JP6734700B2 - Transient analysis device, method, and program - Google Patents

Description

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

In recent years, due to increasing environmental awareness, it is desired to effectively utilize renewable energy and reduce carbon dioxide emissions. In addition, the liberalization of electricity is about to completely liberalize the generation and retail of electricity. Against this background, it is expected that the number of interconnected distributed power sources centered on photovoltaic power generation will increase in the power system. In addition, it is expected that the number of interconnections of electric vehicles and power storage equipment will increase in the power system as a standby 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 device connected/connected do not interfere with each other and achieve the intended purpose. For the analysis of the transient phenomenon caused by such mutual interference, the instantaneous value analysis capable of analysis at the waveform level is effective. 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 performing such an instantaneous value analysis. Other programs that can analyze instantaneous values include EMTP (Electro Magnetic Transients Program) and PSCAD (registered trademark).

Taku Noda, “Development Trend of Electric Power System Instantaneous Value Analysis Program-Development of Domestically-produced Program XTAP-”, Electric Review, pp.60-64, August 2011 issue Taku Noda, “Development Trends 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, the above-mentioned instantaneous value analysis performed by XTAP is to analyze how the voltage or current changes at the waveform level. It is necessary to reduce the time step for 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, one cycle (20 [msec]) of time step is about several hundreds (more). In some cases, it is set to tens of thousands) and the analysis is performed.

As described above, in the above-described XTAP, since it is necessary to reduce the time step for performing the analysis in order to perform the analysis with sufficient accuracy, there is a problem that the calculation amount becomes large and the analysis takes a long time. .. Here, in the instantaneous value analysis, a portion in which the voltage and current waveforms are hardly distorted (a portion in which the voltage and current are substantially sinusoidal) often continues endlessly. If it is possible to reduce the time required for analysis of such a portion in which almost no distortion occurs, 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 phenomenon analysis device, method, and program capable of dramatically reducing the time required for transient phenomenon analysis while ensuring sufficient accuracy. The purpose is to

In order to solve the above-mentioned problems, the transient phenomenon analysis device (1) of the present invention is defined in advance in a first period (T1, T3) set as a period in which distortion of voltage and current waveforms hardly occurs. In the first analysis unit (14a) that performs analysis by the dynamic phasor at the first time step (Δt1) and the second time period (T2) set as the period in which the voltage and current waveforms are significantly distorted, And a second analysis unit (14b) that performs an instantaneous value analysis at a fine second time step (Δt2).
Further, in the transient phenomenon analysis device of the present invention, when the second analysis unit has the second period following the first period, the analysis result of the first analysis unit at the end of the first period. When the first analysis unit starts the instantaneous value analysis using, and the first period continues after the second period, the analysis result of the second analysis unit at the end of the second period. To start the analysis by the dynamic phasor.
Moreover, the transient phenomenon analysis apparatus of the present invention includes a creation unit (14c) that creates a circuit equation to be analyzed used in the analysis of the first analysis unit by a superstar blow method.
Further, in the transient phenomenon analysis device of the present invention, the circuit equation to be analyzed shows a first dynamics term indicating a time change of a direct current component of a voltage and a current, and a time change of a phasor of a fundamental wave component of the voltage and a current. Only the second dynamics term is included.
The transient phenomenon analysis method of the present invention uses the dynamic phasor at the predetermined first time step (Δt1) in the first period (T1, T3) set as the period in which the voltage and current waveforms are hardly distorted. In the first step (S11) of performing the analysis and the second period (T2) set as the period in which the voltage and current waveforms are significantly distorted, the second time step (Δt2) finer than the first time step The second step (S14) of performing value analysis is included.
The transient phenomenon analysis program of the present invention causes a computer to perform a predetermined first time step (Δt1) in a first period (T1, T3) set as a period in which distortion of voltage and current waveforms hardly occurs. In the first analysis means (14a) for performing analysis by the dynamic phasor and the second period (T2) set as the period in which the waveforms of the voltage and the current are greatly distorted, the second time step (which is finer than the first time step ( It functions as the second analysis means (14b) for performing the instantaneous value analysis at Δt2).

