Instruction FACTA UNIVERSITATIS Series: Electronics and Energetics Vol. 30, N o 2, June 2017, pp. 145 - 160 DOI: 10.2298/FUEE1702145E LOAD SHARING METHODS FOR INVERTER-BASED SYSTEMS IN ISLANDED MICROGRIDS  A REVIEW  Augustine M. Egwebe, Meghdad Fazeli, Petar Igic, Paul Holland Electronic System Design Center at College of Engineering, Swansea University, Wales Abstract. This paper explores and discusses various design considerations for inverter- based systems. Different load sharing techniques are presented for the integration of renewable energy sources within islanded microgrids. In off-grid connection, renewable energy sources are often configured to share power based on their rated capacity. This paper explores both conventional and dynamic load sharing interaction between distributed generation units, both in an inductive (high voltage) and resistive (low voltage) networks. Load sharing based on the proper design of virtual impedance is also reviewed. Key words: distributed generation, microgrids, droop control, virtual impedance, photovoltaic, renewable sources. 1. INTRODUCTION The need for clean and reliable energy generation has propelled global activity in various spheres of human endeavor to develop alternative sources of energy. The provision of affordable, reliable and sustainable access to energy in different forms remains one of the key challenges of economic and social development especially in developing countries [1, 2]. While it may be practically impossible to eliminate conventional nuclear and fossil fueled steam turbines, renewable energy sources (RES) offer huge prospects to ease the ever-increasing demand burden on large, centralized conventional power systems. Vast reduction of greenhouse gases emission can also be achieved via RES integration with the existing electricity grid networks [3]. Distributed generation is a term commonly used to describe small-scale and modular power generation sources that are located close to the distribution network rather than large power stations connected to the high voltage transmission network [4, 5]. Distributed generators (DG) includes small-scale fossil and renewable energy generation technologies including wind, photovoltaic, micro-hydro-turbines, biogas, geothermal, tidal, steam turbines with supplementary storage devices like fuel cells and batteries. DG therefore serves as a contrast to conventional large power stations that use a small number of large- scale, frequency controlled generators; it offers enhanced and improved power quality,  Received October 28, 2016 Corresponding author: Augustine Marho Egwebe Electronic System Design Center at College of Engineering, Swansea University, Wales (E-mail: augustine.egwebe@swansea.ac.uk) 146 A. M. EGWEBE, M. FAZELI, P. IGIC, P. HOLLAND enhanced system security, mitigates against issues like blackout and gives better control over the cost of energy [6]. With distributed generation, consumers now have some scales of flexibility on their energy utilization [7]. Increased penetration of green renewable energy requires high-level engineering prowess in maintaining and improving the technologies that make them effective, durable and sustainable [8]. The integration of RES with the existing power network mainly involves the strategies and schemes employed via the use of technologies, processes, and advanced control protocols to balance the production and demand of electrical energy within the network. These control schemes enhance the reliability of energy supply irrespective of the intermittent nature of the renewable source (i.e. fluctuating sunshine or wind profile). They include strategies for the optimal harnessing of the available renewable power, effective energy management, power/voltage device control, intelligent control of energy transformation, islanding detection, and line faults management [7-9]. To balance generated energy with demand in modern microgrids, various renewable sources and converters are often interconnected for load sharing and complimentary energy support. Renewable power generation units are also often supplemented with dispatchable resources such as energy storage systems and local auxiliary generators; where the absence of such resources can result in the malfunctioning of the inverter-based sources (IVBS) [10]. An intermediate solution to some of the problems with the integration of DG with the existing power network is the concept of the microgrid shown in Fig. 1 - an electrical distribution system using distributed energy resources such as generators, storage devices and controllable loads which are coordinated, when connected to the main power network or operated in islanded mode [9, 10]. In grid-connected mode, control measures are relatively easy to be implemented since the utility grid regulates voltage and frequency for loads within the microgrid; whereas in islanded mode voltage and frequency must