Double-Layered Droop Control-Based Frequency Restoration and Seamless Reconnection of Isolated Neighboring Microgrids for Power Sharing

This article describes a seamless reconnection topology for power sharing between distant rural community microgrids (CMGs), which is based on a double-layered droop-controlled (DLDC) frequency restoration scheme. Increased load demand, along with the intermittent nature of renewable energy sources, may result in a power deficit in isolated CMGs. In order to overcome this restriction, the connection of autonomous neighboring CMGs may be a viable alternative to intelligent load shedding. When dealing with active power fluctuation and setting a frequency set point becomes difficult in the absence of a grid frequency reference, this DLDC-based approach can resolve the issue. The DLDC adds a self-synchronized feature by parallel shifting of the <inline-formula> <tex-math notation="LaTeX">$f - P$ </tex-math></inline-formula> slope to restore the operating frequency to its nominal value. The difference in frequency enables to shift the voltage axis accordingly through the change in <inline-formula> <tex-math notation="LaTeX">$V_{d}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$V_{q}$ </tex-math></inline-formula> reference of the terminal voltage for appropriate power sharing. The stability of the proposed controller has been analyzed by using a mathematical model considering communication delay in the distributed secondary controller. Finally, the efficacy of the proposed controller is shown via the use of unique processor-in-the-loop (PIL) experimental findings, in which OPAL-RT and PLECS RT boxes are used to build both the CMGs and a TI-based F28069M microprocessor is utilized as a controller.


I. INTRODUCTION
storage systems (BESS), flywheels, and diesel generators [3], 39 but may not be economical in small-scale installation. How-40 ever, a central storage device can be installed for a particular 41 community-based MG. In this respect, the coupling of neigh-42 boring isolated community microgrids (CMGs) is technically 43 and economically more viable for power sharing in case of 44 any energy deficiency [4], [5], [6]. 45 The CMG is usually connected with the neighboring one 46 through an interfacing inverter. If the CMGs are not pre-47 synchronized, a significant inrush current can pose a major 48 hazard to the entire system. On the other hand, the CMGs 49 should be decoupled in order to ensure system stability in 50 the event of any malfunction/emergency. The development of 51 a smooth connection/recommission topology is thus crucial 52 for the efficient operation of power sharing among adjacent 53 CMGs. 54 The frequency, voltage, and phase angle of both the interface 55 inverters must be identical for a smooth reconnection between 56 contiguous CMG. Additional difficulties include maintaining 57 power-sharing precision and system frequency, especially for 58 the isolated CMGs. The most frequently utilized Q-V and 59 P-f droop control is used for active and reactive power 60 sharing between the MGs. In conventional droop control after 61 attaining the power-sharing accuracy, the frequency may not 62 necessarily maintain the nominal value. As a result, an addi-63 tional control technique is required to restore the frequency 64 and voltage of the CMGs. Thus, a seamless reconnection 65 topology with a frequency restoration feature has to be devel-66 oped to couple the neighboring CMGs for available power 67 sharing. 68 The seamless reconnection and frequency restoration of 69 isolated neighboring CMGs are a relatively new issue as all the 70 regulatory authorities recently started to promote the develop-71 ment of renewable energy-based rural, isolated energy commu-72 nities [7], [8]. However, much research [9] has been conducted 73 for seamless transfer of operation modes between conventional 74 grid and islanded microgrid. A linear integration method [10], 75 phase angle synchronization [11], and virtual impedance-based 76 (synchronverter [12], [13]) reconnection already proposed for 77 the seamless transfer of modes. Most of these methods are 78 based on phase-locked loops (PLLs), which have a built-in 79 restriction on how local loads may be connected. To properly 80 deploy these topologies, the local load must be decoupled 81 during pre-synchronization. The seamless mode transfer based on droop control was sharing as the active power production is sensitive to the 139 phase angle. This distinguishable phenomenon of frequency 140 restoration can bring a significant inaccuracy in active power 141 sharing.

142
In order to maintain the stability and frequency of the 143 system, there should be sufficient active power to execute the 144 frequency restoration controller. The load frequency control in 145 a photovoltaic (PV) generation-based inertialess system can 146 be achieved by sharing the active power with neighboring 147 CMGs. The development of a control approach for smooth 148 reconnection of neighboring CMGs without sacrificing the 149 precision of power sharing and system frequency would be 150 very beneficial.