According to the present invention, in the first period, which is set as a period in which the voltage and current waveforms are hardly distorted, the analysis by the dynamic phasor is performed in the first time step, and the voltage and current waveforms are set to be significantly distorted. In the 2nd period, the instantaneous value analysis is performed in the 2nd time step, which is finer than the 1st time step. Therefore, the time required to analyze the transient phenomenon is dramatically shortened while ensuring sufficient accuracy. There is an effect that can be done.

FIG. 1 is a block diagram showing a main configuration of a transient phenomenon analysis device according to an embodiment of the present 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 a distribution line or a transmission line simulated by analysis by a dynamic phasor. It is a figure which shows the equivalent circuit of the transformer simulated by the analysis by a dynamic phasor. It is a figure which shows the basic circuit of a 2-level AC-DC converter, and the modulation method by 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 in one Embodiment of this invention. 6 is a flowchart showing an example of a transient phenomenon analysis method according to an embodiment of the present invention. It is a figure which shows the power distribution system used for analysis of a transient phenomenon. It is a figure which shows the model of a PV panel. It is a figure which shows the model of PCS. It is a figure which shows the model of the substation for distribution. It is a figure which shows the analysis result by a transient phenomenon analyzer.

Hereinafter, a transient phenomenon 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, but the present invention is not limited to the distribution system and the analysis target is an arbitrary electric circuit such as a power transmission system. be able to.

<Transient phenomenon analyzer>
FIG. 1 is a block diagram showing a main configuration of a transient phenomenon analysis device according to an embodiment of the present invention. As shown in FIG. 1, the transient phenomenon analysis device 1 of the present 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. Analysis of. Such a transient phenomenon analysis device 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 an operation of a user who uses the transient phenomenon analysis device 1 to the arithmetic processing device 14. The output device 12 includes, for example, a liquid crystal display device and a printer, and outputs various kinds of 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), and the like, and stores various parameters PR used in a circuit equation of a power distribution system, a transient phenomenon analysis program PG, and the like.

The arithmetic processing unit 14 uses the parameter PR stored in the auxiliary storage unit 13 according to the transient analysis program PG stored in the auxiliary storage unit 13 based on the operation instruction input from the input unit 11 to generate a transient in the power 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). ) Is provided.

The dynamic phasor analysis unit 14a performs analysis by the dynamic phasor in a period (first period) set as a period in which the voltage and current waveforms of the distribution system are hardly distorted. The details of the dynamic phasor will be described later. The instantaneous value analysis unit 14b performs the instantaneous value analysis in a period (second period) set as a period in which the voltage and current waveforms of the distribution system are significantly distorted. Since the instantaneous value analysis performed by the instantaneous value analysis unit 14b is the same as the conventional instantaneous value analysis, detailed description will be omitted. The circuit equation creation unit 14c creates the circuit equation of the distribution system used in the analysis of the dynamic phasor analysis unit 14a by the superstar blow method. The details of the method of creating the circuit equation by the circuit equation creating unit 14c will be described later.

The transient phenomenon analysis program PG is recorded in a computer-readable recording medium such as a CD-ROM or a DVD (registered trademark)-ROM, or downloaded from a network such as the Internet. It is stored in the auxiliary storage device 13 by being installed in 1. When the transient phenomenon analysis program PG stored in the auxiliary storage device 13 is read and executed, the function of each block 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 creating unit 14c) is realized by software. That is, these functions are realized by the cooperation of software and hardware resources.

<Dynamic phasor theory>
Next, the theory of the dynamic phasor, which is the basis of the analysis performed by the dynamic phasor analysis unit 14a described above, will be described. First, let x=x(t) be an instantaneous value of voltage, current, or the like at time t. Also, consider a window (t−T, t] with respect to time t. Define the time within the interval where τ=0 at the beginning of the window and τ=T at the end, and the Fourier series expansion of the instantaneous value x is performed. When calculated, the following equation (1) is obtained.

In the above equation (1), ω ₀ =2π/T, and the kth-order Fourier coefficient of the instantaneous value x is expressed as <x> _k . Since the window (t−T, t] slides from the past to the future with the passage of time and cuts out one cycle (cycle T) of the instantaneous value x, the Fourier coefficient <x> _k is It becomes a function and is expressed by the following equation (2).
<x> _k in the above equation (2) is a phasor (complex amount) having amplitude and phase information. In the theory of dynamic phasor, this phasor is called a dynamic phasor because it is considered to change dynamically with time.

