JP6491424B2 - Harmonic estimation device, harmonic estimation method, and harmonic estimation program - Google Patents

Description

  The present invention relates to a harmonic estimation apparatus, a harmonic estimation method, and a harmonic estimation program.

  Currently, electronic devices using power electronics technology such as air conditioners and televisions are widely used in the world. In an electronic device using power electronics technology, when alternating current is converted to direct current, alternating current including harmonic current flows, and alternating voltage distortion caused by this flows. Such voltage distortion may lead to unexpected events such as overheating of substation facilities and customer facilities and malfunction of electronic devices.

  In this respect, the voltage distortion of the recent power system is decreasing, but there are distribution lines with large voltage distortion in the city center and some areas. In such a distribution line, it is preferable to analyze rational measurement data and examine a rational countermeasure method. However, at present, there are many unclear points in the mechanism of voltage distortion. Therefore, it is important to analyze the measured data of voltage, current, and power in the power system and customers to clarify the characteristics of the harmonic current generated by each customer, and to clarify the overall mechanism by harmonic analysis. is there.

  As such a harmonic analysis technique, a conventional technique has been proposed in which a harmonic current generated from a customer is input and a harmonic voltage distortion of the entire system is obtained to analyze a voltage distortion mechanism. Further, a conventional technique for estimating the harmonic distribution of the power system under the condition that the number of harmonic generation sources to be estimated is small with respect to the number of measurements has been proposed.

JP 2013-198223 A

Yukihira "Development of Harmonic Source Distribution Estimation Program" Central Research Laboratory Research Report (T98043), May 1999 Hashimoto “Development of Harmonic Analysis Program for Distribution System” Central Research Institute of Electric Power Research Report (182025), April 1983

  However, as described above, the power electro technology is widely used in the world, and the harmonic current is generated from many customers. Under such circumstances, it is difficult to simultaneously measure harmonic currents generated from all consumers. Therefore, it is difficult to perform harmonic analysis using a harmonic current generated from a consumer as an input. In addition, under the condition that the number of harmonic generation sources to be estimated is small with respect to the number of measurements, the state of the harmonics of all customers should be estimated even using the conventional technology that estimates the harmonic distribution of the power system. It is difficult.

  The disclosed technique has been made in view of the above, and an object thereof is to provide a harmonic estimation apparatus, a harmonic estimation method, and a harmonic estimation program that easily estimate the harmonic state of a distribution system. .

  The harmonic estimation device, the harmonic estimation method, and the harmonic estimation program disclosed in the present application are, in one aspect, the estimation formula generation unit, the generation amount of harmonic current per power consumption in a consumer connected to the distribution line, Distribution model of harmonic current generated in each consumer, harmonic group that classifies the harmonic current generated from the customer, delivery harmonic voltage of the distribution line, delivery harmonic current of the distribution line, distribution Based on the impedance in the electric wire, the load capacity of each consumer, and the capacity of the power factor improving capacitor in each consumer, a harmonic including state variables for obtaining an estimated value of the harmonic voltage in each consumer Generate wave estimation formula. The estimated value calculation unit calculates an estimated value of the harmonic voltage in each consumer using the least square method based on the harmonic estimation formula generated by the estimation formula generation unit.

  According to one aspect of the harmonic estimation device, the harmonic estimation method, and the harmonic estimation program disclosed in the present application, it is possible to easily estimate the harmonic state of the distribution system.

FIG. 1 is a diagram of an example of a distribution line model. FIG. 2 is a block diagram of the harmonic estimation apparatus according to the first embodiment. FIG. 3 is a diagram illustrating a diagram representing a group of a phase angle and an amplitude of a harmonic current generated by a consumer. FIG. 4 is a normal distribution model of the phase angle distribution of group A. FIG. 5 is a flowchart of harmonic estimation processing by the harmonic estimation apparatus according to the first embodiment. FIG. 6 is a diagram illustrating the setting of the harmonic characteristics of each consumer for each characteristic group. FIG. 7 is a diagram illustrating setting of impedances of the bank transformer and the distribution line. FIG. 8 is a diagram showing the setting of the SC capacity arranged in each consumer. FIG. 9A is a diagram illustrating setting of the capacity of customers belonging to group A. FIG. 9B is a diagram illustrating setting of the capacity of customers belonging to group B. FIG. 10 is a diagram illustrating the setting of the fifth harmonic voltage of the system. FIG. 11 is a diagram showing the value of the customer load set assuming an actual load. FIG. 12 is a diagram showing the true value and the estimated value of the fifth harmonic voltage as vectors. FIG. 13A is a diagram illustrating a comparison of effective values of the fifth harmonic voltage. FIG. 13B is a diagram illustrating a comparison of the phase angles of the fifth harmonic voltage. FIG. 14 is a diagram showing a numerical comparison between the true value and the estimated value of the fifth harmonic voltage. FIG. 15 is a diagram representing the true value and the estimated value of the fifth harmonic current as vectors. FIG. 16A is a diagram illustrating comparison of effective values of fifth harmonic currents. FIG. 16B is a diagram illustrating a comparison of the phase angles of the fifth harmonic current. FIG. 17 is a diagram showing a numerical comparison between the true value and the estimated value of the fifth harmonic current. FIG. 18 is a block diagram of a harmonic estimation apparatus according to the second embodiment. FIG. 19 is a flowchart of harmonic estimation processing by the harmonic estimation apparatus according to the second embodiment. FIG. 20 is a block diagram of a harmonic estimation apparatus according to the third embodiment.

  Hereinafter, embodiments of a harmonic estimation apparatus, a harmonic estimation method, and a harmonic estimation program disclosed in the present application will be described in detail with reference to the drawings. The harmonic estimation apparatus, the harmonic estimation method, and the harmonic estimation program disclosed in the present application are not limited to the following embodiments.

  First, harmonics that have effects such as heating of equipment and generation of abnormal noise in the power system have many fifth-order components. Therefore, in the following description, a case where the fifth harmonic is handled will be described as an example. Moreover, below, the case where the distribution line model shown in FIG. 1 is used is demonstrated to an example. FIG. 1 is a diagram of an example of a distribution line model.

  In the distribution line model of FIG. 1, a distribution transformer (bank transformer) 100 is connected to the bus. In the distribution measurement, the voltage at the bus voltage measurement point 101 and the current 102 flowing from the bus to the distribution line are measured. In addition to nodes corresponding to the bus voltage measurement point 101, nodes 111 to 116 are present on the distribution line as nodes that are voltage and current measurement points. Nodes 111 to 116 are customer nodes, and each customer is connected. There are high-pressure customers who are high-pressure load customers and low-pressure customers who are low-pressure load customers. Node 111 is a low-pressure consumer. Node 112 is a high voltage consumer with a three-phase load. The node 112 has a series reactor-less SC (Static Capacitor) 121 which is a power factor improving capacitor. Node 113 is a low-pressure consumer. Node 114 is a low-pressure consumer. Node 115 is a high voltage consumer with a three-phase load. And the node 115 has SC151 with a series reactor which is a capacitor for power factor improvement. Node 116 is a high voltage consumer with a three-phase load. The node 116 has a series reactor-less SC 161.

  FIG. 2 is a block diagram of the harmonic estimation apparatus according to the first embodiment. The harmonic estimation apparatus 1 according to the present embodiment includes an input control unit 11, a storage unit 12, a harmonic voltage estimation formula generation unit 13, a harmonic estimation unit 14, and a notification unit 15.

(Data input)
The input control unit 11 receives input from an input device such as a mouse or a keyboard. Specifically, the input control unit 11 receives information on customer harmonic current characteristics, distribution harmonic measurement data, distribution line data, and customer facility data input by an operator using an input device. . In addition, by switching input data, data from a database or a distant measuring instrument is received. Here, each input data will be described in detail.

(Harmonic current characteristics)
The harmonic current characteristics of the customer include a characteristic group, a generation amount of the harmonic current per power consumption, an amplitude distribution model of the harmonic current, and a phase angle distribution model of the harmonic current.

