Enabling Aggregation of Heterogenous Grid-Forming Inverters via Enclaved Homogenization

This paper proposes a control scheme to force homogeneity for heterogenous network of the grid-forming (GFM) inverters in power electronics dominated grid (PEDG) to enable their aggregation and coherent dynamic interaction. Increased penetration of the renewable energy in distributed generation (DG) fashion is moving traditional power system to a highly disperse and complex heterogenous system i.e., PEDG with fleet of grid-forming and grid-following inverters. Optimal coordination, stability assessment, and situational awareness of PEDG is challenging due to numerous heterogenous inverters operating at the grid-edge that is outside the traditional utility centric power generation boundaries. Aggregation of these inverters will not be insightful due to their heterogenous characteristics. The proposed control scheme to force enclaved homogeneity (FEH) enables an insightful aggregation of GFM that can fully mimic the given physical system dynamics. The proposed FEH scheme enables coherent and homogenized dynamic interaction of GFM inverters that enhances the PEDG resiliency. Moreover, different cluster of GFM can be merged into single cluster with minimal synchronization time and frequency fluctuations. Accurate reference models can be achieved that enables effective dynamic assessment and optimal coordination which results in resilient PEDG. Several case studies provided to validate the effectiveness of proposed FEH in network of GFM. Then, GFMs aggregation and developed reference model for the PEDG system is validated via multiple comparative case studies.


I. INTRODUCTION
The traditional power system is under a rapid transition from 23 centrally concentrated generation towards distributed gen-24 eration (DG) to integrate renewable and sustainable energy 25 such as solar PV, windfarms, etc. with the grid. This inte-26 gration requires a power electronics interface to regulate and 27 match the dispatchable power according to the grid codes 28 a model reduction scheme the aggregated model of the given 85 system is derived. For instance, in [17] the authors performs 86 eigenvalue analysis on the model of the cluster under study 87 to find the coherent generation sources. Then, based on this 88 information from the model, the large-order cluster is divided 89 into smaller clusters. The accuracy of the aggregated model 90 derived from the sub-clusters is highly dependent on the 91 precise and consistent information of the system parameters. 92 However, at many instances full information of the model 93 parameters of the given grid cluster is not available. [18] 94 utilizes a DYNRED software to find the slow coherency of 95 the synchronous generators in the grid cluster under study. 96 Nevertheless, the proposed scheme is limited to specific equi-97 librium points and general analysis is not possible. Moreover, 98 it suffers from the parametric uncertainties and imperfections 99 in the modeling. On contrary, the signal-based scheme utilizes 100 the wide-area monitoring for instance synchrophasors. These 101 signals are then used to obtain useful from the system under 102 study. [13] proposed a scheme that determines the coherent 103 generators and partition into electrical area from a large, inter-104 connected power system. This scheme is based on dynamic 105 frequency deviations from generator and non-generator buses 106 with respect to the nominal frequency of the given system. 107 The advantages of using the schemes based on signal mea-108 surement are fast and dynamic identification of coherency 109 and low dependence on the data from the model [19]. But, 110 due to external disturbances the information received via a 111 wide area monitoring device have reliability issues. 112 Originally, the coherency-based aggregation schemes are 113 utilized to derive the reduced-order models for the clus-114 ter of interconnected generators. However, these concepts 115 of coherency can be extended to made applicable for the 116 DGs. Broadly, depending on the implemented control and 117 interaction with the grid the DGs can be classified as grid 118 forming (GFM) inverter-based DGs and grid following (GFL) 119 inverter-based DGs. The primary goal in the control of GFM 120 inverter is to regulate the voltage and frequency of the sys-121 tem. Prevailing from more than two decades droop-based 122 control for GFM has been most mature and widely known 123 scheme [20]. Concepts of droop-based control initiates from 124 the governor action which allow the parallel operation of the 125 multiple DGs. Initially, the frequency based droop control 126 has been proposed in [21] for the islanded AC and unin-127 terruptible power supplies. The improved transient response 128 of the classical frequency-droop control was proposed in 129 [22]. This improvement was proposed by incorporating the 130 integral and a derivative term in the active power path. Power 131 synchronization control (PSC) is another method for con-132 trolling the GFM inverters. PSC has a similar controller 133 structure to droop control structure. Instead of frequency 134 variation the voltage angle is drooped in response to vari-135 ation in the power. The work in [23] proposes a PSC for 136 a HVDC system which improves the converter dynamics 137 operating in the weak grid conditions. Furthermore, the con-138 trol of GFM can mimic a synchronous machine by utiliz-139 ing a swing equation. This type of control is commonly 140 known as virtual synchronous generator (VSG) [24].

