Abstract
Centralized photovoltaic power station is an important part of building a new power system, whose power generation unit is the main equipment of the photovoltaic power station. Therefore, it is the basis of analyzing the harmonic characteristics of photovoltaic power generation to study the harmonic generation mechanism and influencing factors of power generation units and establish the harmonic equivalent model of photovoltaic power generation units. In this paper, firstly, the harmonic generation mechanism is analyzed from the aspects of sinusoidal pulse width modulation (SPWM) and dead time of inverter. Secondly, the correlation analysis of influencing factors of output power of photovoltaic power generation unit is carried out, and then the influence of output power on harmonics is analyzed. Thirdly, the harmonic characteristic model of photovoltaic power generation unit based on actual photovoltaic power station and influencing factors is constructed. Finally, the theoretical simulation of SPWM modulation and dead time is verified and analyzed, and the simulation results of harmonic characteristics are compared with the measured data. The results show that the harmonic characteristic of the centralized photovoltaic power station is mainly to generate high-frequency odd-order harmonics, which will generate extra high-frequency even-order harmonics when the irradiation is too high or too low, and cause interharmonics when the irradiance fluctuates on the DC side of the inverter.
Introduction
Photovoltaic (PV) power generation is one of the main ways of new energy power generation under the new power system [1], but because the structure and operation mode of PV power station are different from the traditional power station, which consists of a large number of power electronic devices, and electronic devices generate a large number of harmonics due to their inherent characteristics, which cause serious harm to the electricity grid [2]. Therefore, it is of great significance to study the harmonic characteristics of grid-connected PV power stations in order to ensure the safe and stable operation of PV power generation.
The continuous increase of PV grid connected capacity makes the grid connected harmonic analysis of PV power generation system attract the general attention of domestic and foreign scholars. Modal analysis, harmonic linearization, time domain analysis and other mathematical methods are used to analyze system harmonics [3, 4, 5]. Chen et al. [3] built a three-phase single-stage PV grid-connected multi-inverter, and studied and summarized the resonance characteristics of the system from three aspects: the number of inverters, considering environmental factors and transmission distance, etc. by using modal analysis method. Li et al. [4] used harmonic linearization to establish positive and negative sequence impedance models of three-phase LCL grid-connected inverter, which was used to study the stability of grid-connected inverter without considering the influence of inverter harmonics. Godinez-Delgado et al. [5] combined companion-circuit analysis (CCA) and numerical differentiation (ND) in time domain analysis to predict harmonic injection at the common coupling point (PCC) between PV power generation system and AC power grid. Focuses are put on PV inverters for an improved analysis of system stability problems due to harmonic interference and control strategies used for harmonic suppression [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. Among them, Wu et al. [7] put forward the equivalent circuit model of controlled source of voltage source inverter, which can get the law of system resonance characteristics under different conditions by changing control parameters and power grid parameters. Jahan et al. [11] proposed an advanced control technology PI
In this paper, a simulation model of centralized PV power station power generation unit connected to Tibet power grid is built based on MATLAB/Simulink. Firstly, based on the case study of a PV power station with an installed capacity of 20 MW in Shannan, Tibet, the harmonic generation mechanism is analyzed from the aspects of inverter modulation mechanism and dead time, with the power generation unit as the core. Then, the correlation analysis is used to summarize the influencing factors of output power of PV inverter, and further analyze the influence of output power on harmonics. Next, the equivalent model of harmonic characteristics of PV power station based on actual inverter sinusoidal pulse width modulation (SPWM), dead zone and PV output power is constructed. Finally, the comparison between the model simulation and the measured data shows that the harmonic equivalent model established in this paper is consistent with the harmonic characteristics of the actual power station, which can provide reference for the harmonic characteristic analysis of new energy generation grid.
Generation units and harmonic generation mechanism in PV power stations
Structure of generation units in PV power stations
In this paper, a 20 MW PV power station in Tibet is taken as an example to introduce its power generation units structure, as shown in Fig. 1, which is mainly composed of PV panels, DC junction boxes, DC junction cabinets, inverters, box-type transformers, station loads and transmission lines.
PV power generation unit structure.