  The characteristic group is a group generated by classification according to the state of the phase angle distribution of the harmonic current generated from the consumer that is the source of the harmonic. Here, a group of consumers will be described. FIG. 3 is a diagram illustrating a group of the phase angle and the amplitude of the harmonic current generated by the consumer. In FIG. 3, the phase angle is represented by the rotation angle of a vector extending from the center representing the fifth harmonic current, and the amplitude is represented by its length. For example, the vector 200 has a phase angle of 0 degree-φ and an amplitude of L.

As a result of analyzing the phase angle of the fifth harmonic current in the high-voltage consumer and the low-voltage consumer, the fifth harmonic current of the three-phase load of the high-voltage consumer is represented by 300 to 330 represented by a region 201 in FIG. It can be seen that the distribution is centered on the fourth quadrant. Harmonic currents belonging to the area 201 is the expected value of the phase angle mu _theta, the standard deviation of the phase angle is sigma _theta. That is, the phase angle of the harmonic current belonging to the area 201 is distributed primarily between the following _μ θ -2σ θ or μ θ + 2σ _θ. When this phase angle distribution according to ^{_{N (μ θ, σ θ 2}} ), the probability that the phase angle is comprised between the following _μ θ -2σ θ or μ θ ₊ 2σ θ is 95.45%. Furthermore, harmonic currents belonging to the area 201 is the expected value of the amplitude mu _A, the standard deviation of the amplitude of sigma _A. In other words, the amplitude of the harmonic currents belonging to the area 202 is distributed primarily between the following μ _A -2σ _A more _{μ A} + _{2σ A.} When the amplitude according to ^{_{N (μ A, σ A 2}} ), the probability that the phase angle is comprised between the following _{μ A -2σ} A more _mu A + 2 [sigma] _A is 95.45%.

Further, the single-phase load of the high-voltage consumer and the fifth harmonic current of the single-phase load and the three-phase load of the low-voltage consumer have the second quadrant of 120 to 180 degrees represented by the region 202 in FIG. Distributed in the center. For the harmonic current belonging to the region 202, the expected value of the phase angle is μθ _′ , and the standard deviation of the phase angle is σθ _′ . That is, the phase angle of the harmonic current belonging to the area 202 is distributed primarily between the following μ θ _{'-2σ θ'} or μ θ _'+ 2σ _θ'. In addition, the harmonic current belonging to the region 202 has an expected amplitude value of μ _{A ′} and an amplitude standard deviation of σ _{A ′} . In other words, the amplitude of the harmonic currents belonging to the area 202 is distributed primarily between the following μ _{A '-2σ A'} or μ _{A '+} 2σ _A'.

  In other words, the generation phase angle of the fifth harmonic current can be classified into a group of region 201 and a group of region 202. Hereinafter, the group of the area 201 is referred to as “group A”, and the group of the area 202 is referred to as “group B”. As described above, the characteristic group is divided into group A and group B. For example, the nodes 112, 115, and 116 in FIG. In addition, the nodes 111, 113, and 114 in FIG.

  Further, the amount of harmonics generated per power consumption is a value obtained by dividing the harmonic current generated by the consumer by the power consumed by the consumer. That is, it is the ratio of the harmonic current to the power consumed by the consumer, and the unit is, for example, “mA / kW” or “A / kW”. In this embodiment, a fixed value obtained statistically for each characteristic group is used as this value. In the present embodiment, the power consumption is the power of the fundamental wave consumed by the consumer.

  The distribution model represents the distribution state of the fifth harmonic current for each characteristic group. It can be estimated that the phase angle distribution of group A is distributed as represented by the normal distribution curve 300 of FIG. 4 is a normal distribution model of the phase angle distribution of group A. FIG. That is, it can be estimated that the phase angles of the fifth harmonic currents belonging to the group A in FIG. 3 are distributed as shown in FIG.

  Here, in FIG. 4, the phase angle distribution of the group A is shown, but this distribution model includes the amplitude distribution of the group A and the normal distribution models of the phase angle distribution and the amplitude distribution of the group B, respectively.

  There are two characteristic groups, group A and group B. Since both the harmonic voltage and the harmonic current are estimated by the same method, group A will be described below as an example.

(Distribution harmonic measurement data)
Distribution harmonic measurement data is measurement data at a distribution substation. The distribution harmonic measurement data has two elements, that is, a distribution line sending voltage and a distribution line sending current 102 which are voltages at the bus voltage measurement point 101 on the secondary side of the bank transformer 100 of FIG. The distribution line delivery harmonic voltage can be obtained by measuring the voltage at the bus voltage measurement point 101, applying a fast Fourier transform (FFT), and extracting a fifth-order harmonic component. Similarly, the distribution line delivery harmonic current can be obtained by measuring the current 102 flowing from the bus voltage measurement point 101 to the node 111, performing FFT, and extracting the fifth-order harmonic component. Here, in FIG. 1, the calculated distribution line delivery harmonic voltage is represented as “Vh”, and the distribution line delivery harmonic current is represented as “Ih”. When the voltage and current are subjected to FFT to extract the fifth harmonic component, the voltage and current at the same point are both based on the same phase angle.

  Thus, the distribution line delivery harmonic voltage Vh and the distribution line delivery harmonic current Ih are obtained by performing FFT on the measured waveform data. That is, the distribution harmonic measurement data is obtained as a complex number based on the phase angle of the fundamental voltage of the reference phase. Here, the polar coordinate system and the orthogonal coordinate system can be converted to each other, and the distribution harmonic measurement data is represented by any one of the coordinate systems.

(Distribution line data)
Distribution line data includes a node that supplies power to the distribution transformer, a bus voltage measurement point on the distribution line, and an impedance between each node. Hereinafter, these impedances are collectively referred to as “impedance of distribution line”. For example, in the case of the distribution line model of FIG. 1, distribution line data includes the impedance in the distribution transformer 100, the impedance of the trunk line between the bus voltage measurement point 101 and the node 111, and the trunk line between the node 111 and the node 112. Including impedance. Further, the distribution line data includes the impedance of the trunk line between the node 112 and the node 113, the impedance of the trunk line between the node 113 and the node 114, the impedance of the branch line between the node 111 and the node 115, and the node 112 and Contains the impedance of the branch line to node 116.

(Customer equipment data)
The customer equipment data includes equipment capacity and SC capacity. The installed capacity is the load of each consumer or the capacity of the power receiving transformer. In the case of the distribution line model of FIG. 1, it is the load of each of the consumers of the nodes 111 to 116 or the capacity of the power receiving transformer. The maximum installation capacity among the installation capacities is the maximum load power of each customer or the capacity of the power receiving transformer, and can be acquired from the installation data. However, when the maximum power is unknown, the maximum installed capacity may be assumed from the contract power. The minimum installed capacity is the minimum power of the consumer. For example, if the minimum value of power to be consumed is determined, the value can be used. However, when the minimum power is not determined, 0 may be used as the minimum equipment capacity.

  The SC capacity is a capacity of a power factor improving capacitor arranged in each consumer. In the case of the distribution line model of FIG. 1, it is each capacity | capacitance of SC121 without a series reactor, SC151 with a series reactor, and SC161 without a series reactor. The SC capacity can be obtained from facility data that the customer has.

(Generation of harmonic voltage estimation formula)
Returning to FIG. 2, the description will be continued. The input control unit 11 causes the storage unit 12 to store the received customer harmonic current characteristic information, distribution harmonic measurement data, distribution line data, and customer facility data. The storage unit 12 is a storage device such as a hard disk.

  The harmonic voltage estimation formula generation unit 13 includes a node admittance matrix generation unit 31 and an estimation formula generation unit 32.

  The harmonic voltage estimation formula generation unit 13 acquires information on the customer's harmonic current characteristics, distribution harmonic measurement data, distribution line data, and customer facility data from the storage unit 12.