Next, the instantaneous value x is differentiated with respect to time t, and the kth-order Fourier coefficient is obtained, and the following equation (3) is obtained.
By modifying the equation (3), the following equation (4) is obtained.
From the above equation (4), the derivative of the k-th order Fourier coefficient is obtained by subtracting the k-th order Fourier coefficient multiplied by jkω ₀ from the k-th order Fourier coefficient obtained by differentiating the original instantaneous value x. You can see that.

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

Next, a state equation of the circuit to be analyzed is set up. Now, suppose that the circuit has M state variables, and attention is paid to the order of K Fourier coefficients. When the equations relating to K orders are listed for each of the M state variables, a state equation relating to KM Fourier coefficients shown in the following equation (5) can be obtained.

However, in the above equation (5), x is a vector listing K Fourier coefficients of degree for each of the M state variables, and u is for each input variable to the circuit such as a voltage source or a current source. It is a vector that enumerates K Fourier coefficients of order. Here, in order to derive each element on the right side corresponding to each element on the left side of the above equation (5), the above equation (4) can be utilized.

When focusing only on the direct current component and the fundamental wave component, at the stage of deriving the above equation (5), the short time constant and the natural vibration of high frequency are removed, and it is possible to remove the large time step (the first time step). High-speed analysis is possible. However, conventionally, there is a drawback in that the state equation shown in the above equation (5) cannot be automatically derived. Therefore, in the present embodiment, the circuit equation ( An alternative to the state equation of the above equation (5) is derived.

<Circuit equation creation method using the superstar blow method>
Next, details of a method for creating a circuit equation by the above-described circuit equation creating unit 14c will be described. In this embodiment, it is possible to automatically derive the circuit equation by first applying the differential operation to each circuit element. It should be noted that the circuit equation is derived for each Fourier coefficient of interest, and these are related by the equation representing the 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 of several expressions.

The first expression of the above expression (6) can be expressed by the Norton type discrete time equivalent circuit shown in FIG. 2A, where Y _k and J _k are the admittance of the equivalent circuit and the current source, respectively. Is the value of. The second equation of the above equation (6) can be expressed by a Thevenin-type discrete time equivalent circuit shown in FIG. 2(b), where Z _k and E _k are the impedance of the equivalent circuit and the voltage source, respectively. Is the value of. 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.

Now, consider an arbitrary circuit in which the number of nodes is N _n and the number of circuit elements is N _b . In this circuit, when the relational expression of all the circuit elements with respect to a certain order is expressed by any of a plurality of expressions shown as the above expression (6), the Spur-Starblow equation of the circuit regarding the order is as follows (7) It can be represented by a formula. In addition, in the following expression (7), the subscript indicating the order is omitted to avoid complicated notation.

However, u in the above equation (7) is a column vector having the voltage of N _n nodes of the circuit as a component, and i and v respectively have the currents and voltages of the N _b circuit elements as components. S is a column vector, and s is a column vector having the value of the current source J _k or the voltage source E _k of the discrete-time equivalent circuit of N _b circuit elements as a component. A is called a branch-to-node connection matrix, and can be easily created from the connection information of the circuit. I is an identity matrix. Since B _i and B _v are coefficients respectively applied to the voltage and current of each circuit element, the coefficients of the relational expression of each circuit element shown in the above equation (6) are stored. For the method of creating the branch-to-node connection matrix A, refer to the following documents, for example.
References: Taku Noda, Kan Miki, Naoki Gibo, Kiyoshi Takenaka, "Development of Instantaneous Power System Analysis Program (Part 1)-Basic Design-", Research Report of Central Research Institute of Electric Power Industry H06002, March 2007

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

When the above equation (7) regarding the kth-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 orders relates K sets of equations, the circuit equations are sequentially solved from time 0 at appropriate time intervals, so that the node voltage of each part of the circuit and the current/voltage of each circuit element are related to the focused order. Time change (that is, dynamic phasor) can be calculated. In many cases, the coupling between orders does not cause any problem even if the delay of the calculation time step is allowed, so that the K sets of equations can be solved independently. However, if delays in calculation time steps cannot be tolerated in the coupling between orders, such as when simulating an AC/DC converter in detail, solve all or some of the K sets of equations simultaneously. Becomes

In this embodiment, the theory of the dynamic phasor is applied in order to simulate at high speed a situation in which a portion where voltage and current waveforms are hardly distorted (a portion where 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 equation (8) remains unchanged regardless of the passage of time, and only y _{k on} the right side changes with the passage of time. The circuit equation creation unit 14c shown in FIG. 1 creates the circuit equation of the distribution system by performing the processing for solving the above-mentioned K sets of equations.

