JP2017215774A - Transient phenomenon analysis device, method, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a transient phenomenon analysis device, method and program capable of securing sufficient accuracy and dramatically shortening the time required for analyzing a transient phenomenon.SOLUTION: A transient phenomenon analysis device 1 comprises a dynamic phasor analysis unit 14a for performing an analysis with dynamic phasor by a prescribed first time in a first period in which distortion of waveforms of voltage and current hardly occurs and an instantaneous value analysis unit 14b for performing an instantaneous value analysis by a second time with a smaller interval than by the first time in a second period in which waveforms of voltage and current distort largely.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a transient phenomenon analysis apparatus, method, and program, and more particularly to a transient phenomenon analysis apparatus, method, and program that are useful when applied to analysis of transient phenomena in a power system.

  In recent years, as environmental awareness has increased, it has been desired to effectively use renewable energy and reduce carbon dioxide emissions. In addition, power liberalization is about to completely liberalize power generation and power retailing. Under such a background, it is expected that the interconnection of distributed power sources centering on photovoltaic power generation will increase in the power system. In addition, it is expected that the electric power system and power storage facilities will increase in the power system as a backup power source in the event of a power failure.

  In order to realize a smart power system, it is necessary that the system control device and the connected / connected devices do not interfere with each other and achieve the intended purpose. Instantaneous value analysis capable of analysis at the waveform level is effective for analysis of transient phenomena caused by such mutual interference. Non-Patent Documents 1 and 2 below disclose a power system instantaneous value analysis program (hereinafter referred to as XTAP (eXpandable Transient Analysis Program)) capable of such instantaneous value analysis. Other programs that can perform instantaneous value analysis include EMTP (Electro Magnetic Transients Program), PSCAD (registered trademark), and the like.

Satoshi Noda, “Development Trend of Power System Instantaneous Value Analysis Program: Development of Domestic Program XTAP”, Electrical Review, pp.60-64, August 2011 Satoshi Noda, “Development Trend of Electric Power System Instantaneous Value Analysis Program in Japan and Overseas”, IEEJ Transactions B, Vol.131, No.11, pp.872-875, November 2011

  By the way, since the instantaneous value analysis performed by the XTAP described above is an analysis of how the voltage or current changes at the waveform level, compared with the period of the waveform for sufficient accuracy analysis. It is necessary to reduce the time increment for the analysis. For example, when an instantaneous value analysis of a three-phase alternating current with a frequency of 50 [Hz] (cycle is 20 [msec]) is performed, for example, the time increment of one cycle (20 [msec]) is about several hundreds (large). In some cases, tens of thousands) are analyzed.

  As described above, in the XTAP described above, in order to perform analysis with sufficient accuracy, it is necessary to reduce the time interval for performing analysis, so that the amount of calculation increases, and there is a problem that analysis requires a long time. . Here, in the instantaneous value analysis, there are many cases where a portion in which the distortion of the voltage and current waveforms hardly occurs (a portion where the voltage and current are almost sinusoidal) continues. If it is possible to reduce the time required for the analysis of such a portion where distortion is hardly generated, it is considered that the instantaneous value analysis can be speeded up.

  The present invention has been made in view of the above circumstances, and provides a transient analysis apparatus, method, and program capable of dramatically reducing the time required to analyze a transient while ensuring sufficient accuracy. For the purpose.

In order to solve the above problems, the transient analysis device (1) of the present invention is preliminarily defined in a first period (T1, T3) set as a period in which almost no distortion occurs in the voltage and current waveforms. From the first time step, in the first analysis unit (14a) that performs the dynamic phasor analysis at the first time step (Δt1) and the second time period (T2) that is set as a time period during which the voltage and current waveforms are greatly distorted A second analysis unit (14b) that performs instantaneous value analysis at a fine second time interval (Δt2).
In the transient phenomenon analysis apparatus according to the present invention, when the second analysis unit has the second period after the first period, the analysis result of the first analysis unit at the end of the first period. The instantaneous value analysis is started using the first analysis unit, and when the first analysis unit is followed by the first period, the analysis result of the second analysis unit at the end of the second period The analysis using the dynamic phasor is started.
In addition, the transient phenomenon analysis apparatus according to the present invention includes a creation unit (14c) that creates a circuit equation to be analyzed, which is used in the analysis of the first analysis unit, by a sputter blow method.
In the transient phenomenon analysis apparatus according to the present invention, the circuit equation to be analyzed indicates a first dynamic term indicating a time change of a DC component of voltage and current and a time change of a phaser of a fundamental wave of voltage and current. Includes only the second dynamics term.
The transient phenomenon analysis method according to the present invention uses a dynamic phasor in a first time interval (Δt1) defined in advance in a first period (T1, T3) set as a period in which almost no distortion occurs in the voltage and current waveforms. In the first step (S11) in which the analysis is performed and the second period (T2) set as a period in which the waveform of the voltage and current is greatly distorted, the second time interval (Δt2) finer than the first time interval is instantaneous. And a second step (S14) for performing value analysis.
The transient phenomenon analysis program according to the present invention causes the computer to operate at a first time interval (Δt1) defined in advance in a first period (T1, T3) that is set as a period in which almost no distortion occurs in the voltage and current waveforms. In a first analysis means (14a) for performing analysis by a dynamic phasor and in a second period (T2) set as a period in which the waveform of the voltage and current is greatly distorted, a second time interval smaller than the first time interval ( It functions as the second analysis means (14b) that performs instantaneous value analysis at Δt2).

  According to the present invention, in the first period set as a period in which almost no distortion occurs in the voltage and current waveforms, analysis is performed by a dynamic phasor in the first time interval, and the voltage and current waveforms are set as a period during which the waveform is greatly distorted. In the second period, the instantaneous value analysis is performed in the second time step that is finer than the first time step, so the time required for the analysis of the transient phenomenon is drastically reduced while ensuring sufficient accuracy. There is an effect that can be done.

