Oscillation power calculation method of line containing external power grid based on amplitude-frequency modulation decomposition

Abstract

The invention discloses an external power grid-containing line oscillation power calculation method based on amplitude-frequency modulation decomposition. The method comprises the following steps: constructing a simplified wind power parallel impedance line grid-connected system model; establishing a standard form of an amplitude-frequency modulation signal; preliminarily calculating oscillation power response based on a simplified wind power parallel impedance line grid-connected system model; decomposing the oscillation power response into a power response under amplitude modulation and a power response under frequency modulation; and projecting the power response under amplitude and frequency modulation excitation to an XY coordinate system by using a phasor method to obtain a final oscillation power amplitude expression. According to the method, the power oscillation response on the external power grid voltage source circuit of the wind power grid-connected system can be accurately obtained, meanwhile, the calculation method is simple and easy to use, and power flow analysis of subsynchronous oscillation can be researched easily.

Description

Technical Field

[0001] This invention relates to a method for calculating the oscillation power of power grid lines with external grids based on amplitude-frequency modulation decomposition, and particularly to a method for calculating the amplitude of the active power oscillation response of a power grid line during a subsynchronous oscillation accident in a new energy system, belonging to the field of power system analysis. Background Technology

[0002] The increase in a large number of new and flexible power electronic control circuits has led to more complex response mechanisms, introducing new stability problems such as wideband oscillations into power systems.

[0003] While existing research has made significant progress in stability analysis, studies focusing on analytical calculations of oscillation power remain relatively scarce.

[0004] In summary, the existence of a simple and feasible mathematical tool to observe the dynamic behavior of power during oscillation would provide assistance to maintenance personnel when oscillations occur on-site. Summary of the Invention

[0005] To address the aforementioned technological gap, this invention provides a method for calculating the oscillation power of power grid lines containing external components based on amplitude-frequency modulation decomposition.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for calculating the oscillation power of power grid lines with external components based on amplitude-frequency modulation decomposition includes,

[0008] Construct a simplified model of a wind power grid connection system via parallel impedance lines;

[0009] Constructing the standard form of amplitude-frequency modulated signals;

[0010] Based on a simplified model of a wind power grid-connected system via parallel impedance lines, the oscillation power response is preliminarily calculated.

[0011] The oscillatory power response is decomposed into the power response under amplitude modulation and the power response under frequency modulation.

[0012] Using the phasor method, the power response under amplitude and frequency modulation excitation is projected onto the XY coordinate system to obtain the final expression for the oscillation power amplitude.

[0013] The simplified model of the wind power grid connection system via parallel impedance lines includes three new energy power stations and six lines L1 to L6, which are transmitted to the external system via transformers.

[0014] Under amplitude-frequency modulation co-excitation, it is approximated by considering three frequency components ω. p =ω0-ω ss ,ω0,ω n =ω0+ω ssThis refers to the current response at subsynchronous frequency, power frequency, and supersynchronous frequency; the subscripts in the subsequent formulas also have the same meaning.

[0015] Voltage amplitude, frequency, and phase are measured using a phase-locked loop. Based on the measurement results, the standard form of the amplitude-frequency modulation signal is obtained as follows:

[0016]

[0017] in:

[0018]

[0019] Where a1 represents the frequency modulation signal, ω0 is the system power frequency, and ω1 is the frequency of the amplitude / frequency modulation signal. and These represent the initial phases of the amplitude / frequency modulation signals, respectively. U0 represents the initial voltage of the node, and A1 and U1 represent the frequency modulation index and amplitude modulation index, respectively.

[0020] Based on a simplified model of a wind power grid-connected system via parallel impedance lines, the active power oscillation response of the lines including the external power grid is preliminarily calculated:

[0021] Consider the external power grid as having an electromotive force of E. 50 For ease of derivation and calculation, the equivalent voltage source of the series impedance line is equivalent to a parallel impedance line, and the equivalent condition is:

[0022]

[0023] Where R pl X pl R represents the resistance and reactance of the parallel equivalent circuit. s X s Z s The values ​​of resistance, reactance, and impedance of the series equivalent circuit.

