CN114912277B - Method and system for modeling complex vector impedance of permanent magnet direct-driven fan based on HSS - Google Patents
Method and system for modeling complex vector impedance of permanent magnet direct-driven fan based on HSS Download PDFInfo
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Abstract
The invention relates to a complex vector impedance modeling method and a complex vector impedance modeling system of a permanent magnet direct-driven fan based on an HSS, and relates to the technical field of permanent magnet direct-driven fan modeling, wherein the method comprises the following steps: acquiring a linear time domain periodic system and representing the linear time domain periodic system as a Fourier series expansion; acquiring a steady-state periodic running track of each frequency harmonic of a linear time domain periodic system; linearizing the linear time domain periodic system to obtain a complex frequency domain linear time-invariant system; obtaining a state space matrix containing any frequency harmonic component based on a complex frequency domain linear time invariant system; and establishing an equivalent impedance model of the alternating current side of the permanent magnet direct-driven fan containing each subharmonic according to the state space matrix. The method can describe the harmonic characteristics of each frequency of the periodic time-varying system, and is suitable for modeling each subharmonic frequency domain of the converter with a large number of switching devices.
Description
Technical Field
The invention relates to the technical field of permanent magnet direct-drive fan modeling, in particular to a complex vector impedance modeling method and system of a permanent magnet direct-drive fan based on an HSS.
Background
The permanent magnet direct-drive fan (PERMANENT MAGNETIC Synchronous Generator, PMSG) has the characteristics of multiple magnetic poles, no need of gear box transmission and low maintenance cost, and is widely applied to land and offshore wind farms. The wind turbine generator is a typical multi-harmonic source system, PWM pulse modulation and switching signals of the power electronic converter can generate some harmonic components when the system operates, and the interaction of different frequency harmonics can influence the dynamic characteristics of an alternating current side and a direct current side of the PMSG, so that the system is possibly unstable in oscillation. In addition, the multi-frequency harmonic coupling characteristic may also cause strong interaction between different wind turbines, thereby causing instability of the system.
The existing PMSG model technical method and the existing problems are that:
The existing PMSG model mainly comprises the following components: a traditional time domain state space model and a single input single output (or single input dual output) impedance model. One of the two models is based on a time domain for modeling, the other model is an input/output system which considers the wind turbine generator as an impedance form, the modeling of the PMSG is not considered from the perspective of frequency harmonic waves, the frequency coupling characteristics generated by PMSG pulse modulation and switching signals cannot be accurately represented, and the influence of the frequency coupling characteristics on the dynamic stability of the grid-connected system of the wind turbine generator cannot be analyzed.
Therefore, the invention provides a PMSG complex vector impedance modeling method based on a Harmonic State-Space (HSS), which fully considers the frequency coupling of PMSG, can describe the Harmonic characteristics of each frequency of a periodic time-varying system and is suitable for modeling each subharmonic frequency domain of a converter containing a large number of switching devices.
Disclosure of Invention
The invention aims to provide a complex vector impedance modeling method and system of a permanent magnet direct-driven fan based on an HSS, which can describe the harmonic characteristics of each frequency of a periodic time-varying system and are suitable for frequency domain modeling of each subharmonic of a converter containing a large number of switching devices.
In order to achieve the above object, the present invention provides the following solutions:
a complex vector impedance modeling method of a permanent magnet direct drive fan based on HSS comprises the following steps:
acquiring a linear time domain period system, wherein the linear time domain period system comprises a permanent magnet direct-drive fan system;
representing the linear time domain periodic system as a fourier series expansion;
Acquiring a steady-state periodic running track of each frequency harmonic of the linear time domain periodic system;
Linearizing the linear time domain periodic system based on the Fourier series expansion and the steady-state periodic running track of each frequency harmonic to obtain a complex frequency domain linear time-invariant system;
obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time-invariant system;
and establishing an equivalent impedance model of the alternating current side of the permanent magnet direct-driven fan containing each subharmonic according to the state space matrix.
Optionally, the state space model of the linear time domain periodic system is:
Wherein the equation is a system state space expression expressed by a complex frequency domain, and the original equation is Wherein the method comprises the steps ofI.e. a state matrix a (t) which is a state space expression,A state vector x (t) which is a state space expression,An input matrix B (t) being a state space expression,I.e. the input vector, also called control vector u (t), of the state space expression.
