JP6540460B2 - Connection phase determination reliability calculation program, apparatus and method - Google Patents

Description

  The present invention relates to a connection phase determination reliability calculation program, a connection phase determination reliability calculation device, and a connection phase determination reliability calculation method.

  Conventionally, a technique has been proposed for determining the connection phase of a transformer even when information on power consumption of only a part of consumers connected to the transformer is available. In this technique, the phase current due to the power consumed by at least one consumer connected to a transformer connected to any of the phases corresponding to the two combinations of distribution lines is calculated. Then, each of the correlation coefficients between the phase current and each of the line currents flowing through each of the plurality of distribution lines is calculated, and the phase is a combination of distribution lines other than the distribution line corresponding to the line current having the smallest correlation coefficient. Is determined as the phase to which the transformer is connected.

JP, 2015-94752, A JP, 2015-161607, A

  As for the connection phase determination method of the prior art, if the conditions (data use period, smart meter introduction rate, etc.) on the use data side are good as an example, the connection phase can be determined with a correct answer rate of 95% or more. However, in addition to the fact that misjudgment can occur stochastically, smart meters for measuring the power consumption of consumers are still in the transition period of widespread use (the adoption rate in 2020 is 80% Target), for a while is expected to operate under adverse conditions. Under such circumstances, in addition to the determination of the transformer connection phase, if the reliability of the determination result can be estimated, the complementary operation is such that the connection phase is measured manually, etc. by limiting to the transformer with low reliability. It will be possible and there will be great benefits in practical operation.

  However, in the prior art, only the determination result of the connection phase is output, and the reliability thereof is not calculated. Also, as a general method of estimating the degree of reliability in the determination problem, a method of obtaining the degree of reliability by applying an index of the determination and logistic regression using correct answer information whether or not it is correct is known. ing. However, in the prior art transformer connected phase determination, since the purpose is primarily the determination of the connected phase, correct answer information can not be used.

  In one aspect, it is an object to obtain the reliability of the determination result of the trans connection phase under the condition that there is no correct information.

  In one aspect, the present invention provides a phase current due to power consumed by at least one consumer connected to a transformer connected to any of a plurality of phases corresponding to a combination of two of a plurality of distribution lines And each of the line current flowing through each of the plurality of distribution lines. Then, the phase to which the transformer is connected is determined based on each of the correlation values indicating the correlation between the phase current and each of the line current. Furthermore, it represents a distribution of vectors having each of the correlation values as an element, and estimates a mixed distribution model having a plurality of components corresponding to each of the plurality of phases, and the transformer is connected based on the mixed distribution model. The reliability of the judgment result of the selected phase is calculated.

  As one aspect, it has an effect that it is possible to obtain the reliability of the determination result of the trans connection phase under the condition that there is no correct information.

It is the schematic which shows an example of a distribution network. It is a block diagram which shows schematic structure of a connection phase determination reliability calculation apparatus. It is the schematic which represented the distribution system by virtual circuit structure. It is a figure which shows distribution of a correlation coefficient vector. It is a figure for demonstrating the dimension compression by orthogonal projection. It is a figure which shows the projection to plane (pi). It is a figure which shows an example of the calculated reliability. It is a block diagram which shows schematic structure of the computer which functions as a connection phase determination reliability calculation apparatus. It is a flowchart which shows an example of a connection phase determination reliability calculation process. It is a figure which shows an example of a power distribution information table. It is a figure which shows an example of a power consumption data table. It is a figure which shows an example of a line current data table. It is a flow chart which shows an example of judgment calculation processing. It is a figure which shows an example of an output result.

  Hereinafter, an example of the embodiment according to the present invention will be described in detail with reference to the drawings.

<On transformer connection phase determination problem>
In the regulatory reform of the power business including the liberalization of the power market and the spread of renewable power, the functions required of the transmission and distribution system, which is a means of transmitting electric power, have recently changed significantly. Among them, in the power distribution system, dealing with distributed power sources such as photovoltaic power generation (Photovoltaics, PV) expected to be introduced in large numbers in the future is a major issue. As an example, it is necessary to manage the voltage so that the supply voltage of the distribution system falls within a certain range (for example, 101 ± 6 V, 202 ± 20 V, etc.).

  The main problem in the voltage management of the conventional distribution system was the voltage drop due to overload, but in the distribution system of the distributed power supply, the reverse power flow for selling electricity occurs, so the voltage rise at that time Is a major problem. Even in the current distribution system, design and operation have been made on the premise of preventing voltage drop, but the problem of voltage rise is hardly assumed. In order to cope with the problem of the voltage rise, examination of a new voltage management system has been started in various places such as utilizing various passive devices and active devices on power electronics.

  Here, in the case of examining a new voltage management system, the problem of the pole transformer connected phase emerges. This means that in the three-phase three-wire distribution system, it is not known which of the three combinations of distribution lines (phases) the transformer at the contact point with the customer is connected to the high voltage side It is a problem. With regard to the connection phase of the transformer, in order to balance three-phase alternating current, loads of multiple customers are selected to be as balanced as possible, but the connection phase of the transformer to which each customer is connected is specifically There is almost no record and control about which one. For this reason, when considering the application of a new voltage management system, it is necessary to first consider it from the investigation of the current state of the connecting phase of the transformer.

  Usually, one transformer is installed for 10 to 20 customers, and considering the entire distribution system, the number of transformers whose connection phase should be determined is enormous. Therefore, when the connection phase of the transformer of the whole distribution system is manually determined, a large cost and time will be spent.

  Therefore, in each of the following embodiments, it is an object to determine the connection phase of the transformer even when only the information of the power consumption of a part of the consumers connected to the transformer can be used. Here, the transformer connection phase determination problem assumed in each embodiment will be described in more detail.

  An example of a distribution network is shown in FIG. The distribution system is a three-phase three-wire system, and there are three possibilities for the connection phase of the pole transformer. Here, the distribution lines on the high voltage side (6.6 kV) are referred to as a-line, b-line and c-line, and ab phase, bc phase and It is considered ca. Although most of the actual pole transformers are single-phase, here, the pole transformers are represented by three phases in order to express that there are a plurality of possibilities in the connection phase. In an actual distribution system, a transformer is usually connected to only one phase, and an operation is performed to balance three-phase loads by assigning one of the phases to each transformer.

