advanced fuzzy polar for optimal dynamic voltage restorer

ADVANCED FUZZY POLAR FOR OPTIMAL DYNAMIC VOLTAGE RESTORER 1

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Margo Pujiantara , Muhammad Abdillah , Rio Indralaksono Department of Electrical Engineering, Institut Teknologi Sepuluh Nopember (ITS), Surabaya 3 PT. PLN (Persero) UPK JJB III, Jl.Slamet No.1 Candi Baru Semarang (INDONESIA) E-mails : [email protected], [email protected], [email protected]

ABSTRACT Dynamic Voltage Restorer (DVR) is a device installed to improve a voltage profile to protect sensitive load from various disturbances. One of the controllers that have been developed is based on fuzzy logic. The large numbers of membership functions of the fuzzy controllers make time response slow. Many researches are proposed to minimize the number of membership function, such as fuzzy polar controller method. By using this method, the number of membership function can be minimized; response time of the controller becomes faster. This paper presents the Dynamic Voltage Restorer (DVR) based on fuzzy polar controller Method. Fuzzy polar method is able to reduce the amount of control rule significantly and makes its control action simpler because fuzzy polar expresses the state at polar coordinate. Over development, addition of parameters Zp, Sg, and Zpmin is able to improve the control signal performance. To investigate the effectiveness level of proposed fuzzy polar control scheme, non-linear simulations is carried out on the DVR to improve a voltage profile in the 3 wire systems with various levels of disturbance conditions. From the simulation result, it is found that the addition of Zp, Sg, and Zp-min parameter on fuzzy polar, called the advanced fuzzy polar, can improve the performance of a voltage recovery by the DVR with an average of 31.16% better than that of the conventional fuzzy polar method. Key words : fuzzy polar, voltage recovery, DVR 1.

INTRODUCTION

An ideal electrical power distribution system gives customers the power flow that is not interrupted and having a pure sinusoidal wave that has been determined. In fact, a power system has a high probability to get disturbance that has impact on power quality. Dynamic Voltage Restorer (DVR) is a power electronic device which has the ability to protect sensitive load from various types of voltage disturbances. DVR is installed between the source and sensitive load to improve a voltage profile caused by disturbances [1]. DVR controls the load voltage by injecting voltage amplitude; phase and harmonic components are needed for the voltage at the load side in ideal circumstances [1]. Many controllers have been developed for DVR; one is based on fuzzy logic. Frequently, time response of the fuzzy logic controllers is slow because of the large number of membership functions [2]. Further development of fuzzy logic was done by Hiyama (1991). He modeled fuzzy rule based on polar areas1) reported to have a better performance than that on the conventional method [2, 3, 4, 5, 6, 7, 8]. Fuzzy Polar has the advantage to solve problems of real time control of manipulator based on detailed mathematical model reported in the previous studies and it was found to be difficult to apply [9]. This is not only because Fuzzy Polar does not require a detail-described study unit in its control scheme but it also because the advantage of Fuzzy Polar expresses the state at polar coordinate so that the amount of control rule is reduced significantly making the control action simpler [10]. Fuzzy Polar controller is intended to improve the performance of the system and further development of this controller has been done [11, 12]. Furthermore, in the form of complex and non-linear model, Fuzzy Polar requires a relatively fast computation time to determine the required control signals [9]. The purpose of Polar Fuzzy control scheme is to simplify the process so that it does not require heavy computing process and application in real-time that might be done [13]. Thus, to solve the problem, i.e. accurate and limited time modeling of dynamic control, Fuzzy Polar method was proposed as a real time control of manipulators. In addition, the previous studies based on Fuzzy Polar were robust methods [14]. The purpose of this paper was to demonstrate the control capabilities of fuzzy polar applied on DVR to improve voltage profile of the system.

1)

Hiyama itself does not directly mention the developed fuzzy with the term Fuzzy Polar. Along with the development of research on fuzzy developed by Hiyama, Thomas H. Ortmeyer called fuzzy as Fuzzy Polar because it uses polar fields in the fuzzyfication process and differentiate it with general fuzzy [11].

2.