Optionally, the linearizing the linear time domain periodic system to obtain a complex frequency domain linear time invariant system specifically includes:
linearization uses the following formula:
Where (jn omega 1+s)xn) is the derivative of the nth harmonic component of the system state variable x (t), Is the multiplication of the state vector by the state coefficient matrix of each subharmonic,The input vector is multiplied by the input coefficient matrix of each subharmonic.
Optionally, the establishing a permanent magnet direct drive fan ac side equivalent impedance model including each subharmonic according to the state space matrix specifically includes:
Constructing a harmonic transfer function according to the state space matrix;
Acquiring alternating-current side voltage and alternating-current side current of a permanent magnet direct-drive fan;
constructing a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the alternating-current side voltage and the alternating-current side current;
And constructing an equivalent impedance model of the alternating-current side of the permanent-magnet direct-drive fan according to the state space model of the permanent-magnet direct-drive fan.
Optionally, the state space model of the permanent magnet direct-drive fan is:
the Deltav αβ＝Δvα+Δjvβ is complex vector of PCC point voltage small signal disturbance under alpha beta static coordinate system, and the combined matrix is an input vector matrix of the state space model; Δi αβ＝Δiα+Δjiβ is complex vector of small-signal disturbance of PCC point current under alpha beta static coordinate system, and the complex vector is combined into a state vector with a matrix as a state space model; "X" means the conjugate of complex vectors, the whole being shaped like Derivative form of state variable = state matrix + state vector + input matrix + input vector.
Optionally, the expression of the equivalent impedance model of the alternating-current side of the permanent magnet direct-drive fan is as follows:
<Δvαβ(s)>＝<Zwf(s)><Δiαβ(s)>
Wherein Z wf(s) is an equivalent impedance matrix of the alternating current side of the permanent magnet direct drive fan, and Z wf(s) is a matrix of 2 x 2; The method is characterized in that the method comprises the steps of respectively inputting state variables and periods of a state space model of a permanent magnet direct-driven fan, wherein Deltav αβ＝Δvα +Deltajvbeta is a complex vector of small-signal disturbance of PCC point voltage under an alpha beta static coordinate system, and Deltai αβ＝Δiα+Δjiβ is a complex vector of small-signal disturbance of PCC point current under the alpha beta static coordinate system; ", represents the conjugate of complex vectors.
Optionally, the state space matrix has a plurality of states.
Optionally, the state space matrix is in the form of:
Wherein, matrix a is Toeplitz matrix, a h is fourier coefficient of h harmonic component of state space model state matrix a (t) of permanent magnet direct drive fan, for example: a 0 is the fourier coefficient of the 0 th harmonic component of the state matrix a (t).
A HSS-based complex vector impedance modeling system for a permanent magnet direct drive fan, comprising:
The linear time domain periodic system acquisition module is used for acquiring a linear time domain periodic system, wherein the linear time domain periodic system comprises a permanent magnet direct-drive fan system;
The Fourier series expansion module is used for representing the linear time domain periodic system as Fourier series expansion;
The steady-state periodic operation track acquisition module is used for acquiring steady-state periodic operation tracks of all frequency harmonics of the linear time domain periodic system;
The linearization module is used for linearizing the linear time domain periodic system based on the Fourier series expansion and the steady-state periodic running track of each frequency harmonic to obtain a complex frequency domain linear time-invariant system;
the state space matrix determining module is used for obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time invariant system;
And the permanent magnet direct-drive fan alternating current side equivalent impedance model building module is used for building the permanent magnet direct-drive fan alternating current side equivalent impedance model containing each subharmonic according to the state space matrix.
