KR20150111458A - High-Speed Method for Large Scale Power Systems - Google Patents

Abstract

Disclosed is a high speed method for fault level constrained-optimal power flow (FLC-OPF), capable of improving the speed of calculation when power network reformation algorithm (NRA) based on FLC-OPF is applied to a large scale system. To achieve the purpose, the method to apply the NRA based on FLC-OPF to the large scale system includes a step (a) of determining matrix components of bus impedance and Thevenin impedance by using Kron reduction in a state in which a consecutive variable (X) having a predetermined connective impact is removed when the large scale system is seen from a fault level constrained-bus; and a step (b) of calculating a Jacobian component and a Hessian component by using the matrix components of the bus impedance and the Thevenin impedance. Therefore, the speed of calculation in the large scale system is improved.

Description

{High-Speed Method for Large Scale Power Systems}

The present invention relates to a high-speed method for large-scale system applications, and more particularly, to a method and apparatus for increasing the calculation speed problem caused by application of a power network reconfiguration algorithm (NRA) based on fault current constraint optimal algebraic calculation (FLC-OPF) (FLC-OPF) for fault current constraint optimal algae calculation (FLC-OPF).

Demand for power systems is continuously increasing due to the development of industry and the improvement of people's standard of living. This increase in power demand is accompanied by the problem of increasing the breaking capacity in accordance with the multi-loop structure in order to increase the transmission system and improve the reliability because of the characteristic of the load area where there is no large-scale power generation facility.

As a result, a lot of fault current surplus occurred due to the concentration of the power supply complex, and in order to overcome this problem, a part of the transmission network is separated and operated, thereby failing to efficiently utilize the transmission facilities.

Currently, in order to solve the problem of exceeding the fault current, it is necessary to repeatedly perform the processes such as fault current calculation, algae calculation, and change of the grid, and to continuously find ways to reconfigure the power system and replace the breaker capacity. Instead of this iterative calculation method, it is required to develop an algorithm that can maximize the efficiency of system operation while simultaneously considering fault current calculation and algae calculation. To this end, a power network reconfiguration algorithm (NRA) based on Fault Current Constrained Optimal Algebraic Computation (FLC-OPF) has been developed.

However, when the FLC-OPF-based NRA is applied to a large-scale system, there is a problem in that it takes a long calculation time when the fault current restriction and the number of the bus separation candidates are very large.

1. Korean Patent No. 0901520, Date of Registration: June 01, 2009 Title of invention: Gap of multi-thread dynamical system by entities / RTI >

SUMMARY OF THE INVENTION The present invention has been conceived in order to solve the above problems, and it is an object of the present invention to provide a power grid reconfiguration algorithm (NRA) based on fault current constrained optimal algae calculation (FLC-OPF) And to provide a method for shortening a calculation time for a component to achieve a high speed.

In order to accomplish the objects of the present invention as described above and to carry out the characteristic functions of the present invention described below, features of the present invention are as follows.

According to one aspect of the present invention, there is provided a method for accelerating a power network reconfiguration algorithm (NRA) based on fault current constrained optimal algebraic computation (FLC-OPF) to a large scale system, the method comprising: (a) Determining the components of the thevenin impedance and the bus impedance matrix using the Kron reduction with the continuous variable (X) having a predetermined coupling effect removed when the system is viewed; And (b) calculating the Jacobian component and the Hessian component using the determined components of the thevenin impedance and the bus impedance matrix.

Here, the step (b) according to one aspect of the present invention may determine the components of the thevenin impedance and the bus impedance matrix according to the following equation (1).

...식 (1)

... (1)

Here, the Z _{f, f:} and advantages f wherein Z _f, Thevenin impedance, which is determined when looking the external system from _{f ':} if the input kl bus jX, a modified Z _{f, f,} said Z _{f, k:} (F, k) elements of the original line impedance matrix _, Z _{f, l} : (f, l) elements of the original line impedance matrix _, Z _{k, f} : _{l, f:} the source bus line impedance matrix (l, f) component, the Z _{k, k:} the source bus line impedance matrix (k, k) element, wherein Z _{l, k:} the source bus line impedance matrix (l, k) element, the Z _{k, l:} the original bus impedance matrix (k, l) and the element Z _{l, l:} the original bus impedance matrix of the (l, l) refers to the elements.

