JP2001078358A - Distribution system model and power flow calculation method for radial system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a practical system model optimal to power flow calculation by approximating a reactive power Q in the constant output control of an effective power P, i.e., the output from a power supply model where induction generators are linked with a system as distributed power supplies. SOLUTION: Assuming the primary effective power P1 is constant in constant output control of an induction machine type distributed power supply model, primary reactive power Q1 outputted from the induction machine type distributed power supply model is approximated by the product of a coefficient a2 and the square term of a voltage v at an link node, the product of a coefficient a1 and the linear term of the voltage v, and the product of a coefficient a0 and the 0 power term of the voltage v. According to the method, power flow calculation for determining voltage/current distribution of a system can be carried out at a higher speed with higher efficiency when distributed power supplies are introduced in a power flow calculation method for radial system where a distribution system model is built in the forward calculation.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to various power distribution system models used for high-speed power flow calculation of a radial system, and to a power flow calculation method using these distribution system models.
Specifically, in performing high-speed power flow calculations for the radial distribution system by the control computer of the distribution office, an induction machine type distributed power supply model as a distributed power supply connected to the grid, a voltage control type inverter type distributed Power supply model,
Inverter-type distributed power supply model with current control method, and a separately-excited SVC as a static var compensator (SVC)
The present invention relates to various distribution system models that are realized by formulating a model and a self-excited SVC model, and a high-speed power flow calculation method using these distribution system models.

[0002]

2. Description of the Related Art A power flow calculation is used when examining an operation method of a power system with respect to a change in a load or power generation in a current system, a stoppage of a transmission line, and the like.
It is indispensable for planning new expansion plans of power plants, transmission lines and substations in the future system. This power flow calculation method is intended mainly for application to a high-voltage distribution system that is a loop system. However, conventionally, the conventional power flow calculation method is also applied to the radial distribution system as it is, and in that case, the convergence characteristics are poor due to the characteristics of the radial distribution system, and the calculation requires a long time.

[0003] Therefore, for only the radial distribution system, a data input step of inputting various data such as a system configuration, a system capacity, a substation voltage and a phase angle, an initial value calculation step of a state variable, and a forward calculation are performed. A high-speed radial distribution system power flow calculation method that sequentially executes a calculation step of a system state quantity, a correction step of a state variable as backward calculation, and a convergence determination step of the state variable,
For example, it is known from Japanese Patent Application Laid-Open No. 8-214458.

On the other hand, in recent years, distributed power sources have been introduced into distribution systems, and reverse power flows in the distribution systems may occur. Therefore, it is necessary to change the conventional system management, operation, and control methods. In particular, regarding the control of the system voltage, the terminal voltage of the consumer is regulated by regulations, and it is required to establish a fine voltage control method. Conventional voltage control has been realized by a distribution transformer and an SVR (automatic voltage regulator) installed as necessary in each feeder. However, if a distributed power supply is connected to the grid,
Since it is difficult to cope with a conventional control device that operates slowly in response to a current in only one direction, it is necessary to consider a new voltage control device such as a power electronics device. Considering that the voltage fluctuation becomes complicated when a large number of distributed power sources are interconnected, the voltage and
In order to calculate the current distribution, analysis using the above-mentioned high-speed power flow calculation for the radial system is necessary.At present, various distribution system models used for the power flow calculation for the radial system have been developed. Absent.

Accordingly, the present invention provides various distribution system models that are optimal and practical for radial system power flow calculation for obtaining voltage / current distribution when a distributed power supply is introduced, and furthermore, use these power flow models. It is intended to provide a calculation method.

[0006]

According to a first aspect of the present invention, there is provided an electric power distribution system model comprising an induction generator-type distributed power supply model in which an induction generator is connected to a system as a distributed power supply. When the constant output control is performed with the active power P being constant, the
And square terms of the product of ₂ and the voltage V of the interconnection nodes, and the product of 1 square terms of coefficients a ₁ and a voltage V, the reactive power Q by the sum of zero power term of the product of the coefficient a ₀ and the voltage V Approximate the coefficient a
₂ is expressed using the active power P, the primary leakage reactance x _{1 of} the induction generator, the secondary leakage reactance x ₂ , and the excitation susceptance b ₀ , and the coefficients a ₁ and a ₀ are expressed by the active power P and the induction power generation. This is expressed using the primary leakage reactance x ₁ and the secondary leakage reactance x ₂ of the machine.

According to a second aspect of the present invention, the distribution system model is an inverter type distributed power supply model in which a voltage control type or current control type inverter is connected to the system as a distributed power source. When the active power P and the injection current I to the system are specified, the reactive power Q corresponding to the specified value of the injection current I is calculated from the calculated voltage V of the interconnection node and the active power P, Q = ± {| I | ² (e ² + f ² ) −P ² }, and determines the sign of the reactive power Q according to the designated power factor.

