Improved P-f/Q-V and P-V/Q-f Droop Controllers for Parallel Distributed Generation Inverters in AC Microgrid

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1 See dscussons, stats, and author profles for ths publcaton at: Improved P-f/Q-V and P-V/Q-f Droop Controllers for Parallel Dstrbuted Generaton Inverters n AC Mcrogrd Artcle n Sustanable Ctes and Socety May 2018 DOI: /j.scs CITATIONS 0 READS authors, ncludng: Josep M. Guerrero Aalborg Unversty 842 PUBLICATIONS 21,628 CITATIONS SEE PROFILE Some of the authors of ths publcaton are also workng on these related projects: Mcrogrds deployment n Israel soco-techno-economc analyss of benefts, challenges and regulatory framework Vew project Smart Communty Energy Management System (SCEMS) Vew project All content followng ths page was uploaded by Josep M. Guerrero on 05 July The user has requested enhancement of the downloaded fle.

2 Improved P-f/Q-V and P-V/Q-f Droop Controllers for Parallel Dstrbuted Generaton Inverters n AC Mcrogrd Chethan Raj D a,, D.N. Gaonkara, Josep M. Guerrero b a Department of Electrcal and Electroncs Engneerng, NITK, Surathkal, Mangalore, Inda b Department of Energy Technology, Aalborg Unversty, Aalborg, Denmark joz@et.aau.dk Abstract-Dstrbuted generaton nverters are generally operated n parallel wth P-f/Q-V and P- V/Q-f droop control strateges. Due to msmatched resstve and nductve lne mpedance, power sharng and output voltage of the parallel DG nverters devate from the reference value. Ths leads to nstablty n the mcrogrd system. Addng vrtual resstors and vrtual nductors n the control loop of droop controllers mprove the power sharng and stablty of operaton. But, ths leads to voltage drop. Therefore, an mproved P-f/Q-V and P-V/Q-f droop control s proposed. Smulaton results demonstrate that the proposed control and the selecton of parameters enhance the output voltage of nverters. Keywords-Dstrbuted generaton nverters, droop control, mcrogrd, output mpedance, vrtual resstors, vrtual nductors. 1. Introducton Dstrbuted generaton (DG) systems use renewable energy resources such as wnd, solar, tdal energy, and some non-renewable energy sources such as fuel cells, gas turbnes, mcroturbnes, and generators [1]. As compared to tradtonal power systems, DG systems are decentralzed and hghly flexble [2]. Hence, accounts for reduced transmsson cost and mproved stablty and relablty of power systems [2]. The dstrbuted power supply n DG systems s not controllable. When drectly connected, causes negatve mpact on the power grd [3]. To avod ths adverse effect on the power grd, Unted States Electrcal Relablty Technology Solutons Consortum has studed the role of dstrbuted power n low-voltage power grds and proposed the concept mcrogrd [4],[5]. Mcrogrd can be categorzed as AC, DC and AC-DC mcrogrds [5], [6],[7]. In AC mcrogrds the parallel operaton of DG nverters can be dvded nto wred and wreless parallel control. Wred parallel control nclude crcular chan control (3C) [8], centralzed control [9], and master slave control [10], among others. Wred parallel control strategy uses nterconnected sgnal lnes for communcaton between the DG nverters. However, too many communcaton sgnal lnes leads to a complex structure of the mcrogrd and nhbts expanson. In order to solve the sgnal lne problem of wred nterconnecton control, a wreless parallel control strategy 1

3 based on actve and reactve power droop control s proposed [11], [12]. Wreless control ncludes droop control [10], [12],[33] reverse droop control [14], herarchcal droop control [12], mproved droop control [15], [16], [17] and vrtual power droop control [18], among others. Droop control n a mcrogrd has a broad applcaton prospects, as t does not requre physcal communcaton lnks and easy to acheve plug and play operaton [11]. The tradtonal P-f/Q-V droop control and P-V/Q-f droop control as the research background, the man research s summarzed on the followng aspects: Droop decouplng control strategy [12], droop coeffcent self-tunng optmzaton algorthm [19], vrtual mpedance control [20], [21]. In an nductve lne envronment, droop control can acheve better results. But, mostly for mcrogrd voltage level of 10 kv the lne mpedance s resstve, thus affects the droop control performance. The use of tradtonal droop control method makes t dffcult to acheve precse power sharng and crculaton suppresson [22]. A varety of mproved droop control methods are proposed. In [23], [24] an mproved droop control s proposed by desgnng control parameters, so that the nverter output mpedance s always nductve. However, ths method has a lmted range of effectve output mpedance adjustment. In [25], by addng dfferental lnks n the tradtonal droop control equaton, the power sharng of the parallel DG nverter s quckly stablzed. But ths leads to harmonc amplfcaton and output voltage dstorton. Vrtual mpedance method [20], [21], [26] s adopted for parallel DG nverters to mprove power sharng under dfferent lne condtons. However, vrtual mpedance does not completely elmnate the nfluence of lne mpedance and ncreases the voltage drop. In an actual mcrogrd system, dfferences n parameters and lne mpedance, makes actve and reactve powers not completely decoupled, thus affectng the accuracy of the droop controllers. In vew of the aforesad problem, by ampltude frequency characterstcs analyss, dfferent control parameters effects on the output mpedance of DG nverters and approprate control parameters are selected. In order to solve the parameters dfferences and uneven dstrbuton of power between the parallel DG nverters n a mcrogrd, vrtual resstors and nductors are added nto the control loop of the droop controllers. The ntroducton of vrtual resstors and nductors cause DG nverter output voltage to drop. In order to renstate the effect, an mproved P-f/Q-V and P-V/Q-f droop wth secondary control s proposed. The paper s organzed as follows. In Secton 2, power flow characterstcs of droop control s presented for DG nverters. In Secton 3, dual loop control parameters are altered usng vrtual resstors and nductors for mprovng power sharng between DG nverters and also secondary control s proposed to mprove the voltage devatons. In Secton 4, smulaton results are presented. Fnally, the concludng remarks are delberated n Secton 5. 2

