JP4845133B2 - High-order harmonic resonance frequency characteristic estimation method - Google Patents

Description

  The present invention relates to a high-order harmonic resonance frequency characteristic estimation method for estimating resonance frequency characteristics of high-order harmonics in a power system.

  In recent years, many control devices using power electronics employ a PWM method based on high-speed switching. For example, in wind power generation or a fuel cell, DC power is generated, and the DC power is converted into AC power by a PWM method using power electronics equipment and supplied to the power system.

The power electronics device generates a high-order harmonic current having a frequency f ₀ during AC / DC conversion by the PWM method, and flows out to the power system. On the other hand, a power factor improving capacitor is installed in the power system, and the frequency f ₀ generated by the power electronics device is close to the natural frequency fn by the power factor improving capacitor of the neighboring power system. a power electronics device is amplified current having a frequency f ₀ generated induces an overcurrent of the power factor improving capacitor generated power quality problems, such as electromagnetic noise and overheating due to resonance.

  For this reason, it is important to know in advance whether or not a power quality problem will occur when the power electronics equipment is connected to the grid. The high-order harmonics here are in the frequency region where the order exceeds the 13th order and the upper limit is 10 kHz.

As a method for analytically examining higher-order harmonic resonance, an equivalent current source is placed at the connection point of power electronics equipment that generates higher-order harmonic current, and the current of the capacitor for power factor improvement is measured using the frequency response method. There are methods for obtaining amplification characteristics. In addition, as a method for identifying the harmonic generation source, a simulation circuit that numerically simulates the distribution system is set, the eigenvalue of this simulation circuit and its eigenvector are calculated, and the resonance frequency of the eigenmode is calculated from the complex part of the eigenvalue. Calculate the sensitivity of each node in its eigenmode from the absolute value of each element of each eigenvector, while frequency analysis based on the charging waveform of one of the power factor correction capacitors connected in parallel to the distribution system To determine the resonance frequency and its intensity in the actual generation mode, compare these to identify the rectifier load that generates commutation vibration, and regard it as a harmonic generation source (for example, patents) Reference 1).
Japanese Patent Laid-Open No. 4-67727

  However, in Patent Document 1, the resonance frequency and sensitivity obtained from the eigenvalue of the simulated circuit and its eigenvector, the resonance frequency in the generation mode actually generated in the distribution system, and its strength are obtained, and the commutation vibration is obtained. Therefore, it is not possible to grasp the resonance frequency characteristics of higher harmonics when a power electronics device is newly connected to the system. Therefore, when a new power electronics device is to be connected to the grid, it cannot be used to determine whether or not there is a problem with the connection.

  On the other hand, in the method of obtaining the current amplification characteristics of the power factor correction capacitor by the frequency response method by placing an equivalent current source at the connection point of the power electronics device to be newly connected to the grid, calculation examples for many frequencies Is necessary and complicated.

  Further, the line impedance RL varies depending on the frequency due to the skin effect or the like. Particularly in the region of higher harmonics, the resistance component R increases rapidly. If this increase in resistance R is ignored, an accurate frequency response cannot be obtained and the practicality becomes poor, so an analysis method considering this is desired.

  An object of the present invention is to provide a high-order harmonic resonance frequency characteristic estimation method capable of accurately grasping the resonance frequency characteristic of a high-order harmonic when a power electronics device is newly connected to a system.

  According to the first aspect of the present invention, there is provided a high-order harmonic resonance frequency characteristic estimation method in which a line impedance of a power system and a power factor improving capacitor of the power system are simulated by an analysis model comprising a linear circuit element RLC. A differential equation is derived, an equivalent circuit by an RLC circuit having a time constant and a natural frequency determined by the eigenvalues of the coefficient matrix of the state differential equation is derived, and the current of the higher-order harmonic current source of the capacitor current for power factor improvement of the equivalent circuit The resonance frequency characteristics of high-order harmonics in the power system are estimated based on the current amplification factor.

  According to a second aspect of the present invention, there is provided a high-order harmonic resonance frequency characteristic estimation method according to the first aspect of the invention, wherein the frequency characteristic of the line impedance due to the skin effect is additionally simulated by an analysis model comprising an RL parallel circuit of a linear element RL. Then, the state differential equation is derived.

  According to a third aspect of the present invention, there is provided a high-order harmonic resonance frequency characteristic estimation method according to the second aspect of the invention, wherein the analysis model includes a multistage connection of the RL parallel circuits to expand a frequency region that can be simulated. Features.