be actively controlled for the continuous and stable performance of the network [11-13]. The microgrid, when operated in islanded mode, must be able to integrate and coordinates several energy resources with appropriate voltage-frequency control strategies. The electrical power generated from DGs must be well regulated to suit sensitive non-linear loads within the distribution level (i.e. computers, motor drives, battery chargers), without causing unregulated constraint on the generator. The control measures in DGs also aim to offer greater power quality control and low voltage ride through required for eliminating transient stability issues [14, 15]. Additionally, microgrids help to reduce congestion on the utility grid, serves as uninterrupted supply for critical loads, encourage the localized generation of power on the consumer side and offer extra support regarding voltage support, demand response as well as spinning reserve via inbuilt storage devices [16]. The hierarchical control approach employed in a microgrid allows autonomously coordinated generation output from DGs and energy storage systems while ensuring the appropriate load sharing and interaction with the National Grid (NG) [17]. In the absence of free generation capacity in the system due to each DG hitting their maximum generating capacity, the microgrid should be self-sustainable without violating sensitive network parameters like voltage and frequency [18]. A microgrid can connect and disconnect from the NG to enable it to operate in either grid-connected or islanded mode using the microgrid central switch shown in Fig. 1. A required basic characteristic of the microgrid is seamless “islanding” and “reconnection” from/to the NG. Disconnection can be as a result of grid events which include faults, voltage collapse, and blackout [8, 19]. All DGs within the microgrid must be well regulated to present peer-to-peer and plug-and-play characteristics. Load Sharing Methods for Inverter-based Systems in Islanded Microgrids  A Review 147 PV Arrays Small Wind Turbine Energy Storage Bank Domestic Houses Small Industries Local Amenities e.g. Hospital Diesel Generator MV Network (10kV) Microgrid Central Switch Transformer PV Arrays LV LV: Low Voltage MV: Medium Voltage MC: Microsource Controller MCC: Microgrid Central Controller MCC MC MC MC MC MC Fig. 1 An example of a microgrid network Islanding detection of distributed generation systems, voltage regulation, protection, power quality improvement and stability of the power system network are some of the technical challenges facing DGs as they are increasingly connected to the microgrids. Accurate and intelligent controller design is thus required to ensure swift interaction with connected loads and the microgrid while ensuring system stability when disconnecting from the NG in the case of fault or disturbance [20]. In this paper, a thorough survey of the core components and techniques required for the effective integration of DGs in an islanded microgrid is presented. Control paradigms to facilitate the efficient load sharing, operation, and energy management of DGs in a microgrid is also presented. 2. INVERTER-BASED SYSTEMS Inverter-based systems (IVBS) play a vital role in the effective integration of renewables with the microgrid at a synchronized system frequency. IVBS are commonly employed for switching DC voltages from renewable sources to AC voltages supplied to the microgrid and locally connected loads [19, 21]. Monitoring and control functionality are essential requirements for the power electronics interface used in IVBS so as to ensure the protection of the DG system and as well as meet the connection specifications of the NG [19]. Active power, reactive power, voltage and frequency at the point of common connection are some of the critical monitoring parameters for these types of systems as shown in Fig. 2. Also, proper conditioning of voltage and current ensures successful control of power flow per specific power references under varying load or DG input sources. Motor drives and distributed generation systems use IVBS due to their inherent advantages of adjustable power factor, low total harmonic distortion (THD), and their high efficiency. 