4 2. Droop control basc prncple 2.1 Power flow characterstcs between equvalent voltage sources A smplfed schematc of parallel DG nverters s shown n Fg.1. The sum of the output mpedance of the nverter and the lne mpedance of DG nverter1 and DG nverter2 s gven by Z1 r1 jx1 R1 Lne jx1lne Z1 1, Z2 r2 jx2 R2Lne jx2lne Z2 2. where r1, r2 are the DG nverters equvalent output resstances; x1, x2 are the nverter equvalent output reactances; R1Lne, R2Lne are the lne resstances; X1Lne, X2Lne are the lne reactances; V com 0 s the ac bus voltage ampltude; V1, V 2 are DG nverter output voltages; 1, 2 are the DG nverter output voltage phase angles; 1, 2 are the total mpedance angles of DG nverters; o1, o 2 are the output currents of DG nverters; o s the load current [27]. Z 1 1 Z 2 2 Vcom 0 r 1 jx1 1Lne 1Lne R jx o1 o 2 o R r jx 2Lne jx 2Lne 2 2 V 1 1 Equvalent crcut of DG nverter1 R L jx L Equvalent crcut of DG nverter2 V 2 2 Fgure 1: DG Inverters equvalent crcut n autonomous mode. The DG nverters output current and power s gven by: V Vcom0, ( 1, 2... ) Z S V P jq n (1) 3

5 where n s the number of DG nverters; P and Q are the actve and reactve power output of the th DG nverter respectvely whch are expressed as: 1 [( cos 2 com com )cos com sn sn ] Z P VV V VV (2) 1 [( cos 2 com com )sn com sn cos ] Z Q VV V VV (3) When the sum of output mpedance and lne mpedance s purely nductve, 90 the equatons (2) and (3) are smplfed as:, so P VV com (4) X Lne Q 2 VV com Vcom (5) X Lne From equatons (4) and (5), t s clear that the power angle determnes the flow of actve power, whereas, voltage ampltude V com determnes the flow of reactve power. Voltage phase angle and actve power, voltage ampltude V com and reactve power, have lnear relatonshp. The P-f/Q-V droop control curve s shown n Fg. 2(a) and control equatons are gven by [10], [11], [27]: f f m ( P P ) (6) V V n ( Q Q ) (7) where f and V are the voltage ampltude and frequency of the DG nverters output; m, n are the P-f/Q-V control coeffcents; P and the th DG nverter output. Q are respectvely the rated actve and reactve power of Smlarly, when the sum of output mpedance and lne mpedance s purely resstve, 0, equatons (2) and (3) are smplfed and the P-V/Q-f droop control curve s as shown n Fg. 2(b). The control equatons are gven by [14], [29]: f f n ( Q Q ) (8) V V m ( P P ) (9) 4

6 f V V max f max f A A V f mn B V mn B 0 Pmax Q max 0 P P Qmax Q (a) P-f/Q-V Droop control curve. V f f max B V max V A A f V mn B f mn 0 Pmax Q max 0 P P Qmax Q (b) P-V/Q-f Droop control curve. Pmax, and Q max, : Maxmum allowable actve and reactve power of the DG nverter. V fmax, and max, : Maxmum output frequency and output voltage ampltude of the DG nverter. fmn, and V mn, : Mnmum frequency and voltage ampltude allowed by the DG nverter. Fgure 2: Droop control characterstcs. 2.2 Power dstrbuton condton between DG nverters When the parallel DG nverters s operated n solated mode, the output frequency and voltage of each DG nverter s the same [30], [31]. The droop control method to acheve a reasonable dstrbuton of the load power, needs to meet the followng equatons. m P m P, n Q n Q, f f, V V (10) X X X X,, V V, (11) 1 Lne 2 Lne 1 Lne 2 Lne m1 m2 n1 n2 5

7 n P n P, m Q m Q, f f, V V (12) R R R R V V,,, (13) 1 Lne 2 Lne 1 Lne 2 Lne n1 n2 m1 m2 Equatons (10), (11), (12) and (13) show that, to realze the proportonal sharng of actve and reactve power of parallel DG nverters, t s necessary to satsfy the followng condtons. 1) Each DG nverter droop coeffcents should be nversely proportonal to the rated capacty. 2) Each parallel DG nverter voltage and frequency should match to the rated value. 3) The output voltage of each DG nverter should have same ampltude and phase. 4) The lne mpedance at the output of each DG nverter s nversely proportonal to droop coeffcents [29], [31]. In a mcrogrd system, the above s the condton of power sharng between DG nverters under the nductve and resstve lne model. In addton, the output mpedance of the nverter and lne mpedance to the load are dfferent, consderng geographcal locaton and other factors, wth a certan degree of randomness, t s dffcult to satsfy equatons (10), (11), (12) and (13) and s dffcult to realze the proportonal power sharng between the DG nverters accordng to the P-f/Q-V, P-V/Q-f droop control schemes. 3. Mcrogrd droop control strategy In a mcrogrd, a droop control s actually used to smulate the droop characterstcs of the synchronous generator to adjust the voltage and frequency of the DG nverters output, so that the mcro-grd can operate under dfferent load requrements. As can be seen from Fg. 3, where L s the flter nductor, C s the flter capactor, r s the flter nductor equvalent resstance and ZLoad s the load mpedance, the droop control model of mcrogrd can be dvded nto two parts: voltage and current loop control model and power droop control model. Frst, the output voltage and current of the mcro-power supply are obtaned by samplng the DG nverter module. The output power of the mcro-power supply s obtaned by the power calculaton unt and the lowpass flter, and then calculated accordng to the actve power droop controller and the reactve power droop controller respectvely. The reference voltage values Vdref and Vqref s fnally adjusted by the voltage PI control and dref and qref are adjusted by the current P control to obtan controllable snusodal modulaton sgnal m to the DG nverter. 6

