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Abstract
energies Article Enhanced Reactive Power Sharing and Voltage Restoration Based on Adaptive Virtual Impedance and Consensus Algorithm 1 , 1 2 3 Mohamed Keddar *, Mamadou Lamine Doumbia , Karim Belmokhtar and Mohamed Della Krachai Department of Electrical and Computer Engineering, Université du Québec à Trois-Rivières, Trois-Rivières, QC G8Z 4M3, Canada; mamadou.doumbia@uqtr.ca Research and Innovation, Nergica, Gaspé, QC G4X 1G2, Canada; kbelmokhtar@nergica.com Department of Electrical Engineering, University of Science and Technology Mohamed Boudiaf, Oran 31000, Algeria; mohamed.dellakrachai@univ-usto.dz * Correspondence: mohamed.keddar@uqtr.ca Abstract: In this paper, power-sharing management control on an AC islanded microgrid is investi- gated to achieve accurate reactive power sharing. The droop control method is primarily used to manage the active and reactive power sharing among the DGs in the microgrid. However, the line impedance mismatch causes unbalanced reactive power sharing. As a solution a consensus-based adaptive virtual impedance controller is proposed, where the consensus algorithm is used to set the reactive power mismatch; then a virtual impedance correction term is generated through a proportional-integral controller to eliminate the line impedance mismatch. Thus, reactive power sharing is achieved without knowledge of the line impedances or using a central controller. Moreover, the consensus algorithm is used to restore the AC bus voltage to the nominal value by estimating the DGs average voltage using neighbor communication to compensate for the decreased magnitude of the voltage reference. Matlab/Simulink is used to validate the accuracy of reactive power sharing and Citation: Keddar, M.; Doumbia, M.L.; voltage restauration achievement of the proposed solution through simulation of different scenarios. Belmokhtar, K.; Krachai, M.D. In addition, a dSPACE DS1104 is used within a developed experimental testbench based on two Enhanced Reactive Power Sharing parallel DGs to validate the effectiveness of the proposed solution in the real world. and Voltage Restoration Based on Adaptive Virtual Impedance and Keywords: consensus control; virtual impedance; microgrids; distributed generation; dSPACE Consensus Algorithm. Energies 2022, 15, 3480. https://doi.org/10.3390/ controller; droop control en15103480 Academic Editor: Ferdinanda Ponci Received: 4 April 2022 1. Introduction Accepted: 3 May 2022 The world energy demand is increasing quickly, and it is expected to reach 50% by Published: 10 May 2022 2050 [1]. This is due to the increase in the population of the world and the rapid develop- ment of technologies. To accommodate this growth in energy demand, the development Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in of new power generation and massive integration of renewable energy become a prior- published maps and institutional affil- ity respecting the agreements on the emission reduction of CO . Recently, several new iations. technologies have been contributing to power generation plants such as the Distributed Generation (DG) using renewable energy sources, Electrolyzers (Ely) and fuel cells (FC), Electric Vehicles (EVs), and Energy Storage Systems (ESSs). Connected to a common bus with a centralized or decentralized controller and power management system with com- Copyright: © 2022 by the authors. munication, they establish a new power generation system called a microgrid (MG). A MG Licensee MDPI, Basel, Switzerland. can operate in both connected mode when it is coupled to the main grid, or autonomous This article is an open access article mode when it is islanded [2,3]. distributed under the terms and The massive integration of Renewable Energy Resources (RES) in MGs can reduce the conditions of the Creative Commons operation cost, increase the benefits on the environment by reducing the CO emissions, Attribution (CC BY) license (https:// and create new power sources [4]. However, the nature of these sources and sudden creativecommons.org/licenses/by/ variations in the weather cause perturbation and instability to the MG, resulting in voltage 4.0/). Energies 2022, 15, 3480. https://doi.org/10.3390/en15103480 https://www.mdpi.com/journal/energies Energies 2022, 15, 3480 2 of 19 and frequency deviations. MGs are considered to have a low system inertia due to the low capacity of the DGs supplied by RES. Furthermore, the sudden changes in the connected loads may lead to critical frequency deviations and power flow management issues during the MG operation [5–7]. In autonomous microgrids, the connected DGs share the load power according to their power ratings for the profitability and to ensure the stability of the MG. The commonly adopted method in power sharing is the droop control approach. Active power sharing between DGs can be easily achieved using the frequency droop control method, whereas the reactive power sharing cannot be achieved easily due to the impedance mismatch between DGs which leads to voltage deviation and system instability [8,9]. To solve the inaccurate reactive power sharing issue, other ameliorated control methods have been developed [10–13]. In [10], a decentralized self-changing control was proposed using the adaptive droop control method. To increase the accuracy of reactive power sharing, an inductive virtual impedance (VI) loop was introduced; however, this method was not examined for a wide scope of working points. In [11], an adaptive droop controller was proposed to ensure dynamic stability of power sharing, where derivatives of active and reactive power are added to the traditional droop controller. Then, droop control gains were tuned adaptively conforming to the output power variations. However, the reactive power sharing was not as expected [12]. A modified Q-V droop control method was introduced in [13] to improve the power sharing accuracy. However, the reactive power sharing difference cannot be completely removed. Other methods based on improved hierarchical control strategies have been pro- posed [14,15]. A secondary controller with a primary droop controller was presented in [14] to achieve accurate reactive power sharing in islanded MGs. However, a communication link between the central controller (CC) and DG’s local controller is needed, increasing the response time and the total cost. In [15], virtual impedance control was applied in islanding MGs at different levels according to transient variations in the active power. A transient control term was used in the traditional droop control by injecting frequency disturbances. However, this approach could result in lower reliability and instability of the MG because of their reliance on the central controller. Moreover, the reactive power sharing was not addressed. Nonetheless, in these methods, power-sharing accuracy, especially reactive power can be influenced by communication congestion or delays regarding the number of connected DGs [16,17]. VI-based methods were widely used to improve reactive power sharing [18–20]. The VI is used to eliminate the impedance mismatch between lines and then improve reactive power sharing as well system stability. Based on injection of disturbances, online impedance estimation, or using MGCC, this approach can flexibly deal with the impedance mismatch between lines as well as the variation in load power, im- proving the dynamic performance of the MG. In order to enhance accurate reactive power sharing between parallel DGs, a complex VI approach including resistive and inductive factors systems was introduced [21,22] where the reactive power sharing was significantly enhanced. Furthermore, the result can be better with communication-based complex VI [23]. However, the communication delays can result in less reactive power sharing accuracy and degraded performance. Recently, consensus algorithms were combined with the adaptive VI approach in order to guarantee accurate power sharing and current harmonics sharing. In addition, the voltage and the frequency value restoration can be achieved using these algorithms. Based on the information from neighbor communication or MGCC systems, the consensus approach is used to guarantee accurate reactive power distribution. The virtual impedance of DGs is tuned by the consensus approach to move towards a common objective in terms of reactive power sharing [24–26]. However, the communication system should be optimized to enhance the MG stability and improve the MG performance. When only the neighbor communication system is used, the MG cost and communica- tion time will be reduced. This kind of communication can be used in one or two directions, depending on the system specifications. Reactive current information can be used in order Energies 2022, 15, 3480 3 of 19 to have accurate reactive power sharing. On the other hand, the active current information is used for active power sharing accuracy [27]. Moreover, to compensate for the voltage deviations and drop caused by the VI, DG output voltage restoration was introduced using a consensus algorithm [23]. The approach uses a communication system between adjacent DGs to exchange information on reactive power sharing and voltage restoration. However, this approach is dependent on communication system reliability. Microgrid reliability and efficiency are related to several parameters such as communication links and control strategy. MGCC presents a very sturdy and efficient control strategy. However, the complex communication system may increase the total cost as well as the impact of