General Mixed Norm Based Adaptive Control Algorithm for Distribution Static Compensator

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ScienceDirect IFAC PapersOnLine 52-24 (2019) 168–173

General Mixed Based Adaptive Control Algorithm for General Mixed Norm Norm Based Adaptive Control Algorithm for General Norm Based Adaptive Control Algorithm for General Mixed MixedDistribution Norm Based Adaptive Control Algorithm for Static Compensator Distribution Static Compensator Distribution Static Compensator Distribution Static Compensator

Haiquan Zhao, Liyuan Li, Xiangping Zeng Haiquan Haiquan Zhao, Zhao, Liyuan Liyuan Li, Li, Xiangping Xiangping Zeng Zeng HaiquanTechnology Zhao, Liyuan Li, Xiangping Zeng the Key Laboratory of Magnetic Suspension and Maglev Vehicle, Ministry of Education, and the School of the of Suspension Technology and Maglev Vehicle, Ministry of and the Key Key Laboratory LaboratoryElectrical of Magnetic Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, Education, and the the School School of of Engineering, Southwest Jiaotong University, Chengdu, 610031, China of Magnetic SuspensionSouthwest Technology and Maglev Vehicle, Ministry of Education, and the School of the Key LaboratoryElectrical Jiaotong University, Chengdu, 610031, China Electrical Engineering, Engineering,(e-mail: Southwest Jiaotong University, Chengdu, 610031, China [email protected]). Electrical Engineering,(e-mail: Southwest Jiaotong University, Chengdu, 610031, China [email protected]). (e-mail: [email protected]). (e-mail: [email protected]). This paper paper presents presents an an implementation implementation of of distribution distribution static static compensator compensator (DSTATCOM) (DSTATCOM) using using Abstract: This Abstract: Thisnorm paper(GMN) presentsbased an implementation of distribution static compensator (DSTATCOM) using Abstract: general mixed adaptive algorithm for the three-phase distribution system. By using Thisnorm paper(GMN) presentsbased an implementation of distribution static compensator (DSTATCOM) using Abstract: general mixed adaptive algorithm for the three-phase distribution system. By general mixed norm (GMN) based adaptive algorithm for the three-phase distribution system. By using norm and l norm as the cost function, the proposed general mixed norm based the convex mixture of l p q general mixed normof(GMN) based algorithm for the three-phase distribution system. By based using and lladaptive as the cost function, the proposed general mixed norm the convex mixture llp norm q norm norm and norm as the cost function, the proposed general mixed norm based the convex mixture of p q algorithm effective obtaining corresponding active and reactive weights of mixed load currents. The and lqthe norm as the cost function, the proposed general norm based the convexis mixture of for lp norm algorithm is for obtaining the active and weights currents. The algorithm algorithm is effective effective for obtaining the corresponding corresponding active and reactive reactive weights of ofofload load currents. The proposed is fast in convergence and has quick response. The performance proposed control algorithm is effective for obtaining the corresponding active and reactive weights of load currents. The proposed algorithm is fast in convergence and has quick response. The performance of proposed control proposed algorithm is fast in convergence and has quick response. The performance of proposed control algorithm is observed under nonlinear load in simulation. The DSTATCOM using GMN algorithm proposed algorithm is fast in convergence and has quick response. The performance of proposed control algorithm is is observed observed under under nonlinear nonlinear load load in in simulation. simulation. The The DSTATCOM DSTATCOM using using GMN GMN algorithm algorithm is is algorithm is effective in the functions such power compensation, elimination algorithm is achieving observed under nonlinear loadas inreactive simulation. The DSTATCOMharmonics using GMN algorithmand is effective in achieving the functions such as reactive power compensation, harmonics elimination and effective in achieving the functions such as reactive power compensation, harmonics elimination and load balancing under linear and nonlinear loads and the test results of Simulink are found satisfactory effective in achieving the functions such as reactive power compensation, harmonics elimination and load balancing under linear and nonlinear loads and the test results of Simulink are found satisfactory load balancing distortion under linear andsupply nonlinear loads andmeeting the test results Simulink are found satisfactory with harmonic of the currents well powerof standards. load balancing under linear and nonlinear loads and the testthe results ofquality Simulink are found satisfactory with with harmonic harmonic distortion distortion of of the the supply supply currents currents well well meeting meeting the the power power quality quality standards. standards. with harmonic distortion of the supply currents well meeting the power quality standards. Copyright © Distribution 2019. The Authors. by Elsevier Ltd.mixed All rights Keywords: staticPublished compensator, general normreserved. based algorithm, power power factor correction, correction, Keywords: Distribution static compensator, general Keywords: Distribution static compensator, general mixed mixed norm norm based based algorithm, algorithm, power factor factor correction, voltage regulation, total harmonic distortion. Keywords: Distribution static compensator, general mixed norm based algorithm, power factor correction, voltage voltage regulation, regulation, total total harmonic harmonic distortion. distortion. voltage regulation, total harmonic distortion.  

