CN102279327B - On-line monitoring and state evaluation system for photovoltaic grid-connected power generation - Google Patents

Abstract

The invention discloses an on-line monitoring and state evaluation system for photovoltaic grid-connected power generation, which includes an electrical quantity acquisition unit, an input unit, an output unit, an ARM9 data management unit, a CPLD/FPGA interface conversion unit, a temperature and illuminance measurement unit, and a power supply unit; ARM9, ARM7 and DSP are used to form a multi-CPU fully embedded system, which greatly improves the reliability of the measurement control unit and has strong scalability; FFT is used as the basic power quality measurement algorithm, and high-precision sampling and synchronous transmission are adopted. For the real-time measurement of environmental parameters, an inter-harmonic measurement algorithm and a harmonic source location and responsibility division method are proposed to realize online real-time comprehensive monitoring of the power quality and operating status of photovoltaic grid-connected power stations, and record various steady-state, transient events. It is convenient for operating staff to intuitively monitor the operating status of photovoltaic grid-connected power stations, and provides reliable data and sufficient evidence for analyzing the causes of disturbances and failures in its operation, which is an important basis for the realization of new energy access to the grid.

Description

Photovoltaic grid-connected power generation online monitoring and status evaluation system

technical field

The invention relates to a distributed new energy grid-connected power generation online comprehensive monitoring platform based on multi-CPU fully embedded design, in particular to an online photovoltaic grid-connected power generation monitoring and status evaluation system.

Background technique

Photovoltaic power generation has the characteristics of less pollution, renewable, mature technology, and convenient installation, and has become one of the most important distributed power sources. Experts and scholars at home and abroad have done a lot of research on photovoltaic power generation. There are large random fluctuations in the output power of photovoltaic power plants with changes in light intensity, which will have adverse effects on both grid-connected and independent photovoltaic systems. Specifically, when the large power grid has sufficient reserve capacity and regulation capacity, it is generally unnecessary to consider the frequency deviation caused by the power fluctuation of the new energy power station, but mainly consider the voltage fluctuation and flicker caused by the power fluctuation. When the power grid in remote areas of the generator set is integrated into new energy power generation systems such as photovoltaic power generation and wind power, the grid frequency offset and frequency stability problems caused by power fluctuations of new energy power stations during isolated operation cannot be ignored. In addition, since the photovoltaic power generation system needs to use power electronic devices to achieve grid connection, the voltage and current harmonics generated by it are also inevitable.

Therefore, it is necessary to establish a photovoltaic grid-connected power generation system measurement technology platform, to study the power quality problems caused by photovoltaic power stations, and to propose corresponding improvement strategies to ensure the reliable and stable operation of the grid-connected photovoltaic power generation system. In addition, it can provide guidance and suggestions for operation control strategies, and can also provide reliable data and reasonable solutions for the grid-connected design and planning of distributed photovoltaic grid-connected power generation systems in the future, and provide a sufficient basis for analyzing problems that arise in actual operation. With the development of my country's new energy power generation technology, photovoltaic power generation monitoring technology has been gradually developed. The monitoring of photovoltaic grid-connected power generation system involves the analysis and calculation of various parameters and the mathematical description of various interference sources and power systems. It is necessary to develop corresponding analysis software and engineering methods. According to the characteristics of photovoltaic grid-connected power generation system, online real-time Systematic analysis of various power quality problems. At present, there is no measurement platform for the comprehensive evaluation of the measurement and operation status of photovoltaic grid-connected power generation systems at home and abroad, and the index system and evaluation method for comprehensive evaluation of the operation status of photovoltaic grid-connected power stations have not yet been established. There are many monitoring and evaluation indicators for photovoltaic grid-connected power stations. When multiple indicators work together in one system, the adverse effects of different combination results on the operation of the distribution network and the degradation of the performance of the power station are very complicated. The problem. In addition, due to the organic synthesis of multiple indicators, the evaluation of a single indicator cannot fully and truly reflect the quality of electric energy, and the coupling relationship between different evaluation indicators (including basic electricity, environmental variables, and power quality, etc.) Objectively and comprehensively evaluate the operating status of the photovoltaic grid-connected power generation system. However, the hierarchical evaluation based on probability statistics and vector algebra or similar methods lacks objectivity due to the single method of weight determination, which is easily affected by the weighting method.