com- munication time delays. Therefore, decentralized control strategies are favored especially in autonomous MG where DGs, loads, and storage systems are from multiple customers. In this case, complex central communication systems should be avoided in order to reduce the information dependency on each DG. Encouraged by this aspect, several attempts have been made by this work. Since the reactive power sharing issue is directly related to the DGs voltage and their behaviors, it can be solved based on information exchange between adjacent DGs and local information through a progressive process. The line impedance can be first estimated and tuned by each DG using the consensus algorithm; then this value can be shared with the neighbors. The VI is adaptively adjusted by the consensus algorithm to remove the mismatch between line impedance, ensuring accurate reactive power sharing without line impedance knowledge. Furthermore, the consensus control is used to compensate and restore the output voltage of each DG to the MG voltage. Therefore, the developed control contributions from this work are summarized as follows: Adaptive virtual impedance control combined with a consensus algorithm is pro- posed for reactive power-sharing accuracy and parallel DGs voltage restoration with line impedance mismatch in autonomous MGs. To achieve accurate reactive power sharing, neighbor information through a uni- directional communication link is used to estimate the VI, reducing the cost and the time delay impact of communication. Additionally, this approach cancels out the line impedance knowledge. The proposed control approach was confirmed by experimental validation using a small-scale laboratory test bench based on MGs with two DGs. The rest of the paper is arranged as follows: Section 2 presents the power sharing using conventional droop, the microgrid configuration, control, and modeling. Section 3 explores the proposed approach based on adaptive VI and consensus algorithms used to have accurate reactive power sharing and system voltage restoration. Then, Section 4 shows the simulation verification and Section 5 presents the experimental validation results of the proposed control approach. Finally, summary and main findings of this paper are presented in Section 6. 2. Droop Control and Reactive Power Sharing Theory Droop control is the most used classical approach to control parallel DGs in power systems. This method presents high flexibility with good reliability and redundancy. It does not require a central controller or communication system and is mostly used in the primary control of MGs. 2.1. Droop Control To analyze the power flow in steady state, it is assumed that the inverter is a controlled voltage source; then the dynamics of the inner control loop can be neglected. Figure 1 illustrates an inverter connected to the point of common coupling (PCC) through a line impedance Z. Energies 2022, 15, x FOR PEER REVIEW 4 of 19 Energies 2022, 15, 3480 4 of 19 Figure 1. Inverter connected the point of common coupling. Figure 1. Inverter connected the point of common coupling. Assuming a balanced 3-phase system, the power flowing in a transmission line can Assuming a balanced 3-phase system, the power flowing in a transmission line can be be derived by: derived by: E V S = P + jQ = V I = E 𝐸 − 𝑉 (1) j¶ 2 𝑆 = 𝑃 + 𝑗𝑄 = 𝑉 ∗ 𝐼 = 𝐸 ∗ ( ) E Ve E jq EV j(q+¶) = E = e e jq Z Z Ze (1) where S, Q, P represent apparent, reactive, and active power, respectively. E represents 𝐸 − 𝑉 ∗ 𝑒 𝐸 𝐸𝑉 𝑗 (𝜃 +𝜕 ) the output voltage = of 𝐸 ∗ the ( power inverter ) = at an ∗ 𝑒 angle − d. ∗ Z𝑒 represents the impedance of the 𝑍 ∗ 𝑒 𝑍 𝑍 transmission line between the inverter and the PCC with angles V and q that represent the where S, Q, P represent apparent, reactive, and active power, respectively. E represents voltage at the PCC with an angle equal to zero. jq the output voltage of the power inverter at an angle δ. Z represents the impedance of the Using Euler ’s simplification and replacing the line impedance by Ze = R + jX, the transmission line between the inverter and the PCC with angles V and θ that represent active and reactive power equations can be written as follows [28]: the voltage at the PCC with an angle equal to zero. P = (R(E V cos d) + XV sin d) (2) Using Euler’s simplification and replacing the line impedance by 𝑍 𝑒 = 𝑅 + 𝑗𝑋 , the 2 2 X + R active and reactive power equations can be written as follows [28]: Q = (X(E V cos d) + RV sin d) (3) 2 2 X + R (2) 𝑃 = (𝑅 (𝐸 − 𝛿𝑠𝑉𝑐𝑜 )+ 𝑛𝑋𝑉𝑠𝑖 𝛿 ) 2 2 𝑋 + 𝑅 In normal cases, the output power of a DG unit is far below the maximum transmission capability of the feeder line; thus, d will be small. For this reason, the approximation cosd!1 (3) and sind!d can be adopted. In addition, assuming that the line impedance is inductive 𝑄 = (𝑋 (𝐸 − 𝛿𝑠𝑉𝑐𝑜 )+ 𝑖𝑅𝑉𝑠𝑛 𝛿 ) 2 2 𝑋 + 𝑅 and satisfies the condition Xi Ri Equations (2) and (3) become: In normal cases, the output power of a DG unit is far below the maximum transmis- X P sion capability of the feeder line; thus, δ wi ll be small. For this reason, the approximation d = (4) EV cosδ→1 and sinδ→δ can be adopted. In addition, assuming that the line impedance is in- ductive and satisfies the condition Xi ≫ Ri Equations (2) and (3) become: XQ E V (5) 𝑋𝑃 (4) 𝛿 ≅ Equations (4) and (5) show that the power angle strongly depends on the active power 𝐸𝑉 and the voltage difference depends on the reactive power. In other words, active power can be frequency controlled and reactive power regulated by voltage. This finding leads to 𝑋𝑄 (5) 𝐸 − 𝑉 ≅ the following common droop control equations: Equations (4) and (5) show that the power angle strongly depends on the active w = w m P (6) 0 p power and the voltage difference depends on the reactive power. In other words, active power can be frequency controlled and reactive power regulated by voltage. This finding V = V n Q (7) leads to the following common droop contro0 l equa Qtions: where V and w , represent the nominal values of the voltage and the frequency, n and m 0 0 Q P 𝜔 = 𝜔 − 𝑚 𝑃 (6) 0 𝑝 represent the droop coefficients, and V, w, represent the nominal output of the voltage and the frequency. Then, the droop control coefficients (n , m ) can be defined by the following Q P V = 𝑉 − 𝑛 𝑄 (7) 0 𝑄 equations [28,29]: Dw max where V0 and ω0, represent the nominm al va =lues of the voltage and the frequency, nQ an(8) d nominal mP represent the droop coefficients, and V, ω, represent the nominal output of the voltage Dv and the frequency. Then, the droop control coefficients (nQ, mP) can be defined by the fol- max n = (9) lowing equations [28,29]: Q nominal 𝑗𝜃 𝑗𝜃 𝑗𝜃 𝑗𝜕 Energies 2022, 15, x FOR PEER REVIEW 5 of 19 𝛥 𝜔 (8) 𝑚 = 𝑖𝑛𝑜𝑚𝑛𝑙𝑎 𝛥𝑣 Energies 2022, 15, 3480 5 of 19 (9) 𝑛 = 𝑖𝑛𝑜𝑚𝑛𝑙𝑎 2.2. Reactive Power Sharing 2.2. Reactive Power Sharing Accurate reactive power sharing cannot be achieved by conventional droop control. Accurate reactive power sharing cannot be achieved by conventional droop control. In In order to solve the issue and eliminate the deviations of the voltage and frequency, sec- order to solve the issue and eliminate the deviations of the voltage and frequency, secondary ond contr ary con ol was trol used. was used Figur . Fi egure 2 shows 2 sho the wsinvestigated the investiga MG ted configuration. MG configurati It on is . composed It is com- of posdistributed ed of distrib generation uted gener(DG) ation ( based DG) ba on sed renewable on renewener able gy ener sour gy ces sourc and es a an battery d a batter storage y stora system ge syst (BSS). em (BS Each S). Ea DG ch DG is connected is connected to to a common a common AC AC bus bus thr though roughan an inverter inverter and and an an L LCL CL ffilter ilter.. Figure Figure 2. Conf 2. Configuration iguration of th of e the inves investigated tigated islan islanded ded micr micr ogri ogrid. d. The control structure of the MG is based on hierarchical control using primary and The control structure of the MG is based on hierarchical control using primary and secondary control levels. The primary control contains the current and voltage control secondary control levels. The primary control contains the current and voltage control loops. While the secondary control contains the consensus algorithm, adaptive virtual loops. While the secondary control contains the consensus algorithm, adaptive virtual im- impedance, and droop control. pedance, and droop control. 