<Dynamic phasor model>
The dynamic phasor model of various circuit elements will be described below. Below, based on the theory of the dynamic phasor, the amplitude and phase of the k-th order Fourier coefficient of the voltage v and the current i across the 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 information on amplitude and phase.

In the present embodiment, analysis by a dynamic phasor is applied in order to quickly simulate a situation where a portion where voltage and current waveforms are hardly distorted (a portion where voltage and current are sinusoidal) continues endlessly. .. Therefore, in the dynamic phasor model of various circuit elements, the direct current component of voltage and current (V ₀ (t), I ₀ (t): first dynamics term) and the fundamental wave component of voltage and current (V ₁ (V ₁ ( In most cases, it is sufficient to consider only t) and I ₁ (t): the second dynamics term.

(1) Resistance When the voltage across the resistance is v, the current flowing through the resistance is i, and the resistance value is R, the relational expression V=Ri holds. Since this relational expression holds for all Fourier coefficients of the orders, the following expression (10) holds for any order k.
Comparing the above equation (10) with the second equation of the above equation (6), it is assumed that Z _k =R, E _k =0 in the Thevenin type discrete time equivalent circuit of FIG. 2(b). It turns out that 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. By substituting the equation (9) into this equation and arranging it, the following equation (11) is obtained.

Next, the discrete time equivalent circuit is obtained by applying the numerical integration method to the equation (11). Specifically, if the calculation time step is Δt and the above equation (11) is rearranged by applying, for example, the backward Euler method, the following equation (12) is obtained. It should be noted that in the following formula (12), the parentheses of V _k and I _k represent not the time but the calculation time step.
Comparing the above equation (12) with the first equation of the above equation (6), Y _k =β _k , J _k =α _k I _{k in} the Norton type discrete time equivalent circuit of FIG. It can be seen that what is put as (n-1) becomes the dynamic phasor model of the inductor.

(3) Capacitor Letting the voltage across the capacitor be v, the current flowing through the capacitor be i, and the capacitance value be C, the relational expression i=C(dv/dt) holds. By substituting the equation (9) into this equation and arranging it, the following equation (13) is obtained.

Next, as in the case of the inductor, when the calculation time step is set to Δt and the above equation (13) is arranged by applying, for example, the backward Euler method, the following equation (14) is obtained. It should be noted that, also in the following expression (14), the parentheses of V _k and I _k represent not the time but the calculation time step.
Comparing the above equation (14) with the second equation of the above 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 put as (n-1) becomes the dynamic phasor model of the capacitor.

(4) Voltage source The voltage source is a power source that generates a specified voltage across the voltage source. In the theory of the dynamic phasor, it is considered that the voltage waveform generated by the voltage source is a periodic waveform of the period T and changes with time. When the Fourier coefficient of the order of interest can be analytically derived 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.

When the Fourier coefficient cannot be analytically derived, it is obtained by numerical integration from the voltage waveform at that time using the definition equation of the Fourier coefficient. High-speed calculation is possible by applying a fast Fourier transform (FFT) algorithm to the numerical integration. As an example often used for simulating the 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 specified. ..

(5) Current Source A current source is a power source that injects a specified current from one end to the other end. In the theory of the dynamic phasor, it is considered that the current waveform injected by the current source is a periodic waveform of the period T and changes with time. When the Fourier coefficient of the order of interest can be analytically derived from the injected current waveform at a certain time, the current value J _k of the Norton type 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 a defining equation, as in the case of the voltage source.

(6) Switch Here, it is assumed that the switch operates a few times during one simulation like a circuit breaker. Considering a switch function σ(t) that returns 1 when the switch is on at time t and 0 when the switch is off, the following equation (16) is provided between the voltage v across the switch and the 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 sufficient to set the relevant rows of the Spaster Blown equations of all orders of interest as shown in the following equation (17).