141
The concept of VSG is proposed in [25]    of DGs are considered enclaved homogenized. This work 197 considers each GFM inverter with heterogenous parameters 198 such as, power ratings, filter parameters, types of controller 199 and controller gains. Thus, this work encompasses more prac-200 tical system which includes inherently heterogenous DGs 201 that will not have similar dynamic response and cannot be 202 enclaved. Therefore, the FEH is devised that is based on 203 autonomously obtaining the equivalent inertia of the given 204 network of DGs. Then, devising the controller gains and this 205 force enclaved homogenization in the PEDG. Furthermore, 206 the dynamic model of the GFM inverter is developed and then 207 based on this model the aggregate reference model for the 208 forced enclave homogenized DGs is devised. The accuracy 209 of the devised aggregate model is validated by comparing its 210 dynamic and steady-state response under a disturbance with 211 the circuit model of individual DGs and aggregated DGs. 212 Furthermore, the proposed FEH scheme was tested under 213 the cluster reconfiguration. Specifically, the case study for 214 the cluster merging was performed when two cluster having 215 different number of DGs are merged. The supervisory layer 216 adjusts the controller parameter in real-time to restore the 217 coherency among the new merged cluster. Comparatively, 218 with the proposed scheme the synchronization time for clus-219 tering was greatly reduced without noticeable frequency and 220 voltage fluctuations.

221
The structure of the remainder of the paper is: section II 222 explains the development of FEH via equivalent inertia emu-223 lation. Section III formulates the model of GFM inverter 224 for dynamical analysis and aggregate reference model. The 225 validation of the proposed scheme is explained in section IV. 226 Finally, the paper is concluded in section V. The structure of the proposed FEH control scheme for the 231 GFM inverters in PEDG is illustrated in Fig. 1. In the PEDG, 232 the conventional active and reactive power droop control 233 relations will no longer be fully decoupled and are given by, 234 where m p = k p (X Z ), n q = k q (R Z ) are the effective 237 frequency and voltage droop gains, respectively. These effec-238 tive droop gains are dependent on the ratios of resistive and 239 inductive line impedances between the two power sharing 240 grid-forming inverters. P nom and Q nom refers to the nominal 241 active and reactive power.
is the determined active power and reac-243 tive power after filtering via low-pass filter. The nominal 244 frequency and voltage are denoted by f 0 and v o ; ω c is the 245 cutoff frequency of the low-pass filter.