2.3. DGs Modeling and Global Control Strategy The control strategy at the primary control level is based on proportional-integral (PI) controllers. Figure 3 shows the global control scheme of inverters for each DG. Sec- ondary control level includes the droop controller, power calculation, the adaptive virtual impedance, and the consensus algorithm with the communication network. References of voltage and adaptive VI value are generated and sent to the primary control level. Af- terward, inverter control signals are generated based on these references. An LCL filter is used to connect the inverter to the AC bus, where L is the inverter side inductor of the 𝑚𝑎𝑥 𝑚𝑎𝑥 Energies 2022, 15, x FOR PEER REVIEW 6 of 19 2.3. DGs Modeling and Global Control Strategy The control strategy at the primary control level is based on proportional-integral (PI) controllers. Figure 3 shows the global control scheme of inverters for each DG. Sec- ondary control level includes the droop controller, power calculation, the adaptive virtual impedance, and the consensus algorithm with the communication network. References of voltage and adaptive VI value are generated and sent to the primary control level. After- Energies 2022, 15, 3480 6 of 19 ward, inverter control signals are generated based on these references. An LCL filter is used to connect the inverter to the AC bus, where Lf is the inverter side inductor of the filter with Rf as internal resistance, 𝐶 f is the capacitor value of the filter and finally, Lg is filter with R as internal resistance, C is the capacitor value of the filter and finally, L is the f f g the inductor of the filter at the grid side with an internal resistance Rg. inductor of the filter at the grid side with an internal resistance R . Figure 3. Global control scheme of DGs. Figure 3. Global control scheme of DGs. The dynamic equations model can be derived using voltage and current law followed The dynamic equations model can be derived using voltage and current law followed by by Pa Park rk transformation transformationas as f follows: ollows: d i E v i 0 w L i d d d d f d 𝑣 0 𝜔 𝐿 𝑑 𝑖 𝐸 𝑖 𝑖 𝑑 (10) 𝑑 𝑑 𝑑 𝑓 𝑑 L = R + (10) f f 𝐿 ∗ [ ] = [ ] − [ ] − 𝑅 [ ] + [ ] [ ] dt𝑓 i E v 𝑓 i w L 0 i q q q q q 𝑣 f 𝑖 𝐸 𝑖 𝑖 𝑞 −𝜔 𝐿 0 𝑞 𝑞 𝑞 𝑞 d 0 wC v i i v d d ld d C 𝑑 𝑣 = 𝑖 𝑖 0+ 𝜔 𝐶 𝑣 (11) f 𝑑 𝑑 𝑓 𝑑 (11) v i i wC 0 v dt 𝐶 ∗ q[ ] = [ q ] − [ ]l+ q [ ] f[ ] q 𝑣 𝑣 𝑖 𝑖 𝑞 −𝜔 𝐶 0 𝑞 where E , E represent direct and quadrature voltage before the filter, V , V after the filter, q q d d where Ed, Eq represent direct and quadrature voltage before the filter, Vd, Vq after the filter, and I , I the current direct and quadrature values. After simplification, the equations of and Id, Iq the current direct and quadrature values. After simplification, the equations of the current and the voltage controllers can be written as follows [2]: the current and the voltage controllers can be written as follows [2]: iv I = K + V V wCV + i pv cq gq re f _d cdre f cd (12) > K iv I = K + V V wCV + i pv cq re f _q cqre f cd gd > ii < V = K + i i w L i + V re f _d pi re f _d ld f lq cq (13) ii V = K + i i w L i + V re f _q pi re f _q lq f ld cd where K , K are the proportional and the integral coefficients of the current PI controller, pi ii K , K are the proportional and the integral coefficients of the voltage PI controller. V pv iv cdref 𝑙𝑞 𝑑𝑡 𝑙𝑑 𝑑𝑡 Energies 2022, 15, 3480 7 of 19 and V are the voltage references calculated by the droop controller. The adaptive VI cqref control is as follows: V V V cdre f c_re f d vi_d = (14) V V V cqre f c_re f q vi_q where V , V represent the references from the adaptive VI controller and V , V vi_d vi_q c_refd c_refq the references of the droop controller. 3. Adaptive Virtual Impedance and Consensus Algorithm In a MG, the active and reactive power are coupled and depend on the output fre- quency and voltage due to the nature of the line impedance, which can be resistive inductive or both. The use of VI in combination with the physical impedance can modify the total output impedance of the DG. In this section, the proposed approach based on adaptive VI and consensus algorithms is explored. 3.1. Adaptive Virtual Impedance VI has been used for many applications recently, such as reactive power sharing by ensuring a consistent and equivalent output impedance for all parallel DGs in the autonomous MGs [2,25–27]. This VI can be adjusted adaptively in order to calculate the total impedance and then the voltage reference. Thus, the total output impedance of a DG can be written as follows [27]: Z = Z + Z + Z (15) i v,i line,i ad p,i Z represents the total output impedance of the DG and the line impedance can be represented by Z . The virtual impedance can be divided into two terms, Z which line,i v,i represents the static virtual impedance value used to ensure an inductive total impedance. The other term, Z represents the adaptive VI. Equation (15) shows that the output adp,i impedance of each DG is increased by the adaptive term in order to match with other DG impedances and eliminate the mismatch. Then, reactive power sharing can be improved using droop control relations. 3.2. Consensus Algorithm In order to have a similar output impedance between different DGs, in this work, the adaptive VI in Equation (14) is calculated and adjusted using a consensus algorithm. To have an accurate reactive power sharing, consensus control is used to reach a general agreement among all MG agents. Thus, the droop control and reactive power coefficients must be designed to be inversely proportional, according to the following equation [26–29]: n Q = n Q = . . . = n Q (16) Q1 1 Q2 2 QN N By replacing (7) in (5), the reactive power flow of each DG can be written as follows: V(E V) n Q = (17) qi i + V Therefore, to satisfy Equation (16), the term Xi/ni of each DG must be the same in Equation (17), from which the following equation can be written: X X X 1 2 N = = . . . = (18) n n n 1 2 N From Equation (18), it can be noticed that the term n must be proportional to the line reactance X . Considering Equation (16), in order to obtain accurate reactive power sharing the reactance of the line must be designed to be inversely proportional to the reactive power, then the following equation can be written [23,25,26]: Energies 2022, 15, 3480 8 of 19 X Q = X Q = . . . = X Q (19) 1 1 2 2 N N The consensus control of the reactive power can be treated as a synchronization problem of a first-order linear agent system [26–28]. Then, Equation (20) is obtained from the linearization of Equation (15): u = n Q = C e (20) Q Qi i nQ niQi where, u is the auxiliary control, e represents the reactive power error between the Q niQi local DG and its neighbor, and C is the coupling gain. The local neighbor ’s reactive nQ power sharing error is represented by: e = a n Q n Q (21) niQi å i j Qi i Qj j j=N where a represents the changes in connection between DGs from the adjacency matrix. ij The whole consensus system can be written in matrix representation as: 2 3 2 3 . . 2 3 2 3 2 3 u n Q n Q a Q Q1 1 Q1 1 1j 1 n Q n Q . . Q1 1 Qj j 6 7 6 7 6 7 6 7 6 7 6 7 6 7 u n Q n Q a 6 Q 7 Q2 Q2 6 2j 7 6 7 1 2 2 6 7 6 7 n Q n Q 6 7 6 7 6 7 Q2 2 Qj j 6 7 6 7 = = (22) 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 j=N 4 5 4 5 4 5 4 5 4 5 . . n Q n Q QN N Qj j u a Q n Q n Q N j N QN N QN N Then the Adaptive VI references in Equation (14) can be presented as follows: V R w L i vi_d vi vi gd = (23) V R w L vi_q vi vi gq L L k vi l vi = u (24) R R k vi r vi where, L and R represent the resistance and inductance of the static impedance. L , and vi vi vi R are the resistance and inductance of the VI. k and k are adjusting gains of the consensus vi l r Energies 2022, 15, x FOR PEER REVIEW 9 of 19 controller. Based on these equations, the adaptive VI implementation is illustrated in Figure 4. Figure 4. Adaptive VI and consensus algorithm implementation. Figure 4. Adaptive VI and consensus algorithm implementation. 3.3. Bus Voltage Restoration 3.3. Bus Voltage Restoration In order to compensate the voltage drop caused by the droop control and the VI, a In order to compensate the voltage drop caused by the droop control and the VI, a secondary voltage controller based on consensus control is used to restore the average voltage secondaof ry each volta DG ge con to the troll MG er ba nominal sed on voltage. consensus This cowill ntroleliminate is used to the revoltage store thdeviation e average between voltage oDGs, f each impr DGove to th the e M power G nom flow inal contr volta ol, ge.and Thiensur s wille el aim reliable inate toperation he voltage of dev the iaMG. tion The average voltage of each DG can be defined as the average output voltage value of all between DGs, improve the power flow control, and ensure a reliable operation of the MG. MG The DGs avera [ge 23,26 vol ,27 ta]: ge of each DG can be defined as the average output voltage value of all MG DGs [23,26,27]: V = (25) 𝑁 j=1 (25) 𝑉 = ∑ 𝑗 = 1 where 𝑉 is the average voltage, Vj is the output voltage of DGj, and N is the total number of DGs connected to the MG. Using the consensus based adaptive VI control, once the virtual impedance is adaptively set and the reactive power sharing is achieved, the droop controller output voltage of each DG becomes the same. However, the DG output voltage at the filter output level cannot be identical for all the DGs due to impedance mismatch, as explained previously. This can cause deviations in the output voltage and exceed the allowable range. Therefore, a secondary control for voltage restoration should be used to regulate the average MG voltage. The DG average voltage estimation can be expressed ̌ ̌ using its own output voltage 𝑉 and its neighbor DG voltage 𝑉 . 𝑖 𝑗 (26) ̌ ̌ ̌ 𝑉 (𝑡 ) = 𝑉 (𝑡 )+ 𝐶 ∫ ∑ (𝑉 (𝑡 )− 𝑉 (𝑡 )) 𝑖 𝑖 𝑣 𝑖 𝑗 where Vi is the voltage of DGi and Cv is a coupling gain. Then, the dynamics of the voltage consensus control can be expressed as follows: ̇ (27) ̌ ̇ ̌ ̌ ( ) ( ) 𝑉 𝑡 = 𝑉 𝑡 + 𝐶 ∑ (𝑉 (𝑡 )− 𝑉 (𝑡 )) 𝑖 𝑖 𝑣 𝑖 𝑗 The implementation of the proposed approach for voltage restoration is shown in Figure 5. Figure 5. Implementation of the reference voltage generator. 4. Simulation Verification In order to verify the effectiveness of the proposed control approach, simulation tests were conducted using MATLAB/Simulink software. The MG shown in Figure 2 was 𝜖𝑛 𝑎𝑖𝑗 𝜖𝑛 𝑑𝑡 𝑎𝑖𝑗 Energies 2022, 15, x FOR PEER REVIEW 9 of 19 Figure 4. Adaptive VI and consensus algorithm implementation. 