Consensus Control for Coordinating Grid-Forming and Grid-Following Inverters in Microgrids

An inverter with GFM control can be modeled as an AC voltage source behind a coupling impedance that can generate a desired constant voltage magnitude and frequency in an islanded microgrid as shown in Figure1 (a). Mathematically, it can be represented as following for an $i^{th}$ inverter:

where $u_{i}^{\delta}$ and $u_{i}^{V}$ are frequency and voltage control inputs or reference signals to the inverter. Several control strategies have been proposed to define the $u_{i}^{\delta}$ and $u_{i}^{V}$ such as virtual oscillator [27], virtual synchronous machine [28] and, droop controls [29, 12]. In this work, we choose a relatively well tested CERTS power-frequency (P-f) droop and var-voltage (Q-V) droop controls as primary GFM controls [1]. These droop controls regulate the frequency and inverter terminal voltage according to (3) and (4) respectively.

where $\omega_{i}^{ref}$ is a reference frequency and act as control input to the inverter i.e. $u_{i}^{\delta}=\omega_{i}^{ref}$. $P_{i}$ and $Q_{i}$ denote real and reactive power outputs of inverter respectively. P-f control is further defined by 3 parameters i.e. $\omega_{i}^{nom}$, $m_{p_{i}}$ and $P_{i}^{set}$ that represent nominal frequency, droop gain and real power set-point as shown in Figure2(a). Similarly, in Q-V droop curve, $V_{i}^{ref}$ denotes a reference voltage signal. However, it is not directly used as voltage control input to the inverter ($u_{i}^{V}$) because we are interested in regulating terminal voltage $V_{i}$ rather than $E_{i}$ directly. Therefore, $u_{i}^{V}$ is obtained by passing $V_{i}^{ref}-V_{i}$ through a PI controller. Q-V control is further defined by 3 parameters i.e. $Q_{i}^{nom}$, $m_{q_{i}}$ and $V_{i}^{set}$ that represent nominal var output (usually taken as 0), droop gain and voltage set-point as shown in Figure2(b). Figure3 shows the full GFM control schematic where measured terminal voltage ($V^{g*}_{i}$) and output power ($,P_{i}^{*},Q_{i}^{*}$) are passed through low pass filter before being used as input to the droop controllers.

The main purpose of P-f droop is to enable multiple inverters to share real power. Q-V droop helps in mitigating circulating var among paralleled inverters.

GFL control enables an inverter to behave like a current source that can inject a specified real power ($P_{i}^{ref}$) and var ($Q_{i}^{ref}$) into the grid as shown. In GFL control, it is achieved using a typical current control loop in d-q reference frame which can be written as,

where $I_{d_{i}}$ and $I_{q_{i}}$ are reference signals for inverter current in d-q reference frame. $V^{d}_{i}$ is d-axis voltage obtained via d-q reference frame transformation that requires both $V_{i}$ and $\delta^{g}_{i}$ as inputs. Therefore, a standard phase locked loop (PLL) is used to estimate $\delta^{g}_{i}$ as $\delta^{PLL}_{i}$ by constantly regulating q-axis voltage, $V^{q}_{i}$, to zero using a PI controller as shown in PLL control block in Figure4 . PLL is an important component of GFL control to measure grid side frequency i.e. $\omega_{i}=\dot{\delta}^{PLL}_{i}$. Similarly, voltage measurements $V_{i}^{g}$ is processed through low pass filter to get $V_{i}$. Thus obtained current reference signals are converted to inverter source voltage ($E_{i},\delta_{i}$) by the current control loop such that the desired $P_{i}^{ref}$ and $Q_{i}^{ref}$ can be injected. The whole schematic sequence of GFL control is shown in Figure4. The detailed description of PLL and current control loop can be obtained from [18].

Instead of providing fixed $P_{i}^{ref}$ and $Q_{i}^{ref}$ set-points, usually an external grid support function is added to GFLs to indirectly regulate voltage and frequency. In this work, we use DER integration standard IEEE1547-based volt/var and freq/watt droop functions as primary control for GFL inverters as defined below.

Similar to GFM droop curves, $P_{i}^{set},\omega^{nom},m_{p_{i}}$ and $Q_{i}^{nom},V_{i}^{set},m_{q_{i}}$ are control parameters of freq/watt and volt/var droop curves as shown in Figure2(c) and (d) respectively. It can be observed here that GFM measures power outputs and dispatches frequency and voltage reference signals whereas it gets revered in GFL.

