1. Introduction
In recent years, photovoltaic (PV) power generation has developed rapidly, and the proportion of PV installed capacity in the power grid is increasing. It is estimated that by the end of 2020, the total globally installed capacity of PV power generation will reach 303 GW [
1,
2,
3,
4]. Like the wind power system, the scalability of PV power generation causes a large-scale grid connection, which will change the system power flow distribution, and even reverse the power flow. Moreover, it will bring voltage fluctuations or voltage over-limits, which will be on the grid. At present, research on the impact of wind power grid-connected power systems is relatively mature, but research on the impact of PV grid-connected power systems is still relatively under evolution. Most of the existing research work is on the impact of distributed PV access on the distribution network [
5,
6,
7,
8,
9], and on the impact of large-scale centralized PV grid-connected systems. With the construction of hundreds of megawatt-scale or even gigawatt-scale PV power plants in various countries, centralized grid-connected PV power generation has become a hot issue of research and the main direction of development [
10]. Therefore, it is necessary to study the impact of a large-scale PV grid connection on the power system.
As conventional energy supply conditions become more severe, PV power generation has become an alternative energy source for scholars. In traditional power distribution networks, PV power sources are often accessed by distributed generation (DG), but they are subject to illumination and climatic conditions. PV power supplies have large fluctuations in active power output, and high-permeability PV power sources will have a large impact on the distribution network’s power flow, which causes voltage quality problems such as voltage deviation and voltage fluctuation [
11,
12,
13]. Therefore, considering the random nature of the PV output, it is of great significance to reasonably constrain its accessible capacity.
PV grid-connecting mainly affects the grid power flow distribution, power quality, and dynamic characteristics. The authors of [
5,
6,
7] used the deterministic load flow (DLF) to study the grid-connected power flow problem, and proposed a distributed power access processing method. However, the output of the PV power generation is randomly determined by the real-time light intensity. The deterministic power flow calculation method cannot fully reflect and evaluate the influencing factors and extents.
Probabilistic load flow calculation methods include the Monte Carlo simulation method [
11,
12,
13], semi-invariant and Gram–Charlier series expansion [
9,
14], and point estimation method [
15,
16]. Among them, the authors of [
12] proposed the system voltage evaluation index with PV, but only considered the impact of a single PV power station. The authors of [
13] calculated the distributed PV capacity, as the radial distribution network can be accepted under the condition of satisfying the voltage constraint, where the PVs are located in the grid end. The authors of [
14] studied the influence of distributed PVs on the distribution network. The authors of [
14] also concluded that a PV grid connection is conducive to improving voltage quality, and this is not necessarily true for centralized PV grid integration. The authors of [
15] analyzed the probabilistic density function (PDF) after the PV grid connection, but ignored the correlation between random variables. The authors of [
17] considered the mutual constraints of the wind speed interval and illumination intensity interval. The authors of [
18] studied the joint probability distribution of the PV unit’s on–off time. The authors of [
19] considered the correlation between the branches and characteristics of the voltage distribution, but the above effects of the PV grid connection on the power of the system branch were not considered.
The new energy power system is experiencing a dual technological revolution. The optimal operation mode of interaction between the supply and demand groups was proposed for the power system planning, decision-making, and safe operation [
20,
21,
22,
23,
24,
25]. The interaction between the supply and demand groups means relying on the benign and orderly interaction between the supply side and the demand side in order to optimize the system operation, to achieve the best safety, economic, and environmental benefits. In [
26], a two-layer optimal scheduling model was established for the intelligent industrial park, in order to participate in the system operation. The scheduling strategy of the source-charge coordinated operation in the smart industrial park was studied, and the active participation of the load in the system operation was realized. The authors of [
27] studied the fuzzy opportunity scheduling model of the power system with wind farms, which showed that the model can achieve good energy saving, emission reduction, and safety economic benefits. From the perspective of supply and demand, in particular, the emergence of a flexible load greatly enhances the interaction between the demand side and the grid, but also increases the risk during the operation of the power system [
28]. Probabilistic currents can reflect the impact of this uncertainty on the operation of the system, and are an important basis for solving the weak links in the power grid. The authors of [
29] proposed a probabilistic power flow calculation method by combining a semi-invariant and Gram–Charlier series expansion. In the literature [
30], a probabilistic power flow algorithm based on a stochastic configuration point method was proposed based on the uncertainty quantization theory. In the literature [
31], the Monte Carlo method was used as the reference value, and the power system with wind and PV power generation was considered as the analysis object. The accuracy of the calculation results of the lower-invariant method for different potentials was compared.