246
The virtual inertia emulation from the grid-forming 247 inverter is formulated by leveraging the swing equa-248 tion of synchronous generator. Considering the frequency 249 VOLUME 10, 2022 df dt where, inertia constant is denoted by H , damping coefficient 256 as D p , and f is termed as rate of change of frequency 257 (ROCOF). By evaluating (4) and (1)  between H and m p is given by, The proposed FEH scheme is based on the calculation of 284 the equivalent inertia constant H EQ of the cluster by lever-285 aging the control parameters. The supervisory control layer 286 receives the information by communicating with primary 287 controllers of each DG. Based on each DGs droop param-288 eters, the virtual inertia emulated by each DG is calculated 289 in (5). Moreover, the equivalent inertia of the cluster is cal-290 culated by (6). Then, based on this equivalent inertia of the 291 cluster, the droop coefficients that will enforce homogeneity 292 among the heterogenous DG are devised in the supervisory 293 layer. Next in the supervisory layer of control the modified 294 droop gains are checked for compliance of the standard EN 295 50438 [33]. This modified droop gains are communicated to 296 the primary controllers of the DGs to incorporate them in the 297 control loop in real-time.  due to the heterogenous parameters as given in Table 1. Furthermore, an additional case study was presented to 345 validate the proposed FEH scheme for achieveing enclaved 346 homogenization. At instant t 2 , a step decrease of 20kW 347 of load is introduced and effect on the frequency dynamic 348 VOLUME 10, 2022 response was observed. Fig. 4(a)  as the rated power of each DG, rated power of the cluster, and 390 controller gains of the clusters that are required to be merged 391 together. Then, based on the new configuration the equivalent 392 inertia (H EQ ) of the new cluster is calculated by (6) and then 393 based on this new H EQ the droop gains required for forcing 394 enclaved homogenization in the new cluster is devised by (7). 395 Furthermore, a real-time validation mechanism is applied to 396 verfiy the new droop gains are consistent with the standards. 397 If the updated droop gains passes this validation checkpoint 398 then these gains are passed to the primary level controller to 399 incorporate the updated droop gains, otherwise, a signal is 400 generated that clusters cannot be merged to form a new clus-401 ter. Furthermore, the synchronization block in the supervisory 402 layer of control ensures the two clusters are synchronized in 403 terms of frequency, voltage angle and RMS value of the PCC 404 voltage.    deviation is depicted at instant t 7 . More importantly the 431 time required for the cluster synchronization and frequency 432 restoration exceeds 0.5 seconds and cluster was merged at 433 time equals to 1.55 seconds. It can be seen that during clus-434 ter merging the DGs were facing very high ROCOF and 435 frequency deviations due to adverse dynamic interactions 436 between the two cluster. Moreover, at instant t 8 a load distur-437 bance was introduced to validate the merging of cluster and it 438 can be verified as the load disturbance was applied the DGs 439 are behaving as a single cluster with herterogenos frequneyc 440 response.

III. AGGREGATION OF GRID-FORMING INVERTER WITH
Furthermore, the state-space model is developed by linearz-457 ing and rearranging (9)- (12) and is given by, where, where ω and ω 0 represents the instantaneous frequency and 468 nominal frequency of DGs, respectively. The voltage angle 469 is denoted by θ, the d-q components of the output current is 470 VOLUME 10, 2022 By evaluating the (14)- (19) a state-space model is derived and 486 given as, where, A2, B3, B4, B5, C4, D5, D6 are at the bottom 490 of the next page, where, the filter capacitor voltage in 491 d-q reference frame is given as v cd and v cq , K pc , K ic , K vc 492 are the PI controller gains, v invd and v inq are the d-q com-493 ponents of the inverter-side voltage. The calculation of the 494 inverter-side voltage involves the ξ dq that is represented as 495 the controller states in d-q reference frame. The state-space 496 representation for the calculation of the controller states is 497 given as, where, Furthermore, the initial values of the states of the 502 grid-forming DG given in matrix B 5 is mentioned in 503 Table 2.