3.3. Bus Voltage Restoration In order to compensate the voltage drop caused by the droop control and the VI, a secondary voltage controller based on consensus control is used to restore the average voltage of each DG to the MG nominal voltage. This will eliminate the voltage deviation between DGs, improve the power flow control, and ensure a reliable operation of the MG. The average voltage of each DG can be defined as the average output voltage value of all MG DGs [23,26,27]: (25) Energies 2022, 15, 3480 9 of 19 𝑉 = ∑ 𝑗 = 1 where 𝑉 is the average voltage, Vj is the output voltage of DGj, and N is the total number where V is the average voltage, Vj is the output voltage of DG , and N is the total number of DGs connected to the MG. Using the consensus based adaptive VI control, once the of DGs connected to the MG. Using the consensus based adaptive VI control, once the virtual impedance is adaptively set and the reactive power sharing is achieved, the droop virtual impedance is adaptively set and the reactive power sharing is achieved, the droop controller output voltage of each DG becomes the same. However, the DG output voltage controller output voltage of each DG becomes the same. However, the DG output voltage at the filter output level cannot be identical for all the DGs due to impedance mismatch, at the filter output level cannot be identical for all the DGs due to impedance mismatch, as explained previously. This can cause deviations in the output voltage and exceed the as explained previously. This can cause deviations in the output voltage and exceed the allowable range. Therefore, a secondary control for voltage restoration should be used to allowable range. Therefore, a secondary control for voltage restoration should be used to regulate the average MG voltage. The DG average voltage estimation can be expressed regulate the average MG voltage. The DG average voltage estimation can be expressed ̌ ̌ using its own output voltage 𝑉 and its neighbor DG voltage 𝑉 . 𝑖 𝑗 ˇ ˇ using its own output voltage V and its neighbor DG voltage V . i j (26) ̌ ̌ ̌ 𝑉 (𝑡 ) = 𝑉 (𝑡 )+ 𝐶 ∫ ∑ (𝑉 (𝑡 )− 𝑉 (𝑡 )) 𝑖 𝑖 𝑣 𝑖 𝑗 ˇ ˇ ˇ V (t) = V (t) + C ai j(V (t) V (t)) dt (26) i i å i j jen where Vi is the voltage of DGi and Cv is a coupling gain. Then, the dynamics of the voltage where V is the voltage of DGi and C is a coupling gain. Then, the dynamics of the voltage i v consensus control can be expressed as follows: consensus control can be expressed as follows: ̇ (27) ̌ ̇ ̌ ̌ ( ) ( ) 𝑉 𝑡 ˇ = 𝑉 𝑡 + 𝐶 ∑ (𝑉 (𝑡 ˇ)− 𝑉 (𝑡 ˇ)) 𝑖 V (t) = 𝑖 V (t) + 𝑣 C ai j𝑖 (V (t) 𝑗 V (t)) (27) l l v å i j 𝑗 jen The implementation of the proposed approach for voltage restoration is shown in The implementation of the proposed approach for voltage restoration is shown in Figure 5. Figure 5. Figure 5. Implementation of the reference voltage generator. Figure 5. Implementation of the reference voltage generator. 4. Simulation Verification 4. Simulation Verification In order to verify the effectiveness of the proposed control approach, simulation tests In order to verify the effectiveness of the proposed control approach, simulation tests were conducted using MATLAB/Simulink software. The MG shown in Figure 2 was were conducted using MATLAB/Simulink software. The MG shown in Figure 2 was modeled in Simulink. The MG is composed of three DGs connected to renewable energy sources (solar or wind) with different rated powers and a battery storage system. All DGs are connected to the AC bus through an LCL filter and an impedance. Moreover, different loads are connected to the AC bus. All DGs are connected to a communication link in order to change information between neighbors. The sharing power ratio is 1:1:0.5 for DG1, DG2, and DG3, respectively. Table 1 shows the parameters used in this simulation. The simulation is divided into three parts. In the first one, reactive power sharing accuracy was verified using the proposed control approach. In the second one, the robustness of the control approach under load changes is explored, and finally, in the third one, the voltage restoration performance was investigated. Table 1. Simulation parameters. Parameters Value Inverter power rating 5 KVA Line voltage 208 V Bus frequency 60 Hz Dc bus voltage 400 V Line impedances line 1 7.5 mH, 0.6 W line 2 4.5 mH, 0.5 W line 3 7.5 mH, 0.6 W Proportional gain in PI current controller Kpi 50 Integral gain in PI current controller Kii 0.5 𝜖𝑛 𝑎𝑖𝑗 𝜖𝑛 𝑑𝑡 𝑎𝑖𝑗 Energies 2022, 15, 3480 10 of 19 Table 1. Cont. Parameters Value Proportional gain in PI voltage controller Kpv 2 Integral gain in PI voltage controller Kiv 0.5 Droop coefficient mP1, mP2 2 10 mP3 4 10 nQ1, nQ2 5 10 nQ3 7.5 10 Load 1 4 kW, 1.1 kVAR Load 2 2.2 kW, 0.6 kVAR Load 3,4 1 kW, 0.25 kVAR 4.1. Case Study #1 Figure 6 represents the active power sharing between the three DGs. The active power was well shared before and after applying the proposed strategy. The reactive power Energies 2022, 15, x FOR PEER REVIEW 11 of 19 Energies 2022, 15, x FOR PEER REVIEW 11 of 19 sharing is shown in Figure 7, where it is not achieved using the conventional method. Energies 2022, 15, x FOR PEER REVIEW 11 of 19 The proposed control strategy was applied at t = 7.5 s, which offers an accurate reactive power sharing in the desired ratio without affecting the active power sharing. The virtual resistance and reactance of each DG are illustrated in Figures 8 and 9. Figure 6. Active power of DGs. Figure 6. Active power of DGs. Figure 6. Active power of DGs. Figure 6. Active power of DGs. Figure 7. Reactive power of DGs. Figure 7. Reactive power of DGs. Figure 7. Reactive power of DGs. Figure 7. Reactive power of DGs. Figure 8. Virtual impedance reactance. Figure 8. Virtual impedance reactance. Figure 8. Virtual impedance reactance. Figure 8. Virtual impedance reactance. Figure 9. Virtual impedance resistances. Figure 9. Virtual impedance resistances. Figure 9. Virtual impedance resistances. 4.2. Case Study #2 4.2. Case Study #2 4.2. Case Study #2 In the second part of the simulations, the performance of the system was tested dur- In the second part of the simulations, the performance of the system was tested dur- ing load changes. In this case study, the renewable resources are operated under deloaded In the second part of the simulations, the performance of the system was tested dur- ing load changes. In this case study, the renewable resources are operated under deloaded mode, their maximum output power is between t = 5 s and t = 7.5. Otherwise, they are ing load changes. In this case study, the renewable resources are operated under deloaded mode, their maximum output power is between t = 5 s and t = 7.5. Otherwise, they are operated under deloaded mode. Initially, the system load is (2.2 kW, 0.6 kVAR), after t = mode, their maximum output power is between t = 5 s and t = 7.5. Otherwise, they are operated under deloaded mode. Initially, the system load is (2.2 kW, 0.6 kVAR), after t = 2.5 s the load was increased to (3.2 kW, 0.85 kVAR), then after t = 5 s, the load was in- operated under deloaded mode. Initially, the system load is (2.2 kW, 0.6 kVAR), after t = 2.5 s the load was increased to (3.2 kW, 0.85 kVAR), then after t = 5 s, the load was in- creased to (4.2 kW, 1.1 kVAR). Finally, at t = 7.5 s the load was reduced to (3.2 kW, 0.85 2.5 s the load was increased to (3.2 kW, 0.85 kVAR), then after t = 5 s, the load was in- creased to (4.2 kW, 1.1 kVAR). Finally, at t = 7.5 s the load was reduced to (3.2 kW, 0.85 kVAR). The simulation results are shown in Figures 11–14. For active and reactive power creased to (4.2 kW, 1.1 kVAR). Finally, at t = 7.5 s the load was reduced to (3.2 kW, 0.85 kVAR). The simulation results are shown in Figures 11–14. For active and reactive power sharing and by ignoring transient periods as shown in Figures 11 and 12, the consensus kVAR). The simulation results are shown in Figures 11–14. For active and reactive power sharing and by ignoring transient periods as shown in Figures 11 and 12, the consensus control eliminates progressively the reactive power error between DGs during all periods sharing and by ignoring transient periods as shown in Figures 11 and 12, the consensus control eliminates progressively the reactive power error between DGs during all periods of load changes. This provides improved power sharing, as shown by these results. The control eliminates progressively the reactive power error between DGs during all periods of load changes. This provides improved power sharing, as shown by these results. The output currents of each DG are shown in Figure 13. It can be seen that the currents are of load changes. This provides improved power sharing, as shown by these results. The output currents of each DG are shown in Figure 13. It can be seen that the currents are well synchronized and proportional to the power demand of each DG. The same result output currents of each DG are shown in Figure 13. It can be seen that the currents are well synchronized and proportional to the power demand of each DG. The same result was reflected on all load change conditions during this simulation period. The load well synchronized and proportional to the power demand of each DG. The same result was reflected on all load change conditions during this simulation period. The load changes during simulation are represented in Figure 14. was reflected on all load change conditions during this simulation period. The load changes during simulation are represented in Figure 14. changes during simulation are represented in Figure 14. Energies 2022, 15, x FOR PEER REVIEW 11 of 19 Figure 6. Active power of DGs. Figure 7. Reactive power of DGs. Energies 2022, 15, 3480 11 of 19 Figure 8. Virtual impedance reactance. Figure 9. Virtual impedance resistances. Figure 9. Virtual impedance resistances. After activating the consensus algorithm control, DG1 and 2 resistance and reactance values become equal. This is due to their equal power-sharing ratios. While the