JP7509417B2 - Harmonic measuring device and islanding detection method using the device - Google Patents

Description

The present invention relates to a harmonic measuring device capable of sequentially measuring the fundamental and harmonic components of an AC signal, and an islanding detection method using the same.

Conventionally, when sampling the waveform of an AC voltage or current whose fundamental frequency is roughly constant, such as from a commercial power source, to measure the harmonic components, the Discrete Fourier Transform (hereinafter referred to as "DFT") and the Fast Fourier Transform (hereinafter referred to as "FFT"), which is an algorithm that speeds up the DFT processing, have been used.

By using sampling data for one cycle of the waveform to be measured and performing calculations on each sampling data to obtain the frequency spectrum of the waveform, it is possible to calculate the DC component, fundamental wave component, and harmonic components. Calculating harmonic components using FFT essentially requires sampling data for one cycle of the fundamental wave. In contrast, technology such as that described in Patent Document 1 is known as a method of calculating harmonics sequentially for each sampling cycle without waiting for the accumulation of sampling data for one cycle of the fundamental wave.

Harmonic analysis is also used in grid-connected systems that use power conditioners (hereinafter referred to as "PCS"). A PCS has an inverter unit that converts DC power generated by distributed DC power sources such as solar cells into AC power, and is a device that adapts the frequency and voltage to the power system in order to connect the DC power source to the power system and use it. In order to use such a device connected to the power system, it is necessary to prevent the PCS from continuing to supply power during a power outage in the power system, which would hinder maintenance work on the power system. There are standards for this islanding detection method and islanding detection device, such as Non-Patent Documents 1 and 2. The "frequency feedback method with step injection" listed in these standards requires condition judgment based on the amplitude of the frequency components of harmonics up to the seventh harmonic, with the commercial power frequency as the fundamental frequency. These standards state that discrete Fourier analysis may be used to calculate the amplitude of these harmonic voltages.

Also, prior art for an islanding detection method related to harmonic measurement is, for example, Patent Document 2.

JP 1999-094887 A JP 2019-193318 A

Japan Electrical Manufacturers' Association Japan Electrical Manufacturers' Association Standard JEM1498 Standard active islanding detection method for single-phase power conditioners for distributed power sources (frequency feedback method with step injection) Japan Electrical Manufacturers' Association Japan Electrical Manufacturers' Association Standard JEM1505 Standard active islanding detection method (frequency feedback method with step injection) for three-phase power conditioners for photovoltaic power generation connected to low-voltage distribution lines

In order to analyze harmonics in real time using conventional FFT, after sampling of one period of data is completed, it is necessary to perform FFT calculations for the first period in the time until the first sampling of the next period. In order to analyze harmonics of multiple orders, trigonometric functions corresponding to each order are required, and the calculation time is longer than that of calculations such as arithmetic operations. Furthermore, in order to obtain the effect of improving the efficiency of the number of calculations with FFT, the number of data points is limited, and design restrictions are imposed, such as setting the number of data points to a power of 2, such as 1024 points (= 2 ^{× 10} points).

The present invention aims to provide a harmonic measuring device that can calculate amplitude information related to harmonics more inexpensively and quickly, and an islanding detection method that uses the calculation method.

In order to achieve the above object, the harmonic measuring device of the present invention has a signal input section, a sampling section, and a harmonic calculation section, the signal input section generates an output signal from an input signal to be measured, the sampling section receives the output signal from the signal input section and outputs sampling data for each sampling period, the harmonic calculation section receives the sampling data from the sampling section and calculates amplitude information relating to zeroth-order or higher k-th order harmonics by discrete Fourier analysis, and the harmonic calculation section calculates amplitude information relating to zeroth-order or higher k-th order harmonics by discrete Fourier analysis. The present invention is characterized in that it is equipped with an M-ary counter that counts the value of n from 0 to M-1 by 1 for each sampling period when the sampling unit outputs the sampling data for M points in one period of the output signal, and a trigonometric function output unit that outputs a trigonometric function value independent of the order k of the harmonic using the value of n counted by the M-ary counter, and is configured to sequentially calculate the cosine coefficient and sine coefficient of the k-th harmonic, which enables calculation of amplitude information related to the k-th harmonic, using the trigonometric function value output from the trigonometric function output unit each time the M-ary counter counts the value of n .

In the above configuration, the harmonic calculation unit includes a k-th harmonic calculation unit that calculates amplitude information related to a k-th harmonic (second or higher), a (k-1)-th harmonic calculation unit that calculates amplitude information related to a (k-1)-th harmonic, and a (k-2)-th harmonic calculation unit that calculates amplitude information related to a (k-2)-th harmonic;
It is preferable that the k-th harmonic calculation unit is configured to sequentially calculate a cosine coefficient and a sine coefficient of the k-th harmonic derived from a Chebyshev polynomial, using, in addition to the value of the trigonometric function output from the trigonometric function output unit, the cosine intermediate value of the (k-1)th harmonic calculated in the process of calculation by the (k-1)th harmonic calculation unit, and the cosine intermediate value and sine intermediate value of the (k-2)th harmonic calculated in the process of calculation by the (k-2)th harmonic calculation unit, each time the M-ary counter counts the value of n.

Furthermore, the values of the trigonometric functions output from the trigonometric function output unit are the values of the following cosine function F _c [n] and sine function F _s [n],

When the cosine intermediate value of the (k-1)th harmonic calculated by the (k-1)th harmonic calculation unit is V _A [k-1, n], and the cosine intermediate value and sine intermediate value of the (k-2)th harmonic calculated by the (k-2)th harmonic calculation unit are V _A [k-2, n] and V _B [k-2, n], respectively, the kth harmonic calculation unit calculates based on the following equation:

(However, when the value of n is 0, the initial values are A[k,-1] = 0 and B[k,-1] = 0. Furthermore, when the sampling data is _vd [n], V _A [0,n] = _vd [n], V _B [0,n] = 0, V _A [1,n] = _vd [n] · _Fc [n], and V _B [1,n] = _vd [n] · _Fs [n].) It is preferable to configure the cosine intermediate values V _A [k,n] and V _B [k,n] of the kth harmonic, and the cosine coefficient A[k,n] and sine coefficient B[k,n] of the kth harmonic to be calculated sequentially.

Furthermore, the k-th harmonic calculation unit includes first and second multipliers, a subtractor, first to third adders, and first and second registers each consisting of a one-stage shift register for the value of n;
The first multiplier multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic by twice the cosine function F _c [n] from the trigonometric function output unit, and the subtractor subtracts the cosine intermediate value V A [k-2,n] of the (k-2)th harmonic from the value 2F _c [n]·V _A [k-1,n] that is the calculation result of the first multiplier. The first adder adds the cosine intermediate value _{V A [} k,n] of the kth harmonic that is the calculation result of the subtractor and the cosine coefficient A[k,n-1] of the kth harmonic at the previous sampling time that is output from the first register, and the cosine coefficient A[k,n] of the kth harmonic that is the calculation result of the first adder is input to the first register, and the cosine intermediate value V _A The second multiplier multiplies F _s [n] by a value obtained by multiplying the sine function F s [n] from the trigonometric function output unit by two, and the second adder adds a sine intermediate value V _B [k-2,n] of the (k-2)th harmonic to the value 2F _s [n]·V _A [k-1,n] which is the calculation result of the second multiplier, and the third adder adds the sine intermediate value V _B [k,n] of the kth harmonic which is the calculation result of the second adder and the sine coefficient B[k,n-1] of the kth harmonic at the previous sampling time which is output from the second register, and the sine coefficient B[k,n] of the kth harmonic which is the calculation result of the third adder is input to the second register, thereby obtaining the cosine intermediate value V _A [k,n] and the sine intermediate value V _B It is preferable that the cosine coefficient A[k,n] and the sine coefficient B[k,n] of the kth harmonic are output.

Alternatively, in the above configuration, the harmonic calculation unit includes a k-th harmonic calculation unit that calculates amplitude information related to a k-th harmonic, which is 1st or higher, and a (k-1)-th harmonic calculation unit that calculates amplitude information related to a (k-1)-th harmonic,
The k-th harmonic calculation unit may be configured to sequentially calculate a cosine coefficient and a sine coefficient of the k- th harmonic derived from the addition theorem of trigonometric functions using, in addition to the value of the trigonometric function output from the trigonometric function output unit, a cosine intermediate value and a sine intermediate value of the (k-1)th harmonic calculated during the calculation process by the (k-1)th harmonic calculation unit, each time the M-ary counter counts the value of n.

In this case, the values of the trigonometric functions output from the trigonometric function output unit are the values of the following cosine function F _c [n] and sine function F _s [n],

When the cosine intermediate value and the sine intermediate value of the (k-1)th harmonic calculated by the (k-1)th harmonic calculation unit are V _A [k-1,n] and V _B [k-1,n], respectively, the kth harmonic calculation unit calculates based on the following equation:

(However, when the value of n is 0, the initial values are A[k,-1] = 0 and B[k,-1] = 0. Furthermore, when the sampling data is _vd [n], V _A [1,n] = _vd [n] · _Fc [n] and V _B [1,n] = _vd [n] · _Fs [n].) It is preferable to configure the cosine intermediate value V _A [k,n] and sine intermediate value V _B [k,n] of the kth harmonic, and the cosine coefficient A[k,n] and sine coefficient B[k,n] of the kth harmonic to be calculated sequentially.