The accessible capacity of the distributed PV power source indicates the maximum capacity of the PV power supply to access the network under the constraints of various technical indicators of the power system [
32]. The present research on the accessible capacity of the distributed power sources has yielded certain results. The authors of [
33] proposed a method for calculating the admission capacity based on the dynamic load security domain, and analyzed the impact of different load levels and of the location of the distributed power grids on the accessible capacity. The authors of [
34] established a distributed power supply capacity optimization model considering the current protection constraints of the distribution network, and made an intelligent algorithm to solve the model. In the literature [
35], based on the voltage-adjusted maximum admission capacity calculation method, a voltage control strategy was proposed in order to improve the operating state and the PV penetration rate. The output fluctuation of the PV power supply causes node voltage fluctuations. The existing literature is mostly limited to the static safety index constraints, such as voltage deviation and network power flow, while research on the voltage fluctuation constraints is relatively rare. The literature [
36,
37] has pointed out that voltage waves should be considered when calculating DG accessible capacity dynamic impact, but there is still a lack of analysis for the impact of different power factors on the accessible capacity of PV power.
In this paper, the steady-state model of the PV power generation system is established. Quantitative research is carried out by considering the correlation of the PV power plant output from the perspectives of PV access capacity and PV access point, based on the Institute of Electrical and Electronics Engineers (IEEE) 14-node system and on two provincial-level power grids in Pakistan. The impact of the large-scale centralized PV grid is also studied when the grid is connected to the system node voltage and branch current. The accessible capacity maximization problems of the distributed PV power supply are established by taking into account the voltage fluctuations of each node of the distribution network, as well as the traditional static safety index constraints. Based on the genetic algorithm, to solve the model, we consider the different power factor operating conditions of the PV power supply, analyze the impact of the output fluctuation on the accessible capacity, and provide a reasonable decision-making scheme for the access planning of the distributed PV power supply in the small-scale power grid. Moreover, this paper establishes a maximum integration capacity optimization model of the PV power, according to the different power factors for the PV power. Moreover, the proposed research analyzes the large-scale PV grid access capacity, PV access point, and multi-PV power plant output by probability density distribution, sensitivity analysis, standard deviation analysis, and over-limit probability analysis.
The rest of the paper is organized as follows.
Section 2 provides the PV power flow calculation modeling.
Section 3 gives the analytical calculations of the probabilistic modeling of the PV grid and its impact on the system performance.
Section 4 gives the voltage characteristics analysis.
Section 5 provides the simulation results and analysis, while
Section 6 concludes the paper.
4. Voltage Characteristics Analysis
The traditional distribution network is generally an open-loop operation, and the single-supply radial structure network shown in
Figure 1 can be used to equilibrate the normal operation of the distribution network [
12]. As the feeder line length in the low-voltage distribution network is usually short, the feeder can be ignored. At the same time, it is considered that the PV power supply distributed to the distribution network often relies on the user’s roof construction, and the capacity is small. It is reasonable to assume that it does not have a pressure regulation capability.
In
Figure 6, the feeder has a total of
nodes. Node 0 represents the bus of the distribution network, which is the common connection point with the upper network. Nodes 1 to
represent the other nodes in the distribution network. If its power value is set to 0, it means that there is no PV power or load on the node.
and
represent the equivalent impedance of the
th feeder and the power flowing through the feeder, respectively.
and
represent the PV power output at node
and the load power, respectively.