8 Mcrogrd network bus(pcc) Dstrbuted Generaton Inverter V dc S1 S S 3 5 A B C LC Flter r L L Lne mpedance R Lne jx Lne S S4 S 6 2 c o R L Load m SPWM m abc L dqo V c, c abc dqo C abc V o, o dqo Power Calculaton Z Load P Q Power droop control abc dqo dqo Current P Control dref qref Voltage PI Control V dref V qref dqo abc Voltage Control V f Droop Control(P-f,Q-V) P n Q n P n Droop Control(P-V,Q-f) Q n Fgure 3: Droop control block dagram. 3.1 Voltage and current dual loop control of DG nverters Voltage and current dual-loop control [21] s the man nverter control strategy as shown n Fg. 4, n whch the current nner loop mproves system stablty, system dynamc response and dampng propertes. The nner current loop feedback s of two types, capactor current mode [26], [31] and nductor current mode [30]. As compared to the nductor current mode feedback, the feedback capactor current mode provdes better nose mmunty, but s unable to carry out nverter current lmt protecton. Research n [21] have shown that, for larger values of current controller proportonal parameter K, better dynamc response of the current loop s acheved. But, f p K p s too large, there s a deteroraton n the system stablty. On the other hand, the smaller values of voltage controller parameter 7 K pv, the DG nverter output mpedance s resstve. If K pv takes larger values, the DG nverter output mpedance s nductve. Smlarly, the selecton of the ntegral parameter K v has a sgnfcant effect on the characterstcs of the nverter output mpedance. In other words, the steady-state as well as the dynamc characterstcs

9 of DG nverter output depends on the parameter desgn of the controller. When the control parameter s a fxed value, t s dffcult to meet the mcrogrd sland operaton n adjustng the voltage ampltude and frequency, durng the changes n power supply fluctuatons. Therefore, t s necessary to control the use of reasonable structure and parameter tunng method to acheve stable control of mcrogrd n slandng mode. In Fg. 4-5, V ref s the voltage loop reference, V0 s the nverter output voltage, K s the gan of the three phase full brdge crcut, G () s and PWM G () s respectvely are the voltage loop and current loop controllers, 0 s the output current of the nverter and c s the capactve feedback sgnal. v V ref G v (s) (s) G 1 KPWM Ls r L 1 Cs V o o Fgure 4: Voltage and current dual loop control block dagram. ref K p V o 1 L KPWM Ls r o C Fgure 5: Current loop block dagram. To make sure the nner current loop has a better trackng performance under dfferent 1 load condtons, the nner current loop cut off frequency s chosen as fb fs [31]. The mpact 5 of the load current o s neglected. Current loop closed loop block dagram s as shown n Fg. 5 and the transfer functon s gven by: ( ) ( ) G ( ) c s G s K PWM s ref ( s) Ls r G (s) KPWM (14) From equaton (14) the ampltude frequency characterstcs of the transfer functon s: 8

10 G ( j) KpKPWM 2 L 2 ( K K r ) 2 p PWM (15) Fg. 6. Current loop control parameter K p 2.5 s obtaned from the bode dagram as shown n Fgure 6: Bode dagram of the current loop. Vref K G () s 1 v K pv s Cs V o Fgure 7: Voltage loop block dagram. In order to avod mutual couplng on the voltage loop and current loop, the cut off frequency of the voltage loop should be less than half of the current loop bandwdth. Hence, voltage loop cutoff frequency s chosen as 800 Hz [31]. From the voltage loop closed loop block dagram as shown n the Fg. 7, the transfer functon s obtaned as: K ( K v pv ) G ( s) G () s v s K Cs ( K v pv ) G ( s) s (16) In equaton (16), at frst, ntegral coeffcent K v s set to 0; the outer voltage cut-off frequency s set to 800 Hz; K pv s obtaned as 0.6. In order to ensure that the system bandwdth 9

11 s wthn the requred range, the selected system bandwdth s f vb = 810 Hz, then K v =290 s obtaned. Voltage loop bode dagram as shown n the Fg. 8. Fgure 8: Bode dagram of the voltage loop. The nverter output mpedance transfer functon s gven by: Z () o s A s A s A s A s A s A A L, A r K K, A LC, A K K C rc, 1 2 p pwm 3 4 p pwm A K K K 1, A K K K. 5 p pwm pv 6 p pwm v (17) (18) Due to the presence of the output flter nductor and nductve components of the devce parameters, the equvalent output mpedance of the nverter s generally consdered nductve. But, equvalent output mpedance of the closed loop of nverter has a relatonshp wth control strategy adopted [22], [27] by adjustng the nverter control parameters. The equvalent output mpedance of the DG nverters can be changed to resstve or nductve. (a) Bode dagram of nverter output mpedance wth dfferent K pv. 10