  Several switches with a built-in sensor are installed on the high voltage side of the power distribution system, and it is possible to obtain measured values of three types of line current and line voltage. The consumer is connected to the secondary side of the transformer and receives a supply of contract voltage (e.g. 100V). A power meter with a communication function such as a smart meter is introduced to some of the consumers, and the power consumption of the customers is measured over time. Although information on the connection relationship between each customer and the transformer is managed by the electric power company, it is generally not recorded and managed until the information on the connection phase to which the transformer is connected.

  Although the information on the transformer connection phase has important meaning for the voltage management of the distribution system, its investigation is costly and time-consuming. Therefore, it is considered to determine the transformer connection phase based on the measurement information of the sensor built-in switch and the power meter on the customer side. In the following, specific conditions of the “transformer connection phase determination problem” will be described.

  The information that can be used to determine the transformer connection phase is as follows.

(1) Measured value of sensor built-in switch ・ Line current on high voltage side of distribution system (a line, b line, c line)
・ Line voltage on the high voltage side of the distribution system (between a and b, between b and c, and between c and a)
(2) Measured value of power meter with communication function ・ Consumer's power consumption (only for some customers who have installed power meter with communication function)
(3) Management information of customers ・ Connection relationship between each customer and transformer (The connection phase of transformer is unknown)

  Although the switch with a built-in sensor in (1) is currently being introduced into the distribution system, it is practical to install one to several or so for one feeder. A feeder is a part of a distribution system extending radially from a distribution substation. In an urban area, one feeder usually includes about 1000 consumers. The penetration rate of the power meter with communication function in (2) is less than 2% as of February 2012, but it is thought that installation will progress rapidly in the future. Although the sampling interval which measures electric energy with a power meter changes with models of a power meter, it is an interval of 30 minutes, for example. As for (3), in addition to the connection relationship information, information on the usage form of the connection phase of the transformer may be included. For example, the connection phase of the power line is usually limited to one per transformer.

  As described above, determining the transformer connection phase based on the currently available information is the “trans connection phase determination problem” which is a premise of the present embodiment.

  When trying to determine the connection relationship of a circuit such as a transformer connection phase from the electrical information of the distribution system, it is generally natural to be based on circuit theoretical calculation. However, the above-mentioned available information is overwhelmingly lacking in information for performing deterministic circuit calculations. Therefore, it is difficult to determine the transformer connection phase by circuit theoretical calculation based on the available information. Therefore, as a second best solution, it is conceivable to determine the trans-connected phase by using statistical correlation information of available information or the like.

  It is conceivable to use power information in order to carry out a correlation analysis method in view of the combination of information available on the high voltage side and low voltage side (customer side) of the distribution system. For power information, direct measurements can be obtained on both the high and low side. It is assumed that the power of each distribution line on the high voltage side can be calculated, and the distribution line serving as the power supply path is uniquely determined for the transformer connection phase to which the customer is connected. In this case, it is possible to determine the transformer connection phase by performing correlation analysis between time series data of power by distribution line and time series data of power consumption of a customer.

  However, for example, as shown in FIG. 1, correlation analysis using power information is applied to a distribution system in which each pole transformer is connected to any one of three phases in a three-phase three-wire system. In principle, it is difficult to determine the transformer connection phase based on the conventional method (the reason will be described later). Therefore, in the present embodiment, determination of a transformer connected phase is performed by correlation analysis using current information, not power information.

<Configuration of Connection Phase Determination Reliability Calculation Device>
As shown in FIG. 2, the connection phase determination reliability calculation device 10 according to the present embodiment includes the customer selection unit 12, the current value calculation unit 14, the correlation coefficient calculation unit 16, the connection phase determination unit 18, and the reliability calculation. A unit 19 and an output processing unit 20 are provided. The connection phase determination unit 18 is an example of the determination unit of the present invention, and the reliability calculation unit 19 is an example of the estimation unit and the calculation unit of the present invention.

  The consumer selection unit 12 receives as an input a transformer ID indicating a transformer for determining the connection phase, and selects a distribution section and a consumer corresponding to the transformer ID.

  Specifically, for example, a distribution system as shown in FIG. 3 is considered. The example of FIG. 3 is a three-phase three-wire circuit, and the transformer is assumed to be a virtually triangular three-phase transformer. In many of the pole transformers in the actual distribution system, single-phase three-wire type is used, and usually only one phase is used, but in FIG. 3, there are multiple possibilities for the connection phase. In order to handle it, the distribution system is expressed by a virtual circuit configuration. In the present embodiment, a section sandwiched between two sensor incorporated switches is referred to as a “distribution section”. Also, the consumer is connected to the secondary side of the transformer.

  The correspondence relationship between the power distribution section and the transformers belonging to the power distribution section, and the correspondence relationship between the transformer and the consumers connected to the transformer are stored in the power distribution information storage unit 22 as power distribution information. The customer selection unit 12 refers to the power distribution information stored in the power distribution information storage unit 22, and selects a power distribution section and a customer corresponding to the received transformer ID.

  The current value calculation unit 14 reads time series data of power consumption in the selected customer, converts time series data of power consumption into time series data of current value, and generates phase current due to power consumption in the customer. Calculate time series data. The time series data of the power consumption in the consumer can use, for example, data measured by a power meter with a communication function such as a smart meter installed in the consumer. The power consumption of the consumer is measured, for example, in units of 30 minutes, and stored in the power consumption data storage unit 24 as time-series data of the power consumption of each consumer.

