Comparison Of Control Algorithms Computer Science Essay

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This paper presents the comparative study of control algorithms of shunt active power filter, a SAPF is used for harmonic elimination as well as reactive power compensation. The references current for SAPF is extracted by using three different methods. These methods are an Instantaneous reactive power theory, a Synchronous reference frame theory, and a new Adaline-based algorithm. Simulations are performed for various operating conditions under; balanced/unbalance, steady/ dynamic load condition, linear/nonlinear loads for both balanced as well as distorted source conditions. These schemes are simulated under MATLAB environment using SIMULINK and PSB toolboxes. The response of the SAPF system in simulation proves the effectiveness of the proposed control techniques.

Index Terms-Adaline, Shunt Active Power Filter (SAPF), instantaneous reactive power (IRP) theory, reactive non -linear loads, reactive power compensation, synchronous reference frame (SRF) theory.

Introduction

The quality of electrical power is one of the major growing concerns for utility as well as consumers. The explosive growth in consumer electronics and domestic appliances has generated a major concern in the electricity supply industry. The power electronics based applications draw non -sinusoidal currents, despite the applied voltage being sinusoidal. This has resulted in serious power quality problems, since most of these non-liner convertors contribute to harmonic injection into the power system, poor power factor, unbalance, reactive power burden, etc. all leading to low system efficiency. The harmonics generated by most of these power electronic devices have the following properties [1]; 1) Lower order harmonics tend to dominate in amplitude 2) If the waveform has half-wave symmetry there are no even harmonics 3) Harmonic emissions from a large number of non-linear loads of same type will be added. Harmonic not only increase the losses but also produce unwanted disturbance to the communication system. The remedies for power-quality (PQ) problems are available in two forms [2]: 1) Passive filters and active filters for existing systems (retrofit) and 2) Establishing new improved PQ converters. The use of the passive filter is a simple, reliable, and cost-effective alternative but its performance is dependent of the load and limitation such that their performance gets affected significantly due to the variation in the filter component values, filter component tolerance, source impedance, resonance, huge size and frequency of ac source. Active filters [1], [2] overcome these drawbacks but are still limited by their rating and cost Active filters of voltage source or current-source inverters basically provide the necessary compensation voltages/currents. A shunt active power filter (SAPF) generates a harmonic current spectrum that is opposite in phase to the harmonic and/or reactive current it perceives at the load end. Harmonic and reactive currents are thus cancelled at the source end and the result is undistorted sinusoidal balanced currents.

Fig. 1. Three-phase system with SAPF.

The hybrid filters combine passive and active filters, reducing the overall cost of the compensating circuit. Fig. 1 shows the general schematic of the voltage source shunt active power filter. The performance of SAPF depends on the control algorithm used for extraction of reference current components. Currently different approaches such as instantaneous reactive power (IRP) theory, flux-based control, synchronous reference frame (SRF) theory, closed loop PI, and scheme based on neural network techniques[4]-[6]. Among these control schemes, IRP and SRF theories are most widely used.

In this paper, a SAPF is controlled using IRP and SRF theories for compensation of reactive power and harmonic current, and these methods are compared with a new Adaline- based control algorithm. This Adaline-based control algorithm is simple and needs less computational efforts [8]-[10]. A fast adaptive linear element (Adaline)-based reference current estimator extracts real positive sequence current component without any phase shift. The estimation of reference currents through Adaline utilizes a least-mean squares (LMS) algorithm for the calculation of weights [8]. A MATLAB-based simulation study is presented for these three control techniques of SAPF under steady state, dynamic load condition and distorted supply voltage condition.

SYSTEM CONFIGURATION

Fig. 1 shows the basic circuit diagram of a SAPF system with lagging power-factor loads connected to a three phase three-wire system. Lagging power-factor load is realized by connecting non-linear resistive-Inductive load an unbalanced load is realized by disconnecting load from phase a using a circuit breaker or connecting additional load to phase a . An distorted condition is realized by adding 5th harmonic component to voltage supply. SAPF is realized using six insulated-gate bipolar transistors (IGBTs) with antiparallel diodes.