It is a block diagram which shows the principal part structure of the transient phenomenon analyzer by one Embodiment of this invention. It is a figure which shows the discrete time equivalent circuit of a circuit element. It is a figure which shows the equivalent circuit of the distribution line or power transmission line simulated by the analysis by a dynamic phaser. It is a figure which shows the equivalent circuit of the transformer simulated by the analysis by a dynamic phaser. It is a figure which shows the modulation method by the basic circuit of a 2 level AC / DC converter, and a PWM system. It is a figure which shows the dynamic phasor model of an AC / DC converter. It is a figure which shows an example of the analysis conditions set by one Embodiment of this invention. It is a flowchart which shows an example of the transient phenomenon analysis method by one Embodiment of this invention. It is a figure which shows the power distribution system used for the analysis of a transient phenomenon. It is a figure which shows the model of PV panel. It is a figure which shows the model of PCS. It is a figure which shows the model of the distribution substation. It is a figure which shows the analysis result by a transient phenomenon analyzer.

  Hereinafter, a transient analysis device, method, and program according to an embodiment of the present invention will be described in detail with reference to the drawings. In the following, the case where the analysis target is a distribution system will be described as an example. However, the present invention is not limited to the distribution system, and any electric circuit such as a power transmission system is the analysis target. be able to.

<Transient phenomenon analyzer>
FIG. 1 is a block diagram showing a main configuration of a transient analysis device according to an embodiment of the present invention. As shown in FIG. 1, the transient phenomenon analysis apparatus 1 of this embodiment includes an input device 11, an output device 12, an auxiliary storage device 13, and an arithmetic processing device 14, and a transient phenomenon that occurs in a distribution system as an analysis target. Perform analysis. Such a transient phenomenon analysis apparatus 1 is realized by, for example, a desktop personal computer.

  The input device 11 includes, for example, a keyboard, a pointing device, and the like, and outputs an instruction according to a user operation using the transient phenomenon analysis device 1 to the arithmetic processing device 14. The output device 12 includes, for example, a liquid crystal display device, a printer, and the like, and outputs various information output from the arithmetic processing device 14. The auxiliary storage device 13 includes, for example, an HDD (Hard Disk Drive), an SSD (Solid State Drive), etc., and stores various parameters PR used in the circuit equation of the power distribution system, a transient phenomenon analysis program PG, and the like.

  Based on the operation instruction input from the input device 11, the arithmetic processing device 14 uses the parameter PR stored in the auxiliary storage device 13 in accordance with the transient phenomenon analysis program PG stored in the auxiliary storage device 13, thereby generating transients in the distribution system. Analyze the phenomenon. The arithmetic processing unit 14 includes a dynamic phasor analysis unit 14a (first analysis unit, first analysis unit), an instantaneous value analysis unit 14b (second analysis unit, second analysis unit), and a circuit equation creation unit 14c (creation unit). ).

  The dynamic phasor analyzing unit 14a performs analysis using a dynamic phasor in a period (first period) set as a period in which distortions hardly occur in the voltage and current waveforms of the distribution system. Details of the dynamic phaser will be described later. The instantaneous value analysis unit 14b performs instantaneous value analysis in a period (second period) set as a period in which the voltage and current waveforms of the distribution system are greatly distorted. The instantaneous value analysis performed by the instantaneous value analysis unit 14b is the same as the conventional instantaneous value analysis, and thus detailed description thereof is omitted. The circuit equation creation unit 14c creates a circuit equation of the power distribution system used in the analysis by the dynamic phasor analysis unit 14a by the sputtering method. Details of the circuit equation creation method by the circuit equation creation unit 14c will be described later.

  The transient phenomenon analysis program PG is recorded on a computer-readable recording medium such as a CD-ROM or DVD (registered trademark) -ROM, or downloaded via a network such as the Internet. 1 is stored in the auxiliary storage device 13. By reading and executing the transient phenomenon analysis program PG stored in the auxiliary storage device 13, the functions of the blocks of the transient phenomenon analysis device 1 (for example, the dynamic phasor analysis unit 14a, the instantaneous value analysis unit 14b, and The circuit equation creation unit 14c) is realized by software. That is, these functions are realized by cooperation of software and hardware resources.

<Theory of dynamic phasors>
Next, the theory of the dynamic phasor that is the basis of the analysis performed by the dynamic phasor analyzing unit 14a described above will be described. First, an instantaneous value such as voltage or current at time t is set to x = x (t). Consider a window (t−T, t) with respect to time t. Define a time in a section where τ = 0 at the start of the window and τ = T at the end of the window, and expand the Fourier series of the instantaneous value x. If it calculates | requires, it will become the following (1) Formula.

In the above equation (1), ω ₀ = 2π / T, and the k-th order Fourier coefficient of the instantaneous value x is expressed as <x> _k . Since the window (t−T, t) cuts out one period (period T) of the instantaneous value x while sliding from the past to the future with the passage of time, the Fourier coefficient <x> _k is determined at the time t. It becomes a function and is expressed by the following equation (2).
<X> _k in the above equation (2) is a phasor (complex quantity) having amplitude and phase information. In the theory of dynamic phasor, this phasor is considered dynamic phasor because it changes dynamically with time.

Next, when the instantaneous value x is differentiated with respect to the time t and the k-th order Fourier coefficient is obtained, the following equation (3) is obtained.
When this equation (3) is modified, the following equation (4) is obtained.
Obtained from equation (4), the derivative of the k-th order Fourier coefficients from k-th order Fourier coefficients but by differentiating the original instantaneous value x, by subtracting the multiplied by a Jkomega ₀ to k-th order Fourier coefficients You can see that

  In the dynamic phasor theory, the order of Fourier coefficients to be analyzed is first determined. Here, since the analysis by the dynamic phasor is intended to perform the analysis more simply than the instantaneous value analysis, only a few orders such as a direct current component and a fundamental wave component are analyzed.

