TRANSACTIONS ON ENVIRONMENT AND ELECTRICAL ENGINEERING ISSN 2450-5730 Vol 1, No 4 (2016) © Urvi N. Patel and Hiren H. Patel  Abstract— In many countries, the grid-code or standards do not allow the Photovoltaic (PV) inverters to exchange reactive power with the grid. Recently, some countries have relaxed the standards. Hence, capacity of the inverters to control reactive power must be utilized. However, the reactive power that a PV inverter can supply is constrained by the maximum power that a PV array generates and changes with the environmental conditions. A reactive power sharing algorithm is proposed that not only ensures proper distribution of reactive power amongst the inverters, but also ensures that the maximum power generated by PV is supplied to the grid. In case of identical PV inverters, the algorithm operates all inverters at nearly equal apparent power leading to nearly equal percentage utilization of the inverters, thereby achieving uniform heating of the similar devices of the inverters. The algorithms are further investigated for power sharing amongst PV inverters of unequal ratings. It is highlighted that the proposed algorithm results into the least change in the utilization factor of a PV inverter, whose power changes due to the change in environmental conditions. The effectiveness of the algorithm over other algorithms in sharing power amongst inverters is displayed through MATLAB/Simulink simulations. Keywords — Photovoltaic, Reactive power, Power sharing. I. INTRODUCTION Last couple of decades have experienced significant rise in the electricity generation from non-conventional energy sources like wind and solar. It is attributed mainly by the increased environmental concern, fast depletion of conventional energy sources, increase in cost of conventional energy sources, and decrease in the cost of renewable based energy generation. In recent years, one of the renewable sources that has seen the fastest growth and penetration in the electrical grid is the solar photovoltaic (PV). The reason for the increase in penetration is the reduced cost of PV system and the encouraging feed-in-tariff policies by the governments. However, increased penetration of PV sources has also given rise to several challenges. The challenges are mainly due to the dependence of PV source’s performance on the environment, which makes it intermittent and uncertain in nature. PV source is connected to the grid through the static power converters [1]. Thus, it is inertia-less source of energy unlike the conventional rotational generators. Hence, if the energy generation in the grid is highly dominated by inertia-less PV (i.e. in a weak grid), the sudden change in output power of PV resulting from the sudden change in irradiation, may affect the stability of grid and the systems connected with the utility. Also, if the power electronic U. N. Patel is with Department of Electrical Engineering, C. K. Pithawala College of Engineering and Technology, Surat, India. (email: urvi.patel@ckpcet.ac.in). converters are not controlled appropriately in such weak electrical grid or a microgrid (MG), they are likely to create issues like harmonic injection, change in voltage levels and power flow, flicker, resonance, mal-operation of protection scheme etc. On the contrary, if the power electronic converters are properly controlled [2]-[3], they can improve the voltage profile and performance of the MG. This can be achieved if PV systems, which are usually commissioned to supply active power, are allowed to inject desired reactive power into the grid. PV systems are usually designed with reasonable margins, and most of the times operate under lightly loaded conditions (in fact inactive at night time). Thus, there is a room for reactive power injection to keep the voltage at a desirable level. This objective, along with the transfer of maximum power generated by PV, can be achieved by controlling the amplitude and phase angle of the output voltage of the inverter. The task becomes challenging when several such PV based distributed energy generators are operating in a MG, which even comprises of other types of renewable energy sources. PV inverters are commonly controlled as current controlled source using P-Q control strategy to exchange active and reactive P and Q respectively, with the microgrid [4]. In islanding mode i.e. when main grid is disconnected, the voltage V and frequency ω are controlled, using P-ω and Q-V droop control methods to share active and reactive power amongst the distributed generators (DG) [5]-[7]. Battery storage is essential in such system when islanded, in order to maintain power balance in the system. Lasseter et al., have presented flexible control and proper coordination amongst DG sources to overcome some problems associated with PV and other non-conventional sources operating simultaneously in a MG [3]. Local power management system for coordination of various DG sources to manage active and reactive power successfully is addressed in [8]-[10]. In [8], fundamental algorithm employing hierarchical droop control of power management is presented, where inverter control is considered as primary control whereas Microgrid Central Controller (MGCC) is under secondary control. Secondary control focuses on power management and optimization algorithm to optimize performance of MG. Power management system plays very important role when MG is having many PV connected inverters, as rapidly varying irradiation condition may cause voltage sags and swells that result in degradation of power quality [16]-[20]. To regulate voltage under such transient condition, PV inverters must have H. H. Patel is with the Department of Electrical Engineering, Sarvajanik College of Engineering & Technology, Surat, India. (e-mail: hiren.patel@scet.ac.in). Power Sharing Strategy for Photovoltaic based Distributed Generators Operating in Parallel Urvi N. Patel and Hiren H. Patel the capability to match-up the VAR requirement quickly [11]. As active power delivered by inverter depends on maximum power that PV can generate under given (environmental) conditions, it is necessary to allocate reactive power amongst inverters in a proper way to have uniform loading of the inverters and to also avoid over loading of inverters [12]. An accurate reactive power sharing control that shares reactive power equally amongst inverters is presented [13]. Total reactive power of the system is calculated by MGCC and the information is passed to all inverters through communication link. Though this method shares reactive power accurately amongst the inverters, in case when active power varies with the change in irradiation, it fails to accurately share the reactive power amongst the PV inverters. It may also cause inverter to work beyond its nominal apparent power transfer capability. In [14], reactive power algorithm is presented which takes into account apparent power limit of each PV connected inverter as well as active power delivered by each PV inverter. Optimal reactive power strategy [15] assigns reactive power to each inverter such that entire system can achieve maximum reactive power transfer capability. However, these algorithms are unable to uniformly utilize apparent power capability of each inverter. The paper proposes an approach to overcome these drawbacks. The proposed reactive power algorithm first determines the active power that PV inverters are supplying under given conditions and based on the available margin it assigns the reactive powers to the inverters. Section II introduces system configuration and control scheme employed for operating PV inverters while the secondary control algorithm implemented in MGCC for accurate reactive power sharing is presented in section III. The results of the simulation study performed in MATLAB/Simulink are included in section IV to demonstrate the performance of algorithm for PV inverters operating in parallel for two different cases: (i) all inverters with equal ratings and (ii) inverters with unequal ratings. II. SYSTEM DESCRIPTION AND CONTROL Fig.1 shows the system configuration considered for evaluation of the proposed algorithm. The microgrid comprises of four identical distributed energy generators that along with the main grid (or a relatively stiff source) supply the local loads. Each DG unit consists of PV as a primary energy source, a three phase inverter and an LC filter. The inverters not only extract the maximum power from the PV but also supply sinusoidal current to the load and grid. PVi shown in Fig. 1 represents a PV array with its dc-dc converter operated with maximum power point tracking control. The DGs are