Influence of Large-scale Distributed Photovoltaic Access on Harmonic Characteristics of Distribution Network

With the development of PV on a large scale, developable rooftop distributed PV becomes a high-quality resource to achieve the double carbon goal. Compared with single-node and low-permeability PV access, large-scale photovoltaic access makes the power grid present high-power electronic characteristics, which has a more complex impact on the harmonic characteristics of the distribution grid. To comprehensively reveal the influence of large-scale distributed photovoltaic access on the harmonicity of the distribution network, this paper first conducts a theoretical analysis of the harmonic generation mechanism. On this basis, build a simulation model based on Matlab/Simulink, considering the measurement indexes of low harmonics and supraharmonics, and the influence of grid-connected location, grid-connected capacity, background harmonics, access mode, and other factors on the harmonic characteristics of the distribution network is simulated and analysed. According to the simulation results, large-scale distributed PV access significantly increases the content of low and supraharmonics in the distribution network, which has a great impact on the harmonic characteristics of the distribution network.


Introduction
To accelerate the realization of the strategic goal of carbon peaking and carbon neutrality, accelerate the decarbonization of electricity, and build a new type of power system, the state has intensively issued many new policies.The official issuance of the Notice on the Pilot Program of Rooftop Distributed Photovoltaic Development for the Entire County (City, District) and the promulgation of the renewable energy development plan of the "14th Five-Year" plan have promoted the large-scale development of rooftop distributed photovoltaic in a standardized and orderly manner, making all kinds of idle rooftops become high-quality resources for localities and enterprises to achieve the dual carbon goals.Thus, entering a new period of historical development [1][2].
The promotion of distributed photovoltaic scale development has significantly increased the installed capacity of photovoltaic, distribution networks due to the high proportion of photovoltaic access showing obvious power electronic characteristics, the harmonic problem of the power grid is not only a local problem on the load side, but harmonic pollution also presents coupling, fluctuation, and universality [3][4][5].
At present, a large number of papers have studied harmonic problems caused by grid-connected distributed PV, mainly concerning the harmonic generation and influence mechanism, factors affecting the harmonic distortion of grid nodes, and the harmonic superposition characteristics of PV at multiple access points.Xie et al. [6] theoretically analyse the output harmonic components of grid-connected photovoltaic inverters.Ruan et al. [7] obtained the influence of illumination, temperature, and ultra-high order background harmonics on the emission characteristics of ultra-high order harmonics on the output side of the photovoltaic inverter through simulation.For the case of single PV access,  simulate the effect of PV systems at different grid connection locations and grid capacity access on the harmonic content of the grid connection.Based on the output characteristics of distributed photovoltaics, Wu et al. [10] consider the impact of PV access on distribution network harmonics based on the power output characteristics of distributed PV, when environmental factors change.In [11], the effect of the switching frequency sidebands of the PV inverter output with ultra-high harmonics on the harmonic characteristics of the distribution network is compared and analysed under different gridconnected locations.For the case of multi-PV access, Cui et al. [12] provides a theoretical analysis of the superposition characteristics of the harmonics generated by multi-distributed PV in the distribution network and the impact of background harmonics on the output harmonics of PV inverters and verifies them with simulations.In [13][14], The influence of multiple photovoltaics connected to the distribution network under different dispersions is compared and analysed.
Current studies on the harmonic impact of distributed PV access on the distribution network focus on the case of small-scale distributed PV access to the low-voltage distribution network at 0.4 kV and below, and the adopted algorithm is difficult to take into account the characteristics of high PV penetration and many access nodes in the context of large-scale PV development.With the existence of fast electronic switches, the content of ultra-high order harmonics in the distribution network increases rapidly, and its influence on the harmonic characteristics of the distribution network should not be neglected [15][16].It is not comprehensive enough to characterize the influence of distributed PV access on the harmonic characteristics simply by using the odd low-frequency harmonic content, total harmonic distortion rate, or ultra-high harmonic content.Because of this, this paper establishes a distributed PV system model and a distribution network model based on Matlab/Simulink, considering low-order and high-order harmonics, and simulates and analyses the effects of the high penetration rate of distributed PV and multi-node convergence on the harmonic characteristics of distribution network under the influence of factors such as grid connection location, grid connection capacity, background harmonics, and access mode.