  Then, the harmonic voltage estimation formula generation unit 13 transmits the impedance of the distribution line and the SC capacity to the node admittance matrix generation unit 31. Further, the harmonic voltage estimation formula generation unit 13 outputs information on the customer's harmonic current characteristics, distribution harmonic measurement data, distribution line data, and customer facility data to the estimation formula generation unit 32.

Node admittance matrix generating unit 31 generates the node admittance matrix Y _h harmonics. Specifically, first, the node admittance matrix generation unit 31 calculates reactance corresponding to the harmonic order of each power factor correction capacitor.

  When the power factor improving capacitor is a series reactorless SC, the node admittance matrix generation unit 31 calculates the reactance of the harmonic by multiplying the reactance of the fundamental wave by 1 / n. Here, n is the order of the target harmonic. That is, in this embodiment, n = 5. For example, the capacitor capacity of the series reactor-less SC acquired from the facility data is Qc, and the system voltage that is the rated voltage is Vb. In this case, the node admittance matrix generation unit 31 calculates the reactance of the harmonics of the series reactor-less SC using the following formula 1. Xcn in Formula 1 represents the reactance of the harmonic of the serial reactor without SC in calculation.

  For example, in the case of the distribution line model of FIG. 1, the node admittance matrix generation unit 31 calculates the reactance of the harmonics in the calculation of the series reactor-less SC 121 and the series reactor-less SC 161 using Equation 1.

  When the power factor improving capacitor is a SC with a series reactor, the node admittance matrix generating unit 31 calculates the reactance of the calculated harmonic by multiplying the capacitive reactance by 1 / n and multiplying the inductive reactance by n. . For example, the capacitor capacity of the series reactor with SC acquired from the facility data is Qc, and the system voltage that is the rated voltage is Vb. Furthermore, k is the absolute value of the ratio of the inductive reactance to the total reactance in the fundamental wave. In this case, the node admittance matrix generation unit 31 calculates the reactance of the harmonic of the SC with the serial reactor in the calculation using the following formula 2. Xcn in Equation 2 represents the calculated reactance of the harmonics of the SC with series reactor.

  For example, in the case of the distribution line model shown in FIG. 1, the node admittance matrix generation unit 31 calculates the reactance of the harmonic in the calculation of the series reactor SC 151 using Equation 2.

  Next, the node admittance matrix generation unit 31 generates a harmonic node admittance matrix Yh using the calculated harmonic reactance of the calculated power factor improvement capacitor and the impedance of the distribution line. Then, the node admittance matrix generation unit 31 transmits the generated node admittance matrix Yh to the estimation formula generation unit 32. In addition, the node admittance matrix generation unit 31 transmits the generated node admittance matrix Yh to the harmonic estimation unit 14.

  Here, the node admittance matrix will be described in detail. When the harmonic order is h, the harmonic voltage of node i is Vhi, and the harmonic current injected into node i is Ihi, the following Equation 3 is established.

In this embodiment, the voltage Vh _{i at} each node i is expressed by the following Equation 4.

  Here, Ehi and Fhi are a real part and an imaginary part of the h-order harmonic voltage of node i.

Each element Yh _ij of the node admittance matrix Yh is expressed by the following formula 5.

Here, when i ≠ j, yh _ij is an admittance of a branch between the node i and the node j. gh _ij is the real part of the admittance of the branch between node i and node j. bh _ij is the imaginary part of the admittance of the branch between node i and node j. zh _ij is the impedance of the branch between node i and node j. rh _ij is the real part of the impedance of the branch between node i and node j. xh _ij is the imaginary part of the impedance of the branch between node i and node j.

When i = j, yh _ii is the admittance of the branch of node i. gh _ii is the real part of the admittance of the branch of node i. bh _ii is the imaginary part of the admittance of the branch of node i. zh _ii is the impedance of the branch of node i. rh _ii is the real part of the impedance of the branch of node i. xh _ii is the imaginary part of the impedance of the branch of node i.

  Here, an example of setting the impedance of the h-th harmonic based on the impedance of the fundamental wave is shown. When the fundamental wave impedance z is r + jx, if this imaginary part is positive, r + jx × h is set. On the other hand, when the imaginary part of the fundamental wave impedance r + jx is negative, r + jx / h is set.

  In this case, the node admittance matrix Yh is expressed by the following Equation 6.

  The estimation formula generation unit 32 receives information on the customer's harmonic current characteristics, distribution harmonic measurement data, distribution line data, and customer facility data from the harmonic voltage estimation formula generation unit 13. Further, the estimation formula generation unit 32 receives the node admittance matrix Yh from the node admittance matrix generation unit 31.

  The estimation formula generation unit 32 generates a measurement equation h (x) using each element of the node admittance matrix Yh. The measurement equation h (x) is an equation for calculating the value of the harmonic voltage and current in the distribution and the value of the harmonic voltage and current in each consumer using the state variables. x is a state variable, and the harmonic voltage at each node is the state variable x.

Here, the measurement equation h (x) will be described in detail. First, the node current measurement equation will be described. The amplitude of the h-th harmonic current Ih _i injected into the node i is expressed by the following Equation 7.

Here, Ch _i is a real part of the h-order harmonic current Ih _i injected into the node i. Dh _i is an imaginary part of the h-th harmonic current Ih _i injected into the node i.

Gh _ij and Bh _ij are elements of the real part and the imaginary part of Yh _ij . Gh _ij and Bh _ij are expressed by Equation 8 below.

On the other hand, the phase angle of the h-th harmonic current Ih _i injected into the node i is expressed by the following Equation 9.

  Furthermore, the sensitivity H (x) of the measurement equation h (x) can be obtained by partial differentiation of the measurement equation h (x) as in the following Equation 10.

Here, the state variable x is expressed by a real part Eh _i and an imaginary part Fh _i of the h-order harmonic voltage of the node i shown in Expression 4. Therefore, by substituting Equation 7 into Equation 10, the sensitivity of the amplitude of the measuring equation of the h-th harmonic current Ih _i to be injected into the node i as in Equation 11 and 12 H (x) is obtained.

Further, by substituting equation 9 into equation 10, the resulting sensitivity of the measuring equation of the phase angle of the h-th harmonic current Ih _i to be injected into the node i as in Equation 13 and 14 H (x).

Next, a node voltage measurement equation will be described. Measurement equation of the real part and the imaginary part of the h-th harmonic voltage Vh _i of node i is expressed by the following equation 15.

Here, the measurement error is taken into consideration where the measurement error of the distribution harmonic measurement value is zerr, and the maximum error of the harmonic voltage measurement value Vzh _i at each node is σVzh _i = zerrVzh _i / 2. The sensitivity H (x) of the node voltage measurement equation is also expressed by Equation 10. Therefore, by substituting Equation 15 into Equation 10, and when i = j, the sensitivity H (x) of the node voltage measurement equation is obtained as in Equation 16 below.

  When i ≠ j, the sensitivity H (x) of the node voltage measurement equation is obtained as in the following Equation 17.

Further, a measurement equation of the h-th harmonic current flowing from the node i to the node j in the branch connecting the node i and the node j will be described. The measurement equation of the real part and the imaginary part of the h-order harmonic current Ih _ij flowing in the branch connecting the node i and the node j is expressed by the following mathematical formula 18.

  The sensitivity H (x) of the measurement equation for the h-th harmonic current flowing in the branch is also expressed by Equation 10. Therefore, the sensitivity H (x) of the measurement equation for the h-th harmonic current flowing in the branch by substituting Equation 18 into Equation 10 is obtained by Equation 19 below.

Note that the h-th harmonic current Ih _ij here is the h-th harmonic current flowing in the branch connecting the node i and the node j, so there is no condition of i = j.

  Using the measurement equation h (x) and the sensitivity H (x) obtained in this way, the estimation formula generation unit 32 obtains a harmonic estimation formula. Therefore, the description of how to obtain the harmonic estimation equation using the measurement equation h (x) and its sensitivity H (x) will be continued.

