JP2020204512A - Three-phase load proportional division method and unbalanced voltage calculation method - Google Patents

Abstract

To provide a three-phase load proportional division method and an unbalanced voltage calculation method which generate a relatively low cost only when a current vector of an inter-line load is calculated and which is relatively small in deviation from an actual situation.SOLUTION: A three-phase load proportional division method for obtaining the voltage unbalance of a distribution system having a three-phase distribution line 10, which includes a conversion step of converting a measurement value of a line current at a node, to which an inter-line load 20 of the three-phase distribution line 10 is connected, into a value of an inter-line current flowing through an inter-line load. The conversion step, in a triangle composed of a current vector of a line current, is a step of fixing a single-phase load power factor and using the vector from the center point where reactive power is equal to each vertex as an inter-line current.SELECTED DRAWING: Figure 4

Description

The present invention relates to a three-phase load apportionment method and an unbalanced voltage calculation method. In particular, the present invention relates to a three-phase load apportionment method and an unbalanced voltage calculation method for obtaining a voltage imbalance in a distribution system.

With the increase in the introduction of residential photovoltaic power generation, there is concern about the expansion of voltage imbalance in the distribution system. In particular, when the impedance increases due to the lengthening of the distribution line at a point far from the substation in the distribution system, a large voltage imbalance occurs even with a slight load bias. If the unbalance rate becomes high, for example, there is a risk that the electric power equipment of the demand destination will stop or the motor will burn out.

The occurrence of voltage imbalance can be confirmed by acquiring the measured values of switches with measurement functions, which are currently being installed in recent years, specifically, the line voltage, line current, and power factor between the three phases. ..

When the voltage imbalance expands and countermeasures are required, connection phase transfer work for single-phase pole transformers is generally carried out. Effective construction is possible if the accurate transfer amount can be calculated based on the measured values at the time of construction design, but since the switch with measurement function does not directly measure the current flowing through the single-phase pole transformer, it is measured. A calculation is required to convert the system current (line current), which is a value, into the line current (phase current) flowing through the line load.

Conventionally, in order to convert a line current into an interline current, for example, in the method described in Non-Patent Document 1, the calculation is performed on the assumption that the one-phase current is known. As another method, assuming that there is no zero-phase component of the current in the △ connection, the line current is the vector from the center of gravity of the triangle composed of the current vector of the line current to each vertex of the triangle. There is.

Japanese Unexamined Patent Publication No. 61-221666

Uchikawa, Uemura: "Development of a method for separating photovoltaic power generation output and load curve in a distribution system and application to measures against voltage imbalance", Central Research Institute of Electric Power Industry Report, 2009-07

However, in the method described in Non-Patent Document 1, it is necessary to separately attach a measuring instrument in order to know the value of the current of one phase, which causes a long attachment time and a high cost.
In addition, the method of using the vector from the center of gravity of the triangle composed of the current vector of the line current to each vertex of the triangle as the current vector of the line current has the advantage that the calculation formula is simple, but the load is extreme. If it is biased to, the power factor of the current between each line will differ greatly from phase to phase, and it is considered that there will be a large deviation from the actual situation.

An object of the present invention is to provide a three-phase load apportionment method and an unbalanced voltage calculation method, which generate a relatively low cost when calculating a current vector of a line current and have a relatively small deviation from the actual state. To do.

In order to achieve the above object, the present invention includes the following configurations.
(1) In a three-phase load apportioning method for obtaining a voltage imbalance in a distribution system having a three-phase distribution wire, a node constituting the distribution system and to which a line load of the three-phase distribution wire is connected. It has a conversion step that converts the measured value of the line current into the value of the line current flowing through the line load, and the conversion step converts the single-phase load power factor in a triangle composed of the current vector of the line current. A three-phase load apportionment method, which is a step in which the line current is a vector from a fixed center point at which the negative powers are equal to each apex.

(2) In the three-phase load apportioning method, the conversion step is composed of a first sub-step for converting the measured value of the switch with a measuring function into a vector value, and a current vector of the linear current included in the vector value. The second sub-step of extending a straight line from each vertex of the first triangle to form a second triangle with an equal power factor, and the center of the circle inscribed in the second triangle are reactive such as the equal power factor. A third sub-step as a power point and a fourth sub-step in which a vector extending from the reactive power factor such as the equal power factor to each vertex of the first triangle is used as a current vector for each line load. You may have.