A distribution system model according to a third aspect is a separately-excited or self-excited static var compensator model,
Separately excited or self-excited static var compensator model, the voltage V _n of the calculated installation node, and slope reactance X _S is the maximum value ± I _max and models the characteristics of positive and negative reactive current is a model output two voltages V _a determined from, in the case of V _a <V _n <V _B with respect to V _B, the difference voltage between the voltage specified value _{V ref (V a <V ref} <V B) and the V _a delta
V and asked to injection or consumption reactive power _{Q = ± V n (ΔV /} X S) from said X _S and the V _n, the static var compensator model of the separately excited, V
_{When n} <V _A , admittance Y _C during capacitor operation
Said V _n injecting reactive power and a Q = Y _C V _n ² look, V _n> V in the case of _B, consumed reactive power from the impedance X _L during reactor operation and the V _n Q = -V _n ² / seek X _L, self-excited static var compensator model of, V
When _n of <V _A or V _n> V _B, and requests the I _max and the V _n invalid injection or consumed from the power Q = ± V _n I _max.

According to a fourth aspect of the present invention, there is provided a power flow calculation method for a radial system, comprising: a data input step of inputting a system configuration of a radial system, power supply capacity, load capacity, line data, transformer data, etc. to a computer; An initial value calculating step of adding a value from an end node of the main distribution line and the branch distribution line to obtain an initial value of a state variable at a head node of each distribution line, and a state at each node of each distribution line using the state variable A step of calculating a system state quantity for sequentially calculating the amount from the head node to the terminal node; a step of correcting a state variable of a head node of each distribution line by an error at a terminal node of each distribution line; A convergence determination step of performing a convergence determination by comparing a state quantity at a node with a determination criterion. In the step of calculating the amount, the reactive power determined by the induction-type distributed power supply model of claim 1 and the specified active power, the reactive power determined by the inverter-type distributed power supply model of claim 2 and the specified active power, and The reactive power obtained by the static var compensator model according to claim 3 is incorporated into the load amount at each node.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the drawings. First, an induction machine type distributed power supply model will be described as an embodiment of the distribution system model according to the present invention. This induction machine type distributed power supply model models a case where an induction generator is connected to a power system as a distributed power supply.

First, based on the equivalent circuit (steady state) in the upper part of FIG. 1 in which the secondary side of the induction machine is converted to the primary side, the electric quantity (active power, reactive power, power factor, torque) of each part of the induction machine is obtained. ) Is calculated. One phase voltage, current,
The impedance is determined as follows. V ₁ : primary terminal voltage, E: primary applied voltage, E ₁ : primary induced voltage, E ₂ ′: primary-side converted value of secondary induced voltage when the motor is at rest (hereinafter, each secondary side voltage) I ₁ : primary current, I ₂ ′: primary current converted value of secondary current, Z ₁ = r ₁ + jx ₁ : primary impedance, Z ₂ ′ = r ₂ ′ + Jsx ₂ ': primary side converted value of secondary impedance at the time of slip s, Y ₀ = jb ₀ : excitation admittance

First, the primary-side active power P ₁ , reactive power Q ₁ , and power factor pf ₁ of the three-phase induction motor are determined. The active power P ₁ and the reactive power Q ₁ are output in the case of an induction generator, and are input in the case of operating as an induction motor. When the induction machine is rotating with the slip s, the speed at which the magnetic flux cuts through the secondary conductor is s times as fast as at rest, and the voltage induced in the secondary conductor is equal to the stationary induced voltage E ₂ at rest. For s
The E _2. At the same time, the frequency of the voltage sE ₂ also becomes sf with respect to f at rest, and the reactance of the secondary circuit also becomes sx ₂ with respect to x ₂ at rest. Taking the above into consideration and calculating the values of the currents and voltages under the condition of Equation 1, the current vectors I ₂ ′ and I ₁ and the voltage vector V ₁ are obtained by considering the equivalent circuit in the upper part of FIG. , The relationships of Expressions 2, 3, and 4 are obtained.

[0013]

(Equation 1)

[0014]

(Equation 2)

[0015]

(Equation 3)

[0016]

(Equation 4)

A first-order applied voltage (induced voltage) vector E is obtained from Equation 4 and substituted into Equation 3 to obtain Equation 5.

[0018]

(Equation 5)

The denominator in the impedance part on the right side of Equation 5 is set as Equation 6, and coefficients a and b in Equation 6 are expressed by Equations 7 and 8, respectively.

[0020]

(Equation 6)

[0021]

[Equation 7] _{a = (r 1 + r 1} x 2 'b 0) s + (r 2' + x 1 r 2 'b 0)

[0022]

B = (x ₂ ′ + x ₁ x ₂ ′ b ₀ + x ₁ ) s + (− r ₁
r ₂ 'b ₀ )

Note that r ₁ , x ₁ ,
b ₀ , r ₂ ′, x ₂ ′ are various quantities in the equivalent circuit in the upper part of FIG. The numerator in the impedance part on the right side of Equation 5 is represented by Equation 9, and the coefficients c and d in Equation 9 are represented by Equations 10 and 11, respectively.

[0024]

(Equation 9)

[0025]

C = (1 + x ₂ 'b ₀ ) s

[0026]

## EQU11 ## d = −r ₂ ′ b ₀

Therefore, Equation 5 becomes Equation 12.

[0028]

(Equation 12)

From the above, the active power P ₁ , the reactive power Q ₁ , and the power factor pf ₁ on the primary side of the three-phase induction motor are as shown in Expressions 13 to 15. The middle and lower parts of FIG. 1 show the flow of energy on the primary side and the secondary side in the induction motor, and the active power P ₁ and the reactive power Q ₁ are shown as inputs to the induction motor, respectively.