  The correlation coefficient calculation unit 16 reads time series data of the line current in the selected distribution section, and calculates a correlation coefficient with the time series data of the current value calculated by the current value calculation unit 14. The time series data of the line current can be obtained from the current value measured by the sensor built-in switch that defines both ends of the power distribution section. In the present embodiment, as shown in FIG. 3, since the circuit of the three-phase three-wire system is assumed, the correlation coefficient calculation unit 16 calculates each line (a line, b line, and c) on the high voltage side of the distribution system. Calculate time series data of line current for line). Then, the correlation coefficient calculation unit 16 determines three types between the time series data of the line current of each of the a line, the b line, and the c line, and the time series data of the current value corresponding to the power consumption at the customer. Calculate the correlation coefficient of

  The connection phase determination unit 18 determines, based on the three types of correlation coefficients calculated by the correlation coefficient calculation unit 16, which phase on the high voltage side the target transformer is connected to. Details of the determination method will be described later.

  The reliability calculation unit 19 calculates the reliability of the determination result of the connection phase determination unit 18 based on the three types of correlation coefficients calculated by the correlation coefficient calculation unit 16. Details of the calculation method will be described later.

  The output processing unit 20 performs processing for displaying the determination result by the connection phase determination unit 18 on a display device or printing with a printing device, and outputs the processed result.

  Here, the principle which can determine a transformer connection phase is demonstrated based on the correlation coefficient of the line current in each line by the side of high voltage | pressure of a distribution system, and the phase current resulting from the power consumption in a consumer.

  When power is consumed in a consumer connected to the secondary side of the transformer, phase current also flows on the primary side of the transformer. The current flowing through each of the high voltage lines can be measured by the sensor built-in switch as described above.

As shown in FIG. 3, a net (complex) line current I (·) _x flowing into one distribution section is defined as the first half of the following equation (1). At this time, the relationship between each line current I (·) _x and the phase current I (·) _i ^y is expressed in the second half of the following equation (1) according to Kirchhoff's law. Note that I (·) is represented by a symbol in which a side point (“·”) is added to a letter (“I”) in a mathematical expression, and indicates that it is a complex number.

Here, I (·) _x is xε {a, b, c} and is a (complex) current flowing through the high-pressure side x-ray. I (·) x _SC1 and I (·) x _SC2 are current values measured at each of the sensor incorporated switches installed at both ends of the x-ray. I (·) ^y is yε {ab, bc, ca} and is the phase current of the transformer y phase. I (·) _i ^y is yε {ab, bc, ca} and is a phase current of the y phase resulting from the power consumption at the ith consumer. n _y is the number of consumers connected to the y phase.

  As can be seen from the equation (1), in the circuit shown in FIG. 3, the phase current of the transformer and the line current of the distribution line are related in a one-to-two manner. Of two of them. Even if the customer is connected to the transformer connected to any phase, one of the two will be duplicated, so the power information will be independent between the high voltage side and the low voltage side (consumer side) It is not suitable for connection phase determination by correlation analysis.

On the other hand, in the current, there is a combination where the phase current and the line current become independent. For example, it can be understood from the equation (1) that the phase current I (·) _i ^ab of the ab phase caused by the power consumption of a customer connected to the ab phase is irrelevant to the line current I (·) _c . There are also combinations that become independent in relation to other phase currents and line currents. Therefore, if such a difference in correlation can be estimated by statistical analysis, it is possible to determine the trans-connected phase. Therefore, in the following, determination of a transformer connection phase by correlation analysis using current information will be described.

  As described above, the high voltage side of the distribution system is configured by a three-phase three-wire system, and there is a phase difference of 2π / 3 between each phase current. Therefore, when the latter part of the equation (1) is expressed using the phase current divided into the amplitude and the phase, the following equation (2) is obtained.

  In addition, since the amplitudes of the phase currents may be added as real values if they are in phase, they can be summarized as the following equation (3).

  Using the equations (2) and (3), the amplitude of the line current of the a-line can be expressed as a phase current as shown in the following equation (4).

  Here, assuming that the distribution system is a symmetric three-phase alternating current, the amplitude of the line current of the a line is as shown in the following equation (5). The symmetrical three-phase alternating current means one in which the three-phase electromotive force and the frequency are equal and the phase difference is all 2π / 3.

  Expressing the relationship between the line current of the a-line and the phase current of the ab phase and the phase current of the ca phase by Taylor expansion of the equation (5) and first approximation as in the following equation (6) can do.

Furthermore, assuming that the load impedances connected to each phase are equal balanced loads, since I ^ab = I ^ca , a linear approximation of the following equation (7) can be obtained for a minute change from the equilibrium state .

  Similar approximations are possible for other line currents, and therefore, it is possible to estimate the minute change of the line current with the three approximations shown in the following equation (8).

In order to apply correlation analysis to current information, time series data I _x (t) of line current and time series data I _d ^y (t) of phase current are defined by the following equation (9-1). In equation (9-1), I _x (t) and I _d ^y (t) represent the measured values of the line current I _x ′ (t) and the measured values of the phase current I ′ _d ^y (t), respectively. , The value expressed by the variation from their time average is used.

In addition, when the line current I _x '(t) flowing in each distribution section as shown in FIG. 3 is obtained from the measurement value of the sensor built-in switch, it can be treated as a real number if the amplitude of the line current is in phase. Therefore, as shown in the following equation (9-2), the line current I _x '(the _{equation with} the sensor built-in switch (SC2)) is subtracted from the measured value of the sensor built-in switch (SC1) upstream: t) is obtained.

Further, the phase current I ' _d ^y (t) attributable to the power consumption in a certain customer d connected to the y phase of the transformer in the equation (9-1) is a power meter using the following equation (10) It can be calculated from the power consumption measured in The voltage value in this case is treated as a constant using a contract voltage. Since the power consumption at the customer measured by the power meter and the current value calculated from the contract voltage (effective value) become the effective value, in equation (10), to obtain the amplitude (maximum value) doing. Although the current value calculated by the equation (10) has only a meaning similar to the average current in the sampling interval of the power meter, if equivalent processing is applied to the line current, statistical analysis can be performed. There is no problem.

Here, P _d (t) is time series data of power consumption in the customer d, V _d is a contract voltage (effective value) of the customer d, and k is a transformer transformation ratio.