Harmonic generation mechanism of inverter
The inverter inverts the DC power emitted from PV panels into AC power to feed into the grid or supply to the load.The harmonic components in the inverter output current can be mainly divided into highorder harmonics and low-order harmonics.
The high-order harmonics of the inverter output mainly originate from the sinusoidal pulse width modulation technique and are distributed around the switching frequency and its integer multiples [17].Through the Fourier analysis of the output voltage of the inverter with bipolar SPWM modulation, it can be obtained that the harmonic voltage amplitude generated by SPWM modulation is influenced by the direct current side voltage and modulation system.Under the steady-state operation condition of the photovoltaic inverter, the modulation system is affected by the inverter output P, Q, and the grid side equivalent impedance, so changes in the distributed photovoltaic grid-connected capacity and gridconnected position will cause changes in the modulation system, which in turn affects the higher harmonics output by the inverter.
Internal factors such as the dead time of the inverter, the non-ideal conduction characteristics of switching devices, as well as external factors such as filter structure, control strategy, power grid background harmonics, and power generation unit output, will lead to the change of low order harmonics of photovoltaic inverter output [18].

Analysis of the harmonic mechanism of multi-distributed photovoltaic access distribution network
This paper adopts the equivalent distributed photovoltaic module of the harmonic current source to establish the equivalent circuit of the distribution network with multiple distributed photovoltaics as shown in Figure 1.
Z Z , most of the harmonic currents generated by the distributed PV system flow through the distribution line to the PCC point, with less impact on the remaining branches.
The harmonic voltage of the photovoltaic access point is Combining Equations ( 1)-( 2) 1, 1, eq h eqL h Z Z shows that the farther a single photovoltaic access point is from the PCC point, the greater 1, eq h Z and 1, eqL h Z are, the greater the harmonic current is from the photovoltaic access point to the PCC point, the higher the harmonic voltage of the photovoltaic access point is.
According to the superposition theorem, it is known that the harmonic current flowing into the system when multiple PV multi-nodes are integrated into the distribution network is

, , eq h eq h eqn h g h PV h PV h PVn h eq h eqL h eq h eqL h eqn h eqLn
From Equation (3) and the principle of harmonic current vector superposition, the access position of each PV and the amplitude and phase of the harmonic current emitted by each PV will affect the harmonic current injected into the system.To verify the impact of large-scale distributed PV access on the harmonic characteristics of the distribution network, this paper adopts the IEEE 33-node distribution network model shown in Figure 2, and the voltage level is 10 kV.The distributed PV modules are all two-stage three-phase PV power generation systems.Assuming that all nodes can be used as PV access points, The PV access points involved in the simulation to analyse the effect of different influencing factors on the harmonic characteristics of the distribution network are marked in Figure 2. The inverter is a common three-phase voltage-type SPWM inverter with double-loop decoupling control and the switching frequency is set to 10 kHz.

Impact of PV grid-connected capacity on harmonics in the distribution network
In the distributed PV large-scale development access system scheme, it is recommended to use 10 kV access within the capacity range of 300 kW~6 MW.Therefore, this paper conducts simulation analysis for the case of access node 6 with the grid-connected capacity of 0.3 MW, 1.5 MW, 2.4 MW, 4.8 MW, and 6.0 MW respectively.Figure 3-5 show the simulation results.Keeping other operating conditions unchanged, as the Photovoltaic access capacity increases, the harmonic currents injected into the PV access point gradually increases, and the corresponding harmonic voltage is also larger, while the base wave voltage of each node is raised relatively small, so the U THD of each node is higher.From Figure 5, when the PV penetration rate is low, the harmonics injected into the distribution network by the PV system are mainly ultra-high harmonics around the inverter switching frequency and its multiplier frequency.As the PV penetration rate increases, the content of low harmonics rises steeply, injecting large amounts of low harmonics into the distribution network.