Optionally, the permanent magnet direct drive fan alternating current side equivalent impedance model building module specifically includes:
a harmonic transfer function construction unit for constructing a harmonic transfer function according to the state space matrix;
the alternating-current side voltage and alternating-current side current acquisition unit is used for acquiring alternating-current side voltage and alternating-current side current of the permanent magnet direct-drive fan;
the permanent magnet direct-drive fan state space model building unit is used for building a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the alternating-current side voltage and the alternating-current side current;
And the permanent magnet direct-drive fan alternating-current side equivalent impedance model construction unit is used for constructing a permanent magnet direct-drive fan alternating-current side equivalent impedance model according to the permanent magnet direct-drive fan state space model.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
The invention is based on the harmonic state space, each state variable of the system is expressed as a Fourier series, the system is linearized based on the steady-state periodic running track of each frequency harmonic, the linear time domain periodic system is converted into a complex frequency domain linear time-invariant system, and a state space matrix containing any frequency harmonic component is deduced based on the state space, so that a PMSG alternating current side equivalent impedance model with multi-frequency harmonic coupling characteristics is obtained.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a complex vector impedance modeling method of a permanent magnet direct drive fan based on an HSS;
FIG. 2 is a flowchart of constructing harmonic transfer functions of LTP system by HSS method of the present invention;
FIG. 3 is a classical structure diagram of the PMSG of the present invention;
FIG. 4 is a schematic diagram of a transfer function of a MIMO system according to the present invention;
Fig. 5 (a) is a diagram comparing the equivalent impedance analysis model (h=3) on the ac side of the PMSG with the PSCAD simulation results, and comparing the magnitudes and phase angles of Z wf11(s) and Z wf22(s), respectively;
fig. 5 (b) is a diagram comparing the equivalent impedance analysis model (h=3) on the ac side of the PMSG with the PSCAD simulation results, and comparing the magnitudes and phase angles of Z wf12(s) and Z wf21(s), respectively;
FIG. 6 (a) is a schematic diagram showing the effect of HSS model harmonic frequency on PMSG AC side equivalent impedance analysis model accuracy, comparing the amplitude and phase angle of Z wf11(s) and Z wf22(s), respectively;
FIG. 6 (b) is a schematic diagram showing the effect of the harmonic frequencies of the HSS model on the accuracy of the PMSG AC equivalent impedance analysis model, comparing the amplitude and phase angle of Z wf12(s) and Z wf21(s), respectively;
fig. 7 is a schematic diagram showing comparison between the equivalent impedance analysis model (h=3) on the ac side of the PMSG and the RTDS hardware in loop experiment results.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a complex vector impedance modeling method and system of a permanent magnet direct-driven fan based on an HSS, which can describe the harmonic characteristics of each frequency of a periodic time-varying system and are suitable for frequency domain modeling of each subharmonic of a converter containing a large number of switching devices.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
First, the technical idea of the present invention is summarized as follows:
The invention provides a complex vector impedance modeling method containing each subharmonic PMSG based on HSS, which can be used for multi-frequency coupling mechanism analysis of a system.
The method mainly comprises the following steps: considering that each state variable and each state space matrix in the PMSG system are periodic time-varying signals, the method expresses each state variable into a form of Fourier series expansion, then linearizes the system based on a steady-state periodic running track of each frequency harmonic, so that a linear time domain periodic system (lineartime-varying periodic system, LTP) is converted into a complex frequency domain linear time invariant system (LINEARTIME INVARIANT, LTI), on the basis, the state space matrix containing any frequency harmonic component is deduced, meanwhile, a PMSG alternating current side equivalent impedance model containing each frequency harmonic is established, and finally the influence of the multi-frequency coupling characteristic on PMSG alternating current side equivalent impedance and a system stability criterion is analyzed by using an example.
Specifically, fig. 1 is a flowchart of a method for modeling complex vector impedance of a permanent magnet direct-driven fan based on an HSS according to the present invention, as shown in fig. 1, and the method for modeling complex vector impedance of the permanent magnet direct-driven fan based on the HSS includes:
Step 101: and acquiring a linear time domain period system, wherein the linear time domain period system comprises a permanent magnet direct drive fan system.
Step 102: the linear time domain periodic system is represented as a fourier series expansion.
Step 103: and acquiring a steady-state periodic running track of each frequency harmonic of the linear time domain periodic system.
Step 104: and linearizing the linear time domain periodic system based on the Fourier series expansion and the steady-state periodic running track of each frequency harmonic to obtain a complex frequency domain linear time-invariant system.
Step 105: and obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time-invariant system.