For the existing photovoltaic and other new energy grid-connected power station monitoring systems, an 8-bit or 16-bit single-chip microcomputer is generally used as the core controller to measure various power quality indicators of the photovoltaic power station. Compared with the new microprocessor, the shortcomings of this type of controller are becoming more and more obvious, such as the chip hardware function is simple, the performance is low, the real-time and scalability are poor, which makes it difficult to upgrade the system, and has certain limitations for the application of intelligent system theory. , and it is difficult to adapt to online harmonic and inter-harmonic calculations. At the same time, the existing photovoltaic grid-connected power station monitoring system does not integrate comprehensive evaluation functions, nor has an evaluation index system for photovoltaics been established, making it difficult to make comprehensive monitoring and objective evaluation of the operating status of photovoltaic grid-connected power stations.

Contents of the invention

In view of the above shortcomings of the online monitoring device for photovoltaic grid-connected power generation, the purpose of the present invention is to provide a more accurate, real-time, low-cost, and comprehensive and objective comprehensive evaluation of photovoltaic grid-connected power generation systems On-line monitoring and status assessment system for photovoltaic grid-connected power generation.

The purpose of the present invention is achieved in this way: an online monitoring and status evaluation system for photovoltaic grid-connected power generation, including a power acquisition unit, a CPLD/FPGA interface conversion unit, an input unit, an output unit, ARM9 data management and monitoring unit, dual A RAM module, a temperature and illuminance measurement unit, and a power supply unit; the power acquisition unit is composed of a signal conditioning module, an A/D acquisition module, an ARM7 sampling control and frequency measurement module, and a DSP processing module connected in series; the power acquisition unit passes through the The dual-port RAM module and the CPLD/FPGA interface conversion unit are connected with the ARM9 data management and monitoring unit; among them, the ARM7 sampling control and frequency measurement module inputs the sampling control signal into the A/D acquisition module; the ARM7 sampling control and frequency measurement module and DSP processing The digital signal output by the module is input to the dual-port RAM transmission module; the input unit is composed of a signal conditioning circuit, an optocoupler isolation and an input DSP processor. The signal conditioning circuit is used to receive and adjust the input signal, and the input signal It is transmitted to the open-in DSP processor through optocoupler isolation, and the open-in DSP processor processes the received open-in signal according to the equal-interval synchronous sampling pulse signal, and then transmits it to the ARM9 data management unit; the open-out unit is processed by the open-out DSP Composed of devices, relays, and anti-spark protection circuits, the DSP processor is used to receive and process the control signals from the upper computer through the ARM9 data management unit and the dual-port RAM transmission module, and the DSP processor is used to output the processed control signals To the relay, the relay switches the power load through the anti-spark protection circuit; the ARM9 data management and monitoring unit is connected to the dual-port RAM transmission module through the CPLD/FPGA conversion interface; the temperature measurement unit and the illumination measurement unit convert the environmental signal into a voltage signal through the sensor , converted into digital signals by A/D acquisition module and DSP processing module.

Compared with the photovoltaic grid-connected power generation monitoring equipment of existing products, the photovoltaic grid-connected power generation online monitoring and status evaluation system has the following advantages:

1. The index system for the comprehensive evaluation of the operating status of photovoltaic power stations is proposed, and the gray correlation analysis method based on gray system theory is used to evaluate the operating status of photovoltaic grid-connected power stations. Based on the measurement and calculation of various power quality indicators, combined with the local environmental parameters of the power station, the correlation degree between each indicator is quantitatively analyzed. The method of combining the improved AHP subjective weighting and objective entropy weighting method is used to obtain objective and accurate weight coefficients. It is convenient for the operation staff to find the problems existing in the operation of the photovoltaic grid-connected power station and improve the transparency of its operation status.

2. Use the high-speed and high-precision DSP chip to detect the interharmonic frequency of the common connection point of the photovoltaic grid-connected power station by using the fourth-order cumulant multi-signal classification (MUSIC) method, and use the Prony method to calculate the amplitude, which can reveal different The characteristics of harmonic sources and inter-harmonics under different disturbance methods provide the necessary support for the harmonic control of photovoltaic grid-connected power stations.

3. ARM7 captures and measures the single cycle cycle, and then divides the signal cycle value at equal intervals as the timer time, keeps the front-end signal to be tested in the timing interrupt and realizes synchronous sampling, and uses 16-bit synchronous A/D to convert data at a rate of 10kHz , so that the measurement accuracy of the device can reach 0.5%; the switching value resolution is 0.1ms; the frequency measurement resolution reaches 0.005Hz.

4. A new type of microprocessor based on the embedded real-time operating system and graphical user interface ARM9 hardware platform is adopted, which has the characteristics of strong processing capability, high real-time performance, and easy upgrade, etc., and provides a solid foundation for the realization of the on-line monitoring system of photovoltaic grid-connected power stations A new way.