[0030]

(Equation 13)

[0031]

[Equation 14]

[0032]

(Equation 15)

Next, the effective power P ₂ on the secondary side is obtained.
As shown in the middle part of FIG. 1, the value obtained by subtracting the secondary copper loss P _c2 from the total secondary input (= primary active power P _{1 −primary} copper loss P _c1 ) is the effective power P ₂ on the secondary side. Become. First, a voltage vector E is obtained from Equation 4 and substituted into Equation 2, to obtain Equation 1
Get 6.

[0034]

(Equation 16)

Since the denominator of the fraction on the right side of Expression 16 is a + jb according to Expression 6, by multiplying the numerator and denominator by (a−jb), Expression 16 is transformed into Expression 17.

[0036]

[Equation 17]

Therefore, the effective power P ₂ on the secondary side of the three-phase induction motor is expressed by the following equation (18).

[0038]

(Equation 18)

Next, the torque T of the induction machine can be expressed by Expression 19 using the electric power P ₂ , the rotor angular velocity ω, the slip s, and the synchronous angular velocity ω ₀ .

[0040]

T = P ₂ / ω = P ₂ / {ω ₀ (1-s)}

The active power P _c2 and the reactive power Q _c2 of the secondary copper loss of the three-phase induction motor are _calculated from the following equation (20) using the following equation (20).
21.

[0042]

(Equation 20)

[0043]

(Equation 21)

Further, the active power P _c1 and the reactive power Q _c1 of the primary copper loss of the three-phase induction motor are _calculated by using the following equations (22) and (22).
23.

[0045]

(Equation 22)

[0046]

(Equation 23)

Next, the reactive power Q ₀ of the iron loss of the three-phase induction motor.
Ask for. Equation 24 is obtained when the voltage vector E is obtained from Equation 4.

[0048]

(Equation 24)

Since the denominator of the fraction on the right side of Equation 24 is a + jb, Equation (25) is obtained by multiplying the numerator and denominator of Equation 24 by (a−jb).

[0050]

(Equation 25)

Therefore, the reactive power Q of the iron loss of the three-phase induction motor
₀ is as shown in Expression 26.

[0052]

(Equation 26)

Next, taking the induction generator as an example, its primary active power P ₁ and primary reactive power Q ₁ are calculated. Table 1 shows the constants of the induction generator converted to the primary phase of the star connection.

[0054]

[Table 1]

When the induction generator is performing constant output control, the primary active power P ₁ of Expression 13 is made constant as shown in Expression 27, and from Expression 14, the voltage characteristic of the primary reactive power Q ₁ with respect to the primary terminal voltage V _{1 is obtained} . Get. As the voltage characteristic, the voltage reactive power Q ₁ as shown in Equation 28 V (V ₁₎
Squared term (Z characteristic: impedance characteristic), squared term (I
It is expanded into a polynomial composed of terms of a characteristic: current characteristic) and a zero-th term (P characteristic: power characteristic). That is, the reactive power output from the induction generator is expressed in a ZIP format, similarly to the conventional load. Note that a ₂ , a ₁ , and a ₀ in Expression 28 are coefficients expressed as a function of P ₁ .

[0056]

[Equation 27] P ₁ = const

[0057]

Q ₁ = f (V ₁ , S) = f (V ₁ , S (P ₁ , V ₁ )) = f (V ₁ , P ₁ ) ≒ a ₂ (P ₁ ) V ² + a ₁ ( P ₁ ) V ¹ + a ₀ (P ₁ ) V ⁰

In the equation (28), a ₂ (P ₁ ), a ₁
(P ₁ ) and a ₀ (P ₁ ) indicate that they are functions of P ₁ as described above. Hereinafter, the derivation of Equation 28 will be described. Excitation susceptance b ₀ in the upper equivalent circuit of FIG. 1 is moved to the left end and treated separately as impedance. Equations 7, 8, and 9 relating to coefficients a, b, c, d
By setting b ₀ of 10, 11 to 0 and x ₂ ′ = x ₂ , r ₂ ′ = r ₂ , a = r ₁ s + r ₂ , b = (x ₁ + x ₂ ) s, c = s, d = When P _{1 of} Equation 13 and Q ₁ of Equation 14 are calculated for one phase assuming 0, Equations 29 and 30 are obtained.

[0059]

[Number 29] _{P 1 = s (r 1 s} + r 2) V 1 2 / {(r 1 s + r
₂ ) ² + s ² (x ₁ + x ₂ ) ² ｝

[0060]

[Number 30] _{^{Q 1 = s 2 V 1 2}} (x 1 + x 2) / {(r 1 s +
r ₂ ) ² + s ² (x ₁ + x ₂ ) ² ｝

By eliminating s from these equations, the following equation 3
The solution of Equations 32 and 33 is obtained by solving the quadratic equation of Q ₁ shown in FIG. It should be noted that the solution on the negative side of Formulas 32 and 33 (Formula 3)
And the use of detailed solution of Q ₁₎ shown in 2.

[0062]

[Number 31] ^{_{P 1 2 (x 1 + x}} 2) = Q 1 (V 1 2 -Q 1 x 1 -Q 1 x 2)

[0063]

(Equation 32)

[0064]

[Equation 33]

By performing the Taylor expansion of Expression 32 near the voltage V ₁ = 1.0 (pu), the approximate expression of Q ₁ in Expression 34 and the coefficient for each order of the voltage V as shown in Expressions 35 to 37 are obtained. _{a 2 (P 1), a} 1 (P 1), to obtain a ₀ to (P _1).
In the coefficient a ₂ (P ₁ ) of V ² (Equation 35), the excitation susceptance b ₀ ignored so far is added.