148 A. M. EGWEBE, M. FAZELI, P. IGIC, P. HOLLAND Inverter Gc-PR(s)Gv-PR(s) Power Controller Ll Cf Lfvi ii voαβ * iiαβ * vcon-αβ ii vo vo io vb io iiαβ voαβ voαβ ab c voαβ ioαβ αβ ab cα β PWM mαβ Vdc θ ÷ * - +Vdc Fig. 2 Generic inverter-based system A conventional inverter circuit consists of controllable transistorized switches, such as IGBTs with parallel diodes to provide a bypass path for transient currents as shown in Fig. 3.a. The three-phase IGBT bridge circuit operates according to the control signal (vcon) generated by the control algorithm of the controller as shown in Fig. 3.b. The three- phase IGBT-based inverter in Fig. 3 consists of six switching devices (Q1 - Q6), which are directly controlled by pulse width modulation (PWM) signals (S1 through S6) to be ON (closed) or OFF (open) according to a well-structured switching pattern to produce the desired output AC waveforms [23, 24]. Vdc S1 Q1 S3 Q3 S5 Q5 S4 Q4 S6 Q6 S2 Q2 a b c van vbn vcn ia ib ic 2 Vdc 2 Vdc + + + - Reference Sine-Wave Generator (vcon) + Carrier Triangular Wave (Sets switching frequency, fsw) + + vcon-a vcon-c vcon-b vtrig S1, S4 S3, S6 S5, S2 Comparator(a) (b) Fig. 3 (a) Three-phase bridge inverter [22]; (b) SPWM control signal generator [22] The use of PWM switching together with closed-loop voltage and current controllers produces a sinusoidal output current in phase with the grid voltage with THD aligned to grid regulations. Conventional grid-mode IVBS in PV applications ensure that: (1) PV modules operate at maximum power point (MPP); (2) the injected AC current into the grid is sinusoidal, with consideration for the IEEE 547 demand standards for grid connection. These standards include issues such as power quality, islanding detection mode, grounding and harmonics. One of the challenges of switching IVBS at high frequencies (2 - 20 kHz) is the creation of high-order harmonics. THD in current and voltage can lead to low power factor, overheating of distribution system components, mechanical oscillation in generators and motors, poor performance of communication equipment, and unpredictable behavior of Load Sharing Methods for Inverter-based Systems in Islanded Microgrids  A Review 149 security protection systems [22, 23, 25]. The low-pass filter connected to the output of the inverter helps to prevent the injection of high-frequency harmonics into the AC bus [23, 25]. Line frequency transformers are used for galvanic isolation when interfacing the microgrid with the NG as shown in Fig. 1. Sinusoidal pulse width modulation (SPWM) is the simplest continuous carrier-based PWM method for generating pulses, and for switching inverter-based devices with a fundamental frequency of 50 or 60 Hz. The main objectives of any modulation scheme are: (1) lower switching losses, (2) reduced THD of output current, (3) minimize computational switching time, (4) better DC bus utilization, and (5) easy digital implementation [26]. In the SPWM-based system in Fig. 2, the three-phase fundamental components of the AC output voltage of the inverter are given by (1) [27-31]. 0 0 0 0 0 0.5 cos( ) 0.5 cos( 120 ) 0.5 cos( 120 ) i a a dc i b b dc i c c dc v m V t v m V t v m V t            (1) where ma, mb, mc = modulation index per phase; Vdc = DC link voltage; and ω0 = fundamental angular frequency of the system. By using the vector-control approach, (1) can be represented as αβ-components hence offering better tracking performance at steady state for the proportional-resonant (PR) controller as shown in (2). dci dci Vmv Vmv   5.0 5.0     (2) The magnitude of the AC output voltage of the DG in (2) is provided in (3) dcdci mVmmVv 5.05.0 22    (3) In (3), the fundamental component of the AC output voltage is thus controlled by controlling the inverter amplitude modulating index m. Where m is defined as the ratio of the amplitude of the modulated signal to that of the carrier signal. The inverter switching process works well for 0 < m < 1 to prevent unwanted harmonic distortion [23, 32, 33]. The DC link voltage Vdc of the inverter-based source must satisfy (3) to avoid PWM over modulation and to ensure the stable operation of the DG in a microgrid. However, when there is a reduction in renewable energy resource level (i.e. wind or solar irradiance level) hence decreasing Vdc, m must increase to maintain vi-αβ in (3). At m = 1; a fixed vi-αβ depends solely on Vdc. Therefore, when designing the IVBS, consideration for the minimum DC link voltage to satisfy (3) must be ensured. The diagrammatic description of the closed-loop control scheme of each inverter- based DG in an islanded microgrid is shown in Fig. 2. The direct Proportional-Resonant (PR) control approach can be used to simplify Fig. 2 as shown in the block diagram representation in Fig. 4. 150 A. M. EGWEBE, M. FAZELI, P. IGIC, P. HOLLAND Gv-PR(s) Gc-PR(s) + + Vdc ÷ * Gpwm(s) * * sLf + rf 1+ + io sCf 1 vovo * iL * iL ic LC - FilterPWM InverterControllers vi Fig. 4 Block diagram of the closed-loop inverter-based source [20, 34] In the closed-loop DG model in Fig. 4, an outer voltage loop Gv-PR is used to control the output voltage of the inverter. The main control objective of Gv-PR is to maintain a clean and balanced DG voltage as close as possible to the given sinusoidal reference voltage so that the THD of the output voltage is minimized. The voltage reference is compared with the measured voltage in αβ-frame to produce an error signal. The error signal is fed into a PR compensator, which in turn generates the current reference signal for the inner current loop. Similarly, in the inner current controller Gc_PR