CONTROL ALGORITHEMS

The control algorithms for an SAPF compute the reference

Compensation currents, reactive power to be injected by the active filter (AF), and therefore, the source current remains at unity power factor (UPF). Since only real power is being supplied by source. The choice of the control algorithm therefore decides the accuracy, response time and switching of the SAPF.

IRP Theory

IRP theory has been initially proposed by Akagi in 1983[4] The theory is based on the transformation of three phase quantities to two phase quantities in α-β frame and calculation of instantaneous active and reactive power in this frame[4][5]. To deal with instantaneous voltages and currents in three phase circuits mathematically, it is adequate to express their quantities as the instantaneous space vectors. A basic block diagram of this theory is shown in Fig. 2.The three phase source voltage at point of common coupling (PCC) and load current are sensed and fed to the controller, in these block all the parameter are processed to generated reference current of fundamental frequency,which are fed to the a hysteresis-based pulse width modulated (PWM) signal generator to generate switching signals fed to SAPF.

Assuming a balanced source, the three-phase instantaneous

voltages can be specified as

(1)

Let this balanced three-phase source supply a nonlinear reactive load with some imbalance. The unbalanced, three-phase, reactive, harmonic-rich load currents can be expressed as

Where,

Phase angles of fundamental currents

in a, b, and c phases;

Phase angles of the nth harmonic

currents in a, b, and c phases;

Three-phase fundamental current

amplitudes

Three-phase nth harmonic current

Amplitudes

Fig.2. Block diagram of the reference current extraction using IRP theory.

To deal with instantaneous voltages and currents in three phase circuits mathematically, it is adequate to express their quantities as the instantaneous space vectors. In a-b-c are fixed on the same plain, and displaced by . On a-axis the instantaneous space vectors and are situated and their amplitude varies in positive and negative directions with time; same for other two phases. These phasors can be transformed

into α-β coordinates using Clark's transformation as follows:

(3)

(4)

Where,

The α and β , axes are the orthogonal coordinates.

are the voltages in the coordinates;

are the currents in the coordinates;

In three-phase conventional instantaneous, the power is calculated as follows:

(5)

Where, p is equal to the conventional equation:

(6)

Similarly, the IRP is defined as:

(7)

Where, q is equal to the conventional equation:

(8)

Therefore, in matrix form, these two powers are given as:

(9)

The α-β currents can be obtained as:

(10)

Where, Δ= (11)

Instantaneous active and reactive powers p and q can be decomposed into an average (dc) and an oscillatory component

(12)

Where 

= Mean value of the instantaneous real power. it is, indeed, the only desired power component to be supplied by the power source. 

= Alternating value of the instantaneous real power. Since does not involve any energy transference from the power source to load, it must be compensated. 

= Mean value of the instantaneous imaginary power 

= Alternating value of the instantaneous imaginary power.

Therefore, the reference source currents and in α-β coordinate are expressed as:

(13)

Through, reverse Clark's transformation these α-β coordinate currents are converted in to a-b-c coordinate as:

(14)

Where is the zero sequence component, which is zero in

three-phase three-wire system.

SRF Method

SRF theory is based on the transformation of currents in

synchronously rotating d-q frame[6][7].Fig. 3 shows the basic building blocks of this theory. The three phase source voltage at point of common coupling (PCC) and load current are sensed and fed to the controller. voltage signal are processed by a phase-locked loop (PLL)to generate unit voltage templates. Current signals are transformed from a-b-c to d-q frame, where these signals are filtered and transformed back to a-b-c frame which are fed to the a hysteresis-based pulse width modulated (PWM) signal generator to generate switching signals fed to SAPF.

Reference Frame transformation is the transformation of a three-phase a-b-c stationery coordinate system to the d-q-0 rotating coordinate system as shown in fig.3.

Fig.3. Reference Frame Transformation

Transformation is made in two steps: First, similar to the p-q theory, current components in α-β coordinates are generated (Clark's transformation), and using θ as a transformation angle, these currents are transformed from α-β to d-q frame defined as (Park's transformation)

(15)

The current can be decomposed into an average (dc) and an oscillatory component as:

(16)

Where 

= Mean value of the instantaneous real current . it is, indeed, the only desired current component to be supplied by the power source. 