5. The fully embedded design method is adopted. The comprehensive evaluation software of photovoltaic grid-connected power generation adopts the Linux embedded real-time operating system with open source code. The measurement platform adopts ARM9, ARM7 and DSP to form a multi-CPU system, which greatly improves the reliability of the measurement control unit. performance and strong scalability.

6. With the embedded human-computer interaction processing module as the system center, the interface between the DSP and the embedded processor adopts a dual-port RAM, and uses a CPLD/FPGA conversion interface to convert one of the DSP's EMIF, IIC, SPI, and HPI bus interfaces Transformed into other bus interfaces to realize data transmission between ARM9, ARM7 and DSP multi-CPU. The combination of CPLD/FPGA and DSP has complementary advantages, flexible structure and strong versatility, which can not only improve the efficiency of data processing and transmission, but also facilitate the maintenance and expansion of the later system.

7. The strong and weak current arrangement of the device is completely separated, which can greatly reduce the coupling of external electromagnetic interference on the weak current side, enhance the anti-interference ability of the device, and ensure the continuous operation stability of the system and the safety and reliability of recorded data.

8. It can display data in real time and has a storage function, which is convenient for data query and management; when a fault occurs, it can conduct in-depth analysis according to the detailed waveforms of parameters before and after the fault; according to monthly statistical data and annual statistical data, further statistics can be used to study equipment aging problems and the mid- to long-term impact of local weather conditions on plant operation.

Description of drawings

Fig. 1 is a hardware design block diagram of the present invention;

Fig. 2 is a software design structural block diagram of the present invention;

Fig. 3 is the interharmonic measurement flowchart that the present invention proposes;

Fig. 4 is the indicator system diagram of the comprehensive evaluation of the operating state of the photovoltaic grid-connected power station proposed by the present invention;

Fig. 5 is a flow chart of the comprehensive evaluation of the operating status of the photovoltaic grid-connected power station proposed by the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

See Figure 1, a hardware structure diagram of an on-line monitoring and status evaluation system for photovoltaic grid-connected power generation, including an electrical quantity acquisition unit, input unit, output unit, ARM9 data management unit, CPLD/FPGA interface conversion unit, temperature and illuminance A measuring unit and a power supply unit; wherein,

The power acquisition unit is composed of a series signal conditioning module, an A/D acquisition module, an ARM7 sampling control and frequency measurement module, and a DSP processing module. The power acquisition unit collects 4-way voltage (three-phase and neutral point voltage) and 4-way current (three-phase and neutral point current) analog quantities, and calculates the three-phase voltage and current fundamental wave phase and three-phase Voltage frequency, and various monitoring indicators of photovoltaic power plants are calculated by DSP; among them, 3 channels of voltage channel frequency, the measurement range is 47~63Hz, and the measurement accuracy is ±0.005Hz; 3 channels of voltage and 3 channels of current phase angle, the measurement accuracy is ±0.1 degree; each phase and 3-phase active, reactive and apparent power and power factor, the accuracy is ±0.5% and ±0.005;

The ARM7 sampling control and frequency measurement module inputs the sampling control signal into the A/D acquisition module; the digital signal output from the ARM7 sampling control and frequency measurement module and the DSP processing module is input into the dual-port RAM transmission module.

The input unit is composed of signal conditioning circuit, optocoupler isolation and input DSP processor. The signal conditioning circuit is used to receive and adjust the input signal, and transmit the input signal to the input DSP processor through optocoupler isolation. The input DSP processor processes the received input signal according to the equal-interval synchronous sampling pulse signal, and then transmits it to the data management unit; The processor receives and processes the control signal transmitted from the upper computer through the ARM9 data management unit and the dual-port RAM transmission module, and sends out the DSP processor to output the processed control signal to the relay, so as to realize the relay output control of the output unit.

CPLD/FPGA interface conversion unit: Considering the incompatibility of DSP and ARM9 embedded platform communication interface, using CPLD/FPGA as interface conversion improves algorithm efficiency and is more suitable for real-time signal processing.

The ARM9 data management and monitoring unit is connected to the dual-port RAM transmission module through the CPLD/FPGA conversion interface; the temperature measurement unit and the illuminance measurement unit convert the environmental signal into a voltage signal through the sensor, which is converted into a digital signal by the A/D acquisition module and DSP processing module Signal. The ARM9 data management and monitoring unit provides photovoltaic power station monitoring data reading and data unified management, realizes the real-time monitoring and evaluation algorithm of photovoltaic power station, and completes the human-computer interaction and data communication functions of the device.