(7) Subordinate power supply For the i-th circuit element, the k-th order Fourier coefficient of voltage is V _k ^i, and the k-th order Fourier coefficient of current is I _k ⁱ . Further, regarding 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 expression of the voltage control voltage source, the current control voltage source, the voltage control current source, and the current control current source is as follows. It is represented by each equation. Therefore, these equations may be used as the relevant row of the spur star blow equation of degree k. The coefficient can be changed depending on the order.

(8) Distribution Line As described above, in the present embodiment, in order to quickly simulate a situation in which a portion where voltage and current waveforms are hardly distorted (a portion where voltage and current are sinusoidal) continues endlessly. Analysis by dynamic phasor is applied. Therefore, in many cases, the Fourier coefficient orders of interest in the dynamic phasor analysis 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 with sufficient accuracy. FIG. 3 is a diagram showing an equivalent circuit of a distribution line or a transmission line that is simulated by analysis using a dynamic phasor. Note that the π-type equivalent circuit can be created by combining the models of the above-described resistance, inductor, and capacitor.

(9) Transformer As described above, in many cases, the Fourier coefficient orders of interest in the dynamic phasor analysis are "0" and "1" (that is, only the DC component and the fundamental component). Therefore, 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 showing an equivalent circuit of a transformer that is simulated by analysis using a dynamic phasor.

The winding resistance R1 and the exciting resistance R2 in FIG. 4A can be simulated by the model of the above resistance, and the leakage inductance L1 and the exciting inductance L2 can be simulated by the model of the above inductance. The ideal transformer TF in FIG. 4 constitutes the equivalent circuit of FIG. 4(b) called a voltage/current exchange system by combining the above voltage control voltage source and current control current source. In this ideal transformer TF, when the turns ratio is n:1, assuming that the fundamental wave voltages of the primary and secondary windings are V ₁ and V ₂ , there is a relation that V ₁ =n·V ₂ due to the voltage control voltage source. It is filled. Similarly, if the fundamental wave currents of the primary and secondary windings are I ₁ and I ₂ , then n·I ₁ =I ₂ is satisfied by the current control current source. Since electromagnetic induction does not occur with respect to the direct current component, both sub power supplies are replaced with a voltage source of zero voltage.

(10) Power Electronics Converter In the theory of dynamic phasor, the power electronics converter can be considered as an order conversion element. Power electronics converters used for interconnection of distributed power sources such as photovoltaic power generation and storage batteries are generally PWM (Pulse Width Modulation) pulse-width modulation (AC/DC) converters, and reactive power compensators (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 showing a basic circuit of a two-level AC/DC converter and a modulation method by the PWM method. The AC/DC converter shown in FIG. 5A is for converting DC to AC by performing on/off control of the semiconductor switching elements Q11, Q12, Q21, Q22, Q31, Q32 at high speed. The on/off control of the semiconductor switching elements Q11, Q12, Q21, Q22, Q31, Q32 is as shown in FIG. 5B, as shown in FIG. 5B, the modulated wave W1 (in most cases, a sine wave) and the carrier wave W2( (Triangular wave) based on the comparison result.

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 contrary, 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 a three-phase alternating current, the timing for turning on the semiconductor switching elements (Q11, Q21, Q31) or the turning on of the semiconductor switching elements (Q12, Q22, Q32). Please note that the timings to be set are different from each other.

In this way, by comparing the modulated wave W1 and the carrier wave W2, a waveform is output to 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. The waveform is obtained. At this time, the higher the frequency of the carrier wave W2, the closer the output waveform becomes to the modulated wave W1. Therefore, considering an ideal state in which the frequency of the carrier wave W2 is infinite, the modulated wave W1 is directly output to the AC side as a voltage waveform. That is, the AC-DC converter viewed from the AC side can be simulated as a voltage source that outputs the voltage represented by the following equation (19).

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

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

By substituting the above equation (19) into the above equation (20), the following equation (21) is obtained.
On the other hand, when the current flowing from the DC side of the AC/DC converter is J ₀ (t), the electric 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, the energy conservation law P _ac =P _dc is instantly satisfied. Therefore, the DC side of the AC/DC converter is as follows. This can be simulated with the current source represented by the equation (23).