12 (b) Bode dagram of nverter output mpedance wth dfferent K v. (c) Bode dagram of nverter output mpedance wth dfferent K p. Fgure 9: Bode dagram of nverter output mpedance wth dfferent parameters varaton K pv, K v and K p. Fg. 9(a) shows that the voltage loop proportonal factor has some nfluence on the DG nverter output mpedance. When K pv 0, the nverter output mpedance at 50 Hz s more nductve. Wth the ncreasng resstve. K pv value the DG nverter output mpedance at 50 Hz s more Fg. 9(b) shows that the voltage loop ntegral factor has some nfluence on the nverter output mpedance. When K =0, the nverter output mpedance at 50 Hz s approxmately more resstve, wth ncreasng capactve. v K v the output mpedance of the DG nverter at 50 Hz s more 11

13 Takng K p =0.1, 2, 20, 50 the DG nverter output mpedance at 50 Hz s as shown n Fg. 9(c). The current loop proportonal coeffcent has lttle effect on the output mpedance nature of DG nverters. Based on the PI control parameters obtaned from the bode dagram n the Fg. 6 and 8, K pv =0.6, K v =290, K p =2.5. The output mpedance of the DG nverters are calculated usng equaton (19). The output mpedance angle at 50 Hz s 83 as shown n the Fg. 10. In ensurng the stablty of the mcrogrd system, the DG nverters output mpedance s approxmated as nductve for P-f/Q-V droop control and resstve for the P-V/Q-f droop control. If the DG nverter closed loop output mpedance desgn s reasonable, t can reduce the mpact of lne mpedance mbalance. Dfferent values of the system parameters of the DG nverters output mpedance magntude and angle has a drect mpact on power sharng. To further reduce the effect of DG nverter output mpedance and lne mpedance effect on the parallel DG nverters, vrtual resstors and nductors are added to the control loop, so that DG nverter output mpedance nature s changed to nductve for the P-f/Q-V droop control and resstve for the P- V/Q-f droop control. 3.2 Vrtual mpedance desgn for DG nverters Fgure 10: Bode dagram of DG nverter output mpedance. Vrtual mpedance control has become a necessary condton for mult voltage source nverter operated n parallel for normal operaton n the mcrogrd system [21], [26]. Equvalent output mpedance of the DG nverters s affected by multple factors, flter parameters, voltage and current control loop parameters, the dfferences of these factors led to nconsstences of power sharng between the parallel DG nverters. Vrtual mpedance block dagram as shown n Fg. 11 and s gven by [25], [29]. V V ref ref Zvro (19) 12

14 V ( ) ( ) o G s Gv s Vref [ G ( s) Gv ( s) Z vr ( s) Zo( s)] o (20) V ref V ref G v (s) (s) G 1 Ls r KPWM L o 1 Cs V o Zvr () s Vrtual nductor s expressed as [16]: Fgure 11: Vrtual mpedance control block dagram. Z sl, Z ( s) vr v o B s B s B s B s B s B (21) B L L K K K 1 2 B LC, B K K C rc v p pwm pv B r K K L K K K B K K K p pwm v p pwm v p pwm v B K K K p pwm v p pwm (22) Fgure 12: Bode dagram of nverter output mpedance wth vrtual nductor. 13

15 If the lne mpedance s nductve, vrtual nductors are added the control loop of the P- f/q-v droop control to mprove the power decouplng effect. Impedance angle at 50 Hz s 88 as shown n the Fg. 12. The parallel nverter output mpedance tends to more nductve, whch has a major role n mprovng the power sharng. Vrtual resstor s expressed as [29]: C s C s C Zvr ( s) Rv, Zo( s) C s C s C s C C L, C r K K K R, C R K K K, C LC 1 2 p pwm pv v 3 v p pwm v 4 C rc K K C, C 1 K K K, C K K K 5 p pwm 6 p pwm v 7 p pwm v (23) (24) Fgure 13: Bode dagram of nverter output mpedance wth vrtual resstor. If the lne mpedance s resstve, vrtual resstor s added the control loop of P-V/Q-f droop control to mprove the power decouplng effect. Impedance angle at 50 Hz s 1.9 as shown n the Fg. 13. The parallel nverter output mpedance tend to be more resstve, whch has a major role n mprovng the power sharng. 3.3 Droop controllers wth frequency and voltage restoraton secondary control In the sland type mcrogrds wth tradtonal P-f/Q-V andp-v/q-f droop control, when the load power fluctuates, the output voltage and frequency of the nverter wll have a large devaton. Vrtual mpedance control provdes decouplng of actve and reactve power for parallel DG nverters, but the vrtual mpedance method nevtably leads to a voltage drop n the mcrogrd system. In order to ensure the qualty of the voltage and hgh precson dstrbuton of 14

16 actve and reactve power, the ntroducton of voltage, frequency and actve power secondary adjustment, so that the voltage and frequency to mantan the rated output, actve and reactve power reasonable dstrbuton. Each nverter unt ncludes reverse droop control and secondary adjustment, wthout the need for a central controller, enhancng system stablty. When the load actve power ncrease to cause the voltage ampltude drop, through the voltage secondary adjustment control to restore the voltage to the rated value. When the load reactve power ncrease to cause the frequency to decrease, the frequency s restored to the rated value by the frequency adjustment. Voltage ampltude and frequency varatons of DG nverters s mproved by proposng secondary control for P-f/Q-V and P-V/Q-f droop control as shown n the Fg The ntroducton of the feedback lnk to acheve the nverter output frequency and voltage ampltude compensaton, so as to mprove the system adaptablty and stablty [17]. The expresson for P-f/Q-V droop control s gven by: m f f ( P P) K aps Ka 1 m s n V Vo Q K aps Ka 1 n s (25) (26) The expresson for P-V/Q-f droop control s gven by: n V Vo ( P P) K bps Kb 1 n s m f f Q K bps Kb 1 m s (27) (28) 15