Temperature measurement unit: the temperature sensor converts the temperature signal into a voltage signal, and the temperature data is obtained after A/D acquisition and data processing, and then the data is sent to the ARM9 data management and monitoring unit through the 485/232 serial port; the light intensity measurement unit tests the photovoltaic Power station irradiance, measurement range 0-1400W/m2, measurement accuracy ± 2%;

Illuminance measurement unit: Similar to the temperature measurement unit, the illuminance measurement unit also uses the 485/232 serial port to send the data to ARM9 after measuring the light intensity data; the temperature measurement unit measures the ambient temperature of the photovoltaic power station, and the measurement range is -30°C to +120°C. Measurement accuracy ±0.5%.

As shown in Fig. 2, the software analysis system of the present invention includes 3 parts of the acquisition unit DSP software system, the ARM7 software system of the sampling control and frequency measurement module, and the ARM9 software system of the data management and monitoring unit. in,

The DSP software system structure diagram is shown in the lower right part of Figure 4. On the one hand, its initialization is to enable and start the module functions involved in the software, and on the other hand, it performs initial value processing on key data, such as reading the data in the power-down memory. data, record startup information, etc. A/D sampling includes 3 functions of sampling point control, A/D conversion and A/D calibration. A/D conversion is divided into two parts: A/D driver and module connection layer code. The driver is divided into A/D initialization, A/D startup, A/D conversion result reading; module connection layer code includes other auxiliary circuit control (such as sample holder, etc.) in the A/D sampling module, A/D conversion result data conversion, etc. A/D calibration is to reduce proportional deviation and fixed deviation on A/D and sampling circuit. The data processing program uses A/D sampling data to calculate and analyze various monitoring variable parameters by using various formulas and calculation methods involved in various monitoring indicators of photovoltaic power plants. The data storage and transmission program involves the EMIF, IIC, SPI, HPI and other interfaces of the DSP. It is necessary to write the driver code of each interface module according to the design situation, and complete the connection layer code with the peripherals.

The ARM7 software system structure diagram is shown in the lower left part of Figure 4, which consists of a sampling pulse trigger program, a frequency phase measurement program and a data transmission program. A/D sampling control must be provided by ARM7 with a capture function interface. ARM7 measures a single cycle through capture, thereby dividing the signal cycle value at equal intervals as the timer time, maintaining the front-end signal to be tested in the timing interrupt and starting A/D sampling. In addition, the acquisition of 3-phase voltage, current phase and voltage frequency is completed by ARM7 processor LPC2132.

As shown in the upper part of Figure 2, the software system structure of the ARM9 data management and monitoring unit is shown in Figure 4, including data transmission program, data processing and management program, serial port communication program (receiving illuminance and temperature measurement data and serial port sending monitoring data ), Ethernet communication program, and various drivers. The main function of the ARM9 software system is to conduct unified management of the collected basic power data, switching status, environmental data and power quality data, etc., and use various information volumes of photovoltaic power plants to comprehensively evaluate the operation status of grid-connected photovoltaic power plants. And refresh and display the measurement data of the photovoltaic power station in real time. At the same time, the monitoring and evaluation results of photovoltaic power plants are transmitted to the host computer through Ethernet communication and displayed in the form of web browsing. In order to provide remote B/S mode services for photovoltaic grid-connected power generation measurement devices, the bottom layer of Ethernet communication adopts TCP/IP protocol. The Ethernet communication program is a data transmission module based on TCP/IP packets. Through this module, remote devices (or connected to another photovoltaic grid-connected power generation measurement device) and client software can be connected, and the data to be transmitted is encapsulated in TCP/IP IP packets transmit data through switches and network cables. Due to the advantages of Ethernet data transmission, the photovoltaic grid-connected power generation measurement device has real remote access and control, making multi-level networking possible. ARM9 software system adopts Linux embedded real-time operating system, which has a complete TCP/IP protocol inside, and its main functions are task scheduling, file management and network communication. The Ethernet communication program application layer adopts MODBUS protocol.

As shown in Figure 3, the measurement of interharmonics is carried out in the following steps:

1) Perform digital/analog conversion on the sampled voltage and current signals;

2) Utilizing the characteristic that high-order cumulants can completely suppress Gaussian noise, the matrix defined by fourth-order cumulants is used to replace the autocorrelation matrix in the traditional second-order MUSIC algorithm for eigenvalue decomposition.

3) Divide the eigenvector space corresponding to the eigenvalue into a signal subspace and a noise subspace, and use the space orthogonality to obtain the power spectrum and frequency of the harmonic source;

4) The magnitude and phase of these interharmonic components are calculated using the least squares method of the Prony method.