  When the harmonic voltage is measured at each consumer, measurement noise is mixed with the measured value of the harmonic voltage. Therefore, when the measured value of the harmonic voltage is z at each consumer, the relationship between the measured value z and the measurement equation h (x) can be expressed by the following Equation 20. In Equation 20, e is measurement noise.

  And the estimated value xe of the harmonic voltage in each consumer is the state variable x which minimizes the measurement noise in Formula 20. In this case, the state variable x that minimizes the measurement noise e is the state variable x that minimizes the evaluation function J expressed by the following Equation 21.

Here, R is a covariance matrix of measurement noise. In R, the diagonal term is variance σ ² and the non-diagonal term is covariance. That is, Formula 21 is expressed as the following Formula 22. Here, the matrix of the third term of Equation 21 corresponds to the matrix D.

As shown in FIG. 3, μ _A is an expected value of the amplitude of the harmonic current generated at the consumer. Further, σ _A is a standard deviation of the amplitude of the harmonic current generated at the customer.

Further, the estimated expression generating unit 32 can obtain the expected value mu _A of the amplitude of the harmonic currents in the following equation 23. K is the amount of harmonic current generated per power consumption input by the operator. P _max is the maximum installed capacity of the consumer, and P _min is the minimum installed capacity of the consumer.

Further, the estimation formula generation unit 32 can obtain the standard deviation σ _A of the amplitude of the harmonic current by the following formula 24.

Further, μ _θ is an expected value of the phase angle of the harmonic current generated by the customer. Σ _θ is the standard deviation of the phase angle of the harmonic current generated by the customer. The estimation formula generation unit 32 statistically calculates from the harmonic current data of the characteristic group input from the operator, that is, each characteristic group in FIG. 3, and obtains μ _θ and σ _θ .

Σ _Vh is a standard deviation of the measured value of the harmonic voltage, and is an error included in the measured value of the harmonic voltage. Σ _Ih is a standard deviation of the measured value of the harmonic current, and is an error included in the measured value of the harmonic current. When the standard deviation σ _Vh of the distribution line delivery harmonic voltage and the standard deviation σ _Ih of the distribution line delivery harmonic current are set to zerr, the estimation formula generation unit 32 uses the following formula: 25. Here, z is Vh or Ih, which is a distribution harmonic measurement value. For example, the maximum error guaranteed by the distributed harmonic measurement value z may be the deviation 2σ. By using the standard deviation σ _Vh of the distribution line delivery harmonic voltage and the standard deviation σ _Ih of the distribution line delivery harmonic current, the estimated value xe can be weighted with a measurement error.

Then, the estimation formula generation unit 32 calculates the expected value μ _{A of} the harmonic current amplitude, the standard deviation σ _A of the amplitude of the harmonic current, the expected value μ _θ of the phase angle of the harmonic current, and the phase angle of the harmonic current. The standard deviation σ _θ , the distribution line delivery harmonic voltage Vh, the distribution line delivery harmonic current Ih, the standard deviation σ _Vh of the distribution line delivery harmonic voltage, and the standard deviation σ _Ih of the distribution line delivery harmonic current are substituted into Equation 22. Thus, Formula 21 is generated.

  In other words, the evaluation function J can be obtained by placing each term of Equation 21 as in Equation 26 below. Here, the broken lines on z, h (x), and diag (R) in Equation 26 are added for explanation, the portion above the broken line is the harmonic measurement result, and the lower portion is the harmonic. The value obtained from the wave current model. Moreover, an estimation formula can be expanded by expanding z, h (x), diag (R), and x according to the number of harmonics measured and the number of customers.

  Then, the following formula 27 is used as a condition for minimizing J.

  Therefore, the estimation formula generation unit 32 generates the following formula 28 using the condition of formula 27 for the generated formula 21. This mathematical formula 28 corresponds to a harmonic estimation formula for estimating a harmonic voltage generated by a consumer. t is a natural number, and t = 0, 1, 2, 3,.

  Thereafter, the estimation formula generation unit 32 transmits Formula 28, which is the generated harmonic estimation formula, to the harmonic estimation unit 14.

(Estimation of harmonic voltage)
The harmonic estimation unit 14 receives a mathematical expression 28 that is a harmonic estimation formula from the estimation formula generation unit 32. Further, the harmonic estimation unit 14 stores the initial value x ₀ of the state variable x predetermined. For example, using the Vh obtained from Equation 3 a measured value z and the expected value μ as Ih as the initial value x _0.

The harmonic estimation unit 14 calculates x ₁ by substituting the initial value x ₀ into Equation 28. Then, to calculate the _{x 2} using the state variable _{x 1.} In this way, the harmonic estimation unit 14 sequentially updates the state variable x to converge the numerical formula 28. For example, the harmonic estimation unit 14 determines to have converged if falls within the threshold variation of x _i is predetermined. Then, the harmonic estimation unit 14 sets the convergence value of _xi as the estimated value xe of the state variable. xe is composed of the harmonic voltage of each node, and xe is an estimated value of the harmonic voltage of each node.

  Further, the harmonic estimation unit 14 acquires the node admittance matrix Yh from the node admittance matrix generation unit 31. And the harmonic estimation part 14 calculates | requires the estimated value ie of the harmonic current generate | occur | produced from a consumer from following Numerical formula 29 using the node admittance matrix Yh and the estimated value xe of a harmonic voltage.

  Further, the harmonic current flowing from the node i to the node j can be obtained by multiplying the difference between the harmonic voltages of the node j and the node i by the admittance between the node i and the node j.

  Thereafter, the harmonic estimation unit 14 transmits the obtained estimated value xe of the harmonic voltage generated by the consumer and estimated value ie of the harmonic current to the notification unit 15.

  The harmonic voltage estimation formula generation unit 13 and the harmonic estimation unit 14 collectively execute the harmonic current and harmonic voltage estimation processing described above.

  The notification unit 15 receives the estimated value of the harmonic voltage and the estimated value of the harmonic current generated from each consumer from the harmonic estimation unit 14. And the notification part 15 displays the estimated value of the harmonic voltage of each consumer, and the estimated value of the harmonic current on a monitor etc., etc., and the estimation result of the harmonic voltage and the harmonic current of each consumer is shown to an operator. To be notified.

  As described above, the harmonic voltage estimation formula generation unit 13 and the harmonic estimation unit 14 use the least square method to measure the measured harmonic voltage, the measured harmonic current, and the customer. The voltage of each node that minimizes the error between the expected value of the harmonic current and the measurement equation is obtained, and the current injected into each node is obtained using the obtained voltage of each node.

  Next, the flow of harmonic estimation processing by the harmonic estimation apparatus 1 according to the present embodiment will be described with reference to FIG. FIG. 5 is a flowchart of harmonic estimation processing by the harmonic estimation apparatus according to the first embodiment.

  The harmonic voltage estimation formula generation unit 13 acquires the harmonic current characteristics of each consumer from the storage unit 12 (step S1). That is, the harmonic voltage estimation formula generation unit 13 acquires a generation amount K of harmonic current per power consumption, a harmonic current phase angle distribution model, and a characteristic group.

  Next, the harmonic voltage estimation formula generation unit 13 acquires the distribution harmonic measurement data from the storage unit 12 (step S2). That is, the harmonic voltage estimation formula generation unit 13 acquires the distribution line delivery harmonic voltage Vh and the distribution line delivery harmonic current Ih.

  Next, the harmonic voltage estimation formula generation unit 13 acquires distribution line data from the storage unit 12 (step S3). That is, the harmonic voltage estimation formula generation unit 13 acquires the impedance of the distribution line.

  Next, the harmonic voltage estimation formula generation unit 13 selects one consumer (step S4).

Next, the harmonic voltage estimation formula generation unit 13 acquires customer facility data of the selected customer from the storage unit 12 (step S5). That is, the harmonic voltage estimation formula generation unit 13 acquires the customer's equipment capacity (P _max , P _min ) and SC capacity.