[0024] Taking into account the internal potential of the power source, the analytical derivation of the power expression in the parallel impedance model yields:

[0025]

[0026] In the formula, U α0 I represents the amplitude of the fundamental voltage. α0 U is the amplitude of the fundamental current. αp U αn These are the amplitudes of the secondary and supersynchronous voltage components, respectively, X p X n The reactances R at the secondary and supersynchronous frequencies are respectively. p R n The resistors are the sub- and supersynchronous frequencies, respectively, where α0 is the phase of the fundamental voltage, and α... I0For the phase of the fundamental current, α p α n These are the phases of the secondary and supersynchronous voltage components, respectively.

[0027] The active oscillation power response is decomposed into the power response under amplitude modulation and the power response under frequency modulation.

[0028] Under amplitude modulation:

[0029] α nE -α0=α0-α pE ,

[0030] Therefore, the oscillation power P can be derived. ssE The expression is:

[0031]

[0032] In the formula, U αpE α is the amplitude of the subsynchronous component in the amplitude-modulated signal after amplitude-frequency decomposition of the original voltage signal. pE α nE These are the phases of the secondary and supersynchronous voltage components in the amplitude modulation signal, respectively.

[0033] Under frequency modulation:

[0034] α nf -α0=α0-α pf ,

[0035] Therefore, the oscillation power P can be derived. ssf The expression is:

[0036]

[0037] In the formula, U αpf α is the amplitude of the subsynchronous component in the frequency modulation signal after amplitude-frequency decomposition of the original voltage signal. pf α nf These are the phases of the secondary and supersynchronous voltage components in the frequency modulation signal, respectively.

[0038] Using the phasor method, the power response under amplitude and frequency modulation excitation is projected onto the XY coordinate system:

[0039] For ease of representation, the following two variables are defined:

[0040]

[0041] Then, setting α0 as the reference angle (0°), we establish an XY coordinate system. The projections of the power phasor onto the X and Y axes are:

[0042]

[0043] The amplitude of the oscillating active power can be expressed as:

[0044]

[0045] It should be noted that, following the above calculation approach, the analytical expression for the amplitude of the oscillating reactive power can also be derived:

[0046]

[0047] In summary, the amplitude of the oscillation's active / reactive power can be expressed as:

[0048]

[0049] The beneficial effects achieved by this invention are as follows: the method calculates the oscillation power response from the amplitude-frequency perspective, which is closer to the physical nature of the oscillation phenomenon; the calculation method is simple, and the calculation results can be used to determine the dynamic behavior of the oscillation power of the external power grid line, and can promptly analyze the impact of the new power system line parameters on the oscillation power, thereby taking rapid measures to repair it and improve the reliability of system operation. Attached Figure Description

[0050] Figure 1 This is a flowchart of the present invention;

[0051] Figure 2 A simplified model of a wind power grid connection system via parallel impedance lines;

[0052] Figure 3 The fitted oscillating voltage waveform;

[0053] Figure 4 This is a curve comparing the actual and calculated active power values ​​of line L1.

[0054] Figure 5 The curve showing the comparison between the actual and calculated reactive power values ​​of line L2;

[0055] Figure 6 This is a curve comparing the actual and calculated values ​​of the ratio of active power to reactive power for line L4. Detailed Implementation

[0056] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0057] like Figure 1 As shown, the method for calculating the oscillation power of a power grid line containing external components based on amplitude-frequency modulation decomposition includes the following steps:

[0058] Step 1: Construct a model of a wind power grid connection system via parallel impedance lines.

[0059] like Figure 2As shown, the simplified wind power grid connection system model includes 3 new energy power stations and 6 lines L1 to L6, with an installed wind power capacity of 4.418 million kilowatts, which are transmitted to the external system via transformers.