Equal power sharing is an important controller objective for both GFM and GFL. For a given system condition, an equal power sharing is achieved when all inverters are maintaining the real power dispatch proportional to their droop in pu with respect to their ratings ($s_{i}$). This can be written as $\eta_{p}=m_{p_{i}}P_{i}/s_{i}$ for each $i^{th}$ inverter, where $\eta_{p}$ denotes an equal power sharing parameter. Similarly, an equal var sharing parameter, $\eta_{q}$ can also be defined. Consequently, an analytical expression for $\eta_{p}$ and $\eta_{q}$ can be obtained as,

Any divergence of $P_{i}$ from $\eta_{p}$ can be seen as a deviation from equal power sharing. In the case of $Q_{i}$, a large deviation from $\eta_{q}$ can cause high circulating vars in the system.

In both GFL and GFM, the main purpose of primary droop controls is to maintain the power sharing and prevent circulating var while providing the frequency and voltage regulation. However, due to their proportional nature, the accurate regulation can not be achieved as they always end up with a steady state deviation in both frequency and voltage. A secondary control is needed to accomplish removal of these errors.

A secondary control is usually applied at GFMs by updating the $P_{i}^{set}$ in (3). However, in that process, the equal power sharing aspect of primary control gets disturbed. To preserve that, coordination among GFM inverters is needed.

Further, if GFLs are not coordinated with GFMs’ secondary control and left with their primary control only, it will lead to undesired performance as one of the following two situations arises: (a) if GFMs secondary control could restore the frequency to nominal on their own, the GFLs will not see the need of participating in power sharing (point A in Figure2(c)); thus freq/watt capability of GFLs remains unutilized or; (b) if GFMs do not have enough capacity to manage the disturbance on their own, GFLs do participate, but it prevents frequency restoration (point B in Figure2(c)). Moreover, in both situations, power sharing also gets disturbed as explained in the case study later. This necessitates a control approach that coordinates among GFL and GFM, which is explored in the next section.

There are two objectives to achieve while designing secondary control for P-f (GFM) and freq-watt (GFL) droop controls i.e. frequency restoration to nominal and equal real power sharing among inverters. To accomplish this, we propose following secondary control for GFL (12) and GFM (13):

Here, $k_{i}^{p}$ is a positive gain for $i^{th}$ inverter and affects the speed of frequency regulation. $P_{i}^{set}$ from primary controls is used as secondary control variable. Following leader-follower concept, both GFL and GFM have real power sharing terms whereas only GFM has an extra frequency restoration term in (13). Thus, (3)+(13) and (7)+(12) make a complete frequency control for GFM and GFL respectively. Note that with no communication, this control will be an equivalent of frequency restoration without ensuring power sharing what we term as uncoordinated secondary control.

Remark 1: Our work assumes that GFL sources will have a planned headroom, required for secondary regulation, based on the recent standards and recommendations (discussed in Section I) that encourage non-dispatchable GFL inverters (such as PV) to participate in frequency regulation by maintaining certain headroom either via storage or curtailment [20, 22]. The optimal headroom planning is an important aspect, though not the focus of this work, and can be referred from some recent proposed methods [35, 36].

Remark 2: Even in the case of planned headroom, intermittency in the GFL source may cause an unexpected reduction in the available headroom. In that situation, the proposed control will be able to converge and achieve full frequency restoration as long as other inverters together have sufficient headroom to compensate for the intermittency, though with compromised power sharing. Let’s assume for $i^{th}$ GFL inverter, the output $P_{i}$ is saturated to a lower value $P_{i}^{max}$ while the power required for equal power sharing is $P_{i}^{eq}$ such that $P_{i}^{max}<P_{i}^{eq}$. In this case, equal power sharing is not possible. However, that information is not known to the GFL controller (12), and it still converges assuming the original droop set-point $P_{i}^{set}=P_{i}^{eq}$. It helps the controller to converge, whereas at the device level, the actual output $P_{i}$ is saturated to $P_{i}^{max}$ and the remaining power is compensated by the other non-saturated inverters.

Similar to previous section, we have two objectives here i.e. voltage regulation and mitigating circulating var by equal var sharing. However, unlike frequency regulation and real power sharing, it is not possible in general to achieve both the objectives accurately. We can achieve the desired internal voltage $E_{i}$ but terminal voltage $V_{i}$ is impacted by network impedance. Therefore, an equal var sharing is not always possible with the accurate voltage regulation in parallel inverter operations as observed and explained by [16, 37]. Therefore, we design a compromise between two objectives as following:

Here, $k_{i}^{q}$ is a positive gain and $V_{i}^{set}$ is a secondary control variable from primary controls. $V^{nom}$ is a nominal voltage usually taken as 1 pu. The trade-off between voltage regulation and var sharing is implemented by scaling coefficients $\alpha$ and $\beta$ for GFM in (15). The tuning of the scaling coefficient will depend on the network and utility requirements. The tuning can also be made adaptive, though we use offline tuning in this study. Thus, (4)+(15) and (8)+(14) make a complete voltage control for GFM and GFL respectively. Note that with no communication, it will be an equivalent of accurate voltage regulation with high circulating var.