Next, a state equation of a circuit to be analyzed is established. Now, assume that there are M state variables in the circuit, and focus on the order of K Fourier coefficients. Enumerating equations related to K orders for each of M state variables, it is possible to obtain state equations relating to KM Fourier coefficients shown in the following equation (5).

  However, x in the above equation (5) is a vector listing K-order Fourier coefficients for each of the M state variables, and u is for each of the input variables to the circuit such as the voltage source and the current source. This is a vector listing K-order Fourier coefficients. Here, in order to derive the respective elements on the right side corresponding to the respective elements on the left side of the above expression (5), the above-described expression (4) can be used.

  When focusing only on the direct current component and the fundamental wave component, the short time constant and the high frequency natural vibration have been removed at the stage of deriving the above equation (5), and in large time increments (first time increments). It becomes possible to analyze at high speed. However, conventionally, there has been a drawback that the state equation shown in the above equation (5) cannot be automatically derived. Therefore, in the present embodiment, the circuit equation ( (Alternative to the state equation of the above equation (5)) is derived.

<Circuit equation creation method using the Spearstrow method>
Next, details of a circuit equation creation method by the circuit equation creation unit 14c described above will be described. In the present embodiment, by first applying a differential operation to each circuit element, automatic circuit equations can be derived. A circuit equation is derived for each Fourier coefficient of interest, and these are related by an expression representing a coupling between orders described later.

The voltage across the circuit element in order k and V _k, indicating the current flowing through the circuit element when the I _k, the relationship between the voltage V _k and current I _k in the various circuit elements, as the following equation (6) It can be reduced to any one of a plurality of equations.

The first equation (6) can be expressed by the Norton discrete time equivalent circuit shown in FIG. 2A, where Y _k and J _k are the admittance and current source of the equivalent circuit, respectively. Is the value of The second expression of the above expression (6) can be expressed by a Thevenin type discrete time equivalent circuit shown in FIG. 2B, where Z _k and E _k are the impedance and voltage source of the equivalent circuit, respectively. Is the value of FIG. 2 is a diagram showing a discrete time equivalent circuit of circuit elements. The third expression in equation (6) is a relational expression when the circuit element is a switch or sub power _{supply, a k, b k, c} k in the equation is a coefficient.

Consider an arbitrary circuit having N _n nodes and N _b circuit elements. In this circuit, when a relational expression of all circuit elements for a certain order is expressed by any one of a plurality of expressions shown as the above expression (6), the circuit's sputter blow equation relating to that order is the following (7) It can be expressed by a formula. In the following formula (7), subscripts representing the orders are omitted in order to avoid complicated notation.

However, u in the above equation (7) is a column vector whose components are voltages of N _n nodes of the circuit, and i and v are current and voltages of N _b circuit elements, respectively. S is a column vector whose component is the value of the current source J _k or voltage source E _k of the discrete-time equivalent circuit of N _b circuit elements. A is called a branch-to-node connection matrix and can be easily created from circuit connection information. I is a unit matrix. Since B _i and B _v are coefficients applied to the voltage and current of each circuit element, the coefficients of the relational expressions of the circuit elements shown in the above equation (6) are stored. For the method of creating the branch-to-node connection matrix A, refer to the following document, for example.
References: Satoshi Noda, Nuki Miki, Naoki Gibo, Kiyoshi Takenaka, “Development of Power System Instantaneous Value Analysis Program (Part 1) —Basic Design”, Research Report of Central Research Institute of Electric Power Industry, H6002, March 2007

  The first stage of equation (7) represents Kirchhoff's current law, the second stage represents Kirchhoff's voltage law, and the third stage represents the characteristics of each circuit element (ie, the relational expression of each circuit element). It will be enumerated. Therefore, the complete state of the circuit can be obtained by solving equation (7). In addition, since the Sputter blow method, which is the same abc phase formulation as the instantaneous value analysis, is used, it is possible to consider the difference in impedance of each phase. It can be seen that the consistency of the information to be transferred is high.

Now, when the above equation (7) related to the k-th order Fourier coefficient is expressed as the following equation (8), when there are K orders of interest, K sets of the following equation (8) are obtained.
Since the coupling between the orders relates to the K sets of equations, the circuit equations are solved sequentially from time 0 in appropriate time increments, so that the node voltage of each part of the circuit and the current / voltage of each circuit element are obtained for the noted order. Time change (that is, dynamic phasor) can be calculated. In many cases, the coupling between the orders does not matter even if the delay in the calculation time is allowed, so the K sets of equations can be solved independently. However, if the delay between the calculation time increments cannot be allowed in the coupling between the orders as in the case of simulating the AC / DC converter in detail, all or some of the K sets of equations can be solved simultaneously. It becomes.

In this embodiment, the dynamic phasor theory is applied in order to simulate at high speed a situation in which a portion in which the voltage and current waveforms are hardly distorted (portion in which the voltage and current are sinusoidal) continues endlessly. Therefore, the circuit handled by the dynamic phasor may be regarded as linear. In such a situation, F _{k on} the left side of the above equation (8) is unchanged regardless of the passage of time, and only y _{k on} the right side changes with the passage of time. The circuit equation creating unit 14c shown in FIG. 1 creates a circuit equation of the distribution system by performing processing for solving the above-described K sets of equations.

<Dynamic phasor model>
The dynamic phasor model of various circuit elements will be described below. In the following, based on the theory of dynamic phasor, the amplitude and phase of the k-th order Fourier coefficient of the voltage v and the current i at both ends of various circuit elements change with time as shown in the following equation (9). And Note that V _k (t) and I _k (t) in the following equation (9) are dynamic phasors having amplitude and phase information.