[0060] Step 2: Construct the standard form of the amplitude-frequency modulation signal.

[0061] Voltage amplitude, frequency, and phase are measured using a phase-locked loop. Based on the measurement results, the standard form of the amplitude-frequency modulation signal is obtained as follows:

[0062]

[0063] in:

[0064]

[0065] Where a1 represents the frequency modulation signal, ω0 is the system power frequency, and ω1 is the frequency of the amplitude / frequency modulation signal. and Let A1 and U1 represent the initial phase of the amplitude / frequency modulation signal, respectively. Let U0 represent the initial voltage of the node, and A1 and U1 represent the frequency modulation index and amplitude modulation index, respectively. The fitted oscillation voltage waveform is shown below. Figure 3 As shown.

[0066] Step 3: Based on a simplified model of a wind power grid connection system via parallel impedance lines, the active power oscillation response of the lines including the external power grid is initially calculated.

[0067] Consider the external power grid as having an electromotive force of E. 50 For ease of derivation and calculation, the equivalent voltage source of the series impedance line is equivalent to a parallel impedance line, and the equivalent condition is:

[0068]

[0069] Where R p X p R represents the resistance and reactance of the parallel equivalent circuit. s X s Z s The values ​​of resistance, reactance, and impedance of the series equivalent circuit.

[0070] Taking into account the internal potential of the power source, the analytical derivation of the power expression in the parallel impedance model yields:

[0071]

[0072] In the formula, U α0 I represents the amplitude of the fundamental voltage. α0 U is the amplitude of the fundamental current. αp U αn These are the amplitudes of the secondary and supersynchronous voltage components, respectively, X p Xn The reactances R at the secondary and supersynchronous frequencies are respectively. p R n The resistors are the sub- and supersynchronous frequencies, respectively, where α0 is the phase of the fundamental voltage, and α... I0 For the phase of the fundamental current, α p α n These are the phases of the secondary and supersynchronous voltage components, respectively.

[0073] Step 4: Decompose the active oscillation power response into the power response under amplitude modulation and the power response under frequency modulation.

[0074] Under amplitude modulation:

[0075] α nE -α0=α0-α pE ,

[0076] Therefore, the oscillation power P can be derived. ssE The expression is:

[0077]

[0078] In the formula, U αpE α is the amplitude of the subsynchronous component in the amplitude-modulated signal after amplitude-frequency decomposition of the original voltage signal. pE α nE These are the phases of the secondary and supersynchronous voltage components in the amplitude modulation signal, respectively.

[0079] Under frequency modulation:

[0080] α nf -α0=α0-α pf ,

[0081] Therefore, the oscillation power P can be derived. ssf The expression is:

[0082]

[0083] In the formula, U αpf α is the amplitude of the subsynchronous component in the frequency modulation signal after amplitude-frequency decomposition of the original voltage signal. pf α nf These are the phases of the secondary and supersynchronous voltage components in the frequency modulation signal, respectively.

[0084] Step 5: Using the phasor method, project the power response under amplitude and frequency modulation excitation onto the XY coordinate system.

[0085] Let α0 be the reference angle (0°), establish an XY coordinate system, and the projections of the power phasor onto the X and Y axes are:

[0086]

[0087] The amplitude of the oscillating active power can be expressed as:

[0088]

[0089] It should be noted that, following the above calculation approach, the analytical expression for the amplitude of the oscillating reactive power can also be derived:

[0090]

[0091] In summary, the amplitude of the oscillation's active / reactive power can be expressed as:

[0092]

[0093] The correctness of the above content was verified by simulation. Comparison curves of the actual and calculated active power values ​​for line L1 and line L2 reactive power are presented, as shown below. Figure 4 , Figure 5 As shown.

[0094] Similarly, a curve comparing the actual and calculated values ​​of the active power to reactive power ratio for line L4 is presented, such as... Figure 6 As shown, the actual values ​​and calculated values ​​fit well, verifying the correctness of the derived formula of this invention.