In addition, the Jacobian component according to an aspect of the present invention calculates a Jacobian matrix of nra x flc from the above-mentioned Thevenin impedance and the bus impedance matrix, and the Ha cyan component is calculated as nra x nra x from the above-mentioned thevenin impedance and the bus impedance matrix. The Hessian matrix of flc can be calculated. Here, nra denotes the number of bus line separations, and nflc denotes the number of the fault current constraints.

In addition, the acceleration method according to one aspect of the present invention is characterized in that (c) the fault current constraint bound to the fault current constraint and the fault current constraint considering only the countermeasure scheme (RA) And calculating the Jacobian component and the Hessian component using a processor having a reduced number of processors.

(D) an objective function according to the following expression (2) necessary for the fault current constrained optimal algae calculation (FLC-OPF) and a constraint condition according to the following expression (3) And calculating the Jacobian component and the Hessian component using the preprocessing auxiliary module without changing the Jacobian component.

... 식 (2)

... (2)

P _gk is an initial value of active power generation of the kth bus, P _{gk is a} generation deviation coefficient, ng is a total number of generators, P _{enk is} k ₍ k ₎ Th continuous variable X, the penalty function for X _k : the kth continuous variable X and the nx: the total number of X variables (the number of candidate busbar separation candidates).

... 식 (3)

... (3)

: 모선 전압크기 상하한 제약 벡터, 상기 P_g : 유효전력 발전 벡터, 상기

: 유효전력 발전 상하한 제약 벡터 및 상기 Q_g : 무효전력 발전 벡터, 상기

: 무효전력 발전 상하한 제약 벡터, 상기 S_t : 선로 조류 벡터, 상기

: 선로 조류 상한 제약 벡터, 상기 FLC_f : f번째 모선 고장 전류 계산 함수,

: f번째 모선 고장전류제약 최대값 및 상기 nflc : 고장전류제약의 총 수를 의미한다.P _kk , Q _tk : Effective power and reactive power injection of the kth bus, P _dk , Q _dk : Active power and reactive power load of the kth bus, P _gk , Q _gk : Effective of the kth bus and reactive power generation, the V _b: line voltage amplitude vector, the

: The upper and lower limit constraint vector of the bus voltage magnitude, P _g : Active power generation vector,

: Active power generation upper limit lower limit constraint vector and Q _g : Reactive power generation vector,

: Constraint Constraint Constraint vector for reactive power generation, S _t : Line vector,

: Line current upper limit vector, FLC _f : fth bus failure current calculation function,

: fth busline fault current constraint maximum value and nflc: total number of fault current constraints.

According to another aspect of the present invention, there is provided a method for increasing the Jacobian component and the Hessian component using a parallel algorithm for parallel computation.

As described above, according to the present invention, a system reconfiguration (bus separation, line transfer) determination considering a fault current problem is a new attempt to reconfigure the system in consideration of the system constraint. If the calculation speed for the real system is improved, It will be able to operate stable.

FIG. 1 is a flowchart illustrating a method of speeding up an FLC-OPF based NRA according to an embodiment of the present invention.
FIG. 2 is a diagram showing a result of inputting a continuous variable X into a bus break point according to an embodiment of the present invention.
3 is a diagram of a simple three-bus system in accordance with an embodiment of the present invention.
Fig. 4 is a diagram showing a system state (before bus separation) after calculation of general optimal algae.
FIG. 5 is a diagram illustrating a calculation result of a fault current constraint optimal alive according to an embodiment of the present invention.
FIG. 6 is a graph showing a tidal current and a fault current value after separating a mother line according to an embodiment of the present invention.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings, so that those skilled in the art can easily carry out the present invention. In the drawings, like reference numerals refer to the same or similar functions throughout the several views.

