1. Introduction

The world is undergoing an energy transition in which governments and academia are looking for solutions to replace fossil fuel-based energy sources with less polluting technologies, including renewable energy systems [1]. Microgrids (MG) are small-scale electrical systems that operate coordinately distributed generators (DGs) and energy storage technologies to supply local loads [2]. In the energy transition context, electrical microgrids play a strategic role, facilitating the integration of DGs into electrical power systems at the distribution level [3], [4], [5], [6].

Microgrids can operate in grid-connected mode or islanded mode. The transition between operation modes improves the reliability of the service provided to users since it allows the segmentation of distribution networks in the event of failures [7], [8]. However, due to the long distances to grid connection points and topographic characteristics of the terrain, in some rural remote zones, it is cost-effective to implement autonomous microgrids designed to operate permanently isolated [9], [10].

The design of control strategies for isolated microgrids must guarantee a reliable and safe operation with a permanent power supply [11], [12]. The most common scheme to implement the operative functionalities of the microgrids is the three-layer hierarchical control presented in Figure 1, in which the strategies are associated with layers according to the time scales and control objectives. An important aspect that must be considered when designing control strategies for microgrids is the communication system. Depending on the communication scheme, the strategies can be classified as centralized, distributed or with no communications [13]. As their names suggest, the first two categories require a communication system to exchange data between the controllers of the DGs, making the operation vulnerable to failures due to realtime data transmission issues, which can affect the achievement of the control objectives [14], [15]. Considering this aspect, strategies with no communications have emerged as an alternative to reduce the dependence on communication systems and improve reliability [16].

Figure 1
General scheme of a three-layer hierarchical control.
Source: elaborated by the authors.

Regarding the secondary layer, the most common strategies to operate without communications are based on low-pass filters [17], [18], [19]. These types of proposals offer a design tradeoff between transient response and accuracy. Specifically, if a fast transient response is set, the frequency restoration presents poor performance. On the contrary, a good restoration of the frequency is only achieved if a slow transient response is set. Aiming to improve these limited static and dynamic properties, in [20] and [21], controls with no communications have been proposed based on a scheme that switches between two configurations driven by a time-dependent protocol.

Ideally, the electrical systems are balanced when the loads connected in their phases are identical. However, for isolated applications, the connected loads are mostly single-phase, causing imbalances. In isolated electrical microgrids, this situation can generate power supply problems such as: 1) inappropriate power-sharing between DGs [22]; and 2) active power oscillation due to negative sequence currents. Despite this, many of the hierarchical control strategies presented in the literature have been designed to operate properly only with a balanced load. This is the case of [20] and [21], in which only balanced charges were considered.

This paper presents a control strategy without communications for the secondary layer of isolated microgrids with unbalanced resistive loads. This proposal takes as its starting point the strategies presented in [20] and [21], and maintaining its operational advantages, adapts the scheme to ensure good operational performance in the presence of unbalanced resistive loads in terms of the power-sharing of the DGs. For this purpose, an adaptation of a Q^-- Z control block inspired by the work presented in [23] is proposed. The strategy adds a signal to the primary control, eliminating the mismatches in the power-sharing between DGs through a negative sequence virtual impedance. The proposal is characterized by its simplicity and effectiveness without requiring communication.

This paper is organized as follows: in Section 2 concepts about hierarchical control focused on the secondary layer are presented. Then, in Section 3 the proposed control block is described. Section 4 presents simulations to verify the operation of the proposal. Finally, Section 5 concludes the main remarks.

2. Hierarchical Control for Islanded Microgrids

This section presents key concepts about hierarchical control and describes the base strategy for the secondary layer without communications that will be adapted to operate in the presence of unbalanced loads.

2.1. Operation of islanded microgrids

The bibliography on control strategies for microgrids is extensive and addresses strategies for connected mode, islanded mode, and transition between modes [24], [25]. However, there is a clear and widespread tendency to organize control strategies in hierarchical structures [26], [27]. The primary layer is usually based on the well-known droop method [28]. This strategy produces a virtual inertia through the emulation of the synchronous generators' operation, allowing distributed generators to achieve a common frequency, which produces the proportional generation of the steady-state powers. However, this method requires the introduction of a deviation in the frequency of operation, which should be restored in the secondary layer [29]. Finally, the tertiary layer acts to control the power flow management of the distributed generators [30], [31]. Figure 1 presents a general scheme of a three-layer hierarchical control.

