134

Shunt Active Power Filter with Fuzzy Logic Interface for Harmonic Reduction

Piotr Majtczak, Szymon Piasecki Warsaw University of Technology (Poland)

majtczap@ee.pw.edu.pl, szymon.piasecki@ee.pw.edu.pl

Abstract— This paper presents analysis of the harmonics

reduction algorithm applied in the three-phase shunt active power filter (SAPF). For the control of proposed SAPF the fuzzy logic decision support (FLDS) is introduced. In the paper operation of the SAPF is described and analyzed, finally experimental results showing operation of the laboratory model are presented and discussed.

I. INTRODUCTION

Nowadays, according to increasing number of power electronic devices and different kinds of loads connected to the common grid the Power Quality (PQ) issue becomes very important problem. High order harmonics generated by non-linear loads connected to the grid causes serious disturbances of the PQ and has negative impact on energy consumers. Expected PQ criteria are described in power quality standards and system operator’s grid codes. Traditionally to fulfill PQ requirements established by grid codes including reduction of high order harmonics passive filters are used. These filters have several disadvantages [1]:

• each harmonic requires its own filter, • risk of the resonance phenomena, • reactive power consumption, • aging of the elements, • size, weight and cost of passive components

Another solution for reduction of high order harmonics, which doesn’t have limitations given by passive filters, is the shunt active power filter. With proper control algorithm the SAPF can be used to compensate reactive power and reduce current high order harmonics, moreover the device is able to operate under unbalanced grid voltages [2]. Increasing role of distributed generation causes increasing requirements and functionalities expected from the SAPF established by different grid codes and power quality standards, and to fulfill them more complex and advanced control strategies are needed [3], [4], [5], [6], [7]. One of the available solutions is the fuzzy logic (FL), which can be applied for control of the SAPF and allows fast response for rapidly changing grid codes and power quality standards. Fuzzy logic already proved being useful as current and voltage controller [8], [9]. However, in this paper the function of FL is focused on flexible and reliable user - SAPF interface which is able to transfer user requirements to grid codes needs in fast and easy way.

A. Shunt Active Power Filter

The principle operation of the SAPF is generation of the appropriate current required to compensate distortion caused by the non-linear load. Fundamental equation describing it is given by (1).

Igrid=ISAPF+Iload (1)

Where: ISAPF – current supplied by SAPF, Igrid – current in

PCC. Block diagram of the analyzed system with SAPF and nonlinear load is presented in Fig. 1. Apparent power flow in analyzed system with SAPF under sinusoidal voltage condition is shown in Fig. 2. Apparent power positive sequence Se

+ generated by the source is delivered to the non-linear load. Se

+ is composed of the fundamental component of voltage and current. Additionally small amount of power SDC-

link is transferred to the DC-link of the SAPF to maintain its voltage around the reference voltage. SCOMP power is delivered by the SAPF to the load in a way to compensate whole non-active power.

Non-linear Load

I line I load

ISAPF

C

Fig. 1. Analyzed system with SAPF and non-linear load.

Source

SAPF

Non-linear Load

Scomp

SloadSe

+

SDC-link

Fig. 2. Apparent power flow of Shunt Active Power Filter.

B. Harmonics Limitations

Power quality standards and grid codes establish rules and regulations for acceptable harmonic distortion in power systems. In Table I part of selected regulation [10] is presented. Chosen harmful effects caused by low power quality are shown in Table II.

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TABLE I POLISH OPERATOR’S GRID CODE IRIESD [10]

Current harmonics for three-phase loads ≤16 A

Odd harmonics

Max. value [A]

Even harmonics

Max. value [A]

3 2.3 2 1.08 5 1.14 4 0.43 7 0.77 6 0.3 9 0.4 15 ≤ n ≤ 39 0.23(8/n) 11 0.33 13 0.21 15 ≤ n ≤ 39 0.15 (15/n)

TABLE II

HARMFUL EFFECTS OF HARMONICS AND PRACTICAL LIMITS* [11]

Equipment Effects Limits Power

capacitors Overheating, premature ageing (breakdown), resonance.

I < 1.3 In, (THD < 83 %) or U < 1.1 Un for 8 hours/days at low voltage

Transformers Losses (ohmic-iron) and excessive overheating. Mechanical vibrations. Noise pollution.

Circuit breakers

Unwanted tripping Uharm / U1; 6 to 12 %

Power electronics

Problems related to waveform (commutation, synchronization).