connected to the PCC through a transformer, which for the sake of simplicity, is not shown in Fig.1. Static Switch A.c Grid PCC S 1 = P 1 + jQ 1 L oa d Z04Z02 Z03Z01 S 2 = P 2 + jQ 2 S 3 = P 3 + jQ 3 S 4 = P 4 + jQ 4 MGCC PV2 PV3 PV4 PV1 Fig.1. System configuration of a Microgrid having four DGs The impedances Zoi, where ‘i’ represents i th DG, takes into account the impedance of interfacing inductor, the impedance of cable and isolation transformer. Active and reactive power management task is performed by MGCC unit using low bandwidth communication links. Microgrid hierarchical structure consists of mainly primary, secondary and tertiary control [10], [11]. Primary control covers inverters’ control present in microgrid whereas secondary control consists of MGCC unit. Tertiary control provides interaction between multiple microgrid and utility grid. Primary and secondary controls are used in this paper while tertiary control is not required at this stage. Inverter control is achieved by active-reactive power (P-Q) control method [4]. P-Q method is used to operate inverter as a controlled current source for desired active and reactive power transfer with grid. Inverter output current is tightly regulated by inner current control loop. Reference currents for current control loop are provided by outer power control loop according to power references provided by MGCC. Phase locked loop (PLL) used for grid synchronization provides desired angle (ρ) for abc to dq frame transformation. Fig.2 shows control circuit diagram for one of the inverters. Fig.3 shows the details of the power and current control loops shown in Fig. 2. The voltage Vdc, across capacitor C is maintained at a desired voltage, Vdcref by a voltage control loop. PV Grid C Inv-1 R L Cf SS PWM Gate Drive Current Control Loop abc/ dq abc/ dq ρ ρρ idq ρ ω Vdq PrefQref PCC Lg+ - Vdc iabc Vsabc Vdcref Power Control Loop idref iqref Vdc P PLL DC Bus Voltage Control PPV Q SS=Static Switch Fig. 2. Control scheme of PV inverter _ / PI _ PI / Lω0 PI +_ Lω0 + + + + +_ +_PI+ + + DC-Bus Voltage control Power control Current control loop + + Vdcref Vdc PPV Pref Qref P Q idref iqref id iq Vd Vq md mq PI- VDC 2 Fig.3. Active-reactive power control To maintain this voltage constant it is ensured that the power obtained from PV array, PPV is entirely transferred to the grid side. This is done through the power control loop, which compares actual DG output power (P) with reference power (Pref). The reactive power reference (Qref) is obtained using the algorithm presented in the next section. Pref and Qref are used to generate required current references idref and iqref for the current control loop. The direct and quadrature axes components of the inverter output currents id and iq, respectively, are obtained through d-q transformation. The current control loop finally determines the direct and quadrature components of the reference waveform from the direct and quadrature axes modulation indices, md and mq, respectively. III. PROPOSED REACTIVE POWER SHARING ALGORITHM As the active power that PV inverters supply is directly dependent on the environmental conditions (mainly irradiation), most of the times the inverters do not operate at their rating and hence, their capacity is not utilized fully. The available margin varies with the irradiation, with maximum at night or when irradiation is the least. The reactive power sharing algorithm shown in Fig. 4 relies on assigning the reactive power algorithm amongst the inverters based on the margin available with each of them. The algorithm starts with initializing the number of inverters (m) and the apparent ratings of the inverters (SiN), where ‘i’ stands for ith inverter. The output power of the PV systems (Pi) is obtained from the maximum power point tracker (MPPT), which ensures that the PV system operates at its maximum (active) power point. As the apparent power ratings (SiN) of the inverters are known and as the inverter must be operated to deliver active power (Pi) to the grid side, the available reactive power (Qi) is expressed as 22 iiNi PSQ  (1) The inverter is capable of supplying and drawing reactive power and it must match the load and grid requirements. Accordingly (2) and (3), assigns the reactive power limits for lagging and leading type of reactive demand, respectively. ii QQ max (2) ii QQ max (3) Hence, at a given instant, the total active power (PT), reactive power (QT) and apparent power (ST) capabilities that the inverters possess to match the reactive power demand of load and to supply the active power of PV systems to grid are represented by (4), (5) and (6), respectively.    