 1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION 1. INTRODUCTION Power quality problems have been present since the Power quality problems have been present since the Power of quality problems have B been present since the inception electric power [Singh et al., 2014]. With the Power quality problems have been present since the inception of electric power [Singh B et al., 2014]. With inception of electric power [Singh B et al.,society, 2014]. more With and the booming development of technology and inception of electric power [Singh B et al., 2014]. With the booming development development of of technology technology and and society, society, more more and and booming more industrial and civilian electrical equipment and devices booming development of technology and society,and more and more industrial and civilian electrical equipment devices morethe industrial and civilian electrical equipment and devices with feature of poor operating power factor, non-linearity, morethe industrial and civilian electrical equipment and devices with feature of poor operating power factor, non-linearity, with the feature of poor operating power factor, non-linearity, unbalance and impact access to distribution network. with the feature of poor have operating power factor, non-linearity, unbalance and impact have access to distribution network. unbalance and impact have access to have distribution network. These advanced solid-state devices led to aa very unbalance and impact have access to have distribution network. These advanced solid-state devices led to very These advanced solid-state devices have led to aquality very comfortable and smooth lifestyle but introduce power These advanced solid-state devices have led to aquality very comfortable and smooth lifestyle but introduce power comfortable and smooth lifestyle but introduce power quality problems into supply system and are the main reason of comfortable and smooth lifestyle but introduce power quality problems into supply system and main reason problems into supply of system and are are the the main Similar reason of of decrease in efficiency the distribution system. to problems into supply system and are the main reason of decrease in of the system. to decrease in efficiency efficiency ofsuch the distribution distribution system. Similar Similar to other kinds of pollution as air, the pollution of power decrease in efficiency of the distribution system. Similar to other kinds kinds of of pollution pollution such such as as air, air, the the pollution pollution of of power power other networks with power quality problems has become an other kindswith of pollution such as problems air, the pollution of power networks power quality has become an networks with issue power quality problems hasin become an environmental with other consequences addition to networks with issue power quality problems hasin become an environmental with other consequences addition to environmental issue with other consequences in addition to financial issues. The mass uses of these nonlinear loads such environmental issue with other consequences in addition to financial issues. The mass uses of these nonlinear loads such financial issues. The mass uses of these nonlinear loads such as solid-state convertion devices, financial issues.power The mass uses of and theserectification nonlinear loads such as solid-state power convertion and rectification devices, as solid-state power convertion and rectification devices, rolling mills, arc furnaces, uninterruptible power supplies as solid-state power convertion and rectification devices, rolling mills, arc furnaces, uninterruptible power supplies rolling mills, arc furnaces, uninterruptible power supplies (UPS), adjustable speed drives (ASD), chemical and medical rolling mills, arc furnaces, uninterruptible power supplies (UPS), adjustable speed drives (ASD), and (UPS), adjustable speed drivessuppliers, (ASD), chemical chemical and medical medical facilities, computer power renewable energy (UPS), adjustable speed drives (ASD), chemical and medical facilities, computer power suppliers, renewable energy facilities,electrified computerrailway powerequipment, suppliers,etc., renewable energy systems, inject harmonics facilities, computer power suppliers, renewable energy systems, electrified electrified railway railway equipment, equipment, etc., etc., inject inject harmonics harmonics systems, into the distribution system and decline the quality of power. systems, electrified railway equipment, etc., inject harmonics into the distribution system and decline the quality of power. into thenonlinear distribution system andloads decline thegive quality of voltage power. These and impulsive also rise to into thenonlinear distribution system andloads decline thegive quality of voltage power. These and impulsive also rise to These nonlinear and impulsive loads also give rise to voltage quality problems such as swell, surge, These nonlinear and impulsive loads alsofluctuation, give rise toimpulse, voltage quality problems such as swell, surge, fluctuation, impulse, quality problems suchinterruptions, as swell, surge, fluctuation, impulse, sag, and momentary etc [Ghosh and Ledwich, quality problems suchinterruptions, as swell, surge, fluctuation, impulse, sag, and momentary etc [Ghosh and Ledwich, sag, and momentary interruptions, etc [Ghosh and Ledwich, 2012]. quality problems affect concerned utilities, sag, andPower momentary interruptions, etc all [Ghosh and Ledwich, 2012]. Power quality problems affect all concerned utilities, 2012]. Power quality problems affect all concerned utilities, customs, and manufactures in terms of costly equipment 2012]. Power quality problems affect all concerned utilities, customs, and manufactures in terms of costly equipment customs, and manufactures in terms of costly equipment damage, production loss, incorrect measurement customs, and manufactures in terms of costly equipment damage, production production loss, loss, incorrect incorrect measurement measurement and and damage, and metering, wastage of raw material energy, loss of damage, production loss, incorrectand measurement and metering, wastage of raw material and energy, loss of metering, wastage of raw material and energy, loss of important data, overloading, heating of generator windings, metering, wastage of raw material and energy,windings, loss of important data, overloading, heating of generator important data, overloading, heating of generator windings, noise and data, vibrations in electrical machines, disturbance and important overloading, heating of generator windings, noise in machines, disturbance noise and and vibrations vibrations in electrical electricalnetworks, machines,mal-operation disturbance and and interference to communication of noise and vibrations in electricalnetworks, machines,mal-operation disturbance and interference to communication of interference to communication networks, mal-operation of protective devices and so on. interference to communication networks, mal-operation of protective devices and so on. protective devices and so on. protective devices and so on.