In the power station, the scheme of block power generation and centralized grid connection is adopted, and the 20 MW grid-connected power generation system is divided into 20 subsystems, each of which is 1 MW connected with a 1250 kVA box transformer to form a subsystem-box transformer unit line. Wherein every 17 PV cell modules in the subsystem are connected in series as one path, and 6 paths are connected in parallel to one DC lightning protection junction box. Every 16 outgoing lines of DC lightning protection junction boxes are respectively connected to two DC junction cabinets, either is connected to a 500 kW inverter, and each two inverters is connected to a 1250 kVA box-type transformer. The unit line increases the line voltage from 0.27 kV to 35 kV through the subsystem inverter components, and every 10 unit wiring units are outgoing and sent to the 35 kV switch cabinet as one incoming line, which is incorporated into the power grid as one 35 kV overhead line. The 20 subsystems of the whole station are equipped with 20 box-type transformers to form a 20-circuit subsystem-box-type transformer unit line.
Grid-connected inverter, the power electronic device as the core of grid-connected and DC/AC conversion in PV power station, is the main source of output harmonics of power station, so its harmonic characteristic factors are more complicated than traditional power equipment such as transformers. In this paper, the output harmonic of power station is analyzed by studying inverter, and the mechanism of inverter output harmonic is analyzed from pulse width modulation (PWM) and dead-time effect.
Harmonics generated by PWM in power electronic devices such as inverters are determined by their working mechanism and cannot be avoided. According to the modulation mechanism, the harmonic voltages generated by the inverter are distributed in groups near the switching frequency, generally high-frequency harmonics. The harmonic frequency is related to the rated capacity of the inverter and the switching frequency. When the rated capacity of the inverter increases and the switching frequency decreases, the harmonic frequency decreases. The inverter of PV power station investigated in this paper is controlled by SPWM, so the harmonic generated by modulation mechanism is analyzed with SPWM strategy as the research object.
The inverter adopts bipolar SPWM. The following conclusions can be drawn by Fourier analysis of the output line voltage
(1) Fundamental component is as Eq. (1):
where,
(2) The amplitude of the harmonic component at (
where,
Equations (1) and (2) show that the amplitude of harmonics generated by SPWM modulation is related to DC side voltage and modulation index, while the frequency is related to modulation wave and carrier angular frequency.
In order to avoid the short circuit caused by the direct connection between the upper and lower bridge arms of the inverter, the control signal of the switching device is usually used to delay for a period of time, because the action of the switching device itself has a certain delay time, resulting in a certain time difference between the actual switching signal and the ideal signal, which is called dead time [27]. Due to the dead time of the device, the actual output voltage of the inverter differs from the ideal output voltage by a pulse error voltage [28]. The average error voltage obtained by equal time voltage area method is as Eq. (3):
where,
During one switching period, the relationship between the average value of the actual output voltage
The harmonic voltage obtained by Fourier decomposition of the error voltage formed by the dead time is as Eq. (5) [29]:
where,
Equations (3)–(5) show that the harmonics generated by the dead zone are mainly related to DC side voltage, carrier frequency, dead zone time and harmonic times. When the number of harmonics increases, the harmonics generated in the dead zone will be reduced, so the influence of the lower harmonics will be mainly considered in the dead zone effect.
Factors influencing output power of PV power generation unit
The output of PV power generation unit mainly depends on the active power output by inverter, whose power is influenced by many meteorological factors such as daily irradiance, ambient temperature, wind speed, humidity and air pressure. In order to determine the influence weight of each meteorological factor on the PV output power, the Pearson correlation coefficient method is adopted through correlation analysis to determine the main factors affecting the power generation capacity, and also to judge the correlation degree between each meteorological factor [30]. The so-called correlation coefficient method, that is, the correlation between two vectors x and y can be expressed by correlation coefficient, and the calculation equation of correlation coefficient is as Eq. (6):
where,
The value range of the correlation coefficient
After the data of a PV power station in Tibet with a 15-minute test point on one day in August 2018 were processed, SPSS was used for correlation analysis. The results of correlation analysis are shown in Table 1.
Correlation analysis results
Note:
Under the condition of double-tail-side test, the correlation among variables is shown in Table 1. The output power (
The above analysis showed that the output power (
According to the conclusion in Section 2.1, the relationship among PV output power, irradiance, temperature, humidity and harmonic voltage distortion rate of the grid point was analyzed with the help of measured data of PV power station.