(3) Using the three-phase load apportionment method of (1) or (2), the step of obtaining the current vector of the line current, the line current at the first node on the primary side, and the second on the secondary side. From the line current at the two nodes, the passing power of the section between the first node and the second node is obtained, the difference between the passing powers is taken, and the section power consumption of the section is obtained. An unbalanced voltage calculation method comprising a step of calculating an unbalanced voltage using the section power consumption.

According to the present invention, it is possible to provide a three-phase load apportionment method and an unbalanced voltage calculation method in which a relatively low cost is incurred when calculating the current vector of the line current and the deviation from the actual state is relatively small. It will be possible.

It is a figure which shows the example of the distribution system which applies the three-phase load apportioning method which concerns on embodiment of this invention. It is a figure which shows the example of the current / voltage vector figure used in the three-phase load apportionment method which concerns on embodiment of this invention. It is a figure which shows the example of the conversion method from the measured value of the line current to the current vector of a phase current used in the three-phase load apportionment method which concerns on embodiment of this invention. It is a figure which shows the example of the conversion method from the measured value of the line current to the current vector of a phase current used in the three-phase load apportionment method which concerns on embodiment of this invention.

[1. Outline of the invention]
In order to calculate the unbalanced voltage of the distribution system, the value of the section power consumption is required. The calculation of the section power consumption requires the current vector of the line load (phase current), and in order to obtain the current vector of the line load, the measured value of the line current is converted into the current vector of the line load. Steps are needed. As this conversion, the reactive power point such as the equal power factor is obtained in the triangle composed of the current vector of the linear current, and the vector extended from the reactive power factor such as the equal power factor to each vertex of the triangle is the current vector of the line load. Is the gist of the present invention.

[2. Calculation of section power consumption]
As described above, the unbalanced voltage is obtained by obtaining the line load in each section from the measured value of the switch with a measurement function and using this line load as the input value for the power flow calculation.

FIG. 1 shows an example of a distribution system. As shown in FIG. 1, it is assumed that the distribution system 1 is composed of six nodes, and the line load 20 is connected to the three-phase distribution wire 10 at each node. Further, a switch 30 with a measurement function is installed at each node, and the value of the line current flowing through the three-phase distribution wire 10 is measured by the switch 30 with the measurement function. Assuming that the active power included in the section power consumption at each node is ΔP _i and the reactive power is ΔQ _i , the line load is ΔP _i ΔQ _i . Conversely, in order to obtain the line load ΔP _i ΔQ _i of each section, the active power ΔP _i and the reactive power ΔQ _i included in the section power consumption at each node may be obtained.

As shown in FIG. 1, the passing electric power at node _i, when the P i + jQ _i, the _P i + jQ _i is the power consumption from node i to node 6. Further, the passing power at the node i-1 is Pi _-1 + jQ _i-1 , which is the power consumption from the node i-1 to the node 6.

Therefore, in order to obtain the power consumption of the section i, the passing power at the node i may be subtracted from the passing power at the node i-1. That is, the power consumption ΔP _i + jΔQ _i in the section _i is
ΔP _i + jΔQ _i = (P _i-1- P _i ) + j (Q _i-1- Q _i ) (1)
In _{and, P i = (P iab P} ibc P ica), when Q i ₌ a _{(Q iab Q ibc Q ica)} , the following equation (2) and (3) is satisfied.
ΔP _i = (P _{(i-1) ab-} P _iab P _{(i-1) bc-} P _ibc P _{(i-1) ca- Pica} ) (2)
ΔQ _i = (Q _{(i-1) ab} −Q _iab Q _{(i-1) bc} −Q _ibc Q _{(i-1) ca} −Q _ica ) (3)

[3. Calculation of section passing power]
As described above, in order to obtain the power consumption of the section i, it is necessary to obtain the section passing power of the node i. Here, the section passing power P _{i +} jQ _i at node i, as shown in the following equation (4) - ((7), the product of the line voltage and the line current.