We create two disturbance events (at $t=1$ and $t=4$) to emphasize the value of the full coordination of GFL-GFM inverters. To begin with, at $t=0$, the whole system is connected to the grid via substation. At $t=1$ (event 1), the networked microgrid (shaded area) is isolated from the rest of the system and substation by opening switch between bus 13 and 152. At $t=4$ (event 2), a load disturbance is simulated by opening switch between bus 60 and 160 that disconnects around 1200 kW load (35%). The frequency responses to these events in all 4 cases are compared in Figure7. The islanding event at $t=1$ leads to a dip in frequency followed by only partial recovery to 59.86 Hz by primary droop control in Case I. It can be seen that only the proposed LFC control (Case IV, blue line) is able to recover the frequency fully back to 60 Hz. The Case II and III control strategies could only restore frequency to 59.92 Hz. However, in response to event 2 at $t=4$, Case II and III are able to recover the frequency overshoot back to 60 Hz along. The different responses to these two events in Case II and III can be attributed to the non-coordination of GFLs as discussed in Section II-D. The event 1 disturbance was large enough to require both GFL and GFM inverters to share their power to meet the total load demand of the microgrid. Therefore, GFLs participate but prevent frequency restoration. Whereas, in event 2, since GFM inverters were enough to manage the load disturbance and could recover the frequency to 60 Hz, GFL don’t see the need for participation and settle at their nominal power without sharing the load as can be observed in Figure8(a).

Consequently, the power sharing performance (MPSI) can be seen in Figure9. LFC control is able to achieve 0 MPSI i.e. equal power sharing in less than 1 second in both the events whereas Cases II and III have non zero MPSI in both disturbances. Note that the non-participation of GFL in event 2 for case II and III leads to a worse power sharing reflected by a higher MPSI value, compared to event 1. Table I summarizes the frequency regulation and real power sharing performance comparison among all cases. The coordinated LFC control (Case IV) is able to achieve frequency restoration as well as accurate power sharing in both events.

This use case demonstrates the need for coordination and verifies that if GFL and GFM left uncoordinated (Case II and III), the inverters capabilities remain under-utilized and controller performance is compromised.

For the same disturbance events, an average voltage responses and var sharing performance (MQSI) in all 4 cases are compared in Figure10 and Figure11, respectively. On investigating the first event at $t=1$, we observe that primary droop controls are not able to bring voltages to nominal 1 pu in case I. Further we observe in Figure10 that Case II and III are able to improve voltage regulation significantly due to GFM’s secondary volt/var control. However, it leads to a very high amount of circulating var as reflected from higher MQSI values compared to the case I, shown in Figure11. This undesired response occurs because each inverter tries to push it’s own voltage to 1 pu by injecting more var with no coordination with other inverters in case II or with GFL in case III. Note that Case III MQSI value is relatively better than Case II because of partial coordination.

On the other hand, the proposed LFC coordinated control in Case IV arrives at a compromise between voltage regulation and var sharing. The voltage is very close to nominal voltage as shown in Figure10 while maintaining MQSI close to 0 in steady state as shown in 11. Table II summarizes the performance trade-off, where the voltage regulation is evaluated by calculating a mean absolute error over all inverters in steady state, defined as $V_{error}={\sum_{i=1}^{N}|V_{i_{t}}-1|}/{N}$, where $N$ denote the total number of inverters. It can be verified that the proposed Case IV is able to improve both $V_{error}$ and MQSI significantly (more than 5 times) compared to Case I. Whereas, in both Case II and III, a highly accurate voltage regulation cost us significantly higher MQSI.

The second event at $t=4$ turns out to be a favorable disturbance for voltages i.e. smaller $V_{error}$ in all cases. Nonetheless, the superior performance of LFC control in voltage regulation as well as var sharing can be observed in this event as well from Table II.

