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The complexity of distribution network model mainly depends on the model scale of grid-connected distributed photovoltaic (PV) power generation. Therefore, the simulation performance of multi-scale PV model is the key factor of the simulation accuracy in the specific operating scenarios of distribution network. In this paper, a multi-scale model of grid connected PV distributed generation system is proposed based on the mathematical model of grid-connected distributed PV power generation. It is analyzed that differences of simulation performance, such as adaptability of simulation step size, accuracy of output and the effect on voltage profile of distribution network, between PV models with different scales in IEEE 33 node example. Simulation results indicate that the multi-scale model is effective in improving the accuracy and efficiency of simulation under different operating conditions of distribution network.

Distributed photovoltaic (PV) grid-connected power generation is an important application of solar energy, which can replace fossil fuels and reduce environmental pollution [

Researchers have built a number of PV models with different scales. A mathematical model of the PV arrays is established [

Although a variety of PV models have been established, the scope of application of each model is limited by its model scale. In this paper, a multi-scale model of grid-connected distributed PV power generation will be established. Through the analysis of the simulation performance of the multi-scale model, PV modeling scale under different application conditions will be specified and the simulation accuracy and efficiency of distribution network can be improved.

As shown in

formed into alternating current by the inverter and filtering process, finally sent to the grid as three-phase alternating current. In this section, the mathematical models of the components of the PV power generation system will be established.

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 _{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 I_{0} 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 _{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

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

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 (

In the different application scenarios, the mathematical model of the PV power generation system described above can be transformed into dynamic models of different scales. According to the scale of the model, dynamic model can be divided into three types: Generalized load model, Model with DC voltage source, and Detailed model.

During the steady state analysis of the power system, the internal structure, the interaction between the various components and the specific adjustment process of internal parameters of PV power generation system can be ignored. Only the average active output power P and the average reactive power output Q over a period of time are used to modify the load data in the power flow calculation equation to simulate the influence of the PV power generation system on the power grid. In this case, the PV power generation system is regarded as a generalized load with negative power consumption (−P, −Q) (

The DC-side output voltage can be assumed to be constant if the light intensity

and temperature are constant, or if the PV system is equipped with a large capacity energy storage device. In this case, the DC-side model structure can be simulated only with a DC voltage source within a certain output power range. The AC side consists of detailed models of the power electronic switch, the LC filter and the control module, simulating the dynamic switching process of the power electronic switch inside the inverter (

When considering the effects of light intensity, temperature variation, MPPT and DC bus voltage variation on the output of PV power generation system, further refinement of the model scale on the DC side of the PV power generation system should be made. The DC side of the PV system consists of detailed models of PV panels, DC-DC converters, and MPPT. It simulates the dynamic output characteristics of the PV system with the AC side detail model (

In order to compare the simulation performance of the multi-scale PV models, IEEE33 node is chosen as the PV application scenario in this paper. As shown in

Based on the above application scenarios, the simulation performance of PV models with different scales is compared in this paper. Simulation hardware environment is a personal computer which has installed MATLAB 2011b, 3 GHz CPU, and 2 GB memory. The simulation model is shown in

The simulation performance of the model mainly includes the dynamic characteristic and the steady state characteristic. Dynamic characteristics are embodied in two aspects: simulation speed and simulation precision. On the premise of ensuring the convergence of the calculation process, the larger simulation step size, and the faster simulation speed. The simulation precision is reflected in the simulation accuracy of the output power of the PV model, when the light intensity changes. In addition, the main factor is the influence of the PV model on the distribution network voltage profile, when the output power is constant.

Therefore, this paper makes a comparison of the performance of the multi-scale PV model in the step size adaptability, output power accuracy, and the effect on distribution network voltage profile.

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

As shown in

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

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 (

It can be seen from

The local curves of the output power of the PV models at different light intensities are shown in

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

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 (

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.

A multi-scale model of grid-connected PV power generation system is built in this paper. The following conclusions can be drawn by comparing the performance of different scale PV models in simulation step adaptability, output power accuracy and the effect on voltage profile of distribution network.

1) The model with DC voltage source and the generalized load model have better step adaptability than the detail model of PV generation system. The model with DC voltage source has a higher application value, considering its ability to simulate complex dynamic characteristics.

2) 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.

3) The three scales of 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.

This paper is supported by Research Program of State Grid Corporation in China (PD71-15-042) and Research Program of State Grid Corporation in Ningxia (PDB11201601764).

Lv, C., Sheng, W.X., Liu, K.Y. and Dong, X.Z. (2017) Research on Multi-Scale Modeling of Grid- Connected Distributed Photovoltaic Power Generation. Energy and Power Engineering, 9, 127-140. https://doi.org/10.4236/epe.2017.94B016