Furthermore, the k-th harmonic calculation unit includes first to fourth multipliers, a subtractor, first to third adders, and first and second registers each consisting of a one-stage shift register for the value of n;
The cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic is multiplied by the value of the cosine function F _c [n] from the trigonometric function output unit in the first multiplier, the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic is multiplied by the value of the sine function F _S [n] from the trigonometric function output unit in the second multiplier, and the value V _B [k-1,n] ·F _S [n] which is the calculation result of the second multiplier is subtracted from the value V _A [k-1,n] ·F _c [n] which is the calculation result of the first multiplier in the subtractor 65, thereby obtaining the cosine intermediate value V _A a cosine coefficient A[k,n] of the kth harmonic at the time of the previous sampling output from the first register is added by the first adder, and the cosine coefficient A[k,n] of the kth harmonic which is the operation result of the first adder is input to the first register, a sine intermediate value V _B [k-1,n] of the (k-1)th harmonic is multiplied by the value of the cosine function F _c [n] from the trigonometric function output unit by the third multiplier, a cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic is multiplied by the value of the sine function F _S [n] from the trigonometric function output unit by the fourth multiplier, and the value V _B [k-1,n]·F _c [n] which is the operation result of _the third multiplier is input to the first _register . It is preferable to configure the digital multiplier to add the k-th harmonic sine intermediate value V _B [k,n] of the k-th harmonic at the previous sampling time which is output from the second register, and then add the k-th harmonic sine intermediate value V B [k,n] of the k-th harmonic at the previous sampling time which is output from the second register, in the third adder, and input the k-th harmonic sine coefficient B[k,n] of the k-th harmonic at the previous sampling time which is output from the second register, thereby outputting the cosine intermediate value V _A [k,n] and sine intermediate value V _B [k,n] of the k-th harmonic, and the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic, respectively.

In the above configuration, it is preferable that the harmonic calculation unit further includes a real-time harmonic analysis unit that can calculate amplitude information related to the kth harmonic for each sampling period M points after the start of calculation.

In the above configuration, the harmonic calculation unit sequentially calculates the cosine coefficient A[k,n] and sine coefficient B[k,n] of the kth harmonic based on the following formula:

It is preferable that the k-th harmonic calculation unit further includes a real-time harmonic analysis unit that can calculate amplitude information related to the k-th harmonic for each sampling period M points after the start of calculation.

In this case, the real-time harmonic analysis unit includes first and second adder-subtractors, first and second registers each consisting of a one-stage shift register for the value of n, and third and fourth registers each consisting of M-stage shift registers for the value of n,
The cosine intermediate value V _A [k,n] of the k-th harmonic is input to the third register, and the first adder/subtractor subtracts the cosine intermediate value V _A [k,n-M] of the k-th harmonic M times earlier output from the third register from a value obtained by adding the cosine intermediate value V A [k,n] of the k-th harmonic cosine coefficient A[k,n-1] of the k-th harmonic at the previous sampling time output from the first register to the cosine intermediate value V _A [k,n] of the k-th harmonic, and inputs the cosine coefficient A[k,n] of the k-th harmonic which is the calculation result of the first adder/subtractor to the first register, and the sine intermediate value V B [k,n] of the k-th harmonic is input to the fourth register, and the second adder/subtractor subtracts the cosine intermediate value V B [k, _n ] of the k-th harmonic M times earlier output from the third register from the sum of the cosine intermediate value V _A [k,n] of the k-th harmonic and the cosine coefficient A[k,n] of the k-th harmonic It is preferable to have a configuration in which the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic M times earlier output from the fourth register are subtracted from the value obtained by adding the sine coefficient B[k,n-1] of the k-th harmonic at the previous sampling time output from the second register to A[k,n], and the sine intermediate value V _B [k,n-M] of the k-th harmonic M times earlier output from the fourth register is input to the second register as the result of the calculation by the second adder-subtractor.

In the above configuration, an isolated operation detection method is provided in a power conditioner unit having a power conversion unit arranged between a DC power source and a power grid, and detects whether the DC power source is disconnected from the power grid and is operating alone,
It is preferable that the islanding detection method is composed of a harmonic measuring device having any of the above-mentioned characteristics, and includes a harmonic measuring unit that measures the harmonic voltage on the output side of the power conversion unit, and a step injection processing unit that starts a step injection of reactive power when a fluctuation occurs in the harmonic voltage measured by the harmonic measuring unit, and detects whether or not the islanding operation is occurring .

The harmonic measuring device and islanding detection method using the harmonic measuring device of the present invention have a simple configuration with a signal input section, a sampling section, and a harmonic calculation section, and the sampling section can obtain the sampling data required for the calculation of the harmonic calculation section, and the harmonic calculation section can calculate amplitude information related to the kth harmonic including a DC component and a fundamental wave component. In addition, by sequentially calculating the cosine coefficient and sine coefficient of the kth harmonic using the trigonometric function value independent of the harmonic order k from the trigonometric function output section each time the M-ary counter counts the value of n, it is possible to calculate amplitude information related to the kth harmonic more cheaply and quickly without using a trigonometric function whose phase is k times higher, regardless of the order k.

1 is a diagram illustrating an example of an overall configuration of a harmonic measuring device according to a first embodiment; FIG. 13 is a diagram showing an example of a calculation process of a DC component and a fundamental wave in a harmonic calculation unit. FIG. 13 is a diagram showing an example of a calculation process of second or higher harmonics in the harmonic calculation unit. FIG. 13 is a diagram illustrating an example of a calculation process of second or higher harmonics in the harmonic calculation unit according to the second embodiment. FIG. 13 illustrates an example of a harmonic calculation unit according to a third embodiment; FIG. 1 is a diagram showing a simplified configuration example of a power conditioner system described in JEM1498 and JEM1505.

The following describes the embodiments of the present invention. However, the present invention is not limited to the following description, and various modifications and changes are possible for those skilled in the art based on the gist of the invention described in the claims or disclosed in the description for carrying out the invention. Such modifications and changes are naturally included in the scope of the present invention.

[First embodiment]
1, 2A, and 2B are diagrams showing an example of a harmonic measuring device according to a first embodiment.
FIG. 1 is a diagram showing an example of the overall configuration of a harmonic measuring device according to a first embodiment.
FIG. 2A is a diagram showing an example of the calculation process of the DC component and the fundamental wave in the harmonic calculation section.
FIG. 2B is a diagram showing an example of calculation processing of second and higher harmonics in the harmonic calculation section.

Figure 1 shows an example of the overall configuration of a harmonic measurement device according to a first embodiment. The harmonic measurement device 10 includes a signal input unit 11, a sampling unit 12 that samples and digitizes a signal input from the signal input unit 11, and a harmonic calculation unit 13 that performs harmonic calculations based on the digitized data.

The signal input unit 11 is a section that receives an input signal v, converts it to an amplitude suitable for input to the subsequent sampling unit 12, filters signal components at or above the Nyquist frequency, and outputs the result as an output signal v _a . The input signal v and the output signal v _a are, for example, voltage signals, but may be other physical quantities such as current, or the input and output may be different physical quantities, such as the input signal being a current and the output signal being a voltage.

The sampling unit 12 receives the output v _a from the signal input unit 11, samples it at a predetermined sampling period T _s , such as 20 μs, and outputs the sampled data v _d [n] for each sampling period T _s . This function can be realized, for example, by a commercially available A/D converter or a microprocessor having a built-in A/D converter function.

The harmonic calculation unit 13 is a part that calculates amplitude information related to the DC component, the fundamental wave _component , and the harmonic component from M points of sampling data _vd [n] obtained for each sampling period Ts, where M is an integer equal to or greater than 2, with the frequency having a fundamental period T _a =M· _Ts being the fundamental wave component. Note that, hereinafter, the DC component will be broadly defined as the zeroth harmonic and the fundamental wave as the first harmonic, and the term "harmonic" will be used to broadly include not only second or higher harmonics but also the DC component and the fundamental wave.

Hereinafter, the reciprocal of the sampling period _Ts is the sampling frequency _fs (=1/ _Ts ), and the reciprocal of the fundamental period _T is the fundamental frequency f _a (=1/T _a ). For example, when the sampling period _Ts mentioned above is 20 μs, the sampling frequency _fs is 50 kHz. Furthermore, when M is 1000 for this sampling period _Ts , the fundamental period T _a is 20 ms, and the fundamental frequency f _a is 50 Hz. Such a setting is convenient, for example, when analyzing the fundamental wave and harmonics of commercial power sources in eastern Japan. However, the periods and frequencies are not limited to these.

Here, in discrete Fourier analysis, for M points v _d [n] (n = 0, 1, ..., M-1), where h is an integer between 1 and (M-1)/2, the amplitude information regarding the h-th harmonic, the cosine component A[h] and sine component B[h] of the h-th harmonic, and the amplitude H _arm [h] of the h-th harmonic, can be expressed by the following equations.

Furthermore, if the DC component is A[0], A[0] can be expressed as follows: Note that this formula is the average value of v _d [n] for M points, and for convenience, it is treated as equivalent to the zeroth harmonic of the cosine component.