  According to the present invention, an equivalent circuit is derived from an RLC circuit having a time constant and a natural frequency determined by the eigenvalues of the coefficient matrix of the state differential equation of the power system, and the higher-order harmonic current of the power factor improving capacitor current of the equivalent circuit is derived. Since the resonant frequency characteristics of high-order harmonics in the power system are estimated based on the current amplification factor with respect to the current of the source, when trying to newly connect the power electronics equipment that is a high-order harmonic current source to the system, It is possible to easily determine whether or not there is a problem with the interconnection.

  In addition, the frequency characteristic of the line impedance due to the skin effect is additionally simulated by an analytical model comprising an RL parallel circuit of the linear element RL, and the state differential equation of the power system is derived, so the higher order harmonics of the line impedance taking the skin effect into consideration. It is possible to accurately estimate the resonance frequency characteristic of the wave. Furthermore, by using an analysis model in which RL parallel circuits are connected in series in multiple stages, the frequency range that can be simulated can be expanded.

  First, considerations up to the present invention will be described. When examining high-order harmonic resonance of a power system, an analysis model of the power system is created, and an eigenvalue and its eigenvector are obtained using the analysis model to obtain a resonance frequency and its sensitivity. However, although the eigenvalues and eigenvectors of the analysis model can understand the frequency and strength of vibration, the higher harmonic current generated by the power electronics device when the power electronics device is newly connected to the grid. It is impossible to determine how much current is amplified by the power factor improving capacitor.

  Therefore, in determining the current amplification factor of the power factor improving capacitor current with respect to the current of the higher harmonic current source, in the present invention, the eigenvalue of the analysis model is generally a complex number in the power system, and the real part of the eigenvalue is a time constant. Focusing on the fact that the imaginary part becomes a natural frequency, an equivalent circuit by an RLC circuit having a time constant and a natural frequency determined by the natural value is derived. Then, a high-order harmonic current source is connected to the derived equivalent circuit to change the high-order harmonic current, and the current gain of the power factor improving capacitor current in the equivalent circuit with respect to the current of the high-order harmonic current source is changed. The resonance frequency characteristics of higher harmonics in the power system are estimated based on the current amplification factor.

  FIG. 1 is a flowchart showing the contents of a high-order harmonic resonance frequency characteristic estimation method according to an embodiment of the present invention. First, a state differential equation of the power system is obtained in order to obtain an eigenvalue of the analysis model of the power system (S1). Hereinafter, a high-voltage distribution system will be described as an example of the power system. In order to simplify the analysis model of the power system, the following assumptions are set.

(1) The line impedance is assumed to be three-phase balanced.

(2) Since the line capacitance is sufficiently smaller than the power factor improving capacitor C, it is ignored.

Thereby, as shown in FIG. 2, the analysis model becomes a single-phase circuit composed of constants such as a working inductance L, a resistance R, and a power factor improving capacitor C. The variables at the time of analysis are the branch currents I (I ₁ , I ₂ ... I _n ) of the branches 11a to 11n of the upper system and the line impedance RL, and the power factor improving capacitors C (C ₁ , C ₂ ... C _n ) Node voltages V (V ₁ , V ₂ ... V _n ) of the branches 12 a to 12 _{n at} the connection points. Further, the power source is only the high-order harmonic equivalent current source J. The state differential equation of the power system is obtained under the above conditions.

Seeking a capacitor _C for power factor improvement shown in Figure 2 the current balance at the connection point is node 12a~12n of (C _{1, C} 2 ... _{C n)} (node current equilibrium), voltage balance in branch 11a~11n (Branch voltage balance equation) is obtained. The node current balance equation is expressed by the following equation (1), and the branch voltage balance equation is expressed by the following equation (2).

From (1) and (2), the state differential equation of the power system is expressed by (3).

Next, the eigenvalue λ of the coefficient matrix of the state differential equation expressed by equation (3) is obtained (S2). The eigenvalue λ of the coefficient matrix of the equation (3) is generally a complex number in the power system. As is well known, when the time constant T ₀ and the natural frequency f ₀ are used, the real part and the imaginary part are expressed by the equation (4). The relationship is as shown.

Since a plurality of eigenvalues λ are generally obtained, a time constant T ₀ and a natural frequency f ₀ are obtained for each eigenvalue λ (S3).

Next, an equivalent circuit by an RLC circuit having a time constant T ₀ and a natural frequency f ₀ is obtained (S4). This equivalent circuit is obtained as many as the number of eigenvalues λ, and the phenomenon in each eigenvalue λ in the eigenmode is considered for each mode, so that the physical evaluation becomes easy and clear.