17 P Q P m f m n Feedback lnk of frequency f V o PI 2 s Feedback lnk of Voltage n PI V o f V f Current and voltage dual loop V ref Fgure 14: Block dagram of secondary control wth P-f/Q-V droop control. P P n V o Feedback lnk of Voltage n PI V o Feedback lnk of Frequency m PI f f V Current and voltage dual loop Vref Q m f 2 s f Fgure 15: Block dagram of secondary control wth P-V/Q-f droop control. In equatons (6), (7), (8) and (9), the frequency dfference f f and the voltage dfference V V o as the feedback sgnal wth PI control to modfy the P-f/Q-V and P-V/Q-f droop coeffcents of the feedback lne to form a mproved droop control method. Adjustng the proportonal coeffcent Kap, Kbp and the ntegral coeffcent K a, K b of the PI control to 16

18 compensate the nfluence of the output voltage varaton of the parallel DG nverters n mcrogrd. The coeffcents m and n are the amplfcaton correcton droop coeffcents, manly to amplfy the feedback part of the voltage and frequency compensaton, because the orgnal feedback coeffcent m and n are too small. 4. Smulaton Results In ths secton, two smulaton models of dstrbuted generaton nverters connected n parallel are bult to verfy the proposed P-f/Q-V and P-V/Q-f mproved droop control strategy wth resstve and nductve lne mpedance to ensure the ratonal allocaton of power between parallel nverters. The smulaton parameters are shown n the Table 1 ( Refer Appendx A). Case 1:Power sharng analyss of P-f/Q-V,P-V/Q-f droop control under resstve lne mpedance. Fgure 16: Actve power sharng usng P-f/Q-V droop control under resstve lne mpedance. Fgure 17: Reactve power sharng usng P-f/Q-V droop control under resstve lne mpedance. 17

19 Fgure 18: Actve power sharng usng P-V/Q-f droop control wth vrtual resstor under resstve lne mpedance. Fgure 19: Reactve power sharng usng P-V/Q-f droop control wth vrtual resstor under resstve lne mpedance. Fgure 20: Parallel nverter output frequency usng P-V/Q-f droop control wth vrtual resstor under resstve lne mpedance. 18

20 Fgure 21: Parallel nverter output voltage usng P-V/Q-f droop control wth vrtual resstor under resstve lne mpedance. Power sharng of parallel nverters s nvestgated wth common load of Pload = 1000 W, Qload = 30 VAR and at 0.5 s sudden local load value of Pload = 900 W, Qload = 30 VAR s added to verfy the dynamc response and lne mpedance of R1Lne jx1lne = 0.5+j0.001 Ω, R2Lne jx2lne = 0.6+j0.002 Ω. Intally P-f/Q-V droop control s appled to the parallel DG nverters and output power of parallel DG nverters does not reach to a gven proportonal load sharng, because of the poor decouplng of power as shown n the Fg When the lne mpedance s resstve P-f/Q-V droop control cannot realze the proportonal load sharng of actve and reactve powers. Now wth the same parameters, P-V/Q-f droop control based on vrtual resstors can reduce the nfluence of the lne mpedance dfference on the parallel nverters by settng the total output mpedance of the DG nverters to be resstve, whch mproves decouplng of power and realze the proportonal load sharng P1=491 W, P2=489 W, Q1=25 VAR, Q2=23 VAR and at load change at 0.5 s, P1=932 W, P2=928 W, Q1=55 VAR, Q2=52 VAR as shown n the Fg and frequency varaton of DG nverters s wthn the range of Hz to Hz, the maxmum fluctuaton of Hz as shown n the Fg. 20. Voltage varaton of DG nverters s V1=310.5 V, V2=309.5 V as shown n the Fg. 21. Thus, the P-V/Q-f droop control wth vrtual resstors ensures that the voltage change s not greater than 5% and the frequency change s not greater than 1%. Ths establshes the fact that better accuracy and effectveness s acheved n the mcrogrd system. Case 2: Power sharng analyss of Secondary control wth P-V/Q-f droop control under resstve lne mpedance 19

21 Fgure 22: Actve power sharng usng secondary control wth vrtual resstor under resstve lne mpedance. Fgure 23: Reactve power sharng usng secondary control wth vrtual resstor under resstve lne mpedance. Fgure 24: Parallel nverter output frequency usng secondary control wth vrtual resstor under resstve lne mpedance. 20

22 Fgure 25: Parallel nverter output voltage usng secondary control wth vrtual resstor under resstve lne mpedance. Power sharng of parallel nverters s nvestgated wth common load of Pload = 1000 W, Qload = 30 VAR and at 0.5 s sudden local load value of Pload = 900 W, Qload = 30 VAR s added to verfy the dynamc response and lne mpedance of R1Lne jx1lne = 0.5+j0.001 Ω, R2Lne jx2lne = 0.6+j0.002 Ω. P-V/Q-f droop control based on vrtual resstors wth secondary control can reduce the nfluence of the lne mpedance dfference on the parallel nverters by settng the total output mpedance of the DG nverters to be resstve, whch mproves decouplng of power and mproves the proportonal load sharng P1=497 W, P2=496 W, Q1=28 VAR, Q2=27 VAR and at load change at 0.5 s, P1=943 W, P2=942 W, Q1=56 VAR, Q2=54 VAR as shown n the Fg and frequency varaton of DG nverters s wthn the range of Hz to Hz, the maxmum fluctuaton of Hz as shown n the Fg. 24. Voltage varaton of DG nverters s V1=311.1 V, V2=310.9 V as shown n the Fg. 25. Thus, the proposed secondary control for P-V/Q-f droop control, ensures voltage ampltude and frequency are restored to the rated value of 50 Hz and 311 V. Case 3:Power sharng analyss of P-f/Q-V,P-V/Q-f mpedance. droop control under nductve lne 21