= Alternating value of the instantaneous real current. Since does not involve any energy transference from the power source to load, it must be compensated. 

= Mean value of the instantaneous imaginary current.  

= Alternating value of the instantaneous imaginary current.

SRF isolator extracts the dc component by low pass filters (LPF's) for each and realized by moving averager at 100Hz. The extracted DC components and are transformed back α-β frame as shown below:

(17)

Fig.4. Block diagram of the reference current extraction using SRF theory.

From these currents, the transformation is made to obtain

three-phase reference source currents in a-b-c coordinates using (13). Reactive power compensation can also be provided by keeping component zero for calculating the reference source currents.

Adaline-Based Control Algorithm

The basic theory of the proposed decomposer has been based on least mean square (LMS) algorithm [9], [10] for training of Adaline, which tracks the unit vector templates to maintain minimum error. The theory can be understood by considering the analysis in single-phase system is as under. A block diagram of Adaline-based control scheme is shown in Fig. 5.The supply voltage may be expressed as

(18)

The load current (2) consists of active current (), reactive current (), and harmonic current () can be decomposed in parts as

(19)

The control algorithm is based on the extraction of current component in phase with the unit voltage template. To estimate fundamental frequency positive sequence real component of load current, the unit voltage template should be in phase with the system voltage and should have unit amplitude further it must be undistorted. For calculation of templates the voltage at PCC is sensed. The sense voltage is filtered through a band pass filter and the instantaneous rms value is computed. The sensed three phase voltages are divided by this instantaneous rms value to get three phase voltage templates. (, , and shown in Fig. 5).

Fig.5. Block diagram of the reference current extraction using Adaline-based theory.

The initial estimates of active and reactive part of current on single-phase basis can be chosen as:

(20)

where weight (Wp) is estimated using Adaline technique. The weight is variable and changes as per the load current and magnitude of phase voltage. This scheme for estimating weights corresponding to the fundamental frequency real component of current (for three-phase system), based on LMS-algorithm-tuned Adaline, tracks the unit voltage templates to maintain minimum error The estimation of weight is given as per the following iterations [10]:

(21)

The value of η (convergence coefficient) decides the rate of

convergence and the accuracy of estimation. The practical range of convergence coefficient lies in between 0.1 and 1.0. Higher values of η provide fast convergence toward the final value but at the expense of some accuracy. Three-phase currents corresponding to the positive-sequence real component of the load current may be computed by multiplying three phase unit templates with equivalent average weight, which is given as

(22)

For proper estimation of reference currents, the weights are averaged to compute the equivalent weight for positive sequence current component in the decomposed form. The averaging of weights helps in removing the unbalance in the

current components.

These three-phase reference source currents are fed to the

hysteresis-based PWM current controller to control the source

currents to follow the reference source currents in UPF mode of operation. These currents are considered as the reference source currents , and along with the sensed source currents , these currents are fed to a hysteresis-based PWM current controller to control the source currents to follow these reference currents. The hysteresis band current controller decides the switching pattern of active power filter [11]. The switching logic is formulated as follows:

If upper switch is OFF and lower switch is ON for leg "a" (SA=1).

If upper switch is ON and lower switch is OFF for leg "a" (SA = 0)

The switching functions SB and SC for phases B and C are determined similarly, using corresponding reference and measured currents and hysteresis bandwidth (HB). This current control results in the control of the slow varying source current (as compared to SAPF currents) and therefore requires less computational efforts.

PI Controller for Maintaining Constant DC Bus Voltage of SAPF

The operation of SAPF system requires ac mains to supply real power needed to the load and some losses (switching losses of devices, losses in reactor, and dielectric losses of dc bus capacitor) in the SAPF. Therefore, the reference source current, used to decide switching of SAPF, has two components: One is the real fundamental frequency component of the load current, and another component, which corresponds to the losses in SAPF, is estimated using a proportional-integral (PI) controller over the dc bus voltage of the SAPF. To compute the second component of active part

reference current, a reference dc bus voltage is compared with sensed dc bus voltage of SAPF. The comparison of sensed dc bus voltage to the reference dc bus voltage of VSC, results in a voltage error, these are fed to PI controller. The output of PI controller accounts for the losses in SAPF and it is considered as loss component of the current, which is added with the weight estimated by the Adaline corresponding to fundamental frequency positive sequence active reference current component. In case of p-q theory this component can be added with the average real power for controlling SAPF. If the control is facilitated by SRF theory, the output of PI regulator can be added with d-axis component of the current signal. For controlling DSTATCOM by Adaline, the output of PI controller is added with the equivalent source currents.

