ ൌ ଓҧ̴ௗ Thes two components (̴݅ௗ ǡ ̴݅ ) are related to magnitude and phase respectively. From these two components it is taken just ̴݅ௗ in order to have the magnitude of the current source replacement vector ଓҧௌ . The magnitude in direct component has to be filtered in order to get the fundamental component that is 50Hz sinusoidal. For this purpose, a Bessel Filter order 2 and cut off frequency of 200rad/sec is used. Then: (5) ݅ௌ̴ௗ ൌ ̴݅ௗ̴௧ௗ The phase-angle of the vector current source replacement will be set to zero in the quadrature component. (6) ݅ௌ̴ ൌ Ͳ ଓҧௌ ൌ ଓҧௌ ሺ݅ௌ̴ௗ ǡ ݅ௌ̴ ሻ ൌ ଓҧௌ ሺ̴݅ௗ̴௧ௗ ǡ Ͳሻ
(7)
Now, the reference can be calculated using (3). The next stage is the current controller, which generates the drive signals to control the voltage source inverter, in order to generate current shape that matches the reference current. vS
Freq
the efficiency [13],[14]. To overcome the variable switching frequency problem, a modified version of the hysteresis controller was developed and adopted. In the regular hysteresis controller, the error function is centred in a fixed pre-set hysteresis band. When the error exceeds the upper or lower hysteresis limits, the hysteresis controller makes an appropriate switching decision to control the error within the pre-defined band. To limit the maximum switching frequency, another limiting stage will be added to the controller. This limiting stag consists of an edge triggered flip-flop and a controlled oscillator. Fig. 6 shows a block diagram of the developed hysteresis controller. When the switching frequency exceeds the maximum limit, the flip-flops and oscillator override the controller command and limit the output frequency; this will lead to increasing hysteresis band in accordance with limited switching frequency. As shown in Fig. 6, i* is the reference current calculated by the reference current generator and iinv is the actual current injected by the voltage source inverter. The fmax signal fed from an oscillator with a frequency that equals the desired maximum switching frequency. IV. CASE STUDY AND DISCUSSION
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iL _ abc
iSr_ abc
i L _ abc
abc
iL_d dq
2ndorderLPF (BesselFunction )
+
iF_ref
To investigate the efficiency and reliability of the proposed control technique, an APF model was built in Matlab/Simulink environment. Different case studies involving various types of AC loads including severe loading conditions were investigated. The case studies are as follows:
i Sr_d
iSr_q=0
dq abc
Fig. 5 procedure of current reference computation.
iinv, a *
iinv, a iinv, b *
iinv, b iinv, c
iinv, c *
Fig. 6. A block diagram of the developed hysteresis controller
Hysteresis control is the most common current control technique because of its simplicity and its fast response. Hysteresis control provides good harmonic suppression. However, as a disadvantage of such a technique, its switching frequency is not fixed. The power losses in semiconductors increase with increasing the switching frequency, therefore, it is very important to limit the switching frequency in highpower applications to minimize the power losses and increase
A. Unbalanced Load with Harmonics The first loading condition is the unbalanced load; a threephase full wave uncontrolled rectifier feeding an RL load was connected to the system. It is known that due to the uncontrolled operation of the diodes, the uncontrolled rectifier injects harmonics to the system which negatively affect the operation of other loads. Another three-phase RL load was simultaneously connected to phases A & B while phase C remained disconnected. The unbalanced RL load was rated 1.5 kW and 1 kVar. Load current and source current are shown in Fig. 7. It can be seen from Fig. 7 (a) that the currents of two phases (A&B) are the same, while the current of the third phase is the current withdrawn by the rectifier only. Moreover, the current waveforms suffer from noticeable distortion. Fig. 7 (b) shows the source current; it is shown that the three phases are balanced and the current waveforms are uniform. This means that the inverter controller succeeds to isolate the load problems (unbalancing and distortion) from the source side. As a part of the experiment, the system was subjected to sudden load increase at t=0.2 Sec. It is shown in Fig. 7 (b) shows that the proposed control is capable of following the sudden change in load. Another merit of the proposed technique is reduction of the total harmonic distortion as shown in Table 1. The THD values are given for the three phases after and before increasing the load. It can be seen that the THD for phase C is
TABLE 1 HARMONIC ANALYSIS FOR SOURCE CURRENT
reduced from 28.16% to 5.35% after compensation, which is accepted according to IEEE Std 519.