23 Fgure 26: Actve power sharng usng P-V/Q-f droop control under nductve lne mpedance. Fgure 27: Reactve power sharng usng P-V/Q-f droop control under nductve lne mpedance. Fgure 28: Actve power sharng usng P-f/Q-V droop control wth vrtual nductor under nductve lne mpedance. 22

24 Fgure 29: Reactve power sharng usng P-f/Q-V droop control wth vrtual nductor under nductve lne mpedance. Fgure 30: Parallel nverter output frequency usng P-f/Q-V droop control wth vrtual nductor under nductve lne mpedance. 23

25 Fgure 31: Parallel nverter output voltage usng P-f/Q-V droop control wth vrtual nductor under nductve lne mpedance. Power sharng of parallel nverters s nvestgated wth common load of Pload = 1200 W, Qload = 25 VAR and at 0.5 s sudden local load value of Pload = 600 W, Qload = 25 VAR s added to verfy the dynamc response and lne mpedance of R1Lne jx1lne = j0.2 Ω, R2Lne jx2lne = j0.3 Ω. Intally P-V/Q-f droop control s appled to the parallel DG nverters and output power of parallel DG nverters does not reach to a gven proportonal load sharng, because of the poor decouplng of power as shown n the Fg When the lne mpedance s nductve P-V/Q-f droop control cannot realze the proportonal load sharng of actve and reactve power. Now wth the same parameters P-f/Q-V droop control wth vrtual nductors can reduce the nfluence of lne mpedance dfference on the parallel DG nverters by settng the total output mpedance of the DG nverters to be nductve, whch mproves decouplng of power and realze the proportonal load sharng P1=591 W, P2=589 W, Q1=21VAR, Q2=19 VAR and at load change at 0.5 s, P1=882 W, P2=878 W, Q1=42 VAR, Q2=38 VAR as shown n the Fg and frequency varaton of DG nverters s wthn the range of Hz to Hz, the maxmum fluctuaton of Hz as shown n the Fg. 30. Voltage varaton of DG nverters s V1=310.6 V, V2=309.6 V as shown n the Fg. 31. Thus, P- V/Q-f droop control wth vrtual nductors ensures that the voltage change s not greater than 5%, the frequency change s not greater than 1% and establshed a better accuracy and effectveness n the mcrogrd system. Case 4:Power sharng analyss of Secondary control wth P-f/Q-V droop control under nductve lne mpedance. 24

26 Fgure 32: Actve power sharng usng secondary control wth vrtual nductor under nductve lne mpedance. Fgure 33: Reactve power sharng usng secondary control wth vrtual nductor under nductve lne mpedance. Fgure 34: Parallel nverter output frequency usng secondary control wth vrtual nductor under nductve lne mpedance. 25

27 Fgure 35: Parallel nverter output voltage usng secondary control wth vrtual nductor under nductve lne mpedance. Power sharng of parallel nverters s nvestgated wth common load of Pload = 1200 W, Qload = 25 VAR and at 0.5 s sudden local load value of Pload = 600 W, Qload = 25 VAR s added to verfy the dynamc response and lne mpedance of R1Lne jx1lne = j0.2 Ω, R2Lne jx2lne = j0.3 Ω. P-f/Q-V droop control based on vrtual nductors wth secondary control can reduce the nfluence of lne mpedance dfference on the parallel DG nverters by settng the total output mpedance of the DG nverters to be nductve, whch mproves decouplng of power and mproves the proportonal load sharng P1=597 W, P2=596 W, Q1=23 VAR, Q2=22 VAR and at load change at 0.5 s, P1=894 W, P2=892 W, Q1=46 VAR, Q2=44 VAR as shown n the Fg and frequency varaton of DG nverters s wthn the range of Hz to Hz, the maxmum fluctuaton of Hz as shown n the Fg. 34. Voltage varaton of DG nverters s V1=311.1 V, V2=310.9 V as shown n the Fg. 35. Thus, the proposed secondary control for P-f/Q-V droop control, ensures voltage ampltude and frequency are restored to the rated value of 50 Hz and 311 V. Case 5: Power sharng analyss of Secondary control wth P-V/Q-f droop control under resstve lne mpedance usng dfferent ratngs DG nverters. 26

28 Fgure 36: Actve power sharng usng secondary control wth dfferent DG ratngs under resstve lne mpedance. Fgure 37: Reactve power sharng usng secondary control wth dfferent DG ratngs under resstve lne mpedance. Fgure 38: Parallel nverter output frequency usng secondary control wth dfferent DG ratngs under resstve lne mpedance. 27