At this time, the covariance σ ^y _xd and the correlation coefficient ^{y y} _xd of the time series data I _x (t) of each line current and the time series data I ^y _d (t) of the phase current are _expressed by the following equation (11-1) It can be defined as

Where σ ^y _d is the deviation of I ^y _d (t), σ _x is the deviation of I _x (t), σ ^y _d is the deviation of I ^y _d (t), T is the time series data It is a sampling point.

The covariance and the correlation coefficient defined by the equation (11-1) are 3 × 3 = 9 depending on the combination of the subscripts x and y. The specific values of these correlation coefficients depend on the temporal change in power consumption at each customer and the transformer connected phase that defines the relationship between the line current and the phase current. It depends on whether it is set. In the present embodiment, since I ^y _d (t) is used only for the calculation of the correlation coefficient, P _d (t) may be used instead of I ^y _d (t). Here, P _d (t) = P ′ _d (t) −μ (P ′ _d (t)) (μ (·) is a time average) (see equation (10)).

  In addition, when applying to an actual problem, since the connection phase of each consumer is unknown, Formula (11-1) is described like the following (11-2) formula.

  Below, the value of the correlation coefficient at the time of making a suitable assumption to time series data of power consumption is explained. By applying the equation (8), time series data of each line current value can be approximated by the following equation (12).

Here, it is assumed that the phase current I _i ^y (t) resulting from the power consumption in each of all the consumers including the customer d follows a mutually independent normal distribution of N (0, σ ₀ ² ). First, (11) and (12) from the equation, the time-series data _I x (t) of the deviation sigma _x, and customer d is the line current when connected to ab-phase _I x of each line current (t) The covariance σ ^ab _xd of the phase current I ^ab _d (t) and the phase current I ^ab _d (t) is obtained as shown in the following equation (13).

(13) The result of the latter part of the equation is that the phase current I _d ^ab (t) of the ab phase caused by the power consumption at the customer d is correlated with only the portion of each line current caused by its own phase current It is obtained from the circumstances that Substituting these results into the definition equation of the correlation coefficient, the correlation coefficient between each line current and the phase current of the ab phase in the case where the customer d is connected to the ab phase is given by the following equation (14) It can be asked to show.

  Similar calculations are possible in the case where the customer d is connected to another phase. The approximate expression of the correlation coefficient between each line current and the phase current, which is divided by the connection phase of the customer d, is collectively described in the following equation (15).

  As shown in the equation (15), the transformer connected phase to which the customer d is connected and the type of the correlation coefficient whose value becomes approximately 0 correspond one to one. In addition, as for correlation coefficients other than the correlation coefficient in which the value is approximately 0, it has a value corresponding to the distribution to the connection phases of the entire customer.

  Up to this point, the trial calculation has been advanced assuming that the demander d is single, but when information on power consumption of a plurality of demanders connected to the same transformer can be used, the determination accuracy of the transformer connection phase It is possible to improve

Specifically, the determination accuracy of the transformer connection phase can be improved by considering a virtually large customer taking the sum of the power consumption of each customer at each measurement time. For example, it is assumed that time series data of power consumption of n _d consumers are available. Further, it is assumed that the distribution of the phase current due to the power consumption in this virtual consumer conforms to the normal distribution of N (0, n _d σ ₀ ² ). In this case, the approximate expression of the correlation coefficient is rewritten as the following equation (16), and the difference between the correlation coefficients changes in proportion to n _d .

  The actual phase current does not necessarily have a normal distribution as assumed above. However, even in the general case, among the three types of correlation coefficients, there is one line type corresponding to the correlation coefficient that is smaller than the other, corresponding to the connection phase of the transformer. The same is true for Focusing on this point, we calculate and compare the correlation coefficient between the time series data of the line current for each line on the high voltage side of the distribution system and the time series data of the phase current caused by the power consumption of the customer. Thus, the connection phase of the transformer to which the customer is connected can be determined. Specifically

Is a logic such as the following equation (17) as an example of the determination criterion of the trans connection phase with respect to the connection phase unknown correlation coefficient: x _xd (x ({a, b, c}).

_{ad ad} = min { _{ad ad} , _bd , _{cd cd} } → bc phase connection _bd = min { _{ad ad} , _bd , _{cd cd} } → ca phase connection (17)
_{cd cd} = min { _{ad ad} , _bd , _{cd cd} } → ab phase connection

Next, the accuracy of the transformer connected phase determination problem using the correlation coefficient will be described. In a three-phase alternating current distribution system, in order to improve transmission efficiency of power, it is general that a connection in which loads are balanced in three phases is adopted. Therefore, it is assumed that the relationship of n _ab = n _bc = n _ca = N / 3 holds, where N is the total number of customers of the distribution section to be determined. In this case, the variation width of each of the line coefficients of the correlation coefficient shown in equation (16) is as shown in equation (18) below.

If equation (18) is used as an index, it is possible to estimate the difficulty of the determination problem according to the conditions of the data to be used. As an example, when N = 300 and n _d = 1 are substituted, the value becomes ΔΔ ̃about 0.071. This value is a size that is generally regarded as “no correlation” in general correlation analysis, but since Eq. (18) is an estimate under one ideal condition, it corresponds to the connection phase. The variation width of the correlation coefficient is considered to correspond approximately to the upper limit. Since the realistic variation width is expected to be smaller than this, how does the determination of the transformer connection phase according to this method detect a very small difference in correlation between current signals buried in noise? It becomes a problem to say.

  Next, determination of the connection phase and calculation of the reliability of the determination result will be described.

  In this embodiment, the distribution shape of the calculation result of the correlation coefficient with respect to a large number of transformers is estimated, and the connection phase is determined and the reliability is calculated using this result. Specifically, vectors having three types of correlation coefficients are defined for each transformer, and their probability distributions are estimated using a mixed distribution model, thereby performing connected phase determination with reliability.

Here, a correlation coefficient vector having three types of correlation coefficients as elements is represented by a coordinate system (ρ _ad , _bd , _{cd cd} ) introduced by the following equation (19). Here, e _a , e _b and e _c are triaxial bases.