[0066]

Q ₁ ３４a ₂ (P ₁ ) V ² + a ₁ (P ₁ ) V ¹ + a ₀ (P ₁ ) V ⁰

[0067]

(Equation 35)

[0068]

[Equation 36]

[0069]

(37)

Next, using the numerical values of Table 1 presented earlier,
The detailed solution of Q ₁ obtained by Expression 32 and the approximate solution of Q ₁ obtained by Expressions 34 to 37 are three-dimensionally displayed as a function of voltage V ₁ (V in the figure) and active power P ₁ (P in the figure). FIG. 2 shows the result. In FIG. 2, (a) is a detailed solution,
(B) is an approximate solution. Similarly, those displaying 2D reactive power Q ₁ the voltages V ₁ to the effective power P ₁ which is a parameter 3, the reactive power Q ₁ with respect to voltages V ₁ that was active power P ₁ Parameter 2-dimensional display Fig. 4
(A) is a detailed solution and (b) is an approximate solution. As apparent from FIGS. 2 to 4, the approximate solution is very close to the detailed solution.

As described above, in the present embodiment, the induction machine type
Primary active power with distributed power model performing constant output control
P₁Constant (P₁= Const), the induction machine type
Primary reactive power Q output by the distributed power model₁Into Equation 34
Therefore, it can be approximated. And in equation 34
V^Two, V¹, V⁰Each coefficient a_Two(P₁), A₁(P₁), A₀
(P₁) Is a known one as shown in equations 35 to 37.
Next leakage reactance x ₁, Secondary leakage reactance x_Two,one
Next active power P₁And excitation susceptance b₀By
Since it can be calculated first,
The primary reactive power Q output by the induction machine type distributed power model
₁Can be easily obtained.

Next, an embodiment of an inverter type distributed power supply model will be described as a distribution system model described in claim 2. When a rotating machine such as a photovoltaic power generator, a synchronous machine, or an induction machine (such as a wind power generator) is connected to a system via an inverter, an inverter-type distributed power supply model is provided. The inverter-type distributed power supply model includes a voltage control method and a current control method depending on the difference in the control method. The voltage control method performs control based on the system voltage that is connected, and the current control method performs control based on the current injected from the model into the system. Therefore, the voltage-controlled inverter-type distributed power supply model can be considered as a constant voltage source, and the current-controlled inverter-type distributed power supply model can be considered as a constant current source. However, in either control method, there is a maximum value of the current that can be injected into the system according to the capacity of the generator. Therefore, the control is performed in consideration of the maximum value of the current. Generally, voltage-controlled inverters can be said to be the mainstream.

Also, as in the induction machine type distributed power supply model,
If the induction machine is directly connected to the grid, the device characteristics become complicated because of the above-mentioned voltage characteristics. However, when an induction machine is connected to a system via an inverter, the voltage-controlled inverter-type distributed power supply model provided with the induction machine has an active power P (inverter output power) and a voltage V (Inverter output voltage) can be modeled as so-called P and V designations. However, as described above, there is a restriction on the maximum value of the current that can be injected into the system, and when the maximum value is reached, the current is fixed at a constant current. In this case, similarly to the current control method, the injection current (output current of the distributed power supply model) I becomes a designated value in addition to the active power P,
In other words, P and Q are designated. The handling of the power flow calculation when the output active power P and the output current I of the distributed power supply model are specified is considered as follows. That is, based on the calculated voltage value V of the node to which the distributed power supply model is connected and the specified power value P, a reactive power value Q corresponding to the specified current value I is calculated based on Expression 38.

[0074]

## EQU38 ## VI ^* = P + jQ (V: calculated node voltage, I: output current value of distributed power supply (I ^* is a complex conjugate thereof), P + jQ: power value of node)

By transforming Equation 38 as V = e + jf, Equation 39 is obtained, and Equations 40 to 42 are obtained from Equation 39.

[0076]

I ^* = (P + jQ) / (e + jf)

[0077]

I ^* I = | I | ² = {(P + jQ) / (e + jf)} × {(P−jQ) / (e−jf)} = (P ² + Q ² ) / (e ² + f ² )

[0078]

Q ² = | I | ² (e ² + f ² ) −P ²

[0079]

Q = ± {| I | ² (e ² + f ² ) −P ² }

Here, depending on the designation of the power factor of the distributed power supply model, the solution is either + or-in equation (42). Equation 4
According to 2, the calculated node voltage V (= e + jf)
And the absolute value | I | of the output current of the distributed power supply model and the active power P, the reactive power Q can be calculated. If the P and Q values are incorporated into the load value at the node, and the power flow is calculated, good.

Next, an embodiment of a separately-excited SVC model will be described as a distribution system model described in claim 3. S
When the reactive power on the load side fluctuates, the VC also fluctuates in the reactive power of the system, and the system voltage fluctuates accordingly.
This is a device that suppresses fluctuations in the system voltage by injecting capacitive or inductive reactive power into the system by flowing a leading or lagging reactive current. FIG. 5 is a characteristic diagram of the separately excited SVC. In FIG. 5, I _n the voltage (absolute value) of the reactive current, V _n is a node which SVC is installed the SVC is output, I _max is the maximum current, the voltage specified value V _ref node, X _S (= [Delta] V / I _n) is the slope reactance of the characteristics of SVC, V _a, V _B is a reactive current output respectively ±
This is the voltage when I _max is exceeded. V for separately excited SVC
_ref, I _max, X _S, and the impedance X _L in the case of SVC operates as a reactor, the admittance Y _C when also operates as a capacitor is input.