resistance 4.2. Case Study #2 and reactance values for DG3 are larger because the sharing ratio of this DG is lower In the second part of the simulations, the performance of the system was tested dur- than the others. The output currents corresponding to the three DG units are indicated in in g Figur loade cha 10. Figur nges. e In 10 b,c thishows s case ast zoom udy,befor the re e and newa after ble the reapplication sources are of o the pepr raoposed ted under deloaded Energies 2022, 15, x FOR PEER REVIEW 12 of 19 consensus controller. Before the application of the proposed method, there was a phase mode, their maximum output power is between t = 5 s and t = 7.5. Otherwise, they are shift between the three DGs currents. After t = 7.5 s, the output currents of DGs become operated under deloaded mode. Initially, the system load is (2.2 kW, 0.6 kVAR), after t = synchronized and proportional to the nominal power demanded by loads and the phases 2.5 s the load was increased to (3.2 kW, 0.85 kVAR), then after t = 5 s, the load was in- are almost identical. creased to (4.2 kW, 1.1 kVAR). Finally, at t = 7.5 s the load was reduced to (3.2 kW, 0.85 kVAR). The simulation results are shown in Figures 11–14. For active and reactive power sharing and by ignoring transient periods as shown in Figures 11 and 12, the consensus control eliminates progressively the reactive power error between DGs during all periods of load changes. This provides improved power sharing, as shown by these results. The output currents of each DG are shown in Figure 13. It can be seen that the currents are well synchronized and proportional to the power demand of each DG. The same result was reflected on all load change conditions during this simulation period. The load changes during simulation are represented in Figure 14. (a) (b) (c) Figure 10. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying Figure 10. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying the proposed controller. the proposed controller. 4.2. Case Study #2 In the second part of the simulations, the performance of the system was tested during load changes. In this case study, the renewable resources are operated under deloaded mode, their maximum output power is between t = 5 s and t = 7.5. Otherwise, they are operated under deloaded mode. Initially, the system load is (2.2 kW, 0.6 kVAR), after t = 2.5 s the load was increased to (3.2 kW, 0.85 kVAR), then after t = 5 s, the load was increased to (4.2 kW, 1.1 kVAR). Finally, at t = 7.5 s the load was reduced to (3.2 kW, 0.85 kVAR). The simulation results are shown in Figures 11–14. For active and reactive Figure 11. Active power of DGs. power sharing and by ignoring transient periods as shown in Figures 11 and 12, the consensus control eliminates progressively the reactive power error between DGs during Figure 12. Reactive power of DGs. Figure 13. Output current of DGs. Energies 2022, 15, x FOR PEER REVIEW 12 of 19 Energies 2022, 15, x FOR PEER REVIEW 12 of 19 Energies 2022, 15, x FOR PEER REVIEW 12 of 19 (a) (a) (a) Energies 2022, 15, 3480 12 of 19 (b) (c) (b) (c) (b) (c) all periods of load changes. This provides improved power sharing, as shown by these Figure 10. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying results. The output currents of each DG are shown in Figure 13. It can be seen that the Figure 10. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying the proposed controller. Figure 10. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying currents are well synchronized and proportional to the power demand of each DG. The the proposed controller. same result was reflected on all load change conditions during this simulation period. The the proposed controller. load changes during simulation are represented in Figure 14. Figure 11. Active power of DGs. Figure 11. Active power of DGs. Figure 11. Active power of DGs. Figure 11. Active power of DGs. Figure 12. Reactive power of DGs. Figure 12. Reactive power of DGs. Figure 12. Reactive power of DGs. Figure 12. Reactive power of DGs. Energies 2022, 15, x FOR PEER REVIEW 13 of 19 Figure 13. Output current of DGs. Figure 13. Output current of DGs. Figure 13. Output current of DGs. Figure 13. Output current of DGs. Figure 14. Load profile. Figure 14. Load profile. 4.3. Case Study #3 The third simulation case was dedicated to voltage restoration control. At the begin- ning, one load was connected to the AC bus, then at time t = 1.5 s the restoration control was activated. To verify the effectiveness of the voltage restoration control, another load was connected to the AC bus at t = 3 s. The results of this simulation are shown in Figures 15–20. Initially, the output voltages of the three DGs are lower than the reference voltage as shown in Figure 15. After application of the proposed control (at t = 1.5 s), the output voltage of each DG was increased until the average voltage was set to the MG nominal voltage. The active and reactive power sharing was always maintained, as shown in Fig- ures 16 and 17. Likewise, the output frequency was maintained within the allowed limits (Figure 18). Figure 19 shows the average voltage of the AC bus. The latter is equal to 120 V after the activation of the restoration control algorithm, which represents the nominal value. The currents of DGs are illustrated in Figure 20, an increase regarding the power- sharing ratio for each DG was observed after time t = 3 s due to the load increase. The load changes during simulation are represented in Figure 21. Figure 15. Output voltage of DGs. Figure 16. Active power of DGs. Figure 17. Reactive power of DGs. Energies 2022, 15, x FOR PEER REVIEW 13 of 19 Energies 2022, 15, x FOR PEER REVIEW 13 of 19 Energies 2022, 15, x FOR PEER REVIEW 13 of 19 Figure 14. Load profile. Figure 14. Load profile. Figure 14. Load profile. 4.3. Case Study #3 4.3. Case Study #3 The third simulation case was dedicated to voltage restoration control. At the begin- 4.3. Case Study #3 The third simulation case was dedicated to voltage restoration control. At the begin- ning, one load was connected to the AC bus, then at time t = 1.5 s the restoration control The third simulation case was dedicated to voltage restoration control. At the begin- ning, one load was connected to the AC bus, then at time t = 1.5 s the restoration control Energies 2022, 15, 3480 13 of 19 was activated. To verify the effectiveness of the voltage restoration control, another load ning, one load was connected to the AC bus, then at time t = 1.5 s the restoration control was activated. To verify the effectiveness of the voltage restoration control, another load was connected to the AC bus at t = 3 s. The results of this simulation are shown in Figures was activated. To verify the effectiveness of the voltage restoration control, another load was connected to the AC bus at t = 3 s. The results of this simulation are shown in Figures 15–20. Initially, the output voltages of the three DGs are lower than the reference voltage 4.3. Case Study #3 was connected to the AC bus at t = 3 s. The results of this simulation are shown in Figures 15–20. Initially, the output voltages of the three DGs are lower than the reference voltage as shown in Figure 15. After application of the proposed control (at t = 1.5 s), the output The third simulation case was dedicated to voltage restoration control. At the begin- 15–20. Initially, the output voltages of the three DGs are lower than the reference voltage as shown in Figure 15. After application of the proposed control (at t = 1.5 s), the output voltage of each DG was increased until the average voltage was set to the MG nominal ning, one load was connected to the AC bus, then at time t = 1.5 s the restoration control was as shown in Figure 15. After application of the proposed control (at t = 1.5 s), the output voltage of each DG was increased until the average voltage was set to the MG nominal activated. To verify the effectiveness of the voltage restoration control, another load was voltage. The active and reactive power sharing was always maintained, as shown in Fig- voltage of each DG was increased until the average voltage was set to the MG nominal connected to the AC bus at t = 3 s. The results of this simulation are shown in Figures 15–20. voltage. The active and reactive power sharing was always maintained, as shown in Fig- ures 16 and 17. Likewise, the output frequency was maintained within the allowed limits Initially, the output voltages of the three DGs are lower than the reference voltage as shown voltage. The active and reactive power sharing was always maintained, as shown in Fig- ures 16 and 17. Likewise, the output frequency was maintained within the allowed limits (Figure 18). Figure 19 shows the average voltage of the AC bus. The latter is equal to 120 in Figure 15. After application of the proposed control (at t = 1.5 s), the output voltage of ures 16 and 17. Likewise, the output frequency was maintained within the allowed limits (Figure 18). Figure 19 shows the average voltage of the AC bus. The latter is equal to 120 each DG was increased until the average voltage was set to the MG nominal voltage. The V after the activation of the restoration control algorithm, which represents the nominal (Figure 18). Figure 19 shows the average voltage of the AC bus. The latter is equal to 120 active and reactive power sharing was always maintained, as shown in Figures 16 and 17. V after the activation of the restoration control algorithm, which represents the nominal value. The currents of DGs are illustrated in Figure 20, an increase regarding the