in Fig. 4, the reference current from the outer voltage loop is compared with the measured output current. The error signal is fed into a PR controller to generate the reference signal for the PWM generator. The controlled output wave from the current controller is transformed back to the abc-frame using the abc/αβ-coordinate transformation principle, to generate the reference control signal for the inverter switching devices. The bandwidth of the inner current controller is usually designed to be much faster than the outer voltage loop to achieve a fast dynamic response. In general, the voltage and current controllers are designed to provide nearly perfect sinusoidal output voltage waveforms at a nominal switching frequency and to offer good damping for the output filter of the inverter and the rejection of high-frequency disturbances. vcα ioα + vcβ ioβ vcβ ioα - vcα ioβ vcα vcβ ioβ ioα p q- - ωf s + ωf ωf s + ωf P Q ω * - mpP V * - nqQ 1 s ω0 θ V Fig. 5 Droop controlled power sharing for islanded DG [30] The dynamics of the control scheme depends mainly on the bandwidth of the PQ controller shown in Fig. 4, since the bandwidth of the current and voltage controller, are designed to be much higher than that of the PQ controller [25]. The power controller block is used for accurate sharing of P and Q according to the droop characteristics as shown in Fig. 5 [10]. The low-pass filter with cutoff frequency wf is used to extract the average powers as shown in Fig. 5. The non-ideal PR controller adopted in this paper can overcome two well-known drawbacks of conventional PI controller: (1) the inability to track a sinusoidal reference with zero steady-error, (2) poor disturbance rejection capability. This is due to the PR controller infinite gain at the fundamental frequency [35], thus reducing steady state error to zero. Load Sharing Methods for Inverter-based Systems in Islanded Microgrids  A Review 151 Equation (4) shows the transfer function of the adopted practical non-ideal PR controller to achieve finite gain at the AC line frequency. 22 s2s s2 (s) oci ci pPR K K KG     (4) Fig. 6 Frequency response of a PR controller for Kp = 0.01, Ki = 1 and ωc = 1, 5, 15, 25, 50, 100 rad/s The frequency response of (4) shows a wider bandwidth around the 50 Hz resonant frequency which helps to minimize any slight frequency variation due to load disturbance. The PR controller’s bandwidth can be varied with the damping factor ωc as shown in Fig. 6. It can be seen that ωc has an effect on both the magnitude and phase of the controller. When choosing ωc, there has to be a compromise between the reduction of sensitivity and steady state error. 2.1. Current controller design The design objective of the current controller is to have a high loop bandwidth with sufficient stability margins. It is noted from control laws that systems with greater gain margins can withstand greater changes in the systems parameters before becoming unstable in the closed loop response. When designing via frequency response analysis, the goal is to predict the closed-loop behavior from the open-loop response of the current control loop shown in Fig. 4. The closed-loop transfer function of the current loop when the output current is assumed as disturbance is given in (5) [36]. Feedforward terms are added to the current loop in order to decouple the αβ components of the output voltage [37]. (s)(s)(s)1 (s)(s)(s) (s) * LfpwmPRc LfpwmPRc L L c GGG GGG i i G     (5) where Gc-PR is the PR current controller; GLf is the transfer function of the LC filter respectively; Gpwm(s) = 1 / (1+1.5Tss) represents the PWM and computational delay with 152 A. M. EGWEBE, M. FAZELI, P. IGIC, P. HOLLAND respect to the sampling period Ts. By setting ωc in (4) equal to 10 rad/s, (5) can be tuned for a closed-loop bandwidth of 1 kHz to give Kp and Ki of 12.5Ω and 250Ω respectively. Note that the bandwidth of (5) is usually selected as one-tenth of the switching frequency. 2.2. Voltage controller design The voltage controller is also based on the PR structure discussed in (4), where a generalized integrator is used to achieve a zero steady-state error. The closed-loop dynamic behavior of the DG in Fig. 4 is approximated as an equivalent Thevenin equation as given in (6):             ooooo o xxx PRcpwmff o xxx PRvPRcpwm o iZvGv i CsBAs GGrsL v CsBAs GGG v (s)(s) (s)(s)(s)(s)(s) * 2 * 2 (6) where Ax = LfCf; Bx = (rf + Gpwm(s)GcPR(s))Cf; Cx = Gpwm(s)GcPR(s)GvPR(s); GvPR(s) is the PR capacitor voltage controller; rf is the parasitic resistance of the filter inductor; Go(s) is the control closed-loop system transfer function; Zo(s) is the output impedance. Fig. 7 shows the open-loop frequency response of the DG’s voltage loop when the output current is assumed as disturbance, the positive high gain margin (46.4 dB) and phase margin (79.3 degrees) both confirm the stability of the overall system. The bandwidth of the voltage