Similarly, B[0], which corresponds to the zeroth harmonic of the sine component, is set to 0.
The harmonic measuring device 10 according to the first embodiment is characterized in that the results obtained by these calculations can be calculated efficiently under certain conditions, and this will be explained below.

2A shows an example of the flow of calculation processing of the DC component and the fundamental wave in the harmonic calculation unit 13. In the following formula, n is an integer from 0 to M-1, and the sampling data at time n· _Ts is represented as v _d [n]. In addition, hereafter, the order h of the harmonic is represented as k (≧0). Then, processing is performed as follows from the sampling data v _d [n] obtained at each time _Ts .

Figure 2 (A) shows the series of processes related to the DC component and the fundamental wave in the form of a block diagram. To realize this series of calculation processes, the harmonic calculation unit 13 includes an M-ary counter 21, a trigonometric function output unit 22, and a low-order component calculation unit 23.

The M-ary counter 21 is a part that increases the value of n by 1 to M-1 every sampling period _Ts and returns to 0. It may be understood as a configuration that outputs the remainder when a variable that increases by 1 is divided by M.
The trigonometric function output section 22 outputs the values of the cosine function F _c [n] and the sine function F _s [n] according to the value of n.
These are functions expressed as follows, respectively.

Then, every time the input signal v is sampled at intervals of a sampling period T _s , sampling data v _d [n] is input to the low-order component calculation unit 23 .

Each time the low-order component calculation unit 23 receives the value of n counted by the M-ary counter 21, it performs calculation processing using the sampling data v _d [n] from the sampling unit 12 and the values of the cosine function F _c [n] and sine function F _s [n] output from the trigonometric function output unit 22, to calculate, in discrete Fourier analysis, a cosine coefficient A[0,M-1] that is M times the DC cosine component A[0], a cosine coefficient A[1,M-1] that is M/2 times the fundamental wave cosine component A[1], and a sine coefficient B[1,M-1] that is M/2 times the fundamental wave sine component B[1]. In addition, in the course of the calculation process, the low-order component calculation unit 23 outputs a cosine intermediate value V _A [0, n] for calculating the DC cosine coefficient A [0, M-1], a cosine intermediate value V _A [1, n] for calculating the fundamental wave cosine coefficient A [1, M-1], and a sine intermediate value V _B [1, n] for calculating the fundamental wave sine coefficient B [1, M-1], and can also output a sine intermediate value V _B [0, n] (= 0) that is equal to the DC sine component B [0].

First, this sampling data v _d [n] is held as an intermediate value for performing necessary calculations later, the cosine intermediate value V _A [k,n] for k=0, that is, V _A [0,n].
Then, the cosine coefficient A[k,n] for k=0, that is, A[0,n], is stored by performing the following calculation using A[0,n-1], which is the cosine coefficient at the time of the previous sampling:

In this way, the low-order component calculation unit 23 includes a DC component calculation unit 31 that calculates a DC cosine coefficient A[0,n] from the sampling data v _d [n]. The DC component calculation unit 31 includes an adder 32 and a register 33, and adds a DC cosine intermediate value V _A [0,n], which is the sampling data v _d [n] from the sampling unit 12, to a DC cosine coefficient A[0,n-1] at the previous sampling time output from the register 33 by the adder 32, and inputs the DC cosine coefficient A[0,n], which is the calculation result of the adder 32, to the register 33, thereby outputting the DC cosine intermediate value V _A [0,n] and the DC cosine coefficient A[0,n] to the high-order component calculation unit 24 described later.

In the figure, the portion of register 33 marked SR(1) represents a one-stage shift register for n. Similarly, an M-stage shift register would be represented as SR(M). The other registers 46, 47, 57, 58, 73, and 74, described below, will also be represented as shift registers in the same way.

As is clear from this calculation process, A[0,n] is the value obtained by accumulating the sampling data v _d [n]. Since n is the output value of the M-ary counter 21 that outputs 0 to M-1, by defining A[0,-1]=0 as the initial value when the value of n is 0, it can be seen that the value of A[0,n] when n=M-1, i.e., A[0,M-1], is the sum of M points of sampling data v _d [n] where n is from 0 to M-1.
That is, it looks like this:

This value is M times the DC component A[0], where M is a known value determined by the settings, so it can be said that the DC component A[0] has been obtained by the DC component calculation unit 31. For the convenience of calculations in later stages and to avoid extending the processing time due to unnecessary calculations, we will continue the explanation as if it were treated as is, but if necessary, A[0,M-1] can be divided by M at that time.

Next, for convenience of subsequent calculations, the sine intermediate value _VB [k,n] for k=0, i.e., _VB [0,n], is defined as always 0 as follows: The DC component calculation unit 31 further includes an intermediate value output unit 34 that always sets the DC sine intermediate value _VB [0,n] to 0 regardless of the value of n and outputs it to the subsequent high-order component calculation unit 24.

Next, the calculation corresponding to k=1, that is, the part that calculates the fundamental wave component, will be described.
The following calculations are performed with the cosine intermediate value V _A [1,n] and the sine intermediate value V _B [1,n] for k=1.

Then, the cosine intermediate value V _A [1, n] and the sine intermediate value V _B [1, n] are respectively integrated as follows.

In this way, the low-order component calculation unit 23 includes a fundamental wave component _calculation unit 41 that calculates the cosine coefficient A[1, n] of the fundamental wave and the sine coefficient B[1, n] of the fundamental wave from the sampling data v d [n] and the values of the cosine function _{F c} [n] and the sine function F s [n]. The fundamental wave component calculation unit 41 includes multipliers 42 and 43, adders 44 and 45, and registers 46 and 47. The multiplier 42 multiplies the sampling data v _d [n] from the sampling unit 12 by the cosine function F _c [n] from the trigonometric function output unit 22, and the adder 44 adds the cosine intermediate value V _A [1, n] of the fundamental wave which is the calculation result of the multiplier 42 and the cosine coefficient A [1, n-1] of the fundamental wave at the previous sampling time which is output from the register 46, and inputs the cosine coefficient A [1, n] of the fundamental wave which is the calculation result of the adder 44 to the register 46. Meanwhile, the multiplier 43 multiplies the sampling data v _d [n] from the sampling unit 12 by the sine function F _s [n] from the trigonometric function output unit 22, and the multiplier 43 multiplies the sine intermediate value V _B [1,n] and the sine coefficient B[1,n-1] of the fundamental wave at the previous sampling time output from register 47 are added by adder 45, and the cosine coefficient B[1,n] of the fundamental wave which is the calculation result of adder 45 is input to register 47, thereby outputting the cosine intermediate value V _A [1,n] of the fundamental wave, the sine intermediate value V _B [1,n] of the fundamental wave, the cosine coefficient A[1,n] of the fundamental wave, and the sine coefficient B[1,n] of the fundamental wave to the higher-order component calculation unit 24 described later.

As is clear from these calculation processes, A[1,n] is the value obtained by accumulating the cosine intermediate value V _A [1,n] for k=1, and B[1,n] is the value obtained by accumulating the sine intermediate value V _B [1,n] for k=1. Since n is the output value of the M-ary counter 21, which outputs values from 0 to M-1, by defining A[1,-1]=0 and B[1,-1]=0 as the initial values when the value of n is 0, it can be seen that the cosine coefficient A[1,M-1] and sine coefficient B[1,M-1] for k=1 and n=M-1 are as follows:

These are the values obtained by multiplying the discrete Fourier transform of the fundamental wave by M/2. As with the DC component, these values are M/2 times the fundamental wave component, where M is a known value determined by settings, so it can be said that the fundamental wave component calculation unit 41 has obtained the fundamental wave cosine component A[1] and the fundamental wave sine component B[1]. For the convenience of calculations in later stages and to avoid extending the processing time due to unnecessary calculations, we will continue with the explanation as if they were used as is, but if necessary, they can be divided by M/2 at that time.

The same applies when obtaining the calculation results of second and higher harmonic components below.
Fig. 2(B) shows an example of the flow of calculation processing in the harmonic calculation unit 13, which shows a flow of sequentially calculating a k-th harmonic component using (k-2)th and (k-1)th harmonic calculations for k equal to or greater than 2, assuming that there are calculation results obtained by processing the DC component and fundamental wave in Fig. 2(A).To realize this series of calculation processing, the harmonic calculation unit 13 further includes a high-order component calculation unit 24 shown in Fig. 2(B) in addition to the above-mentioned M-ary counter 21, trigonometric function output unit 22, and low-order component calculation unit 23.

The high-order component calculation unit 24, assuming that the order k is 2 or more, performs calculation processing each time it receives the value of n counted by the M-ary counter 21 using the cosine intermediate value V _A [k-2,n] of the (k-2)th harmonic, the sine intermediate value V _B [k-2,n] of the (k-2)th harmonic, and the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic output from the low-order component calculation unit 23 and the high-order component calculation unit 24, and the values of the cosine function F _c [n] and sine function F _s [n] output from the trigonometric function output unit 22, to calculate a cosine coefficient A[k,M-1] that is M/2 times the cosine component A[k] of the kth harmonic and a sine coefficient B[k,M-1] that is M/2 times the sine component B[k] of the kth harmonic in discrete Fourier analysis.

Here, the following calculation is performed using the cosine intermediate value V _A [k-2,n] and sine intermediate value V _B [k-2,n] for the (k-2)th order, the cosine intermediate value V _A [k-1,n] for the (k-1)th order, and the already calculated cosine function F _c [n] and sine function F _s [n].