In the present embodiment, analysis by a dynamic phasor is applied in order to simulate at high speed a situation in which a portion where the distortion of the voltage and current waveforms hardly occurs (a portion where the voltage and current are sinusoidal) continues. . For this reason, the dynamic phasor model of various circuit elements includes a DC component of voltage and current (V ₀ (t), I ₀ (t): first dynamics term) and a fundamental component of voltage and current (V ₁ ( t), I ₁ (t): the second dynamics term) only is considered to be considered in most cases.

(1) Resistance When the voltage across the resistor is v, the current flowing through the resistor is i, and the resistance value is R, the relational expression V = Ri holds. Since this relational expression holds for Fourier coefficients of all orders, the following expression (10) holds for an arbitrary order k.
When the above equation (10) is compared with the second equation of the above equation (6), in the Thevenin type discrete time equivalent circuit of FIG. 2 (b), Z _k = R, E _k = 0. Is a dynamic phasor model of resistance.

(2) Inductor When the voltage across the inductor is v, the current flowing through the inductor is i, and the inductance value is L, the relational expression v = L (di / dt) holds. Substituting the above equation (9) into this equation and rearranging results in the following equation (11).

Next, a discrete time equivalent circuit is obtained by applying a numerical integration method to the above equation (11). Specifically, when the calculation time increment is Δt and the above equation (11) is rearranged by applying, for example, the backward Euler method, the following equation (12) is obtained. In the following equation (12), it should be noted that the parentheses of V _k and I _k represent not the time but the calculation time step.
When the above equation (12) is compared with the first equation of the above equation (6), in the Norton discrete time equivalent circuit of FIG. 2A, Y _k = β _k , J _k = α _k I _k It can be seen that what is placed as (n-1) is the dynamic phasor model of the inductor.

(3) Capacitor When the voltage across the capacitor is v, the current flowing through the capacitor is i, and the capacitance value is C, the relational expression i = C (dv / dt) holds. Substituting the above equation (9) into this equation and rearranging results in the following equation (13).

Next, similarly to the inductor, if the calculation time step is Δt and the above equation (13) is rearranged by applying, for example, the backward Euler method, the following equation (14) is obtained. In the following equation (14), it should be noted that the parentheses of V _k and I _k represent not the time but the calculation time step.
When the above equation (14) is compared with the second equation of the above-described equation (6), Z _k = β _k , E _k = α _k V _{k in} the Thevenin type discrete time equivalent circuit of FIG. It can be seen that what is placed as (n-1) is a dynamic phasor model of the capacitor.

(4) Voltage source The voltage source is a power source that generates a specified voltage at both ends thereof. In the dynamic phasor theory, the voltage waveform generated by the voltage source is a periodic waveform of period T and is considered to change with time. When the Fourier coefficient of the order of interest can be derived analytically from the generated voltage waveform at a certain time, the voltage value E _k of the Thevenin type discrete time equivalent circuit shown in FIG. specify. At this time, Z _k = 0.

If the Fourier coefficient cannot be derived analytically, it is obtained by numerical integration from the voltage waveform at that time using the Fourier coefficient definition formula. If a fast Fourier transform (FFT) algorithm is applied to numerical integration, high-speed calculation is possible. As an example often used for simulating system voltage, when the effective value V _m and the phase θ of the commercial frequency voltage source change with time, the voltage E ₁ (t) shown in the following equation (15) is designated. .

(5) Current source A current source is a power source that injects a specified current from one end to the other end. In the dynamic phasor theory, the current waveform injected by the current source is a periodic waveform of period T and is considered to change with time. When the Fourier coefficient of the order of interest can be derived analytically from the current waveform to be injected at a certain time, the current value J _k of the Norton discrete time equivalent circuit shown in FIG. specify. At this time, Y _k = 0. When the Fourier coefficient cannot be derived analytically, it is obtained by numerical integration using the definition formula, as in the case of the voltage source.

(6) Switch Here, a switch that operates only several times during one simulation, such as a circuit breaker, is assumed. Considering a switch function σ (t) that returns 1 if the switch is on at time t and 0 if it is off, the following equation (16) is used between the voltage v across the switch and the flowing current i. The relationship shown is established.

Here, since the switch does not have frequency characteristics (that is, the on / off state of the switch differs depending on the frequency), the above equation (16) holds for all Fourier orders k. Therefore, it is only necessary to set the relevant lines of the sputtering blast equations for all the orders of interest as shown in the following equation (17).

(7) Dependent power supply For the i-th circuit element, the k-th order Fourier coefficient of the voltage is V _k ⁱ and the k-th order Fourier coefficient of the current is I _k ⁱ . For the j-th circuit element, the k-th order Fourier coefficient of the voltage is V _k ^j, and the k-th order Fourier coefficient of the current is I _k ^j . When the j-th circuit element controls the i-th circuit element, the relational expressions of the voltage control voltage source, the current control voltage source, the voltage control current source, and the current control current source are as follows: Represented by each formula. Therefore, these formulas may be used as the corresponding lines of the degree K superstar blow equation. It should be noted that the coefficient can be changed depending on the order.

(8) Distribution line As described above, in the present embodiment, in order to simulate at high speed a situation in which a portion where the distortion of the voltage and current waveforms hardly occurs (portion where the voltage and current are sinusoidal) continues. Analysis by dynamic phasor is applied. Therefore, in many cases, the orders of the Fourier coefficients of interest in the analysis by the dynamic phasor are “0” and “1” (that is, only the DC component and the fundamental component), and the distribution line is the π-type equivalent circuit shown in FIG. Can be simulated sufficiently accurately. FIG. 3 is a diagram illustrating an equivalent circuit of a distribution line or a transmission line simulated by an analysis by a dynamic phasor. Note that the π-type equivalent circuit can be created by combining the models of the above-described resistor, inductor, and capacitor.