*Extracted from Schneider Electric "Cahier Technique" no.199

C. Fuzzy Logic

Lotfi Zadeh presented the original paper formally defining fuzzy logic theory in 1965 [12]. Fuzzy logic is a precise logic of imprecision and approximate reasoning - a feature which is widely unrecognized. Fuzzy model consist of if-then rules (2) that describe the interaction between linguistic variables instead of numerical ones.

if (x is Ai) and (y is Bi), then (z is Ci) (2)

where x, y, z are process state variables (crisp-values) associated with Ai, Bi and Ci - fuzzy sets (linguistic values) [13].

The if-part of the rule is called rule-antecedent and describes inputs. Then-part of the rule is called rule-consequent and defines output. A fuzzy set is represented by the membership functions mi, that associate a real number µi ∈ (0,1), called degree of membership, within the set. A block diagram of a fuzzy model is shown in Fig. 3. Input signals require three fundamental steps to generate output [14]:

1) fuzzification of actual input values; 2) fuzzy inference; 3) defuzzification of fuzzy output.

Fuzzification is the process of calculation a crisp value (e.g. x) to represent an input's degree of membership to one or more fuzzy sets (e.g. A1) which make it compatible with the

fuzzy expression in the rule-antecedent. Membership functions are shown in Fig. 4.

Fuzz

ifica

tion

Inference

x

y

µAi(x)

µBi(y) Def

uzzi

ficat

ion

mout(z)

Fig. 3. General scheme of fuzzy logic system [15].

Fuzzy inference computes a rule strength τi ∈ (0, 1) by combining the fuzzified inputs using the fuzzy combination process. Then associates the output membership function to the rule strength. The rule strength can be calculated with a T-norm operation (e.g., minimum, product, etc.) among the membership degrees of the antecedents corresponding to the input values x and y (τi = T[µAi(x), µBi(y)]).

1

0

m1 m2 m3 m4

intput

De

gre

e of

m

em

bers

hip

Fig. 4. Membership functions.

The output fuzzy set Ci has membership function mCi(z) = min(mci(z)τi). The obtained membership functions are combined into one fuzzy output distribution. This is usually done by mout(z) = max (mCi(z)) (fuzzy “or” operation). The output of the inference procedure mout(z) often is desired to be a crisp value. This operation is called defuzzification. It may be done by several methods, like Mean-of-Maximum (MOM), Center-of-Sums (COS), and Center-of-Mass(COM) or others [15],[16],[17]. The choice of defuzzification procedure derives from a compromise between accuracy and computational effort. The output crisp value is calculated as the center of the area below the combined membership function mout(z). The defuzzification with usage of COM method is presented in Fig. 5.

µ

De

gre

e of

Me

mb

ers

hip

10.80.60.40.20

output1 2 3 4 5 6 7

crisp value Fig. 5. Defuzzification using COM method [15].

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II. IMPLEMENTATION

A. Control Algorithm

In presented work the output power and DC-link voltage of the SAPF are controlled by Direct Power Control Space Vector Modulated (DPC-SVM) algorithm [18]. Block diagram of the applied control strategy divided for powers and DC-link voltage control and harmonics compensation block is presented in Fig. 6. The harmonic compensator block is realized with use of band-pass filters [19]. In analyzed case the DC-voltage reference value (UDC_REF) it set to 600 (V). The reactive power QREF injected by the SAPF during the operation is set adjustable to achieve zero phase shift between grid voltage and current. UDC_REF is compared with measured DC-Link voltage and an error is given on UDC PI controller.

Power Estimation

αβ abc

αβ

dq

αβ abc

Uαβ

Qref

Uline

Iline

AC

DC

Harmonic Compensation Non-

linearLoad

αβ abc

ISAPF

Uαβ

SV

M

UD

C_ref

PI PI

PI

UDC

Iαβ2

Fig. 6. Block diagram of implemented control strategy based on Direct Power Control with Space Vector Modulation and Harmonic Compensation [20].

Output of the controller multiplied by measured DC-Link voltage gives reference value of the active power. Reference values of active and reactive powers are compared with values estimated using ‘instantaneous reactive power theory’ based on measured grid voltage and current in SAPF line. An error is given to input of power PI controllers. Outputs of the power PI controllers are reference values for Space Vector Modulator [21], [22], [23].

B. Harmonics Compensation Method

The SAPF to reduce current harmonics needs an additional compensation algorithm. Block diagram of this method based on transformations into synchronous rotating frames (SRF) [24] is presented in Fig. 7. Currents measured in point of common coupling (PCC) are transformed into stationary reference frame (αβ coordinate system) and then to synchronously rotating frame (marked as dq coordinate system) with multiplication of grid voltage basic frequency.

Iα

αβ dq

αβ dq

αβ dqIβ

Band-pass filter

Band-pass filter

Band-pass filter

7φ

-5φ

nφ -nφ

-7φ

5φ

Uα

Uβ

++

dqαβ

dqαβ

dqαβ

Fig. 7. Harmonic Compensation in SRF based on band-pass filters [20].