FIG. 3 is a circuit diagram of an equivalent circuit using an RLC circuit having a time constant T ₀ and a natural frequency f ₀ . The equivalent circuit is an RLC circuit including line impedances R ₀ and L ₀ and a power factor improving capacitor C, and a high-order harmonic current source Jλ is arranged in parallel with the power factor improving capacitor C. The relationship between the resistance R ₀ , the working inductance L ₀ , the power factor improving capacitor C, the time constant T ₀ , and the natural frequency ω ₀ (ω ₀ = 2πf ₀ ) of this equivalent circuit is expressed by the following equation (5). become.

  Then, the current ic of the power factor improving capacitor C of the obtained equivalent circuit is obtained, and the amplification factor Q (ω) of the current ic with respect to the current source Jλ is obtained (S5). A resonance frequency characteristic is estimated based on the characteristic of the amplification factor Q (ω) (S6).

That is, the equation of the equivalent circuit shown in FIG. 3 is expressed by the following equation (6).

From this equation (6), the amplification factor Q (ω) is expressed by equation (7).

Further, L ₀ C and CR ₀ in the equation (7) are expressed by the equations (5) to (8).

Therefore, when Eq. (8) is substituted into L ₀ C and CR ₀ of Eq. (7), the amplification factor Q (ω) of each eigenmode is expressed as follows: angular frequency ω, time constant T ₀ , eigenangular frequency ω ₀ Therefore, the amplification factor Q (ω) of each eigenmode can be easily obtained by calculation.

Thus, an equivalent circuit is derived from an RLC circuit having a time constant T ₀ and a natural frequency f ₀ determined by the eigenvalue λ of the coefficient matrix of the state differential equation of the power system, and the power factor improving capacitor current _ic of the equivalent circuit is derived. Since the resonance frequency characteristics of high-order harmonics in the power system are estimated based on the amplification factor Q (ω) with respect to the current of the high-order harmonic current source Jλ, a power electronics device that is a high-order harmonic current source is newly added to the system. It is possible to easily determine whether or not there is a problem in the connection when trying to connect to the system.

  Next, consideration of the skin effect of the line impedance RL will be described. The line impedance RL has a frequency characteristic as shown in FIG. 4, and in particular, the resistance R increases rapidly as the frequency f increases, while the working inductance L decreases slightly. Since current amplification by resonance is proportional to (L / R), practical accuracy cannot be ensured if this is ignored. Then, next, the simulation method of the frequency f dependence of resistance R and action inductance L is examined.

  The point when considering the dependence of the frequency f is that a simulation method that is a linear state differential equation that takes advantage of the eigenmode method is essential. In polynomial approximation such as Lagrangian interpolation, which is often used for function approximation, the equations are nonlinear and eigenvalues cannot be obtained.

Therefore, as a simulation method for keeping the state differential equation linear, an RL parallel circuit of linear elements R _p and L _p shown in FIG. 5 is considered. As is well known, the equivalent resistance R _e and equivalent inductance L _e of this RL parallel circuit are given by the following equation (9).

Since the equivalent resistance R _e increases and the equivalent inductance L _e decreases with the frequency f from the equation (9), the line frequency characteristic of the line impedance RL can be simulated. As shown in FIG. 6, in the simulation circuit, the base portion is shared by a series RL circuit of a resistor R _s and an action inductance L _s , and the anti-frequency characteristic is shared by an RL parallel circuit of an equivalent resistance R _e and an equivalent inductance L _s. It becomes a circuit.

On the other hand, since the increase rate of the equivalent resistance R _e decreases at the inflection point f _m as shown in FIG. 7, when the frequency region to be simulated is wide, approximation of the frequency region higher than the inflection point f _m is performed. Accuracy is reduced. The inflection point f _m is expressed by equation (10).

Further, the equivalent resistance _Re is expressed by equation (11).

By setting a high inflection point f _m, (11) the equivalent resistance R _e from the equation, the approximation accuracy of the low frequency range becomes higher increase start of frequency f is decreased. FIG. 8 is a characteristic diagram showing the frequency characteristic of the resistor R using one RL parallel circuit. The dotted line is the frequency characteristic of the resistor R (R = R _s + R _e ), and the solid line is the frequency characteristic of the resistor R (R = R _s ). As can be seen from the frequency characteristic of the dotted resistance R (R = R _s + R _e ), the frequency f that can be simulated does not reach 3 kHz.