527
The aggregate reference model is perturbed under a distur-528 bance by changing the load. Two case studies ( Fig. 7 and 529 Fig. 8) are presented to validate the proposed approach. 530 To verify the accuracy of the developed aggregate reference 531 model a comparison between the circuit model and mathe-532 matical model is presented. In Fig. 7 and Fig. 8, the labels 533 Agg CM and Agg MM represents the aggregate circuit model 534 and aggregate mathematical model signals respectively for 535 each of the presented parameters. The labels DG 1 to DG 5 are 536 the individual DGs circuit-based signals for each of the pre-537 sented parameters. Additionally, in the case studies various 538 parameters of individual DGs is also presented and discussed. 539 For the aggregated reference model, the initial conditions for 540 the states are given in the Table 2. It is worthy to note that before and after load increase 557 the active power injection from aggregate reference model, 558  19.45 A before 566 instant t 3 and 58.70 A after t 3 . Additionally, the summation 567 of the inductor L 1 current in d-axis of each individual DGs 568 before and after disturbance is 19.45 A and 58.70 A, respec-569 tively. Thus, this summation of current also matches with the 570 developed aggregate reference model. Fig. 7(c) illustrates the 571 dynamics in the inductor L 1 current in q-axis for the devel-572 oped aggregate reference model, aggregate circuit model and 573 the five individual DGs. Majorly, a step increase was in active 574 load at instant t 3 , thus the inductor L 1 current in q-axis remain 575 near to the zero. Although there is a small deviation at instant 576 t 3 when load was switching to higher value but again in very 577 minimal time the q-axis current of the aggregate reference 578 model returns to zero with a negligible deviation. Moreover, 579 as seen in the zoom in windows the developed aggregate 580 reference model and circuit model matches each DG's output. 581 The output current in d-axis for the aggregate reference 582 model, aggregate circuit model and the five individual DGs is 583 shown in the Fig. 7(d). To cater the step increase in the active 584 power, the output current increases and that is verified in 585 Fig. 7(d). Specifically, at instant t 3 value of output current in 586 d-axis for the aggregate reference model and aggregate circuit 587 model increases from 19.35 A to the 58.60 A. Although 588 the developed aggregate reference model shows a ringing at 589 instant t 3 but that is for very minimal duration and ultimately 590 settles to the value that exactly matches the aggregate circuit 591 model. Moreover, the summation of the output current in 592 d-axis for the five individual DGs matches with the aggregate 593 reference model before and after instant t 3 . Fig. 7 The transients in the aggregate reference model due to the 604 sudden decrement in the load at instant t 4 is presented in 605 this case study. Fig. 8(a) Fig. 8(b) and (d) illustrates the decrement in the induc-617 tor L 1 current and output current in d-axis from the aggre-618 gate reference model, aggregate circuit model and five DGs. 619 Significantly, at instant t 4 , the output current in d-axis of 620 the aggregate reference model and aggregate circuit model 621 decreases from 58.51 A to 19.38 A. Moreover, the summation 622 of currents from the five DGs also matches with the devel-623 oped aggregate reference model. Fig. 8(d)  The developed aggregate reference model of cluster of PEDG 637 is tested for the reactive power support after adding a reactive 638 load. One of the primary roles of the GFM inverter is to 639 supply reactive power in case of requirement of reactive 640 power from the grid. Specifically, at instant t 5 a reactive load 641 of 2000 VARs is connected, and effect of reactive load addi-642 tion was studied on the developed aggregate reference model 643 and compared with the full-scale circuit model of PEDG clus-644 ter. Fig. 9 (a) illustrates the reactive power profile of aggregate 645 reference model and circuit model. It can be verified at instant 646 t 5 the reactive power from the aggregate reference model 647 and circuit model increases from 0 to 2000 VARs to supply 648 the reactive load. The developed aggregate model closely 649 matches the circuit model with a small diminishing ripple. 650 Moreover, the inductor L 1 q-axis current from the aggregate 651 reference model and the circuit model depicted in Fig. 9 (b). 652 It changes from 0 to −7.58 A to supply the current to a 653 reactive load. Fig. 9 (c) illustrates the output current from 654 the aggregate reference model and the circuit model that also 655 changes from 0 to −7.62 A. Although the output from the 656 aggregate reference model has a small ripple but it diminishes 657 within a short duration and proposed control is able to supply 658 the reactive power without any instability. The small dimin-659 ishing ripple is also present in the output from the circuit 660 model. This is because the controller is trying to regulate 661 demand of reactive power and the system is transitioning. 662 Additionally, the stable operation of the proposed control 663 and the developed aggregate reference model is verified in 664 Fig. 9 (d). The d-axis component of the PCC voltage from the 665 aggregate reference model and circuit model is 169 V with a 666 small negligible ripple and even this ripple dies down at t = 667 1.2 s. Thus, this case study validates the stable operation and 668 reactive power support of proposed FEH control. Moreover, 669 the developed aggregate reference model closely matches its 670 circuit model under feeding a reactive load. 671 VOLUME 10, 2022