Effect of different access locations on harmonics in the distribution network
The grid-connected capacity is 2.4 MW, the photovoltaic permeability of the distribution network is 55%, and the distribution network is connected at nodes 6, 15, 18, and 27 respectively.The total voltage harmonic distortion rate and harmonic current content of each node are simulated and analyzed under different grid-connected positions.Figure 6-7 show that under the same PV access capacity, the farther the PV access point is from the PCC point, the greater the harmonic current flowing through each node of the distribution network, and the higher the total harmonic distortion rate of the nodes.The vast majority of the harmonic currents are injected by distributed PV flow from the grid connection point to the PCC node, the closer the node to the PCC point on the line, the smaller the change in the total voltage harmonic distortion rate.The non-DG access branch line is less affected, has low harmonic current content at each node, and the total voltage harmonic distortion rate is close to the intersection of the branch line with the DG access point to the PCC point branch line.Figure 8 shows that when the PV access capacity is certain, the distributed PV access location is different, the equivalent network-side impedance is different, and the regulation system m changes.The low harmonic content of the PV access point increases with the backward movement of the access point, and the ultra-high order harmonic voltage amplitude changes with the change of the regulation system m .

4.3.
The effect of background harmonics on the harmonic characteristics of the distribution network 4.4.Maintain a distributed PV access capacity of 2.4 WM for node 6.The frequency harmonics other than fundamental wave are set at the power point to achieve the injection of background harmonics into the distribution network.Table 1 shows the simulation parameters of the background harmonics.Comparing and analyzing the harmonic voltage of the photovoltaic access point with or without background harmonics in Figure 9, after adding the background harmonics, more frequencies of ultrahigh harmonics are introduced, mainly distributed near the   s b f f  frequency and the high-frequency background harmonics, where s f is the switching frequency and b f is the background harmonic frequency.Combined with the paper [19], it can be known that the accurate tracking of the photovoltaic grid-connected current to the reference current is affected by the background harmonics, which causes the photovoltaic system to inject additional ultra-high-order harmonic components into the grid except for the switching frequency and its frequency doubling.Figure 9 The harmonic content of the grid-connected point when considering the background harmonics

The effect of PV access uniformity on the harmonic characteristics of the distribution network
When the distribution network is planned to connect distributed PV with a larger total capacity, the single node access distributed PV capacity should not be too large considering the light conditions, installation location, and other resource distribution as well as the power quality and is usually scattered to multiple nodes for access.In this paper, the photovoltaic access uniformity index is introduced to quantitatively describe the grid-connected position and grid-connected capacity of distributed photovoltaic and other factors that have a large impact on the harmonics of the distribution network.
Considering the factors affecting the harmonic characteristics of the distribution network and the access characteristics of large-scale distributed PV with multiple nodes and high permeability, this paper establishes the following indicators of PV access uniformity based on the paper [20].
In the Equation, J is the photovoltaic access uniformity index of the distribution network; i Z is the line impedance from the node i to the power point; is the standard deviation function of n samples; DPV S is the total installed photovoltaic capacity of the distribution network; i S is the photovoltaic access capacity of the node i ; , i DPV S is the proportion of the photovoltaic access capacity of the node i to the total installed PV capacity.The greater the uniformity of distributed photovoltaic access, the farther the overall access location of the multi-photovoltaic is from the power node, and the farther the relative distance between the multiphotovoltaic connection points is.
In this paper, the influence of high-proportion photovoltaic access on harmonic characteristics will be studied respectively under two access modes of multi-photovoltaic access single-branch and multiphotovoltaic access multi-branch.