However, when the value of n is 0, the initial values are defined as A[k,-1]=0 and B[k,-1]=0.

To realize such calculation processing, high-order component calculation unit 24 includes multipliers 51 and 52 , a subtractor 53 , adders 54 , 55 and 56 , and registers 57 and 58 . Then, high-order component calculation unit 24 multiplies, in multiplier 51, the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic output from low-order component calculation unit 23 or high-order component calculation unit 24 by twice the value (=2F _c [n]) of the cosine function F _c [n] from trigonometric function output unit 22, and subtracts, in subtractor 53, the cosine intermediate value V A [k-2,n] of the (k-2)th harmonic output from low-order component calculation unit 23 or high-order component calculation unit 24 from the value 2F _c [n]·V _A [k-1,n] that is the calculation result of multiplier 51, to obtain the cosine intermediate value V _A [k-2,n] of the kth harmonic that is the calculation result of subtractor _53. An adder 55 adds together A[k,n] and the cosine coefficient A[k,n-1] of the k-th harmonic at the time of the previous sampling output from a register 57, and the cosine coefficient A[k,n] of the k-th harmonic which is the calculation result of the adder 55 is input to a register 57. Meanwhile, a multiplier 52 multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic which is output from the low-order component calculation unit 23 or the high-order component calculation unit 24 by a value obtained by multiplying the sine function F _s [n] from the trigonometric function output unit 22 by two (=2F _s [n]), and inputs the value 2F _s [n]·V _A [k-1,n] which is the calculation result of the multiplier 52 to the sine intermediate value V _B The kth harmonic wave component is calculated by adding the kth harmonic intermediate value V _B [k,n] and the sine coefficient B[k,n-1] of the kth harmonic at the previous sampling time output from register 58 to adder 56, and the sine coefficient B[k,n] of the kth harmonic at the previous sampling time output from register 58 is input to register 58, thereby outputting the cosine coefficient A[k,n] and sine coefficient B[k,n] which are the calculation results of the kth harmonic component, and further outputting the cosine intermediate value V A [k,n] and sine intermediate value V _B [k,n] of the kth harmonic to another high-order component calculation unit 24 which calculates the (k+1)th harmonic component and the (k+2 ₎ th harmonic component.

Here, the calculation of the cosine intermediate value V _A [k,n] and the sine intermediate value V _B [k,n] will be explained.
Regarding trigonometric functions, it is easy to verify that the following equation holds as an identity by, for example, expanding the first term on the right-hand side and calculating specific exponential functions.

ここで、ｅは自然対数の底であり、ｊは虚数単位である。

Here, e is the base of the natural logarithm and j is the imaginary unit.

左辺および右辺それぞれの実部同士および虚部同士それぞれが等しいことから、

Since the real parts and imaginary parts of the left and right sides are equal,

となる。この式は、ｋ倍角の余弦関数と正弦関数を表わすチェビシェフの多項式として知られている。

This formula is known as the Chebyshev polynomial, which represents the k-fold cosine and sine functions.

Using these results, the cosine intermediate value V _A [k,n] and the sine intermediate value V _B [k,n] can be transformed as follows:

From these, it can be seen that A[k,n] and the sine intermediate value V _B [k,n] are equal to the following values, respectively.

By performing this calculation process using the high-order component calculation unit 24, it is possible to obtain the cosine component of the kth harmonic as A[k, M-1] and the sine component of the kth harmonic as B[k, M-1] by multiplying them by M/2 using only the results of the harmonic calculations up to the (k-1)th order, without using a trigonometric function with a phase that is k times higher.

Furthermore, since A[k, M-1] and B[k, M-1] are M/2 times the amplitude of the cosine component and sine component of the kth harmonic, respectively, it is possible to obtain M/2 times the amplitude of the kth harmonic by taking the mean square.
Furthermore, if necessary, the phase component of the kth harmonic can also be obtained.

In this way, it can be seen that a configuration can be obtained that can obtain information on the cosine amplitude and sine amplitude of the kth harmonic for each fundamental period T _a (M sampling points) for the input signal v input to the signal input section 11 of the harmonic measuring device 10.

[Second embodiment]
FIG. 3 is a diagram showing an example of the configuration of a harmonic measuring device 10 according to the second embodiment.
In the first embodiment, the amplitude of the harmonics of consecutive orders from k=1 is calculated as a sequential calculation based on the results of two lower orders, for example, the results obtained by k=1 and k=0 in the case of k=2. In the second embodiment, the amplitude is calculated as a sequential calculation based on the results of only the next lower order. Therefore, in the harmonic measuring device 10 shown in FIG. 1, only the configuration of the harmonic calculation unit 13 is different from that of the first embodiment. Note that the configuration for k=0 is the same as that of the first embodiment, and the configuration for the calculation processing of the DC component shown in FIG. 2A can be applied as it is to the second embodiment. In addition, in the low-order component calculation unit 23 shown in FIG. 2A, the fundamental wave component calculation unit 41 for the calculation processing of the fundamental wave can be omitted in the second embodiment.

The high-order component calculation unit 24 of the harmonic calculation unit 13 shown in Fig. 3 performs the following calculation for k ≥ 1. In the first embodiment, V _A [k-2,n] and V _B [k-2,n] were used in the calculation related to the k-th harmonic, but V _B [k-1,n] was not used in the calculation. In contrast, in the second embodiment, V _A [k-2,n] and V _B [k-2,n], which are information related to the (k-2)th harmonic, which is the harmonic component two orders lower, are not used in the calculation related to the k-th harmonic, but instead V _B [k-1,n] is used in the calculation to obtain similar results.

In other words, here, assuming that the order k is 1 or more, each time high-order component calculation unit 24 receives the value of n counted by M-ary counter 21, it performs arithmetic processing using the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic and the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic output from low-order component calculation unit 23 and high-order component calculation unit 24, and the values of the cosine function F _c [n] and sine function F _s [n] output from trigonometric function output unit 22, to calculate a cosine coefficient A[k,M-1] that is M/2 times the cosine component A[k] of the kth harmonic and a sine coefficient B[k,M-1] that is M/2 times the sine component B[k] of the kth harmonic in discrete Fourier analysis.

To realize such calculation processing, high-order component calculation section 24 includes multipliers 61 , 62 , 63 , and 64 , a subtractor 65 , adders 55 , 56 , and 66 , and registers 57 and 58 . Then, high-order component calculation unit 24 multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic output from low-order component calculation unit 23 or high-order component calculation unit 24 by the value of the cosine function F _c [n] from trigonometric function output unit 22 in multiplier 61, multiplies the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic output from low-order component calculation unit 23 or high-order component calculation unit 24 by the value of the sine function F _S [n] from trigonometric function output unit 22 in multiplier 64, and subtracts the value V _B [k-1,n] ·F _S [n] which is the calculation result of multiplier 61 from the value V _A [k-1,n] ·F _c [n] which is the calculation result of multiplier 61 in subtractor 65, thereby obtaining the cosine intermediate value V _A [k,n] and the cosine coefficient A[k,n-1] of the k-th harmonic at the time of the previous sampling output from register 57 are added by adder 55, and the cosine coefficient A[k,n] of the k-th harmonic which is the calculation result of adder 55 is input to register 57. Meanwhile, the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic which is output from low-order component calculation unit 23 or high-order component calculation unit 24 is multiplied by the value of the cosine function F _c [n] from trigonometric function output unit 22 by multiplier 63, and the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic which is output from low-order component calculation unit 23 or high-order component calculation unit 24 is multiplied by the value of the sine function F _S [n] from trigonometric function output unit 22 by multiplier 62, and the value V _B [k-1,n]·F _c The adder 66 adds the value V _A [k-1,n]·F _S [n] which is the calculation result of the multiplier 62 to F S [n], and the adder 56 adds the sine intermediate value V _B [k,n] of the kth harmonic which is the calculation result of the adder 66 and the sine coefficient B[k,n-1] of the kth harmonic at the previous sampling time which is output from the register 58, and the sine coefficient B[k,n] of the kth harmonic which is the calculation result of the adder 56 is input to the register 58, thereby outputting the cosine coefficient A[k,n] and sine coefficient B[k,n] which are the calculation results of the kth harmonic component, and further outputs the cosine intermediate value V _A [k,n] and sine intermediate value V _B [k,n] of the kth harmonic to another high-order component calculation unit 24 which calculates the (k+1)th harmonic component.

The sequential calculations in the above formula are based on the fact that the real and imaginary parts of the left and right sides of the following formula, which relates to trigonometric functions, are equal. That this equality holds can be easily shown by adding the exponents on the right side based on the law of exponents. From another perspective, this can also be said to be the result of calculations based on the addition theorem of trigonometric functions, with the two argument angles being (k-1)θ and θ. Note that here too, the initial values when the value of n is 0 are defined as A[k,-1]=0 and B[k,-1]=0.

