CN106815441B - Traction network voltage calculation method considering multiple off-line arcing of pantograph-catenary of motor train unit - Google Patents
Traction network voltage calculation method considering multiple off-line arcing of pantograph-catenary of motor train unit Download PDFInfo
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Abstract
The invention discloses a method for calculating traction network voltage considering multiple off-line arcing of a pantograph-catenary of a motor train unit, which comprises the steps of firstly establishing a traction network distribution parameter equivalent model comprising n pi-shaped equivalent models connected in series, introducing a mathematical model of the pantograph-catenary off-line arc into the traction network distribution parameter equivalent model to establish an arc model, and establishing a traction network loop state space model considering nonlinear dynamic arcing based on a state space theory; carrying out discretization processing on the traction network loop state space model by using a numerical analysis method; and finally, researching the traction net pressure fluctuation under the conditions of multiple arc burning and arc extinguishing of the bow net based on a state space analysis method. The state space analysis method adopted by the invention not only can solve the problem of the change research of the traction network voltage under the condition of multiple arcing, but also can be used for the analysis of the arcing occurring in the over-phase, and can be popularized and used for the analysis of the voltage and the current change when other arcs of a power system occur and the research of other nonlinear or time-varying models.
Description
Technical Field
The invention relates to the technical field of electric arc influence and protection in a high-speed railway, in particular to a method for calculating traction network voltage for calculating multiple off-line arcing of a pantograph-catenary of a motor train unit.
Background
The high-speed railway pantograph-catenary system vibrates, a track or a catenary is not smooth and excessively equal, and along with repeated arcing of the pantograph-catenary, a high-amplitude overvoltage phenomenon is generated to threaten the network voltage of a traction network, so that the voltage waveform of an injected train body is distorted, and the main traction transformer and electrical equipment in the train are damaged to influence the safe operation of the train. Direct site surveys are difficult due to randomness, instability, and non-linearity of the bow net offline arc. Therefore, it is necessary to analyze the fluctuation of the traction pressure in consideration of the multiple arcing and arc extinguishing of the pantograph-catenary.
At present, the research on bow net electric arc mainly focuses on the analysis of physical and chemical characteristics inside the electric arc, the design of an electric arc weakening device is started from the material, other theories mainly focus on the research of establishing different electric arc mathematical models and the like, the existing mathematical models can well reflect the physical characteristics of the electric arc, but few phenomena are analyzed on the influence of the bow net electric arc on the whole traction net, and the fluctuation of the car body and the traction net voltage is difficult to determine when the bow net is off-line and burnt.
Disclosure of Invention
In view of the above problems, the invention aims to provide a method for calculating the traction network voltage of multiple off-line arcing of a pantograph-catenary of a motor train unit, which is not only suitable for analyzing the influence of off-line arcing generated under the normal operation condition of the high-speed motor train unit, but also can be used for researching the influence of arcing generated by over-phase separation. The technical method comprises the following steps:
a method for calculating traction network voltage for calculating multiple off-line arcing of a pantograph-catenary of a motor train unit comprises the following steps:
step 1: establishing a traction network distribution parameter equivalent model comprising n series-connected pi-type equivalent models for the high-speed railway AT traction network, introducing a mathematical model of bow net off-line electric arc into the traction network distribution parameter equivalent model to establish an electric arc model, and establishing a traction network loop state space model considering nonlinear dynamic arcing based on a state space theory;
step 2: carrying out discretization processing on the traction network loop state space model by using a numerical analysis method;
and step 3: according to the discretized traction network loop state space model, the pantograph bow voltage waveform of the pantograph-catenary primary arcing is solved, each state variable result obtained by the arcing solution is stored and serves as a secondary arcing state variable initial value, iterative solution is carried out until the traction network voltage waveform of the pantograph-catenary multiple off-line arcing of the motor train unit is obtained.
Furthermore, the arc model is obtained by combining a Habedankk equivalent arc model with a Mayr arc model and a Cassie arc model and modifying, and the mathematical model representation mode is as follows:
wherein g is the instantaneous arc conductance of the Habedank equation; i is the instantaneous arc current of the Habedank equation; gcTransient conductance which is part of the entire arc equation Cassie; gMInstantaneous conductance, which is part of the overall arc equation Mayr; v is train speed; tau is0Is an initial time constant; α, γ, β are all correlation constants that affect arc dynamics.
Furthermore, the traction network distribution parameter equivalent model in the step 1 has (2n-1) state variables, a system matrix A of a (2n-1) × (2n-1) order state equation is solved, and a state equation of the system is obtained by inputting a matrix B:
wherein x (t) is a state variable, u (t) is an input vector; selecting the state variable x (t) as:
x(t)＝[is(t) u(t) i1(t) u1(t) i2(t) u2(t) … in(t) un(t) im(t)]
the input vector u (t) is:
u(t)＝[uS(t)]
in the formula uS(t) is the bus voltage of the traction substation,
phi is the initial phase angle.
Solving a state equation:
wherein the system matrix A is a (2n-1) × (2n-1) order tri-diagonal matrix, Rarc(t) is an arc nonlinear dynamic resistance; state variable ij(t) (j ═ 1,2, …, n) traction grid currents at different distances from the traction substation; u. ofi(t) (i ═ 1,2, …, n) is the traction network voltage at different distances from the traction substation, where u isn(t) is also the voltage of the pantograph head of the motor train unit roof; i.e. im(t) is the arc current, i.e. the load current; the arc voltage is expressed as:
uarc(t)＝im(t)Rarc(t)
and selecting proper n according to the length of the contact net line and the arc generation position to obtain the characteristic waveform of the arc and the voltage waveforms of all positions on the traction net.