(9) Transformer As described above, the orders of the Fourier coefficients of interest in the analysis by the dynamic phasor are often “0” and “1” (that is, only the direct current component and the fundamental wave component). For this reason, the transformer can be sufficiently accurately simulated by the basic equivalent circuit (Steinmetz equivalent circuit) of the transformer shown in FIG. FIG. 4 is a diagram illustrating an equivalent circuit of a transformer that is simulated by analysis using a dynamic phasor.

The winding resistance R1 and the excitation resistance R2 in FIG. 4A can be simulated by the above-described resistance model, and the leakage inductance L1 and the excitation inductance L2 can be simulated by the above-described inductance model. The ideal transformer TF in FIG. 4 constitutes an equivalent circuit of FIG. 4B called a voltage / current exchange system by combining the voltage control voltage source and the current control current source. This ideal transformer TF has a relationship of V ₁ = n · V ₂ by the voltage control voltage source when the turn ratio is n: 1 and the fundamental wave voltages of the primary and secondary windings are V ₁ and V _2. It is filled. Similarly, assuming that the fundamental wave currents of the primary and secondary windings are I ₁ and I ₂ , n · I ₁ = I ₂ is satisfied by the current control current source. Incidentally, since no electromagnetic induction occurs with respect to the direct current component, both sub power supplies are replaced with voltage sources having a voltage of zero.

(10) Power electronics converter In the dynamic phasor theory, the power electronics converter can be considered as an order conversion element. A power electronics converter used for interconnection of a distributed power source such as photovoltaic power generation or a storage battery is generally an AC / DC converter using PWM (Pulse Width Modulation), and a reactive power compensator (STATCOM: STATic var). A PWM type AC / DC converter is also used for the COMpensator. Therefore, a dynamic phasor model of a PWM type AC / DC converter (hereinafter simply referred to as “AC / DC converter”) will be described.

  FIG. 5 is a diagram illustrating a basic circuit of a two-level AC / DC converter and a modulation method using a PWM method. The AC / DC converter shown in FIG. 5 (a) performs conversion from direct current to alternating current by performing on / off control of the semiconductor switching elements Q11, Q12, Q21, Q22, Q31, and Q32 at high speed. The on / off control of the semiconductor switching elements Q11, Q12, Q21, Q22, Q31, and Q32 is performed as shown in FIG. 5B. The modulated wave W1 (in most cases, a sine wave) to be output and the carrier wave W2 ( This is based on the comparison result with a triangle wave.

  Specifically, when the modulated wave W1 is larger than the carrier wave W2, the upper semiconductor switching elements (Q11, Q21, Q31) are turned on, and the lower semiconductor switching elements (Q12, Q22, Q32) are turned off. To do. On the other hand, when the modulated wave W1 is smaller than the carrier wave W2, the upper semiconductor switching elements (Q11, Q21, Q31) are turned off and the lower semiconductor switching elements (Q12, Q22, Q32) are turned on. Since the AC / DC converter shown in FIG. 5 is for three-phase AC, the timing at which the semiconductor switching elements (Q11, Q21, Q31) are turned on or the semiconductor switching elements (Q12, Q22, Q32) are turned on. It should be noted that the timing to set is different from each other.

Thus, by comparing the modulated wave W1 and the carrier wave W2, a waveform is output on the AC side with a duty ratio proportional to the modulated wave W1, and by smoothing this with a filter, the waveform is similar to the modulated wave W1. A waveform is obtained. At this time, the higher the frequency of the carrier wave W2, the closer the output waveform approaches the modulated wave W1. Therefore, considering an ideal state where the frequency of the carrier wave W2 is infinite, the modulated wave W1 is output as a voltage waveform to the AC side as it is. That is, the AC / DC converter viewed from the AC side can be simulated as a voltage source that outputs a voltage represented by the following equation (19).

Here, E _1a (t), E _1b (t), and E _1c (t) in the above equation (19) are values of the voltage source of each phase on the AC side, and D _a (t), D _b (t ), D _c (t) is a dynamic phasor assuming that the modulated wave W1 of each phase on the AC side determined by the control system is a sine wave, and E ₀ (t) is a voltage on the DC side. Dynamic phasor. From the above equation (19), it can be seen that the DC voltage is converted into the fundamental voltage.

Next, the active power output from the AC / DC converter to the AC side is expressed by the following (20) using I _1a (t), I _1b (t), and I _1c (t) as dynamic phasors of current flowing out from each phase on the AC side. ).

Substituting the above equation (19) into the above equation (20) yields the following equation (21).
On the other hand, if the current flowing from the DC side of the AC / DC converter is J ₀ (t), the power input from the DC side is expressed by the following equation (22).
Considering an ideal condition in which the loss of the AC / DC converter can be ignored, since the energy conservation law P _ac = P _dc is established instantaneously, the DC side of the AC / DC converter eventually becomes the following ( It can be simulated by the current source expressed by the equation (23).

  As described above, the dynamic phasor model of the AC / DC converter is based on the three-phase voltage control voltage source that converts the DC voltage on the DC side into the fundamental voltage on the AC side according to the above equation (19), and the above equation (23). A current-controlled current source that converts a fundamental current on the AC side into a DC current on the DC side can be used. Such an AC / DC converter can be represented by a circuit shown in FIG. FIG. 6 is a diagram illustrating a dynamic phasor model of the AC / DC converter. The AC / DC converter can also be represented by a circuit in which the AC side is simulated by a current source, as shown in FIG.

<Method of solving circuit equations considering coupling between orders>
As described above, when there are K orders of interest, K sets of equations (8) are associated and solved. The connection between these Spasterblow equations can be solved individually when the delay in calculation time can be tolerated, or when the dependency relations can be sequentially substituted by solving the Spatterblow equations according to a certain order. However, if the coupling is dense and cannot be solved by the above method, it is necessary to solve the K sets of Superstar blow equations simultaneously.