As described above, the dynamic phasor model of the AC/DC converter has a three-phase voltage control voltage source for converting the DC voltage on the DC side into the fundamental wave voltage on the AC side according to the above equation (19), and the above equation (23). It can be configured by a current control current source for converting an AC side fundamental wave current into a DC side DC current. Such an AC/DC converter can be represented by the circuit shown in FIG. FIG. 6 is a diagram showing a dynamic phasor model of the AC/DC converter. The AC/DC converter can also be represented by a circuit whose AC side is simulated by a current source, as shown in FIG. 6B.

<Solution of circuit equation considering coupling between orders>
As described above, when there are K orders of interest, K sets of equations (8) are associated and solved. When the connection between these superstar blow equations can tolerate the delay of the calculation time step, or when the superstitial blow equations can be sequentially substituted by solving the superstar blow equation according to a certain order, they can be solved individually. However, when the coupling is tight and cannot be solved by the above method, it is necessary to solve the K sets of superstar blow equations simultaneously.

Here, focusing on only the direct current component and the fundamental wave component, and writing these two Spaster-Blow equations including the coupling between the orders, they are expressed by the following equation (24).

R ₀₁ in the above equation (24) is a matrix including coefficients corresponding to order conversion elements that refer to the voltage/current of the fundamental wave in the circuit related to the DC component, and most of the elements are 0. Similarly, R ₁₀ in the equation (24) is a matrix including coefficients corresponding to the order conversion elements that refer to the voltage/current of the DC component in the circuit related to the fundamental wave component, and most of the elements are 0. By solving the above equation (24), it is possible to obtain a solution that simultaneously satisfies the superstar blow equation for the direct current component and the fundamental wave component.

The above formula (24) is a formula in the case of including only the direct current component and the fundamental wave component, but it can be easily extended to the case where the order of arbitrary K Fourier coefficients is focused. A node voltage of each part of the circuit at each time and each circuit are created by creating an expression including K orders of interest (an expression similar to the expression (24) above) and sequentially solving it from time 0 at an appropriate time step. The voltage and current of the device can be obtained for each order. By superimposing the solutions of all orders, the corresponding waveform can be obtained in the range of the considered orders.

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

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

Next, the user sets the analysis conditions. For example, a user operating the input device 11 of the transient phenomenon analysis device 1 performs a process of setting a period for performing analysis by a dynamic phasor, a period for performing instantaneous value analysis, and a time step for performing these analyses. FIG. 7 is a diagram showing an example of analysis conditions set in the embodiment of the present invention. It should be noted that FIG. 7 shows an example of changes over time in the waveform of the voltage or current of the three-phase alternating current for easy understanding.

Time t0 in FIG. 7 is a time at which a voltage and an event in which the voltage greatly changes are simulated. Further, 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 and the fluctuation of the voltage caused by the above event are expected to be settled, and is set by, for example, a user's rule of thumb. Examples of the event include opening and closing of a switch (breaker). In order to simplify the description, it is assumed that the above event is simulated at only time t0 shown in FIG.

Since the period T1 before the time t1 and the period T3 after the time t2 are periods in which the waveforms of the voltage and the current hardly distort (the period in which the sinusoidal voltage and the current continue), the dynamic phasor. Is set to the period (first period) in which the analysis is performed. Further, since the period T2 between the times t1 and t2 is a period in which the waveforms of the voltage and the current are greatly distorted by the above event (a period in which the voltage and the current largely deviate from the sine wave), an instantaneous value analysis is performed. (Second period).

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

When the above input is completed and the user gives an instruction to start the analysis, the transient phenomenon analysis processing that occurs in the power distribution system is performed according to the flowchart shown in FIG. FIG. 8 is a flowchart showing an example of the transient phenomenon analysis method according to the embodiment of the present invention. When the analysis process is started, first, the dynamic phasor analysis unit 14a shown in FIG. 1 performs analysis by the dynamic phasor (step S11). For example, in the period T1 shown in FIG. 7, the analysis by the dynamic phasor is performed with 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 time (time t1) of the period T1 shown in FIG. 7 or the analysis result immediately before that is delivered. Next, the arithmetic processing unit 14 shown in FIG. 1 determines whether or not the analysis for the entire period is completed (step S13). For example, it is determined whether the analysis is completed in all of the periods T1 to T3 shown in FIG.

