CN114552657B - Dynamic stability analysis method for vehicle network system considering phase-locked loop angular frequency change - Google Patents

Dynamic stability analysis method for vehicle network system considering phase-locked loop angular frequency change Download PDF

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CN114552657B
CN114552657B CN202210317322.3A CN202210317322A CN114552657B CN 114552657 B CN114552657 B CN 114552657B CN 202210317322 A CN202210317322 A CN 202210317322A CN 114552657 B CN114552657 B CN 114552657B
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CN114552657A (en
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刘志刚
喻文倩
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Southwest Jiaotong University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/02—Conversion of ac power input into dc power output without possibility of reversal
    • H02M7/04—Conversion of ac power input into dc power output without possibility of reversal by static converters
    • H02M7/12—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/145—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a thyratron or thyristor type requiring extinguishing means
    • H02M7/155—Conversion of ac power input into dc power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a thyratron or thyristor type requiring extinguishing means using semiconductor devices only
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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Abstract

The invention discloses a vehicle network system dynamic stability analysis method considering phase-locked loop angular frequency change, which specifically comprises the following steps: firstly, a state equation of a circuit part of the vehicle network system is established through a simplified equivalent circuit. Then, through carrying out dynamic equation description on the angular frequency in the phase-locked loop and the time delay in the controller, a vehicle network system time domain state equation model considering the dynamic angular frequency is obtained; secondly, according to the established SSA model, obtaining a balance point of the system; furthermore, the Jacobian matrix is solved, and circuit parameters and control parameters are analyzed through a root locus method, so that the influence on the stability of the vehicle network system is reduced; then, drawing a stable region of the parameter by a design-oriented analysis method; and finally, verifying the accuracy of theoretical analysis results through simulation and hardware-in-loop platform. The invention improves the precision of the model, can reflect the influence of the circuit and the control parameter on the stability of the vehicle network system, and has quick calculation and short time consumption.

Description

Dynamic stability analysis method for vehicle network system considering phase-locked loop angular frequency change
Technical Field
The invention belongs to the field of high-speed railway time domain state equation modeling, and particularly relates to a vehicle network system dynamic stability analysis method considering phase-locked loop angular frequency change.
Background
In recent years, four-quadrant voltage source converter motor train units of an AC-DC-AC structure have been widely adopted, and it is generally considered that the main reason for the LFO phenomenon of a train network system is parameter mismatch between a traction network and the motor train unit. In order to avoid the occurrence of the LFO phenomenon and ensure the reliable operation of the system, the influence of research parameters on the stability of the vehicle network system is necessary.
At present, most documents mainly analyze the stability of a vehicle network system by establishing a small signal impedance model 2 under the dq domain. Although this method is not difficult in each step of calculation, the frequency coupling process is omitted in the modeling process, so that the analysis result is only effective in the low frequency band, but there is an error in the analysis result in the middle-high frequency band. Document 3 considers the coupling process of partial frequencies by using a modeling method based on harmonic linearization, but ignores w p ±nw 1 Is a frequency coupling term of (a). In document 4, an αβ impedance model is derived based on the dq impedance model, and the critical value change condition of various parameters when the converter is switched between the rectification and inversion operation modes is analyzed. The essence of the impedance model is to the vehicle network systemThe input/output impedance of (2) is calculated, and the operation process is complicated. Document 5 establishes an HSS model of a single-phase rectifier, and analyzes the dynamic characteristics of a harmonic transfer function using eigenvalues. For the HSS modeling process, the higher the harmonic order considered, the more accurate the resulting model will be. It is also worth noting that the impedance modeling process of a single-phase rectifier is more difficult and computationally complex than a three-phase rectifier due to the asymmetry of the single-phase rectifier.
To sum up:
1) Most of modeling modes of the vehicle network system adopt impedance models in a frequency domain, and the modeling process is complex. The equation model of the time domain is less researched, and an accurate mathematical model taking dynamic changes of the phase-locked loop into consideration is not used for describing the equation model.
2) In the stability analysis, the traditional frequency domain analysis method is complex and takes a long time. The characteristic value and the design-oriented analysis method can display the stability analysis result more quickly and clearly.
Therefore, the time domain state space modeling method is introduced into the stability analysis of the vehicle network system, and meanwhile, the dynamic angular frequency in the phase-locked loop is considered, an accurate mathematical model is established, the influence of the parameters on the system can be rapidly and accurately judged, and the stability range of the parameters is provided.