As previously mentioned, the hierarchical layers divide the strategies according to the operational dynamics, so it is possible to decouple the design and analysis of each of its layers [32]. The interest of this work is to analyze the operation of the primary and secondary layers. The findings presented can be generalized to operate in conjunction with different tertiary layer strategies.

The use of communication systems is also fundamental in the way hierarchical control operates in isolated microgrids. The strategies can be classified into three configurations: centralized, distributed, or without communications [33]. In the first category, the strategies are governed by a microgrid central controller (MGCC). The DG controllers send measured signals to the MGCC, which receives and manages the information. The MGCC performs calculations and sends back control signals to the DGs periodically. In the second category, the strategies operate distributed, so the MGCC is not required since the control system is designed to rely on the data interchange between the DGs. These categories have in common the use of communication systems for their operation, making them vulnerable to communication issues such as link failures, data transmission delays, and noise disturbances, among others [14], [15].

Although in the second case, reliability improves since it does not depend on the correct functioning of a single equipment (the MGCC), the complexity of installation can increase when numerous DGs are connected. For these reasons, the third category has emerged, in which decentralized control strategies that do not use communication systems are proposed [16]. These types of strategies eliminate the risk of operational failures due to communication issues, although these do not avoid the need to implement a MGCC for other functions such as the DGs coordination during the black start process. Since fewer control layers and operational actions rely on the MGCC performance, the MG will be more reliable [34].

2.2. Secondary layer without communications

The droop control can be defining in equation 1 for frequency regulation as follows

where the frequency ω rely on the active power P, ω₀ and m are frequency reference and droop control gain, respectively. Active power P corresponds to the instantaneous active power p filtered using a low-pass filter with a cutoff frequency ω_c such as equation 2 to achieve high power-quality injection

where, P(s) and p(s) are Laplace transform of P and p, respectively.

This general definition of droop control is decentralized as it operates exclusively using the local measurements (p and ω). The error in the operating frequency concerning the reference o₀ can be recovered by the secondary layer, adding an extra term δ as follows

According to how the delta term is calculated, the secondary layer is classified.

The decentralized proposal presented in [20] defines δ as

where k_i is a constant parameter and /c(t) is a control parameter driven by a time protocol (sgn corresponds to the sign function or signum function). This time-domain expression can be analyzed in the frequency domain as a switching control with two operation modes: a filtered proportional controller and an integral controller, as follows:

being C the last value calculated by the filter just before k(t) = 0. Figure 2 presents a scheme of the operation of this proposal. Notice that the value of k(t) controls the transition between modes and affects the cutoff frequency of the low-pass filter. Thus, the time protocol can drive the value of k(t) to obtain the best features of both the filtered proportional controller and the integral controller. This proposal is characterized by a fast speed of response and a good frequency recovery.

Figure 2
Secondary Switched Control proposed in [20].
Source: elaborated by the authors.

Figure 3 presents the time protocol for variable k(t). This time-protocol is launched when an "event" is detected. According to [20], an "event" is a change in the power delivered or in the frequency of the MG caused by the connection and disconnection of loads and new DGs. Thus, it is possible to implement different approaches for the detection, such as a send-on-delta strategy based on a definition of thresholds for variables such as frequency or active power rate variations [35]. The time protocol is composed of three operation zones: a first operation zone that starts when the event is detected at t_e, in which k(t) has a constant value of k_max during a duration of Δ_et. Then, a second operation zone in which k(t) changes in a linear ramp from k_max to 0 during Δ_ramp, according to equation 5 these operation zones correspond to the filtered proportional controller. Finally, a third operation zone after t = t_ramp, the switched control maintaining the last value calculated (C in equation 5).

Figure 3
Time protocol for variable k(t) [20].

This strategy was designed to operate on balanced microgrids. However, as will be verified later, the presence of unbalanced loads can lead to problems with the power-sharing performance. For this reason, an additional control block is proposed.

3. Proposed Control Strategy

This section presents the proposed control strategy for the secondary layer of isolated microgrids with unbalanced resistive loads.