Step 106: and establishing an equivalent impedance model of the alternating current side of the permanent magnet direct-driven fan containing each subharmonic according to the state space matrix.
Based on the steps 101-106, the specific implementation process of the invention is as follows:
Step 1: deriving periodic signals in exponential form and their properties.
The function of step 1 is to derive a theorem applicable to any LTP system, i.e. "for any LTP system, both state variables and state space matrices can be represented as exponential forms of the complex domain" and derive the following step 2 derivation of the HSS model based on the result of step 1. The role of step 1 is to demonstrate that for any LTP system, the state variables and state space matrices can be represented in exponential form in the complex domain.
Specifically, let a state space expression of the LTP system be:
wherein, In the form of the derivative of the state vector, a (t) is the state matrix, x (t) is the state variable, B (t) is the input matrix, u (t) is the input vector, also called the control vector, y is the output vector, C (t) is the output matrix, and D (t) is the feed forward matrix.
To convert an LTP system to an LTI system in the frequency domain, a periodic signal is first converted to an exponential form in the complex domain. The periodic signal (Exponentially Modulated Periodic Signal, EMPS) in the form of a complex domain index is typically expressed as the product of the periodic signal and the complex domain index signal, let u (t) be the periodic input signal of the system, expressed in the form of a complex domain index as follows:
Wherein u n is a coefficient of a Fourier series of the periodic signal;
ω—arbitrary reference frequency of the periodic system.
The above equation is a periodic signal in the form of a complex domain index. The above equation shows that all signals in the complex domain can be represented in EMPS form, i.e. EMPS can equivalently represent all signals with physical meaning, which is a necessary condition for the LTP system to convert into an LTI system in the frequency domain. In addition, according to the Floquet theory, the transient response of the LTP system can be equivalently characterized by a state transition matrix:
Where Φ (t) =e A(t) denotes the state transition matrix of the system, the term P -1(t0)x(t0 to the right of the equation) is a constant, term e Q(t-t0) denotes the exponential matrix, P (t) is a periodic transformation matrix, and Q denotes the diagonal matrix of eigenvalues of the LTP system state space matrix. Depending on the nature of the state transition matrix, equation (3) is taken into equation (1) and expressed in EMPS form, namely:
The variable v (t) exists such that the state quantity x (t) satisfies the following similarity transformation:
x(t)＝P(t)v(t)
assuming t 0 =0, the variable v (t) can be represented by a state transition matrix:
Where Φ (t, τ) =Φ (t, 0) ·Φ (0, τ), and Φ (t, 0) =e Q(t),Ф(0,τ)＝e-Q(τ). Thus, the formula (6) can be rewritten as:
Bringing formula (2) into the EMPS form of variable v (t) available in formula (7):
assuming s l＝jω1 +s, formula (8) can be rewritten as:
Is provided with
And bringing formula (9) into formula (4) to obtain:
X s (t) in equation (10) is the state variable x (t) in EMPS.
The above analysis procedure shows that both the state variables and the state space matrix of the LTP system can be represented in exponential form in the complex domain, which is the basis for building the HSS model.
Step 2: the deducing HSS method rewrites the LTP system, wherein the corresponding 'state space matrix containing any frequency harmonic component' obtained by deducting in the step 2 is the formula (16), and the deduced state space equation is the formula (15).
Step 1 has demonstrated that for any LTP system, its state variables and state space matrix can be represented in exponential form in the complex domain, thus representing the state variables and state space matrix of equation (1) in exponential form in the complex domain yields equation (11), i.e., since the state variables, input outputs, and state transition matrices in the LTP system state space model are all periodic functions, which can be represented by EMPS, the system state space model can be rewritten as:
Wherein the equation is a system state space expression expressed by a complex frequency domain, and the original equation is Wherein the method comprises the steps ofI.e. a state matrix a (t) which is a state space expression,A state vector x (t) which is a state space expression,An input matrix B (t) being a state space expression,I.e. the input vector, also called control vector u (t), of the state space expression.