SYSTEM MODELLING

Dynamic Voltage Restorer (DVR) function is to restore the voltage profile during disturbance like sags and dips occur. Simply put DVR recovery voltage profile by adding a voltage or absorb the excess voltage on distribution networks. This simple principle also allows the DVR to restore the voltage profile due to harmonic distortion [5, 6]. These voltages are injected in synchronized with the voltages in the distribution networks [2]. In general, the DVR configuration consists of Booster Transformer, Voltage Source Inverter (VSI), control system, Energy storage (DC S1 & DC S2 as shown in Figure 1) and filters to dampen current harmonics caused by switching of the booster transformer when the injection voltage is performed. DVR implements compensation by injecting active power into the distribution network due to disturbance [1, 4, 8]. Therefore, the limit of compensation process will be determined by the capacity of energy storage [8]. In this paper, the modeling was done by eliminating filters and performing sensing the voltage at the load side after the injection was done as shown in Figure 1. So the DVR function was to recover the interference voltage dips, sags and harmonic distortions caused by switching process to inject a voltage in the system. Booster transformer would inject a voltage in accordance with the level of disturbance at the load bus voltage so that it became close to the ideal and constant. Booster Transformer obtained the injection voltage source from the Voltage Source Inverter (VSI) controlled by the Voltage Regulator. Large injection voltage applied is shown in equation 1 [15].

Vi  Vs  Vinj

(1)

where, Vl Vs Vinj

Voltage at Sensitive Load Voltage at Transmission when Sags or Dips or Harmonic Distortion Occur Voltage Injection

Fig. 1. Scheme of the DVR using the Fuzzy Polar Controller

Vd ref

Vabc

Vd +-

Vd

Vq ref

Vabc to dq0

Vq

Fuzzy Polar Control

Vq V0

dq0 PWM to abc

V0 ref

+

V0

Fig. 2. DVR controller model using Fuzzy Polar

Reference signal from the sensing (V1) was converted into a signal dq0. The dq0 reference signal is then compared to the reference signal dq0 when no interference occured or was in the normal state so that it could recognize if the value of the error signal happened. Error signal would be processed by the controller Fuzzy Polar. The control signal was returned to the form abc signal which then became the input of the PWM control signal as shown in Figure 2. 3.

PROPOSED METHOD

Proposed Fuzzy Polar controller wasthe propose considered to be applied using a micro-computer, A/D and D/A interface [16]. In this paper, the proposed Fuzzy Polar method was used to improve a voltage profile by adding the integral/differential information from the error signal as an input fuzzy. However, the control signal improvements to improve the voltage profile within the restrictions that had been deregulated were not possible using fixed parameters. To resolve these problems, the additional information in the form of integral or differential of the error signal as an input fuzzy was done [13]. The addition of input information was also intended to allow the control signals to generate Fuzzy Polar to be able to recover the signal voltage when subjected to disturbances as quickly as possible and complied with the limits transient performance.

Fig. 3. Fuzzy Polar decision Table rules [17]

Fig. 4. Membership function Fuzzy Polar rules [17]

Fuzzy Polar controller has three main components namely rule base, fuzzyfication and defuzzification. Rule Fuzzy Polar is shown in Figure 3. There are seven fuzzy levels used for high accuracy, among others, NB (Negative Big), NM (negative medium), NS (negative small), Z (zero), PS (positive small), PM (positive medium), and PB (positive big). In Figure 3, a diagonal line Z (zero) represents a switching line dividing the control action into two parts. The upper switching line is a negative signal to provide a negative control signal and the lower switching line is a positive signal to provide a positive control signal. Rule Fuzzy Polar can be described as in Figure 4. One of the uniquenesses and the benefits of Fuzzy Polar was the transformation rule base on a phase plane in polar coordinates as shown in Figure 5. Therefore, the number of control rules required were reduced significantly [10].

Switching Line

Switching Line

As.Za(k)

As.Za(k)

Sektor A /2

Sektor A /2

/2 D(k)

p(k)  (k)

/2

D(k) p(k)  (k)

Zs(k)

O

O*

O 45

Sektor B

Zs(k)

45

Sektor B

ZSS

(a) Zss is set to zero (Conventional Fuzzy Polar)

(b) Zss parameter is set to certain value (Advanced Fuzzy Polar)

Fig. 5. Rule base Fuzzy Polar on polar coordinate [17, 4, 6,7, 8,18, 19]