FIG. 1 is a flowchart illustrating an example of a speedup method (S100) using an FLC-OPF based NRA according to an embodiment of the present invention.

1, an acceleration method S100 according to an exemplary embodiment of the present invention includes steps S110 to S110 for applying a power network reconfiguration algorithm (NRA) based on fault current constrained optimal almanaculation (FLC-OPF) S150.

First, in step S110 according to the present invention, when the large-scale system is viewed from the bus line of the fault current constraint, the continuous variable X having a predetermined cooperative effect is removed, and the components of the thevenin impedance and the bus impedance matrix . At this time, the components of the thevenin impedance and the bus impedance matrix can be determined by the following equation (1).

...식 (1)

... (1)

Here, Z _{f , f} means the thevenin impedance determined when the external system is viewed from the high-order f, and Z _{f , f '} means the corrected Z _f , _f when the kl bus line jX is input. In addition, the Z _{f, k} means a (f, k) element of the source bus line impedance matrix, the Z _f, and _l represents a (f, l) component of the source bus line impedance matrix, and the Z _{k, f} is (K, f) element of the original line impedance matrix.

Further, the Z _l as in equation _{(1), f} represents a (l, f) components of the original bus impedance matrix, the Z _k, and _k refers to the (k, k) element of the source bus line impedance matrix and , wherein Z _{l, k} is the source bus line impedance matrix (l, k) refers to the elements, and the Z _{k, l} refers to the (k, l) of the original bus impedance matrix of elements, and the Z _{l, l} is the original (L, l) element of the matrix impedance matrix of "

In this case, since the components of the thevenin impedance and the bus impedance matrix according to the present invention depend on the magnitude of the voltage of the continuous variable X and the load bus line which are supplied to the bus breaker, the continuous current (X) It is desirable to use Kron reduction to determine the components of the thevenin impedance and the bus impedance matrix.

In this case, the Kron reduction refers to a matrix including a bus line to which a fault current restriction included in the corresponding system is applied, and adjacent bus lines corresponding to a countermeasure scheme (bus separation, RA), and other bus lines to be reduced.

Then, in step S120 according to the present invention, the Jacobian component and the Hessian component are calculated using the components of the thevenin impedance and the bus impedance matrix determined in step S110.

In this case, the Jacobian component and the Hessian component, which are calculated, calculate the Jacobian matrix of nra × flc from the transformed Sheffield impedance and the bus impedance matrix using the Kron reduction, and the Hessian component is transformed using the Kron reduction From the impedance and the bus impedance matrix, we calculate the nra × nra × flc Hessian matrix. Nra denotes the number of bus line separations, and nflc denotes the number of fault current constraints.

In this way, when calculating the Jacobian component and the Hessian component from the bus line of the fault current constraint, it takes a long time to calculate the Jacobian component and the Hessian component.

Thereafter, in step S130 according to the present invention, a processor capable of reducing the number of fault current limitations and countermeasures for high-speed calculation of the Jacobian and Hessian components described above can be used.

Generally, in relation to the fault current constraint, it is possible to distinguish between "binding" constraints and "non-binding" constraints through preliminary calculations. For the measure (RA), it is possible to distinguish between an electrically close ("close") RA and a far RA. In other words, it is desirable to analyze only the input data and to consider only the RA that is electrically close to the bound FLC.

Theoretically, by applying the voltage pattern according to the FLC-OPF, it is possible to select the FLC which has the possibility of the constraint violation among the unbound FLC in the input data. Nevertheless, even if one of the RAs is applied, the effect is different, but it can reduce the fault current value of almost all the buses.

Thus, by using a processor that reduces the number of fail current constraints and countermeasures taking into account only the fault current constraint bound in the fault current constraint and the countermeasure (RA) of the electrically closed bus line separation, When only electrically close RAs are included, the number of RAs considered in the FLC-OPF is reduced to enable faster calculations.

Thereafter, in step S140 according to the present invention, the objective function according to the following equation (2) necessary for the fault current constrained optimal algae calculation (FLC-OPF) and the constraint conditions according to the following equation (3) For example, a TOMLAB auxiliary module with a reconstructed library) is used to calculate Jacobian and Hessian components.