The solution of the state variable in the above formula is in the form of fourier series, x -∞,…,x-1,x0,x1,…,x∞, according to the harmonic balance theory, it is known that the steady state values of the subharmonics of the LTP system are linearly independent, and then the derivative of the subharmonics in the periodic steady state running track is also linearly independent, and then the formula (11) can be simplified as follows:
Two sides of the pair (12) are divided simultaneously The method can obtain:
Where (jn omega 1+s)xn) is the derivative of the nth harmonic component of the system state variable x (t), Is the multiplication of the state vector by the state coefficient matrix of each subharmonic,The input vector is multiplied by the input coefficient matrix of each subharmonic.
In the above equation, the differential equivalent of the nth harmonic component of the LTP system state variable x (t) is expressed as the sum of the state coefficient matrix of each subharmonic and the input coefficient matrix. When linearizing in the vicinity of the system steady-state periodic motion trajectory, all coefficients in equation (13) are time-invariant, which converts the LTP system to an LTI system in the frequency domain. Similarly, the output of the state space model can also be represented by a fourier series:
Considering the respective subharmonics and writing in the form of a matrix, the formulas (13) and (14) can be expressed as:
The matrix a is shown as a formula (16), wherein a h is a fourier coefficient of an h harmonic component of a (t), and N is a diagonal matrix formed by each harmonic component, as shown as a formula (17), and the model is a harmonic state space matrix, and can be used for constructing harmonic transfer functions (Harmonic transfer function, HTF), and the process is shown in fig. 2.
Wherein, matrix a is Toeplitz matrix, a h is fourier coefficient of h harmonic component of state space model state matrix a (t) of permanent magnet direct drive fan, for example: a 0 is the fourier coefficient of the 0 th harmonic component of the state matrix a (t).
Step 3: a PMSG harmonic state space model is built, wherein step 1 and step 2 represent an arbitrary LTP system as in formula (1) to the form of formulas (15), (16) and (17) and deduce a state space matrix containing arbitrary frequency harmonic components. And then, step 3 deduces and establishes a 'PMSG alternating current side equivalent impedance model containing each subharmonic' by using the methods of step 1 and step 2, which is equivalent to the result that the deducing of the steps 1 and 2 is generic, and step 3 applies the model to the PMSG model, wherein the PMSG is also an LTP system, so that the alternating current side equivalent impedance model of the PMSG system is deduced.
Specifically, in order to build a harmonic state space model of the PMSG, it is first necessary to derive a complex vector-based state space model of the PMSG, as shown in equation (18),
Wherein:
In the formula (19), deltav αβ＝Δvα+Δjvβ is the complex vector of the small-signal disturbance of the voltage of the PCC point under the alpha beta static coordinate system, deltai αβ＝Δiα+Δjiβ is the complex vector of the small-signal disturbance of the current of the PCC point under the alpha beta static coordinate system; ", represents the conjugate of complex vectors. The complex vector expression of the voltage and current of the ac side of the PMSG can be obtained according to the circuit structure of the PMSG in fig. 3:
Wherein, deltad αβ、Δdα * β is a complex vector of GSC switch duty cycle disturbance response under a static coordinate system;
deltav αβ、Δvα * β -complex vector of the grid-side voltage disturbance component under the static coordinate system;
Δi αβ、Δiα * β —complex vector of current disturbance component at the lower net side of the stationary coordinate system;
In the formula (20), D αβ0(t)＝Dα0(t)+jDβ0 (t) represents a complex vector of GSC switch duty ratio in a stationary coordinate system; and V dc0·Dαβ0(t)＝Vc0(t)＝ωLfiαβ0(t)+vαβ0(t),Vc (t) represents the PMSG network side filter capacitor ground voltage in the stationary coordinate system. When considering converter multi-frequency harmonics, the expression of V c (t) and its conjugate V C * (t) is:
Wherein V c0,Vc1,…,Vch represents the coefficients of the V c0 (t) fourier series; the available PMSG state space model is:
Wherein:
It can be seen that:
In the above formula, i αβ0 (t) represents the steady state value of the complex vector of the PMSG output current in the stationary coordinate system, v αβ0 (t) represents the steady state value of the complex vector of the PMSG grid-connected point voltage in the stationary coordinate system, and there are:
a harmonic state space model of the PMSG can be obtained by combining equation (15), equation (22) and equation (25), namely:
the Deltav αβ＝Δvα+Δjvβ is complex vector of PCC point voltage small signal disturbance under alpha beta static coordinate system, and the combined matrix is an input vector matrix of the state space model; Δi αβ＝Δiα+Δjiβ is complex vector of small-signal disturbance of PCC point current under alpha beta static coordinate system, and the complex vector is combined into a state vector with a matrix as a state space model; "X" means the conjugate of complex vectors, the whole being shaped like Derivative form of state variable = state matrix + state vector + input matrix + input vector.