  An example of drawing such vectors corresponding to a large number of transformers as a three-dimensional scatter diagram is shown in FIG. Each point in FIG. 4 corresponds to a correlation coefficient vector of an individual transformer. In FIG. 4, in order to make the explanation easy to understand, although the shading of each point is made different corresponding to the correct answer of the transformer connection phase, the correct answer of the transformer connection phase is unknown in an actual application scene.

  Even though the correctness of the transconnected phase is unknown, the group distribution of the correlation coefficient vector is a mixed distribution divided into three parts as shown in FIG. 4 from the physical property of the problem of determining the transconnected phase. It can be seen that it can be modeled. As a mixture distribution model, in particular, assuming a mixture normal distribution, it can be defined as the following equation (20).

Here, τ _k is a mixing ratio, μ _k is an average vector, and S _k is a variance-covariance matrix. The parameters τ _k , μ _k , S _k (k = 1, 2, 3) of this three-dimensional mixed normal distribution model having three components are directly determined using the maximum likelihood method and the EM algorithm etc. It is also possible. However, in mixed distribution estimation, when the number of parameters is large, the amount of calculation increases and the stability of estimation also decreases. Therefore, in the present embodiment, it is considered to reduce the number of parameters by reducing the dimensionality of the three-dimensional model of equation (20) while avoiding the decrease in the determination accuracy of the connection phase. Therefore, considering a plane π having a normal vector in the (1, 1, 1) direction in the space of the correlation coefficient vector shown in FIG. 4, all samples of the correlation coefficient vector are orthogonally projected on this plane π Do.

As shown in FIG. 5, when an arbitrary correlation coefficient vector を is decomposed into a vector _{h h} parallel to (1, 1, 1) and a vector _{v v} parallel to the plane π, it is a three-dimensional vector A point obtained by orthogonal projection of a point corresponding to ρ on the plane π can be expressed by 二_v ′ which is a two-dimensional vector. This projective transformation causes the rho _h component to be lost in the information possessed by the original vector rho.

Here, [rho considering the geometric meaning of the _h components, [rho _h component further ρ _ad, ρ _bd, value decomposition on the three axes of the [rho _cd is equal. Further, the basis of the logic of the transformer connected phase determination based on the correlation coefficient is the comparison of the magnitudes of three correlation coefficients as shown in equation (17). Combining these facts, it can be seen that the _{h h} component affects the three correlation coefficients by the same magnitude, and does not affect the determination result of the connection phase. Therefore, by reducing the dimensionality of data by orthogonal projection onto the plane π, it is possible to realize reduction of the calculation amount of mixture distribution estimation without losing information of connection phase.

If a coordinate system (x, y) as shown in FIG. 6 is set to express the vector _{v v} ′ in FIG. 5 in two dimensions on the plane π, orthogonal projection to the plane π is expressed by It can be defined by a linear transformation such as an equation.

  Further, the expression of a two-dimensional mixed normal distribution formed by projective transformation on the plane π at this time can be expressed as the following expression (22) using coordinates (x, y).

  In the present embodiment, the EM algorithm used to estimate the mixture distribution is a type of non-linear optimization. The algorithm is a calculation process in which an E step of calculating the expected value of the distribution and an M step of maximizing the likelihood are sequentially repeated until the predetermined convergence determination condition is satisfied. Therefore, the amount of calculation required to estimate the parameters of the distribution varies greatly depending on the nature of the data used, even when the distribution model is fixed. In addition, in the case of estimating a mixed normal distribution having correlations among parameters as in the present embodiment using the EM algorithm, the calculation process of each step becomes complicated, so the amount of calculation is discussed. It is difficult to do.

However, if the distribution is further constrained a little, estimates of the computational complexity of each EM step are known, for example, in the following reference, and so on.
Reference: Shoko Akaho, "Estimation method of position, scale and rotational parameter of probability distribution using ECM method", Transactions of the Institute of Electronics, Information and Communication Engineers, D-II, Information system, II-Pattern processing J82-D-II (12), 2240-2250, 1999-12-25.
In this paper, ECM algorithm (Expectation-Conditional Maximization, a type of generalized EM algorithm) in the case where the axis of each component of the mixed normal distribution is parallel to the coordinate axis (when there is no rotation parameter) It estimates using. The computational complexity of each step of the ECM algorithm is estimated to be approximately O (dNk) (d: number of dimensions of data, N: number of data points, k: number of components of mixed normal distribution, O is Landau symbol).

  In the present embodiment, N is invariant before and after dimensional compression of data, and k is the same with k = 3, but the dimensionality of data is reduced from 3 to 2, so that one EM step is performed. The amount of calculation is first reduced to about 2/3. In addition, although it is difficult in this case to quantitatively describe the speed of convergence due to the repetition of the EM step, the number of parameters of the distribution to be estimated is reduced from 30 to 18 with dimensional compression. As a result, the search space for the solution is significantly reduced, and the number of convergences can be reduced when comparing under the same convergence judgment condition.

If the distribution parameters of equation (22) are estimated by the EM algorithm or the like after projective transformation of the correlation coefficient vector to the plane π, the points (x, y) corresponding to the respective transformers disposed on the plane π are mixed The probability P _k (x, y) that is generated from the k-th component (k = 1, 2, 3) of the distribution is estimated by the following equation (23). In the example of FIG. 6, the components of the ab phase, the bc phase, and the ca phase correspond to the order of k = 1, 2, and 3, respectively.

Therefore, for the transformer corresponding to the point (x, y), the probability that it belongs to each of the three connection phases can be estimated, so it can be determined that the one with the largest probability is the connection phase of the transformer . Further, since P _k corresponding to the determination result is also a probability that the result is a correct answer, it is possible to use this value as the reliability (correct answer probability) of the determination result of the trans-connected phase.

  FIG. 7 shows the result of calculating the reliability (probability of correct answer) of the phase determination result of the trans connection arranged on the plane π from the estimation result of the mixture normal distribution. In FIG. 7, the distribution of the reliability estimated on the plane π is expressed by gray shades.