In FIG. 5, between points A and B, the reactive current output from the SVC is calculated by the following equation 43 according to the slow preactance. Then, the voltage V _n V _B
When it is above, it works as a simple reactor, and when it is below V _A , it works just as a capacitor.

[0083]

[Number 43] I _n = ΔV / X _S

At the node where the SVC is installed, only the reactive current is injected with respect to the voltage of the node, and only the reactive power Q is injected into the system. Here, in order for only the reactive power Q to be injected under a certain node voltage, the following relationship must be satisfied when the node voltage is e + jf and the injected reactive power is jQ.

[0085]

(E + jf) (g + jh) ^* = jQ ((g + jh): reactive current vector, (g + jh) ^* is its conjugate complex number)

[0086]

(Eg + fh) + j (fg−eh) = jQ

[0087]

[Equation 46] (eg + fh) = 0

[0088]

(Fg−eh) = Q

By substituting h = −eg / f obtained from Expression 46 into Expression 47, Expression 48 is obtained.

[0090]

G = Qf / (e ² + f ² ), h = −Qe / (e ² + f ² )

[0091] Here, since it is ^{√ (g 2 + h 2)} = I n, to obtain a formula 49-51.

[0092]

[Equation 49]

[0093]

[Equation 50]

[0094]

Equation 51] ^{Q = √ (e 2 + f} 2) I n = V n I n

From the equation 51, the reactive power Q injected or consumed by the separately excited SVC model can be calculated from the absolute value of the node voltage and the absolute value of the reactive current. Specifically, the voltage V _n nodes separately excited SVC model is installed voltage V _A, the magnitude relation between V _B, can be calculated by the following equation 52-55. That is, when V _n <V _A , the injected reactive power is represented by Expression 52.

[0096]

Q = Y _C V _n ²

When V _A <V _n <V _B , the injected reactive power (when V ₁ −V _1ref <0) is given by Equation 53, and the reactive power consumption (when V ₁ −V _1ref > 0) is given by Equation 54. Become.

[0098]

Q = V _n (ΔV / X _S )

[0099]

Q = -V _n (ΔV / X _S )

When V _n > V _B , the reactive power consumption is given by
It becomes 5.

[0101]

[Number 55] Q = -V _n ² / X _L

Next, an embodiment of a self-excited SVC model will be described as a distribution system model according to the third aspect. FIG. 6 is a characteristic diagram of the self-excited SVC. In FIG. 6, between points A and B, according to the slow reactance,
The reactive current output from the SVC is calculated by the aforementioned equation (43). When the voltage V _n becomes below V _B above or V _A,
Reactive current I _n is fixed to ± I _max. Actually, when the voltage reaches the overvoltage or the undervoltage, the trip occurs due to the operation of the overvoltage relay or the undervoltage relay, but here, the operation of these relays is not simulated. in this case,
The specified voltage value V _ref , the maximum current value I _max , and the slow reactance X _S are input as parameters to the self-excited SVC model.

In the self-excited SVC model,
Node voltage V_nAnd the voltage V_A, V _BDue to the size relationship with
Thus, it can be calculated by the following equations 56 to 59. You
That is, V_n<V_AIn the case of, the injected reactive power is represented by Expression 56.

[0104]

[Expression 56] Q = V _n I _max

[0105] For _{V A <V n <V B} , ( the case of V ₁ -V _1ref <0) injecting reactive power (in the case of V ₁ -V _1ref> 0) Equation 57, consumption reactive power to the formula 58 Become.

[0106]

Q = V _n (ΔV / X _S )

[0107]

Q = −V _n (ΔV / X _S )

When V _n > V _B , the reactive power consumption is given by
It becomes 9.

[0109]

Q = −V _n I _max

Next, as an embodiment of the invention described in claim 4, a high-speed power flow calculation method (Backward-Forward method) for a radial system using the various distribution system models will be described. First, consider a state equation in which the power flowing into each branch of the system and the node voltage are state quantities. In systems with two nodes in FIG. 7, if the branch is distribution line, the effective power P ₂ at the node 2, the reactive power Q _2, the voltage V _2, | V ₂ | respect ^2, the following equations 60 to 63 Holds. The admittances Y ₁ and Y ₂ of the line are assumed to be capacitive because of the line charging capacity. Where the subscript " _1,2 "
Unlike the suffixes corresponding to “primary” and “secondary” in the embodiment of the induction machine type distributed power supply model described above, they correspond to “node 1” and “node 2”.

[0111]

[Equation 60]

In equation (60), P ₁ is the active power flowing into the node 1, Q ₁ is the reactive power, P _{loss, 1} is the active power loss at the node 1, and P _L2 is the active power of the load at the node 2. . Here, P ₂ is P ₁ , Q ₁ , |
It is represented by a function f _P of V ₁ | ² .