151
This article proposes a methodology for seamless reconnec-152 tion between neighboring CMGs using self-synchronization 153 control based on a double-layered droop-controlled (DLDC) 154 approach. The suggested method restores the system's fre-155 quency to its nominal value while also precisely sharing the 156 available power. In this perspective, the main contribution of 157 this research is abridged as follows. 158 1) The DLDC is designed by adding a self-synchronized 159 feature to enable parallel shifting of the f -P slope to 160 restore the operating frequency to its nominal value. The 161 difference in frequency ( ω) will then shift the voltage 162 axis appropriately through the change in V d and V q 163 reference of the terminal voltage for appropriate power 164 sharing.

165
2) A seamless reconnection of neighboring isolated CMGs 166 is proposed in order to support each other, in the case 167 of any power contingency. Both the CMGs are able to 168 support the local loads as well as the neighboring CMG 169 loads. The seamless reconnection feature of the isolated 170 CMGs is the distinctive feature of this article.

171
3) A unique processor in the loop (PIL) hardware model 172 has been developed in order to verify the accuracy of 173 the proposed controller. OPAL-RT and PLECS hardware 174 simulator has been used to design the power circuit, 175 and the controller is designed on the TI-based F28069M 176 microprocessor.

177
The rest of this article is organized as follows. Section II 178 describes the detailed control feature of the developed sys-179 tem. Sections III and IV illustrate the mathematical model 180 and stability analysis of the proposed controller, respectively. 181 Section V discusses the complete working principle of the 182 proposed system, and Sections VI and VII show the efficacy 183 of the proposed controller with the help of simulated and real-184 time experimental results.

186
In this section, the complete design of the proposed 187 controller has been presented, which will be used in the 188 subsequent system development. Fig. 1 shows a generalized 189 schematic representation for two adjacent, isolated CMGs. 190 Both CMGs are presumed to be PV-based MGs, with BESS 191 serving as a backup power source in each of the two CMGs. 192 Each of the CMGs has its own set of local loads to manage. 193 In the subsequent section, the properties of the primary voltage 194 and current control have been analyzed, and furthermore, the 195 distributed secondary control objectives have been proposed 196 to achieve the purposes.  A distributed secondary controller has been proposed in 223 this research work. The proposed secondary controller restores 224 the system frequency to its nominal value and helps for 225 the seamless reconnection of the CMGs and the available 226 active power sharing. The secondary controller generates 227 the frequency and voltage control inputs for the primary 228 controller. 229

1) Frequency Restoration and Power Sharing:
The main 230 focus of this part of the secondary control is to restore the 231 frequency to its nominal value and to improve the active 232 power-sharing accuracy. The conventional frequency droop 233 control ( f -P), as shown in (3), is a very well-known and 234 established technique for power sharing. A disadvantage of 235 this technique is the nominal value of frequency and voltage 236 changes if output active and reactive power is a deviation 237 from its nominal value (P 0 ). If the ratio of active/reactive 238 power varies, the voltage and frequency fluctuate, which can 239 cause improper power sharing between CMGs. This is the 240 most important tradeoff between transient responsiveness and 241 stability: deciding how much gain to use [29].

242
In order to solve this problem, improved droop control is 243 proposed, as shown in Fig. 2(a). The deviation of active power 244 from its nominal value can be compensated on its own by 245 shifting the f -P droop line to restore the system frequency. 246 By shifting this, the system frequency can be controlled 247 to its rated value individually in each CMG. To eliminate 248 the frequency deviation, a correction factor is added to the 249 frequency droop equation in terms of a time-varying filter of 250 the frequency error ( ω). with frequency ω 0 , provides the active power P 1 . Due to 255 the change of any load demand, the frequency drifts to ω n 256 (point B). At that moment, the power supplied by the inverter 257 is P 2 . After activating the frequency restoration control, the 258 frequency droop gain is adjusted (to the C point) such that 259 the system frequency returns to its nominal value, preserving 260 the inverter's power output. The same topology is adopted 261 for both the synchronizing isolated inverter of the CMGs. 262 This frequency restoration feature eventually reduces the phase 263 angle error between the participating inverters. This acts as 264 a natural "presynchronization" step, without requiring any 265 additional control action for that. The droop line may be 266 changed to point D once the seamless coupling controller 267 is engaged to achieve precise power sharing as per common 268 demand.

269
In conventional droop control for the i th inverter 270 For f -P Droop Control: where k ω is the f -P droop coefficient, and when the active 274 power is P n , the frequency is ω n .
Furthermore, the instantaneous power of the i th CMG 276 inverter (P i ) can be calculated as or can be written as For the control requirement, in order to maintain the unity 292 power factor, as the I oiq reference is zero, the change in active 293 power ( P i ) could be represented as the change in the d-axis which is the case in the present scenario.