controller is tuned to be about one-fifth of the bandwidth of the current controller as shown in the closed loop frequency response in Fig. 8, to give Kp and Ki values of 0.5Ω and 7 Ω respectively. Fig. 7 Open-loop frequency response of the DG voltage loop Load Sharing Methods for Inverter-based Systems in Islanded Microgrids  A Review 153 Fig. 8 Closed-loop frequency response of the DG voltage loop 2.3. Virtual impedance design for P and Q decoupling Go(s) vo * +- io vo Zv(s) + - Zo(s) → Go(s) vo * +- io vo Go(s)Zv(s)+Zo(s) Fig. 9 Block diagram representation of virtual impedance loop In order to ensure a stable output impedance of the DG, the output DG voltage is dropped proportionally with the output current as shown in Fig. 9 and explained in (7): * ( ) ( ( ) ( ) ( )) o o o o v o o v G s v G s Z s Z s i   (7) The output impedance of the inverter is re-designed to mitigate the influence of control parameters and line impedance on the power-sharing accuracy around the fundamental frequency as shown in Fig. 9, to share the power precisely between the distributed IVBS [34]. References [21, 34, 38, 39] proposes a design scheme to eliminate the impact of DG output impedance on the overall system dynamics; hence the virtual impedance loop was implemented for power decoupling and restraining of circulating current between DGs. A performance comparison of virtual impedance techniques used in droop-controlled islanded microgrids was presented in [40, 41]. It was noted that the virtual inductive loop helps to improve the output impedance of the inverters such that it becomes predominantly inductive thereby improving the power-sharing accuracy of the droop control algorithm. Similarly, a virtual resistive loop increases the output impedance of the inverters such that it becomes more resistive. The overall effect of impedance mismatches is also reduced by 154 A. M. EGWEBE, M. FAZELI, P. IGIC, P. HOLLAND the virtual resistance loop thereby improving the current sharing. A virtual resistance allows sharing of linear and nonlinear loads in microgrid applications without introducing additional losses in the network and improves the stability of the microgrid [41]. According to Fig. 10, the magnitude of the IVBS output impedance at the fundamental frequency is approximately zero. This shows the effectiveness of the designed control parameter of the voltage and current loop. Hence, the output impedance of the IVBS is designed to be equal to the virtual impedance around the fundamental frequency as shown in Fig. 10. Fig. 10 also illustrates the effect of the virtual inductance on the overall output impedance of the IVBS. As can be seen, the overall output impedance become more inductive as the virtual inductance increases. Fig. 10 Output impedance frequency response of the IVBS with varying virtual inductance 3. CONVENTIONAL LOAD SHARING SCHEMES IN AN ISLANDED MICROGRID Load sharing without communication between the parallel DGs is the most favored option in an autonomous microgrid as the network can be complex and can span over a large geographical area [19, 42]. Numerous literature has studied and presented the droop scheme so that parallel DGs can be locally controlled to deliver required active and reactive power to the microgrid network. By adopting the droop scheme, two local independent network quantities (voltage and frequency) are controlled to regulate active and reactive power with consideration for the allowable frequency and voltage deviation within the microgrid. The small-signal stability analysis of the droop scheme has also been explored in the various literature [19, 30, 43]. One major concern with the droop scheme is its sensitivity to the imbalance in the system’s closed-loop output impedance and line impedance, which can lead to poor coupling between the active and reactive power [21, 42]. Load Sharing Methods for Inverter-based Systems in Islanded Microgrids  A Review 155 The complex power delivered to the common bus in Fig. 2 can be expressed as shown in (8). jQPS  (8) 2 2 cos( ) cos sin( ) sin o b b o b b V V V P Z Z V V V Q Z Z                   (9) where P and Q are the active and reactive power delivered by the DG; Vo is the AC output voltage of the DG; Vb is the bus voltage; Z is the magnitude of the output impedance, and ϴ is the phase angle of the output impedance. 3.1. Active power-frequency droop scheme Conventionally, the output impedance is considered to be purely inductive (i.e. Z ≈ jX), hence (9) is re-written as in (10).          