... 식 (2)

... (2)

Here, P _gk represents active power generation of the kth bus, P _gko represents an initial value of active power generation of the kth bus, and P _gk represents a power generation deviation coefficient.

₍ N ₎ denotes a total number of generators, P _{enk (.) Denotes} a penalty function for a k-th continuous variable X, X _k denotes a k-th continuous variable X, Means the number of variables (the number of candidates for separation of buses).

... 식 (3)

... (3)

는 모선 전압크기 상하한 제약 벡터를 의미하며, 상기 P_g 는 유효전력 발전 벡터를 의미하고, 상기

는 유효전력 발전 상하한 제약 벡터를 의미하며, 상기 Q_g 는 무효전력 발전 벡터, 상기

: 무효전력 발전 상하한 제약 벡터, 상기 S_t : 선로 조류 벡터, 상기

: 선로 조류 상한 제약 벡터를 의미한다.Here, P _tk and Q _tk denote the active power and reactive power injection of the kth bus, P _dk and Q _dk denote the active power and reactive power load of the kth bus, and P _gk and Q _dk Means the generation of reactive power and reactive power of the kth bus. In addition, the V _b represents a line voltage amplitude vector, and the

Denotes the upper limit and lower limit constraint vector of the bus voltage, P _g Means an active power generation vector,

Denotes the active power generation upper and lower limit constraint vector, and Q _g Is a reactive power generation vector,

: Constraint Constraint Constraint vector for reactive power generation, S _t : Line vector,

: Line bound upper limit constraint vector.

는 f번째 모선 고장전류제약 최대값을 의미하며, 상기 nflc는 고장전류제약의 총 수를 의미한다.Also, FLC _f denotes the f-th bus failure current calculation function,

Denotes the maximum value of the fth busline fault current constraint, and nflc denotes the total number of fault current constraints.

Here, the first term of the objective function applied in Equation (2) and Equation (3) represents the minimization of the deviation of the active power generation amount with respect to the initial power generation amount. This objective function term is expressed in a second-order expression, so it can be used as a function of the power generation cost expressed as a second derivative. And the second term of the objective function refers to either a penalty function or an additional objective function that causes the continuous variable X to move to a very small value representing bus merge or to a large value (in this case, 10 [pu]) representing bus separation.

Thus, applying the TOMLAB auxiliary module can reduce the calculation time for Jacobian and Hessian components by about 50%.

Finally, in step S150 according to the present invention, a Jacobian component and a Hessian component may be calculated using a parallel algorithm for parallel computation. As a result of applying the parallel algorithm, it is confirmed that some calculation time can be shortened in some cases.

The application of the parallel algorithm to the FLC-OPF means a method of calculating the fault currents and calculating their influence on the FLC (Jacobi and Hessian) independently in several threads.

However, when computing on one computer, a parallel operation processor and a large amount of memory may be required. However, when a plurality of computers actually allow calculation of respective Jacobian and Hessian matrices, the effect of parallel operation is increased .

Fault Current Constraint

The fault current limit applied at each step above can be expressed by the following equation (4).

...식 (4)

... (4)

Represents the above formula (4) V _f is a high breakdown voltage before (pre-fault voltage) in advantages in f and _ff Z means the Thevenin impedance is determined when viewed from the external grid and advantages. And, I _{f, max} means the maximum allowable fault current of CB (Circuit Breaker) installed in high-strength. At this time, assuming that the fault current constraint appears to depend only on V _f , that is, when the system configuration has not changed at all, the upper fault current constraint corresponds to a linear constraint when Z _ff is a constant.

To apply this fault current constraint, it is applicable when the fault current experienced at each point of the power system is lower than I _{f , max} . That is, it can be used to determine whether the fault current increase factors in the system maintain the current system configuration and additionally how much more applicable.