296
Now, assuming Finally, 299 ω 01 = ω n + K p I oid (10) 300 Furthermore, in the Laplace domain, (4) and (7) can be 301 written as Equation (11) can be written as where ω s is the additional filter cutoff frequency and K g is 307 its time-varying gain. It is interesting to further expand the 308 following equation: Hence, the proposed droop control is a modified version inverters to operate closely to the nominal frequency. After 322 achieving the synchronization, ω should be equal to zero, 323 and at that moment, the q-axis component (V oq ) also becomes 324 zero. In this way, phase synchronization is accomplished 325 by restoring the system's frequency to its nominal value. 326 The simplified structure of the proposed controller has been 327 presented in Fig. 3. The previous section discusses how the restoration of sys-331 tem frequency eventually helps to self-synchronize the CMG 332 inverters. CMGs will be used in one of the two ways to 333 conduct this study: either independently (meeting just its own 334 load requirement) or linked with other CMGs. In the case 335 of operating in standalone mode, the proposed control layout 336 (as shown in Fig. 3) defines the operating frequency and 337 voltage as per the nominal value of the set points. However, 338 in interconnection mode, a secondary control architecture is 339 required for power management and protection. The proposed 340 secondary control layout for the voltage and frequency set 341 point calculation is presented in Fig. 4. For a smooth transition 342 between standalone mode and interconnected mode, a con-343 nection and disconnection strategy is presented as depicted in 344 Fig. 5. This secondary control scheme produces the neces-345 sary frequency and voltage deviation for a smooth transition 346 between standalone mode and interconnected mode. These 347 voltage and frequency deviations for coupling and decoupling 348 (V cop and f cop for coupling and V dec and f dec for decoupling) 349 contribute to defining the new set points of the primary 350 controller's voltage and frequency.

351
As the CMGs are also capable of working in standalone 352 modes, the voltage and frequency set points should be defined 353 by the local controllers.        established. Similarly, the controller is prepared for the system 410 disconnection when P err and Q err fall below 0.001 p.u. and 411 the power of CMG1 and CMG2 exceeds their rated values. 412 Fig. 6 shows the connection and disconnection criteria for the 413 coupling and decoupling controller.

416
In this section, the mathematical modeling and the sta-417 bility analysis of the proposed system have been discussed. 418 Fig. 7 shows the simplified structure of interconnected stand-419 alone CMG. The equivalent circuit diagram consists of two 420 voltage sources, LC filter, rural network, and loads. The 421 simplified controller structure with voltage and current control 422 loop, droop control, and double-layered frequency restoration 423 control is depicted in Fig. 3. In this section, the mathematical 424 model of each individual component of the control structure 425 is developed. The active power control between the CMGs is 426 generally achieved by changing the phase angle between the 427 CMG inverters. This is usually accomplished by using droop 428 control where the frequency is regulated by using the droop 429 equation as follows: where k ω is the droop gain, ω 1 is the output frequency of the 432 CMG1, ω 0 is the nominal frequency, and P is the power 433 supplied from CMG1 to CMG2 (or vice versa). The phase 434 angle difference is modified according to the function of power 435 supplies to another CMG. The phase angle difference between 436 the CMGs can be defined as follows: In (15), ω i and ω j are the final output frequency of CMG1 439 and CMG2, respectively.

440
In the coupled system (they will be adopted to a common 441 frequency) in case of any load change, the output frequency 442 will change and will settle down in a steady-state frequency. 443 The settled steady-state frequency is most likely to differ from 444

471
The transformation of α-β frame to d-q frame is shown in 472 the previous equation, where θ 01 is obtained from (17).

473
The state-space equations of each inverter output current, 474 filtered voltage, and load current are shown as follows.
The transmission line dynamics are shown in the following 486 state-space equations: The power calculation and droop equations are presented as 492 follows: The power equations after filter can be written as the 496 following, where ω c is the filter cutoff frequency: The mathematical derivation for the double-layered droop 502 controller can be retrieved from (7) to (13).