X V X VV Q X VV P bbo bo 2 cos sin   (10) The power droop controller in Fig. 5 aims to adjust the frequency and voltage difference relative to increasing load in a stable manner. In an inductive-based microgrid, the droop equation is expressed as (11) and shown in Fig. 13. * * 0 0 * * ( ); ( ) p o q m P P V V n Q Q               (11) Where ω* is the fundamental frequency; V* is the AC reference voltage; P* and Q* are the reference active and reactive powers; ɸ is the power angle, P and Q are the instantaneous active and reactive power of the DG. The droop gains mp and nq are calculated for a given range of frequency and voltage as shown in (12) rated q rated p Q VV n P m minmaxminmax ;      rated q rated p Q VV n P m minmaxminmax ;      (12) Fig. 11 Steady-state characteristic of conventional droop scheme 156 A. M. EGWEBE, M. FAZELI, P. IGIC, P. HOLLAND Equation (11) indicates that the active power of the DG is dependent on the power angle, whereas the voltage amplitude difference mainly influences the reactive power. Equation (13) shows the load distribution for N-parallel connected DGs in a microgrid when (11) is adopted. NqNqq NpNpp QnQnQn PmPmPm   ... ... 2211 2211 (13) 3.2. Active power-voltage droop scheme It is noted in the various literature that the performance of the conventional droop control is severely affected by the resistance-to-inductance (R/X) ratio of output and the line impedance. Equation (9) is given as (14) when the output impedance of the DG is resistive (i.e. Z ≈ R): sin cos 2   R VV Q R V R VV P bo bbo   (14) Since low voltage microgrid electrical distribution networks present a high R/X ratio, the voltage amplitude is used to control active power, while reactive power is controlled by the system frequency as shown in (15). * * 0 0 * * ( ); ( ) p o o q m Q Q V V n P P           (15) rated p Q m minmax    ; rated q P VV n minmax   3.3. Virtual impedance load sharing scheme The active and reactive power can also be well autonomously controlled using the virtual impedance scheme in (16) without any requirement for additional power controller as studied in [43]. Equation (16) ensures accurate load sharing between the DGs and compensates reactive power differences due to output voltage mismatches, or line impedance mismatches. In order to avoid the steady-state frequency deviation, a PLL is introduced. This way, the PLL adjust the phase of the inverter, and the system is controlled by a virtual resistance controlling current as in a dc electrical system. Reference [44] proposes an autonomous loading sharing scheme using the virtual resistance loop and a synchronous reference frame phase-locked loop. This scheme provides for both instantaneous current sharing and fast dynamic response of the paralleled IVBS. The relationship between the Ioαβ and the virtual resistance Rv for N-DGs is given as (16). vNNovovo vNNovovo RIRIRI RIRIRI     ... ... 2211 2211 (16) The small-signal analysis shows that the output α and β axis output currents of paralleled inverters are inversely proportional to their virtual resistances since the current Load Sharing Methods for Inverter-based Systems in Islanded Microgrids  A Review 157 sharing performance is just influenced by the output impedance ratio instead of the output impedance value of the DGs [43]. 1 V I1 * (P) 2 V * I1(P) I2 (P)I2 * (P) I(P) Fig. 12 Characteristics of virtual impedance droop (V-P) 3.4. Energy saving via dynamic load sharing Reference [10] presented a dynamic load sharing scheme for photovoltaic (PV) inverter-based systems in an inductive microgrid, by using the PV array’s current vs voltage characteristics in defining an operating range for the inverter-based source. The dynamic load sharing scheme is based on the available solar power to ensure an efficient load sharing interaction with other DGs, without the need for energy support from local connected fossil-fuelled auxiliary generator and thereby providing significant energy saving compared with conventional static droop control techniques. In the dynamic loading scheme, the droop gains of the power controller in (11) are re- defined for dynamic load interaction between the DGs [45] as follows: avail q DC p Q V n P m      ; max  (17) where PDC-max is the maximum available power of the PV array which is deduced from the maximum power curve in Fig. 13. Qavail is the available reactive power that the DG can supply as defined in (18). 22 DGratedavail PSQ  (18) Figure 14 shows the load sharing profiles of two DGs interfaced to the islanded microgrid [10]. Fig. 14.b shows load sharing based on the conventional droop scheme in (11), where a drop in the available power of DG2 causes similar drop in DG1 even though it has enough available capacity. As a result, the total generation becomes less than the load, the auxiliary generator (AG) is thus triggered on to supply the shortage in supply Paux. In Fig. 14.c, the load is adaptively shared based on the available PV power using (17). Thus, a drop in the available energy in DG2 causes a proportional drop in its contribution to PLoad. Similarly, DG1 dynamically compensate for this drop by supplying more power. Hence no extra power is required from the AG (Paux ≈ 0 in Fig. 14.c). 158 A. M. EGWEBE, M. FAZELI, P. IGIC, P. 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