Among them, the calculation method of interharmonic parameters based on the fourth-order cumulant MUSIC method is as follows:

The harmonic and interharmonic detection signals of the power system can be expressed as:

为初始相角；v(n)为噪声项。借助Hilbert变换将上式转换为复频率信号，可得：In the formula: y(n) is the sampling signal; n is the number of sampling points; T _S is the sampling interval; M is the number of harmonics and inter-harmonics contained; A _i is the amplitude of the i-th harmonic component; f _i is the frequency of the i-th harmonic component;

is the initial phase angle; v(n) is the noise term. Using the Hilbert transform to convert the above formula into a complex frequency signal, we can get:

In the formula, ω _i =2πf _i nT _s . The fourth-order cumulant of y(n) is defined as:

c _4y (τ ₁ ,τ ₂ ,τ ₃ )=m _4y (τ ₁ ,τ ₂ ,τ ₃ )-m _2y (τ ₁ )m _2y (τ ₃ -τ ₂ )

-m _2y (τ ₂ )m _2y (τ ₃ -τ ₁ ) (3)

-m _2y (τ ₃ )m _2y (τ ₁ -τ ₂ )

Among them, take the sequence y ₁ =y(n), y ₂ =y(n+τ ₁ ), ..., y _k =y(n+τ _k-1 ), let m _ky represent the k-order moment of the random variable y:

${\mathrm{<span\; class="notranslate">\; m</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; \&infin;</span>}^{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; k</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; dy</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Define C _p+1 as the fourth-order cumulant matrix of the signal:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span>& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&Center\; Dot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>\\ <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&Center\; Dot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>& <span\; class="notranslate">\; \&CenterDot;</span>\\ {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>& {\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the formula, C _s is the signal matrix, and C _v is the noise matrix.

When v(n) is Gaussian noise, C _v =0, C _p+1 =C _s due to the suppression of Gaussian noise by the fourth-order cumulant, and C _p+1 is a conjugate symmetric Toeplitz matrix. rank C _s = M, C _s decomposes on eigenvalues to get:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

e _i is the eigenvector corresponding to the eigenvalue λ _i , and the eigenvectors are orthogonal. Divide the p+1-dimensional vector space formed by eigenvectors e ₁ ,...,e _p+1 into two subspaces, since rankC _s =M, there must be M non-zero eigenvalues and p+1-M zeros Eigenvalues. The eigenvectors e ₁ ,..., _em corresponding to non-zero eigenvalues form a signal space:

where a _i is a constant. And the eigenvectors e _M+1 corresponding to zero eigenvalues, ..., e _p+1 form a noise space:

Where β _k is a constant. Since the vectors in the signal space and the noise space are orthogonal, their linear combination is also orthogonal, namely:

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Let e(ω)=[1, e ^jω ,..., e ^jωM ], then e(ω _i )=e _i , so we have

${\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

The above formula should be 0 at ω=ω _i , and if β _k =1, the MUSIC spectrum can be estimated

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; MUSIC</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

在ω＝ω_i处应为无穷大，但由于四阶累积量矩阵是估计值，必然存在误差，因此

为有限值，但呈现出很尖的峰值。It is the form of the MUSIC spectrum, and it can be known from the above formula

It should be infinite at ω=ω _i , but since the fourth-order cumulant matrix is an estimated value, there must be errors, so

is a finite value, but presents a very sharp peak.

When v(n) is non-Gaussian noise, C _v ≠0 in formula (5), rankC _s =M, rankC _v =p+1. Similarly, the M eigenvectors corresponding to C _s are stretched into a signal space, and the p+1 eigenvalues corresponding to C _v are stretched into a noise space:

Where β _k is a constant. According to the orthogonality of the eigenvectors, we can get:

${\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1,2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Similarly, the MUSIC spectrum of the original signal can be estimated by the following formula:

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; MUSIC</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

的谱图呈现很尖的峰值。Similarly, at ω=ω _i ,

The spectrum shows a sharp peak.

Dividing ω into hundreds of equally spaced units gives

ω _i =2πiΔf (15)

Then substitute each ω _i value into (11) or (14) to obtain the ω values corresponding to all peaks, and the frequency at the peak can be judged by the abscissa.

The frequency estimation accuracy of the fourth-order MUSIC method is related to the estimation accuracy of the fourth-order cumulant matrix on the one hand, and related to the decomposition of signal and noise matrices on the other hand. In order to obtain accurate and effective fourth-order cumulant matrix estimation, the number of samples N can be increased, and the sampling frequency can also be changed to improve the estimation accuracy. In actual calculation, it is estimated with the help of Akaike's Information Criterion (AIC).