  The harmonic voltage estimation formula generation unit 13 selects one characteristic group (step S6).

The estimation formula generation unit 32 generates a harmonic current model of the consumer (Step S7). Specifically, the estimation formula generation unit 32 obtains the expected value μ _θ and standard deviation σ _θ of the phase of the harmonic current generated by the consumer from the harmonic current phase angle distribution model. Further, the estimation formula generation unit 32 uses the generation amount K of harmonic current per power consumption and the installed capacity (P _max , P _min ) of the customer to expect the amplitude of the harmonic current generated by the customer. Determine μ _A and standard deviation σ _A.

  The harmonic voltage estimation formula generation unit 13 determines whether or not the processing has been completed for all the characteristic groups belonging to the selected consumer (step S8). When the characteristic group which has not performed the process remains (step S8: No), the harmonic voltage estimation formula production | generation part 13 returns to step S6.

  On the other hand, when the process is completed for all the characteristic groups (step S8: affirmative), the harmonic voltage estimation formula generation unit 13 determines whether the process is completed for all the consumers (step S9). ). When there is a customer who has not performed the process (No at Step S9), the harmonic voltage estimation formula generation unit 13 returns to Step S4.

  On the other hand, when the processing is completed for all the consumers (step S9: affirmative), the node admittance matrix generation unit 31 generates a node admittance matrix Yh from the impedance of the distribution line and the SC capacity of each customer ( Step S10). Then, the node admittance matrix generation unit 31 transmits the generated node admittance matrix Yh to the estimation formula generation unit 32.

The estimation formula generation unit 32 uses the distribution line delivery harmonic voltage Vh, the distribution line delivery harmonic current Ih, and the predetermined measurement error zerr, and the distribution line delivery harmonic voltage standard deviation σ _Vh and the distribution line delivery harmonic. The standard deviation σ _Ih of the wave current is obtained. Further, the estimation formula calculation generation unit 32 obtains a measurement equation h (x) using the node admittance matrix Yh. Then, the estimation formula generation unit 32 generates Formula 21 by using the obtained values in Formula 26. Thereafter, the estimation formula generation unit 32 creates a harmonic estimation formula expressed by Formula 28 using Formula 27 in Formula 21 (step S11). Then, the estimation formula generation unit 32 transmits the generated harmonic estimation formula to the harmonic estimation unit 14.

  The harmonic estimation unit 14 receives the harmonic estimation formula from the estimation formula generation unit 32. And the harmonic estimation part 14 calculates the estimated value of a harmonic voltage from a harmonic estimation formula (step S12). Specifically, the harmonic estimation unit 14 updates the state variable to converge the harmonic estimation formula, and acquires the convergence value as the estimated value of the harmonic voltage.

  Furthermore, the harmonic estimation unit 14 calculates an estimated value of the harmonic current by using the node admittance matrix for the calculated estimated value of the harmonic voltage (step S13).

  The harmonic estimation unit 14 transmits the estimation result to the notification unit 15. The notification unit 15 notifies the operator of the estimation result received from the harmonic estimation unit 14 (step S14).

  Next, the accuracy of the estimation result of harmonics by the harmonic estimation apparatus 1 according to the present embodiment will be described together. Below, the case where a harmonic is estimated using the distribution line model of FIG. 1 is demonstrated. Here, a case where the line capacity is set to 4000 kVA and the length of the trunk line is set to about 4 km will be described.

First, preconditions for explaining harmonic estimation by the harmonic estimation apparatus 1 are determined. FIG. 6 is a diagram illustrating the setting of the harmonic characteristics of each consumer for each characteristic group. The characteristic groups in FIG. 6 correspond to characteristic groups A and B shown in FIG. In FIG. 6, the generation amount (K) of the harmonic current per power consumption, the expected value (μ _θ ) and the standard deviation (σ _θ ) of the generated harmonic phase are shown for each characteristic group. ing. Nodes 112, 115 and 116 belong to group A. Nodes 111, 113, and 114 belong to group B.

  Moreover, FIG. 7 is a figure showing the setting of the impedance of a bank transformer and a distribution line. The trunk line 101-111 represents the impedance between the bus voltage measurement point 101 and the node 111 in FIG. Further, trunk lines 111-112, 112-113, and 113-114 represent impedances between nodes having respective signs. Branch lines 111-115 and 112-116 also represent the impedance between the nodes having the respective symbols.

  FIG. 8 is a diagram showing the setting of the SC capacity allocated to each consumer. As shown in FIG. 1, SCs are arranged at nodes 112, 115 and 116. The serial reactorless SC 121 of the node 112 has a capacity of 300 kvar. Further, the SC 151 with the series reactor of the node 115 has an SC capacity of 100 kvar, and further 6% of the series reactor is arranged. This series reactor 6% is k = 0.06 in Equation 2. Further, the serial reactorless SC 161 of the node 116 has an SC capacity of 600 kvar.

  FIG. 9A is a diagram illustrating setting of the capacity of customers belonging to group A. FIG. 9B is a diagram illustrating setting of the capacity of customers belonging to group B. Here, the installed capacity of each consumer shown in FIGS. 9A and 9B is used.

  In the description here, the phase angle of the upper fifth harmonic voltage of the bank transformer 100 is as shown in FIG. 10, and the phase angle of the fundamental voltage at the bus voltage measurement point 101 at no load is used as a reference. 0 degrees. The distortion factor of the fifth harmonic voltage is 1.0% with respect to the amplitude of the fundamental voltage. FIG. 10 is a diagram illustrating the setting of the fifth harmonic voltage of the system.

  Further, for verification of the estimation result, assuming the actual load, the load of each customer is set as shown in FIG. 11, and the simulation is performed based on the set load, and the harmonic voltage of each node and each The result of the harmonic current injected into the node is the true value. FIG. 11 is a diagram showing the value of the customer load set assuming an actual load. Then, the distribution voltage and current of the distribution line of the substation are extracted as measurement data from the obtained true value, and the harmonic voltage of each node calculated by the harmonic estimation device 1 according to the present embodiment using the extracted measurement data. And the harmonic current injected into each node is an estimated value.

  FIG. 12 is a diagram showing the true value and the estimated value of the fifth harmonic voltage as vectors. FIG. 12 shows a pair of arrows 500 to 507 in which a solid line arrow and a broken line arrow are paired. The solid line arrow included in each arrow pair represents a true value, and the broken line arrow represents an estimated value. Yes. An arrow pair 500 represents the true value and the estimated value of the fifth harmonic voltage generated at the upper level of the bank transformer 100. An arrow pair 501 represents the true value and the estimated value of the fifth harmonic voltage generated at the bus voltage measurement point 101. Arrow pair 502 represents the true value and estimated value of the fifth harmonic voltage generated at node 111. Arrow pair 503 represents the true value and estimated value of the fifth harmonic voltage generated at node 112. Arrow pair 504 represents the true value and estimated value of the fifth harmonic voltage generated at node 113. Arrow pair 505 represents the true value and estimated value of the fifth harmonic voltage generated at node 114. Arrow pair 506 represents the true value and estimated value of the fifth harmonic voltage generated at node 115. Arrow pair 507 represents the true value and estimated value of the fifth harmonic voltage generated at node 116. The vector shown here represents the amplitude as an effective value.

  FIG. 13A is a diagram illustrating a comparison of effective values of the fifth harmonic voltage. FIG. 13B is a diagram illustrating a comparison of the phase angles of the fifth harmonic voltage. 13A and 13B are diagrams in which the vector of FIG. 12 is divided into amplitude and phase angle, respectively. In FIG. 13A, the vertical axis represents the harmonic voltage effective value, that is, the amplitude of the harmonic voltage, and the horizontal axis represents the location where the harmonic voltage is generated. In FIG. 13B, the vertical axis represents the harmonic voltage phase angle, and the horizontal axis represents the location where the harmonic voltage is generated. In both FIGS. 13A and 13B, a black bar graph represents a true value, and a white bar graph represents an estimated value.