Multi-photovoltaic access to a single branch.
High penetration rate PV is connected to the same distribution network branch, maintaining a total access capacity of 3.6 MW, distribution network PV penetration rate of 82.4%, simulation analysis of PV in four different PV uniformity access on the harmonic characteristics of the distribution network.Table 2 shows the simulation parameters of different photovoltaic access uniformity.
As it is shown in Figure 10, when the J is similar, the harmonic distortion levels of each node of the distribution network are close.With the increase of photovoltaic access uniformity, the U THD of the distribution network nodes tends to increase gradually, and the node with the maximum U THD is in the photovoltaic access point farthest from the power point.According to the four access schemes with different photovoltaic access uniformity, when a single branch needs to be connected to highpermeability photovoltaic, connect as many photovoltaic cells as possible to the nodes close to the power point to reduce the photovoltaic access uniformity and avoid the phenomenon that the THD of multinode voltage exceeds the standard in the case of Scheme 3.  Figure 11 shows that the overall harmonic current content of the distribution network nodes is positively correlated with the PV access uniformity.The harmonic currents flowing into the system are vectorially superimposed when photovoltaic access to the distribution network at multiple nodes.The harmonic currents injected into the system at PV centralized access node 6 in Scheme 4 are nearly linearly superimposed.In other multi-node access schemes, the harmonic currents injected into each access point have phase differences, and the harmonic currents can increase or decrease each other, so the harmonic currents flowing from node 6 to the power point are significantly larger than those in Schemes 1 and 2. When high permeability photovoltaics are connected to different distribution network branches, the total access capacity is maintained at 3.6 MW, and the photovoltaic penetration rate is 82.4%.The simulation analyses the effect of the following three different PV uniformity access schemes on the harmonic characteristics.Table 3 shows the simulation parameters of multiple photovoltaic access multiple branches.
Table 3  Figure 12-13 show that the U THD and the harmonic current at each node meet the requirements of the national standard and the overall increase with the increase of J .The high U THD and harmonic current at each node of the branch where nodes 18-22 in schemes 1 and 2 are located are because Schemes 1 and 2 have significantly more distributed PV capacity grid-connected in this branch than Scheme 3.
According to the comprehensive Figure 10-13, the increase of the harmonic current and the U THD at the nodes injected into the distribution network through the decentralized uniform access to multiple branches is much smaller than that of accessing the same branch when the same capacity PV is connected with the same uniformity.Therefore, in the context of distributed PV scale development, it is better to choose multiple branches for decentralized access when the total capacity of PV access to the distribution network is large.In addition, the intersection of multiple PV access branches flowing to the PCC point in the three different PV uniformity access schemes is node 1, which is close to the PCC point.From the ultra-high harmonic amplitudes in Figure 14-15, the ultra-high harmonic amplitudes in the harmonic voltage and harmonic current of node 1 are negatively correlated with the PV access uniformity.Comprehensive Figure 12-15 show that the closer the overall access location of distributed PV connected to multiple branches is to the PCC point, the closer the relative location is between each PV, i.e., the smaller the PV access uniformity is, the smaller the harmonic content is in the voltage and current of the common coupling point, but the rate of ultra-harmonic content is high.If the distribution network contains loads sensitive to ultra-harmonics, the impact of both low and ultra-harmonics on the distribution network should be taken into account.

Conclusion
This paper presents a simulation analysis of large-scale distributed PV multi-node and high-permeability access to the distribution network in the context of distributed PV scale development, and the following conclusions are drawn based on the simulation results: (1) The larger the PV access capacity and the farther the access point is from the power point, the higher the total harmonic distortion rate at the access point, the significant increase in the content of low harmonics, and the gradual decrease in the content of ultra-high harmonics near the switching frequency and its multiples.
(2) The tracking of the PV grid-connected current to the reference current is affected by the background harmonics of the distribution network, which increases the harmonic distortion rate at the PV access point and at the same time makes the inverter inject more frequencies of ultra-high harmonics into the grid.
(3) The impact of distributed PV grid connection on the harmonic characteristics of the distribution network increases with the increase of the uniformity of PV access when high penetration distributed PV is connected, under both access modes of multi-PV access to a single branch and multi-PV access to multiple branches.When the photovoltaic access uniformity is similar, the influence of distributed and uniform access to multiple branches is less than that of a single branch.

Figure 1
Figure 1 Equivalent circuit of distribution network with multiple distributed photovoltaics points used while accessing different capacities PV grid connection points used while accessing different locations Multi-photovoltaic access the PV junction in the single-branch access mode Multi-photovoltaic access the PV junction in the multi-branch access mode   

Figure 3
Figure 3  The total harmonic distortion of each node voltage when the access capacity changes.

Figure 4 Figure 5 Figure 6
Figure 4 Harmonic content for current of each node when grid-connected capacity changes

Figure 7 Figure 8
Figure 7 Harmonic current content of each node when the access position changes

Figure 10 Figure 11
Figure 10 The total harmonic distortion of each node voltage under different grid-connected schemes -photovoltaic access to multiple branches.

Table 2
Simulation parameters of multi-photovoltaic access single branch Simulation parameters of multiple photovoltaic access multiple branches