In the Fuzzy Polar, the condition of the input information signal was represented as a point/state in the polar field or phase plane as shown in Figure 5. Information of condition/state of signal that had to be controlled was represented as a point p(k) and the condition/state of the expected signal/reference signal was represented as an origin/equilibrium point (O) on the phase plane. The main working principle of the Fuzzy Polar was to change the input signal to a reference signal or equilibrium point (O) [20]. Therefore, control signals were required to shift the current state signal p(k) to the reference signal. The phase plane was divided into Sector A on the first quadrant and sector B in the third quadrant. Both sectors were defined as the range of control action for strengthening or positive signal to increase the signal voltage below the reference/expected state and the attenuation control signal or a negative signal to lower the voltage signal exceeding the reference/expected state. Control action on the phase plane then was transformed into two membership functions during the process of fuzzyfication, where the linguistic variables of the membership functions were based on numerical input. These two sectors in the Figure 5 was defined as two polar membership functions N(k) and P(k). The function of P(k) was to provide an increase voltage grade and N(k) functions to provide a grade reduction of the voltage. In addition, the point region of the right half-plane represented the current condition of the signal voltage exceeding the expected voltage and when they were at a point on the left of the half-plane that the condition of the signal voltage was less/lower than the expected voltage conditions. Parameter Za was the error signals from the signal controlled to equilibrium point/desired state. Zs 2) parameters were obtained from integrating/differentiating Za while parameter Zp was obtained from integrating/ differentiating Zs as shown in Figure 6. Each parameter:Za, Zs, Zp was obtained at each sampling time [20] and the value of the signal parameters Za, Zs, Zp would be zero in the final steady state or when there was no longer any disturbance occured [21, 22].

d dt

d dt

Zp (k)

Fuzzy Logic Control Rules

Zs (k) Error e(k)

Za (k)

U

Fig 6. Signal Conditioning Several adjustable parameters including As, Dr, α, Sg and Zp-min were set on specific operating point refered to the specific disturbance (level voltage drop). These parameters were determined through experiments, and fixed during the operation due to the robustness of Fuzzy Polar scheme [13, 22]. As, a derivative multiplier [11], was a positive scaling factor as weighting function [14] to Za(k) [13]. The amount of phase compensation was modified through the parameters of As. Dr controller parameter was a parameter that was inversely related to gain [11]. Dr was also a fuzzy distance level for radial member [20]. α was the angle at the membership function overlap between sectors A and B [23, 20]. Sg was the gain shift and Zp was the deadband [22].

Z ss  0.0,

for Z p (k )  Z p min

Z ss  S g . Z p (k ),

(2)

for Z p (k )  Z p min

(3)

Based on the equation 2-3, ZSS provided a measure of shift sizing of the origin O to O* [22]. Figure 5.b. showed a shift ZSS for positive Zp(k). In certain cases, the use of parameters Sg and Zp-min did not have a significant effect in obtaining optimal control signal [20] so that it could be ignored by setting Sg = 0, Zp-min = 0. At the time of tuning parameters of Fuzzy Polar, Sg parameter value was set to zero [20]. Fuzzification process signal input into phase plane with polar coordinates P(k) = [D(k), θ(k)] was shown by Equation 4-5 [24, 20, 25, 2] as follows: 2

D( k )  ( Z s ( k )  Z ss )  ( As .Z a ( k ))

 ( k )  tan

1

 As .Z a ( k )     Z s ( k )  Z ss 

2

(4) (5)

In Fuzzy Polar, there were two membership function namely membership function angle θ(k) and membership function radius D(k). Linguistic variables of angle membership function were weakening the N(k) and/or strengthening P(k) [22], where N(k) +P(k) = 1 as shown in Figure 7.

2)

In further developments, Hiyama adding Zp parameters as additional information to improve performance of the developed fuzzy, and the parameters Sg and Zp-min to limit the effect caused by the parameter Zp. Hiyama mention the development of its fuzzy as the Advanced Fuzzy Logic [22]. Zp parameters in conventional Fuzzy Polar is not used, or assumed to be zero.

grade



N( )

P( )

1

0 0

90 135 180 270 315  [ derajat ]

360

Fig. 7. Angle Membership Function and Amplitudo of Fuzzy Polar [26, 25, 18, 16, 19] .