を線間電流の電流ベクトル

に変換する必要がある。
この線電流の電流ベクトルから線間電流の電流ベクトルへの変換の際、次項で説明する按分方法を用いる。 Therefore, in order to obtain the section passing power of node i, it is necessary to obtain the line current of node i, and in order to obtain the line current of node i, the measured value of the switch with the measurement function of node i is used. After converting a certain scalar quantity into a vector quantity using the current / voltage vector diagram shown in FIG. 2, the current vector of the line current.

The line current current vector

Need to be converted to.
When converting the current vector of the line current to the current vector of the line current, the apportionment method described in the next section is used.

[Proportioning method from line current to line current]
When converting the line current current vector to the line current current vector, a straight line is extended at an equal power factor from each vertex of the first triangle composed of the line current current vector to form a second triangle. , The vector extending from the center of gravity of the second triangle (here, referred to as “invalid power point such as equal power factor”) to each apex of the first triangle is defined as the current vector of the line current.
The specific method is as follows.

As shown in FIG. 3, of the current vector of the line current shown in equation (8), the vector indicating the I _ia,
I _ia = (x ₁ , y ₁ ) (10)
, And _the vector indicating the _{I ics,}
I _ic = (-x ₂ , -y ₂ ) (-I _ic = (x ₂ , y ₂ )) (11)
And the vector indicating I _ib is
I _ib = -I _c- I _a (12)
Suppose that Further, it is assumed that the power factor is cos θ.

Three current vectors _{I ia, I ib,} among the vertices of the triangle formed by _{-I ics,} vertex which is the intersection of _{I ib} and _{-I ic} (x, y) ₌ through _(x 2, _{y 2),} Draw a straight line with a slope of tan θ. The mathematical formula representing this straight line is the following formula (13).

Similarly, a straight line with a slope of tan (θ-2π / 3) is drawn through the apex (x, y) = (0,0), which is the intersection of I _ia and −I _ic . The mathematical formula representing this straight line is the following formula (14).

Similarly, a straight line with a slope of tan (θ + 2π / 3) is drawn through the apex (x, y) = (x ₁ , y ₁ ), which is the intersection of I _ia and I _ib . The mathematical formula representing this straight line is the following formula (15).

Next, the intersection m _c of the straight line represented by the straight line equation 14 of formula _13, straight intersection m _a represented by the straight line equation 15 of formula _14, the straight line of the formula 15 seeking straight intersection m _b represented by preparative formula 13, obtaining the center of gravity m _abc of an equilateral triangle whose vertices are the three points.

As shown in FIG. 4, from this center of gravity _mabc , the vertices of the original triangle, (x, y) = (x ₁ , x ₂ ), (x, y) = (x ₂ , y ₂ ), Let the vectors to (x, y) = (0,0) be I _iab , I _ibc , and I _ica , which are the current vectors of the line currents, respectively.

The details of the mathematical expression expansion will be described below.
Applying the addition theorem to equations (14) and (15) yields the following equations (14') and (15').

m _c, since the intersection of the formula (13) and (14) = expression (14 '), the coordinates of _{m c} is a solution of the following simultaneous equations (16).

coordinates (, x y) of m _c is expressed by the following equation obtained from the simultaneous equations (16) (17).

Similarly _{m a,} since the intersection of the formula (14) = expression (14 ') and (15) = expression (15'), the coordinates of _{m a} is a solution of the following simultaneous equations (18) ..

coordinates (, x y) of m _a is represented by the following equation obtained from the simultaneous equations (18) (19).

Similarly _{m b,} since the intersection of the formula (13) and (15) = expression (15 '), the coordinates of _{m b} is a solution of the following simultaneous equations (20).

coordinates (, x y) of m _b is expressed by the following equation obtained from the simultaneous equations (20) (21).

m _{a, m} b, the center of gravity _{m abc} triangle whose vertices _{m c} is
_{m abc = 1/3 × (} m a + m b + m c) (22)
_Therefore, the coordinates of _mabc are expressed by the following equation (23).