29 Fgure 39: Parallel nverter output voltage usng secondary control wth dfferent DG ratngs under resstve lne mpedance. Power sharng of parallel nverters s nvestgated wth common load of Pload = 1400 W, Qload = 80 VAR and at 0.5 s sudden local load value of Pload = 600 W, Qload = 80 VAR s added to verfy the dynamc response and lne mpedance of R1Lne jx1lne =0.5+j0.001 Ω, R2Lne jx2lne = 0.6+j0.002 Ω. P-V/Q-f droop control based on vrtual resstors wth secondary control can reduce the nfluence of the lne mpedance dfference on the parallel nverters by settng the total output mpedance of the DG nverters to be resstve, whch mproves decouplng of power and mproves the proportonal load sharng P1=697 W, P2=696 W, Q1=38 VAR, Q2=37 VAR and at load change at 0.5 s, P1=994 W, P2=992 W, Q1=76 VAR, Q2=74 VAR as shown n the Fg and frequency varaton of DG nverters s wthn the range of Hz to 50 Hz, the maxmum fluctuaton of Hz as shown n the Fg. 38. Voltage varaton of DG nverters s V1=311 V, V2= V as shown n the Fg. 39. Thus, the proposed secondary control for P-V/Q-f droop control wth dfferent DG ratngs under resstve lne mpedance, ensures voltage ampltude and frequency are restored to the rated value of 50 Hz and 311 V. Case 6: Power sharng analyss of Secondary control wth P-f/Q-V droop control under nductve lne mpedance usng dfferent ratng DG nverters. 28

30 Fgure 38: Actve power sharng usng secondary control wth dfferent DG ratngs under nductve lne mpedance. Fgure 39: Reactve power sharng usng secondary control wth dfferent DG ratngs under nductve lne mpedance. Fgure 40: Parallel nverter output frequency usng secondary control wth dfferent DG ratngs under nductve lne mpedance. 29

31 Fgure 41: Parallel nverter output voltage usng secondary control wth dfferent DG ratngs under nductve lne mpedance. Power sharng of parallel nverters s nvestgated wth common load of Pload = 1300 W, Qload = 60VAR and at 0.5 s sudden local load value of Pload = 600 W, Qload = 60VAR s added to verfy the dynamc response and lne mpedance of R1Lne jx1lne = j0.2 Ω, R2Lne jx2lne = j0.3 Ω. P-f/Q-V droop control based on vrtual nductors wth secondary control can reduce the nfluence of lne mpedance dfference on the parallel DG nverters by settng the total output mpedance of the DG nverters to be nductve, whch mproves decouplng of power and mproves the proportonal load sharng P1=647W, P2=646W, Q1=28VAR, Q2=27VAR and at load change at 0.5 s, P1=944W, P2=942W, Q1=56VAR, Q2=54 VAR as shown n the Fg and frequency varaton of DG nverters s wthn the range of 49.99Hz to 50Hz, the maxmum fluctuaton of Hz as shown n the Fg. 40. Voltage varaton of DG nverters s V1=311.1 V, V2=310.9 V as shown n the Fg. 41. Thus, the proposed secondary control for P-f/Q-V droop control wth dfferent DG ratngs under resstve lne mpedance, ensures voltage ampltude and frequency are restored to the rated value of 50Hz and 311V. 30

32 Appendx A Table 1: Parameters of Parallel DG nverters(3kva Ratng) Symbol Value Descrpton f s 10 khz Inverter swtchng frequency. L 4 mh Flter nductor. C 10 µf Flter capactor. r 0.1 Ω Flter nductor equvalent resstance. V dc 700 V DC lnk voltage. f 50 Hz Fundamental frequency. R v 1 Ω Vrtual resstors. L v 5 mh Vrtual nductors. m 1,m 2 n 1,n rad/s/w, V/VAR P-f/Q-V droop coeffcents. n 1,n 2 m 1,m 2 m, 1 m V/W, P-V/Q-f droop coeffcents rads/var rad/s/w, Improved P-f/Q-V droop coeffcents. n, 1 n V/W, Improved P-V/Q-f droop coeffcents. V o 311 V Output voltage of nverter(mcrogrd system voltage). K ap, K a 0.8, 20 PI control parameter for mproved P-f/Q-V droop control. K bp, K b 0.8, 20 PI control parameter for mproved P-V/Q-f droop control. Table 2: Electrcal parameters of dfferent lnes Type of lne R(Ω/Km) X(Ω/Km) R/X Low voltage lne Medum voltage lne Hgh voltage lne

33 Table 3: Parameters of Parallel DG nverters(3kva, 9KVA Ratng) Symbol Value Descrpton f s 10 khz Inverter swtchng frequency. L 7mH Flter nductor. C 20 µf Flter capactor. r 0.2 Ω Flter nductor equvalent resstance. V dc 700 V DC lnk voltage. f 50 Hz Fundamental frequency. R v 2 Ω Vrtual resstors. L v 6 mh Vrtual nductors. m 1 m 2 n 1 n rad/s/w, rad/s/w, V/VAR, V/VAR. P-f/Q-V droop coeffcents. n 1, n 2 m 1 m 2 m, 1 m V/W, P-V/Q-f droop coeffcents V/VAR, rad/s/var, rad/s/w rad/s/w,0.05rad/s/w. Improved P-f/Q-V droop coeffcents. n, 1 n V/W,0.2 V/W Improved P-V/Q-f droop coeffcents. V o 311 V Output voltage of nverter(mcrogrd system voltage). K ap, K a 1.2, 25 PI control parameter for mproved P-f/Q-V droop control. K bp, K b 1.4, 28 PI control parameter for mproved P-V/Q-f droop control. 5. Concluson In ths paper, analyss of mproved P-f/Q-V and P-V/Q-f droop control wth secondary control for DG parallel nverters n mcrogrd s proposed consderng lne and output mpedance. Proportonal ntegral controller s adopted to ensure accurate trackng of the output voltage of the nverter to the reference value and the nfluence of the controller parameters on the voltage closed loop transfer functon and the equvalent output mpedance of the nverter s analyzed. In order to match the total output mpedance of the nverter and lne mpedance n parallel, the P- V/Q-f and P-f/Q-V droop control strategy based on the nductve and resstve vrtual mpedance s adopted to mprove the total output mpedance of the nverter through the vrtual mpedance. The proposed P-f/Q-V and P-V/Q-f droop control,adaptvely compensates the vrtual resstor and nductor voltage drop to mprove output voltage ampltude accuracy to the reference value. Smulaton results show the ratonalty and effectveness of the proposed mproved control method. 32