A 0(s) is laplace transform of the state space matrix a (t) when D αβ0(t)＝Vc0,iαβ0(t)＝I0,vαβ0(t)＝V0 is taken, and a ±1(s),A±2(s),…,A±h(s) can be obtained by analogy; similarly, B ±1(s),B±2(s),…,B±h(s) is available. From equation (26), the PMSG ac-side equivalent impedance considering the multi-frequency coupling characteristic can be deduced as:
Wherein Z wf(s) is the PMSG alternating current side equivalent impedance matrix, which is a matrix of 2 x2, The method is a state variable and period input of a PMSG state space model, and refers to formulas (18) and (19), wherein Deltav αβ＝Δvα +Deltajvβ is a complex vector of PCC point voltage small signal disturbance under an alpha beta static coordinate system, and Deltai αβ＝Δiα +Deltajiβ is a complex vector of PCC point current small signal disturbance under the alpha beta static coordinate system; ", represents the conjugate of complex vectors.
For ease of understanding, fig. 4 shows the multiple-input multiple-output transfer function of a PMSG grid-tied system. The observation graph shows that the HSS model is used for equivalently solving a PMSG impedance model considering multi-frequency coupling by constructing a transfer function of a PMSG alternating-current multi-frequency harmonic disturbance response component with respect to small disturbance harmonic voltage input.
The invention verifies the effectiveness and accuracy of the proposed method through simulation and RTDS hardware in-loop experiments.
The complete structure of the PMSG used for simulation is shown in fig. 3, the parameters of the PMSG are shown in table 1, and the d-axis and q-axis parameters of the inner loop current controller are set as follows: k pid＝0.92,kiid＝105;kpiq＝0.71,kiiq = 158. The amplitude-frequency characteristic pairs obtained by the PMSG alternating-current side equivalent impedance and PSCAD/EMTDC simulation frequency sweep which are derived by the analysis method and consider multi-frequency coupling are shown in fig. 5 (a) and 5 (b), the solid line represents the analysis result, and the dotted line represents the simulation result.
Table 1 parameters of permanent magnet direct drive synchronous generator
The harmonic order h=3 of the analytical model shows that the similarity of the two curves is high, and the effectiveness of the method is demonstrated. In addition, Z wf11(s) and Z wf22(s) in fig. 5 represent diagonal elements in the PMSG ac-side equivalent impedance matrix Z wf(s) derived based on the HSS method. By observing fig. 5 (a) and 5 (b), the following can be concluded:
1) Z wf11(s) jumps in phase around 50Hz, which is mainly caused by the phase-locked loop;
2) The high frequency characteristic of the system mainly depends on the parameters of the capacitance and the inductance of the PMSG port filter, and the high frequency characteristics of the positive and negative sequence impedances are the same.
3) Z wf11(s) and Z wf22(s) exhibit negative resistance effects around the fundamental frequency in which the wind turbines are susceptible to interaction with the ac grid, which may lead to system oscillations.
4) Off-diagonal elements Z wf12(s) and Z wf21(s) in Z wf(s) reflect the frequency coupling characteristics of the system. And, when the dq axis controller parameter is asymmetric, the amplitude of Z wf12(s) and Zwf21(s) in the low frequency range is close to Z wf11(s), and the frequency coupling characteristic generated by PMSG grid connection is not negligible.
Fig. 6 (a) and 6 (b) reflect the effect of considering the harmonic order on PMSG impedance modeling accuracy in the HSS model of the PMSG. It can be seen from the figure that the higher the number of harmonics considered in the HSS model, the more accurate the analytical impedance model. However, the higher the harmonic frequency in the HSS model, the larger the calculation amount, and generally, the higher the accuracy of the analytical model is when h=3.
