Abstract
This paper investigates a fixed-time distributed voltage and reactive power compensation of islanded microgrids using sliding-mode and multi-agent consensus design. A distributed sliding-mode control protocol is proposed to ensure voltage regulation and reference tracking before the desired preset fixed-time despite the unknown disturbances. Accurate reactive power sharings among distributed generators are maintained. The secondary controller is synthesized without the knowledge of any parameter of the microgrid. It is implemented using a sparse one-way communication network modeled as a directed graph. A comparative simulation study is conducted to highlight the performance of the proposed control strategy in comparison with finite-time and asymptotic control systems with load power variations.
MICROGRIDS are small-scale electrical distribution networks, consisting of distributed power sources, loads and energy storage systems. Primary control of microgrids maintains the stability of frequency and voltage, which causes the magnitudes of frequency and voltage to deviate from their nominal values. Emerged as a natural control system for microgrids, distributed secondary control restores the frequency and the voltage to their nominal operation points and achieves accurate power sharing in both grid-connected and islanded operation modes.
Distributed secondary control has been widely discussed in literature [
Furthermore, the distributed secondary controllers can be categorized into asymptotic controllers [
Sliding-mode control (SMC) is widely used to design the control systems and has been applied in the areas including robotics [
Considering the advantages of SMC and obviating the shortcomings of the secondary microgrid controllers, a fixed-time distributed SMC-based control approach is proposed for the secondary control of AC microgrid. Hence, the voltage regulation and reference tracking before the desired preset fixed-time can be ensured. And the accuracy of reactive power sharing is ensured among distributed generators (DGs) at its nominal levels. These objectives are guaranteed despite the uncertain microgrid parameters and the unknown disturbances. Moreover, the design procedure is model-free since no prior knowledge of load power demand, transmission line impedance or the microgrid topology is required.
The rest of the paper is organized as follows. In Section II, a large-signal dynamic model of islanded microgrids is presented. Section III presents the design of the fixed-time distributed secondary controller with voltage and reactive power sharing. A comparative simulation study on finite-time asymptotic secondary controllers and conventional power sharing protocol with load power variations is presented in Section IV. Finally, Section V concludes the paper.
An islanded microgrid is adopted with DGs, where every DG , contains a primary energy source connected to a voltage-source converter (VSC), an RL series filter, a step-up transformer () with transformation ratio , and a shunt capacitor attenuating the impact of high-frequency voltage harmonics of the local load. Each DG is connected to a set of neighboring DGs at the corresponding point of common coupling (PCC) through transmission lines modeled as a RL series circuits. A schematic of two connected DGs is depicted in

Fig. 1 Schematic of two connected DGs.
DG can be modeled in the d-q framework by the follwoing large-signal dynamical model [
(1) |
where and are the direct and quadratic components of the output current of DG i, respectively; and are the direct and quadratic components of the output voltage of DG i, respectively, and the output voltage of DG i is also the voltage of PCC ; is the feed-forward coefficent; and are the references of the direct and quadratic components of the terminal voltage of VSC, respectively, which are calculated by the local voltage and current of VSC controller [
The state-space matrices , , , and are defined as [
(2) |
(3) |
(4) |
where is the output pulsation of DG i and is its output frequency; is the transmission line impedance; and is the transmission line reactance.
The output active and reactive power and can be calculated from the output voltage and current in the d-q frame using:
(5) |
where is the cut-off frequency of the low-pass filters used to extract the fundamental component of and .
The communication network of the microgrid is described using graphs. Consider a -order weighted directed graph (digraph) with set of nodes and set of directed edges. weight is associated with every edge. if there is an edge from node to node . If agent communicates its state information to agent , then . is called the adjacency matrix of the graph . The graph Laplacian matrix of , , is defined as , where and .
Unlike the existing models of microgrids, the interactions between DGs are considered in the proposed model. It also includes the nonlinearties introduced by the filter, the shunt capacitance, the loads, and the step-up transformers.
The control system developed in this paper is a secondary control strategy with voltage and reactive power sharing in hierarchical control framework. The primary control is given as:
(6) |
where and are the secondary control output voltage and reactive power droop coefficient, respectively. DG generates the desired voltage reference, thus and . Then, (6) can be written as:
(7) |
Since , the output voltage magnitude of DG i satisfies . Thus, controlling the output voltage magnitude is the same as controlling its direct component.
The primary voltage and reactive power control aligns the output voltage magnitude to the d-axis of the voltage reference.
Secondary voltage control is designed to ensure a good trade-off between the conflicting objectives of voltage regulation and maintain the reactive power sharing accuracy in the same pattern as in the primary control:
(8) |
where is the maximum allowable voltage deviations.
Differentiating the voltage droop characteristics twice will yield:
(9) |
where is the auxiliary control input. According to (9), the secondary voltage and reactive power control of islanded microgrids can be transformed to a leader-follower second-order consensus problem for the following linear second-order multi-agent system:
(10) |
Definition: the leader-follower second-order consensus in multi-agent systems is presented as:
(11) |
where is the position of the agent; and is the agent control input.
Leader-follower second-order consensus in multi-agent system (11) is achieved under any initial conditions and . We can obtain:
(12) |
We propose the non-singular terminal sliding-mode auxiliary control law based on the voltage magnitude and the reactive power information from the neighbors of DG i:
(13) |
(14) |
(15) |
where and are the voltage tracking errors and the derivative, respectively; and are the reactive power sharing errors and the derivative, respectively, and and are the reactive power droop coefficients; is a time constant; is the lowest upper-bound of the sliding-time; is the pinning gain and it is non-zero only for the agents that have access to the reference voltage amplitude ; and , , , , , , , and are the control parameters that verifies the following conditions:
(16) |
Denote , and is the reactive power droop coefficient. and with are defined as:
(17) |
(18) |
is the sliding surface defined as:
(19) |