Here, when focusing on only the direct current component and the fundamental wave component, and writing down these two spear blow equations including the coupling between the orders, the following equation (24) is obtained.

R ₀₁ in the above equation (24) is a matrix including a coefficient corresponding to the order conversion element that refers to the voltage / current of the fundamental wave in the circuit relating to the direct current component, and most of the elements are zero. Similarly, R ₁₀ in the above (24) is a matrix containing the coefficients corresponding to the order conversion element that refers to voltage and current of the DC component in the circuit relating to the fundamental wave component, most elements are zero. By solving the above equation (24), it is possible to obtain a solution satisfying the scatter blow equation of the direct current component and the fundamental wave component at the same time.

  Note that the above equation (24) is an equation in the case where only the direct current component and the fundamental wave component are included, but can be easily extended when focusing on the order of any K Fourier coefficients. By creating an equation including the K orders of interest (the same equation as the above equation (24)) and solving it sequentially from time 0 in appropriate time increments, the node voltages of each part of the circuit at each time and each circuit The voltage / current of the element can be obtained for each order. If the solutions of all orders are overlapped, a corresponding waveform can be obtained within the range of orders considered.

<Transient phenomena analysis method>
Next, a transient phenomenon analysis method using the transient phenomenon analysis apparatus 1 described above will be described. When analyzing a transient phenomenon, first, the user inputs the distribution system to be analyzed. Specifically, the input device 11 of the transient phenomenon analysis device 1 is operated by the user, and processing for inputting all circuit elements constituting the power distribution system to the arithmetic processing device 14 is performed according to the user's instruction.

  When the input of the power distribution system is completed and the user gives an instruction to create a circuit equation, the circuit equation creating unit 14c shown in FIG. 1 performs a process of deriving the circuit equation of the power distribution system using the above-described sputter blow method. Is called. For passive circuit elements such as resistors and capacitors, a model used in the instantaneous value analysis unit 14b is automatically created by a conventional method. However, for active circuit elements such as a power electronics converter, It is necessary to separately create a model used in the instantaneous value analysis unit 14b. Various parameters PR used in the created circuit equation are stored in the auxiliary storage device 13.

  Next, analysis conditions are set by the user. For example, a user who operates the input device 11 of the transient phenomenon analysis apparatus 1 performs a process of setting a period for performing analysis using a dynamic phasor, a period for performing instantaneous value analysis, and a time step for performing these analyses. FIG. 7 is a diagram illustrating an example of analysis conditions set in an embodiment of the present invention. FIG. 7 shows an example of a change over time in the waveform of a three-phase AC voltage or current for easy understanding.

  A time t0 in FIG. 7 is a time at which a voltage and an event in which the voltage greatly fluctuates are generated in a simulated manner. The time t1 is an arbitrary time set before the time t0, and the time t2 is an arbitrary time set after the time t0. The time t2 is a time at which the voltage generated by the event and the fluctuation of the voltage are expected to be settled, and is set according to, for example, a user's rule of thumb. Examples of the event include opening / closing of a switch (breaker). Here, in order to simplify the explanation, it is assumed that the above-described event is simulated only at time t0 shown in FIG.

  The period T1 before the time t1 and the period T3 after the time t2 are periods in which almost no distortion occurs in the voltage and current waveforms (a period in which the sinusoidal voltage / current continues). Is set to the period (first period) for performing the analysis. Further, the period T2 between the times t1 and t2 is a period in which the voltage and current waveforms are greatly distorted by the above-described event (a period in which the voltage / current greatly deviates from the sine wave). (Second period).

  Further, the time interval Δt1 (first time interval) for performing the analysis in the periods T1 and T3 is set to about several [msec] in order to shorten the time required for the analysis. On the other hand, the time interval Δt2 (second time interval) for analysis in the period T2 is set to about several [μsec] in order to perform analysis with sufficient accuracy. These time increments can be arbitrarily set according to the purpose and accuracy of the analysis. However, the analysis by the dynamic phasor is intended to shorten the time required for the analysis of the period in which the voltage and current waveforms are hardly distorted. Therefore, the time increment Δt1 in the periods T1 and T3 is equal to the period T2. Is set to be coarser than the time increment Δt2 for analysis. Note that the time increments in the periods T1 and T3 can be varied.

  When the above input is completed and an instruction to start analysis is given by the user, a transient phenomenon analysis process occurring in the distribution system is performed according to the flowchart shown in FIG. FIG. 8 is a flowchart illustrating an example of a transient phenomenon analysis method according to an embodiment of the present invention. When the analysis process is started, first, the dynamic phasor analysis unit 14a shown in FIG. 1 performs analysis using a dynamic phasor (step S11). For example, in the period T1 shown in FIG. 7, the analysis by the dynamic phasor is performed at the time step Δt1.

  When the analysis by the dynamic phasor is completed, the analysis result at the end of the analysis is transferred from the dynamic phasor analysis unit 14a to the instantaneous value analysis unit 14b (step S12). For example, the analysis result at the end point (time t1) of the period T1 shown in FIG. 7 or the analysis result immediately before it is delivered. Next, it is determined by the arithmetic processing unit 14 shown in FIG. 1 whether or not the analysis for the entire period has been completed (step S13). For example, it is determined whether or not the analysis is completed in all of the periods T1 to T3 illustrated in FIG.

  When it is determined that the analysis for the entire period has not been completed (when the determination result in step S13 is “NO”), the instantaneous value analysis using the analysis result delivered in step S12 is the instantaneous value analysis. Implemented by the unit 14b (step S14). For example, in the period T2 shown in FIG. 7, the instantaneous value analysis is performed at time intervals Δt2. On the other hand, when it is determined that the analysis for the entire period has been completed (when the determination result in step S13 is “YES”), the series of processing illustrated in FIG. 8 ends.