これらの結果を用いると、余弦中間値Ｖ_Ａ［ｋ，ｎ］および正弦中間値Ｖ_Ｂ［ｋ，ｎ］はそれぞれ、以下の様に変形できる。

Using these results, the cosine intermediate value V _A [k,n] and the sine intermediate value V _B [k,n] can be transformed as follows:

これらのことから、Ａ［ｋ，ｎ］および正弦中間値Ｖ_Ｂ［ｋ，ｎ］が、第１の実施の形態と同様、それぞれ以下と同値であることがわかる。

From these, it can be seen that A[k,n] and the sine intermediate value V _B [k,n] are the same as in the first embodiment, respectively, as follows:

By performing this calculation process using the high-order component calculation unit 24, it is possible to obtain the cosine component of the kth harmonic as A[k, M-1] and the sine component of the kth harmonic as B[k, M-1] by multiplying them by M/2 using only the results of the harmonic calculations up to the (k-1)th order, without using a trigonometric function with a phase that is k times higher.

Furthermore, since A[k, M-1] and B[k, M-1] are M/2 times the amplitude of the cosine component and sine component of the kth harmonic, respectively, it is possible to obtain M/2 times the amplitude of the kth harmonic by taking the mean square.
Furthermore, if necessary, the phase component of the kth harmonic can also be obtained.

In this way, it can be seen that a configuration can be obtained that can obtain information on the cosine amplitude and sine amplitude of the kth harmonic for each fundamental period T _a (M sampling points) for the input signal v input to the signal input section 11 of the harmonic measuring device 10.

[Third embodiment]
4 is a diagram showing an example of the harmonic calculation unit 13 according to the third embodiment. In the figure, a high-order component calculation unit 24 constituting the harmonic calculation unit 13 is provided with adders and subtractors 71 and 72 instead of the adders 55 and 56 shown in Fig. 2(B) and Fig. 3, and also provided with registers 73 and 74 in addition to the registers 57 and 58. In this case, the high-order component calculation unit 24 inputs the cosine intermediate value V _A [k,n] of the k-th harmonic calculated by the high-order component calculation unit 24 to a register 73 consisting of an M-stage shift register SR(M), and an adder-subtractor 71 subtracts the cosine intermediate value V _A [k,n-M] of the k-th harmonic M times earlier output from the register 73 from a value obtained by adding the cosine intermediate value V _{A [k,n] of the k-th harmonic at the previous sampling time output from the register 57 to the cosine intermediate value V A} [k,n] of the k-th harmonic, and inputs the cosine coefficient A[k,n] of the k-th harmonic calculated by the high-order component calculation unit 24 to the register _57. a k-th harmonic intermediate value VB[k,n] of the k-th harmonic M sampling periods earlier output from register 74, from which an adder/subtractor 72 subtracts the sine intermediate value _VB [k,n-M] of the k-th harmonic M sampling periods earlier output from register 74 from a value obtained by adding the sine intermediate value VB[k,n] of the k-th harmonic to the sine coefficient _B [k,n-1] of the k-th harmonic at the previous sampling time output from register 58, and inputs the sine coefficient B[k,n] of the k-th harmonic resulting from the calculation by adder/subtractor 72 to register 58, thereby outputting the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic, thereby making it possible to calculate amplitude information related to the k-th harmonic for each sampling period Ts _M sampling periods after the start of calculation.

In the first and second embodiments, the amplitude of the k-th harmonic is obtained for each period T _a , that is, for each M sampling points (n=0, 1, 2, ..., M-1). In the third embodiment, registers 73 and 74 using M-stage shift registers SR(M) are provided in the place of the adders 55 and 56 located before the output stage, and the adders 55 and 56 are replaced with adders and subtractors 71 and 72 to configure a real-time harmonic analyzer 70 so that the values of V _A and V _B M points before are subtracted. The initial values of the M-stage shift registers SR(M) are preferably set to 0 for all M stages.
In this case, A[k, n] and B[k, n] are expressed as follows:

In this way, after acquiring data for M points from the start of calculation in the harmonic calculation unit 13, the calculation results of A[k,n] and B[k,n] will be the calculation results based on the data acquired for the immediately preceding M points. Therefore, after acquiring data for M points from the start of calculation, the amplitude information (A[k], B[k], _Harm [k]) relating to the kth harmonic is obtained for each sampling period _Ts .

[Fourth embodiment]
FIG. 5 is a simplified diagram of the configuration of a power conditioner described in JEM1498 and JEM1505, which are standards of the Japan Electrical Manufacturers' Association. In the frequency feedback method with step injection defined in these standards, the voltage of the commercial power supply is monitored, and the necessity of starting step injection is judged from the fundamental wave and the second to seventh harmonic components for the commercial frequency. It is sufficient to calculate the harmonic components up to a relatively small finite order, up to the seventh order, while at the same time, since it is a detection means related to safety, a high speed response is required. Therefore, it can be said to be a good example of using harmonic analysis based on the harmonic measuring device 10 like the configuration example so far.

The operation of each part of the PCS 100 in FIG. 5 will be briefly described below.
The PCS 100 is disposed between a DC power source 200 such as a solar cell and a power system (for example, a commercial power system) 300. This PCS 100 is an example equipped with an islanding detection device of a frequency feedback method with step injection, and is configured with a hardware unit 110 and a software unit 120. The hardware unit 110 is configured with an inverter unit 111 that converts DC power supplied from the DC power source 200 into AC power, a system frequency detection unit 112, and a voltage measurement unit 113 that performs fundamental wave measurement and harmonic measurement. Here, the inverter unit 111 is a device that converts the power supplied from the DC power source 200 into AC power.

The software unit 120 is a part that performs numerical calculations and logical judgments based on numerical data and logic signals, and is composed of, for example, a CPU (Central Processing Unit), a microprocessor, an FPGA (Field Programmable Gate Array), or a PLD (Programmable Logic Device). The software unit 120 has a current control processing unit 121 that performs control to operate the inverter unit 111 appropriately, and this current control processing unit 121 is controlled based on information from a phase difference measurement synchronization processing unit 122 and an adder unit 123.

The phase difference measurement synchronization processing unit 122 operates based on a signal generated by the system frequency measurement processing unit 124, which processes a signal obtained from the system frequency detection unit 112, which is the part that detects the frequency of the power system 300 including the commercial power source.

The adder 123 is a part that adds up the signals from the reactive power injection processor 125 and the step injection processor 126. The information obtained by these additions is used by the current control processor 121 as information necessary for controlling the inverter unit 111.

The step injection processing unit 126 is a component that calculates the step injection amount, which is information necessary for controlling the inverter unit 111, based on information from the system frequency measurement processing unit 124 and the voltage calculation unit 127.

The isolated operation determination unit 128 determines whether or not isolated operation has occurred based on changes in the system frequency.

In such a PCS 100, the conditions for determining operation using the fundamental wave component and second to seventh harmonic components of the commercial power supply _VAC are defined in the aforementioned JEM standard, and the aforementioned harmonic measuring device 10 can be applied to the harmonic measuring unit 130 of the PCS 100, which is composed of a voltage measuring unit 113 and a voltage calculating unit 127.

The PCS100 is provided with an islanding detection system that detects whether the DC power supply 200 is isolated from the power grid 300 and in islanding operation, so that the DC power supply 200 equipment including the PCS100 does not continue to supply power to the system load in an islanding operation state when the power grid 300 is stopped for some reason. This system is configured to measure the harmonic voltage on the output side of the inverter unit 111 with the harmonic measurement unit 130, and when a fluctuation occurs in the harmonic voltage, the step injection processing unit 126 starts step injection of reactive power, thereby detecting islanding operation.

[summary]
As described above, the harmonic measuring device 10 according to the first to fourth embodiments can have a simple configuration having a signal input unit 11, a sampling unit 12, and a harmonic calculation unit 13, as shown in FIG. 1.

Here, the signal input unit 11 generates an output signal v _a from the input signal v to be measured, and the sampling unit 12 is configured to receive the output signal v _a from the signal input unit 11 and output sampling data v _d [n] for each sampling period _Ts , thereby enabling the sampling unit 12 to obtain the sampling data v _d [n] required for calculations by the harmonic calculation unit 13.

Furthermore, the harmonic calculation unit 13 receives the sampling data v _d [n] from the sampling unit 12, and uses discrete Fourier analysis to calculate amplitude information related to the k-th harmonic (0th or higher), such as the cosine component A[k] of the k-th harmonic, the sine component B[k] of the k-th harmonic, and the amplitude H _arm [k] of the k-th harmonic. The harmonic calculation unit 13 can calculate amplitude information related to the k-th harmonic including a DC component and a fundamental wave component.

In the harmonic measuring device 10 configured as described above, the harmonic calculation unit 13 is provided with an M-ary counter ₂₁ that counts the value of n from 0 to M-1 in increments of 1 for each sampling period Ts when the sampling unit 12 outputs M points of sampling data _vd [n] in one period of the output signal v _a , and a trigonometric function output unit 22 that uses the value of n counted by the M-ary counter 21 to output values of a cosine function _Fc [n] and a sine function _Fs [n] as trigonometric function values independent of the harmonic order k, and is configured to sequentially calculate the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic, which enable calculation of amplitude information related to the k-th harmonic, using the value of the trigonometric function output from the trigonometric function output unit 22 each time the M-ary counter 21 counts the value of n.

Therefore, each time the M-ary counter 21 counts the value of n, the harmonic calculation unit 13 sequentially calculates the cosine coefficient A[k,n] and sine coefficient B[k,n] of the kth harmonic using the trigonometric function value that is independent of the harmonic order k from the trigonometric function output unit 22, thereby making it possible to calculate amplitude information related to the kth harmonic more cheaply and quickly without using a trigonometric function whose phase is k times higher, regardless of the order k.