[0095] To address the power oscillation problem in new energy systems including external power grid lines, a calculation method for power amplitude oscillation response is presented from the perspective of amplitude-frequency modulation through theoretical analysis and formula derivation in a simplified system. The calculation method is simple and easy to use, and is suitable for rapid response through calculation when subsynchronous oscillation events occur in the field.

[0096] As described above, the present invention has been explained in detail. Obviously, any modifications that do not substantially depart from the inventive point and effect of the present invention and are obvious to those skilled in the art are also included within the protection scope of the present invention.

Claims

1. A method for calculating power of a line oscillation containing an external power grid based on amplitude-frequency modulation decomposition, characterized in that: Comprising, A simplified wind power through parallel impedance line grid-connected system model is constructed, which includes 3 new energy stations and 6 lines L1-L6, and is sent to the external system through the transformer; Under the amplitude modulation common excitation, the approximate is to consider three frequency components w p = w0- w ss , w0, w n = w0+ w ss That is the current response of the sub-synchronous frequency, power frequency, super-synchronous frequency, the voltage amplitude, frequency and phase measurement are carried out through the phase-locked loop, and the standard form of the amplitude modulation signal is obtained according to the measurement results: Wherein, In particular, a1 represents the frequency modulation signal, ω0 is the system power frequency, ω is the frequency of the amplitude / frequency modulation signal, With respectively represent the initial phase of the amplitude / frequency modulation signal, U0 represents the initial voltage of the node, A1, U1 represent the frequency modulation index and the amplitude modulation index, respectively.

2. The method according to claim 1, characterized in that, Based on the simplified model of the wind power grid-connection system through the parallel impedance line, the active oscillation power of the line with external grid is calculated preliminarily, and the external grid is regarded as an equivalent voltage source with E 50 The series impedance line is equivalent to the parallel impedance line for the convenience of derivation and calculation, and the equivalent condition is that: where R p , X p are resistance and reactance values of the parallel equivalent circuit, R s , X s , Z s are resistance, reactance and impedance values of the series equivalent circuit; taking into account the internal potential source, the power analytical expression derivation in the parallel impedance model gives: where U α0 is the fundamental voltage amplitude, I α0 is the fundamental current amplitude, U αp , U αn are the sub- and super-synchronous voltage component amplitudes, X p , X n are the sub- and super-synchronous frequency reactances, R p , R n are the sub- and super-synchronous frequency resistances, a0is the fundamental voltage phase, a I0 is the fundamental current phase, a p , a n are the sub- and super-synchronous voltage component phases. The active oscillation power response is decomposed into the power response under amplitude modulation and the power response under frequency modulation; Under amplitude modulation, α nE -α0＝α0-α pE Oscillating power P ssE The expression is: In the formula, U αpE is the amplitude of the subsynchronous component in the amplitude modulation signal after the amplitude-frequency decomposition of the original voltage signal, and α pE , α nE are the phases of the subsynchronous and supersynchronous voltage components in the amplitude modulation signal, respectively. Under frequency modulation, α nf -α0＝α0-α pf Oscillating power P ssf The expression is: In the formula, U αpf is the amplitude of the subsynchronous component in the frequency modulation signal after amplitude-frequency decomposition of the original voltage signal, and α pf , α nf are the phases of the subsynchronous and supersynchronous voltage components in the frequency modulation signal, respectively. Thus, the oscillation power is decomposed into the power response under amplitude and frequency modulation excitation.

3. The method according to claim 2, characterized in that, Using the phasor method, the power response under amplitude and frequency modulation excitation is projected to the XY coordinate system, and the following two variables are defined for convenience of expression: Let α0 be the reference angle (0°), establish the XY coordinate system, and the projection of the power phasor on the X axis and Y axis is: According to the above calculation idea, the analytical expression of the oscillation reactive power amplitude can also be obtained: In summary, the oscillation active / reactive power amplitude can be expressed as:

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