Load
B. Single Phase Load This case represents an extreme case for residential applications; all the connected loads are single phase and the other two phases are not loaded. A half wave rectifier is connected to the same phase (phase A) which produces DC components in the phase current. The load and source currents are shown in Fig. 8. The APF succeeds to re-balance the load current seen from the source side. Another critical problem is compensated here, which is the DC current component.
0.4 Sec
0.8 Sec
Phase A
7.88%
5.24%
5.33%
2.94%
Phase B
7.88%
5.24%
5.33%
2.95%
Phase C
28.16%
9.47%
5.35%
2.99%
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Fig. 8. Single phase load (a) Load current (b) Source current. 40
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D. Phase loss A Phase loss event is created in the simulation by disconnecting one of the supply phases (phase C). In this case the operation of the controller is reversed from the previous cases as the controller is responsible for compensating the load current not the source current. This is done automatically by the controller. Fig. 10 (a) shows the three phase current of the source, it can be seen at 0.3 second the current of phase C falls to zero and the other two phases are unbalanced.
0.8 Sec
V (V)
C. Induction Motor A 5.4 HP direct online three phase induction motor is connected to the system. This case is one of the common cases in the industrial applications. A small induction motor was used intentionally, because of considering the fact that small induction motors are characterized with lower power factor. The P.F of the motor is estimated to be 0.4 without compensation. Simulation results are shown in Fig. 9; Fig. 9 (a) shows the voltage and current waveforms for one of the load phases (phase A), it is seen that the current and voltage are shifted from each other due to the low load power factor. Fig.9 (b) shows that source voltage and current waveforms are in phase, which reflects the achieved improvement of P.F to unity. This is done by setting the quadrature component of the reference current to zero.
Source
0.4 Sec
-100 -200 0.3
20
Current (A)
0.36
0.38
0.4 Time (Sec) (b)
0.42
0.44
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Fig. 9. Induction load (a) Load phase current and voltage (b) Source phase current and voltage.
0
30 20
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Fig. 7. Unbalanced loading condition (a) Load current (b) Source current.
-30 0.15
Fig. 10. Phase loss event (a) Load current (b) Source current.
[7]
Fig. 10 (b) shows the load current, it is shown that after 0.3 sec the controller succeeds to reproduce the third phase current and compensates for the lost phase. It is noticed that the voltage magnitude of the reproduced phase is less than the other two phases, this can be fixed by increasing the capacity of the DC link capacitor. The capacity of the DC link can be increased either by increasing the capacitance or the DC voltage which can be a good application for ultra-capacitors to be utilized. V. CONCLUSION In this paper, a synchronous reference frame based controller is modified to be adequate to operate with unbalanced loads. This controller was used to control APF to compensate for different power quality issues for both balanced and unbalanced non-linear loads. Also, a modified version of the hysteresis controller was presented to overcome the problem of variable switching frequency and to appropriately control the switching frequency. A model for the APF and its controller is built in Matlab/SIMULINK. Different loading conditions were simulated to verify the effectiveness of the system. The simulated loading conditions were selected to represent extreme and worst cases such as low power factor, highly distorted load current, single phase loading and complete failure of one of the supply phases. Simulation results show that the controller deals automatically and successfully with various severe power quality issues. It isolates these problems and prevents it from being seen by the supply. This controller is simple and requires less computation and can be used for improved operation and utilization for the available energy sources.
[8]
[9] [10]
[11] [12]
[13] [14]
ACKNOWLEDGEMENT
This work was partially supported by grants from the Office of Naval Research (ONR) and the U.S. Department of Energy (DOE). REFERENCES [1] [2] [3] [4]
[5]
[6]
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