Fig. 2 Block diagram of fixed-time distributed voltage and reactive power controller.
is an upper bound of the reaching time of the secondary SMC of DG i, .
The desired prefixed upper bound of the settling time is expressed as:
(20) |
Theorem: if the control protocol in (15), (16), (17), and (18) is applied, then the fixed-time leader-follower consensus tracking is achieved before the prefixed settling time upper bound (20). Thus, voltage regulation and reference tracking are met in the fixed-time without hindering reactive power sharing, i.e., is verified.
Proof: the result in the Theorem is valid for and , separately [
Remark 1: the term can be neglected for sufficient high values of and low values of , and is verified by the upper bound of the prefixed settling time. However, for very small values of , the effect of the term can be reduced but can not be negligible without hindering the controller performance as high values of increase the chattering effect.
Remark 2: an important feature of the proposed control approach is that the design procedure is straightforward. No knowledge of the microgrid parameter is required. The desired settling-time upper bounds are specified directly in the control law, which makes the tuning process simple. And the only step left is to choose and as explained in Remark 2. In addition, the convergence at the desired settling-time is mathematically guaranteed despite the unknown disturbances.
The performance of the proposed fixed-time secondary voltage control is verified with load power variations in comparison with finite-time and asymptotic secondary voltage control. The performance of the proposed protocol of fixed-time reactive power sharing in maintaining power sharing accuracy is compared with the conventional one in [

Fig. 3 Topology of microgrid.
Except for the internal voltage and current loop parameters, the DG specifications are adopted from [

Fig. 4 Active power variation of load.

Fig. 5 Reactive power variation of load.
The parameters of voltage and reactive power controllers are set as: , , and , . As is very small, several values of and are tested to reduce the term without increasing the chattering effect. , , and achieve the desired effect and will be used in this paper.
To highlight the efficiency of the proposed fixed-time control, the finite-time and the asymptotic secondary controllers in [
The simulations are conducted considering the following scenario.
1) At : the simulation is initialized and the primary control is activated.
2) At s: the proposed secondary control system is applied.
3) At s: active power and reactive power of load 4 are increased.
4) At s: active power and reactive power of load 2 are decreased.
5) At s: load 1 is disconnected from the microgrid.
The results of the simulations are shown in Figs.

Fig. 6 DG1 output voltage using proposed fixed-time control, finite-time control and asymptotic control. (a) Output voltage. (b) Zoom on time lapse [0.79 s, 0.815 s]. (c) Zoom on time lapse [0.99 s, 1.02 s]. (d) Zoom on time lapse [1.19 s, 1.22 s]. (e) Zoom on time lapse [1.39 s, 1.42 s].

Fig. 7 Control signal of proposed fixed-time controller, finite-time control and asymptotic control. (a) Control signal Vind. (b) Zoom on time lapse [0.8 s, 2 s].

Fig. 8 Error of reactive power sharing using proposed and conventional approaches. (a) . (b) . (c) .
At s, the secondary control is activated.
The primary reactive power control represents the benchmark for power sharing accuracy, i.e., the nominal level to be maintained within the microgrid. The proposed fixed-time secondary control achieves efficient voltage reference tracking while maintaining of power sharing accuracy.
Load power variations begin at s as shown in Figs.
The control signals displayed in
In this paper, a fixed-time distributed voltage and reactive power secondary control approach for islanded AC microgrids has been designed. The proposed distributed sliding-mode controller ensures voltage regulation and reference tracking before the upper bound of prefixed settling-time despite the unknown disturbances. And accurate reactive power sharing among DGs is maintained. The comparative simulation conducted with load power variations confirms the performance of the controller in voltage regulation and reference tracking before the desired fixed-time, and the accuracy of reactive power sharing is maintained. Simulation results show that the proposed fixed-time control provides better performance in term of voltage regulation and reference tracking than finite-time and asymptotic approaches, which can achieve fast regulation reference tracking at the expense of the system stability with severe voltage fluctuations.
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