In addition, the validity of the method is verified through the analysis model and the RTDS hardware in-loop experimental result comparison analysis. Fig. 7 compares the equivalent impedance of the PMSG ac side obtained by the analytical model and the frequency sweep experiment, and it can be seen from the figure that the experimental result is substantially identical to the analytical model. It is noted that the difference between the experimental sweep result and the analytical model in the low frequency range (frequency <200 Hz) is larger than in the high frequency range, which is related to the presence of more interference signals in the fundamental frequency range.
In addition, based on the method, the invention also provides a complex vector impedance modeling system of the permanent magnet direct-driven fan based on the HSS, which comprises the following steps:
a linear time domain periodic system acquisition module for acquiring a linear time domain periodic system, the linear time domain periodic system comprises a permanent magnet direct drive fan system.
And the Fourier series expansion module is used for representing the linear time domain periodic system as Fourier series expansion.
The steady-state periodic operation track acquisition module is used for acquiring steady-state periodic operation tracks of all frequency harmonics of the linear time domain periodic system.
And the linearization module is used for linearizing the linear time domain periodic system based on the Fourier series expansion and the steady-state periodic running track of each frequency harmonic to obtain a complex frequency domain linear time-invariant system.
And the state space matrix determining module is used for obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time-invariant system.
And the permanent magnet direct-drive fan alternating current side equivalent impedance model building module is used for building the permanent magnet direct-drive fan alternating current side equivalent impedance model containing each subharmonic according to the state space matrix.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (5)
1. The complex vector impedance modeling method of the permanent magnet direct-driven fan based on the HSS is characterized by comprising the following steps of:
acquiring a linear time domain period system, wherein the linear time domain period system comprises a permanent magnet direct-drive fan system;
representing the linear time domain periodic system as a fourier series expansion;
Acquiring a steady-state periodic running track of each frequency harmonic of the linear time domain periodic system;
linearizing the linear time domain periodic system based on the Fourier series expansion and steady-state periodic running tracks of each frequency harmonic to obtain a complex frequency domain linear time invariant system, which comprises the following steps:
linearization uses the following formula:
Where (jn omega 1+s)xn) is the derivative of the nth harmonic component of the system state variable x (t), Is the multiplication of the state vector by the state coefficient matrix of each subharmonic,Multiplying each subharmonic input coefficient matrix with an input vector;
obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time-invariant system;
Establishing an equivalent impedance model of the alternating current side of the permanent magnet direct-driven fan containing each subharmonic according to the state space matrix, wherein the equivalent impedance model comprises the following specific steps:
Constructing a harmonic transfer function according to the state space matrix;
Acquiring alternating-current side voltage and alternating-current side current of a permanent magnet direct-drive fan;
constructing a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the alternating-current side voltage and the alternating-current side current, wherein the permanent magnet direct-drive fan state space model is as follows:
The Deltav αβ＝Δvα+Δjvβ is complex vector of PCC point voltage small signal disturbance under alpha beta static coordinate system, and the combined matrix is an input vector matrix of the state space model; Δi αβ＝Δiα+Δjiβ is complex vector of small-signal disturbance of PCC point current under alpha beta static coordinate system, and the complex vector is combined into a state vector with a matrix as a state space model; ". Times" represent the conjugate of complex vectors;
Constructing a permanent magnet direct-drive fan alternating-current side equivalent impedance model according to the permanent magnet direct-drive fan state space model, wherein the permanent magnet direct-drive fan alternating-current side equivalent impedance model expression is as follows:
Δvαβ(s)＝Zwf(s)Δiαβ(s)
Wherein Z wf(s) is an equivalent impedance matrix of the alternating current side of the permanent magnet direct drive fan, Z wf(s) is a matrix of 2x 2, The method is characterized in that the method comprises the steps of respectively inputting state variables and periods of a state space model of a permanent magnet direct-driven fan, wherein Deltav αβ＝Δvα+Δjvβ is a complex vector of small-signal disturbance of PCC point voltage under an alpha beta static coordinate system, deltai αβ＝Δiα+Δjiβ is a complex vector of small-signal disturbance of PCC point current under the alpha beta static coordinate system, and 'x' represents conjugation of the complex vector.