The impact of intermittent nature of GFL sources is observed by simulating an intermittency event (e.g., cloud cover) on GFL 2, 5 and, 8 at t=2.5 that reduces their maximum power output by from 350 kW to 225 kW. It can be observed in Figure12 (top), where after the islanding event 1 at t=1, all inverters converge to an equal power sharing dispatch. At t=2.5, due to intermittency, GFL 2 power converges to 225 kW while inverters (1 and 3) compensate for it. A similar behavior is followed by other inverters as well. Along with convergence, a full restoration of frequency to 60 Hz is also maintained in the intermittent event as shown in Figure12 (bottom). However, power sharing is disturbed, reflecting a lower MPSI value of 0.15, as reported in Table III. It compares the impact of intermittent events of different magnitude on power sharing and frequency deviation. It can be observed that higher intermittency worsens the power sharing with no impact on frequency deviation. The system can only handle the $P^{max}$ reduction of intermittent GFLs till 200 kW due to limited headroom availability with all other inverters at t=2.5. Further note that, in these intermittencies, with reducing real power headroom, there is more room for reactive power in the inverter. Therefore, the voltage regulation is not affected negatively by intermittency as observed in Table III.

After comparative evaluation against existing control strategies, we now test the robustness of the LFC control in cases of reduced communication and communication link failure compared to full communication topology for the islanding disturbance at $t=1$. In a reduced communication case, each microgrid is considered as one cluster with one leader GFM inverter as shown in Figure13. The communication across these clusters is only maintained through leader GFMs i.e. inverter 1, 4, and 7 and all other communication across the clusters are disabled. It can be noticed in Figure14 that even with the reduced communication, the same steady state performance for frequency restoration and power sharing can be achieved as full communication case, though with a little slower control dynamics. Power sharing convergence takes around 0.5 seconds more due to less communication as shown in Figure14 (bottom). Table IV tabulates the impact on all the performance indices. It can be seen that only var sharing is affected by the reduced communication (MQSI increases from 0.04 to 0.14), though it is still significantly better than all other control methods i.e. Case I,II and III. It is worth noting that to achieve a good trade-off between $V_{error}$ and MQSI, scaling parameters $\alpha$ and $\beta$ had to be re-tuned with the reduced communication pattern.

On the other hand, the communication link failure case is simulated by disconnecting a link between inverter 4 and 7 with no update in controller parameters. The overall performance of this case is similar to full communication case as can be seen in Figure14 and Table IV except a slight worsening of var sharing (increase in MQSI from 0.04 to 0.05).

As discussed earlier, communication graph must be connected for convergence of consensus. With $N=9$ in our study, the minimum and maximum possible communication links are 8 and 36, respectively. We conduct a sensitivity study by simulating various connected communication topology with different number of links in the range of 8 to 36, using a random sampling. The consequential convergence rates (seconds required to converge) are plotted in Figure15. It is observed that compared to the full communication (all 36 links), the convergence rate increases very slowly till topology with around 12 links. However, convergence rate rises sharply closer to the minimum threshold i.e. 8 links. Nonetheless, we observe that the controller converges at optimal steady-state in all topologies. Further, we verify that the consensus is not able to converge the communication links are reduced below 8 as it does not remain connected anymore.

To test the ‘plug-n-play’ feature, we simulate a scenario by disconnecting inverter 2 at t=2 and reconnecting back at t=3 as shown in Figure16 It can be seen the controller can quickly adapt in both situations and other inverters adjust their power to restore frequency as well converge to equal power sharing. A similar performance is observed at voltage regulation as well. Controller’s adaptability with new devices is one of the key factors to facilitate 100% DER integration in power system.

We also test the controller performance in the event of multiple microgrids switching in a networked microgrid as shown in Figure6. After initial islanding at $t=1$, microgrid switches $sw$ ${1\_2}$ and $sw$ ${2\_3}$ are opened at $t=4$ so that all 3 microgrids become islanded networks, each with 1 GFM and 2 GFL inverters. Figure17 (top) shows the total generation profile in each microgrid. The solid and dashed lines denote the real and reactive power respectively. The microgrid 2 can be seen to have the largest adjustment in real power at $t=4$ and therefore it goes through the highest frequency transient peak as shown in Figure17 (middle). Due to different real power adjustments, all 3 microgrids have different transient responses but settle back to nominal frequency. Figure17 (bottom) shows the voltage response of each microgrid. Note that since the var demand increases in microgrid 1 (Figure17 (top), dashed black line) unlike microgrid 2 and 3, its voltage transients are also different. Nonetheless, all microgrids are able to settle the voltage at 1 pu.

Table V lists all the performance indices values for each microgrid. It is interesting to note that all 3 microgrids are able to achieve an equal var sharing (MQSI=0) along with a accurate voltage regulation ($V_{error}=0$). This is possible in these smaller microgrids because of the electrical proximity of all 3 inverters within each microgrid. Similarly, an equal real power sharing (MPSI=0) is achieved within each microgrid after switching out from a common power sharing in a large networked-microgrid. The results show the quick adaptability of the proposed LFC controller in an emerging networked microgrid scenarios.