The harmonic calculation unit 13 of the harmonic measuring device 10 according to the first embodiment includes a k-th harmonic calculation unit that calculates amplitude information related to the k-th harmonic of the second or higher order, a (k-1)-th harmonic calculation unit that calculates amplitude information related to the (k-1)-th harmonic, and a (k-2)-th harmonic calculation unit that calculates amplitude information related to the (k-2)-th harmonic. The k-th harmonic calculation unit here is the high-order component calculation unit 24 shown in FIG. 2(B) for all orders k of the second or higher order. The (k-1)-th harmonic calculation unit is the fundamental wave component calculation unit 41 shown in FIG. 2(A) when k=2, and is the high-order component calculation unit 24 shown in FIG. 2(B) when k≧3. Furthermore, if k=2, the (k-2)th harmonic calculation unit becomes the DC component calculation unit 31 shown in FIG. 2(A), if k=3, it becomes the fundamental wave component calculation unit 41 shown in FIG. 2(A), and if k≧4, it becomes the higher-order component calculation unit 24 shown in FIG. 2(B).

In either case, each time M-ary counter 21 counts the value of n, high-order component calculation unit 24 corresponding to the k-th harmonic calculation unit is configured to sequentially calculate the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic derived from the Chebyshev polynomial, using, in addition to the trigonometric function value output from trigonometric function output unit 22, the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic calculated in the process of calculation by the (k-1)th harmonic calculation unit, and the cosine intermediate value V _A [k-2,n] and sine intermediate value V _B [k-2,n] of the (k-2)th harmonic calculated in the process of calculation by the (k-2)th harmonic calculation unit.

Therefore, high-order component calculation unit 24 is able to sequentially calculate the cosine coefficient _A [k,n] and sine coefficient B[k,n] of the k-th harmonic through calculation processing employing Chebyshev polynomials, using the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic, and the cosine intermediate value V _A [k-2,n] and sine intermediate value V B [k-2,n] of the (k-2)th harmonic.

In the harmonic measuring device 10 according to the first embodiment, the values of the trigonometric functions output from the trigonometric function output unit 22 are the values of the cosine function F _c [n] and sine function F _s [n] shown in the above equation 8, and when the cosine intermediate value of the (k-1)th harmonic calculated by the (k-1)th harmonic calculation unit is V _A [k-1,n] and the cosine intermediate value and sine intermediate value of the (k-2)th harmonic calculated by the (k-2)th harmonic calculation unit are V _A [k-2,n] and V _B [k-2,n], respectively, the high-order component calculation unit 24 serving as the kth harmonic calculation unit calculates the cosine intermediate value V _A [k,n] and the sine intermediate value V _B [k-2,n] of the kth harmonic based on the equation shown in the above equation 15. [k, n], and the cosine coefficient A[k, n] and sine coefficient B[k, n] of the kth harmonic are sequentially calculated.

Here, A[k,-1]=0 and B[k,-1]=0 as initial values when the value of n is 0. In addition, when the sampling data is v _d [n], the intermediate cosine value of the (k-2)th harmonic when k=2 is V _A [0,n]=v _d [n], the intermediate sine value of the (k-2)th harmonic is V _B [0,n]=0, the intermediate cosine value of the (k-1)th harmonic when k=2 or the intermediate cosine value of the (k-2)th harmonic when k=3 is V _A [1,n]=v _d [n]·F _c [n], and the intermediate sine value of the (k-2)th harmonic when k=3 is V _B [1,n]=v _d [n]·F _s [n].

This enables the high-order component calculation unit 24 to sequentially calculate not only the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic, but also the cosine intermediate values V _A [k,n] and V _B [k,n] of the k-th harmonic during the calculation process, each time the M-ary counter 21 counts the value n.

Furthermore, in the harmonic measuring device 10 according to the first embodiment, the high-order component calculation unit 24 serving as the k-th harmonic calculation unit includes first and second multipliers 51, 52, a subtractor 53, first to third adders 54, 55, 56, and first and second registers 57, 58 each consisting of a one-stage shift register for the value of n,
The cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic is multiplied by a value obtained by multiplying the cosine function F _c [n] output from the trigonometric function output unit 22 by two (=2F _c [n]) in a first multiplier 51, and the cosine intermediate value V _A [k-2,n] of the (k-2)th harmonic is subtracted by a subtractor 53 from the value 2F _c [n]·V _A [k-1,n] that is the calculation result of the first multiplier 51 to obtain the cosine intermediate value V _A A first adder 55 adds A[k,n] and the cosine coefficient A[k,n-1] of the k-th harmonic at the previous sampling time output from a first register 57, and the cosine coefficient A[k,n] of the k-th harmonic which is the calculation result of the first adder 55 is input to the first register 57. A second multiplier 52 multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic by twice the sine function F _s [n] from the trigonometric function output unit 22 (=2F _s [n]), and the value 2F _s [n]·V _A [k-1,n] which is the calculation result of the second multiplier 52 is input to the first register _57. The kth harmonic intermediate value V A [k,n] and the sine intermediate value V _B [k,n] of the kth harmonic at the previous sampling time output from the second register 58 are added in a third adder 56, and the sine coefficient B[k,n] of the kth harmonic at the previous sampling time output from the second register 58 is input to the second register 58, thereby outputting the cosine intermediate value V _A [k,n] and sine intermediate value V _B [k,n] of the kth harmonic, and the cosine coefficient A[k,n] and sine coefficient B[k,n] of the kth harmonic.

Therefore, high-order component calculation unit 24 is capable of sequentially calculating the cosine intermediate value V _{A [k,n] and sine intermediate value V B} [k,n] of the k-th harmonic, and the cosine coefficient A[k,n] and sine coefficient _B [k,n] of the k-th harmonic, using only six calculation units, namely multipliers 51 and 52, subtractor 53, and adders 54, 55, and 56, and two registers 57 and 58.

Instead, the harmonic calculation unit 13 of the harmonic measuring device 10 according to the second embodiment includes a k-th harmonic calculation unit that calculates amplitude information related to the k-th harmonic, which is 1st or higher, and a (k-1)-th harmonic calculation unit that calculates amplitude information related to the (k-1)-th harmonic. The k-th harmonic calculation unit here is the high-order component calculation unit 24 shown in FIG. 3 for all orders k of 1st or higher. In addition, the (k-1)-th harmonic calculation unit is the DC component calculation unit 31 shown in FIG. 2(A) when k=1, and is the high-order component calculation unit 24 shown in FIG. 3 when k≧2.

In either case, the high-order component calculation unit 24 corresponding to the k-th harmonic calculation unit is configured to sequentially calculate the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic derived from the addition theorem of trigonometric functions, using the cosine intermediate value V _A [k-1,n] and sine intermediate value V _B [k-1,n] of the (k-1)th harmonic calculated in the course of the calculation process by the (k-1)th harmonic calculation unit, in addition to the trigonometric function value output from the trigonometric function output unit 22, each time the M-ary counter 21 counts the value of n.

Therefore, the high-order component calculation unit 24 is able to sequentially calculate the cosine coefficient _A [k,n] and sine coefficient B[k,n] of the k-th harmonic using the cosine intermediate value V _A [k-1,n] and sine intermediate value V B [k-1,n] of the (k-1)th harmonic through calculation processing utilizing the addition theorem of trigonometric functions.

Furthermore, in the harmonic measuring device 10 according to the second embodiment, when the values of the trigonometric functions output from the trigonometric function output unit 22 are the values of the cosine function F _c [n] and the sine function F _s [n] shown in the above equation 8, and the cosine intermediate value and the sine intermediate value of the (k-1)th harmonic calculated by the (k-1)th harmonic calculation unit are V _A [k-1, n] and V _B [k-1, n], respectively, the high-order component calculation unit 24 serving as the kth harmonic calculation unit sequentially calculates the cosine intermediate values V _A [k, n] and V _B [k, n] of the kth harmonic and the cosine coefficient A [k, n] and sine coefficient B [k, n] of the kth harmonic based on the formula shown in the above equation 21.

Here, A[k,-1]=0 and B[k,-1]=0 as initial values when the value of n is 0. Furthermore, when the sampling data is v _d [n], the intermediate cosine value of the (k-1)th harmonic when k=2 is V _A [1,n]=v _d [n]·F _c [n], and the intermediate sine value of the (k-1)th harmonic when k=2 is V _B [1,n]=v _d [n]·F _s [n].

This enables the high-order component calculation unit 24 to sequentially calculate not only the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic, but also the cosine intermediate values V _A [k,n] and V _B [k,n] of the k-th harmonic during the calculation process, each time the M-ary counter 21 counts the value n.