  In addition, the reliability calculation method of the determination result of the connection phase mentioned above is a thing independent of the logic of connection phase determination. For example, whether the logic of connected phase determination of correlation coefficient vector is conventional geometric or is based on distribution estimation of other determination index vectors, the similar mixed distribution of which distribution is composed of three components If it has, it is possible to use the above-mentioned reliability.

  The connection phase determination reliability calculation device 10 can be realized, for example, by a computer 40 shown in FIG. The computer 40 includes a CPU 41, a memory 42 as a temporary storage area, and a non-volatile storage unit 43. The computer 40 also includes an input / output interface (I / F) 44 to which the input / output device 48 is connected. The computer 40 also includes a read / write (R / W) unit 45 that controls reading and writing of data to the recording medium 49, and a network I / F 46 connected to a network such as the Internet. The CPU 41, the memory 42, the storage unit 43, the input / output I / F 44, the R / W unit 45, and the network I / F 46 are connected to one another via a bus 47.

  The storage unit 43 can be realized by a hard disk drive (HDD), a solid state drive (SSD), a flash memory, or the like. A connection phase determination reliability calculation program 50 for causing the computer 40 to function as the connection phase determination reliability calculation device 10 is stored in the storage unit 43 as a storage medium. The CPU 41 reads out the connection phase determination reliability calculation program 50 from the storage unit 43 and develops it in the memory 42, and sequentially executes the processes possessed by the connection phase determination reliability calculation program 50.

  The connection phase determination reliability calculation program 50 includes a customer selection process 52, a current value calculation process 54, a correlation coefficient calculation process 56, a connection phase determination process 58, a reliability calculation process 59, and an output processing process 60.

  The CPU 41 operates as the customer selection unit 12 shown in FIG. 2 by executing the customer selection process 52. Further, the CPU 41 operates as the current value calculation unit 14 shown in FIG. 2 by executing the current value calculation process 54. Further, the CPU 41 operates as the correlation coefficient calculation unit 16 shown in FIG. 2 by executing the correlation coefficient calculation process 56. Further, the CPU 41 operates as the connection phase determination unit 18 illustrated in FIG. 2 by executing the connection phase determination process 58. In addition, the CPU 41 operates as the reliability calculation unit 19 illustrated in FIG. 2 by executing the reliability calculation process 59. Further, the CPU 41 operates as the output processing unit 20 shown in FIG. 2 by executing the output processing process 60. As a result, the computer 40 executing the connection phase determination reliability calculation program 50 functions as the connection phase determination reliability calculation device 10.

  The function realized by the connection phase determination reliability calculation program 50 can also be realized by, for example, a semiconductor integrated circuit, more specifically, an application specific integrated circuit (ASIC) or the like.

<Operation of Connection Phase Determination Reliability Calculation Device>
Next, the operation of the connection phase determination reliability calculation device 10 according to the present embodiment will be described. When a plurality of transformer IDs indicating transformers to be subjected to connection phase determination are input to the connection phase determination reliability calculation device 10, the connection phase determination reliability calculation device 10 executes the determination process shown in FIG.

  In step S10 of the determination process shown in FIG. 9, the consumer selection unit 12 receives the plurality of input transformer IDs. Next, in step S12, one transformer ID is selected from the plurality of transformer IDs input.

  Next, in step S14, the customer selection unit 12 selects a distribution section and a customer corresponding to the selected transformer ID from the distribution information storage unit 22. Here, in the power distribution information storage unit 22, for example, a power distribution information table as shown in FIG. 10 is stored. In the distribution information table of FIG. 10, for each customer, a customer ID indicating the customer, a transformer ID indicating a transformer to which the customer is connected, and a distribution section ID indicating a distribution section to which the transformer belongs Are associated and stored. Here, as shown in FIG. 3, it is assumed that a distribution system in which a number of distribution sections connected in series are interposed between sensor built-in switches installed on the upstream side and the downstream side of the distribution system. Then, for example, a distribution section ID indicating a distribution section sandwiched between the sensor built-in switch (SC1) and the sensor built-in switch (SC2) is defined as "I1-2".

  Also, the power distribution information table of FIG. 10 includes a data availability flag indicating whether power consumption data of each customer is available. For example, when a power meter such as a smart meter installed in a customer is connected to the connection phase determination reliability calculation device 10 via a network, it is assumed that power consumption data of the customer is available. , Data availability flag is set to "presence".

  Therefore, the customer selection unit 12 selects the customer ID and the distribution section ID associated with the transformer ID that matches the transformer ID selected in step S12. In addition, when selecting customer ID, a data availability flag selects the thing of "presence". In addition, when there are a plurality of corresponding customer IDs, the plurality of customer IDs are acquired.

  Next, in step S16, the current value calculation unit 14 reads from the power consumption data storage unit 24 the power consumption data corresponding to the customer ID selected in step S14. The power consumption data storage unit 24 stores, for example, a power consumption data table as shown in FIG. In the power consumption data table of FIG. 11, the power consumption [kWh] measured by the smart meter at a constant sampling time interval (30 minutes in the example of FIG. 11) is stored as time series data of power consumption for each customer. It is done.

  If there is one customer ID selected in step S14, the power consumption data corresponding to the customer ID may be read from the power consumption data table as it is. For example, in the example of FIG. 10 and FIG. 11, when the transformer ID = T1 is selected, only the customer ID = d1 is selected. Therefore, from the power consumption data table, the consumption corresponding to the customer ID = d1 You can read the power data as it is.

  Further, when there are a plurality of customer IDs selected in step S14, a plurality of power consumption data corresponding to the plurality of customer IDs are read. Then, the power consumption amount for each sampling time of the plurality of power consumption data is added to create power consumption data of a virtual customer.