Recent researches aim to deal with the PQ problems such as Recent researches aim to with the such Recent researches aim to deal deal with the PQ PQ problems problems such as as harmonic, reactive power, and unbalancing. DSTATCOM Recent researches aim to deal with the PQ problems such as harmonic, reactive power, and unbalancing. DSTATCOM harmonic, reactive power, and unbalancing. DSTATCOM technology is considered as the best technology to mitigate harmonic, reactive power, and unbalancing. DSTATCOM technology is to technology is considered considered as as the the best best technology technology to mitigate mitigate all problems. wide technology is consideredpower as the quality best technology mitigate all the the current-based current-based power quality problems.to A A wide all the current-based power quality problems. A wide spectrum on architecture and topologies of DSTATCOM has all the current-based power quality of problems. A wide spectrum on architecture and topologies DSTATCOM has spectrum on architecture and topologies of DSTATCOM has been developed [Mahela and Shaik, 2015], DSTATCOM also spectrum on architecture and Shaik, topologies of DSTATCOM DSTATCOM also has been developed [Mahela and 2015], been developed [Mahela and Shaik, 2015], DSTATCOM also finds applications in different areas [Reddy, 2012; Aly et al., been developed [Mahela and Shaik, 2015], DSTATCOM also finds applications in different areas [Reddy, 2012; Aly et al., finds applications in different areas [Reddy, 2012;2018]. Aly etThe al., 2017; Kandpal et al., 2016; Kandpal and Hussain, finds applications in different areas [Reddy, 2012;2018]. Aly etThe al., 2017; Kandpal et al., 2016; Kandpal and Hussain, 2017; Kandpal et al., 2016; Kandpal and Hussain, 2018]. The type control for DSTATCOM determines 2017;of Kandpal etalgorithm al., 2016;used Kandpal and Hussain, 2018]. The type of control algorithm used for DSTATCOM determines type of control algorithm used forofDSTATCOM determines its effectiveness. The validity the control algorithm type of control algorithm used forofDSTATCOM determines its effectiveness. The validity the control algorithm its effectiveness. The validity of the control algorithm depends upon how quickly and accurately the reference its effectiveness. The validity of the control algorithm depends upon how quickly and accurately the reference depends upon how quicklyfrom andthe accurately the reference components are determined distorted load currents. depends upon how quickly and accurately the components are are determined determined from from the the distorted distorted load load reference currents. components currents. The algorithms built for generating the appropriate pulses for components arebuilt determined from the distorted loadpulses currents. The algorithms for generating the appropriate for The algorithms built for generating the appropriate pulses for VSC to overcome power quality problems are designed either The algorithms built for generating the appropriate pulses for VSC to overcome power quality problems are designed either VSC to overcome power quality problems are designed either in frequency or time Conventional time-domain VSC to overcome powerdomain. quality problems are designed either in frequency or time domain. Conventional time-domain in frequency time domain. Conventional time-domain commonly usedor algorithms for DSTATCOM include in frequency orcontrol time domain. Conventional time-domain commonly for DSTATCOM include commonly used used control control algorithms algorithms for DSTATCOM include (( p  q ) theory [Peng et al., instantaneous reactive power commonly used control algorithms for DSTATCOM include p  q ) theory [Peng instantaneous reactive power et al., al., instantaneous reactive power ( p  q) theory [Peng et 1998], synchronous rotating frame (SRF) theory ( p  q ) theory [Peng et al., instantaneous reactive power 1998], synchronous synchronous rotating rotating frame frame (SRF) (SRF) theory theory 1998], [Bhattacharya et 1992], 1998], synchronous frametemplate (SRF) method, theory [Bhattacharya et al., al., rotating 1992], unit unit template method, [Bhattacharya et al., 1992], unit template method, symmetrical component theory [Rao and Mishra, 2007] and [Bhattacharyacomponent et al., theory 1992],[Rao unit template method, symmetrical and Mishra, 2007] symmetrical component theory [Rao andcontrol Mishra, 2007] and and so on. Least mean square (LMS) based algorithm as symmetrical component theory [Rao andcontrol Mishra, 2007] and so on. Least mean square (LMS) based algorithm as so on. Least mean square (LMS) based control algorithm as the time-domain algorithms not only has fast processing so on. Least meanalgorithms square (LMS) based control algorithm as the time-domain not only has fast processing the time-domain algorithms not only has fast processing speed and requires less calculations the the time-domain algorithms not only but has also fast avoids processing speed and requires less calculations but also avoids the speed andofrequires less imposes calculations but also of avoids the operation PLL which some amount delay in speed andofrequires less imposes calculations but also of avoids the operation PLL which some amount delay in operation of PLL which imposes some amount of delay in computation [Zhao et al., 2014]. In order to relieve the defect operation of PLL which imposes some amount of delay in computation [Zhao et al., 2014]. In order to relieve the defect computation [Zhao et al., 2014]. In order to relieve the defect of LMS algorithm that the choice of the step-size must computation [Zhao et al., 2014]. In order to relieve the defect of LMS LMS algorithm algorithm that that the the choice choice of of the the step-size step-size must must of consider compromise the steady-state error, fast of LMS aaalgorithm thatamong the choice the step-size consider compromise among the low lowof steady-state error,must fast consider a compromise among the low steady-state error, fast convergence rate and good tracking capability-the consider a compromise among the low steady-state error, fast convergence rate and good tracking capability-the convergence rate and good tracking capability-the convergence rate after the unknown system occurs a sudden rate and good tracking capability-the convergence rate after the system occurs sudden convergence rate after the unknown unknown system occurs aabased sudden change [Singh and Solanki, 2009], more algorithms on convergence rate after the unknown system occurs abased sudden change [Singh and Solanki, 2009], more algorithms on change [Singh and Solanki, 2009], more algorithms based on LMS with improved performance for control of change [Singh and Solanki, performance 2009], more algorithms based on LMS with improved for control of LMS with improved performance for control of DSTATCOM have been presented, such as normalized least LMS with improved performance for control of DSTATCOM have been presented, such as normalized least DSTATCOM have been presented, such as normalized least mean (NLMS) algorithm, leaky LMS algorithm [Arya and DSTATCOM have been presented, such as normalized least mean (NLMS) algorithm, leaky algorithm and mean (NLMS) algorithm, leaky LMS LMS algorithmet [Arya [Arya and Singh, 2013], LMS [Mangaraj al., mean algorithm, leaky LMS algorithmet [Arya and Singh, (NLMS) 2013], sparse sparse LMS algorithm algorithm [Mangaraj al., 2016], 2016], Singh, 2013], sparse LMS algorithm [Mangaraj et al., 2016], Singh, 2013], sparse LMS algorithm [Mangaraj et al., 2016],