In a defuzzyfication phase, linguistic variables were converted back into numeric variable as the output of the Fuzzy Polar controller based on the membership function. Defuzzyfication process was shown by equation (6-8) [27, 24, 25]. Fuzzy control rules took current conditions into the equilibrium point (O) to produce the desired control signal. N ( ( k ))  P ( ( k )) (6) U (k )  .G ( k ).U max N ( ( k ))  P ( ( k ))

N ( (k ))  P( (k ))  1

(7)

U ( k )  {N ( ( k ))  P( ( k ))}.G( k ).U max

(8)

G(k) represented the gain factor determined/influenced by the distance D(k) of the system state p(k) while Umax was the maximum allowable control effort [25]. Hence, by equation (8-10) below [28], the maximum gain at the Fuzzy Polar was influenced by the value of comparison Umax/Dr [20].

G(k ) 

D(k ) Dr

, for Dr  D ( k )

(9)

G ( k )  1.0, for Dr  D( k )

(10)

In another study [10], the function of the gain factor G(k) could be modified as shown in equation 11-13 and depicted as in Figure 3.6. A small linear gain function representing G(k) was to prevent the system state from hunting around equilibrium point. D(k) was used to determine the number of gain settings required in the process of computerization to calculate the required control signals.

G(k ) 

D(k ) Dr

, for 0.1 Dr  D ( k ) (11)

 D(k )    Dr 

G(k )  

n

, for 0.1 Dr  D ( k )

G ( k )  1.0, for Dr  D( k )

(12) (13) Fig 8. Gain function

4.

RESULT AND DISCUSSION

In this paper, simulations were performed to test the performance of the Fuzzy Polar controller on the DVR by placing sensing disturbances on the load side. Thus, the Fuzzy Polar controller had to be able to control the DVR in order to restore the voltage profile due to disturbance and harmonic distortions caused by switching on the injection process that was performed by the DVR. In this paper, DVR controller was tested with a variety of disturbances with various levels of depth. Some parameters controller Fuzzy Polar determined in advance as the basis of determining the other parameters. In this study, the parameters As = 0.19 and α = 90 ° determined fixed value [15] and Sg&Zss parameters while set to be 0 to simplify the determination of other parameters. Determination of other Fuzzy Polar controller parameters were done by providing a substantial disruption to occur voltage sags 0% as shown in Figure 9. It was intended to determine the maximum of the error signal which may occur on each axis d, q and 0 as shown in Figure 10-12. Large maximum error signal representing the required level of recovery was needed or represented the value of the parameter Dr.

From Figure 10-12, it could be recognized that the value of Dr for each axis d, q and 0 was as shown in Table 4.1. In this paper, the maximum gain at Fuzzy Polar was given at 1000 times or it could be written as Umax/Dr = 1000 so that the value of Umaxof each axis d, q and 0 could be written as shown in Table 1. Table1. Adjusted parameter on Fuzzy Polar controller Dr d = 1.0000 Dr q = 0.4879 Dr 0 = 0.0555

Umax d = 1000 Umax q = 487.9 Umax 0 = 55.00

Fig. 9. Voltage source when voltage sags 0% occur

Fig. 10. Error signal-d when voltage sags 0% occur

Fig. 11. Error signal-q when voltage sags 0% occur

Fig. 12. Error signal-0 when voltage sags 0% occur

In this paper, Fuzzy Polar controller was tested to recover the voltage profile on the system having disturbance: 1 phase to ground (1FG), 2 phases to phase (2FF), 2 phases to ground (2FG) and 3 phases to phase (3FF) with various levels. The simulation results were shown in Figure 13-15. Table 2-3 showed the results of the recovery voltage and the voltage THD due to switching during the injection process performed by the DVR. Table 4.2-3, showed that the addition of variable Sg did not describe a significant influence. In addition, parameter values Sg were tuned to obtain best value through experiment. Table 2 Restoration performance using proposed DVR with Sg = 0 (conventional Fuzzy Polar) Study Case Voltage Sags Voltage Restoration (pu) THDv (%) Error Voltage Restoration (%) Average Error (%)

70%

3FF 50%

30%

70%

2FF 50%

30%

70%

2FG 50%

30%

70%

1FG 50%

30%

.9966

.9949

.9939

.9978

.9967

.9956

.9980

.9961

.9955

.9983

.9972

.9963

.31

.35

.37

.28

.29

.30

.28

.30

.32

.26

.26

.28

.44

.51

.61

.22

.33

.44

.20

.39

.45

.17

.28

.37

.3675

Table 3 Restoration performance using proposed DVR with Sg = 35 (advanced Fuzzy Polar) Study Case Voltage Sags Voltage Restoration (pu) THDv (%) Error Voltage Restoration (%) Average Error (%)