[0113]

[Equation 61]

In this equation 61, Q _{loss, 1} is the reactive power loss at node 1 and _QL2 is the reactive power of the load at node 2. Here, Q _{2 is} also represented by a function f _{Q of} P ₁ , Q ₁ , | V ₁ | ² .

[0115]

(Equation 62)

In Equation 62, e ₁ and f ₁ are the real part (effective part) and the imaginary part (ineffective part) of the vector V ₁ ,
e ₂ and f ₂ are the real part and the imaginary part of the vector V ₂ .

[0117]

[Equation 63]

In equation (63), | V ₂ | ² is also P ₁ , Q
₁ , | V ₁ | ² is represented by the function f _V. That is, by using the active power P ₁ , the reactive power Q ₁ , and the voltage V ₁ at the node ₁ , the active power P ₂ as the state quantity at the node ₂ ,
The reactive power Q ₂ and | V ₂ | ² can be expressed as described above. When there is a branch, the tidal current flowing through the branch line may be considered in the above-described equation of state.

If the branch is a transformer, the admittance Y ₁ = n (n-1) / Z _L , Y ₂ = in FIG.
(1-n) / Z _L as (n is transformer ratio, Z _L is a transformer leakage inductance), active power P _2, the reactive power Q _2, the voltage V ₂ and | by ² Equation 64 - 67 | V ₂ expressed. Here, since it is assumed that Y ₁ and Y ₂ are capacitive, it is necessary to note that a minus is added when Y ₁ and Y ₂ are actually substituted.

[0120]

[Equation 64]

[0121]

[Equation 65]

[0122]

[Equation 66]

[0123]

[Equation 67]

[0124] Also in this _{case, P 2, Q 2, |} V 2 | 2 is P _1,
Q ₁ , | V ₁ | ² are represented by functions f _P , f _Q , f _V.
From the above, when the power supply voltage is assumed to be constant, in the radial system, considering the relationship between the upstream and downstream nodes, the power flow from the power supply and the power flowing out to each branch line is assumed to be a state variable. The calculation may be performed, and the other variables may be sequentially calculated from the power supply end using the state equation. In the normal high-pressure power flow calculation, the state variables of all nodes are used as state variables, whereas in the method of the present invention, the state variables are greatly reduced by using the power output from the distribution line to each branch line. It is possible to realize high-speed power flow calculation by reducing the power flow.

FIG. 9 is a schematic diagram of the Backward-Forward method. 11 bus system shown (bus numbers # 000 to # 2j
In n _2j ), the conventional method such as the Newton-Raphson method requires the number of state variables as many as the number of nodes. But Backwa
In the rd-Forward method, only the amount of power flowing into the distribution line or the branch line is a state variable. _Therefore , three power amounts P ₀₀₀ + jQ ₀₀₀ , P _1i0 + jQ _1i0 , P _2i0 + j indicated by thick arrows in FIG.
Q _2i0 only, and the state variable decreases from 11 to 3.
In FIG. 9, F1 to F3 indicate distribution lines. Further, using these three state variables, the state quantity of each node below the three state variables can be obtained by successive calculation (the thin line arrow in FIG. 9). Further, there is no electric power flowing out from the terminal (broken arrow in FIG. 9) as a constraint condition.
Modify the state variables.

FIG. 10 is a flowchart of the process according to the Backward-Forward method. Hereinafter, description will be made in order. (1) Data input (S1) System configuration, power supply capacity, load capacity, line data (line impedance, etc.), transformer data (rated voltage and number of taps,
Tap width) is input to the computer.

(2) Initial Value Calculation (S2) Next, the load amount (load power) is calculated using the initial estimated value of each voltage.
Is calculated, and the total of the load amounts added from the terminal nodes is calculated as the power flowing into each branch distribution line (for example, the distribution line F2 in FIG. 9), that is, the initial value of the state variable (P in the distribution line F2).
_1i0 + _jQ1i0 ).

(3) Calculation of system state quantity (forward calculation by sequential calculation) (S3) Using the obtained state variables, if the branch is a distribution line, the above equations 60 to 63 are used, and if the branch is a transformer, The state quantities (active power, reactive power, and voltage) are sequentially calculated from the power supply toward the terminal node according to the equations 64 to 67.

(4) Correction of state variables (reverse calculation) (S
4) Modify state variables based on the fact that there is no power drain from end nodes. That is, the inflow power at the head node of each branch distribution line is corrected by the error at the terminal node. The correction amount of the inflow power of the branch distribution line is the sum of the correction amount of the branch distribution line and the correction amount of the branch distribution line from the branch distribution line.

(5) Convergence Judgment (S5) A convergence judgment is made based on whether or not the absolute value of the power of the terminal node has become smaller than a certain judgment reference value.

FIG. 11 shows the concept of the forward calculation and the backward calculation described above. In the forward calculation of FIG.
The downstream state quantity is obtained from the upstream state quantity in the path, and the downstream state quantity is similarly obtained for the path branched from this path. Hereinafter, the calculation proceeds in the same manner. In the backward calculation of FIG. 11B, convergence calculation is performed while changing the state variable of the head node based on the power value of the terminal node of the path, and the power of the terminal node is similarly calculated for the branch source path via the path. The convergence calculation is performed while updating the state variable of the head node based on the value. Hereinafter, the calculation proceeds in the same manner. In this method, since the number of state variables is significantly reduced, high-speed calculation is possible as compared with the method using the state variables of all nodes.