Each compensated harmonic has dedicated rotating frame. In case of this work 5th, 7th, 11th and 13th harmonics are compensated. Selected signal is filtered by band-pass filter which gives information about amplitude of harmonic current. Output of the filter is transformed back to stationary reference frame and summed with other filtered signals. Final signal is added to main reference voltages for SVM.

C. Fuzzy Logic Algorithm

In presented work fuzzy logic membership functions were designed using values from Table I. Fig. 8 shows designed membership function for first input. Electrical data are converted into labels “Positive Large (PL),” “Positive Medium (PM),” “Positive Small (PS),” “Zero (Z),” “Negative Small (NS),” “Negative Medium (NM),” “Negative Large (NL)”. Second input determines change of current amplitude (Fig. 9) with labels “Negative Change (NC),” “Zero,” “Positive Change”. Rules can be designed in Matlab and then imported as source code file to selected control system.

T-norm used in antecedent part of rule is minimum (3).

µA∩B= min(µAi (x), µBi (y)) (3)

Membership functions are triangular and trapezoidal-shaped. Input for FL module is calculated using discrete Fourier transform [25], [26].

1

0

PL PM PS Z NS NM NL

I5thHARM (%) 15

Deg

ree

of

mem

bers

hip

Fig. 8. Designed membership functions for 5th harmonic current (input 1).

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Output membership functions are “Decrease Small (DS),” “Proper (P),” “Increase Small (IS),” “Increase Big (IB)” (Fig. 11). Fig. 10 shows decision surface for mapping amplitude of harmonic current with its changes in time. The 21-rules proposed in decision support are shown in Table III.

TABLE III

RULES

∆I5THHARM

PC Z NC I5TH

HARM

PL DS P P

PM DS IS P

PS DS IS P

Z IB IS P

NS IB IS IS

NM IB IS IS

NL IB IB IS

1

0

PC Z NC

∆ I5thHARM

De

gre

e of

m

em

bers

hip

Fig. 9. Membership functions for change of 5th harmonic current amplitude (input 2).

Fig. 10. Surface mapping amplitude to amplitude change of harmonic current.

The output of the FLDS is suggestion for the user how to set gain in harmonic controller.

1

0

DS P IS

De

gre

e of

m

em

bers

hip

IB

1-1 Output

Fig. 11. Membership functions for decision (output).

D. Example

In case shown in Fig. 13 5th harmonic current is larger than required value (NS) and there is no change in its amplitude (Z). FLDS output is “Increase small (IS)”. After chosen by the designer time interval FLDS once again analyzes input data. If current amplitude changed from NS to Z but level of compensation stopped (Z) output is again “increase small (IS)”. In the next step, after users interaction input 1 is still in membership function “Z” but there is “negative change (NC)” in input 2 then output is “proper (P)”. Similar situation is in the next step: input 1 after fuzzification is “PS”, input 2 is “Z”, because of the weak gain of the regulator - an answer is “IS”. After increasing the gain amplitude fall further. Rule “PS and NC is P” is strongest. During next data evaluation, current amplitude is “PM” and still falling “NC”. Output is set to “P”. Finally amplitude is set as “PL” and change has stopped “Z”. FLDS output is “P”. Harmonic controller is properly tuned.

In Fig. 12 whole procedure is presented. Numbers on the left side are rules numbers defined in rule base. Each row represents states described earlier which took place in time from oldest to newest. Interesting situation is when rule 12 is evaluated. Second input is partially in set “Z” and “NC”. After inference output “P” is chosen instead of “IS”.

Fig. 12. Rule evaluation using Matlab’s rule viewer. From the left rule number, input 1, input 2, output membership function strengths and rules.

III. EXPERIMENTAL RESULTS

In this part experimental results showing operation of the harmonic compensation algorithm are presented. Parameters of the laboratory setup are collected in Table IV.

Fig. 13 shows steady state operation of the active rectifier supplied by close to ideal sinusoidal voltage under nominal load. Measured grid current THD factor is equal to 2.5 %.

TABLE IV

EXPERIMENTAL PLATFORM PARAMETERS

System parameters in Experimental Studies Control platform PC with dSpace 1103 card Switching frequency 5 [kHz] Control algorithm DPC-SVM Rated power 3.5 [kW] Type of Operation Harmonic Compensation Type of Grid Filter L=2.8 [mH] Nominal Grid Voltage 230 [V] Nominal DC-Link Voltage 600/650 [V] DC-Link Capacitance 470 [µF] Load 100 [Ω]

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Fig. 13. Steady state operation of the active rectifier supplied by sinusoidal grid voltage under nominal load. a) Grid current and voltage waveforms (from the top: grid voltage, converter DC-Link voltage, grid current of phase A and phase B, b) grid current spectrum with THD factor, c) grid voltage spectrum with THD factor.