Reference is made to:
[1]：LIU Zhigang，ZHANG Guinan，LIAO Yicheng.Stability research of high-speed railway EMUs and traction network cascade system considering impedance matching[J].IEEE Transactions on Industry Applications，2016，52(5)：4315-4326.
[2]: zhang Guina, zhang Bo, gold, etc. study of the mechanism of harmonic propagation between traction drive systems accounting for network pressure fluctuations [ J ]. Electric automation devices, 2021, 41 (2): 186-192.
[3]：Zhang Han,Liu Zhigang,Wu Siqi,et al.Input impedance modeling and verification of single-phase voltage source converters based on harmonic linearization[J].IEEE Trans-actions on Power Electronics,2018,34(9):8544-8554.
[4]：HARNEFORS Lennart，YEPES Alejandro G.，Vidal Ana，et al.Passivity-based controller design of grid-connected VSCs for prevention of electrical resonance instability[J].IEEE Transactions on Industrial Electronics，2014，62(2)：702-710.
[5]：WANG Xiongfei，BLAABJERG Frede，LOH Poh Chiang.Passivity-based stability analysis and damping injection for multi-paralleled VSCs with LCL filters[J].IEEE Transactions on Power Electronics，2017，32(11)：8922-8935.
Disclosure of Invention
The invention aims to establish a time domain state space equation aiming at the low-frequency oscillation phenomenon of a vehicle network system, take the dynamic angular frequency of a phase-locked loop into consideration, analyze the influence of a circuit and control parameters on the stability of the vehicle network system through a root track and a design-oriented method, draw the stability range of various parameters and provide a theoretical basis for the stable operation of the system. Therefore, the dynamic stability analysis method of the car network system is provided, wherein the dynamic stability analysis method considers the angular frequency change of the phase-locked loop.
The invention relates to a vehicle network system dynamic stability analysis method considering phase-locked loop angular frequency change, which comprises the following steps:
step 1: listing a state equation of the circuit part according to the simplified equivalent circuit model; and (3) by considering the change of the angular frequency in the phase-locked loop and the time delay part in control, neglecting the secondary coupling frequency, and constructing a vehicle network system time domain state space equation model considering the dynamic angular frequency.
S11: state equation of circuit part:
Figure GDA0004074112680000021
Figure GDA0004074112680000022
Figure GDA0004074112680000023
in the formula e d And e q Is the voltage of PCC on dq axis, i d And i q Is the grid-side current in the dq coordinate system. u (u) dc Representing the output dc voltage. Omega PLL Is the output angular frequency of the PLL.
Figure GDA0004074112680000024
And->
Figure GDA0004074112680000025
Is the output of the current inner loop controller. The equivalent resistance and the inductance of the vehicle-mounted side are respectively R n And L n And (3) representing. C (C) d Representing the capacitance on the DC side, R d Representing the equivalent resistance on the dc side.
S12: PCC node voltage e n Q-axis voltage component after dq decoupling and coordinate conversion, e q The expression of (2) is:
Figure GDA0004074112680000031
wherein L is s And R is s Respectively represent the equivalent inductance and the equivalent resistance of the traction network side, u sD 、u sQ Respectively represent the power supply voltage u s Components of the D and Q axes in the traction grid side DQ coordinate system; θ represents the angle between the DQ coordinate system of the traction network side and the DQ coordinate system of the single-phase rectifier side, and the dynamic equation expression of the θ/dt=ω - ω is as follows PLL ；
S13: the angular frequency dynamics in a phase locked loop are described as:
Figure GDA0004074112680000032
/>
wherein k is upll And k ipll Respectively representing the proportional gain and the integral coefficient of a PI controller in the phase-locked loop; t represents time, ω k Representing the dynamic angular frequency in the phase locked loop.
S14: and (3) in the time delay part, after the simplification by using the third-order Pade approximation, the expression of the state equation is written as follows:
Figure GDA0004074112680000033
y x ＝C x x x +D x u x
wherein x is x ＝[x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ] T Is a new auxiliary state variable that is to be used,
Figure GDA0004074112680000034
representing the time derivative of the auxiliary state variable, +.>
Figure GDA0004074112680000035
Is the output variable, u x ＝[d d ,d q ] T Is an input variable, A x ，B x ，C x And D x Is a parameter matrix related to time delay, and the specific expression is:
Figure GDA0004074112680000036
Figure GDA0004074112680000037
Figure GDA0004074112680000038
where τ represents a time constant and I represents an identity matrix.