  Furthermore, FIG. 14 shows a result of numerical comparison between the true value of the harmonic voltage in FIG. 12 and the amplitude and phase of the estimated value individually. FIG. 14 is a diagram showing a numerical comparison between the true value and the estimated value of the fifth harmonic voltage.

  As shown in FIGS. 12 to 14, it can be confirmed that the true value and the estimated value of the fifth harmonic voltage generated at each location are in good agreement.

  FIG. 15 is a diagram representing the true value and the estimated value of the fifth harmonic current as vectors. In FIG. 15, arrow pairs 510 to 516 in which a solid line arrow and a broken line arrow are paired are described. A solid line arrow included in each arrow pair represents a true value, and a broken line arrow represents an estimated value. Yes. Arrow pair 510 represents the true value and estimated value of the fifth harmonic current flowing from bus voltage measurement point 101 to node 111. Arrow pair 511 represents the true value and estimated value of the fifth harmonic current generated at node 111. Arrow pair 512 represents the true value and estimated value of the fifth harmonic current generated at node 112. Arrow pair 513 represents the true value and estimated value of the fifth harmonic current generated at node 113. Arrow pair 514 represents the true value and estimated value of the fifth harmonic current generated at node 114. Arrow pair 515 represents the true value and estimated value of the fifth harmonic current generated at node 115. Arrow pair 516 represents the true value and estimated value of the fifth harmonic current generated at node 116. The vector shown here represents the amplitude as an effective value.

  FIG. 16A is a diagram showing a comparison of effective values of the fifth harmonic current. FIG. 16B is a diagram illustrating a comparison of the phase angles of the fifth harmonic current. 16A and 16B are diagrams in which the vector of FIG. 12 is divided into amplitude and phase angle, respectively. In FIG. 16A, the vertical axis represents the harmonic current effective value, that is, the amplitude of the harmonic current, and the horizontal axis represents the generation location of the harmonic current. In FIG. 16B, the vertical axis represents the harmonic current phase angle, and the horizontal axis represents the location where the harmonic current is generated. 16A and 16B, the black bar graph represents the true value, and the white bar graph represents the estimated value.

  Further, FIG. 17 shows a result of individual numerical comparison between the true value of the harmonic current and the amplitude and phase angle of the estimated value in FIG. FIG. 17 is a diagram showing a numerical comparison between the true value and the estimated value of the fifth harmonic current.

  As shown in FIGS. 15 to 17, it can be confirmed that the true value and the estimated value of the fifth harmonic current generated at each location are in good agreement.

  Thus, it turns out that the estimated value of the harmonic voltage and electric current in each place on a distribution line calculated | required using the harmonic estimation apparatus which concerns on a present Example approximates a measured value. That is, the estimated values of the harmonic voltage and the harmonic current at each location on the distribution line obtained using the harmonic estimation apparatus according to the present embodiment are used for analyzing the mechanism by grasping the harmonics of the entire distribution line. This can contribute to countermeasures against the occurrence of voltage distortion.

  As described above, the harmonic estimation apparatus according to the present embodiment uses the harmonic method of least squares using the customer's harmonic current characteristics, distribution harmonic measurement data, distribution line data, and customer facility data. An estimated value of the voltage of each node that minimizes the error between the wave measurement value and the calculated value is obtained. Furthermore, the harmonic estimation apparatus according to the present embodiment obtains the current of each node using the obtained estimated value of the voltage of each node. Thus, the harmonic estimation apparatus according to the present embodiment can obtain the harmonics generated from each customer connected to the distribution line without using the measured value of the harmonics generated from the customer. Therefore, the trouble of measuring a large number of harmonics can be saved, and the state of harmonics in the distribution system can be easily estimated.

  The harmonic estimation apparatus according to the present embodiment uses the voltage of each node of the fundamental wave estimated using the substation measurement data, and the phase angle of the harmonic current generated from the customer due to the power flow of the fundamental wave Correct the deviation. FIG. 18 is a block diagram of a harmonic estimation apparatus according to the second embodiment. In the following description, the description of the functions of the same parts as those in the first embodiment will be omitted.

  The harmonic estimation apparatus 1 according to the present embodiment includes a phase shift calculation unit 16 in addition to the input control unit 11, the storage unit 12, the harmonic voltage estimation formula generation unit 13, the harmonic estimation unit 14, and the notification unit 15. doing.

  The input control unit 11 receives input of distribution measurement data in addition to the information described in the first embodiment. The distribution change measurement data receives an input of a fundamental wave voltage for distribution line delivery and a fundamental wave current for delivery line delivery from the operator. Specifically, the input control unit 11 receives input of information expressed by the bus voltage and the active power P and the reactive power Q of the distribution line delivery current as the distribution line delivery voltage and the distribution line delivery current. Then, the input control unit 11 stores the received distribution measurement data in the storage unit 12.

  The phase shift calculation unit 16 acquires the distribution measurement data, the distribution line impedance, the customer's facility capacity, and the customer's SC capacity from the storage unit 12. Further, the phase shift calculation unit 16 acquires the node admittance matrix Yh from the node admittance matrix generation unit 31.

  In addition, the phase shift calculation unit 16 stores a measurement error zerr in advance, similarly to the estimation value generation unit for the measurement value of the distribution measurement data. Then, the phase shift calculation unit 16 obtains the standard deviation of the fundamental wave sending voltage and the standard deviation of the fundamental wave sending current using Equation 25 as the standard deviation of the measured value. Similarly, the standard deviation of the active power P and the reactive power Q of the power flow of the distribution line is obtained using Formula 25.

Further, the phase shift calculation unit 16 sets the maximum installed capacity P _max of each consumer as the maximum value of the active power and the minimum installed capacity P _min as the minimum value of the active power, and uses obtaining an expected value mu _P of the active power in.

Moreover, the phase shift calculation part 16 calculates | requires the standard deviation (sigma) _P of the active power in each consumer using the following Numerical formula 31 from the maximum installation capacity _Pmax and minimum installation capacity _{Pmin of} each consumer.

Next, the phase shift calculation unit 16 calculates the maximum value Q _max of reactive power in each consumer by the following equation 32 assuming the power factor pf.

Further, the phase shift calculation unit 16 calculates the minimum value Q _min of reactive power in each consumer using the following Expression 33.

Then, the phase shift calculation unit 16 calculates the expected value μ _Q of reactive power at each consumer using the following formula 34 from the maximum value and the maximum value of reactive power.

Further, the phase shift calculation unit 16 calculates the standard deviation σ _Q of the reactive power at each customer using the following formula 35 from the maximum value and the maximum value of the reactive power.

Here, the measurement equation h (x) will be described in detail. The effective power P _i injected to the node i is expressed by the following Expression 36.

Further, the reactive power Q _i injected into the node i is expressed by the following Expression 37.

Further, by substituting Equation 36 and Equation 37 into Equation 10, the sensitivity H (x) of the measurement equation of the active power P _i and the reactive power Q _i injected into the node i is obtained as in the following Equations 38 and 39.

Here, the measurement equation h (x) will be described in detail. In the node i, the effective power P _ij flowing from the node i to the node j is expressed by the following formula 40.

In node i, the measurement equation of reactive power Q _ij flowing from node i to node j is expressed by the following equation 41.

Further, by substituting Equation 40 and Equation 41 into Equation 10, the sensitivity H () of the measurement equation of the active power P _ij and the reactive power Q _ij flowing from the node i to the node j at the node i as in the following Equations 42 and 43: x) is obtained.

  In Equations 42 and 43, there is no condition for i = j.

  Then, the phase shift calculation unit 16 generates a fundamental wave estimation formula using a mathematical formula obtained by correcting the mathematical formula 5 into a formula related to the voltage of the fundamental wave with the harmonic order n = 1.