m i iT PP 1 (4)    m i iT QQ 1 (5) 22 TTT QPS  (6) If output currents of all the inverters are equal, temperature of similar devices of the different inverters can be made equal. This can be realized if all the inverters operate with the same apparent power. Hence, the inverters are made to operate with the reference apparent power (STnew) to have uniform utilization and heating. ])1[( imSS TTnew  (7) The algorithm evaluates the condition expressed by (8), and if STnew exceeds SiN, the reference apparent and reactive powers are set to values SiN and Qimax (or Qimin), respectively. iNTnew SS  (8) The algorithm then assigns the reference reactive power Qiref and Pi for each inverter, where the active power references (Pi) for the inverters are obtained from the MPPT. Once any inverter is assigned the reference active and reactive powers, the total unassigned active and reactive powers to be supplied by the remaining inverters are updated by subtracting the Qiref and Pi assigned to the earlier inverters from PT and QD, where QD is the reactive power demand of the load. The remaining active power (PTn) to be supplied and reactive power demand to be met (QTn) is calculated as shown in (9), and (10), respectively.     1 0 i i iTTn PPP where 0 0 P (9)     1 0 i i irefDTn QQQ where 00 refQ (10) Accordingly, the apparent power (Si) that i th inverter must supply is obtained by (11)  imQPS TnTni  )1(/ 22 (11) Hence, the reference reactive power for the ith inverter is 22 iiiref PSQ  (12) IV. SIMULATION RESULTS To demonstrate the effectiveness of the above control strategy, microgrid system shown in Fig.1 is simulated in MATLAB/Simulink. In addition to the proposed control algorithm, two more control approaches: (optimal reactive power [15] and equal reactive power sharing [13]) are also evaluated and the results are compared with that obtained with the proposed control algorithm. Two different cases are considered for comparing the performance of this algorithm. Calculate PT & QT using(4) and (5) respectively Is i=i+1 Start YES 22 TTT QPS  ?iNTnew SS  Initialize SiN=Nom. Apparent power m=No. of PV inverters 22 PiSQ iNi  i=1 Is i=m ? NO YES B iNinew SS  iiref QQ  NO ])1[( imSS TTnew  Measure Pi=Active power of i th inverter 00 P 00 refQ Measure QD=Reactive power demand Calculate PTn ,QTn using (9) and (10) Calculate Si using (11) 22 iiiref PSQ  i=i+1 Is i=m ? END A A B C C NO YES i=1 Fig. 4. Proposed reactive power sharing algorithm In case (i), all the inverters are considered to have the equal ratings while in case (ii), inverters of unequal ratings are considered. Case (i): Equal DG ratings The parameters considered for evaluating the performance of the algorithms using the system of Fig. 1 are mentioned in TABLE I. As shown, all DGs are considered to have the equal nominal apparent power rating of 500 kVA. TABLE I RATINGS AND PARAMETERS FOR THE SYSTEM OF FIG.1 Nominal power rating of DG1 (S1N) 500 kVA Nominal power rating of DG2 (S2N) 500 kVA Nominal power rating of DG3 (S3N) 500 kVA Nominal power rating of DG4 (S4N) 500 kVA Grid voltage(Vg), Frequency(f) 415V, 50 Hz Line parameter (Z01=Z02=Z03=Z04) L=100µH,R=2.07mΩ,Cf=2500µF Load 1.92 MVA, 0.78 power factor (lag) No of PV inverters (m) 4 Fig. 5 shows the results with the optimal reactive power sharing (ORPS) algorithm. Reactive power references for inverters shown in TABLE II are calculated using the ORPS algorithm of [15], while the active power references for the inverters are set at the value equal to the maximum power that the corresponding PV system generates at a given instant. The active power generated by PV arrays PV1, PV2, PV3 and PV4 till t=0.5s are 400kW, 300kW, 250kW and 450kW, respectively. A step change in irradiation on PV array PV1 occurs at t=0.5s, which results in the output of PV1 to decrease to 200kW. At t=1s, step change in irradiation on PV array PV3 occurs, resulting into the change in the output power from 250kW to 400kW. Reactive power references for the inverters obtained with optimum reactive