1. Introduction
In recent years air pollution and haze have caused health issues around all the world. It is now becoming a more and more serious social problem that calls for less fossil fuels and more renewable energy. As a large consumer of fossil fuels, the transportation sector has emitted about 25% of the greenhouse gases produced by energy-related sectors, so the automobile’s energy structure mode change is imperative [
1]. The demand of green transportation is growing rapidly due to these problems, and electric vehicles (EVs) are widely regarded as a proper solution for this problem. Some countries and regions, such as China and Europe, will start researching the exit schedule of traditional-fuel vehicles [
2,
3]. This will contribute to the enhancement of the development and deployment of electric vehicles and lead to more and more EVs entering the market [
4].
A large number of EVs require a large charging infrastructure to supply the electricity need. Generally, the EV power battery capacity varies from about 20 kWh to more than 100 kWh. According to the SAE J1772 standard [
5], there are three charging standards for EVs that have been developed [
6,
7,
8]:
Level 1: The charging equipment uses single-phase AC power of 120 V voltage and 12 to 16 A current. It takes more than 10 h for a level 1 charger to charge a 20 kWh EV battery from 0% state of charge (SOC) to 100% SOC.
Level 2: The charging equipment uses 208–240 V single-phase AC power to provide up to 19.2 kW of charging power, needing at least 1 h for charging a 20 kWh EV battery to full SOC.
Level 3: This also known as fast-charging, the voltage used in this system is rated to 380 V in the AC side, 600 V in the DC side, and the maximum current is up to 400 A to provide a maximum 240 kW charge power. A 100 kWh EV battery can be fully charged within less than half an hour.
The common slow-charging piles are usually located in residential and office or shopping mall building parking lots, which cannot satisfy the sudden charging requirement due to the limitations of time and space. As a supplement to the slow charging, the EV fast-charging station is a necessary supplement and vital components for public acceptance of electric vehicles because it can greatly improve the ease of use for the EV owners. It makes the electricity energy refill as easy as refueling gasoline.
The EV fast-charging station generally consists of a distribution transformer and multiple fast-charging piles that are three-phase AC–DC voltage source converters (VSC) to generate the DC voltage for the EV battery. Since the fast-charging piles can provide a maximum charging power more than 200 kW, suppose that a EV fast-charging station contains 10 charging piles, when 10 are EVs charging simultaneously, the load can be up to 2000 kW, which is about the same as a residential or office building. Large numbers of EVs connecting to the urban power grid through EV fast-charging stations will change the dynamic characteristics of the power system since the fast-charging piles are controlled power electronic devices. EV fast-charging stations, together with the VSC-connected renewable generators, e.g., wind power and solar power, lead the power grid to power electronic features and make the AC grid relatively weak [
9,
10]. Under such a situation, the interaction between the VSCs and the AC power grid will lead to complex oscillation problems. Such oscillation instability issues appeared in railway traction and supply systems where pantograph rising has been reported, a swing of the peak value of the grid side voltage appears on the sinusoidal wave as a low-frequency oscillation (LFO) [
11]. In Texas and the Hebei province of China, interaction between wind power plants and the power grid lead to a sub-synchronous oscillation that will influence the stability of the power plant [
12,
13]. Sub-synchronous oscillation between the wind power plants even led to tripping of power plant units in Xinjiang. These instability issues are known to be caused by the power electronic interface loads and generators, such as electric vehicles, wind power plants, solar power plants, and electrified railway interaction with the power grid and interaction between these loads and generation.
Compared with the traditional LFO, the mechanism of interaction among VSCs and the AC grid is more complex and has not been fully understood. These kinds of power electronic interfaced oscillation and instability issues are generally analyzed from the viewpoint of small disturbances by the method of eigenvalues based on the state space model [
14] and the impedance method based on frequency theory [
15,
16,
17]. The eigenvalue method is difficult to apply in the large-scale system with the high penetration of power electronic interfaced loads and generators due to its requirement of detailed models and parameters of the converters and the power system. Compared with the eigenvalue method, the impedance-based method regards the interaction system as two sub-systems, comprised of the load side converter and the source side AC grid at the point of common coupling (PCC). Only the output and input characteristics at the PCC of both sub-systems are concerned in this method to analyze the stability of the interaction system. In recent years the impedance method has been adopted in the stability analysis for grid-connected VSCs [
18,
19]. Jian has proposed an impedance-based method in [
19] by using the Nyquist criterion to analyze the stability of grid connected inverters. However, this method is developed for the single input and single output (SISO) system, and it is not suitable for stability analysis of the fast-charging station.
Generally, the three-phase AC–DC fast-charging piles are controlled in the dq frame. Thus, this paper builds the mathematical model of the three-phase fast-charging pile under the dq frame by using the transformation relationship between stationary frame and rotate frame. The fast-charging pile is considered as a multi-input multi-output (MIMO) system under the dq frame. In this mathematical model, the input variable and output variable are both two-dimensional vectors, the output impedance and input admittance are also a two-dimensional square matrix. The stability of the MIMO system can be analyzed based on the impedance-based method. That is based on the output impedance matrix of the grid side and the input admittance matrix of the fast-charging pile side.
In the
dq frame dynamic model, the traditional impedance-based method cannot be used for stability analysis. For the MIMO system with the asymmetric impedance/admittance matrix, the generalized Nyquist criterion proposed by MacFarlane and Postlethwaite is widely used for stability assessment [
20]. Except the generalized Nyquist criterion, some other methods are proposed for the AC cascade system, such as singular value criterion [
21,
22], D channel criterion [
23,
24,
25], and norm criterion [
26]. Compared with traditional methods, such as the Bode diagram, Nyquist criterion, dominate pole, etc., these methods are simpler in calculation. Singular value criterion and norm criterion have some conservatism in stability analysis, and the D channel criterion is obtained from experimental results of high power factor cascade systems, and it is not a sufficient condition, theoretically. The application of D channel criterion is limited since its validity in other AC cascade system cannot be guaranteed. A forbidden region-based stability analysis method in the
dq frame that can be classified as a D channel criterion is proposed in [
27]. Since the high power factor condition cannot be met when instability occurs, the D channel criterion cannot be used for the EV fast-charging station stability analysis. Based on these methods, a novel stability criterion based on a different forbidden region from [
28] is adopted for stability analysis of an EV fast-charging station in this paper.
This paper develops the dynamic impedance model of the EV fast-charging system in the
dq frame at the point of common coupling, and stability of the fast-charging station is analyzed by using the novel forbidden region-based criterion. The rest of the paper is organized as follows: the detailed description of the EV fast-charging system, including the structure, connection, and control diagram is proposed in
Section 2. Then the dynamic model of the EV fast-charging station and grid interaction system is presented in
Section 3. In this part, the control system topology of the three-phase voltage source converter is presented, the dynamic model includes the matrix form input admittance of the fast-charging pile and the matrix output impedance of the AC grid side. The input admittance of the fast-charging pile is derived from the current control loop by using the frame transformation, and the dynamic model of the grid side is obtained through the output impedance of the grid system, including the power source, transformer, and distribution line, is presented. Frequency domain stability analysis is presented in
Section 4. Furthermore, the time domain simulations are presented in
Section 5 to validate the model proposed in this paper.