2405-8963 Copyright © 2019. The Authors. Published by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2019.12.401



Haiquan Zhao et al. / IFAC PapersOnLine 52-24 (2019) 168–173

variable step-size LMS algorithm [Badoni et al., 2015; Arya et al., 2012] combined LMS-LMF algorithm [Srinivas, et al., 2016], nonlinear adaptive Volterra LMS algorithm [Patel et al., 2017], variable forgetting factor recursive least-square (RLS) algorithm [Badoni et al., 2015], LLMF control algorithm [Agarwal et al., 2016], Kalman filter based LMS algorithm [Chittora et al., 2016], adaptive neuro-fuzzy LMSbased control algorithm [Badoni et al., 2016] and so on. All of these algorithms are designed for the particular system and achieve PFC, ZVR and load balancing modes by extracting reference supply currents from the sensed signals and comparing them with the observed supply currents to generate the appropriate pulses for the VSC. In this paper, a general mixed norm (GMN) algorithm based control of DSTATCOM is proposed for improvement of power quality problems such as reactive power compensation, harmonic elimination and load balancing in power factor correction and zero voltage regulation mode. Other than standard LMS algorithm with only a single error norm used as the cost function for adaptive filtering, the GMN is formed as a convex mixture of lp norm and lq norm as the cost function to increase convergence speed and substantially reduce the steady-state coefficients’ errors under specific environments [Ma et al., 2017a; Ma et al., 2017b]. According to the choice of mixing parameter, we use sigmoid function of the error at node k to adaptively select the mixing parameter which can be automatically adjusted with the variation of error. The proposed algorithm is computational not expensive. Simulation results prove the accuracy and efficiency of the proposed algorithm for control of DSTATCOM. 2. SYSTEM CONFIGURATION The configuration of three-leg VSC-based DSTATCOM which can improve power quality in distribution system is shown in Fig.1. This system includes a three-phase nonlinear load which is fed by three-phase, 415V, 50Hz grid. Rs and Ls are considered as supply resistance and inductance respectively. VSC with a dc storage capacitor ( Cdc ) injects compensating current at points of common coupling (PCC) through the interface inductor ( Li ) which is used to filter out the ripples in the compensating current. Ripple filters R f and C f eliminate the high switching frequency noise produced by operation of VSC. A three-phase uncontrolled diode bridge rectifier is modeled as a nonlinear load with series RL * * , isb , branch on the dc side. Reference source currents ( isa * ) derived from our control algorithm operate compensator isc system. When compensator system tracks reference currents by hysteresis current controller, it injects compensating currents ( i Ca , iCb , iCc ) into ac supply to eliminate distortion by the load current ( iLa , iLb , iLc ). Here vsa , vsb , vsc , and isa , isb , isc represent the three-phase supply voltage and current respectively. We establish a Simulinkbased model by using Sim Power System tool box in Matlab

169

software. The corresponding values required for simulation are shown in Appendix. Source