Next, how to incorporate each distribution system model into the Backward-Forward method will be described. All the distribution system models are considered when calculating the state quantities of each node in the calculation of the system state quantities (forward calculation by sequential calculation) (S3) in FIG.

(1) Induction motor type distributed power supply model In this distributed power supply model, active power P is calculated at a node, and reactive power Q is approximately calculated by the equation 34 using the calculated voltage V. Equations 60 and 61 and Equations 64 and 6 use the P and Q values as the power injected into the node.
The load values P _L2 and Q _L2 in (5) are taken (reflected).

(2) Voltage control type inverter type distributed power supply
Model Calculation of system state variables in Fig. 10 (forward calculation by sequential calculation)
In (S3), the active power P and the voltage V are specified.
By specifying P and V, power flow is calculated and reactive power Q is calculated.
Confuse. The output power of the distributed power model is
Calculate the flow, this is the maximum value I _maxIf it does not exceed
Continue with the calculation in the downstream direction. Maximum value I_maxBeyond
Then, the active power P and the current I are fixed.
P and Q are specified using the reactive power Q obtained by Equation 42
And recalculate the node. And P, Q designation
Current output of the distributed power model using the voltage V calculated at the time
Calculate the force and this is the maximum value I_maxP, V finger if below
The calculation of that node is redone as usual.

(3) Current control type inverter type distributed power supply model Calculation of system state quantity in FIG. 10 (forward calculation by sequential calculation)
In (S3), P and Q are designated and the node is calculated by using the reactive power Q obtained from the designated values of the active power P and the current I by Expression 42.

(4) Separately-excited / self-excited SVC model In these SVC models, in calculating the state quantity of a node, the reactive power Q calculated by Equations 52 to 55 or 56 to 59 is used as the injection power of the node as Equation 61 , 6
The load quantity _QL2 at 5 is taken in.

[0137]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First, an operation example of a voltage controlled inverter type distributed power supply model will be described. FIG. 12 shows a target model system, in which G is a power supply for sending (delivery voltage is 6600 [V]), and system capacity is 10 [MVA]. Here, CG indicates a voltage control type inverter type distributed power supply model, and 0 to 5 indicate nodes. The impedance of the distribution line F is 0.2727 + j0.426 [Ω / k
m], and the distance between all nodes is 1.0 [km]. Each node load is 200 [kW] with a constant power load, and the power factor is 0.9 with a delay. The distributed power supply model CG is connected to the terminal node 5, and the output designation value is 200 [kVA].
The specified voltage value is 6600 [V], and the power factor is positive (reactive power is injected).

[0138] when obtained by simulation and an output current I _G and the current maximum value I _max of the distributed power model, the voltage distribution of each node in the following two types shown in FIG. 13. a. Current maximum value 0.04 [pu] (about 105 [A]):
Case the output current I _G does not exceed the current maximum value I _max (I _G
<I _max ) b. Current maximum value 0.03 [pu] (approximately 79 [A]): the output current I _G is greater than the current maximum value I _max Case (I _G> I
_max ) Note that the legend in FIG. 13 corresponds to a and b described above.

[0139] According to FIG. 13, the case a output current I _G of the distributed power model does not exceed the current maximum value I _max, P,
Since V is specified, the voltage of the terminal node is set to the specified value of 6600 [V] according to the voltage control. However, in the case b the output current I _G is greater than the current maximum value I _max,
It can be seen that the voltage of the terminal node has not reached the specified value of 6600 [V] because P and I are equivalent to the specified P and Q with P and I fixed. From the above, it was confirmed that the voltage-controlled inverter-type distributed power supply model was operating properly.

Next, an operation example of the current-controlled inverter-type distributed power supply model will be described. The target model system is the same as that of FIG.
The distribution line impedance and the contents of each node load are the same as those in the above-described voltage control system. The difference is that the specified output current value of the distributed power supply model is c. 0.03 [pu], d. 0.04 [pu], e. This is a point changed to 0.05 [pu]. The legend in FIG.
e. The power factor of the distributed power supply model is positive (reactive power is injected) as in the case of the voltage control method.

In the current-controlled inverter-type distributed power supply model, it is assumed that a specified current value in consideration of the maximum current value is input when data is input. Therefore, the specified current value is set to 0.03 [pu], 0.04 [pu], 0.05
If the value is increased to [pu], the reactive power Q also increases accordingly. Referring to FIG. 14, it can be seen that the reactive power increases with an increase in the specified current value, and the voltage V also increases. From this, it was confirmed that the current control type inverter type distributed power supply model was operating properly.

[0142]

As described above, according to the present invention, an induction machine type distributed power supply model, a voltage control type inverter type distributed power supply model, a current control type inverter type distributed power supply model, and a separately-excited SVC which have not been considered in the past. Model, self-excited S
In addition to formulating the VC model, it is possible to provide a power flow calculation method for a radial system in which these distribution system models are incorporated in forward calculation, and to obtain a voltage and current distribution of the system when a distributed power source is introduced. Power flow calculation can be further speeded up and its efficiency can be increased.

[Brief description of the drawings]

FIG. 1 is a diagram showing an equivalent circuit of an induction machine and a flow of energy.

FIG. 2 is a diagram showing a three-dimensional display of reactive power as a function of voltage and active power.