Specifically, Formula 21 is corrected as follows. That is, the measured value Vh of the distribution line delivery harmonic voltage is converted into the measurement value of the fundamental delivery voltage. Further, the measured value Ih of the distribution line delivery harmonic current is converted into the measurement values of the fundamental wave delivery currents P _ij and Q _ij . Furthermore, σ _Vh is converted into a standard deviation of the fundamental wave delivery voltage, and σ _Ih is transformed into a standard deviation of the fundamental wave delivery current. Also, the expected value mu _A of the amplitude of the harmonic current generated in the customer is converted to the expected value mu _P of the active power in the consumer. Further, the expected value μ _θ of the phase angle of the harmonic current generated at the consumer is converted into the expected value μ _Q of reactive power at the consumer. Further, σ _A is converted into a standard deviation σ _P of active power at the consumer, and σ _θ is converted into a standard deviation σ _Q of reactive power at the consumer. Specifically, an evaluation function J for generating a fundamental wave estimation formula is obtained by placing each term of Formula 21 as in Formula 44 below. Here, the broken lines described in z, h (x), and diag (R) in Formula 44 are added for explanation, and the part above the broken line is the measurement result of the distribution line delivery, and the lower part is The value obtained from customer data is shown. Further, the estimation formula can be expanded by expanding z, h (x), diag (R), and x according to the number of measured fundamental waves and the number of consumers.

  And using this evaluation function J, the phase shift calculation part 16 can produce | generate a fundamental wave estimation formula by the method similar to the production | generation of the harmonic estimation formula by the estimation formula production | generation part 32 demonstrated in Example 1. FIG. .

  Furthermore, the phase shift calculation unit 16 uses the generated fundamental wave estimation formula to calculate the fundamental voltage at each consumer in the same manner as the estimation value calculated by the harmonic estimation unit 14 described in the first embodiment. Can be sought. That is, the phase shift calculation unit 16 obtains the voltage of each node of the fundamental wave that minimizes the error between the measured value of the fundamental wave and the calculated value of the fundamental wave in the transformation by the least square method.

  Here, the estimated value of the voltage at each node is represented by the magnitude and phase angle of the voltage. Therefore, the phase shift calculation unit 16 obtains a difference between the phase angle of the fundamental wave sending voltage and the phase angle of the estimated value for each customer, and calculates the phase angle shift for each customer. Then, the phase shift calculation unit 16 transmits the calculated phase angle shift in each consumer to the estimation formula generation unit 32.

The estimation formula calculation unit 32 receives a phase angle shift at each consumer from the phase shift calculation unit 16. Then, the estimation formula calculation unit 32 sets the phase angle shift at each customer to the expected value μθ of the phase angle of the harmonic current generated at each customer, which is 5 times higher than the harmonic, ie, 5th. by adding the value for correcting the expected value mu _theta phase angle of the harmonic current generated by each customer. In this way, the estimation formula calculation unit 32 corrects the distribution of the phase angle of the harmonic current generated at each consumer.

The following Expression 45 is obtained by using the estimated value θ _i of the phase angle of the fundamental wave voltage at each consumer with the phase angle θ ₀ of the fundamental wave sending voltage as a reference, and the h-th harmonic generated at the consumer. An expected value μ _θ− ′ obtained by correcting the expected value μ _θ− of the phase angle of the wave current.

  And the estimation formula calculation part 32 produces | generates the harmonic estimation formula of the harmonic voltage which generate | occur | produces in each consumer by the method similar to Example 1 using the distribution of the corrected phase angle. Thereafter, the harmonic estimation unit 14 uses the harmonic estimation formula generated by the estimation formula calculation unit 32 to obtain the estimated values of the harmonic voltage and the harmonic current generated in each consumer.

  Next, with reference to FIG. 19, the flow of the harmonic estimation process by the harmonic estimation apparatus 1 according to the present embodiment will be described. FIG. 19 is a flowchart of harmonic estimation processing by the harmonic estimation apparatus according to the second embodiment.

  Further, the phase shift calculation unit 16 acquires distribution measurement data that is measurement data of the distribution substation from the storage unit 12 (step S101). Distribution measurement data includes distribution line delivery voltage and distribution line delivery current.

  Furthermore, the phase shift calculation unit 16 acquires distribution line data from the storage unit 12 (step S102).

  The phase shift calculation unit 16 selects a consumer (step S103). Next, the phase shift calculation unit 16 acquires customer facility data (step S104). And the phase shift calculation part 16 determines whether all the consumers were selected (step S105). When there is an unselected customer (No at Step S105), the phase shift calculation unit 16 returns to Step S103.

  On the other hand, when all the consumers are selected (step S105: Yes), the node admittance matrix generation unit 31 generates the node admittance matrix Yh from the impedance of the distribution line and the SC capacity of each customer (step S106). ). Then, the node admittance matrix generation unit 31 transmits the generated node admittance matrix Yh to the phase shift calculation unit 16.

  The phase shift calculation part 16 produces | generates the fundamental wave voltage estimation formula which estimates the voltage of the fundamental wave in a consumer (step S107). Next, the phase shift calculation unit 16 calculates an estimated value of the fundamental wave voltage at the consumer (step S108).

  Then, the phase shift calculation unit 16 calculates the shift in the phase angle of the fundamental wave voltage at the consumer from the estimated value of the fundamental wave voltage at the consumer and the estimated value of the fundamental wave voltage at the change (step S109).

  Next, the phase shift calculation unit 16 calculates the phase angle shift of the fundamental wave voltage in all the consumers connected to the distribution line in order to correct the phase angle distribution of the harmonic current of the consumer. The harmonic order h is multiplied and transmitted to the estimation formula generator 32 (step S110).

  Then, the harmonic estimation apparatus 1 performs the process of step S1-14 of FIG. 5, and calculates the estimated value of the harmonic voltage and harmonic current of each consumer. When the process of step S7 is executed, the estimation formula generation unit 32 executes a correction process for the phase angle distribution of the customer harmonic current. The notification unit 15 notifies the operator of the estimated values of the harmonic voltage and current generated at each consumer (step S111).

  As described above, the harmonic estimation apparatus according to the present embodiment is generated in each customer using the phase angle distribution model of the harmonic current corrected by using the phase angle deviation of the fundamental wave voltage. Calculate estimated values of harmonic voltage and harmonic current.

  In this respect, when the load current corresponding to the active power increases due to the inductive reactance component of the line, the voltage phase angle of the fundamental wave at the end of the line is delayed several degrees with respect to the bus voltage of the distribution line. At this time, the load device that generates the harmonic current generates a harmonic current with reference to the voltage phase angle at the point where the device is connected. Therefore, if there is a deviation in the phase angle of the fundamental voltage, the generated harmonic current In the phase angle, a shift of the order of the harmonic of the shift in the phase angle of the fundamental voltage occurs. The deviation in the phase angle of the fundamental voltage affects the estimation result of the harmonic voltage.

  Therefore, as in the harmonic estimation apparatus according to the present embodiment, the phase angle distribution of the harmonic current can be corrected by correcting the phase angle distribution of the harmonic current with the deviation of the phase angle of the fundamental wave voltage. It is possible to obtain the estimated values of the harmonic voltage and current with higher accuracy.

  FIG. 20 is a block diagram of a harmonic estimation apparatus according to the third embodiment. The harmonic estimation apparatus 1 according to the present embodiment is different from the second embodiment in that the active power consumed by the load of each consumer and the output of the distributed power source arranged in each consumer are estimated. FIG. 20 is a block diagram of a harmonic estimation apparatus according to the third embodiment. In the following description, description of functions of the same parts as those in the second embodiment is omitted.

  The harmonic estimation apparatus 1 according to the present embodiment includes a power consumption / distributed power supply output estimation unit 17 in addition to the units of the second embodiment.

  The phase shift calculation unit 16 transmits the fundamental wave voltage of each node and the node admittance matrix of the fundamental wave to the power consumption / distributed power supply output estimation unit 17.