  When the instantaneous value analysis in step S14 ends, the analysis result at the time of the end of analysis is transferred from the instantaneous value analysis unit 14b to the dynamic phasor analysis unit 14a (step S15). For example, the analysis result at the end point (time t2) of the period T2 shown in FIG. 7 or the analysis result immediately before it is delivered. Thereafter, it is determined by the arithmetic processing unit 14 shown in FIG. 1 whether or not the analysis for the entire period has been completed (step S16). For example, it is determined whether or not the analysis is completed in all of the periods T1 to T3 illustrated in FIG.

  When it is determined that the analysis for the entire period has not been completed (when the determination result in step S16 is “NO”), the analysis by the dynamic phasor using the analysis result delivered in step S15 is performed. This is performed by the analysis unit 14a (step S11). For example, in the period T3 shown in FIG. 7, the analysis by the dynamic phasor is performed at the time step Δt1. On the other hand, when it is determined that the analysis for the entire period has been completed (when the determination result in step S16 is “YES”), the series of processing illustrated in FIG. 8 ends.

  As described above, in this embodiment, the analysis by the dynamic phasor and the instantaneous value analysis are alternately performed while the analysis result at the time of the end of the analysis is passed between the dynamic phasor analyzing unit 14a and the instantaneous value analyzing unit 14b. Is called. For this reason, for example, a transient phenomenon in which the voltage and current waveforms are greatly distorted, such as when the circuit breaker is opened and closed, can be analyzed in a short time while ensuring sufficient accuracy.

  In addition, the dynamic phasor analysis performed by the dynamic phasor analysis unit 14a can take into account the difference in impedance for each phase, and the number of harmonics included in the calculation, similar to the instantaneous value analysis performed by the instantaneous value analysis unit 14b. Therefore, the dynamics of the circuit can be taken into consideration, and the consistency with the instantaneous value analysis is good. For this reason, as described above, the analysis by the dynamic phasor and the instantaneous value analysis are alternately performed while the analysis result at the time of the end of the analysis is delivered, so that the analysis can be performed with high accuracy.

<Analysis example>
The inventor of the present application actually performed an analysis of a transient phenomenon generated in the distribution system using the above-described transient phenomenon analysis apparatus 1. FIG. 9 is a diagram showing a power distribution system used for analysis of transient phenomena. As shown in FIG. 9, the distribution system 20 used for the analysis includes a PV panel (PhotoVoltaic panel: solar cell panel) 21, a PCS (Power Conditioning System: power conditioner) 22, a distribution line 23, and a distribution substation 24. Thus, a mega solar is linked to the end of the distribution line 23.

The PV panel 21 was simulated with a simple equivalent circuit shown in FIG. FIG. 10 is a diagram showing a model of a PV panel. FIG. 10A is a diagram showing a simple equivalent circuit of a PV panel, and FIG. 10B is a diagram showing a time profile of a current source value J _pv . The model shown in FIG. 10A has a maximum output when the DC voltage is 350 [V] and the current source value J _pv is 11429 [A]. Since the current source current also flows through the resistor R _eq , the current source value J _pv is not necessarily the output current. For example, the output current is 5714 [A] (2 [MW]) at the maximum output point.

  The PCS 22 is equivalent to four 500 [kW] machines, and its main circuit is simulated by the equivalent circuit of FIG. FIG. 11 is a diagram illustrating a PCS model. 11A is a diagram showing an equivalent circuit of the main circuit of the PCS 22, and FIG. 11B is a block diagram of a DC-AVR (Automatic Voltage Regulator) provided in the main circuit. FIG. 11C is a block diagram of a PLL (Phase Locked Loop) circuit provided in the main circuit.

Comparing the equivalent circuit shown in FIG. 11A and the circuit shown in FIG. 6B, it can be seen that the PCS 22 is expressed as a dynamic phasor model of the AC / DC converter. In the equivalent circuit shown in FIG. 11A, the left side is a DC circuit and the right side is an AC circuit. Therefore, the current source J _dc is considered in the circuit equation relating to the direct current component, and the current sources J _a , J _b and J _c are considered in the circuit equation relating to the fundamental wave component.

The DC capacitor is 400 [mF], and control by DC-AVR is performed so that the voltage V _dc becomes 350 [V] which is the rated voltage. DC-AVR performs PI control as shown in FIG. 11B, draws a direct current by the current source J _dc so that the voltage V _dc becomes 350 [V], and the current source J _a , J _b , J _c The same amount of power is output to the AC side. In order to inject current into the AC side, it is necessary to synchronize the phase with the AC voltage. Therefore, set the PLL circuit shown in FIG. 11 (c) as a control system synchronizes the phase of the phase θ and the current source J _a is the output, the current source J _b, J _c from its synchronized allowed phase - The phase was synchronized with a phase delayed by 2π / 3 [rad]. The DC-AVR and PLL circuits were processed separately from the circuit equations, and the same backward Euler method as the circuit equations was used for numerical integration.

The distribution line 23 has a length of 10 [km] and was simulated by the π-type equivalent circuit shown in FIG. The constants per unit length were R = 0.1264 [mΩ / m], L = 1.041 [μH / m], and C = 11.25 [pF / m] (for positive phase). The distribution substation 24 was simulated by an equivalent circuit shown in FIG. FIG. 12 is a diagram illustrating a model of a distribution substation. The inductance L _ss is 1.44 [mH] (each phase) as the inductance of the bank transformer and the upper system. The voltage source _Ess is a three-phase balanced voltage source (50 [Hz]) with a line effective value of 6.6 [kV] to simulate the system voltage, and its neutral point is grounded with a resistance of 10 [kΩ]. . When the termination resistance connected to the open delta of the GPT (Grounded Potential Transformer) installed in the distribution substation 24 is 25 [Ω], it is equivalent to 10 [kΩ] when converted to the neutral grounding resistance.