70%

3FF 50%

30%

70%

2FF 50%

30%

70%

2FG 50%

30%

70%

1FG 50%

30%

.9972

.9950

.9939

1.001

.9993

.9978

1.001

.9981

.9959

1.001

.9985

.9969

.35

.36

.37

.71

.66

.63

.64

.64

.33

.51

.42

.34

.28

.50

.61

.10

.07

.22

.10

.19

.41

.10

.15

.31

.2530

Fig. 13. 1FG Voltage Sags 50% occur

Fig. 14. Restoration 1FG Voltage Sags 50% with Conventional Fuzzy Polar

Fig. 15. Restoration 1FG Voltage Sags 50% with Advanced Fuzzy Polar

5.

CONCLUSION

Advanced Fuzzy Polar that was proposed by adding parameters Zp, Sg, and Zp-min on conventional fuzzy polar showed that the performance of control signal in non-linear simulations carried out on the DVR improve. From the simulation result done with various levels of disturbances as shown in Tables 4.2-4.3, it was known that the Advanced Fuzzy Polar could improve the performance and the effectiveness of control signal of the Fuzzy Polar for the voltage recovery by the DVR with an average of 31.16% better than that of the conventional Fuzzy Polar. REFERENCES [1] Margo P, M Heri P, M Ashari, Imanda, “Dynamic Voltage Restorer Menggunakan Boost Transformer Star Connected with Backpropagation Neural Network Controller for Voltage Sags Restoration”, SMELDA, Malang-Indonesia, December 2005. [2] Margo Pujiantara, Mauridhi Hery P, Mochamad Ashari, Hendrik, T. Hiyama, “Balanced Voltage Sag Correction using Dynamic Voltage Restorer Based on Fuzzy Polar Controller”, ICICIC - Kumamoto Japan, September 2007. [3] Margo P, M Heri P, M Ashari, Zaenal P A, “Dynamic Voltage Restorer (DVR)-Based Fuzzy Logic Controller with A Blocking of Zero Sequence to Overcome Voltage Dips Due to Balance And Unbalance Disturbances”, IES-Surabaya, Indonesia, November 2006. [4] Margo P, M Heri P, M Ashari, “DVR Modeling Based on Fuzzy Polar Controller to Restore Balanced and Unbalanced Sag Voltage”, SITIA-Surabaya, Indonesia, Mei 2007. [5] Margo Pujiantara, Mauridhi Hery P, Mochamad Ashari, Zaenal PA, T. Hiyama, “Dynamic Voltage Restorer Based on Fuzzy Polar as Voltage Restorer and Voltage Distortion Compensator”, ICA – Bandung Indonesia, October 2009. [6] Margo Pujiantara, Mauridhi Hery P, Mochamad Ashari, Zaenal PA, T Hiyama, “Fuzzy Polar Dynamic Voltage Restorer as Voltage Sag Restorer and Active Filter without Zero Sequence Blocking”, Gelagar, September 2008. [7] Margo Pujiantara, Mauridhi Hery P, Mochamad Ashari, H Suryoatmojo, T. Hiyama, “Advanced DVR with Zero-Sequence Voltage Component And Voltage Harmonic Elimination for Three-Phase Three-Wire Distribution Systems”, Journal IPTEK, November 2009. [8] Margo Pujiantara, Mauridhi Hery P, Mochamad Ashari, Zaenal PA, T Hiyama, “Compensation of Balanced and Unbalanced Voltage Sags using Dynamic Voltage Restorer Based on Fuzzy Polar Controller”, IJAER- Research India Publications, Vol.3 No.3 – 2008, pp. 879-890. [9] C. M. Lim, T. Hiyama, “Application of Fuzzy Logic Control Manipulator”, IEEE Transactions on Robotics and Automation, Vol. 7, No. 5, October 1991. [10] C. M. Lim, T. Hiyama, “Comparison Study Between a Fuzzy Logic Stabiliser and Self-tuning Stabiliser”, Elsevier, Computer in Industry 21 pp.199-215, 1993.

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