As shown in Fig. 2, the output of PV power station under different irradiance and temperature is determined by irradiance, and temperature has little influence on PV output.
Irradiance-temperature-PV output power diagram.
As shown in Fig. 3, the output of PV power station under different irradiance and humidity is determined by irradiance, and humidity has little effect on PV output.
Irradiance-humidity-PV output power diagram.
Figure 4 is a diagram showing the relation between harmonic voltage distortion rate and PV output power, irradiance, temperature and humidity at the grid point of PV power plant, wherein the cone type represents increment, which means that harmonic voltage distortion rate increases with the increase of PV output power, irradiance, temperature and humidity.
As shown in Fig. 4, the irradiance is the main factor affecting the PV output power and the harmonic voltage distortion rate of the drawing point, followed by temperature and humidity. Therefore, the input variables of the harmonic equivalent model of PV power generation unit studied in this paper are mainly irradiance and temperature.
PV modules and PV inverters are used as the core components in the PV power generation unit. In this section, the basic parameters and structure were used as the research basis. The modeling idea is shown in Fig. 5.
In the figure, based on the conclusion in Section 2, irradiance
Table of PV power station parameters
Table of PV power station parameters
The relation diagram of harmonic voltage distortion rate and various factors.
Modeling thought diagram.
Simulation analysis of SPWM modulation
To verify the accuracy of the analysis conclusion in section 1.2, the MATLAB/Simulink simulation model shown in Fig. 6 was built. The three-phase inverter model had the DC voltage of 700 V, the fundamental frequency of the inverter of 50 Hz, and the three-phase RLC load module acting as the system load. The active load and reactive load were 1 kW and 500 Var, respectively.
Simulation diagram of grid-connected inverter under bipolar SPWM modulation.
The output voltage harmonics under different parameters (
Harmonic analysis diagram of inverter output voltage under different parameters.
The following conclusions can be drawn by observing Fig. 7:
The comparison and analysis of the two groups of parameters (a), (b), (c) and (d) show that under the same carrier frequency, the larger the modulation degree, the larger the output voltage of grid-connected inverter and the less the output harmonic content. Further analysis shows that the output fundamental voltage amplitude of grid-connected inverter is proportional to the modulation degree The comparison and analysis of the two groups of parameters (a), (b), (c) and (d) show that when the modulation wave is constant and the carrier frequency is small, the grid-connected inverter only outputs odd harmonics. When the carrier frequency increases, the grid-connected inverter starts to output odd and even harmonics, and the output voltage increases, but the output harmonic content decreases. The simulation analysis is consistent with the theoretical analysis in Section 2.2.
To verify the accuracy of the analysis conclusion in Section 2.3, a dead time module was added on the basis of Fig. 6, and the dead time was set to 4
Simulation diagram of grid-connected inverter considering dead zone time under bipolar SPWM modulation.
The analysis method is the same as that in Section 5.1, and the output voltage harmonics under four groups of parameters were compared and analyzed. The corresponding FFT analysis results are shown in Fig. 9.
Harmonic analysis diagram of inverter output voltage under different parameters.
The measured environmental data were substituted into the figure.
Diagram of measured results and simulation result.
As shown in Fig. 9, the amplitude of fundamental voltage of grid-connected inverter output is reduced to varying degrees, and the harmonic distortion rate of output voltage is increased to varying degrees considering the influence of dead time. The enlarged view of Fig. 9c shows that relatively obvious low-order harmonic injection occurs after the dead zone is added. The simulation results are consistent with the theoretical analysis in Section 2.3.
According to the modeling thought in Fig. 5 and the parameters listed in Table 2, a grid-connected model of centralized PV power station generation units was built to simulate and analyze harmonic characteristics under the MATLAB environment. The input of measured environmental data is shown in Fig. 10. The measured and simulated results are shown in Fig. 11a and b.
Due to the large difference between the harmonic contents of the simulation data and the measured data, some harmonics in Fig. 11b are not obvious, so three representative moments of input data, namely 0.3 s (average irradiance), 0.5 s (lowest irradiance) and 0.8 s (highest irradiance), were selected for further comparative analysis, as shown in Fig. 12.
Comparison of harmonic content of simulation and measured data under different environmental factors.