power control are mentioned in TABLE II. Fig. 5, shows active, reactive and apparent power of inverters 1 through 4. (a) (b) (c) Fig. 5. Results with ORPS algorithm: (a) active power fed by DGs, (b) reactive power shared by the inverters, (c) apparent power of each inverter. TABLE II UTILIZATION FACTOR OF EACH DG FOR ORPS ALGORITHM Time Interval (s) Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi t=0-0.5 400 300 500 1.00 300 373 478 0.95 250 310 398 0.79 450 218 500 1.00 t=0.5-1 200 262 329 0.65 300 392 493 0.98 250 325 410 0.82 450 218 500 1.00 t=1-2 200 282 345 0.69 300 400 500 1.00 400 300 500 1.00 450 218 500 1.00 0 0.5 1 1.5 2 0 100 200 300 400 500 P ( k W ) v P P P P 2 1 3 4 0.5 1 1.5 2 0 100 200 300 400 500 Q ( k V A R ) v Q Q Q Q 4 3 2 1 0.5 1 1.5 2 200 300 400 500 600 Time (s) S ( k V A ) v S S S S 1 3 4 2 1 It is observed from Figs. 5(a) and (b) that, when P1 is decreased from 400kW to 200kW at t=0.5s, Q1 changes from 300kVAR to 262kVAR. Not only Q1, but Q2 through Q4 also changes. Similarly at t=1s, when P3 increases to 400kW, Q1 through Q3 changes. Thus, if power generated by any one of the PV array changes, the reactive power references and hence, the reactive power supplied by all the inverters change (except those which are operating at their limits SiN). Fig. 5(c) shows that inverters 1 and 4 operate at their maximum apparent power limits (S1N and S4N, respectively) till t=0.5s. At t=0.5s, when P1 reduces, Q1 also reduces simultaneously and hence, from t=0.5s to t=0.1s only inverter 4 operates at its full capacity. It is observed that the change in Pi and Qi is such that the ratio Pi/Qi remains equal for all the inverters that do not reach the rated capacity. An index defined as utilization factor (Si/SiN) is used to indicate the extent to which the capacity of the inverter is utilized. It is also observed from the TABLE II that all the inverters are operating at different utilization factors. The utilization factors vary greatly showing that some of the inverters operate much below their rated capacity when some others have already hit their limits. For example, inverter-1 operates with the lowest utilization factor (0.65 from t=0.5s till 1s and 0.69 from t=1s till 2s) while inverter-4 is operating at its limit. The unequal utilization of the inverters, not only results into unequal losses, efficiency and heating of different inverters, but may damage the inverters that continuously operate at their apparent power limits. Fig. 6 shows the results obtained with equal reactive power sharing (ERPS) algorithm [13], according to which reactive power demand is equally shared amongst the inverters. The irradiation pattern on the PV array is considered the same as that considered for the evaluation of ORPS approach. Fig. 6 shows active, reactive and apparent powers respectively, of inverters 1 through 4. If it is intended to meet the total reactive power demand of the load mentioned in TABLE I (1200kVAR) through the inverters 1 through 4 using ERPS control, each inverter must output 300kVAR. Hence, the reference reactive power for inverter 1,2 and 3 are set equal to 300kVAR (reactive power demand of load = 1200kVAR) while for inverter- 4 which hits its apparent power limit, it is restricted to 218 kVAR. It is observed from Figs. 6(a)-(c), and TABLE III that, even if the active power supplied by the PV array changes, the effect is not observed in the reactive power sharing. It is also evident from Fig. 6(c) that inverter-4 continuously operates at its rated capacity of 500kVA. Inverters 1 and 3 also operate at their rated capacities for some time. It is also observed that Si (for i=1, 2 and 4) remains almost constant for t=0.5s to 2s inspite of the change in P3 at t=1s. The reason being no change in Pi and Qi (for i =1, 2 and 4) for this period. Unlike ORPS the reactive power demand of the load is not met fully inspite of the fact that many inverters still operate below their rated limits. Thus, the inverters are not utilized optimally and also the percentage utilization of all the inverters varies greatly. Fig.7 shows performance with proposed algorithm when same pattern of irradiation on the PV array as that considered for ORPS and ERPS is maintained. At t=0.5s, when the irradiation of PV1 decreases resulting into the decrease in the (a) (b) (c) Fig. 