DSTATCOM

PCC

IGBT-based VSC

Cdc Vdc

IGBT

Interfacing inductors

Pulses to VSC

Ripple filters

Control Algorithm Nonlinear balanced/ unbalanced load

Fig. 1. Schematic diagram of the distribution system with three-phase DSTATCOM 3. PROPOSED ALGORITHM The proposed algorithm for control of DSTATCOM is based on GMN method. The control algorithm is divided into three parts. In first part, the GMN-based adaptive algorithm which extracts the weighted values of fundamental active and reactive power for the estimation of reference supply currents is described. The second part deals with the evaluation of the in-phase unit and quadrature unit templates. The third part generates reference supply currents and switching pulses for the three-phase VSC-based DSTATCOM using hysteresis current controller. The block diagram of the GMN-based control algorithm is depicted in Fig.2. LPF + + +

-

1/3

+

PI

LPF

+

Estimation of reference currents

Fundermental weights extraction for phase ‘b’

+ + +

Fundermental weights extraction for phase ‘c’

Estimation of PCC voltage amplitude and unit vectors

Gating pulses to VSC

+

LPF

-

+

1/3

LPF

Hysteresis Current controller

-+

PI

Fig. 2. Block diagram of the GMN-based control algorithm. 3.1 General Mixed Norm Based Control Algorithm The cost function of GMN is a convex combination of two error norms as [Ma et al., 2017a; Ma et al., 2017b; Song and Zhao, 2018]

J GMN (w(n))  

1  1 p q E  e(n)   (1   ) E  e(n)      p q

(1)

Haiquan Zhao et al. / IFAC PapersOnLine 52-24 (2019) 168–173

170

where E ( ) denotes the expectation operator, p  1 , q  1 , and   [0,1] , is a mixing parameter. The e(n) denotes the error and can be expressed as T

e(n)  il (n)  ilf (n)  il (n)  w (n)x(n)

The unit quadrature reactive template components for three phase PCC voltages are expressed as:

(2)

where il (n) and ilf (n) are the desired and the estimated quantities of load currents, input vector x(n)  [ x(n) x(n 1)......x(n  L  1)]T and weight vector

w(n)=[w1 (n) w 2 (n)......wL (n)]T , L is the length of the vector

uqa  u pb / 3  u pc / 3

(8)

uqb  3u pa / 2  (u pb  u pc ) / 2 3

(9)

uqb   3u pa / 2  (u pb  u pc ) / 2 3

(10)

3.3 Estimation of Reference Supply Currents

T

w(n) , ( ) indicates transpose. In the algorithm, we seek the optimal weight vector by minimizing the instantaneous GMN. Taking the gradient of JGMN (w(n)) with respect to w(n) , we have

J GMN (w (n)) w (n)    e( n )

p 1

  ( e( n )

w ap (n  1)  w ap (n) +  ( eap (n)

sign(e(n))u(n)  (1   ) e(n)

p 1

The active weight component of phase ‘a’ at sampling instant (n  1) th is estimated as

 (1   ) e(n)

q 1

q 1

sign(e( n))u( n)

p 1

and sign( ) indicates the sign function. Using the gradient descend method, the resulting update is [Song and Zhao, 2018]

p 1

 (1   ) e(n)

q 1

)sign(e(n))u(n)

(4)

where  denotes the step size. According to the choice of mixing parameter, we use the sigmoid function method in [Ma et al., 2017a; Ma et al., 2017b] to select the mixing parameter adaptively. The specific form is

 ( n) 

1 1  exp(e(n))

eap (n)  ila (n)  u pa (n)w ap (n)

+  ( ebp (n)

p 1

(6)

The unit in-phase active template components for three phase PCC voltages (vsa , vsb , vsc ) are computed as follows: (7)

 (1   ) ebp (n)

q 1

)sign(ebp (n))u pb (n)

(13)

w cp (n  1)  w cp (n) +  ( ecp (n)

p 1

 (1   ) ecp (n)

q 1

)sign(ecp (n))u pc ( n)

(14)