According to the power system analysis theory [
11], when the distributed PV power source is not connected, the voltage deviation
of the node at the feeder
is given as follows:
After the PV power source is connected to the feeder node, the output current direction is opposite to the load. The voltage deviation
of node
after accessing the PV power source can be expressed as follows:
Voltage fluctuations are generally based on time-domain simulation analysis. Let
be the instantaneous change of electromagnetic power output from the PV power supply at node
. Then, when
, the approximate numerical calculation method of the voltage fluctuation is given as follows:
where
represents the voltage fluctuation value at node
caused by DG power fluctuations.
The fluctuation of the PV power output produces significant voltage fluctuations. Let
be the PV power supply power fluctuation coefficient, which is the instantaneous change of the output electromagnetic power, and that accounts for the rated power. Then, the ratio is calculated by the approximation of the voltage fluctuation as follows:
4.1. Accessible Capacity Optimization Model
In this paper, the PV maximum access capacity optimization model is established. In addition to the common static safety index constraints, the voltage fluctuation index is not limited. The genetic algorithm and Newton–Raphson algorithm are used to calculate the power flow.
4.1.1. Objective Function
Assuming that the PV of the access node is operating at its rated power, then the PV accessible capacity is expressed as the sum of the rated power of the grid-connected PV units. Based on this, the objective function of the accessible capacity maximization problem is given as follows:
where
is the rated power of the node
and
is the number of PV units.
4.1.2. Restrictions
In addition to the static safety constraints, such as the common voltage deviation constraints and line thermal constraints, the mathematical model can be expressed as follows:
where
and
represent the upper and lower limits of the node
voltage, respectively;
represents the upper limit of the voltage fluctuation;
represents the maximum power of the PV power source; and
and
are the line active power amplitude and the maximum allowable power value of the line, respectively.
4.2. Model Solving
A large number of studies have shown that genetic algorithms can successfully deal with optimization problems [
13]. When solving the accessible capacity optimization model, the Newton–Raphson algorithm has been used to solve the power flow and make the individual satisfy the constraints expressed by Equations (6)–(9). The conditions and calculation principles are shown in
Figure 7.
6. Conclusions
This paper analyzes the large-scale PV access capacity, PV access point, and multi-PV power plant output by probability density distribution, sensitivity analysis, standard deviation analysis, and over-limit probability analysis. The correlation of the PV power plant output from the perspectives of PV access capacity and PV access point, based on the IEEE 14-node system and two provincial-level power grids, are used to produce quantitative research. From the perspective of improving the network loss, the PV access point should take the heavy-duty node. When the PV grid-connected capacity is large, the PV access point should be connected to the high-voltage network and sent out through the low-resistance line. From the perspective of voltage control, it is necessary to choose a strong reactive power adjustment node or to configure an automatic voltage regulator. The simulation experiment was carried out from the examples of the IEEE 33-node distribution network standard, and the following conclusions were obtained: (1) The distributed PV power supply can effectively support the voltage level of the distribution network node, but may cause voltage deviation and voltage fluctuation, which can exceed the limit. (2) The accessible capacity of the PV power sources is closely related to its power fluctuation coefficient. When the output electromagnetic power fluctuation amplitude is small under the same power factor, the voltage deviation is the main factor affecting the accessible capacity. When the fluctuation amplitude is large, the voltage fluctuation index becomes the main influencing factor; at the same time, the power factor of the PV power source can be lowered. (3) According to the optimization model proposed in this paper, the offline maximum access capacity countermeasure table is generated, which provides scientific decision-making schemes for the grid-connected capacity of the PV power sources under different illumination conditions, in order to improve the grid’s consumption of distributed power sources. This paper deploys limited power electronics technologies that have improved on the power efficiency and simple hardware design of the PV standards. Recent trends focus on more efficient and limited power electronics technologies in this field. In the future, various influencing factors should be considered comprehensively, the capacity of PV power plants should be properly allocated, and the ability of the grid to absorb intermittent power sources can be improved, so that centralized large-scale PV power generation can become a reality.