Here, when the fault current of the system is high, it is difficult to apply the linear fault current constraint when reducing the fault current level by applying bus splitting or the like. Of course, when a variety of busbar separation schemes are proposed that allow the fault current level of the grid to fall within the maximum allowable fault current of each CB, apply a linear fault current constraint and use a commonly used objective function to determine which busbar separation scheme Can be used to determine whether or not it is possible to maintain the high efficiency of the operation expressed as.

However, in this embodiment, the final target by default, because the formula (4) to determine the Measures of bus separate to reduce the high level of fault current below the allowable current CB is broken around the voltage V _f It is not a linear constraint that depends only on size. In the fault current analysis, the bus line load (P _L + jQ _L ) uses the magnitude V _L of the voltage of the bus line to convert it into the form of a constant impedance load. For this, the following equation (5) is applied.

...식 (5)

... (5)

In the analysis of the common fault current, the equivalent load impedance can be determined using the equation (5) described above for each load bus line determined by the algae solution. However, when applying the optimal algebraic calculation, And the calculated value of the thevenin equivalent impedance in the high-frequency f is inevitably changed. For this reason, the fault current constraint needs to be nonlinearly included in the optimal algebraic calculation.

Consider continuous variable X

In order to be able to deal with countermeasures such as bus separation directly in the above steps, it is possible to process jX as a continuous variable by connecting the jX to the separating point positive bus as shown in FIG. Of course, it may be possible to designate a decision as to whether or not to separate a bus line separation candidate by a binary variable, but in this embodiment, it is considered as a continuous variable in order to secure convergence.

As shown in FIG. 2, an example of a simulation performed to determine whether it is possible to apply a continuous X (series reactance) variable to apply a bus break or line switch to reduce the fault current is described. This makes it possible to determine that a continuous variable X is applicable. Here, a simple system as shown in FIG. 3 is applied.

As shown in FIG. 3, the test system includes two generators and supplies the load of the bus 3 using the generated power. The voltage limit for each bus was set to 0.95 ~ 1.05 [pu]. Then, the reactance is connected to the first bus line and the second bus line by X. In this simulation, this is considered as a bus line separation candidate.

First, general optimal algae calculation was applied without separating 1-2 candidate sites. The system state in the solution of the optimal algae calculation can be shown in Fig. In this state, the fault current of bus # 1 and bus # 2 is 29.5 [pu], and the fault current of bus # 3 is 19.5 [pu].

First, the solution of applying the fault current constraint optimal algebraic calculation is obtained so that it can be applied to a simple system. The maximum value of the fault current limit used here was 27 [pu] in all buses. The results are shown in Fig. As shown in FIG. 5, the value of the continuous variable X injected into the bus separation candidate satisfying the added fault current constraint was determined to be 0.04.

However, there are two solutions that can be applied in measures such as separation of buses, such as integration or separation of relevant points. When the X value is 0.04, it is necessary to judge whether it should be separated or vice versa. And we need to move the X value to two desired discrete points.

In Fig. 6, the algae solution and the fault current result are described when the X value is 8. It can be seen that the fault current level is lower than when X is 0.04, but the voltage of the third bus is 0.928 [pu], which violates the voltage limit. The method applied to determine the algae solution shown in Fig. 6 is a general algae calculation.

From these results, it can be seen that to calculate the fault current constrained optimal algae considering the continuous variable X applied to the network reconfiguration by inputting to the bus line separation site, In order to prevent this phenomenon, it is necessary to find out what additional X-related objective function (penalty function) should be applied. However, theoretically, it is possible to fully consider the voltage and reactive power constraints even after application of countermeasures such as bus separation that meets the fault current limit.

The following conclusions can be drawn from the simulation results for the simple 3-bar test system described above. First, the FLC-OPF including the X variable can be used to find the X value satisfying the operating constraints and the fault current constraints. Second, since OPF is basically considered, it provides a solution that satisfies line heat capacity constraint, bus voltage constraint, and power constraint. Third, when X is at the median value in the final solution, it can be judged as the result of a perfect bus separation (X). Fourth, theoretically, it is possible to consider the voltage and reactive power constraints sufficiently even if a general OPF is applied after measures such as bus separation that meets the fault current limit are applied.