6. Results with ERPS algorithm: (a) active power fed by DGs, (b) reactive power shared by the inverters, (c) apparent power of each inverter (a) (b) (c) Fig. 7. Results with Proposed algorithm: (a) active power fed by DGs, (b) reactive power shared by the inverters, (c) apparent power of each inverter 0 0.5 1 1.5 2 0 100 200 300 400 500 P ( k W ) v P P P P 2 1 3 4 0.5 1 1.5 2 0 100 200 300 400 Q ( k V A R ) v Q Q Q Q 1 2 4 3 0 0.5 1 1.5 2 200 300 400 500 600 Time (s) S ( k V A ) v S S S S 1 2 3 4 0 0.5 1 1.5 2 0 100 200 300 400 500 P ( k W ) v P P P P 2 1 3 4 0.5 1 1.5 2 0 100 200 300 400 500 Q ( k V A R ) v Q Q Q Q 1 4 3 2 0.5 1 1.5 2 300 400 500 600 Time (s) S ( k V A ) v S S S S 1 2 3 4 output power of inverter 1, the reactive power of inverter 1 increases. Simultaneously, the reactive powers of all other inverters decrease in spite of the fact that there is no change in the power output from PV arrays PV2, PV3 and PV4. This results into minimizing the gap of percentage utilization of different inverters. Similarly, at t=1s when P3 changes from 250kW to 400kW, reactive power of all the inverters changes to achieve better sharing of the active and reactive power amongst them. TABLE IV shows the active, reactive and apparent powers shared by the inverters over the different periods. Unlike ORPS and ERPS, the utilization factors vary little for all the DGs indicating uniform loading of the inverters. The three algorithms are tested even with a different load having a leading power factor (PF). TABLE V shows the results obtained with a load of 1.16 MVA, 0.86 power factor (lead). It is observed that even with leading power factor, proposed algorithm performance is superior. Standard deviations of the utilization factors of the various inverters are calculated, to quantify the effectiveness of the algorithm to distribute the apparent power equally amongst the inverters. Standard deviations of the utilization factors for the three schemes for the case represented by TABLE V are 0.204, 0.147 and 0.055. The least the standard deviation better is the performance. Case (ii): Unequal DG ratings The three algorithms are also evaluated for the case when all DGs of the system shown in Fig. 1 have unequal ratings. The nominal ratings for the DGs are mentioned in TABLE VI. The load, line parameters, capacitance C and the grid voltage are considered same as that of case (i). In this case the active power generated by PV arrays PV1, PV2, PV3 and PV4 are 200kW, 300kW, 400kW and 500kW, respectively. A step increase in irradiation on PV array PV1 occurs at t=0.5s, which results in the output of PV1 to increase to 300kW. At t=1s, irradiation on PV array PV3 decreases suddenly, resulting into the change in its output power from 400kW to 200kW. The active, reactive and apparent power sharing by inverters 1 through 4 with ORPS control are displayed in Fig. 8 and the results are quantified in TABLE VII. Figs. 8(a) and (b) shows that when PV1 is increased from 200kW to 300kW at t=0.5s, Q1 also increases from 171kVAR to 240kVAR. Hence its apparent power increases, leading to its utilization factor of 0.96. The reactive powers of inverters 2 through 4 decrease with their active powers still at the same values. Thus, S2 through S4 decrease lowering the utilization of inverters 2 through 4. This increases the miss-match in the utilization factors. The miss-match further increases after t=1s, when the output power of PV3 decreases from 400kW to 200kW. The decrease in P3 at t=1s is associated with the simultaneous decrease in Q3. Hence, to meet the reactive power demand of the load, more reactive power needs to be supplied by inverters 1, 2 and 4. Hence, while the utilization factor of inverter-3 decreases, utilization factor of other inverter increases .Thus, inverter-3 is the least utilized inverter with utilization factor of 0.45 while inverter-1 is fully utilized with the utilization factor of 1.00. Fig. 5(c) also highlights that after t=1s, inverter-1 operates at its apparent power limit (S1N). It is observed from TABLE VII that the percentage change (decrease) in utilization factor of inverter-3 in response to the decrease in output power P3 of inverter-3 is -47%. Fig. 9 shows the power shared by DGs (having ratings mentioned in TABLE VI) when operated with ERPS algorithm. The same shading pattern, adopted