MATLAB-BASED MODEL OF SAPF SYSTEM

Fig. 6 shows the basic simulation model of SAPF system that correlates to the system configuration shown in Fig. 1 in terms of source, load, SAPF, and control blocks. The nonlinear load is modeled using a three-phase diode bridge converter connected to ac mains. At the dc bus of diode bridge converter. Simulation of the SAPF system is carried out using ode45(stiff/NDF) solver. This SAPF model is simulated with the above described p-q, SRF, and Adaline-based theories.

C:\Users\Sush\Pictures\1235.tif

Fig.6. MATLAB-based model of SAPF system.

Fig. 7. MATLAB-based model of current extraction using

(a) IRP, (b) SRF, and (c) Adaline-based theories.

Fig. 7(a)-(c) shows the simulation models for these theories that are inconsistent with the control schemes shown in Figs. 3-5. The model is assembled using the mathematical blocks of SIMULINK block set.

RESULTS AND DISCUSSION

The following observations are made based on the performances of SAPF. SAPF is studied for all three methods of control techniques.

Control of SAPF by IRP Theory

Fig. 8 shows the dynamic performance of a SAPF, Fig.9.shows the performance of SAPF under distorted voltage condition for same load condition using the IRP-theory-based current extractor. The considered load is resistive-reactive. The considered load is resistive-inductive load consisting of R=25 Ω & L=5 mH. For dynamic condition the linear load has been increased from at 0.6s to 0.65s, and unbalance is introduced at 0.7s to 0.75s.

C:\Users\Sush\Desktop\New folder\paper.tif

Fig. 8. Dynamic performance of a SAPF controlled using SRF theory.

This theory is easily implementable and excellent steady-state performance. Moreover, under distorted condition calculation of the reference source current is not accurate fundamental frequency of load current. Due to this it fails to compensation of harmonic current. Having delay in compensation due to the LPF used for filtering power signals.

Control of SAPF by SRF Theory

Fig. 8 shows the dynamic performance of a SAPF,Fig.9.shows the performance of SAPF under distorted voltage condition for same load condition using the SRF-theory-based current extractor SRF theory. Simulation is carried out for similar load changes, unbalanced conditions and distorted condition as of the previous case. The effect of delay due to LPF used for filtering signals in d-q frame can be seen in the extracted reference current waveform. The operation of PLL is slow, and it also imposes some amount of delay in computation

C:\Users\Sush\Desktop\New folder\distor.tif

Fig. 9. Performance of a SAPF under distorted supply voltage condition using IRP theory.

Fig. 10. Dynamic performance of a SAPF controlled using SRF theory.

Control of SAPF by ADALINE Theory

The performance of SAPF under dynamic and distorted supply voltage condition is shown in Fig. 12-13, using Adaline technique. An advantage of the Adaline-based extractor is that it requires less computational efforts, and therefore, the implementation of this technique is much simpler.

Fig. 11. Performance of a SAPF under distorted supply voltage condition using SRF theory.

Fig. 12. Dynamic performance of a SAPF controlled using ADALINE theory.

Fig. 13. . Performance of a SAPF under distorted supply voltage condition using SRF theory.

CONCLUSION

The mathematical derivation of the IRP, SRF, Adaline theory has been employed to demonstrate the behavior of SAPF. Simulated results have verified the effectiveness of these control algorithms. The Adaline-based technique utilizes LMS algorithm to calculate the weights, and these calculations are performed online therefore the algorithm is able to extract

reference current components in case of varying load condition which otherwise is not possible with other neural network based current extraction techniques.

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