When it is determined that the analysis for the entire period is not completed (when the determination result in step S13 is “NO”), the instantaneous value analysis using the analysis result passed in step S12 is the instantaneous value analysis. It is implemented by the unit 14b (step S14). For example, in the period T2 shown in FIG. 7, the instantaneous value analysis is performed with the time step Δt2. On the other hand, when it is determined that the analysis for the entire period is completed (when the determination result in step S13 is “YES”), the series of processes illustrated in FIG. 8 is completed.

When the instantaneous value analysis in step S14 is completed, the analysis result at the time when the analysis is completed 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 time (time t2) of the period T2 shown in FIG. 7 or the analysis result immediately before that is delivered. After that, the arithmetic processing unit 14 shown in FIG. 1 determines whether or not the analysis for the entire period is completed (step S16). For example, it is determined whether the analysis is completed in all of the periods T1 to T3 shown 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 passed in step S15 is performed by the dynamic phasor. It is implemented 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 with the time step Δt1. On the other hand, when it is determined that the analysis for the entire period is completed (when the determination result in step S16 is “YES”), the series of processes illustrated in FIG. 8 is completed.

As described above, in this embodiment, the dynamic phasor analysis unit 14a and the instantaneous value analysis unit 14b alternately perform the analysis by the dynamic phasor and the instantaneous value analysis while passing the analysis result at the analysis end time. Be seen. Therefore, for example, a transient phenomenon in which the voltage and current waveforms are greatly distorted, such as when a circuit breaker is opened and closed, can be analyzed in a short time while ensuring sufficient accuracy.

Further, the dynamic phasor analysis performed by the dynamic phasor analysis unit 14a can take into consideration the difference in impedance for each phase, like the instantaneous value analysis performed by the instantaneous value analysis unit 14b, and the number of harmonics included in the calculation. Therefore, the dynamics of the circuit can be considered, and the consistency with the instantaneous value analysis is good. Therefore, 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 passed, and thus the accurate analysis can be performed.

<Analysis example>
The inventor of the present application actually analyzed the transient phenomenon occurring in the power distribution system using the transient phenomenon analysis device 1 described above. FIG. 9 is a diagram showing a power distribution system used for transient phenomenon analysis. 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) 22, a distribution line 23, and a distribution substation 24. That is, a mega solar is linked to the end of the distribution line 23.

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

The PCS 22 was set for four 500 [kW] machines, and the main circuit thereof was simulated by the equivalent circuit of FIG. FIG. 11 is a diagram showing a model of PCS. Note that FIG. 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 represented as a dynamic phasor model of an 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 for the direct current component, and the current sources J _a , J _b , J _c are considered in the circuit equation for the fundamental wave component.

The DC capacitor is 400 [mF], and control by DC-AVR is performed so that the voltage V _dc becomes the rated voltage of 350 [V]. The DC-AVR is PI controlled as shown in FIG. 11(b), the direct current is extracted by the current source J _dc so that the voltage V _dc is 350 [V], and the DC sources are controlled by the current sources J _a , J _b , and J _c. Outputs the same amount of power 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, the PLL circuit shown in FIG. 11(c) is assembled as a control system, and the phase θ which is the output thereof and the phase of the current source J _a are synchronized, and the current sources J _b and J _c are changed from the synchronized phase to − It was synchronized with the phase delayed by 2π/3 [rad]. The DC-AVR and PLL circuits were processed separately from the circuit equation, and the same backward Euler method as in the circuit equation was used for numerical integration.

The distribution line 23 has a length of 10 [km] and is 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 the equivalent circuit shown in FIG. FIG. 12 is a diagram showing a model of a distribution substation. The inductance L _ss is the inductance of the bank transformer and the upper system, and is set to 1.44 [mH] (each phase). The voltage source E _ss is a three-phase balanced voltage source (50 [Hz]) having an effective value between lines of 6.6 [kV] to simulate the system voltage, and its neutral point is grounded by a resistance of 10 [kΩ]. .. When the terminating resistance connected to the open delta of the GPT (Grounded Potential Transformer) installed in the distribution substation 24 is 25 [Ω], the equivalent ground resistance is 10 [kΩ].