From the original signal, the sampling length is N, and the fourth-order cumulant matrix C _p+1 has p+1 eigenvalues, which are arranged in order of λ ₁ >λ ₂ >...>λ _p+1 . make

$\mathrm{<span\; class="notranslate">\; AIC</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}\mathrm{<span\; class="notranslate">\; g</span>}{<span\; class="notranslate">\; [</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="p\; +"\; filenames="HDA0000059744870000041.png"\; state="\{\{state\}\}">p</figure-callout></span><figure-callout\; id="1"\; label="p\; +"\; filenames="HDA0000059744870000041.png"\; state="\{\{state\}\}">\; </figure-callout>}<span\; class="notranslate">\; </span><span\; class="notranslate">+</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

When m increases from 0 to p+1, m corresponding to the smallest AIC(m) is the signal subspace dimension.

Using the least square method in the Prony algorithm to estimate the amplitude and phase parameters of the inter-harmonic components, the specific method is as follows:

Taking a set of M exponential functions with arbitrary frequency, amplitude and phase as an example, its form is:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

b _i and z _i are complex numbers, and let

b _i =A _i exp(jθ _i ) (18a)

z _i =exp((a _i +j2πf _i )Δt) (18b)

construct cost function

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 19</span>}<span\; class="notranslate">\; )</span>$

A _i , θ _i , a _i , f _i can be obtained by minimizing the sum of squared errors. In order to understand this nonlinear equation system, the conventional Prony method needs to construct an autocorrelation matrix and use the SVD-TLS algorithm to solve the least squares estimation of a _i , and then calculate other parameters. In the application of the Prony method in this paper, since the frequency fi _and the number M of harmonics and interharmonics have been obtained in the estimated power spectrum, z _i becomes a known quantity (z _i is also called a Prony pole ) and since the attenuation factor a _i =0, the exponential model equation (17) reduces to a linear equation with unknown parameters b _i . Expressed in matrix form, it is

$\mathrm{<span\; class="notranslate">\; Zb</span>}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

In the formula

$\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; 1</span>}& <span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>& \mathrm{<span\; class="notranslate">\; 1</span>}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}& <span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\\ <span\; class="notranslate">\; \&Center\; Dot;</span>& <span\; class="notranslate">\; \&Center\; Dot;</span>& & <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>& <span\; class="notranslate">\; \&Center\; Dot;</span>& & <span\; class="notranslate">\; \&Center\; Dot;</span>\\ <span\; class="notranslate">\; \&Center\; Dot;</span>& <span\; class="notranslate">\; \&Center\; Dot;</span>& & <span\; class="notranslate">\; \&Center\; Dot;</span>\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& <span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span>& {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; )</span>$

b=[b ₁ , b ₂ ,...,b _p ] ^T (21b)

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; one</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; )</span>$

Since z _i are different, the matrix Z is of full rank, and the least squares solution of equation (20) is

$\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; Z</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; ]</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; Z</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; two</span>}<span\; class="notranslate">\; )</span>$

After obtaining _bi , the amplitude and phase of each frequency component in the signal can be calculated according to the following formula

As shown in FIG. 4 , the index system for the comprehensive evaluation of the operating status of photovoltaic grid-connected power stations proposed by the present invention includes three categories, namely power quality indexes, electric energy indexes and environmental indexes. Among them, the power quality indicators include power supply voltage allowable deviation, voltage fluctuation, voltage flicker, access point voltage harmonic level, odd and even current harmonic distortion rate, three-phase voltage allowable unbalance and duration, voltage temporary Droop depth and duration, power supply interruption time, frequency tolerance and its duration, and the DC component injected into the power station that needs to be considered for the grid-connected photovoltaic power generation system, that is, the three-phase current unbalance. Electric energy indicators include active power change rate, power factor and power generation efficiency. Environmental metrics include hourly average light intensity and temperature.

Figure 5 is a flow chart of comprehensive evaluation of the operating status of photovoltaic grid-connected power stations. The specific evaluation process is as follows:

①Select evaluation indicators that can reflect the operating characteristics of photovoltaic power plants, calculate each weight coefficient with the improved AHP subjective weighting method and objective entropy method, and linearly weight the subjective weight and objective weight to obtain the combined weight coefficient of each index w _j .

② Take the ideal value of the power quality index as its ideal sample (such as zero harmonic distortion rate, zero frequency deviation, etc.). Combined with the national power quality standard to limit the standard samples of each level to classify it. Each single index is divided into 5 grades evenly within the limit value range to describe the available grid-connected photovoltaic power station evaluation index standard matrix.

③ Generate a data matrix C based on the ideal sample, standard matrix and data samples to be evaluated, and use C _{i, j} to represent each data item in the matrix.

④Using the difference between the ideal sample C _{1, j} and the standard matrix, and the corresponding items of the data samples to be evaluated to establish an absolute difference matrix Δ, and Δ _{i, j} represents each data item in the matrix.