Under the above conditions, the distribution system 20 shown in FIG. 9 was analyzed by setting the time step Δt1 for analysis to 2 [msec] in consideration of only the direct current component and the fundamental wave component. FIG. 13 is a diagram illustrating an analysis result obtained by the transient phenomenon analysis apparatus. In FIG. 13, the analysis results obtained by the conventional instantaneous value analysis are shown for comparison. Referring to FIG. 13, the output voltage V _{pcs of the} PCS 22 is a time profile of the current source value J _pv provided in the simplified equivalent circuit (see FIG. 10A) simulating the PV panel 21 (FIG. 10B). It can be seen that it fluctuates according to the change of the reference). Further, referring to FIG. 13, it can be confirmed that the output voltage V _{pcs of the} PCS 22 varies in accordance with the change of the error signal ΔV _dc input to the PI controller (see FIG. 11B). From the above, it can be seen that the DC-AVR achieves the desired control. In addition, it can also be confirmed that the analysis result obtained by this analysis is almost the same as the analysis result by the conventional instantaneous value analysis.

  When performing the above analysis by the conventional instantaneous value analysis, it is necessary to simulate switching by PWM, and therefore, the time interval for performing the analysis needs to be set to about 1 [μsec]. On the other hand, in this analysis, it is possible to perform the same analysis at a time interval of about 2 [msec], which is 2000 times that, and the time required for the analysis can be drastically reduced. The time interval (about 2 [msec]) in this analysis is set to accurately simulate the control system, and can be set to a coarser time step depending on the analysis target. .

  Note that the above analysis is performed for the purpose of demonstrating the analysis by the dynamic phasor, and therefore only the analysis by the dynamic phasor is performed. As shown in FIG. 13, it can be confirmed that the analysis by the dynamic phasor almost coincides with the analysis result by the conventional instantaneous value analysis. As described above, the analysis by the dynamic phasor is consistent with the instantaneous value analysis. Is good. Therefore, it is sufficient if the periods (periods T1, T3 and T2) described with reference to FIG. 7 are set and the analysis by the dynamic phasor and the instantaneous value analysis are alternately performed according to the flowchart shown in FIG. It can be easily understood that it is possible to dramatically reduce the time required for the analysis of the transient phenomenon while ensuring the accuracy.

  The transient phenomenon analysis apparatus, method, and program according to an embodiment of the present invention have been described above, but the present invention is not limited to the above-described embodiment, and can be freely changed within the scope of the present invention. . For example, in the above-described embodiment, an example in which the circuit equation of the power distribution system used in the analysis of the dynamic phasor analysis unit 14a is created by the sputter blow method, but the circuit equation is obtained by using a nodal analysis method or a modified nodal analysis method. Can also be created.

  In the above-described embodiment, the example in which the circuit equation creation unit 14c is provided in common to the dynamic phasor analysis unit 14a and the instantaneous value analysis unit 14b has been described (see FIG. 1). However, although the circuit equations used in the dynamic phasor analysis unit 14a and the instantaneous value analysis unit 14b are the same, the values of many elements are different. Therefore, the dynamic phasor analysis unit 14a and the instantaneous value analysis unit You may make it provide a circuit equation preparation part individually with respect to each of 14b.

  In the above-described embodiment, an example in which the transient phenomenon analysis apparatus 1 is realized by a desktop personal computer has been described. However, the transient phenomenon analysis apparatus may be realized in the form of a server connected to a network. In such a form, for example, the analysis target and the analysis condition are transmitted to the server from the terminal device operated by the user, and the analysis result of the analysis performed on the server is returned to the terminal device.

1 Transient Phenomenon Analysis Device 14a Dynamic Phaser Analysis Unit 14b Instantaneous Value Analysis Unit 14c Circuit Equation Creation Unit T1 to T3 Period Δt1 Time increment Δt2 Time increment

Claims (6)

A first analysis unit that performs analysis by a dynamic phasor in a first time interval defined in advance in a first period that is set as a period in which distortion of voltage and current waveforms hardly occurs;
A second analysis unit for performing an instantaneous value analysis in a second time interval finer than the first time interval in a second period set as a period in which the waveform of the voltage and current is greatly distorted;
Transient phenomenon analysis device. The second analysis unit starts the instantaneous value analysis using the analysis result of the first analysis unit at the end time of the first period when the second period continues after the first period,
When the first period continues after the second period, the first analysis unit starts the analysis by the dynamic phaser using the analysis result of the second analysis unit at the end time of the second period. ,
The transient phenomenon analysis apparatus according to claim 1.   The transient analysis device according to claim 1, further comprising a creation unit that creates a circuit equation to be analyzed, which is used in the analysis of the first analysis unit, by a sputter blow method.   The circuit equation to be analyzed includes only a first dynamics term indicating a time change of a DC component of voltage and current, and a second dynamics term indicating a time change of a phasor component of a fundamental wave of voltage and current. The transient analysis device described. A first step of performing analysis by a dynamic phasor in a first time interval defined in advance in a first period set as a period in which distortion of voltage and current waveforms hardly occurs;
A second step of performing an instantaneous value analysis in a second time step finer than the first time step in a second period set as a period in which the waveform of the voltage and current is greatly distorted;
Transient phenomenon analysis method including Computer
First analysis means for performing analysis by a dynamic phasor in a first time interval defined in advance in a first period set as a period in which distortion of voltage and current waveforms hardly occurs;
A second analysis means for performing an instantaneous value analysis in a second time interval finer than the first time interval in a second period set as a period in which the voltage and current waveforms are greatly distorted;
Transient phenomenon analysis program to function.