The average magnitude of the fundamental active power components of reference supply current is obtained as

w pavg  (w ap  wbp  w cp ) / 3

(15)

* The set dc voltage reference value ( Vdc ) subtracts

DSTATCOM’s sensed dc-bus voltage ( Vdc ) which is passed through the low pass filter to get the error, it can be obtained by * vde  Vdc  Vdc

and the error

The amplitude of voltage at PCC is expressed as:

(12)

w bp (n  1)  w bp (n)

3.2 Generation of Unit In-phase and Quadrature Templates

u pa  vsa / Vt , u pb  vsb / Vt and u pc  vsc / Vt

(11)

Similarly, the active weight component for phase ‘b’ and ‘c’ are derived as

(5)

In this case,  (n) belongs to the range of [0,1] .This method can adjust the mixing parameter automatically by the variation of the error and avoid the manual setting at the same time.

2 (vsa 2  vsb 2  vsc 2 ) Vt  3

)sign(eap (n))u pa (n)

where eap (n) is the error in active load component of phase

(3)

=w(n)+ ( e(n)

q 1

‘a’ at sampling instant (n) th and is estimated as

)sign(e( n))u( n)

w(n+1)=w(n)  JGMN (w(n))

 (1   ) eap (n)

(16)

(vde ) is processed through the proportional-

integral controller to control the dc bus voltage. The output of this PI controller is considered as a loss component of the VSC and is expressed as w d



w d  k pd vde  kid vde dt

(17)

k pd and kid are the proportional and integral gains of the dc-bus voltage controller respectively.



Haiquan Zhao et al. / IFAC PapersOnLine 52-24 (2019) 168–173

* * * ira  w q uqa , irb  w q uqb , irc  w q uqc

The total active weight component w p of the supply reference currents is obtained as

w p  w pavg  w d

(18)

The in-phase active power components of reference supply currents are expressed as * * * iaa  w p u pa , iab  w p u pb , iac  w p u pc

w aq (n  1)  w aq (n) +  ( eaq (n)

p 1

 (1   ) eaq (n)

q 1

)sign(eaq (n))uqa (n)

(20)

w bq (n  1)  w bq (n) +  ( ebq (n)

p 1

 (1   ) ebq (n)

q 1

)sign(ebq (n))uqb ( n)

(21)

w cq (n  1)  w cq (n) +  ( ecq (n)

p 1

 (1   ) ecq (n)

q 1

)sign(ecq (n))uqc (n)

(22)

where eaq (n) represents the error in reactive load component of phase ‘a’ at sampling instant (n)th and is given as

eaq (n)  ila (n)  uqa (n)w aq (n)

(23)

The mean value of the fundamental reactive power components of reference supply current is also obtained as

w qavg  (w aq  wbq  w cq ) / 3

(24)

Again, the voltage error between sensed PCC voltage Vt and its set reference value Vt* is given as

vte  Vt*  Vt

(25)

Then the voltage error is fed to the ac voltage PI controller. The output of the ac voltage PI regulator for maintaining the PCC voltage to rated value is expressed as



w t  k pt vte  kit vte dt

(26)

k pt and kit are the proportional and integral gains of the AC voltage controller respectively. Total weighted value of fundamental reactive components of the supply reference currents is obtained as

w q  wt  w qavg

Finally, adding the active * * * and reactive (iaa , iab , iac )

(27)

The three-phase reference reactive power components of supply currents can be stated as

power power

(28)

components components

(ira* , irb* , irc* ) of supply currents of each of the three phases, total reference currents are expressed as * * * * * * * * * isa  iaa  ira , isb  iab  irb , isc  iac  irc

(19)

The reactive weight components of phase ‘a’, ‘b’, ‘c’ at sampling instant (n  1) th are estimated using the following equations:

171

(29)

Estimated current errors between total reference currents

(isa* , isb* , isc* ) and sensed supply currents are fed to hysteresis current controller to generate appropriate switching pulses for VSC used as DSTATCOM.