power- Likewise, the output frequency was maintained within the allowed limits (Figure 18). V after the activation of the restoration control algorithm, which represents the nominal value. The currents of DGs are illustrated in Figure 20, an increase regarding the power- sharing ratio for each DG was observed after time t = 3 s due to the load increase. The load Figure 19 shows the average voltage of the AC bus. The latter is equal to 120 V after the value. The currents of DGs are illustrated in Figure 20, an increase regarding the power- sharing ratio for each DG was observed after time t = 3 s due to the load increase. The load activation of the restoration control algorithm, which represents the nominal value. The changes during simulation are represented in Figure 21. sharing ratio for each DG was observed after time t = 3 s due to the load increase. The load currents of DGs are illustrated in Figure 20, an increase regarding the power-sharing ratio changes during simulation are represented in Figure 21. cha for each nges d DG uri wasnobserved g simula after tion time are t = re 3pr s due esen toted the load in Fi incr gure ease. 21. The load changes during simulation are represented in Figure 21. Figure 15. Output voltage of DGs. Figure 15. Output voltage of DGs. Figure 15. Output voltage of DGs. Figure 15. Output voltage of DGs. Figure 16. Active power of DGs. Figure 16. Active power of DGs. Figure 16. Active power of DGs. Figure 16. Active power of DGs. Figure 17. Reactive power of DGs. Figure 17. Reactive power of DGs. Figure 17. Reactive power of DGs. Figure 17. Reactive power of DGs. Energies 2022, 15, x FOR PEER REVIEW 14 of 19 Energies 2022, 15, x FOR PEER REVIEW 14 of 19 Energies 2022, 15, x FOR PEER REVIEW 14 of 19 Energies 2022, 15, x FOR PEER REVIEW 14 of 19 Energies 2022, 15, 3480 14 of 19 Figure 18. Frequency of DGs. Figure 18. Frequency of DGs. Figure 18. Frequency of DGs. Figure 18. Frequency of DGs. Figure 18. Frequency of DGs. Figure 19. Average AC bus voltage. Figure 19. Average AC bus voltage. Figure 19. Average AC bus voltage. Figure 19. Average AC bus voltage. Figure 19. Average AC bus voltage. Figure 20. Output current of DGs. Figure 20. Output current of DGs. Figure 20. Output current of DGs. Figure 20. Output current of DGs. Figure 20. Output current of DGs. Figure 21. Load profile. Figure 21. Load profile. Figure 21. Load profile. 5. Experimental Validation Figure 21. Load profile. Figure 21. Load profile. 5. Experimental Validation In order to validate the proposed control approach, the simulation results were com- 5. Experimental Validation pared with experimental ones. A laboratory-scale MG was constructed and used to validate In order to validate the proposed control approach, the simulation results were com- 5. Experimental Validation the proposed control. A dSPACE DS1004 control board was used to implement different 5. Ex In pe o rrd ime ern to ta va l V li ad li ad te atth ion e pr oposed control approach, the simulation results were com- pared with experimental ones. A laboratory-scale MG was constructed and used to vali- control algorithms. Two inverters were built using Infineon IKCM30F60GD smart modules In order to validate the proposed control approach, the simulation results were com- pared with experimental ones. A laboratory-scale MG was constructed and used to vali- with two In o DC rdpower er to va supplies. lidate The the inverters proposar ed e connected control a to ppr theoAC ach, bus ththr e si ough mula LCL tion results were com- date the proposed control. A dSPACE DS1004 control board was used to implement dif- pared with experimental ones. A laboratory-scale MG was constructed and used to vali- d filters. ate th Inductors e propowith sed dif cofn er tr ent ol. values A dS wer PA eCE added DS1 to0the 04 inverter controloutput board to wa repr s esent used to implement dif- pared with experimental ones. A laboratory-scale MG was constructed and used to vali- ferent control algorithms. Two inverters were built using Infineon IKCM30F60GD smart date the proposed control. A dSPACE DS1004 control board was used to implement dif- ferent control algorithms. Two inverters were built using Infineon IKCM30F60GD smart date the proposed control. A dSPACE DS1004 control board was used to implement dif- modules with two DC power supplies. The inverters are connected to the AC bus through ferent control algorithms. Two inverters were built using Infineon IKCM30F60GD smart modules with two DC power supplies. The inverters are connected to the AC bus through ferent control algorithms. Two inverters were built using Infineon IKCM30F60GD smart LCL filters. Inductors with different values were added to the inverter output to represent modules with two DC power supplies. The inverters are connected to the AC bus through LCL filters. Inductors with different values were added to the inverter output to represent modules with two DC power supplies. The inverters are connected to the AC bus through the line impedances. Finally, two inductive resistive loads are connected to the AC bus LCL filters. Inductors with different values were added to the inverter output to represent the line impedances. Finally, two inductive resistive loads are connected to the AC bus LCL filters. Inductors with different values were added to the inverter output to represent through contactors to allow connection or disconnection of these loads. The experimental the line impedances. Finally, two inductive resistive loads are connected to the AC bus through contactors to allow connection or disconnection of these loads. The experimental the line impedances. Finally, two inductive resistive loads are connected to the AC bus parameters are illustrated in Table 2 and the benchmark is shown in Figure 22. through contactors to allow connection or disconnection of these loads. The experimental parameters are illustrated in Table 2 and the benchmark is shown in Figure 22. through contactors to allow connection or disconnection of these loads. The experimental parameters are illustrated in Table 2 and the benchmark is shown in Figure 22. parameters are illustrated in Table 2 and the benchmark is shown in Figure 22. Energies 2022, 15, 3480 15 of 19 Energies 2022, 15, x FOR PEER REVIEW 15 of 19 the line impedances. Finally, two inductive resistive loads are connected to the AC bus through contactors to allow connection or disconnection of these loads. The experimental parameters are illustrated in Table 2 and the benchmark is shown in Figure 22. Table 2. Experimental parameters. Parameters Value Table 2. Experimental parameters. Power rating 500 VA Parameters Value Line voltage 40 V Power rating 500 VA Bus frequency 60 Hz Line voltage 40 V DC bus voltage 80 V Bus frequency 60 Hz Line impedances DC bus voltage 80 V line 1 0.82 mH, 0.02 Ω Line impedances line 2 1.2 mH, 0.03 Ω line 1 0.82 mH, 0.02 W line 2 1.2 mH, 0.03 W Proportional gain in PI current controller Kpi 100 Proportional gain in PI current controller Kpi 100 Integral gain in PI current controller Kii 0.5 Integral gain in PI current controller Kii 0.5 Proportional gain in PI voltage controller Kpv 50 Proportional gain in PI voltage controller Kpv 50 Integral gain in PI voltage controller Kiv 1.5 Integral gain in PI voltage controller Kiv 1.5 Droop coef Dro ficient op coefficient −3 mP1 2 10 mP1 2 × 10 mP2 4 10 −3 mP2 4 × 10 nQ1 5 10 −3 nQ1, 5 × 10 nQ2 7.5 10 −3 nQ2 7.5 × 10 Figure 22. Laboratory experimental benchmark. Figure 22. Laboratory experimental benchmark. 5.1. Case Study #1 5.1. Case Study #1 The The first first scenario scenario o of f ex experimental perimental va validation lidation wa was s cacarried rried out out to ve to rif verify y the the shasharing ring of active and reactive powers. The power-sharing ratio used in these tests is the same for the of active and reactive powers. The power-sharing ratio used in these tests is the same two DGs. Figure 23 shows the active power. It is well shared between the two inverters, for the two DGs. Figure 23 shows the active power. It is well shared between the two before and after the application of the proposed approach. The reactive power sharing is inverters, before and after the application of the proposed approach. The reactive power shown in Figure 24. It was not achieved using the conventional method until the applica- sharing is shown in Figure 24. It was not achieved using the conventional method until the application tion of the pr ofothe posed proposed control contr strategy ol strategy after t = after 7.5 s t wh = 7.5 ichs awhich llows a allows ccurate accurate reactiver pow eactive er sharing. The output currents of inverters are illustrated in Figure 25. Figure 25b,c, shows power sharing. The output currents of inverters are illustrated in Figure 25. Figure 25b,c, shows a zoom a be zoom fore befor and ae fter and the after activa the tio activation n of the prof opos the ed pr con oposed troller contr . A pha oller se.-sh Aift phase-shift between the output currents was observed before the application of the proposed control. After t = between the output currents was observed before the application of the proposed control. After 7.5 s, tth =ey 7.5 be s,com they e sy become nchron synchr ized. onized. Energies 2022, 15, x FOR PEER REVIEW 16 of 19 Energies 2022, 15, x FOR PEER REVIEW 16 of 19 Energies 2022, 15, 3480 16 of 19 Energies 2022, 15, x FOR PEER REVIEW 16 of 19 Figure 23. Active power of DGs (1 div = 10 W). Figure 23. Active power of DGs (1 div = 10 W). Figure 23. Active power of DGs (1 div = 10 W). Figure 23. Active power of DGs (1 div = 10 W). Figure 24. Reactive power of DGs (1 div = 10 VAR). Figure 24. Reactive power of DGs (1 div = 10 VAR). Figure 24. Reactive power of DGs (1 div = 10 VAR). Figure 24. Reactive power of DGs (1 div = 10 VAR). (a) (a) (a) (b) (c) Figure 25. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying Figure 25. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying ththe e pr pr opos oposed ed con contr trololler ler (1(1 di div v = = 5 5 AA/50 /50 V). V). 5.2. Case Study #2 5.2. Case Study #2 In the second scenario, another experimental test was carried out to verify the robust- In the second scenario, another experimental test was carried out to verify the robust- (b) (c) ness of the proposed approach by increasing load. The load was increased from (280 W, ness of the proposed approach by increasing load. The load was increased from (280 W, 30 VAR) to (380 W, 60 VAR) (b) at time t = 10 s. As expected, the results are similar to (cthe ) 30 VAR) to (380 W, 60 VAR) at time t = 10 s. As expected, the results are similar to the simulation, both DGs follow the change and the active and reactive power was shared Figure 25. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying simulation, both DGs follow the change and the active and reactive power was shared accurately as shown in Figures 26 and 27, respectively. Figure 28 shows the voltage of Figure 25. Output currents of DGs, (a) output current, (b) zoom before, and (c) zoom after applying the proposed controller (1 div = 5 A/50 V). accurately as shown in Figures 26 and 27, respectively. Figure 28 shows the voltage of the the load, a slight drop was observed when the load increases. Figure 29 shows the load the proposed controller (1 div = 5 A/50 V). load, a slight drop was observed when the load increases. Figure 29 shows the load changes during simulation. The output currents of each DG are shown in Figure 30 at the changes during simulation. The output currents of each DG are shown in Figure 30 at the 5.2. Case Study #2 top. The currents are well synchronized with the same amplitude, then increase when the 5.2. Case Study #2 In the second scenario, another experimental test was carried out to verify the robust- load rises, while the DGs output voltage keeps the same value as shown in the same figure In the second scenario, another experimental test was carried out to verify the robust- at the bottom. This confirms the effectiveness of the consensus control algorithm and the ness of the proposed approach by increasing load. The load was increased from (280 W, adaptive VI. Finally, the output voltages of each inverter are shown in Figure 31. They ness of the proposed approach by increasing load. The load was increased from (280 W, 30 VAR) to (380 W, 60 VAR) at time t = 10 s. As expected, the results are similar to the 30 VAR) to (380 W, 60 VAR) at time t = 10 s. As expected, the results are similar to the simulation, both DGs follow the change and the active and reactive power was shared simulation, both DGs follow the change and the active and reactive power was shared accurately as shown in Figures 26 and 27, respectively. Figure 28 shows the voltage of the accurately as shown in Figures 26 and 27, respectively. Figure 28 shows the voltage of the load, a slight drop was observed when the load increases. Figure 29 shows the load load, a slight drop was observed when the load increases. Figure 29 shows the load changes during simulation. The output currents of each DG are shown in Figure 30 at the changes during simulation. The output currents of each DG are shown in Figure 30 at the top. The currents are well synchronized with the same amplitude, then increase when the top. The currents are well synchronized with the same amplitude, then increase when the load rises, while the DGs output voltage keeps the same value as shown in the same figure load rises, while the DGs output voltage keeps the same value as shown in the same figure at the bottom. This confirms the effectiveness of the consensus control algorithm and the at the bottom. This confirms the effectiveness of the consensus control algorithm and the adaptive VI. Finally, the output voltages of each inverter are shown in Figure 31. They adaptive VI. Finally, the output voltages of each inverter are shown in Figure 31. They Energies 2022, 15, 3480 17 of 19 Energies 2022, 15, x FOR PEER REVIEW 17 of 19 Ene Ene rg rg ii ee s s 22 00 22 22 , ,15 15 , ,x x F F O O R R P P E E ER ER R R E E V V II EW EW 17 17 o o ff 19 19 Energies 2022, 15, x FOR PEER REVIEW 17 of 19 Energies 2022, 15, x FOR PEER REVIEW 17 of 19 top. The currents are well synchronized with the same amplitude, then increase when the load rises, while the DGs output voltage keeps the same value as shown in the same figure re at re pr the pr ese ese bottom. nn t t th th e e pha This pha se se confirm aa a a nn dd b s b the vol vol ta ef ta f ges. ectiveness ges. They They aof a re re the well well consensus s s yn yn chr chr oo nn contr iz iz ed ed ol wi wi algorithm th th th th ee sa sa m m and e e RR M the M SS represent the phase a and b voltages. They are well synchronized with the same RMS represent the phase a and b voltages. They are well synchronized with the same RMS represent the phase a and b voltages. They are well synchronized with the same RMS adaptive VI. Finally, the output voltages of each inverter are shown in Figure 31. They va va lue. lue. value. value. value. represent the phase a and b voltages. They are well synchronized with the same RMS value. Fig Fig ure ure 2 2 66 . .A A ct cive tive pp ow ow er e rof of DG DG s s( 1 (1 d d i i= = 11 00 W) W) . . Figure 26. Active power of DGs (1 di = 10 W). Figure 26. Active power of DGs (1 di = 10 W). Figure 26. Active power of DGs (1 di = 10 W). Figure 26. Active power of DGs (1 di = 10 W). Fig Fig ure ure 2 2 77 . .Rea Rea ct cive tive pp ow ow er er of of DG DG s s( 1 (1 d d iv iv = = 11 00 VA VA R) R) . . Figure 27. Reactive power of DGs (1 div = 10 VAR). Figure 27. Reactive power of DGs (1 div = 10 VAR). Figure 27. Reactive power of DGs (1 div = 10 VAR). Figure 27. Reactive power of DGs (1 div = 10 VAR). Figure 28. Output voltage of DGs. Fig Figure ure 2 28 8.. Out Outpu putt v vol oltta ag ge e of of D DG Gs. s. Fig Figure ure 2828. . Out Output put vol voltage tage of of DG DGs. s. Figure 28. Output voltage of DGs. Figure 29. Load profile. Fig Fig Figure ure ure 2 2 29. 9 9. . Lo Lo Load a ad d pr pr pr ofi ofi ofile. le le.. Figure 29. Load profile. Figure 29. Load profile. Figure 30. Output current of DGs (1 div = 5 A/50 V). Fig Figure ure 3 30 0.. Out Outpu putt ccurr urren entt of of D DG Gs s (1 (1 di div v = = 5 5 A A/5 /50 0 V). V). Figure 30. Output current of DGs (1 div = 5 A/50 V). Figure 30. Output current of DGs (1 div = 5 A/50 V). Figure 30. Output current of DGs (1 div = 5 A/50 V). Energies 2022, 15, 3480 18 of 19 Energies 2022, 15, x FOR PEER REVIEW 18 of 19 Figure 31. Output voltage of DGs (1 div = 5 A/50 V). Figure 31. Output voltage of DGs (1 div = 5 A/50 V). 6. Conclusions 6. Conclusions In this paper, a new power flow management algorithm was proposed to improve In this paper, a new power flow management algorithm was proposed to improve reactive power sharing between parallel inverters in islanded MGs. The proposed strategy reactive power sharing between parallel inverters in islanded MGs. The proposed strategy was based on the adaptive VI approach with consensus algorithms in order to ensure better was based on the adaptive VI approach with consensus algorithms in order to ensure bet- reactive power sharing under line impedance mismatch. The consensus algorithm was ter reactive power sharing under line impedance mismatch. The consensus algorithm was used to estimate and adjust the values of the VI. Then, the obtained VI was added to the used to estimate and adjust the values of the VI. Then, the obtained VI was added to the total impedance to calculate the new reference voltage for the primary controller. This total impedance to calculate the new reference voltage for the primary controller. This control approach improves reactive power sharing without the need of a central controller control approach improves reactive power sharing without the need of a central controller or the line impedance value. The consensus algorithm uses a simple communication link or the line impedance value. The consensus algorithm uses a simple communication link between neighbors’ DGs, minimizing the cost and increasing the efficiency of the MG. between neighbors’ DGs, minimizing the cost and increasing the efficiency of the MG. Furthermore, to compensate for the output voltage drop produced by the VI, a secondary Furthermore, to compensate for the output voltage drop produced by the VI, a secondary voltage controller based on a consensus algorithm was used. This controller can restore voltage controller based on a consensus algorithm was used. This controller can restore the average voltage of each DG to the nominal MG voltage. This eliminates the voltage the average voltage of each DG to the nominal MG voltage. This eliminates the voltage deviation between DGs and ensures reliable operation of the MG under hierarchical control. deviation between DGs and ensures reliable operation of the MG under hierarchical con- Finally, simulations and experimental results were presented to validate the perfor- trol. mance and feasibility of the proposed controller. These results show that the overall control Finally, simulations and experimental results were presented to validate the perfor- system provides a complete solution for improving MGs dynamic performance, accurate