S15: the time domain state space equation of the single-phase vehicle network system is obtained by integrating the expression:
Figure GDA0004074112680000039
wherein x= [ i ] d ,i q ,u dc ,m id ,m iq ,m dc ,θ,ω PLL ,x x ] T Representing a state variable that is indicative of a state,
Figure GDA0004074112680000041
representing the input variable, u= [ u ] sD ,u sQ ,U dcref ] T Representing the control variable. m is m id 、m iq And m dc Are all auxiliary state variables in the controller, u sD And u sQ Respectively represent the power supply voltage u s Components of the D-axis and Q-axis in the traction grid side DQ coordinate system.
Step 2: and according to the established time domain state space equation model, solving the balance point of the system by utilizing a Newton iteration method.
Step 3: and solving the Jacobian matrix of the vehicle network system, and analyzing the influence of the circuit and the control adoption number on the stability of the vehicle network system according to the root track.
Step 4: and drawing a stable region of the parameter by a design-oriented analysis method on the basis of the built model.
Step 5: and verifying theoretical analysis results on the Simulink simulation and hardware-in-loop platform.
The beneficial technical effects of the invention are as follows:
1. according to the invention, the dynamic angular frequency and time delay part of the phase-locked loop are brought into the modeling process of the time domain state space model, so that the accuracy of the model is improved, and the influence of a circuit and control parameters on the stability of the vehicle network system can be reflected.
2. The modeling process and the analysis process are relatively simple, the signals do not need to be converted from the time domain to the frequency domain in the modeling process, and the characteristic value and design-oriented analysis method are rapid in calculation and short in time consumption.
Through Simulink simulation and hardware after loop verification, the invention establishes a time domain state space vehicle network system model after the dynamic angular frequency and time delay of the phase-locked loop are considered in detail, can well analyze the influence of circuits and control parameters on the low-frequency oscillation phenomenon, reveals the generation reasons and mechanisms of the phenomenon, and is beneficial to making corresponding inhibition measures for the phenomenon.
Drawings
Fig. 1 is a model of a vehicle network system of the present invention.
Fig. 2 is a control block diagram of the circuit of the present invention.
FIGS. 3 (a) -3 (d) are respectively the net side inductances L s Sampling time T s DC side capacitor C d And current loop proportional gain k ip A plot of the root locus of the change.
FIGS. 4 (a) -4 (d) are respectively the net side inductances L s Sampling time T s DC side capacitor C d And current loop proportional gain k ip And a low-frequency oscillation simulation result diagram.
FIGS. 5 (a) -5 (d) are the net side inductances L, respectively s Sampling time T s DC side capacitor C d And current loop proportional gain k ip And a low-frequency oscillation semi-physical experiment result diagram.
FIG. 6 shows inductance L for different network sides s When T s When=5e-5 s, k ip _C d A stable boundary on a plane.
FIG. 7 shows the sampling time T for different sampling times s When C d When=4.5 mF, L s _k ip A stable boundary on a plane.
FIG. 8 shows the capacitance C for different DC sides d When L s When=2mh, k ip _T s Stable boundaries on the facets.
FIG. 9 is an illustration of inner loop proportional gain k for different currents ip When C d When=4.5 mF, T s _L s A stable boundary on a plane.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
This example takes a simplified single-phase vehicle network system as an example. FIG. 1 is a model of a single-phase vehicle network system, consisting of a simplified traction network, etcThe effective circuit and the equivalent circuit of the vehicle-mounted single-phase rectifier. Wherein u is s Representing the equivalent power supply at the traction network side, L s And R is s The equivalent inductance and the equivalent resistance of the traction network side are respectively represented. The voltage at PCC is denoted as e n 。i n Representing the current on the net side. The equivalent resistance and the inductance of the vehicle-mounted side are respectively R n And L n And (3) representing. C (C) d Representing the capacitance on the DC side, R d Representing the equivalent resistance on the dc side.