earlier for ORPS of case (ii), is considered. The reference reactive power for all the inverters is set equal to 300kVAR to meet the load’s reactive power demand (TABLE VIII). Fig. 9(c) shows that after t=0.5s, inverter-1 continuously operates at its rated capacity 400kVA and hence, is unable to meet its desired reactive power share of 300kVAR. Like earlier case with ERPS control, the reactive TABLE III UTILIZATION FACTOR OF EACH DG FOR ERPS ALGORITHM Time Interval(s) Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi t=0-0.5 400 300 500 1.00 300 300 424 0.84 250 300 390 0.78 450 218 500 1.00 t=0.5-1 200 300 360 0.72 300 300 424 0.84 250 300 390 0.78 450 218 500 1.00 t=1-2 200 300 360 0.72 300 300 424 0.84 400 300 500 1.00 450 218 500 1.00 TABLE IV UTILIZATION FACTOR OF EACH DG FOR PROPOSED ALGORITHM Time Interval(s) Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi t=0-0.5 400 229 460 0.92 300 354 464 0.92 250 393 466 0.93 450 222 500 1.00 t=0.5-1 200 374 424 0.85 300 311 432 0.86 250 355 434 0.86 450 159 477 0.95 t=1-2 200 405 452 0.90 300 356 465 0.93 400 262 478 0.95 450 175 482 0.96 TABLE V COMPARISON OF THE VARIOUS ALGORITHM FOR LEADING PF LOAD Algorithms Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi ORPS 300 -180 350 0.70 200 -120 233 0.46 150 -90 175 0.35 350 -210 408 0.82 ERPS 300 -150 335 0.67 200 -150 250 0.50 150 -150 212 0.42 350 -150 380 0.76 Proposed 300 0 300 0.60 200 -233 307 0.61 150 -271 309 0.61 350 -96 362 0.72 TABLE VI Ratings Of Dg Of The System Of Fig.1 For Case (ii) Nominal power rating of DG1 (S1N) 400 kVA Nominal power rating of DG2 (S2N) 500 kVA Nominal power rating of DG3 (S3N) 600 kVA Nominal power rating of DG4 (S4N) 700 kVA power demand of the load is once again not met fully. Thus, the inverters are not utilized optimally. Significant variation in utilization factors is observed. Also the percentage change in the utilization factor of inverter-3 due to change in P3 at t=1s is -27.7%. The power sharing, the utilization factors and the variation in the utilization factors are highly dependent on the nominal ratings of the inverters and the load. Fig. 10 shows performance of proposed algorithm with same pattern of irradiation on the PV array as considered earlier for ERPS and ORPS algorithm of case (ii). It is observed from TABLE IX that during t=0s to t=0.5s, the proposed algorithm tries to share the apparent power equally amongst all the inverters. Hence, as the inverter-1 reaches its limit, it is operated at 400kVA (100% capacity), while inverters 2, 3 and 4 are operated around 500kVA demonstrating the tendency of equalizing the reactive power sharing. At t=0.5s, when the irradiation of PV1 increases resulting into the increase in the output power of inverter 1, the output reactive power of inverter 1 decreases. Simultaneously the reactive powers of all other inverters increase. TABLE VIII UTILIZATION FACTOR OF EACH DG FOR ERPS ALGORITHM Time Interval(s) Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi t=0-0.5 200 300 360 0.90 300 300 424 0.84 400 300 500 0.83 500 300 583 0.83 t=0.5-1 300 265 400 1.00 300 300 424 0.84 400 300 500 0.83 500 300 547 0.78 t=1-2 200 265 400 1.00 300 300 424 0.84 200 300 360 0.60 500 300 547 0.78 (a) (b) (c) Fig.9. Results with ERPS algorithm (a) active power fed by DGs, (b) reactive power shared by the inverters, (c)apparent power of each inverter This results into minimizing the miss-match in the reactive powers of the inverters and hence, reduces the gap of percentage utilization of different inverters. Thus, the algorithm inherently has the feature of minimizing the mismatch. But still the mismatch is relatively large. This is due to the equal apparent power sharing principle of the algorithm, which inspite of the unequal nominal kVA rating of the inverters, tries to allocate the apparent power equally amongst the DG inverters. Hence, it results into the unequal utilization factor of the DGs. At t=1s when P3 changes from 400 kW to 200kW, Q3 increases and Q4 and Q2 decrease to achieve better power sharing amongst the inverters. The least utilization factor of 0.6 is observed for inverter-3. It is observed from TABLE IX that percentage decrease in utilization factor for inverter-3 (due to 0.5 1 1.5 2 0 100 200 300 400 500 600 P ( k W ) v P P P P 4 3 2 1 0.5 1 1.5 2 100 200 300 400 Q ( k