  For example, in the example of FIG. 10 and FIG. 11, when transformer ID = T2 is selected, customer ID = d2 and d3 are selected. Note that d4 is not selected because the data availability flag is "absent". Then, the power consumption data corresponding to the customer ID = d2 and the power consumption data corresponding to the customer ID = d3 are read from the power consumption data table. And, the power consumption of “0:00” = 0.65 + 0.51 = 1.16, the power consumption of “0:30” = 0.62 + 0.44 = 1.06, etc. Power consumption data for various consumers. As a result, power consumption data with an improved S / N ratio can be obtained compared to the case where power consumption data corresponding to individual customer IDs is used as it is, and the accuracy of the correlation coefficient calculated in the subsequent processing is improved.

  Next, in step S18, the current value calculation unit 14 converts the power consumption data read in step S16 or the power consumption data of a virtual customer created according to equation (10) into a current value. This current value corresponds to time-series data of the phase current resulting from the power consumption of the selected customer.

  Next, in step S20, the correlation coefficient calculation unit 16 reads from the line current data storage unit 26 three types of line currents in the distribution section indicated by the distribution section ID selected in step S14. The line current data storage unit 26 stores, for example, a line current data table as shown in FIG. In the line current data table of FIG. 12, the net measured at a constant sampling time interval (30 minutes in the example of FIG. 12) at each of the a, b and c lines of the distribution section indicated by the distribution section ID. The current value [A] is accumulated as time series data of the line current. As the current value of the line current, the value calculated by the equation (9-2) can be used using the current value measured by the sensor built-in switch disposed at both ends of the power distribution section.

Next, in step S22, the correlation coefficient calculation unit 16 uses the phase current caused by the power consumption of the consumer converted in step S18 and the line current read in step S20 ((11- 2) Calculate the three types of correlation coefficients shown in the equation. Specifically, the phase current caused by the power consumption at the customer is I'd (t) of equation (10), and the three types of line currents are I'x (t) of equation (9-2) , X ∈ {a, b, c}. Since it is possible to calculate I _d (t) and I _x (t), _x c {a, b, c} obtained by converting these into fluctuation from the average value from the equation (9-1), Substituting in the equation), the correlation coefficients _{ad ad} , _bd and ρ _cd are calculated.

  Next, in step S24, the consumer selection unit 12 determines whether or not the processing has been completed for all of the transformer IDs received in step S10. If there is an unprocessed transformer ID, the process returns to step S12, the customer selecting unit 12 selects the next transformer ID, and repeats the process. On the other hand, if the process has been completed for all the transformer IDs, the difference calculation process is executed in step S26.

  Here, the determination calculation process will be described with reference to FIG.

In step S262, a plane π having the correlation coefficient vector having the correlation coefficient calculated in step S22 as an element, as a normal vector to each axis corresponding to three phases, the reliability calculation unit 19 Calculate the coordinates of the point orthogonally projected to. Specifically, the reliability calculation unit 19 uses (x, y) the vector having the correlation coefficient (ρ _ad , _bd , _{cd cd} ) calculated for each transformer ID as an element by the equation (21). Convert to coordinates.

  Next, in step S 264, the reliability calculation unit 19 expresses the equation of the two-dimensional mixed normal distribution that can be project-transformed on the plane π using the coordinates (x, y) in equation (22) The parameters are estimated using the maximum likelihood method and the EM algorithm.

Next, in step S266, using the parameters estimated in step S264, the connection phase determination unit 20 determines three connection phases according to equation (23) for each (x, y), that is, for each transformer ID. Calculate the probability P _k (x, y) belonging to each of k = 1, 2, 3. In the example of FIG. 6, k = 1 corresponds to the ab phase, k = 2 corresponds to the bc phase, and k = 3 corresponds to the ca phase. Then, the connection phase determination unit 20 determines the connection phase corresponding to the component k for which the probability P _k (x, y) is largest as the connection phase of the transformer indicated by the transformer ID corresponding to the point (x, y). . For example, if it is calculated that P _{1 = ab} (x, y) = 0.6, P _{2 = bc} (x, y) = 0.3, P _{3 = ca} (x, y) = 0.1, then connection The phase determination unit 20 determines that the connection phase of the transformer indicated by the transformer ID corresponding to the point (x, y) is the ab phase.

Next, in step S268, the reliability calculation section 19, the probability calculated in step S266 _P k (x, y) maximum value, i.e., the probability corresponding to the determined component as a connection phase _P k (x , Y) are used as the reliability of the determined connection phase. Then, the process returns to the connection phase determination reliability calculation process shown in FIG.

  Next, in step S28, the output processing unit 20 adds the reliability of the determination result to the determination result of the connection phase determined for each transformer ID, for example, as shown in FIG. The phase determination reliability calculation process ends.

As explained above, according to the connection phase determination reliability calculation device 10 according to the present embodiment, the time series data of the line current for each line on the high voltage side of the distribution system and the phase current due to the power consumption in the consumer The correlation coefficient with the time series data of is calculated for each transformer. Then, assuming that the distribution of each point on the plane when a three-dimensional correlation coefficient vector having three types of correlation coefficients as elements is compressed in two dimensions as a mixed distribution model having three components, mixing is performed. Estimate the parameters of the distribution model. Then, calculate the probability P _k (x, y) that each point is generated from the k-th component of the mixture distribution, and from the k at which P _k (x, y) is maximized, While making the determination, the value of P _k (x, y) is used as the reliability of the determination result. This makes it possible to obtain the reliability of the determination result of the transformer connection phase under the condition that there is no correct information.

  Furthermore, by compressing the three-dimensional correlation coefficient vector in two dimensions, the amount of calculation of parameter estimation of the mixed distribution can be suppressed, and the stability of the estimation is also improved. Also, in dimension compression, orthogonal projection is performed on a plane having a vector symmetrical to an axis corresponding to each of the three types of correlation coefficients as a normal vector. Therefore, the components removed by dimensional compression are components that have the same magnitude on any axis. Therefore, in the present embodiment in which the connection phase is determined by comparing the magnitudes of the correlation coefficients, it is possible to realize the reduction of the calculation amount by the dimensional compression without reducing the determination accuracy of the connection phase.