2. The HSS-based complex vector impedance modeling method of a permanent magnet direct drive fan of claim 1, wherein the state space model of the linear time domain periodic system is:
wherein the equation is a system state space expression expressed in the complex frequency domain, wherein I.e. a state matrix a (t) which is a state space expression,A state vector x (t) which is a state space expression,An input matrix B (t) being a state space expression,I.e. the input vector u (t) of the state space expression.
3. The HSS-based permanent magnet direct drive fan complex vector impedance modeling method of claim 1, wherein the state space matrix is a plurality of.
4. The HSS-based complex vector impedance modeling method of permanent magnet direct drive fan of claim 3, wherein one of said state space matrices has a matrix form of:
The matrix A is Toeplitz matrix, A h is the Fourier coefficient of the h harmonic component of the state matrix A (t) of the state space model of the permanent magnet direct drive fan, and A 0 is the Fourier coefficient of the 0 th harmonic component of the state matrix A (t).
5. The utility model provides a permanent magnetism direct drive fan complex vector impedance modeling system based on HSS which characterized in that includes:
The linear time domain periodic system acquisition module is used for acquiring a linear time domain periodic system, wherein the linear time domain periodic system comprises a permanent magnet direct-drive fan system;
The Fourier series expansion module is used for representing the linear time domain periodic system as Fourier series expansion;
The steady-state periodic operation track acquisition module is used for acquiring steady-state periodic operation tracks of all frequency harmonics of the linear time domain periodic system;
The linearization module is used for linearizing the linear time domain periodic system based on the Fourier series expansion and the steady-state periodic running track of each frequency harmonic to obtain a complex frequency domain linear time-invariant system, and specifically comprises the following steps:
linearization uses the following formula:
Where (jn omega 1+s)xn) is the derivative of the nth harmonic component of the system state variable x (t), Is the multiplication of the state vector by the state coefficient matrix of each subharmonic,Multiplying each subharmonic input coefficient matrix with an input vector;
the state space matrix determining module is used for obtaining a state space matrix containing any frequency harmonic component based on the complex frequency domain linear time invariant system;
the permanent magnet direct-driven fan alternating current side equivalent impedance model building module is used for building a permanent magnet direct-driven fan alternating current side equivalent impedance model containing various subharmonics according to the state space matrix, and specifically comprises the following steps:
a harmonic transfer function construction unit for constructing a harmonic transfer function according to the state space matrix;
the alternating-current side voltage and alternating-current side current acquisition unit is used for acquiring alternating-current side voltage and alternating-current side current of the permanent magnet direct-drive fan;
the permanent magnet direct-drive fan state space model construction unit is used for constructing a permanent magnet direct-drive fan state space model according to the harmonic transfer function, the alternating-current side voltage and the alternating-current side current, and the permanent magnet direct-drive fan state space model is as follows:
The Deltav αβ＝Δvα+Δjvβ is complex vector of PCC point voltage small signal disturbance under alpha beta static coordinate system, and the combined matrix is an input vector matrix of the state space model; Δi αβ＝Δiα+Δjiβ is complex vector of small-signal disturbance of PCC point current under alpha beta static coordinate system, and the complex vector is combined into a state vector with a matrix as a state space model; ". Times" represent the conjugate of complex vectors;
The permanent magnet direct-driven fan alternating-current side equivalent impedance model construction unit is used for constructing a permanent magnet direct-driven fan alternating-current side equivalent impedance model according to the permanent magnet direct-driven fan state space model, and the permanent magnet direct-driven fan alternating-current side equivalent impedance model expression is as follows:
Δvαβ(s)＝Zwf(s)Δiαβ(s)
Wherein Z wf(s) is an equivalent impedance matrix of the alternating current side of the permanent magnet direct drive fan, Z wf(s) is a matrix of 2x 2, The method is characterized in that the method comprises the steps of respectively inputting state variables and periods of a state space model of a permanent magnet direct-driven fan, wherein Deltav αβ＝Δvα+Δjvβ is a complex vector of small-signal disturbance of PCC point voltage under an alpha beta static coordinate system, deltai αβ＝Δiα+Δjiβ is a complex vector of small-signal disturbance of PCC point current under the alpha beta static coordinate system, and 'x' represents conjugation of the complex vector.
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