3.1. Grid-forming inverter

Figure 4 shows a general scheme of a grid-forming inverter. The DC voltage source presents the DC stage composed of a distributed power source connected through a converter and a DC-link capacitor. At the output of the IGBT power inverter, an LC filter (L_ín, C) is connected to reduce the high-frequency harmonics [36]. Then, the elements L_T and R_T represent a coupling transformer to connect the inverter to the point of coupling.

Figure 4
General scheme of a grid-forming inverter.
Source: elaborated by the authors.

The sensed signals are i, v, i₀ that correspond to the inverter output current, the voltage at the capacitor of the LC filter and the current injected to the coupling transformer, respectively. These signals are transformed to the aß framework through the Clarke transformation, and their fundamental positive and negative sequence components are extracted through a double second-order generalized integrator (DSOGI) [37], [38].

The fundamental positive sequence components, v⁺_1αß and i⁺_o,1αß, are used for the primary layer block (droop control) and the instantaneous active power p is calculated according to [23] as follows:

The secondary layer based on the switched control is highlighted in green in Figure 4. It receives the frequency ω and calculates the compensation parameter δ for the primary layer to mitigate the frequency error.

3.2. Proposed control

As previously indicated, the proposed strategy is inspired and adapted from the work presented in [23]. The proposed control corresponds to a Q^- - Z block, which is based on the calculation of a virtual output impedance as a function of the negative reactive power. First, the negative reactive power Q^- is adapted by [23] using αβ components instead of components.

This reactive power term is used to calculate an output impedance Z using the expression:

where Z₀, k^- and Q_o^- are an initial output impedance, a proportional negative control coefficient, and an initial negative reactive power, respectively. These parameters can be set to improve the operation of the proposed strategy. Then, the term Z is operated with the negative current i_o1^-, as

This v^-_αβ,ref signal is applied to the primary control of the hierarchical control structure. The block of the proposed control is highlighted in red in Figure 4.

4. Simulation Results

In order to verify the proposed control strategy, a simulation is implemented in Matlab-Simulink. The simulation was executed on an isolated AC microgrid with the topology presented in Figure 5.

Figure 5
Simulated microgrid.
Source: elaborated by the authors.

The grid is composed of three identical inverter-based DGs named DC₁, DG₂ and DG₃, which operate in grid-forming mode. The experimental test reproduces the black start of a microgrid, with the DGs and a local load Z_L being connected sequentially (main load Z_G is connected during all the simulations). DG₁ and DG₂ are connected at t = 0[s] and t = 15[s], respectively. Then, local load Z_L is connected at t = 30[s]. Finally, DG₃ is connected at t = 45 [s].

The impedances Z_F1 and Z_F2 emulate the conductors that connect the equipments and loads. Figure 6 describes the configuration of the loads. The main load Z_c is balanced, as shown in Figure 6(a), while the local load presents an unbalance, as shown in Figure 6(b). It is worth indicating that the load is unbalanced in such a way that the effects on the control strategies were perceptible. The microgrid configuration parameters are described in the Table 1.

Figure 6
Configuration of the loads: a) Three-phase global load ZG. b) Three-phase local load ZL.
Source: elaborated by the authors.

Table 1
Microgrid parameters

Parameter	Symbol	Quantity
Droop coefficient	m	0.5 rad/(kW. s)
LC Filter	𝐿𝑖𝑛,𝑅𝑖𝑛, 𝐶,𝑅	15 𝑚𝐻, 2.04 Ω, 20 𝜇𝐹, 11.33 Ω
Model coupling transformers	𝐿𝑇, 𝑅𝑇	1 𝑚𝐻, 0.5 Ω
Feeder impedance	𝑍𝐹1;𝑍𝐹2	65 𝑚Ω, 2 𝑚𝐻; 110 𝑚Ω, 0.8 𝑚𝐻
Switching frequency	𝑓𝑠𝑤	10 kHz
DC voltage source	𝑉𝐷𝐶	400 V
Local load	𝑍𝐿	24.2 Ω
Global load	𝑍𝐺	96 Ω
Unbalanced local load	𝑍𝐿𝐵𝐶	72.6 Ω
Initial negative reactive power	𝑄𝑜	170 VAr
Initial output impedance	𝑍0	4 Ω
Proportional negative control coefficient	𝑘−	0.01 Ω/𝑉𝐴𝑟
Maximum k gain	𝑘𝑚𝑎𝑥	0.3
Secondary layer parameter	𝑘𝑖	90 rad/s
Time interval for constant time	Δ𝑐𝑡	5 s
Time interval for ramp	Δ𝑟𝑎𝑚𝑝	5 s