In the above embodiment, the case of estimating the parameter of the mixed distribution representing the distribution when the three-dimensional correlation coefficient vector is compressed in two dimensions has been described, but from the three-dimensional distribution without performing dimensional compression. The parameters of the mixture distribution may be estimated. In this case, the parameters of the mixture distribution shown in equation (20) are estimated. Then, using P _k (x, y) in which “g _k (x, y)” in equation (23) is replaced with “f _k (x, y)”, determination of the connection phase and calculation of reliability are performed. You can do it.

  Although the connection phase determination reliability calculation program 50 has been described above as being stored (installed) in the storage unit 43 in the above, it is provided in the form of being recorded on a storage medium such as a CD-ROM or a DVD-ROM. It is also possible.

  Further, the following appendices will be disclosed regarding the above embodiment.

(Supplementary Note 1)
On the computer
A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines The phase to which the transformer is connected is determined based on each of the correlation values indicating the correlation with each of the line currents flowing through
Representing a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases,
A connected phase determination reliability calculation program that executes processing of calculating the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model.

(Supplementary Note 2)
The distribution of vectors having each of the correlation values as an element is projected as a mixture distribution model onto a plane having, as a normal vector, a vector symmetrical to an axis corresponding to each of the correlation values. Connection phase determination reliability calculation program described above.

(Supplementary Note 3)
The point which the vector which makes each of the correlation value in the mixed distribution model the element shows the probability generated from each of the plurality of components which the mixed distribution model has as the degree of reliability Connection phase determination reliability calculation program described above.

(Supplementary Note 4)
The connected phase determination reliability calculation program according to any one of appendices 1 to 3, wherein a phase having the highest calculated reliability is determined as the phase to which the transformer is connected.

(Supplementary Note 5)
A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines A determination unit that determines a phase to which the transformer is connected based on each of the correlation values indicating the correlation with each of the line currents flowing through the
Representing a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases,
A calculation unit that calculates the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model;
Connection phase determination reliability calculation device including.

(Supplementary Note 6)
The calculation unit projects, as the mixed distribution model, a distribution of vectors having each of the correlation values as an element on a plane having, as a normal vector, a vector symmetrical to an axis corresponding to each of the correlation values. The connected phase determination reliability calculation device according to claim 5, wherein the distribution is used.

(Appendix 7)
The calculation unit calculates, as the reliability, a probability that a point indicated by a vector having each of the correlation values in the mixture distribution model as an element is generated from each of the plurality of components of the mixture distribution model. The connection phase determination reliability calculation device according to Appendix 5 or 6.

(Supplementary Note 8)
The connected phase determination reliability calculation device according to any one of appendices 5 to 7, wherein the determination unit determines the phase having the highest reliability calculated by the calculation unit as the phase to which the transformer is connected.

(Appendix 9)
On the computer
A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines The phase to which the transformer is connected is determined based on each of the correlation values indicating the correlation with each of the line currents flowing through
Representing a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases,
A connected phase determination reliability calculation method, which executes processing of calculating the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model.

(Supplementary Note 10)
A distribution obtained by projecting, as the mixed distribution model, a distribution of vectors having each of the correlation values as an element onto a plane having, as a normal vector, a vector symmetrical with respect to an axis corresponding to each of the correlation values. Connection phase determination reliability calculation method as described.

(Supplementary Note 11)
The point indicated by the vector having each of the correlation values in the mixture distribution model as the reliability is calculated as the probability generated from each of the plurality of components in the mixture distribution model. Connection phase determination reliability calculation method as described.

(Supplementary Note 12)
The connected phase determination reliability calculation method according to any one of appendices 9 to 11, wherein a phase having the highest calculated reliability is determined as the phase to which the transformer is connected.

(Supplementary Note 13)
On the computer
A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines The phase to which the transformer is connected is determined based on each of the correlation values indicating the correlation with each of the line currents flowing through
Representing a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases,
A storage medium storing a connected phase determination reliability calculation program for executing processing of calculating the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model.

DESCRIPTION OF SYMBOLS 10 Connection phase determination reliability calculation apparatus 11 Determination part 12 Consumer selection part 14 Current value calculation part 16 Correlation coefficient calculation part 18 Connection phase determination part 19 Reliability calculation part 20 Output processing part 22 Distribution information storage part 24 Power consumption data Storage unit 26 Line current data storage unit 40 Computer 41 CPU
42 Memory 43 Storage Unit 49 Recording Medium 50 Connection Phase Determination Reliability Calculation Program

Claims (6)

On the computer
A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines The phase to which the transformer is connected is determined based on each of the correlation values indicating the correlation with each of the line currents flowing through
Representing a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases,
A connected phase determination reliability calculation program that executes processing of calculating the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model.   A distribution obtained by projecting a distribution of vectors having each of the correlation values as a component onto a plane having a vector symmetrical to an axis corresponding to each of the correlation values as a normal vector is used as the mixed distribution model. The connected phase determination reliability calculation program according to 1).   The probability that a point indicated by a vector having each of the correlation values in the mixture distribution model as the reliability is calculated as a probability generated from each of the plurality of components of the mixture distribution model. The connection phase determination reliability calculation program according to Item 2.   The connected phase determination reliability calculation program according to any one of claims 1 to 3, wherein a phase having the highest calculated reliability is determined as the phase to which the transformer is connected. A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines A determination unit that determines a phase to which the transformer is connected based on each of the correlation values indicating the correlation with each of the line currents flowing through the
An estimation unit that represents a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases;
A calculation unit that calculates the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model;
Connection phase determination reliability calculation device including. On the computer
A phase current due to power consumed by at least one customer connected to a transformer connected to any of a plurality of phases corresponding to two combinations of a plurality of distribution lines, and each of the plurality of distribution lines The phase to which the transformer is connected is determined based on each of the correlation values indicating the correlation with each of the line currents flowing through
Representing a distribution of vectors having each of the correlation values as an element, and estimating a mixed distribution model having a plurality of components corresponding to each of the plurality of phases,
A connected phase determination reliability calculation method, which executes processing of calculating the reliability of the determination result of the phase to which the transformer is connected based on the mixed distribution model.