From these conclusions, it is more convergent to construct the optimization problem to make the decision about the bus separation at discrete variables and to construct the optimization problem considering the continuous variable X when convergence is sought for the solution of this problem And it was found.

It is also possible to determine whether the bus line separation or integration for the continuous variable X described above is determined by X> 10.0 [pu]: bus line separation and X <0.0001 [pu]: bus line integration.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the exemplary embodiments or constructions. You can understand that you can do it. The embodiments described above are therefore to be considered in all respects as illustrative and not restrictive.

Claims (6)

As an accelerating method to apply the power network reconstruction algorithm (NRA) based on the fault current constraint optimal algebraic calculation (FLC-OPF) to a large scale system,
(a) determining the components of the thevenin impedance and the bus impedance matrix using the Kron reduction with the continuous variable (X) having a predetermined cooperative influence removed when the large-scale system is viewed from the bus line of the fault current constraint; And
(b) calculating a Jacobian component and a Hessian component using the determined components of the thevenin impedance and the bus impedance matrix;
/ RTI &gt;
The method according to claim 1,
The step (b)
Wherein the components of the thevenin impedance and the bus impedance matrix are determined according to the following equation (1).

... (1)
here,
Z _{f , f} : Modified Z _f , _f , Z _{f , k} : In case of inputting the Z _{f , f '} : kl bus line jX, determined by observing the external system at the high- the impedance matrix (f, k) element, the Z _{f, l:} source power line impedance matrix (f, l) element, the Z _{k, f:} the source bus line impedance matrix (k, f) component, the Z _{l, f:} the source bus line impedance matrix (l, f) component, the Z _{k, k:} the source bus line impedance matrix (k, k) element, wherein Z _{l, k:} the source bus line impedance matrix (l, k) element, It means the original bus impedance matrix of the (l, l) element: the Z _{k, l:} the original bus impedance matrix (k, l) and the element Z _{l, l.}
3. The method of claim 2,
The Jacobian component calculates a Jacobian matrix of nra x nflc times from the Tehenan impedance and the bus impedance matrix, and the Hessian component computes a Hechian matrix of nra x nra x nflc from the Tebman impedance and the bus impedance matrix .
Nra denotes the number of bus line separations, and nflc denotes the number of the fault current constraints.
The method according to claim 1,
(c) using a processor that reduces the number of fail current constraints and countermeasures taking into account only the fault current constraints bounded during the fault current constraint and the countermeasures (RA) of electrically closed buses And calculating the Jacobian component and the Hessian component.
The method according to claim 1,
(d) using the pretreatment auxiliary module without changing the objective function according to the following equation (2) necessary for the fault current constrained optimum algae calculation (FLC-OPF) and the constraint condition according to the following equation (3) And calculating the Hessian component based on the calculated Hessian component.

... (2)
The P _gk: k-th active power generation of the bus bar, the P _gko: k-th initial value of the active power generation of the bus bars, wherein: power variation coefficient, the ng: _(.) The total number of generators, the P _enk: k-th consecutive The penalty function for the variable X, X _k : the k-th continuous variable X, and the nx: total number of X variables (number of candidates for separating bus bars).

... (3)
P _kk , Q _tk : active power and reactive power injection of the kth bus, P _dk , Q _dk : active power and reactive power load of the kth bus, P _gk , Q _gk : Reactive power generation, V _b : bus voltage magnitude vector,

: The upper and lower limit constraint vector of the bus voltage magnitude, P _g : Active power generation vector,

: Active power generation upper limit lower limit constraint vector and Q _g : Reactive power generation vector,

: Constraint Constraint Constraint vector for reactive power generation, S _t : Line vector,

: Line current upper limit vector, FLC _f : fth bus failure current calculation function,

: means the maximum value of the fth bus failure current constraint and nflc: the total number of fault current constraints.
The method according to claim 1,
(e) calculating the Jacobian component and the Hessian component using a parallel algorithm that performs parallel computation.

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