In Fig. 14 operation of the active rectifier with supplying grid voltage distorted by 4.5% of 5th and 7th harmonics is presented. Converter operates without harmonics compensation module, measured grid current THD factor increased to 24.7 %.

Fig. 14. Steady state operation of the active rectifier supplied by grid voltage distorted by 5th and 7th harmonics under nominal load without harmonics compensation functionality. a) Grid current and voltage waveforms (from the top: grid voltage, converter DC-Link voltage, grid current of phase A and phase B, b) grid current spectrum with THD factor, c) grid voltage spectrum with THD factor.

Fig. 15 presents operation of the active rectifier supplied by grid voltage distorted by 4.5% of 5th and 7th harmonic but with active harmonic compensation module. With compensation of 5th and 7th harmonic grid current THD factor is reduced from 24.7% to 4.7%. Furthermore, to obtain lower current THD factor, 11th and 13th harmonics are additionally compensated, the result is shown in Fig. 16, obtained current’s THD factor is reduced to only 3.3%.

Fig. 15. Steady state operation of the active rectifier supplied by grid voltage distorted by 5th and 7th harmonics under nominal load with harmonics compensation functionality. a) Grid current and voltage waveforms (from the top: grid voltage, converter DC-Link voltage, grid current of phase A and phase B , b) grid current spectrum with THD factor, c) grid voltage spectrum with THD factor.

The converter is expected to compensate currents’ high-order harmonics during large voltage distortion. Fig. 17 and Fig. 18 show operation of the active rectifier with proposed harmonic compensation algorithm supplied by grid voltage distorted by 8% of 5th, 7th, 11th harmonics and 4% of 13th harmonic. Fig 17 shows operation of the converter without compensation module, grid voltage THD factor is 15.6% and grid current THD factor without compensation is equal to 48.4%. Amplitude of 5th and 7th current harmonics exceeds 40% of fundamental harmonic. Fig. 18 shows the same situation as in Fig. 17 but DPC-SVM algorithm has active harmonic compensation module. Amplitudes of 5th, 7th, 11th and 13th harmonics are significantly reduced. Grid current THD factor is decreased to 5.7%.

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Fig. 16. Steady state operation of the active rectifier supplied by grid voltage distorted by 5th and 7th harmonics under nominal load with additional 11th

and 13th harmonics compensation. a) Grid current and voltage waveforms (from the top: grid voltage, converter DC-Link voltage, grid current of phase A and phase B , b) grid current spectrum with THD factor, c) grid voltage spectrum with THD factor.

Fig. 17. Steady state operation of the active rectifier supplied by grid voltage distorted by 5th, 7th , 11th and 13th harmonics under nominal load without harmonics compensation functionality. a) Grid current and voltage waveforms (from the top: grid voltage, converter DC-Link voltage, grid current of phase A and phase B , b) grid current spectrum with THD factor, c) grid voltage spectrum with THD factor.

Fig. 18. Steady state operation of the active rectifier supplied by grid voltage distorted by 5th, 7th, 11th and 13th harmonics under nominal load with harmonics compensation functionality. a) Grid current and voltage waveforms (from the top: grid voltage, converter DC-Link voltage, grid current of phase A and phase B , b) grid current spectrum with THD factor, c) grid voltage spectrum with THD factor.

Presented results show ability of the proposed harmonics compensation functionality to strong reduction of the grid current high order harmonics expressed by THD. Obtained grid current waveforms are balanced and close to ideal sinusoidal shape, grid current THD factor is significantly reduced.

IV. CONCLUSIONS

In this paper a concept of the SAPF supported by fuzzy logic decision system is introduced. Control method of the SAPF based on Direct Power Control and extended by harmonic compensation module is presented. Harmonic compensation method based on synchronous rotating frames is described, analyzed and verified by series of experimental results. Obtained experimental results show very good features and operation of proposed method. Moreover, fuzzy logic decision support system for analyzed SAPF has been developed to help determinate its harmonic compensation regulator gain without requirement of an expert knowledge from the user. This knowledge is required only once at fuzzy sets definition stage. Proposed fuzzy logic based algorithm allows to easily configure rules in manner of linguistic description. This mean that even required standard/code is changed, rules can be easily updated. Such ability should be taken into account in planning future intelligent networks.

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ACKNOWLEDGMENT

This work has been supported by the National Science Centre, Poland, based on decision DEC-2012/05/B/ST7/01183 and partially by the European Union in the framework of European Social Fund through the Warsaw University of Technology Development Program, realized by Centre for Advanced Studies

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