FIG. 2 is a control block diagram of the circuit, in which U dcref And e qref Respectively representing a reference value of the DC side voltage and a voltage e at PCC n Reference value of q-axis voltage after dq decomposition. I dref And I qref Representing the current references of the d-axis and q-axis of the net side current after dq decomposition, respectively. k (k) up And k ui The proportional gain and the integral coefficient of the voltage outer loop PI controller are represented respectively. k (k) ip And k ii Representing the proportional gain and the integral coefficient, respectively, in the current inner loop PI controller. k (k) upll And k ipll Representing the proportional gain and the integral coefficient of the PI controller in the phase locked loop, respectively. Parameters of the vehicle network system are shown in table 1.
TABLE 1 vehicle network System model parameters
Figure GDA0004074112680000051
The root track, simulation result, semi-physical experiment result and design-oriented analysis result of this embodiment are composed of the following steps.
1) By varying the net side inductance L in the model built s Sampling time T s DC side capacitor C d And current loop proportional gain k ip Carrying out linearization treatment on the model at the balance point to obtain a Jacobian matrix, further obtaining a characteristic value of the system, and observing the change of the characteristic value of the system, wherein when the real part of a certain characteristic value exceeds an imaginary axis, the system is unstable;
FIGS. 3 (a) - (d) are network side inductances L, respectively s SamplingTime T s DC side capacitor C d And current loop proportional gain k ip Is a root trace change graph of (1). When the net side inductance L s At 4.2mH, the real part of the maximum eigenvalue crosses the imaginary axis, and the system will appear unstable, at which time the frequency of system oscillation is 2.1Hz. Similarly, it can be observed that, when the sampling time T s 2e-4s, DC side capacitor C d 8mF and current loop ratio gain k ip At 1.3, the real parts of the eigenvalues all pass through the left half plane to the right half plane, which means that the system is unstable, and the frequencies of oscillation are 3.1Hz, 2.1Hz and 2.2Hz respectively.
2) By changing the net side inductance L in Matlab\siulink simulation s Sampling time T s DC side capacitor C d And current loop proportional gain k ip The size of the system can be observed to generate an oscillation waveform;
FIGS. 4 (a) - (d) are respectively network side inductances L s Equal to 4.3mH, sampling time T s Increase to 2e-4s, DC side capacitance C d Increasing to 8mF and current loop ratio gain k ip The simulation waveform when reduced to 1.4 shows that the system has low-frequency oscillation phenomena with frequencies of 2.1Hz, 3Hz, 2Hz and 2.3Hz respectively. It can be seen that the critical value of the parameter and the oscillation frequency result are very close to each other compared to the theoretical analysis result.
3) Testing on a semi-physical platform, and observing the influence of a circuit and control on the system stability of the vehicle network system;
in order to further verify the theoretical analysis result, a semi-physical experiment platform is built. The model of the vehicle network system is split into two parts of a controlled object (main circuit) and a control algorithm, and the two parts are respectively downloaded into a hardware-in-loop real-time simulation system and a rapid prototyping control system by StarSim software and are connected through a physical input/output module to form a closed loop test loop.
FIGS. 5 (a) - (d) are network side inductances L, respectively s Up to 4.5mH and sampling time T s Increase to 2.2e-4s, DC side capacitance C d Increasing to 8mF and current loop ratio gain k ip Is reduced to1.3, waveforms of an ac side voltage current and a dc side voltage taken from an oscilloscope. The experimental result on the semi-physical platform can be found to be similar to the Matlab\Simulink simulation result.
The theoretical analysis result, the parameter critical value and the oscillation frequency between the Matlab\Simulink simulation result and the experimental result on the semi-physical platform are specifically shown in the tables 2 and 3.
TABLE 2 parameter threshold values
Figure GDA0004074112680000061
TABLE 3 Low frequency oscillation frequency
Figure GDA0004074112680000071
The theoretical analysis result, the Matlab\Simulink simulation result and the semi-physical platform experimental result are basically consistent.
4) Drawing a stable region of the parameter by adopting a design-oriented analysis method
First from the net side inductance L s Sampling time T s DC side capacitor C d And current loop proportional gain k ip And 3 parameters are selected to form a parameter plane, one variable in the 3 parameters is temporarily used as a constant value, one variable is used as an independent variable, the other parameter is used as a numerical value of an ordinate, and the stability critical value of the parameter is calculated by using the characteristic value analysis method and recorded. And respectively solving corresponding ordinate parameter critical values by changing the values of the independent variable parameters. And finally, drawing the recorded critical points into a stable boundary curve through least square fitting. The results are shown in FIGS. 6-9.