503
Considering all the above equations, the state matrix of a 504 CMG will be 505 Similarly, all the equations for another CMG can be 507 obtained and the state-space matrix can be written as Finally, the state-space matrix for coupled CMG can be 510 written as A fixed communication delay for exchanging information 513 among the DGs and primary and secondary controllers has 514 been considered. The linear distributed control law for voltage 515 Fig. 9. Development of the proposed system with improved controllers. and frequency control with delay has been shown in the 516 following: active power can be represented as The state equations of the delayed secondary controllers are 528 given as follows: The eigenvalues shown in Table I   The coupled system is linearized around an operating point 542 and all the eigenvalues are shown in Table I. The correspond-543 ing damping ratio is also calculated. All the eigenvalues can be 544 divided into two groups-well-damped eigenvalues and poten-545 tially problematic eigenvalues. The eigenvalues with damping 546 ratios less than 30% are considered as problematic eigenvalues, 547 as these are not damped quickly. The oscillations created due 548 to these values eventually affect the system performance. The 549 consequences due to these oscillations can result in loss of 550 efficiency, control system instability, and mainly wear and tear 551 on equipment. Oscillations in output voltage and current can 552 create harmonics and affect the power quality. The proposed 553 secondary controller with a fixed communication delay has 554 less number of problematic eigenvalues and maintains the sys-555 tem stability. In order to further improve the system stability, 556 a predictive/robust controller design is required, as has been 557 duly acknowledged in the scope of extension of the work in 558 future. The integration technique of the proposed DLDC with the 561 coupling and decoupling controller is presented in Fig. 9.

562
In order to make it compact, the detailed control topology of 563 CMG1 participating inverter control is only shown in Fig. 9,    simulation time instant 1 s, both the loads are increased to 598 5 kW, and the effectiveness of the proposed controller is 599 analyzed. The voltage and current profile of the CMG1 is 600 shown in Fig. 10. It can be observed that both voltage and 601 current are in phase and voltage amplitude remains stable 602 after load change. In the second situation, both the CMGs are 603 connected to 7-kW loads, and at the simulation time instant 604 1 s, both the loads are increased to 11 kW. Fig. 11 shows 605 the power and frequency profile of the CMG2. A comparison 606 is shown in the frequency profile with the proposed DLDC 607 and conventional droop control. According to the simulation 608 results, the frequency profile of the suggested droop control is 609 considerably smoother and more stable than that of traditional 610 droop control. The frequency profile with conventional droop 611 control is oscillating in nature during any transient; however, 612 both the frequencies are within the acceptable limit.

614
As discussed in Section III, a control topology is developed 615 to demonstrate a smooth, seamless transition from standalone 616 mode to interconnected mode. When the enable signal of the 617 coupling controller is triggered, the controller generates the 618 required frequency and voltage deviation for the seamless 619 transition, which contributes to defining the final voltage 620 and frequency set point values of the CMG inverters. After 621 checking the required connection criteria, as shown in Fig. 6, 622 the breaker connecting to the network and both the CMGs 623 come to coupled condition.   In order to demonstrate that, the CMG1 is connected to the  without affecting the system stability. In this case study, 651 initially, both the CMGs have a 12-kW load demand. In this 652 condition, another 2-kW load demand is increased in CMG1 653 then; according to the control architecture provided in Fig. 6, 654 the decoupling controller triggered automatically. As soon as 655 all of the conditions for disconnecting have been met, the 656 breaker is activated, and both CMGs are isolated. As shown 657 in Fig. 14, both the CMGs are supplying 24-kW load demand 658 initially, and at 1-s simulation time when the CMG1 load 659 demand is increased by 2 kW, the disconnection controller 660 operates; without affecting the system stability, a seamless 661 disconnection occurs. The system frequency was maintained 662 after the disconnection and the CMGs are supplying the local 663 load demand individually.

665
In this case study, a reconnection is attempted immediately 666 after a disconnection occurs, to check the efficacy of all the 667 proposed controllers. Like the previous case study initially, the 668 load demand of both the CMGs is 12 kW, and at the simulation 669 time 1 s, 2-kW load demand in CMG1 is increased. In this 670 situation, the decoupling controller operates and decouples the 671 CMGs. Immediately after that, at simulation time 1.5 s, the 672 excess 2-kW load demand is reduced, and again, the coupling 673 controller enable signal is triggered and the seamless coupling 674 is achieved in 0.03 s. As shown in Fig. 15, throughout the 675 simulation, the frequency remains in the allowable range, 676 which enables a seamless reconnection again. while the frequency is maintained within the acceptable limit. 696 Now, in order to restore the frequency, the frequency restora-697 tion controller is triggered. As captured in Fig. 16, shown in 698 the zoomed frequency plot, the frequency is restored to its 699 nominal value. It can be also observed that the frequency is

717
The decoupling controller's effectiveness was tested in this 718 case study using a similar strategy. When both CMGs are 719 first linked, the entire load demand is split evenly between 720 them. When the decoupling controller is activated, the CMGs 721 decouple and provide each CMG load requirement separately. 722 Fig. 18 shows that the decoupling is smooth and that the 723 system stability is maintained without causing any abrupt 724 transients in the voltage/current profile. It can also be observed 725 that seamless decoupling is achieved in one switching 726 cycle.