⑤ Transform the absolute difference matrix according to the following formula to obtain the correlation coefficient matrix:

${\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="min"\; filenames="HDA0000059744870000041.png"\; state="\{\{state\}\}">min</figure-callout></span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="max"\; filenames="HDA0000059744870000041.png"\; state="\{\{state\}\}">max</figure-callout></span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}{{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; no</span>}}{\underset{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 0.5</span>}<span\; class="notranslate">\; *</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="max"\; filenames="HDA0000059744870000041.png"\; state="\{\{state\}\}">max</figure-callout></span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; twenty\; four</span>}<span\; class="notranslate">\; )</span>$

In the above formula, ξ _i (j) represents the degree of correlation between the j-th index of the i-th sample to be evaluated and the j-th index of the standard sample. The larger the value of ξ _i (j), the closer the sample to be evaluated is to the standard sample.

⑥Calculate the degree of correlation between the sample matrix to be evaluated and the standard matrix by combining the weight coefficient w _j and the correlation coefficient ξ _i (j):

${\mathrm{<span\; class="notranslate">\; r</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 25</span>}<span\; class="notranslate">\; )</span>$

Among them, the process of calculating each weight coefficient with the improved AHP subjective weighting method and objective entropy method is as follows:

A) form a data matrix B=(b _ij ) _m*n according to the samples obtained from the measurement data;

B) carry out dimensionless processing to matrix B;

C) According to the selected index, calculate the information entropy h _j of each index to form the information entropy matrix H _j , the calculation method is as follows:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; ij</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; log</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 26</span>}<span\; class="notranslate">\; )</span>$

D) According to the information entropy matrix, calculate the difference degree D _j =1-H _j of each index, and then calculate the weighting coefficient w' _j of each index:

${{\mathrm{<span\; class="notranslate">\; w</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 27</span>}<span\; class="notranslate">\; )</span>$

In vector form W'=(w' ₁ , w' ₂ , w' ₃ ,..., w' _m ,) represents the objective weight of each indicator;

E) Establish a hierarchical structure chart by grading the importance of indicators;

F) According to the hierarchy diagram, establish a judgment matrix A=(a _ij ) _n*n through pairwise comparison of each index, and solve the maximum eigenvalue and corresponding eigenvector for this matrix.

G) normalize the feature vector obtained in the previous step to obtain W", that is, the subjective weight vector obtained by improving AHP;

H) Perform linear weighting on W' and W" obtained in step 4 and step 7 to obtain the final weight index vector W=(w ₁ , w ₂ , w ₃ ,...,w _m ,) , the linear weighting formula is as follows:

w _j ＝0.5*w′ _j +0.5*w″ _j (28)

Finally, it is noted that the above embodiments are only used to illustrate the technical solutions of the present invention without limitation. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or Equivalent replacements without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the scope of the claims of the present invention.

Claims (1)

1. parallel network power generation on-line monitoring and a state evaluating method, utilizes parallel network power generation on-line monitoring and status assessing system, and this system comprises:

Electric quantity acquisition unit, CPLD/FPGA interface conversion unit, open into unit, output unit, ARM9 data management and monitoring means, dual port RAM module, temperature and illumination photometry unit and power supply unit; Described electric quantity acquisition unit is mainly made up of signal condition module, A/D acquisition module, ARM7 controlling of sampling and frequency measurement module and DSP processing module, signal condition module output two paths of signals, one road signal sends to ARM7 controlling of sampling and frequency measurement module after squaring circuit is processed, another road signal sends to A/D acquisition module after over-sampling keeps resume module, and A/D acquisition module output signal sends to DSP processing module; Electric quantity acquisition unit is connected with ARM9 data management and monitoring means with CPLD/FPGA interface conversion unit by dual port RAM module successively; Wherein, sampling control signal is inputted A/D acquisition module by ARM7 controlling of sampling and frequency measurement module; The digital signal input dual port RAM transport module of ARM7 controlling of sampling and frequency measurement module and the output of DSP processing module; Open into unit and formed by signal conditioning circuit, light-coupled isolation and DSP processing module, described signal conditioning circuit is opened into signal for reception and adjustment, and will open into signal and be transferred to DSP processing module through light-coupled isolation, DSP processing module is according to Synchronous Sampling Pulse signal uniformly-spaced, and opening after signal is processed of receiving is transferred to ARM9 Data Management Unit; Outputing unit is made up of DSP processing module, relay, sparkproof holding circuit, DSP processing module receives and processes the control signal that host computer transmits by ARM9 Data Management Unit, dual port RAM transport module, DSP processing module is exported control signal after treatment to relay, and relay is by the electrical load of sparkproof holding circuit switching; ARM9 data management and monitoring means are connected with dual port RAM transport module by CPLD/FPGA translation interface; Temperature measurement unit and illumination photometry unit convert ambient signal to voltage signal by sensor, are converted into digital signal by A/D acquisition module and DSP processing module;