  The harmonic estimation unit 14 transmits the calculated harmonic current estimated value ie generated at each consumer to the power consumption / distributed power supply output estimation unit 17.

  The power consumption / distributed power output estimation unit 17 uses the fundamental wave voltage of each node and the fundamental node admittance matrix received from the phase shift calculation unit 16 to obtain consumer power consumption P1 and reactive power. Furthermore, the power consumption / distributed power output estimation unit 17 adds the reciprocal of the generation amount K of the harmonic current per power consumption to the estimated value ie of the harmonic current generated at each consumer received from the harmonic estimation unit 14. By multiplying, the power consumption P2 when the harmonic current ie occurs is obtained.

  Since the output of the distributed power supply connected to the distribution line does not include harmonics, the power consumption P2 obtained from the estimated value ie of the harmonic current is the power consumed by the load device. In this manner, the power consumption / distributed power output estimation unit 17 estimates the power consumption P2 of the load device of each consumer. On the other hand, the consumer power consumption P1 obtained using the fundamental voltage of each node and the fundamental wave node admittance matrix includes the power consumption P2 of the load device and the output P3 of the distributed power supply. That is, the power consumption P1 of the consumer is a value obtained by subtracting the output P3 of the distributed power source from the power consumption P2 of the load device (P1 = P2-P3).

  Furthermore, the power consumption / distributed power output estimation unit 17 calculates the distributed power output P3 by calculating P3 = P2-P1 at each consumer.

  Then, the power consumption / distributed power output estimation unit 17 transmits the estimated value of the active power consumed by the load of each consumer and the output of the distributed power source linked to each consumer to the notification unit 15.

  The notification unit 15 receives the estimated value of the active power consumed by the load of each consumer and the output of the distributed power source provided to each consumer from the power consumption / distributed power source output estimation unit 17. And the notification part 15 notifies an operator by displaying on the monitor the estimated value of the active power consumed with the load of each consumer, and the information of the output of the distributed power source provided in each consumer. .

  As described above, the harmonic estimation apparatus according to the present embodiment, in addition to the estimated value of harmonics generated at each consumer, the estimated value of active power consumed by the load of each consumer and each It is possible to notify the output of the distributed power source connected to the consumer. Thereby, the operator can acquire more information on the customer connected to the distribution line, and can more appropriately operate and manage the distribution line.

DESCRIPTION OF SYMBOLS 1 Harmonic estimation apparatus 11 Input control part 12 Storage part 13 Harmonic voltage estimation formula production | generation part 14 Harmonic estimation part 15 Notification part 16 Phase shift calculation part 17 Power consumption / distributed power supply output estimation part 31 Node admittance matrix production | generation part 32 Estimation Expression generator

Claims (11)

Generation amount of harmonic current per power consumption in consumers connected to distribution lines, distribution model of harmonic current generated in each of the consumers, harmonic group that classifies the harmonic current generated from the consumers, Based on the distribution harmonic voltage of the distribution line, the distribution harmonic current of the distribution line, the impedance in the distribution line, the load capacity of each consumer, and the capacity of the power factor improving capacitor in each consumer An estimation formula generation unit that generates a harmonic estimation formula including a state variable for obtaining an estimated value of the harmonic voltage at each node of the connection point of each wire and the connection point of each consumer;
An estimated value calculation unit that calculates an estimated value of the harmonic voltage at each node using a least square method based on the harmonic estimation formula generated by the estimation formula generation unit. Wave estimation device.   The estimation formula generation unit includes a matrix creation unit that creates a node admittance matrix based on the impedance in the distribution line, the capacity of the load of each consumer, and the capacity of the power factor correction capacitor in each consumer. The harmonic estimation apparatus according to claim 1.   The harmonic estimation apparatus according to claim 1, wherein the estimation formula generation unit generates the harmonic estimation formula at each node using a measurement equation including a state variable and a measurement error.   The estimated value calculating unit further calculates an estimated value of the harmonic current at each node using the calculated estimated value of the harmonic voltage and the node admittance matrix created by the matrix creating unit. The harmonic estimation apparatus according to claim 2.   The matrix creation unit uses a value obtained by multiplying the capacitive reactance of the fundamental wave of the power factor improving capacitor at each consumer by one-order of the harmonic component as a harmonic reactance, and induces the power factor improving capacitor. The harmonic estimation apparatus according to claim 2, wherein the node admittance matrix is created using a value obtained by multiplying the characteristic reactance by the order of the harmonic component as a harmonic reactance. Based on the distribution voltage of the distribution line, the distribution current of the distribution line, the impedance in the distribution line, the load capacity of each consumer, and the capacity of the power factor improving capacitor in each consumer, A phase calculator that calculates a voltage phase angle shift of the flowing fundamental wave;
The estimation formula generation unit corrects the phase angle distribution of the harmonic current generated in each consumer using the voltage phase shift of the fundamental wave calculated by the phase calculation unit. Harmonic estimation apparatus as described in any one of claim | item 1 -5. The phase calculation unit includes:
Based on a measurement equation including a state variable and a measurement error, a fundamental wave voltage estimation expression generation unit that generates an estimation expression of the fundamental wave voltage at each of the nodes;
Based on the fundamental voltage estimation formula generated by the fundamental voltage estimation formula generator, a fundamental voltage estimator that calculates an estimate of the fundamental voltage at each node using the least squares method;
The calculation unit for obtaining a phase angle deviation between the estimated value of the fundamental wave voltage of each consumer calculated by the fundamental wave voltage estimation unit and the estimated value of the distribution line delivery voltage. 6. Harmonic estimation apparatus according to 6. Based on the distribution voltage of the distribution line, the distribution current of the distribution line, the impedance in the distribution line, the load capacity of each consumer, and the capacity of the power factor improving capacitor in each consumer, A phase calculation unit that calculates a deviation of a voltage phase angle of a flowing fundamental wave, and calculates an estimated value of active power and reactive power in each consumer based on the load capacity of each consumer;
Based on the estimated value of active power and reactive power in each consumer calculated by the phase calculator and the estimated value of harmonic current in each node calculated by the estimated value calculator, in each consumer The harmonic estimation apparatus according to claim 4 , further comprising a power consumption calculation unit that calculates power consumption.   The power consumption calculation unit is based on the estimated value of active power and reactive power in each consumer calculated by the phase calculation unit and the estimated value of harmonic current in each node calculated by the estimated value calculation unit. The harmonic estimation apparatus according to claim 8, wherein an output of a distributed power source at each consumer is estimated. Generation amount of harmonic current per power consumption in consumers connected to the distribution line, phase angle distribution of harmonic current generated in each of the consumers, harmonic group that classifies the harmonic current generated from the consumers, Based on the delivery harmonic voltage of the distribution line, the delivery harmonic current of the distribution line, the impedance in the distribution line, the load capacity of each consumer, and the capacity of the power factor improving capacitor in each consumer, A harmonic estimation formula including a state variable is generated for obtaining an estimated value of the harmonic voltage at each node of the connection point of each distribution line and each consumer,
A harmonic estimation method, wherein an estimated value of a harmonic voltage at each of the nodes is calculated using a least square method based on the generated harmonic estimation formula. Generation amount of harmonic current per power consumption in consumers connected to the distribution line, phase angle distribution of harmonic current generated in each of the consumers, harmonic group that classifies the harmonic current generated from the consumers, Based on the delivery harmonic voltage of the distribution line, the delivery harmonic current of the distribution line, the impedance in the distribution line, the load capacity of each consumer, and the capacity of the power factor improving capacitor in each consumer, A harmonic estimation formula including a state variable is generated for obtaining an estimated value of the harmonic voltage at each node of the connection point of each distribution line and each consumer,
A harmonic estimation program that causes a computer to execute a process of calculating an estimated value of a harmonic voltage at each of the nodes using a least square method based on the generated harmonic estimation formula.

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