FIG. 3 is a diagram showing a two-dimensional display of reactive power with respect to active power using voltage as a parameter.

FIG. 4 is a diagram in which reactive power with respect to voltage is two-dimensionally displayed using active power as a parameter.

FIG. 5 is a characteristic diagram of a separately excited SVC.

FIG. 6 is a characteristic diagram of a self-excited SVC.

FIG. 7 is an explanatory diagram of a two-node system.

FIG. 8 is an explanatory diagram of a two-node system.

FIG. 9 is a schematic diagram of the Backward-Forward method.

FIG. 10 is a flowchart of the Backward-Forward method.

FIG. 11 is a conceptual diagram of forward calculation and backward calculation.

FIG. 12 is an explanatory diagram of a model system in the embodiment.

FIG. 13 is a diagram showing a voltage distribution of each node in the example.

FIG. 14 is a diagram showing a voltage distribution of each node in the example.

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Yoshikazu Fukuyama 1-1, Tanabe-Nitta, Kawasaki-ku, Kawasaki-shi, Kanagawa Prefecture Inside Fuji Electric Co., Ltd. (72) Inventor Kazusuke Nakanishi 1, Tanabe-Nitta, Kawasaki-ku, Kawasaki-ku, Kanagawa Prefecture 1 No. 1 Inside Fuji Electric Co., Ltd. (72) Inventor Takuya Watanabe 1-1, Tanabe Nitta, Kawasaki-ku, Kawasaki City, Kanagawa Prefecture Inside Fuji Electric Co., Ltd. (72) Hiroki Okabayashi 1, Tanabe Nitta, Kawasaki-ku, Kawasaki City, Kanagawa Prefecture No. 1 Fuji Electric Co., Ltd. F term (reference) 5G066 AA01 AA03 AE09

Claims (4)

[Claims] 1. A distribution system model used for power flow calculation of a power system in which distributed power sources are interconnected, wherein the distribution system model is an induction machine type distributed power source model in which an induction generator is interconnected as a distributed power source in the system. , and the the induction machine type dispersed generator model is the product of square term of the voltage V of the coefficients a ₂ and interconnection node when the constant output control active power P which is the output as a constant, the coefficient a ₁ and Voltage V
The product of 1 square terms of approximating the reactive power Q by the sum of zero power term of the product of the coefficient a ₀ and the voltage V, and the coefficients a _2, the effective power P, the primary leakage reactance x of induction generator _1, the secondary leakage reactance x _2, represented using excitation susceptance b _0, the coefficients a ₁ and a _0, the active power P, the induction generator primary leakage reactance x _1, using a secondary leakage reactance x ₂ A distribution system model characterized by being represented by. 2. A distribution system model used for power flow calculation of a power system to which a distributed power source is connected, wherein the distribution system model includes a voltage control type or a current control type inverter connected to the system as a distributed power source. This is an inverter-type distributed power supply model. This inverter-type distributed power supply model is configured such that when an active power P as an output thereof and an injection current I to the system are specified,
From the calculated voltage V of the interconnection node and the active power P, a reactive power Q corresponding to the specified value of the injection current I is expressed by: Q = ± {| I | ² (e ² + f ² ) −P ² } A distribution system model that calculates and determines whether the reactive power Q is positive or negative according to a specified power factor. 3. A distribution system model used for power flow calculation of a power system in which distributed power sources are interconnected, wherein the distribution system model is a separately-excited or self-excited static var compensator model, self-excited static var compensator model is determined from the voltage V _n of the calculated installation nodes, the slope reactance X _S is the maximum value ± I _max and models the characteristics of positive and negative reactive current is a model power secondary One of the voltage V _a, in the case of V _a <V _n <V _B with respect to V _B, the difference voltage between the voltage specified value _{V ref (V a <V ref} <V B) and the V _a delta
V and asked to injection or consumption reactive power _{Q = ± V n (ΔV /} X S) from said X _S and the V _n, the static var compensator model of the separately excited, in the case of V _n <V _A , The admittance Y _C during the operation of the capacitor and the above-mentioned V _n
Seeking injected reactive power Q = Y _C V _n ² and a, in the case of V _n> V _B, the reactive power Q = -V _n ² / X _L consumed from the impedance X _L during reactor operation and the V _n The self-excited static var compensator model calculates the reactive power injected or consumed from I _max and V _n when V _n <V _A or V _n > V _B , and Q = ± V _n I _max A distribution system model characterized by the following. 4. A data input step for inputting a system configuration of a radial system, a power supply capacity, a load capacity, line data, transformer data, etc. to a computer, and an initial calculation value of a load amount is provided at an end of a main distribution line and a branch distribution line. An initial value calculation step of adding an initial value of a state variable at a head node of each distribution line by adding from a node; and sequentially calculating a state quantity at each node of each distribution line from the head node to a terminal node using the state variables. Calculating the state variables of the distribution line, correcting the state variables of the top node of each distribution line by the amount of error at the terminal node of each distribution line, and comparing the state variables at the terminal nodes with the criterion. A convergence determination step of performing a convergence determination; and a radial system power flow calculation method, comprising: a step of calculating the system state quantity; The reactive power determined by the distributed power supply model and the specified active power, the reactive power determined by the distributed power supply model of the inverter and the specified active power, and claim 3.
A reactive power calculation method for a radial system, wherein the reactive power obtained by the static var compensator model is taken into the load at each node.