Furthermore, in the harmonic measuring device 10 according to the second embodiment, the high-order component calculation unit 24 serving as the k-th harmonic calculation unit includes first to fourth multipliers 61 to 64, a subtractor 65, first to third adders 55, 56, and 66, and first and second registers 57 and 58 each consisting of a one-stage shift register for the value of n,
The cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic is multiplied by the value of the cosine function F _c [n] from the trigonometric function output unit 22 in a first multiplier 61, and the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic is multiplied by the value of the sine function F _S [n] from the trigonometric function output unit 22 in a second multiplier 64. The value V _A [k-1,n] · F _c [n] which is the calculation result of the first multiplier 61 is subtracted by the value V _B [k-1,n] · F _S [n] which is the calculation result of the second multiplier 64 in a subtractor 65, to obtain the cosine intermediate value V _A A first adder 55 adds V B [k-1,n] and the cosine coefficient A[k,n-1] of the kth harmonic at the time of the previous sampling output from the first register 57, and the cosine coefficient A[k,n] of the kth harmonic which is the calculation result of the first adder 55 is input to the first register 57. A third multiplier 63 multiplies the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic by the value of the cosine function F _c [n] from the trigonometric function output unit 22. A fourth multiplier 62 multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic by the value of the sine function F _S [n] from the trigonometric function output unit 22. A fourth multiplier 62 multiplies the value V _B [k-1,n]·F _c [n] which is the calculation result of the third multiplier 63 by the value V _A The second _adder 66 adds the k-th harmonic sine intermediate value V _B [k,n] which is the calculation result of the second adder 66, and the k-th harmonic sine coefficient B[k,n-1] at the previous sampling time which is output from the second register 58, and the third adder 56 adds the k-th harmonic sine intermediate value V B [k,n] which is the calculation result of the third adder 56, and inputs the k-th harmonic sine coefficient B[k,n] which is the calculation result of the third adder 56 to the second register 58, thereby outputting the cosine intermediate value V _A [k,n] and sine intermediate value V _B [k,n] of the k-th harmonic, and the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic, respectively.

Therefore, high-order component calculation unit 24 is capable of sequentially calculating the cosine intermediate value V A [k,n] and sine intermediate value V _B [k,n] of the k-th harmonic, and the cosine coefficient A[k,n] and sine coefficient _B [k,n] of the k-th harmonic, using only eight calculation units, namely multipliers 61 to 64, subtractor 65, and adders 55, 56, 66, and two registers 57, 58.

Moreover, the harmonic calculation unit 13 of the harmonic measuring device 10 according to the third embodiment further includes a real-time harmonic analysis unit 70 that makes it possible to calculate amplitude information related to the kth harmonic for each sampling period Ts M _points after the start of calculation.

Therefore, after acquiring data for M points from the start of calculation, the harmonic calculation unit 13 can sequentially calculate the calculation results based on the acquired data for the M points immediately prior to that as the cosine coefficient A[k, n] and sine coefficient B[k, n] of the kth harmonic, and can acquire amplitude information related to the kth harmonic for each sampling period _Ts .

Furthermore, the harmonic calculation unit 13 of the harmonic measuring device 10 according to the third embodiment further includes a real-time harmonic analysis unit 70 that enables amplitude information regarding the k-th harmonic to be calculated for each sampling period Ts M points after the start of calculation so that the cosine coefficient A[k, n] and sine coefficient B[k, n] of the k-th harmonic are sequentially calculated based on the formula shown in the above equation 26. This real-time harmonic analysis unit 70 is included in the high-order component calculation unit 24 that serves as the k- _th harmonic calculation unit shown in FIG. 2(B) of the first embodiment and FIG. 3 of the second embodiment.

Therefore, each time the M-ary counter 21 counts the value of n, the harmonic calculation unit 13 can sequentially calculate the calculation results based on the acquired data for the immediately preceding M points as the cosine coefficient A[k, n] and sine coefficient B[k, n] of the k-th harmonic, and can acquire amplitude information related to the k-th harmonic for each sampling period _Ts .

The real-time harmonic analyzer 70 includes first and second adder-subtractors 71, 72, first and second registers 57, 58 each consisting of a one-stage shift register for the value of n, and third and fourth registers 73, 74 each consisting of an M-stage shift register for the value of n,
The cosine intermediate value V _A [k,n] of the k-th harmonic is input to the third register 73, and the first adder/subtractor 71 subtracts the cosine intermediate value V _A [k,n-M] of the k-th harmonic M times earlier output from the third register 73 from a value obtained by adding the cosine intermediate value V A [k,n] of the k-th harmonic at the previous sampling time output from the first register 57 to the cosine intermediate value V _A [k,n] of the k-th harmonic to obtain the cosine coefficient A[k,n] of the k _- th harmonic obtained as a result of the calculation by the first adder/subtractor 71, and inputs the cosine intermediate value V _B [k,n] of the k-th harmonic to the fourth register 74. The sine intermediate value V B [k,n-M] of the k-th harmonic M times earlier output from the fourth register 74 is subtracted from the value obtained by adding the sine coefficient B[k,n-1] of the k-th harmonic at the previous sampling time output from the second register 58 to [k,n], and the sine intermediate value V _B [k,n-M] of the k-th harmonic M times earlier output from the fourth register 74 is input to the second register 58 as the calculation result of the second adder-subtractor 72. In this way, the cosine coefficient A[k,n] and sine coefficient B[k,n] of the k-th harmonic are output.

Therefore, the real-time harmonic analyzer 70 can obtain amplitude information regarding the k-th harmonic for each sampling period _Ts simply by adding third and fourth registers 73 and 74, each of which is made up of an M-stage shift register for the value of n.

In addition, in a fourth embodiment in which the harmonic measuring device 10 is applied to the PCS 100, the PCS 100 is provided with an inverter unit 111, which serves as a power conversion unit, between the DC power source 200 and the power system 300, and is provided with an islanding detection method (system) for detecting whether the DC power source 200 is isolated from the power system 300 and operating alone. The islanding detection method here is configured with any of the harmonic measuring devices 10 in the first to third embodiments, and includes a harmonic measuring unit 130 that measures the harmonic voltage on the output side of the inverter unit 111, and a step injection processing unit 126 that starts step injection of reactive power when a fluctuation occurs in the harmonic voltage measured by the harmonic measuring unit 130, thereby detecting the islanding operation of the PCS 100 including the DC power source 200.

This makes it possible to provide an islanding detection method using the harmonic measuring device 10 that achieves cheaper and faster calculation processing.

The PCS 100 may be modified to a configuration other than that shown in the figure. The DC power source 200 is not limited to a DC power source such as a solar cell, but may be other DC power sources such as wind power generation, fuel cells, and storage batteries. In addition, the hardware section 110 and the software section 120 may be modified to a configuration other than that shown in the figure by adding other functions. The above-mentioned harmonic measuring device 10 can be applied to any device that requires harmonic analysis of the input signal v, in addition to the PCS 100.

10 Harmonic measuring device 11 Signal input section 12 Sampling section 13 Harmonic calculation section 21 M-ary counter 22 Trigonometric function output section 23 Low-order component calculation section 24 High-order component calculation section 31 DC component calculation section 32, 44, 45, 54, 55, 56, 66 Adder 33, 46, 47, 57, 58, 73, 74 Register (shift register)
34 Intermediate value output section 41 Fundamental wave component calculation section 42, 43, 51, 52, 61, 62, 63, 64 Multiplier 53, 65 Subtractor 70 Real-time harmonic analysis section 71, 72 Adder/subtractor 100 PCS (power conditioner)
110 Hardware section 111 Inverter section (power conversion section)
112 System frequency detection unit 113 Voltage measurement unit 120 Software unit 121 Current control processing unit 122 Phase difference measurement synchronization processing unit 123 Addition unit 124 System frequency measurement processing unit 125 Reactive power injection processing unit 126 Step injection amount processing unit (islanding operation detection method)
127 Voltage calculation unit 128 Islanding operation determination unit 130 Harmonic measurement unit (islanding operation detection method)
200 DC power source (solar cell)
300 Power system (commercial power supply V _AC )

Claims (11)

A signal input unit;
A sampling unit;
A harmonic calculation unit;
having
The signal input unit generates an output signal from an input signal to be measured,
the sampling unit receives the output signal from the signal input unit and outputs sampling data for each sampling period;
the harmonic calculation unit receives the sampling data from the sampling unit and calculates amplitude information related to zeroth or higher k-th harmonics by discrete Fourier analysis;
The harmonic calculation unit calculates amplitude information regarding zeroth or higher k-th harmonics by discrete Fourier analysis,
an M-ary counter that counts the value of n from 0 to M-1 in increments of 1 for each sampling period when the sampling unit outputs M points of sampling data in one period of the output signal;
a trigonometric function output unit that uses the value of n counted by the M-ary counter to output a value of a trigonometric function that does not depend on the order k of a harmonic,
a trigonometric function output unit that outputs a trigonometric function value to the harmonic measuring device, the trigonometric function output unit being used to sequentially calculate a cosine coefficient and a sine coefficient of a k-th harmonic, the cosine coefficient and the sine coefficient being sequentially calculated ... The harmonic calculation unit includes:
a k-th harmonic calculation unit that calculates amplitude information relating to a k-th harmonic, which is second or higher;
A (k-1)th harmonic calculation unit that calculates amplitude information related to a (k-1)th harmonic;
A (k-2)th harmonic calculation unit that calculates amplitude information related to a (k-2)th harmonic,
The k-th harmonic calculation unit is
2. The harmonic measuring device according to claim 1, wherein each time the M-ary counter counts the value of n, a cosine coefficient and a sine coefficient of a k-th harmonic derived from a Chebyshev polynomial are sequentially calculated using, in addition to the value of the trigonometric function output from the trigonometric function output unit, the cosine intermediate value of the (k-1)th harmonic calculated in the process of calculation by the (k- 1 )th harmonic calculation unit, and the cosine intermediate value and sine intermediate value of the (k-2)th harmonic calculated in the process of calculation by the (k-2)th harmonic calculation unit. The trigonometric function values output from the trigonometric function output unit are the following cosine function F _c [n] and sine function F _s [n] values,