V A R ) v Q Q Q Q 2 3 4 1 0.5 1 1.5 2 0 200 400 600 800 Time (s) S ( k V A ) v S S S S 1 2 3 4 (a) (b) (c) Fig. 8. Results with ORPS algorithm: (a) active power fed by DGs, (b) reactive power shared by the inverters, (c) apparent power of each inverter TABLE VII UTILIZATION FACTOR OF EACH DG FOR ORPS ALGORITHM Time Interval(s) Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi t=0-0.5 200 171 263 0.65 300 257 395 0.79 400 342 526 0.87 500 425 656 0.93 t=0.5-1 300 240 384 0.96 300 240 384 0.76 400 320 512 0.85 500 400 640 0.91 t=1-2 300 276 407 1.00 300 277 408 0.81 200 185 272 0.45 500 462 680 0.97 0.5 1 1.5 2 0 100 200 300 400 500 600 P ( k W ) v P P P P 4 3 2 1 0.5 1 1.5 2 0 100 200 300 400 500 Q ( k V A R ) v Q Q Q Q 4 3 2 1 0.5 1 1.5 2 200 400 600 800 Time (s) S ( k V A ) v S S S S 2 4 1 3 change in P3 at t=1s) is -13.8%, which is relatively smaller than that observed with ORPS (-47%) and ERPS (-27.7%). (a) (b) (c) Fig.10. Results with proposed algorithm (a)active power fed by DGs, (b)) reactive power shared by the inverters, (c)apparent power of each inverter TABLE IX UTILIZATION FACTOR OF EACH DG FOR PROPOSED ALGORITHM Time Interval(s) Pi (kW) Qiref (kVAR) Si (kVA) Uti. Fac. Si/SNi t=0-0.5 200 346 399 0.99 300 388 500 0.98 400 310 500 0.83 500 154 520 0.74 t=0.5-1 300 265 399 0.99 300 400 500 0.99 400 338 523 0.87 500 197 537 0.76 t=1-2 300 265 399 0.99 300 344 450 0.90 200 412 450 0.75 500 179 500 0.75 V. CONCLUSION In case of renewable energy source (PV or wind) based DG, the reactive power that it can supply varies as the active power supplied by it changes. The conventional algorithm, which relies on the sharing of equal reactive power amongst the inverters, fails under such case. Not only the inverter gets overloaded but also the distribution of the total apparent power amongst the inverters vary greatly leading to uneven percentage utilization of the inverters. The optimal reactive algorithm also suffers from similar drawbacks. It is observed that the proposed algorithm maintains operation of all inverters within their nominal ratings and yet they are able to match the total reactive power demand of the load. As the reactive power assigned to the inverters is linked with the available reactive power capabilities, the inverter that supplies lesser active power is controlled to share a greater amount of reactive power. If the DG inverters have equal kVA ratings, then with the proposed algorithm, not only the apparent power sharing is better than other algorithms but the utilization factors of the inverters are also nearly similar. However, as the algorithm tries to share the apparent power equally amongst the inverters, the utilization factors are not the same for the inverters of unequal kVA ratings. But the algorithm always operates to minimize the miss-match in the utilization factors. 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National Institute of Technology), South Gujarat University, Surat, India, in 2000, and the M.E. degree in Electrical engineering in 2009 from the M. S. University, Baroda, India She is currently working as an Assistant Professor in the Department of Electrical Engineering at C. K. Pithawalla College of Engineering and Technology, Surat and pursuing Ph.D. in electrical engineering. Her current research interests include distributed generation, renewable energy and microgrid issues. She is a Life Member of the Indian Society for Technical Education and a member of IEEE. Hiren Patel received the B.E. degree in electrical engineering from the S.V. Regional College of Engineering and Technology (now S.V. National Institute of Technology), South Gujarat University, Surat, India, in 1996, and M. Tech. in energy systems and PhD in Electrical Engineering degree from the Indian Institute of Technology Bombay (IITB), Mumbai, India in 2003 and 2009, respectively. He is working as a Professor and Dean, R&D at the Sarvajanik College of Engineering and Technology, Surat. His current research interests include computer aided simulation techniques, distributed generation, and renewable energy, especially energy extraction from photovoltaic arrays. He has to his name several publications in international and national journals and conferences. He is a Life Member of the Indian Society for Technical Education and the Institute of Engineers.