  Thus, it can be seen that the frequency region that can be approximated by one RL parallel circuit is limited. Therefore, a higher frequency region is simulated by adding a second RL parallel circuit having a higher inflection point fm and connecting them in series.

  FIG. 9 is a simulation circuit diagram in which two RL parallel circuits for simulating anti-frequency characteristics are connected in series. In this case, in the frequency region up to 10 kHz, the maximum error is generally about 2%, which is sufficiently practical. Furthermore, when the accuracy is improved or the simulated frequency region is expanded, it can be dealt with by increasing the number of series stages of the RL parallel circuit.

  Next, the fact that the circuit equation when the frequency characteristic is simulated by adding the RL parallel circuit is linear will be described by taking an example in which two RL parallel circuits are connected in series. The effect on the state differential equation due to the addition of the RL parallel circuit appears in the coefficient matrix of inductance and resistance.

Now, in FIG. 9, the nodes at both ends of the branch n is j, and k, the current I _n is the flow to k from j. The current flowing through the resistor R _p1 of the first RL parallel circuit is I _{p1, n} , and the current flowing through the resistor R _p2 of the second RL parallel circuit is I _{p2, n} . In this case, the voltage balance equation is expressed by equation (12).

If this is expressed in all branch bodies, it is expressed by equation (13).

As a result, the entire circuit equation becomes a linear state differential equation capable of calculating eigenvalues as in the following equation (14), and even if the number of RL parallel circuits is increased to two or more, generality is not lost.

Similarly to the case of the above-described equation (3), the eigenvalue λ of the coefficient matrix of the state differential equation shown by the equation (14) is obtained, and the time constant T ₀ and the natural frequency f ₀ are obtained for each eigenvalue λ. An equivalent circuit by an RLC circuit having T ₀ and natural frequency f ₀ is obtained. Then, a current i _c of the resulting equivalent circuit of the power factor improving capacitor C, determine the amplification factor Q (omega) for current source J _lambda of the current i _c, the characteristics of the amplification factor Q (omega) Resonance frequency characteristics are estimated (S6).

  In this way, the frequency characteristic due to the skin effect of the line impedance RL is additionally simulated by an analysis model composed of an RL parallel circuit of the linear element RL, and the state differential equation of the power system is derived, so the skin effect of the line impedance RL is taken into account. The resonance frequency characteristics of higher harmonics can be estimated. Furthermore, by using an analysis model in which RL parallel circuits of linear elements RL are connected in series in multiple stages, the frequency range that can be simulated can be expanded.

The flowchart which shows the content of the high-order harmonic resonance frequency characteristic estimation method concerning embodiment of this invention. The simulation figure which shows an example of the analysis model of the electric power grid | system in embodiment of this invention. The circuit diagram of the equivalent circuit by the RLC circuit which has the time constant and natural frequency of the analysis model of the electric power system in embodiment of this invention. The frequency characteristic figure of line impedance RL of an electric power system. The circuit diagram of the RL parallel circuit which simulates the versus frequency characteristic of the line impedance RL of an electric power system. A simulation circuit of a line impedance RL of a power system including an RL parallel circuit that simulates frequency characteristics. The frequency characteristic figure of the equivalent resistance of the RL parallel circuit which simulates a frequency characteristic. The characteristic view which shows the frequency characteristic of resistance R using one RL parallel circuit. The simulation circuit diagram which connected in series two RL parallel circuits which simulate a frequency characteristic.

Explanation of symbols

11 ... branch, 12 ... node

Claims (3)

The line impedance of the power system and the power factor improving capacitor of the power system are simulated by an analysis model composed of a linear circuit element RLC to derive a state differential equation of the power system,
Deriving an equivalent circuit by an RLC circuit having a time constant and a natural frequency determined by the eigenvalues of the coefficient matrix of the state differential equation,
A high-order harmonic resonance characterized by estimating a resonance frequency characteristic of a high-order harmonic in a power system based on a current amplification factor of a capacitor current for power factor improvement of the equivalent circuit with respect to a current of a high-order harmonic current source Frequency characteristic estimation method.   2. The high-order harmonic resonance frequency characteristic estimation according to claim 1, wherein the state differential equation is derived by additionally simulating the frequency characteristic of the line impedance due to the skin effect with an analytical model comprising an RL parallel circuit of a linear element RL. Method.   The high-order harmonic resonance frequency characteristic estimation method according to claim 2, wherein the analysis model includes a multistage connection of the RL parallel circuits in order to expand a simulatable frequency range.

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