With this _{m abc, I} iab a current vector of the line current when the power factor cos _[theta], I _{ibc, I ica} can be expressed as the following formula.
_{I iab = m abc -I ia =} m abc - (x 1, y 1) (24)
_{I ibc = m abc -I ic =} m abc - (x 2, y 2) (25)
I _ica = _mabc (26)

Equation (24), equation (25), and using equation (26), _I iab a current vector of the line current when the power factor cos _[theta], I _ibc, After determining the _{I ica,} flow of the description In other words, the line current of node i is used to obtain the section passing power of node i, the section passing power of node i is used to obtain the section power of section i, and the section power of section i is calculated. The unbalanced voltage can be obtained by obtaining the line load of the node _i from the included active power ΔP _i and the reactive power ΔQ _i and using the line load of the node i as an input value for the power flow calculation. Further, based on this unbalanced voltage, it is possible to obtain the transfer amount of the single-phase load to be transferred.

[4. Effect of this embodiment]
The three-phase load apportionment method according to the present embodiment is a three-phase load apportionment method for obtaining a voltage imbalance of a distribution system having a three-phase distribution line, and is a line at a node to which the line-to-line load of the three-phase distribution line is connected. It has a conversion step that converts the measured value of the current into the value of the line current flowing through the line load, and the conversion step fixes the single-phase load power factor in the triangle composed of the current vector of the line current. Then, the step is to set the vector from the center point where the invalid powers are equal to each vertex as the line current.
This makes it possible to provide a three-phase load apportionment method in which a relatively low cost is incurred when calculating the current vector of the line current and the deviation from the actual state is relatively small.

Further, in the three-phase load apportionment method according to the present embodiment, the step of converting the above-mentioned line current value into the current vector of the line load is the first sub-setting of converting the measured value of the switch with measurement function into a vector value. A step and a second sub-step to form a second triangle by extending a straight line with an equal power factor from each vertex of the first triangle composed of the current vector of the linear current included in this vector value, and the second The third sub-step with the center of gravity of the triangle of 2 as the ineffective power point such as the equal power factor, and the vector extending from the ineffective power factor such as the equal power factor to each apex of the first triangle are used as the current vector of the interline load. It has a fourth sub-step to be performed.
As a result, the reactive power of the power passing through the measurement point and the reactive power of the power consumption in the section can be in three-phase equilibrium.

Further, the unbalanced voltage calculation method according to the present embodiment includes a step of obtaining the current vector of the line current by using the above-mentioned three-phase load apportionment method, and the line current at the first node on the primary side. From the line current at the second node on the next side, the passing power of the section between the first node and the second node is obtained, the difference between the passing powers is taken, and the section power consumption of the section is calculated. It has a step of obtaining and a step of calculating an unbalanced voltage using this section power consumption.
This makes it possible to supply high-quality electricity with no voltage bias between the phases without the need to install expensive voltage imbalance countermeasure equipment, and facilitates voltage management work.

[5. Modification example]
In the above embodiment, the reactive power point such as the equal power factor is obtained by using a mathematical formula, but a different method, for example, the reactive point such as the equal power factor may be geometrically obtained by drawing. ..

1 distribution system 10 Three-phase between distribution line 20 wire loads 30 instrumented switch _{m abc} such power factor etc. the reactive power point _{I iab, I ibc,} current vector _{I ica} phase current

Claims (3)

In the three-phase load apportionment method for obtaining the voltage imbalance of a distribution system having a three-phase distribution wire,
It has a conversion step of converting the measured value of the line current at the node to which the line load of the three-phase distribution wire is connected into the value of the line current flowing through the line load.
The conversion step is a step in which the single-phase load power factor is fixed in a triangle composed of the current vectors of the line currents, and the vector from the center point where the reactive powers are equal to each vertex is used as the line current. , Three-phase load apportionment method. The conversion step
The first sub-step to convert the measured value of the switch with measurement function into a vector value,
A second sub-step to form a second triangle by extending a straight line with an equal power factor from each vertex of the first triangle composed of the current vector of the linear current included in the vector value.
A third sub-step in which the center of gravity of the second triangle is a reactive power point such as the equal power factor, and
In the fourth substep, the vector extending from the reactive power point such as the equal power factor to each vertex of the first triangle is used as the current vector of the interline load.
The three-phase load apportionment method according to claim 1. The step of obtaining the current vector of the line current by using the three-phase load apportionment method according to claim 1 or 2.
From the line current at the first node on the primary side and the line current at the second node on the secondary side, the passing power in the section between the first node and the second node is obtained. The step of taking the difference of the passing power and obtaining the section power consumption of the section, and
An unbalanced voltage calculation method comprising a step of calculating an unbalanced voltage using the section power consumption.

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