The cosine intermediate value of the (k-1)th harmonic calculated by the (k-1)th harmonic calculation unit is defined as V _A [k-1, n];
When the cosine intermediate value and the sine intermediate value of the (k-2)th harmonic calculated by the (k-2)th harmonic calculation unit are V _A [k-2, n] and V _B [k-2, n], respectively,
The k-th harmonic calculation unit is configured to calculate the k-th harmonic based on the following formula:

(However, when the value of n is 0, the initial values are A[k,-1]=0 and B[k,-1]=0. Furthermore, when the sampling data is _vd [n], V _A [0,n]= _vd [n], V _B [0,n]=0, V _A [1,n]= _vd [n]· _Fc [n], and V _B [1,n]= _vd [n]· _Fs [n].)
3. The harmonic measuring device according to claim 2, wherein the cosine intermediate values V _A [k,n] and V _B [k,n] of the kth harmonic and the cosine coefficient A [k,n] and sine coefficient B [k,n] of the kth harmonic are sequentially calculated. The k-th harmonic calculation unit is
The input/output circuit includes first and second multipliers, a subtractor, first to third adders, and first and second registers each consisting of a one-stage shift register for the value of n;
a cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic is multiplied by a value obtained by multiplying the cosine function F _c [n] output from the trigonometric function output unit by two in the first multiplier, and the cosine intermediate value V _A [k-2,n] of the (k-2)th harmonic is subtracted by the subtractor from a value 2F _c [n]·V _A [k-1,n] which is the result of the operation of the first multiplier, and the cosine intermediate value V _A [k-2,n] of the kth harmonic is added by the first adder to the cosine intermediate value V A [k,n] of the kth harmonic at the previous sampling time which is output from the first register, and the cosine coefficient A[k,n-1] of the kth harmonic at the previous sampling time which is output from the first register is input to the first register;
the second multiplier multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic by twice the sine function F _s [n] from the trigonometric function output unit, the second adder adds the sine intermediate value V _B [k-2,n] of the (k-2)th harmonic to the value 2F _s [n]·V _A [k-1,n] which is the calculation result of the second multiplier, the third adder adds the sine intermediate value V _B [k,n] of the kth harmonic which is the calculation result of the second adder and the sine coefficient B[k,n-1] of the kth harmonic at the previous sampling time which is output from the second register, and the sine coefficient B[k,n] of the kth harmonic which is the calculation result of the third adder is input to the second register;
4. The harmonic measuring device according to claim 3, wherein the device is configured to output a cosine intermediate value V _A [k,n] and a sine intermediate value V _B [k,n] of the kth harmonic, and a cosine coefficient A [k,n] and a sine coefficient B [k,n] of the kth harmonic, respectively. The harmonic calculation unit includes:
a k-th harmonic calculation unit that calculates amplitude information regarding a k-th harmonic, which is 1st or higher;
A (k-1)th harmonic calculation unit that calculates amplitude information related to a (k-1)th harmonic,
The k-th harmonic calculation unit is
2. The harmonic measuring device according to claim 1, wherein each time the M-ary counter counts the value of n , a cosine coefficient and a sine coefficient of a k-th harmonic derived from an addition theorem of trigonometric functions are sequentially calculated using, in addition to the trigonometric function value output from the trigonometric function output unit, a cosine intermediate value and a sine intermediate value of the (k-1)th harmonic calculated in the course of calculation processing by the (k -1) th harmonic calculation unit. The trigonometric function values output from the trigonometric function output unit are the following cosine function F _c [n] and sine function F _s [n] values,

When the cosine intermediate value and the sine intermediate value of the (k-1)th harmonic calculated by the (k-1)th harmonic calculation unit are V _A [k-1,n] and V _B [k-1,n], respectively,
The k-th harmonic calculation unit is configured to calculate the k-th harmonic based on the following formula:

(However, when the value of n is 0, the initial values are A[k,-1]=0 and B[k,-1]=0. In addition, when the sampling data is _vd [n], V _A [1,n]= _vd [n]· _Fc [n], and V _B [1,n]= _vd [n]· _Fs [n].)
6. The harmonic measuring device according to claim 5, wherein the cosine intermediate value V _A [k,n] and the sine intermediate value V _B [k,n] of the kth harmonic, and the cosine coefficient A [k,n] and the sine coefficient B [k,n] of the kth harmonic are sequentially calculated. The k-th harmonic calculation unit is
The input/output circuit includes first to fourth multipliers, a subtractor, first to third adders, and first and second registers each consisting of a one-stage shift register for the value of n;
a cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic is multiplied by the value of the cosine function F _c [n] from the trigonometric function output unit in the first multiplier, a sine intermediate value V _B [k-1,n] of the (k-1)th harmonic is multiplied by the value of the sine function F _S [n] from the trigonometric function output unit in the second multiplier, and a value V _B [k-1,n] ·F _S [n] which is the calculation result of the second multiplier is subtracted from a value _{V A} [k-1,n] ·F _c [n] which is the calculation result of the first multiplier in the subtractor, [k, n] and the cosine coefficient A[k, n-1] of the kth harmonic at the previous sampling time output from the first register are added by the first adder, and the cosine coefficient A[k, n] of the kth harmonic which is the calculation result of the first adder is input to the first register;
The third multiplier multiplies the sine intermediate value V _B [k-1,n] of the (k-1)th harmonic by the value of the cosine function F _c [n] from the trigonometric function output unit, the fourth multiplier multiplies the cosine intermediate value V _A [k-1,n] of the (k-1)th harmonic by the value of the sine function F _S [n] from the trigonometric function output unit, and the second adder adds the value V _A [k-1,n] ·F _S [n] that is the result of the operation of the third multiplier to the value V _B [k-1,n] ·F _c [n] that is the result of the operation of the second adder, to obtain the kth harmonic sine intermediate value V _B [k, n] and the sine coefficient B[k, n-1] of the kth harmonic at the previous sampling time output from the second register are added by the third adder, and the sine coefficient B[k, n] of the kth harmonic which is the calculation result of the third adder is input to the second register,
7. The harmonic measuring device according to claim 6, wherein the device is configured to output a cosine intermediate value V _A [k,n] and a sine intermediate value V _B [k,n] of the kth harmonic, and a cosine coefficient A [k,n] and a sine coefficient B [k,n] of the kth harmonic, respectively. The harmonic calculation unit includes:
The harmonic measuring device according to any one of claims 1 to 7, further comprising a real-time harmonic analysis unit that is capable of calculating amplitude information relating to the kth harmonic for each sampling period M points after the start of calculation. The harmonic calculation unit includes:
The cosine coefficient A[k,n] and the sine coefficient B[k,n] of the kth harmonic are calculated successively based on the following formula:

The harmonic measuring device according to claim 3 or 6, characterized in that the k-th harmonic calculation unit further comprises a real-time harmonic analysis unit that can calculate amplitude information regarding the k-th harmonic for each sampling period M points after the start of calculation. The real-time harmonic analysis unit is
a first and second adder/subtractor, a first and second register each consisting of a one-stage shift register for the value of n, and a third and fourth register each consisting of an M-stage shift register for the value of n;
a cosine intermediate value V _A [k,n] of the k-th harmonic is input to the third register, and the first adder/subtractor subtracts the cosine intermediate value V _A [k,n-M] of the k-th harmonic M times earlier output from the third register from a value obtained by adding the cosine coefficient A[k,n-1] of the k-th harmonic at the previous sampling time output from the first register to the cosine intermediate value V _A [k,n] of the k-th harmonic, and inputs the cosine coefficient A[k,n] of the k-th harmonic which is the calculation result of the first adder/subtractor to the first register;
The sine intermediate value V _B [k,n] of the k-th harmonic is input to the fourth register, and the second adder/subtractor subtracts the sine intermediate value V _B [k,n-M] of the k-th harmonic M times earlier output from the fourth register from a value obtained by adding the sine coefficient B[k,n-1] of the k-th harmonic at the previous sampling time output from the second register to the sine intermediate value V _B [k,n] of the k-th harmonic, and inputs the sine coefficient B[k,n] of the k-th harmonic which is the calculation result of the second adder/subtractor to the second register;
10. The harmonic measuring device according to claim 9 , wherein the device is configured to output a cosine coefficient A[k, n] and a sine coefficient B[k, n] of the kth harmonic. An isolated operation detection method is provided in a power conditioner unit having a power conversion unit arranged between a DC power source and a power grid, and detects whether the DC power source is disconnected from the power grid and is operating alone,
A harmonic measuring unit configured by the harmonic measuring device according to any one of claims 1 to 10 and measuring a harmonic voltage on an output side of the power conversion unit;
and a step injection processing unit which, when a fluctuation occurs in the harmonic voltage measured by the harmonic measuring unit, starts a step injection of reactive power, thereby detecting whether or not the plant is operating alone.

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