mance and feasibility of the proposed controller. These results show that the overall con- reactive power sharing, and output voltage restoration, while ensuring the robustness of trol system provides a complete solution for improving MGs dynamic performance, ac- the MGs under connected load changes, uncertainties, and possible disturbances. curate reactive power sharing, and output voltage restoration, while ensuring the robust- ness of the MGs under connected load changes, uncertainties, and possible disturbances. Author Contributions: Conceptualization, M.K.; methodology, M.K. and M.L.D.; software, M.K. and M.D.K.; validation, M.L.D., K.B. and M.D.K.; resources, M.K. and M.D.K.; writing—original draft Author Contributions: Conceptualization, M.K.; methodology, M.K. and M.L.D.; software, M.K. preparation, M.K.; writing—review and editing, M.L.D., K.B. and M.D.K.; visualization, M.K. and and M.D.K.; validation, M.L.D., K.B. and M.D.K.; resources, M.K. and M.D.K.; writing—original M.D.K.; supervision, M.L.D. and K.B. All authors have read and agreed to the published version of draft preparation, M.K.; writing—review and editing, M.L.D., K.B. and M.D.K.; visualization, M.K. the manuscript. and M.D.K.; supervision, M.L.D. and K.B. All authors have read and agreed to the published version Funding: This research received no external funding. of the manuscript. Institutional Review Board Statement: Not applicable. Funding: This research received no external funding. Informed Consent Statement: Not applicable. Institutional Review Board Statement: Not applicable. Data Inform Availability ed Consent Statement: Statement Not : Not applicable. applicable. Conflicts of Interest: The authors declare no conflict of interest. Data Availability Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. IRENA. World Energy Transistion Outlook-1.5 C Pathway; International Renewable Energy Agency (IRENA): Abu Dhabi, United References Arab Emirates, 2021. 1. IRENA. World Energy Transistion Outlook-1.5 ° C Pathway; International Renewable Energy Agency (IRENA): Abu Dhabi, United 2. Keddar, M.; Doumbia, M.L.; Belmokhtar, K.; Della Krachai, M. A new energy management strategy of an autonomous microgrid Arab Emirates, 2021. based on virtual impedance in multilevel droop controlled inverters. In Proceeding of International Conference on Advanced 2. Keddar, M.; Doumbia, M.L.; Belmokhtar, K.; Della Krachai, M. A new energy management strategy of an autonomous microgrid Electrical Engineering (ICAEE), Algiers, Algeria, 19–21 November 2019. based on virtual impedance in multilevel droop controlled inverters. In Proceeding of International Conference on Advanced 3. Shahbazitabar, M.; Abdi, H.; Nourianfar, H.; Anvari-Moghaddam, A.; Mohammadi-Ivatloo, B.; Hatziargyriou, N. An Introduction Electrical Engineering (ICAEE), Algiers, Algeria, 19–21 November 2019. to Microgrids, Concepts, Definition, and Classifications. Microgrids, Power Systems; Springer: Cham, Switzerland, 2021. 3. Shahbazitabar, M.; Abdi, H.; Nourianfar, H.; Anvari-Moghaddam, A.; Mohammadi-Ivatloo, B.; Hatziargyriou, N. An Introduc- 4. Mahmood, D.; Javaid, N.; Ahmed, G.; Khan, S.; Monteiro, V. A Review on Optimization Strategies Integrating Renewable Energy tion to Microgrids, Concepts, Definition, and Classifications. Microgrids, Power Systems; Springer: Cham, Switzerland, 2021. Sources Focusing Uncertainty Factor—Paving Path to Eco-Friendly Smart Cities. Sustain. Comput. Inform. Syst. 2021, 30, 100559. 4. Mahmood, D.; Javaid, N.; Ahmed, G.; Khan, S.; Monteiro, V. A Review on Optimization Strategies Integrating Renewable En- [CrossRef] ergy Sources Focusing Uncertainty Factor—Paving Path to Eco-Friendly Smart Cities. Sustain. Comput. Inform. Syst. 2021, 30, 5. Kim, Y.-S.; Kim, E.-S.; Moon, S.-I. Frequency and Voltage Control Strategy of Standalone Microgrids with High Penetration of Intermittent Renewable Generation Systems. IEEE Trans. Power Syst. 2016, 31, 718–728. [CrossRef] Energies 2022, 15, 3480 19 of 19 6. Kerdphol, T.; Rahman, F.S.; Mitani, Y.; Watanabe, M.; Kufeoglu, S. Robust Virtual Inertia Control of an Islanded Microgrid Considering High Penetration of Renewable Energy. IEEE Access 2018, 6, 625–636. [CrossRef] 7. Ma, D.; Liu, M.; Zhang, H.; Wang, R.; Xie, X. Accurate power sharing and voltage regulation for AC microgrids: An event-triggered coordinated control approach. IEEE Trans. Cybern. 2021, 1–11. [CrossRef] [PubMed] 8. Raj, D.C.; Gaonkar, D.N. Frequency and voltage droop control of parallel inverters in microgrid. In Proceedings of the 2016 2nd International Conference on Control, Instrumentation, Energy & Communication (CIEC), Kolkata, India, 28–30 January 2016; pp. 407–411. 9. Bouzid, A.E.; Sicard, P.; Yamane, A.; Paquin, J.N. Simulation of droop control strategy for parallel inverters in autonomous AC microgrids. In Proceedings of the 2016 8th International Conference on Modelling, Identification and Control (ICMIC), Algiers, Algeria, 15–17 November 2016; pp. 701–706. 10. Hamzeh, M.; Mokhtari, H.; Karimi, H. A decentralized self-adjusting control strategy for reactive power management in an islanded multi-bus MV microgrid. Can. J. Electr. Comput. Eng. 2013, 36, 18–25. [CrossRef] 11. Mohamed, Y.; El-Saadany, E.F. Adaptive decentralized droop controller to preserve power sharing stability of paralleled inverters in distributed generation microgrids. IEEE Trans. Power Electron. 2008, 23, 2806–2816. [CrossRef] 12. Mahmood, H.; Michaelson, D.; Jiang, J. Reactive power sharing in islanded microgrids using adaptive voltage droop control. IEEE Trans. Smart Grid 2015, 6, 3052–3060. [CrossRef] 13. Zhou, J.; Cheng, P. A Modified Q V Droop Control for Accurate Reactive Power Sharing in Distributed Generation Microgrid. IEEE Trans. Ind. Appl. 2019, 55, 4100–4109. [CrossRef] 14. He, J.; Li, Y.W.; Blaabjerg, F. Voltage Stability and Reactive Power Sharing in Review of Active and Reactive Power Sharing Strategies in Hierarchical Controlled Microgrids. IEEE Trans. Power Electron. 2015, 30, 3389–3401. [CrossRef] 15. Micallef, A.; Apap, M.; Staines, C.S.; Guerrero, J.M. Secondary Control for Reactive Power Sharing in Droop-Controlled Islanded Microgrids. In Proceedings of the 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Aalborg, Denmark, 25–28 June 2012; pp. 492–498. 16. Han, Y.; Li, H.; Shen, P.; Coelho, E.A.A.; Guerrero, J.M. Review of active and reactive power sharing strategies in hierarchical controlled microgrids. IEEE Trans. Power Electron. 2017, 32, 2427–2451. [CrossRef] 17. Schiffer, J.; Seel, T.; Raisch, J.; Sezi, T. Voltage Stability and Reactive Power Sharing in Inverter-Based Microgrids With Consensus- Based Distributed Voltage Control. IEEE Trans. Control Syst. Technol. 2016, 24, 96–109. [CrossRef] 18. Zhu, Y.; Zhuo, F.; Wang, F.; Liu, B.; Gou, R.; Zhao, Y. A virtual impedance optimization method for reactive power sharing in networked microgrid. IEEE Trans. Power Electron. 2016, 31, 2890–2904. [CrossRef] 19. Mahmood, H.; Michaelson, D.; Jiang, J. Accurate reactive power sharing in an islanded microgrid using adaptive virtual impedances. IEEE Trans. Power Electron. 2015, 30, 1605–1617. [CrossRef] 20. He, J.; Li, Y.W.; Guerrero, J.M.; Vasquez, J.C.; Blaabjerg, F. An islanding microgrid reactive power sharing scheme enhanced by programmed virtual impedances. In Proceedings of the 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), Aalborg, Denmark, 25–28 June 2012; pp. 229–235. 21. Hoang, T.V.; Lee, H.H. An Adaptive Virtual Impedance Control Scheme to Eliminate the Reactive-Power-Sharing Errors in an Islanding Meshed Microgrid. IEEE J. Emerg. Sel. Top. Power Electron. 2017, 6, 966–976. [CrossRef] 22. Zandi, F.; Fani, B.; Sadeghkhani, I.; Orakzadeh, A. Adaptive complex virtual impedance control scheme for accurate reactive power sharing of inverter interfaced autonomous microgrids. IET Gener. Trans. Distrib. 2018, 12, 6021–6032. [CrossRef] 23. Zhang, H.; Kim, S.; Sun, Q.; Zhou, J. Distributed adaptive virtual impedance control for accurate reactive power sharing based on consensus control in microgrids. IEEE Trans. Smart Grid 2017, 8, 1749–1761. [CrossRef] 24. An, R.; Liu, Z.; Liu, J. Successive-approximation-based virtual impedance tuning method for accurate reactive power sharing in islanded microgrids. IEEE Trans Power Electron. 2020, 36, 87–102. [CrossRef] 25. Yu, L.; Shi, D.; Xu, G.; Guo, X.; Jiang, Z.; Jing, C. Consensus Control of Distributed Energy Resources in a Multi-Bus Microgrid for Reactive Power Sharing and Voltage Control. Energies 2018, 11, 2710. [CrossRef] 26. Alsafran, A.S.; Daniels, M.W. Consensus Control for Reactive Power Sharing Using an Adaptive Virtual Impedance Approach. Energies 2020, 13, 2026. [CrossRef] 27. Lyu, Z.; Wei, Q.; Zhang, Y.; Zhao, J.; Manla, E. Adaptive Virtual Impedance Droop Control Based on Consensus Control of Reactive Current. Energies 2018, 11, 1801. [CrossRef] 28. Sultani, J.F. Modelling, Design and Implementation Of D-Q Control in Single-Phase Grid-Connected Inverters for Photovoltaic Systems Used in Domestic Dwellings; De Montfort University: Leicester, UK, 2013. 29. Keddar, M.; Doumbia, M.L.; Belmokhtar, K.; Della Krachai, M. Experimental Validation of an Accurate Reactive Power-Sharing Approach Based on Adaptive Virtual Impedance and Consensus Control. In Proceedings of the 12th International Renewable Energy Congress (IREC), Hammamet, Tunisia, 26–28 October 2021; pp. 1–6.
Journal
Energies – Multidisciplinary Digital Publishing Institute
Published: May 10, 2022
Keywords: consensus control; virtual impedance; microgrids; distributed generation; dSPACE controller; droop control