Nowadays, the harmonic problem of centralized large photovoltaic power stations is lacking. Based on the data of the actual centralized photovoltaic power station in Tibet, we study the dynamic effects of the modulation mechanism, dead zone time, and output power on the harmonic voltage and build a specialized harmonic source model of Tibet for 1 MW photovoltaic power generation unit to analyze its harmonic characteristics.
As shown in Fig. 11a and b, the centralized PV power station mainly outputs odd-order harmonics such as 3, 5, 7, …, 43, 45 and 47, among which the high-frequency harmonics are mainly concentrated in the odd-order harmonics such as 21, 23, 25, 35, 37, 41 and 43, which are consistent with the theoretical analysis in Section 2.2.
Figure 12a–c show that with the increase of irradiance, the distortion rate of harmonic voltage increases, in which the content of higher harmonics (35, 37, 39, 43, 45, 47, 49, etc.) becomes larger, and a small amount of even harmonics is generated in addition to odd harmonics. When the irradiance is the lowest, the harmonic voltage distortion rate and the content of each harmonic wave are also greater than that of the irradiance, possibly because the inverter output power is low when the irradiance is the lowest. It is concluded that when the output power of the inverter is less than a certain proportion of the rated power, the harmonic voltage distortion rate will also increase.
Point-by-point comparison of (a), (b) and (c) reveals that the harmonic voltage distortion rate of the simulation data is obviously higher than that of the measured data, and the content of low-order harmonics in the simulation data is low, because the low-order harmonics in this model are mainly calculated according to the dead time, ignoring the influence of the background voltage harmonics on the inverter. The content of higher harmonics in the simulation data is high, because the modeling of higher harmonics filtering equipment in PV power plants is neglected in this model. In addition, it is found in the process of simulation that when the DC voltage fluctuates due to the change of irradiance, many non-integer harmonics-interharmonics are generated. In this study, the emphasis is on harmonic characteristics analysis of integer multiples of harmonics in PV power plants, so interharmonics are not studied and discussed.
According to the analysis of the harmonic characteristics of the centralized photovoltaic power station, there are two main ideas of harmonic suppression mode. The former, on the one hand, transforms the inverter itself, by improving the phase number of the rectifier device or using the high power factor rectification, so that it does not produce the harmonic itself, so as to solve the low harmonic problem. On the other hand, the energy storage device with a certain capacity is used to suppress output power fluctuations, thus solving the problems of high harmonic and interharmonic. The latter uses a filter device used to solve the low harmonic and high harmonic to make harmonic compensation to the centralized photovoltaic power station.
Conclusions
In this paper, the characteristics of grid-connected harmonics of the centralized PV power station in Tibet were analyzed theoretically and simulated under the plateau environment. The following conclusions are drawn:
First of all, the correlation analysis of the measured data reveals that the irradiance is the main factor affecting the PV output power and the harmonic voltage distortion rate of the drawing point, followed by the temperature and humidity. According to the theoretical and simulation analysis, when the carrier frequency of grid-connected inverter is constant, the amplitude of the output fundamental voltage of grid-connected inverter is proportional to the modulation degree Through building the grid-connected simulation model of the centralized PV inverter, it is concluded that the irradiance is the key meteorological factor affecting the harmonics.
High irradiance will increase the harmonic voltage distortion rate, especially the higher harmonic parts, such as 39th, 43rd and 45th harmonics, and also will produce a small amount of even harmonics, such as 36th, 38th and 42nd harmonics. Low irradiance will also increase the harmonic voltage distortion rate, especially in the high frequency odd and even harmonics, such as the 33rd-35th, 37th, 39th, 43rd-49th harmonics, etc. Irradiance fluctuation will lead to voltage fluctuation on the DC side of inverter, resulting in many non-integer harmonics-interharmonics.
In practical application, it can be used as a reference to analyze the harmonic characteristics of grid-connected PV power plants in Tibet. At the same time, increasing the output power of the inverter to make it close to the rated output power and stabilizing the DC side voltage of the inverter to reduce the generation of interharmonics is also the focus of this paper in the future.
Footnotes
Acknowledgments
The work was financially supported by Interaction between Traction Load of Railway Connected to Power Network in Tibet of Sichuan-Tibet Railway (No. XZ202101ZR0107G).