Under the above conditions, the distribution system 20 shown in FIG. 9 was analyzed by setting only the direct current component and the fundamental wave component and setting the time step Δt1 for analysis to 2 [msec]. FIG. 13 is a diagram showing an analysis result by the transient phenomenon analysis device. Note that, in FIG. 13, the analysis results by the conventional instantaneous value analysis are shown in a superimposed manner for comparison. Referring to FIG. 13, the output voltage V _{pcs of the} PCS 22 is a time profile of the value J _pv of the current source provided in the simple equivalent circuit (see FIG. 10A) simulating the PV panel 21 (FIG. 10B). It can be confirmed that it is fluctuating according to changes in Also, referring to FIG. 13, it can be confirmed that the output voltage V _{pcs of the} PCS 22 changes 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 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-mentioned analysis by the conventional instantaneous value analysis, it is necessary to simulate the switching by PWM, and therefore it is necessary to set the time step for performing the analysis 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 dramatically shortened. The time step (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. ..

Since the above analysis is performed for the purpose of demonstrating the analysis by the dynamic phasor, 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 agrees with the analysis result by the conventional instantaneous value analysis, and as described above, the analysis by the dynamic phasor is consistent with the instantaneous value analysis. Is good. Therefore, it is sufficient to set the periods (periods T1, T3 and period T2) described with reference to FIG. 7 and alternately perform the dynamic phasor analysis and the instantaneous value analysis according to the flowchart shown in FIG. It is easy to understand that it is possible to dramatically reduce the time required to analyze transient phenomena while ensuring accuracy.

The transient phenomenon analysis device, method, and program according to the 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 modified within the scope of the present invention. .. For example, in the above-described embodiment, an example in which the circuit equation of the distribution system used in the analysis of the dynamic phasor analysis unit 14a is created by the superstar blow method has been described. However, the circuit equation may be obtained by using the node analysis method or the modified node analysis method. Can also be created.

Further, in the above-described embodiment, an example in which the circuit equation creation unit 14c is provided in common for 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 have the same shape, the values of many elements are different, so the dynamic phasor analysis unit 14a and the instantaneous value analysis unit are different. You may make it provide a circuit equation preparation part separately for each of 14b.

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

DESCRIPTION OF SYMBOLS 1 Transient phenomenon analyzer 14a Dynamic phasor analyzer 14b Instantaneous value analyzer 14c Circuit equation generator T1-T3 Period Δt1 hour step Δt2 hour step

Claims (6)

A first analysis unit that performs analysis by a dynamic phasor in a first time interval that is defined in advance in a first time period that is set as a time period during which waveforms of voltage and current are hardly distorted;
In a second period set as a period in which the voltage and current waveforms are significantly distorted, a second analysis unit that performs an instantaneous value analysis in a second time step that is finer than the first time step,
A transient phenomenon analyzer. When the second period continues after the first period, the second analysis unit starts the instantaneous value analysis using the analysis result of the first analysis unit at the end point of the first period,
When the first period continues after the second period, the first analysis unit starts the analysis by the dynamic phasor using the analysis result of the second analysis unit at the end of the second period. ,
The transient phenomenon analysis device according to claim 1. The transient phenomenon analysis device according to claim 1 or 2, further comprising: a creation unit that creates a circuit equation to be analyzed used in the analysis of the first analysis unit by a spar star blow method. The circuit equation to be analyzed includes only a first dynamics term indicating a time change of a direct current component of a voltage and a current, and a second dynamics term indicating a time change of a phasor of a fundamental wave component of a voltage and a current. The transient analysis device described. Computer
A first step of performing analysis by a dynamic phasor at a first time interval defined in advance in a first time period set as a time period during which waveforms of voltage and current are hardly distorted,
In a second period set as a period in which the voltage and current waveforms are greatly distorted, a second step of performing an instantaneous value analysis in a second time step finer than the first time step,
Transient analysis method including. Computer,
A first analysis means for performing analysis by a dynamic phasor at a first time interval defined in advance in a first time period set as a time period during which the voltage and current waveforms are hardly distorted;
Second analysis means for performing an instantaneous value analysis at a second time step finer than the first time step in a second time period set as a time period during which the voltage and current waveforms are greatly distorted,
A transient phenomenon analysis program that works as a function.