Concrete estimation flow is as follows:

1. the selected evaluation index that can reflect photo-voltaic power generation station operation characteristic, calculate each weight coefficient with the subjective enabling legislation of improved AHP and objective Information Entropy, and subjective weight and objective weight are carried out to linear weighted function, obtain the combining weights coefficient w of each index of power quality index _j;

Power quality index comprises: admissible deviation of supply volt-age, voltage fluctuation, voltage flicker, access point voltage harmonic level, odd Current harmonic distortion rate, even Current harmonic distortion rate, three-phase voltage allow degree of unbalancedness and duration, the voltage dip degree of depth and duration, power failure time, frequency permissible variation and duration thereof, and DC component is injected in the power station that need consider for grid-connected photovoltaic power generation system;

2. taking the ideal value of power quality index as its ideal sample, the master sample that limits each grade in conjunction with quality of power supply national standard carries out classification processing to it; Each single index of power quality index is on average divided into 5 grades and describes and can obtain grid-connected photovoltaic power generation station evaluation index canonical matrix in limits;

3. according to ideal sample, canonical matrix and data sample generated data Matrix C to be assessed, with C _i,jeach data item in representing matrix;

4. utilize ideal sample C _{1, j}set up absolute difference matrix Δ with the difference of canonical matrix, to be assessed the each respective items of data sample, with Δ _i,jeach data item in representing matrix;

5. according to following formula, absolute difference matrix is converted and obtains correlation coefficient:

${\mathrm{\&xi;}}_i\left(j\right)=\frac{\underset{1\&le;j\&le;n}{\underset{1\&le;i\&le;(m-1)}{\min }}{\mathrm{\&Delta;}}_{i,j}+\underset{1\&le;j\&le;n}{\underset{1\&le;i\&le;(m-1)}{0.5*\max }}{\mathrm{\&Delta;}}_{i,j}}{{\mathrm{\&Delta;}}_{i,j}+\underset{1\&le;j\&le;n}{\underset{1\&le;i\&le;(m-1)}{0.5*\max }}{\mathrm{\&Delta;}}_{i,j}}---\left(24\right)$ Correlation coefficient ξ in above formula _i(j) correlation degree of i j index of j indicators and standards sample of data sample to be assessed of expression; ξ _i(j) value more represent data sample to be assessed and master sample more approaching;

6. in conjunction with weight coefficient w _jwith correlation coefficient ξ _i(j) calculate the degree of association of data sample matrix to be assessed and canonical matrix:

$r_i=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j{\mathrm{\&xi;}}_i\left(j\right)---\left(25\right);$

Wherein, calculate each weight coefficient flow process with the subjective enabling legislation of improved AHP and objective Information Entropy as follows:

1) data sample to be assessed obtaining according to measurement data, forms data matrix B=(b _ij) _m*n;

2) matrix B is carried out to nondimensionalization processing;

3), according to selected index, calculate the information entropy h of each index _j, form information entropy matrix H _j, computing method are as follows:

$h_j=\frac{-\left(\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{p}_{\mathrm{ij}}{\log }_2{p}_{\mathrm{ij}}\right)}{{\log }_{2}n}---\left(26\right)$ Described selected index is the evaluation index that can reflect photo-voltaic power generation station operation characteristic;

4) according to information entropy matrix H _j, calculate the diversity factor D of each selected index _j=1-H _j, and then obtain the weighting coefficient w ' of each selected index _j:

${w^{\&prime;}}_j=\frac{d_j}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{d}_j}---\left(27\right)$ With vector form W '=(w ' ₁, w ' ₂... w ' _j... w ' _n) represent the objective weight of each index;

5) by the classification in index significance level, set up hierarchical chart;

6), according to hierarchical chart, by comparing between two between each index, set up judgment matrix A=(a _ij) _n*n, and to this Matrix Solving eigenvalue of maximum and character pair vector;

7) proper vector obtained in the previous step is normalized and obtains W ' ', improve the subjective weight vectors that AHP obtains;

8) W ', the W ' ' that step 4 and step 7 are obtained carry out linear weighted function, obtain final each selected index weights index vector W=(w ₁, w ₂... w _j..., w _n), linear weighted function formula is as follows:

w _j=0.5*w' _j+0.5*w'' _j (28)

Wherein W "=(W " ₁, W " ₂... W " _j, W " _n).

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