As can be seen in fig. 6, the larger the net side inductance, the smaller the stability area, when the sampling time is fixed. Fig. 7 illustrates that the larger the sampling time, the smaller the stable region when the dc side capacitance is unchanged. It can be observed from fig. 8 that for different dc-side capacitances, the larger the capacitance, the smaller the stable region when the net-side inductance parameter is fixed. Fig. 9 shows that when the current loop ratio gain is changed and the capacitance parameter is not changed, the larger the gain is, the larger the stable region is.

Claims (1)

1. A dynamic stability analysis method of a vehicle network system considering phase-locked loop angular frequency change is characterized by comprising the following steps:
step 1: listing a state equation of the circuit part according to the simplified equivalent circuit model; the method comprises the steps of constructing a vehicle network system time domain state space equation model taking dynamic angular frequency into consideration by considering the change of the angular frequency in a phase-locked loop and a time delay part in control and ignoring secondary coupling frequency;
s11: state equation of circuit part:
Figure FDA0004074112670000011
Figure FDA0004074112670000012
Figure FDA0004074112670000013
in the formula e d And e q Is the voltage of PCC on dq axis, i d And i q Is the grid-side current in the dq coordinate system, u dc Represents the output DC voltage omega PLL Is the output angular frequency of the PLL,
Figure FDA0004074112670000014
and->
Figure FDA0004074112670000015
Is the output of the current inner loop controller; the equivalent resistance and the inductance of the vehicle-mounted side are respectively R n And L n Representation, C d Representing the capacitance on the DC side, R d Representative ofEquivalent resistance of the direct current side; PCC is the connection point between the traction network equivalent circuit and the single-phase rectifier equivalent circuit;
s12: PCC node voltage e n Q-axis voltage component after dq decoupling and coordinate conversion, e q The expression of (2) is:
Figure FDA0004074112670000016
wherein L is s And R is s Respectively represent the equivalent inductance and the equivalent resistance of the traction network side, u sD 、u sQ Respectively represent the power supply voltage u s Components of the D and Q axes in the traction grid side DQ coordinate system; θ represents the angle between the DQ coordinate system of the traction network side and the DQ coordinate system of the single-phase rectifier side, and the dynamic equation expression of the θ/dt=ω - ω is as follows PLL ；
S13: the angular frequency dynamics in a phase locked loop are described as:
Figure FDA0004074112670000017
wherein k is upll And k ipll Respectively representing the proportional gain and the integral coefficient of a PI controller in the phase-locked loop; t represents time, ω k Representing dynamic angular frequency in the phase locked loop;
s14: and (3) in the time delay part, after the simplification by using the third-order Pade approximation, the expression of the state equation is written as follows:
Figure FDA0004074112670000018
y x ＝C x x x +D x u x
wherein x is x ＝[x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,x 6 ] T Is a new auxiliary state variable that is to be used,
Figure FDA0004074112670000019
representing the time derivative of the auxiliary state variable, +.>
Figure FDA0004074112670000021
Is the output variable, u x ＝[d d ,d q ] T Is an input variable, A x ，B x ，C x And D x Is a parameter matrix related to time delay, and the specific expression is: />
Figure FDA0004074112670000022
Figure FDA0004074112670000023
Figure FDA0004074112670000024
D x ＝-I
Wherein τ represents a time constant and I represents an identity matrix;
s15: the time domain state space equation of the single-phase vehicle network system is obtained by integrating the expression:
Figure FDA0004074112670000025
wherein x= [ i ] d ,i q ,u dc ,m id ,m iq ,m dc ,θ,ω PLL ,x x ] T Representing a state variable that is indicative of a state,
Figure FDA0004074112670000026
representing the input variable, u= [ u ] sD ,u sQ ,U dcref ] T Representing a control variable; m is m id 、m iq And m dc Are all auxiliary state variables in the controller, u sD And u sQ Respectively represent the power supply voltage u s Components of the D and Q axes in the traction grid side DQ coordinate system; u (U) dcref A reference value representing a direct-current side voltage;
step 2: according to the established time domain state space equation model, solving a balance point of the system by utilizing a Newton iteration method;
step 3: solving a Jacobian matrix of the vehicle network system, and analyzing the influence of a circuit and control parameters on the stability of the vehicle network system according to the root track;
step 4: drawing a stable region of the parameter by a design-oriented analysis method on the basis of the built model;
step 5: and verifying theoretical analysis results on the Simulink simulation and hardware-in-loop platform.
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