4. SIMULATION RESULTS AND DISCUSSION The simulation model based on GMN control algorithm for distribution system with DSTATCOM is developed in Matlab/Simulink environment. The model is run in voltage regulation mode and its performance is investigated under nonlinear and unbalanced load. Results are shown for steadystate as well as dynamics performance of DSTATCOM and the design parameters are given in Appendix. 4.1 Characteristics of Intermediate Signals for GMN-based Algorithm of DSTATCOM The characteristics of intermediate signals for GMN-based DSTATCOM under nonlinear unbalancing load is shown in Fig.3. This figure represents the waveforms of PCC voltages (v pcc ) , phase ‘a’ current of supply (isa ) , phase ‘a’ current of load (ila ) , average value of the active weight component inphase to supply voltages (w pavg ) , total active weight component (w p ) , average value of the reactive weight component in-quadrature to supply voltages (w qavg ) , total reactive weight component average value of the active weight component in-phase to supply voltages (w q ) , supply currents

(is ) and reference supply currents (is* ) . The load

currents from 0.36s to 0.40s are unbalanced by removing the phase ‘a’ of load. At 0.40s, the phase ‘a’ is reconnected. Since the overall load is reduced between 0.36s and 0.40s, the magnitude of weights is lower but the weights build back to their higher values when the load is reconnected at 0.40s. The value of weights reaches stable state again at about 0.44s which proves the fast and accurate control of proposed algorithm. It can also be observed that the supply currents are balanced sinusoidal with reduced magnitude during unbalancing while with higher magnitude during balancing.

Haiquan Zhao et al. / IFAC PapersOnLine 52-24 (2019) 168–173

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500 0 -500 50

0 -50 50 0

Fig. 4. Weights corresponding to fundamental active power

-50 40

components (w pavg ) for GMN versus LMS/F

20

5. CONCLUSION

0 40

A three-phase DSTATCOM based on GMN control algorithm has been implemented in a distribution system through simulation. And the steady-state and dynamic response of DSTATCOM have been studied for ZVR mode under nonlinear balanced and unbalanced loads. GMN control algorithm has been used for extraction of fundamental active and reactive power components of load currents to obtain reference supply currents used for generating the switching pulses of VSC used as DSTATCOM. The distortions of PCC voltages and supply currents are well below 5%, which is well within the limit specified by IEEE519 standard. The power quality improvement functions of DSTATCOM, such as reactive power compensation, harmonics elimination, and load balancing have been well proven.

20 0 5

0 -5 20 0

-20 50 0

-50 50

ACKNOWLEDGMENTS

0 -50 0.36

0.38

0.40

0.42 Time（s）

0.44

0.46

0.48

This work was partially supported by National Science Foundation of P.R. China (Grant: 61871461, 61571374, 61433011), Sichuan Science and Technology Program (Grant: 19YYJC0681)

Fig. 3. Characteristics of intermediate signals using GMNbased control algorithm.

Appendix:

4.2 Comparative Performance of GMN-based Control Algorithm

AC mains: 415V, 3-ph, 50Hz; ripple filter: R f  5  and C f  10 μF ; Load: three-phase diode-based rectifier with

The proposed algorithm is compared with LMS/F algorithm in [Srinivas et al., 2016]. Fig.4 shows the convergence performance of fundamental active weight of load current for LMS/F-based and GMN-based control algorithms under load balancing and unbalancing. The load currents from 0s to 0.40s are unbalanced and from 0.40s to 0.60s are balanced. It is observed from the result that the GMN-based control algorithm shows smaller static error in weight achieved compared with LMS/F-based algorithm. Smaller oscillation ensures better performance and stability of the proposed algorithm under varying load conditions.

Rout  15.6  and Lout  200 mH ; rating of VSC: 20 kVA ; dc-bus capacitance: 6800  F ; reference dc-bus voltage: 700 V ; Interfacing inductors ( Li )  3.1 mH . GMN-based

control algorithm: step size   0.02 , p  1.1 , q  1.4 ; filter cutoff frequency of active average weight (w pavg ) : 15 Hz ; filter cutoff frequency of reactive average weight (w qavg ) : 20 Hz .

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