A PV cell is a device that converts solar energy into electrical energy. A PV array consists of a large number of PV cells to produce large amounts of electrical energy. The equivalent circuit of the PV array is shown in Figure 2, where I_ph represents the photo generated current, I_d represents the diode junction current, R_s represents the series resistance, and R_sh represents the parallel resistance.

According to the principle of the circuit, the relationship between the output current and the output voltage of the PV array is shown in Equation (1), where I₀ represents the reverse saturation current, q represents the electronic charge, n represents the diode factor, k represents the Boltzmann constant, and T re- presents the absolute temperature.

Equation (1) can be simplified using four measurable parameters such as open circuit voltage V_oc, short circuit current I_sc, maximum power point voltage V_m, and maximum power point current I_m. The simplified expression is as Equations (2)-(4).

The PV array mathematical model consists of Equations (2) to (4). The model can directly reflect the influence of external environment on the output characteristics of PV arrays, because its four parameters (V_oc, I_sc, V_m, I_m) change directly

with the light intensity S and ambient temperature T.

In this paper, Boost circuit is chosen as the DC-DC converter of PV power generation unit. Its topology is shown in Figure 3. When the switch T_c is conducting, the input voltage will charge the inductor L, in order to make its current rise. When T_c is turned off, L starts to discharge. Then its voltage and input voltage are superimposed on each other, so that the output voltage is higher than the input voltage.

According to the principle of Boost circuit, its input resistance can be expressed as follows:

As shown in Equation (5), when the load resistance R is fixed, the greater the switch duty cycle D, the smaller the input impedance R_in, and vice versa.

As shown in the analysis above, R_in can be changed by adjusting D. Therefore, the MPPT can be implemented by controlling the input resistance to be equal to the PV output resistance. In this paper, the perturbation observation method is adopted as the MPPT strategy, and the algorithm flow is shown in Figure 4.

In this paper, the DC-AC converter converter is composed of a three-phase full-bridge inverter and an LC-type filter. The topology of the converter is shown in Figure 5.

The state equation of the DC-AC converter in the three-phase stationary coordinate system can be obtained based on the Kirchhoff voltage law (KVL).

In order to facilitate the control, the three-phase static coordinate system is transformed into two-phase dq rotating coordinate system through the park transformation. The equation of state of the DC-AC converter in rotating coordinate system is as follows:

At the same time, the power calculation formula in the rotating coordinate system can be derived:

If the gridside voltage space vector direction and d-axis direction is the same, e_q is zero when the network side voltage is a standard symmetrical three-phase sine wave. Therefore, Equation (8) can be simplified as follows:

The control strategy of DC-AC converter can be designed by using the ma-

thematical relations of Equation (7) and Equation (9).

Inverter control strategy includes two types: voltage source control strategy and current source control strategy. The current-source control strategy is used in this paper to control the inverter of grid-connected PV models.

In this control strategy (Figure 6), firstly, the power reference value, is transformed into the current reference value, by using Equation (9). Then, the inverter output voltage reference value, is obtained through the current control loop. Finally, the decoupling control of the inverter output power is realized by controlling the duty cycle of each power electronic switch in the inverter with the voltage reference.

In order to compare the step size adaptation of different scale models, the different scales of the PV model are calculated in the application scenarios, with three different simulation steps: 5 μs, 50 μs and 200 μs. The output currents of the PV models are recorded.

As shown in Figure 12, when the step size is 5 μs, the output current of all three models can reach the stable state within the 0.04 s. Thus, in the case of 5 step size, the three models are all able to effectively simulate the output characteristics of the PV model in the dynamic state.

As shown in Figure 13, when the step size is increased to 50 μs, the model with DC voltage source and the generalized load model are still able to maintain stable output currents, but the output current of detailed model produces fluctuation with about 20 times the rated amplitude. Due to the fluctuations in the 0.2 seconds is still not able to decay to the rated value, the output current waveform can be considered a serious distortion. It shows that the simulation capability of the detailed model is more sensitive to the simulation step than two other models. At present, the step size needed by the distribution network digital analog

hybrid real-time simulation is about 20 μs - 50 μs. Thus, the PV detailed model is not completely applicable to the distribution network digital analog hybrid real- time simulation.

Since the detailed model has a large fluctuation when the simulation step size is 50 μs, only the output current waveforms of the model with DC voltage source and the generalized load model are compared when the simulation step size is 200 μs.

As shown in Figure 14, when the simulation step size is increased to 200 μs, the amplitude and period of DC voltage source model output current are basically the same as the generalized load model, although the local waveform of its output current fluctuates. It can be seen that the model with DC voltage source and the generalized load model can accurately represent the output characteristics of PV generation systems even in the step size of 200 μs.

In addition, although the model with DC voltage source and the generalized load model have the same excellent step adaptability, the model with DC voltage source has a higher application value, considering its ability to simulate complex dynamic characteristics.

In order to compare the output power of the multi-scale PV models under the same conditions, the simulation step is set as 5 μs and the light intensity is changed step by step according to the order of 100%, 30% and 70% of the rated value. The output active power curves of the three models are plotted in the same figure (Figure 15) while the output power of the PV array is indicated by a dotted line as a reference.

It can be seen from Figure 15 that the active power output of the three PV models can be stabilized within 0.1 second after each illumination intensity change, and the variation law of the output curve is the same as the light intensity. It indicates that all three PV models have a certain ability to simulate the PV output power within a certain range.

The local curves of the output power of the PV models at different light intensities are shown in Figure 16. It can be seen from Figure 16(a) that the output

power of three PV models is approximately equal to the output power reference value under the rated light intensity. When the light intensity changes, as shown in Figure 16(b) and Figure 16(c), PV detailed model can accurately simulate the output power of PV arrays. On the contrary, the other two models do not have DC side detailed structure, only adjust the output power with the change ratio of light intensity, resulting in a certain error in output power. Therefore, when the needed accuracy of PV output power is high, it is appropriate to select the PV detailed model to simulate the PV generation system.

In order to compare the influence of PV models on voltage profile in distribution network, the voltage profile curves of the three PV models under stable operation are plotted on the same figure (Figure 17). At the same time, the voltage profile of the distribution network without PV is indicated by a red dotted line.

It can be seen that when the PV model is connected to the distribution network, the voltage of each point has a different degree of rise, and the three PV models have no significant difference in the voltage profile. Therefore, when only the voltage profile is the object of study, the generalized load model with higher computation speed is more suitable.