4.1. Simulation using Only Primary Control Layer

First, the simulation was performed using only the primary control layer. The same value of the droop coefficient m was implemented for all the DGs considering converters with equal nominal powers. The results for the instantaneous three-phase active powers and frequencies are presented in Figure 7.

In these figures, it is possible to clearly observe the effect of the droop method. The primary layer performs fast and accurate power-sharing between the DGs, despite the unbalanced load. However, as previously discussed, the droop characteristic produces a deviation in the frequency. From t = 0[s] to t = 15[s], when only DGi is operating, the frequency presents the greatest deviation because this inverter must deliver all the power demanded. Once the other DGs are connected, the deviation is reduced since the power-sharing is performed.

4.2. Simulation using the Secondary Switched Control

Next, the simulation was performed using the secondary switched control presented in [20]. The results for the instantaneous three-phase active powers and frequencies are presented in Figure 8.

Figure 7
Results using only droop method. a) Instantaneous three-phase active powers for each DG. b) Frequencies for each DG.
Source: elaborated by the authors.

Figure 8
Results using secondary switched control. a) Instantaneous three-phase active powers for each DG. b) Frequencies for each DG.
Source: elaborated by the authors.

The operation of this control strategy requires detection of "events", which in this case are the connection of the DGs at t = 0[s], t = 15[s] and t = 45[s], and the connection of the unbalanced local load Z_L at t = 30[s].

Since before t = 30[s] the microgrid operates with balanced loads, it is possible to appreciate the proper functioning of the strategy. During the first operation zone that starts when each event is detected (see figure 3), an accurate power-sharing is done during 5[s]. However, an appreciable error in the frequency recovery can be noted. Next, the parameter k(t) changes in a linear ramp during 5[s], compensating for the frequency error and showing a good dynamic response. Finally, once the frequency deviation is eliminated, the control switched maintaining the last value calculated until the next event is detected. However, despite the good results of the control strategy when the microgrid is balanced, from t = 30[s], once the unbalanced local load Z_L is connected, an error in the steady-state power-sharing is appreciated. Between 40[s] and 45[s], the difference between the active power delivered by DG₁ and DG₂ is around 50 [W].

Furthermore, between 55[s] and 60[s], the difference between the active power delivered by D G₁ and D G₂ , and DG₁ and DG₃ are around 55[W] and 40 [W], respectively. This is because the switched secondary control strategy fails to act over the negative sequence component of the generated powers.

4.3. Simulation using the proposed secondary control layer

Finally, the simulation was performed using the proposed secondary control layer for unbalanced loads. The results for the instantaneous three-phase active powers and frequencies are presented in Figure 9.

Figure 9
Results using unbalanced power-sharing algorithm proposed. a) Instantaneous three-phase active powers for each DG. b) Frequencies for each DG.
Source: elaborated by the authors.

These results allow verifying that the proposed control mitigates the power-sharing error observed in the previous simulation. Thus, with the added control block, it is possible to maintain the performance of the switched control (good dynamic response and frequency restoration in steady state), without being affected by the impact on the negative sequence generated by the operation of unbalanced loads.

5. Conclusions

This paper presented a secondary control strategy to operate in isolated microgrids with unbalanced loads. The proposal does not require the use of communications, as it is based on a communicationless secondary switched control, to which it was adapted a Q^--Z control block. This block adds a signal to the primary control, eliminating the mismatch in the power-sharing between DGs through a negative sequence virtual impedance. The selected simulation results show the effectiveness of the proposal in the presence of unbalanced resistive loads.

This work corresponds to the first approximation of the proposed control. Future works will further develop aspects related to the design of the control parameters, stability analysis, and operation in the presence of different unbalanced loads.

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Notes

Author notes

^a Emails: andres2218078@correo.uis.edu.co^bjuanmrey@uis.edu.co^cmarialem@uis.edu.co

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