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A consensus-based distributed control method of coordinated VSGs with communication time delays in isolate microgrid is proposed. When time delays are considered in communication, there are some effects on frequency restoration and active power output allocation. In the control structure, only local information exchange is needed, while the final frequency can be controlled to the nominal value and the VSGs can automatically share loads according to their rated values. An AC microgrid with three VSGs and some loads is implemented. The proposed control strategy is verified by MATLAB/ Simulink simulation results.

Microgrids are active clusters of distributed generators (DG), energy storages and loads [

Therefore, virtual synchronous generator (VSG) is proposed to solve those problems mentioned before. Generally, VSG is based on synchronous generator transient model to imitate its operating characteristics [

Compared with the decentralized control, the distributed control can achieve global management through exchanging information between neighbor VSGs [

Nevertheless, when information is exchanged between connected VSGs through communication, time delays from both message transmission and processing should be considered [

Therefore, in this paper, a consensus-based distributed control method considering communication time delays of coordinated VSGs in isolate is designed. With node-to-node distributed communication, the proposed control method only needs several information exchanged between neighbors and the compute is not complex. In addition, the model with time delays has more practical value for engineering application.

The rest of this paper is organized as follows. In Section II, the model of VSG is implemented and the coordinated control structure of VSGs is formed. Furthermore, consensus algorithm with time delays will be presented. In Section III, the consensus-based control with time delays of coordinated VSGs is proposed. In Section IV, some simulations are realized to show the results of coordinated VSGs with different time delays. Finally, conclusion is summarized in section V.

In general, VSG consists of a three phase legs and a three-phase LCL filter. The typical topology of VSG is shown in

In _{d}, L, C and R are DC voltage, the filter inductance, capacitor and resistance, respectively. u_{0} = (u_{a}, u_{b}, u_{c})^{T} and i_{0} = (i_{a}, i_{b}, i_{c})^{T} are output three-phase voltage and current, which can be used to compute active and reactive power. The traditional droop control strategy is generally employed in VSGs.

The active power-frequency controller is shown in

It is shown in _{0}, w and θ are rated angular frequency, actual angular frequency and angle.

In _{a} is nominal frequency, P_{a} is nominal active power output. Firstly the operation node is A. When load power increases to P_{b}, the operation node moves from A to B, and corresponding frequency is f_{b}. As we can see from

It can be seen from

The consensus algorithm is benefit for distributed cooperative control of VSGs. Consider an undirected graph, the adjacency matrix A represents the connection condition of communication topology. Because the nodes are mutually connected, A is a symmetric matrix. Meanwhile, the degree matrix D, is a diagonal matrix, where the degree of vertex stands for the number of connected VSGs. The Laplacian matrix L of an undirected graph is then defined as

When the communication topology is satisfied with the demand of a spanning tree, which means each node can reach every node by acertain way, then L is positive semi-definite with one zero eigenvalue [

The consensus algorithm can be described as

where x_{i}, x_{j} are control variables of VSG_{i} and VSG_{j}, n is the number of VSGs, γ is

called the diffusion constant and l_{ij} is the element of L. If time delays are taken into consideration, formula (2) is modified as

In the simplest case of τ_{i} = τ_{j} = τ, it means that transmission and processing time delays of all VSGs are equal. When the system meets the demand of a spanning tree and time delays are in a certain range, all VSGs may globally reach an average-consensus as described below

In a word, consensus algorithm can be used to reach active power output agreement among VSGs.

According to the coordinated control structure of VSGs and the consensus algorithm, the control method is depicted as follows

where P_{i}^{set} and P_{i}^{inj} are rated active power and actual value of VSG_{i} and p_{i}^{reg} is the regulated value of active power, the subscript i is the serial number of VSGs. D_{p,i}, D_{p,j} are the damping coefficient of VSG_{i} and VSG_{j}. k_{p,i} is the frequency restoration coefficient of VSGi. J_{i} is the imaginary moment of inertia, ω_{0} is rated angular frequency.

Neighbor VSGs will exchange the information to achieve consensus. Finally, according to the consensus algorithm, when

then

According to (8), the active power output of each VSGs are determined by their rated active power [

In practice, transmission and processing time delays should be considered. When time delays are introduced, the control method can be described as

In accordance with (5) and (9), the control block diagram for each VSG is shown in

As is shown in

An AC microgrid with three VSGs and one aggregate load was implemented to test the effectiveness of the consensus-based distributed control formulation (5) and (9) presented in Section III.

The main parameters of simulation are that P_{1}^{set} = 10 kW, P_{2}^{set} = 20 kW, P_{3}^{set} = 30 kW, D_{p}_{1} = 1000 kW/rad・s^{−1}, D_{p}_{2} = 2000 kW/rad・s^{−1}, D_{p}_{3} = 3000 kW/rad・s^{−1}, k_{p}_{1} = k_{p}_{2} = k_{p}_{3} = 4 s and J_{1} = J_{2} = J_{3} = 1.061 kg・m^{2}.

It can be seen from _{1} can communicate with VSG_{2}, while VSG_{2} and VSG_{3} have communication links.

At 0 s, three VSGs will provide energy to the common load, whose power consumption is 60 kW. Different value of time delays are considered, including τ = 0, it represents no time delay, τ = 0.1 s, τ = 0.2 s, τ = 0.3 s and τ = 0.5 s.

Simulation results of system frequency are shown in

As is shown in Figures 7(a)-(c), for the increase of load, the system frequency declines and it takes about 1s for frequency to restore to 50 Hz. However, when time delays are chosen to be 0.3 s and 0.5 s, shown in

Simulation results of active power output are also shown in

It can be observed from _{1}^{inj}, P_{2}^{inj} and P_{3}^{inj} are about 10 kW, 20 kW and 30 kW, respectively. So the active power output allocation ratio is 1:2:3, which is equal to the scale of the rated value of three VSGs.

In

However, if the time delay is 0.3 s or 0.5 s, as is shown in

In this paper, a consensus-based distributed control with time delays for coordinated VSGs is designed. With node-to-node distributed control, the communication cost decreases and the communication stability increases. Under ideal condition, there is no communication time delays and the system performsvery well. However, in practical engineering, time delays cannot be avoided. If the time delays are large enough, the system will not be stable. This research can provide useful reference for the application of VSG in microgrid and active power distribution network. In the future, we will research the maximum boundary of time delays, which can maintain system stability

This work was funded by the National Natural Science Foundation of China (Grant Nos. 51321005, 51207076) and China Postdoctoral Science Foundation (2016M601025).

Chen, L.J., Wang, Y.Y., Zheng, T.W. and Sun, Z.Q. (2017) Consensus-Based Distributed Control with Communication Time Delays for Virtual Synchronous Generators in Isolate Microgrid. Energy and Power Engineering, 9, 102- 111. https://doi.org/10.4236/epe.2017.94B013