34 6. References [1] Guerrero J M, Blaabjerg F, Zhelev T, Hrmmer K, Monmasson E, Jeme S, Comech, Frau J I. Dstrbuted generaton: towards a new energy paradgm. IEEE Industral electroncs magazne, 2010, 1(4): [2] Chowdhury A A S, Agarwal K, Dono Koval. Relablty modelng of dstrbuted generaton n conventonal dstrbuton systems plannng and analyss. IEEE Transactons on ndustry applcatons, 2003, 39(5): [3] Furkan A, Mohammad S A. Feasblty study,desgn and mplementaton of smart polygeneraton mcrogrd at AMU. Internatonal journal of Sustanable ctes and socety,2017,35: [4] Nayanar V, Kumaresan N, Gounden N G A.Wnd drven SEIG supplyng DC mcrogrd through a sngle stage power converter. Internatonal journal of engneerng Scence and technology, 2016,19(3): [5] Lasseter R H. Mcrogrds. In: Proceedngs of Power Engneerng Socety Wnter meetng, 2002, [6] Chengshan W, Zhangang Y, Shouxang W, Yanbo C. Analyss of structural characterstcs and control approaches of expermental mcrogrd systems. Automaton of Electrc Power Systems, 2010, 34(1): (n Chnese). [7] Zhang L, Wu T, Xng Y, K. Sun, Guerrero J M. Power control of dc mcrogrd usng dc bus sgnalng. IEEE Twenty-sxth Appled power electroncs conference and exposton, 2011, 1-7. [8] Wu T F, Chen Y K, Huang Y H. 3C strategy for nverters n parallel operaton achevng an equal current dstrbuton. IEEE Transactons on Industral Electroncs, 2000, 47(2): [9] Guerrero J M, Hang L, Uceda J. Control of dstrbuted unnterruptble power supply systems. IEEE Transactons on Industral Electroncs, 2008, 55(8): [10] Y Pe, Jang, X Yang, Z Wang. Auto master slave control technque of parallel nverters n dstrbuted AC power systems and UPS. In: Proceedngs of IEEE PESC, 2004, [11] Chandorkar M C, Dvan D M, Adapa R. Control of parallel connected nverters n standalone ac supply systems. IEEE Transactons on Industry Applcatons, 1993, 29(1): [12] Guerrero J M, Chandorkar M C, Lee T L, Loh P C. Advanced control archtectures for ntellgent mcrogrds-part-i: Decentralzed and Herarchcal control. IEEE Transactons on Industral Electroncs, 2013, 60(4): [13] Guerrero J M, Vcuna L G de, Matas J, Castlla M, Mret J. A wreless controller to enhance dynamc performance of parallel nverters n dstrbuted generaton systems. IEEE Transactons on Power Electroncs, 2004, 19(5): [14] Vandoorn T L, DeKoonng J D M, Meersman B, Guerrero J M, Vandevelde L. Automatc power sharng modfcaton of P/V droop controllers n low voltage resstve mcrogrds. IEEE Transactons on Power Electroncs, 2012, 27(4): [15] Yao L, Hua H, Me S, Yao S, Hubn C, X L. A control strategy of reactve power sharng for parallel dstrbuted mcrosources. Journal of Central South Unversty, 2015, 46(2): [16] Hang H, Lu Y, Sun Y, Su M, Guerrero J M. An mproved reactve power sharng n slanded mcrogrd. IEEE Transactons on Power Electroncs, 2015, 30(6): [17] Qmng C, Syuan C, Ynman C, Xaolong Y, Qang Z. Multple master slave mxed coordnated control for mcrogrd based on mproved droop control. Automaton of electrc power systems, 2016, 40(20): (n Chnese). [18] Wu T, Lu Z, Lu S W, You Z. A unfed vrtual power decouplng method for droop controlled parallel nverters n mcrogrds. IEEE Transactons on Power Electroncs, 2016, 31(8): [19] Xaofeng S, Juan W, Yanjun T, L Xn. Control of DG connected nverters based on self adaptable adjustment of droop coeffcent. Proceedngs of the CSEE, 2013, 33(36): (n Chnese). [20] Guerrero J M, Vcuna L G, Mata J. Output mpedance desgn of parallel connected ups nverters wth wreless load sharng control. IEEE Transactons on Industral Electroncs, 2005, 52(4): [21] Xongfe Wang, Yun We Le, Frede Blaabjerg, Poh chang Loh. Vrtual mpedance based control for voltage source and current source converters. IEEE Transactons on Power Electroncs, 2015, 30(12): [22] Chengshan W, Zhaoxa X, Shouxang W. Multple feedback loop control scheme for nverters of the mcrosource n mcrogrds. Transactons of Chna Electro Techncal socety, 2009, 24(2): (n Chnese). [23] Brabandere K D, Bolsens B, Van J. A voltage and frequency droop control method for parallel nverters. IEEE Transactons on Power Electroncs, 2007, 22(4),

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