Furthermore, the concrete steps of discretizing the traction network loop state space model are as follows:
1) the expression of the arc model after discretization is as follows:
where Δ t is the step size, tkK Δ t, denotes tkTime of day;
2) discrete processing of a traction network loop state space model:
if t is not less than 0k≤tendThat is, when the initial state is 0, the selected reference time is tendIf the step length h is Δ t, the overall iteration number is tendH; at tk<t≤tkWithin + delta t time, the system matrix A and the input matrix B are continuous, and all the state variable values x at the momentkAre all known, then tk+1The state response at the time is expressed as:
the above formula is simplified to the following simplified form:
in the formula (I), the compound is shown in the specification,
obtaining a discrete state equation from tk、tk-1And (5) time parameter expression is substituted into the arc discrete model expression to obtain a traction network loop discrete state model.
Further, the specific steps of step 3 are:
1)tkstarting at the moment of 0, substituting the initial parameters to solve an arc equation to solve a first state equation;
2) the result of the previous calculation versus the time parameter tk+1＝tk+ Δ t, state variable parameter xkAnd arc parameter gkUpdating, and continuously correcting the system matrix A once per iteration until an iteration time limit t is metk>tendStopping calculation until the calculation is finished, and finally realizing the solution of the nonlinear state equation;
3) and for the re-arcing condition after the arc is extinguished, correcting the voltage value of the traction network according to the output nth pantograph bow voltage waveform parameter, and iterating again to obtain the voltage waveform change of the traction network after the n +1 th pantograph bow-type arc is ignited.
The invention has the beneficial effects that: the invention takes the phenomena of multiple arc blowout and arc burning of the pantograph-catenary during the running process of the motor train unit into consideration, adopts a state space analysis method, can solve the operation complexity caused by repeatedly building modules when different arc models are simulated and analyzed by software, can also directly utilize an analysis result to solve the research on the transient voltage change of the pantograph head under the condition of multiple arc burning, is suitable for analyzing the influence of off-line arc burning generated under the normal running working condition of the high-speed motor train unit, can also be used for researching the influence of arc burning generated by over-phase separation, and has certain universality.
Drawings
Fig. 1 is a traction network series equivalent model.
FIG. 2 is a computational flow that accounts for the traction network arc state equation.
FIG. 3-1 shows that the load is mainly resistive (R)m＝56.2Ω，Lm0mH) arc net off-line arc electrical characteristic curve.
FIG. 3-2 shows the load being predominantly inductive (R)m≈0Ω，Lm91.6mH) arc net off-line arc electrical characteristic curve.
FIGS. 3-3 show the load as resistive (R)m＝56.2Ω，Lm91.6mH) arc net off-line arc electrical characteristic curve.
Fig. 4-1 is a once-through arcing traction net pressure waveform.
Fig. 4-2 is a secondary arcing traction net pressure waveform.
Detailed Description
The invention is described in further detail below with reference to the figures and specific embodiments. The state space theory and the numerical analysis method are combined, one-time off-line arcing condition is considered, the traction network voltage change during multiple times of arcing can be considered simultaneously, the actual multiple times of arcing of the bow network is closer to, and the method comprises the following specific steps:
step 1: establishing a traction network loop and an arc state space model
According to FIG. 1, the traction net model is composed of n pi-shaped parts R, L, C connected in series, Rm、LmIs the equivalent resistance and the inductance of the load,Rarcnon-linear resistance model for arc equivalence, RS、LSRespectively representing the equivalent impedance u of the transformer of the traction substationS(t) is the traction substation bus voltage, ij(t) (j ═ 1,2, …, n) is the traction network current at different distances from the traction substation, ui(t) (i ═ 1,2, …, n) is the traction network voltage at different distances from the traction substation.
The mathematical model of the bow net off-line electric arc is introduced into the traction net distribution parameter equivalent model to establish an electric arc model, the electric arc model is obtained by combining a Habedank equivalent electric arc model with a Mayr electric arc model and a Cassie electric arc model and correcting, and the nonlinear characteristic of the electric arc can be better reflected.
Determining the position of an electric arc, assuming that a traction network state space model is formed by connecting n pi-type equivalent lumped parameter models in series, the established traction network state space model has (2n-1) state variables, solving a system matrix A of a (2n-1) x (2n-1) order state equation, and inputting a matrix B to obtain the state equation of the system as follows:
wherein x (t) is a state variable, u (t) is an input vector; selecting the state variable x (t) as:
x(t)＝[is(t) u(t) i1(t) u1(t) i2(t) u2(t) … in(t) un(t) im(t)]
the input vector u (t) is:
u(t)＝[uS(t)]
in the formula uS(t) is the bus voltage of the traction substation,
phi is an initial phase angle;
solving a state equation:
the system matrix A of the above equation of state is a tri-diagonal matrix of order (2n-1) × (2n-1), Rarc(t) is the arc nonlinear dynamic resistance, and in the A matrix, only the A ((2n-1), (2n-1)) elements are time-varying, the rest are constant, and the input matrix B is constant.
As can be seen from FIG. 1, the state variable im(t) is the arc current, i.e. the load current, ui(t) (i ═ 1.. n) is the traction grid voltage at different distances from the traction substation, and the arc voltage can be expressed as:
uarc(t)＝im(t)Rarc(t)
and selecting proper n according to the length of the contact net line and the arc generation position, so that the arc characteristic waveform and the voltage waveform of any position of the contact net can be obtained.
Step 2: discretizing the traction network loop state space model:
because the arc model is nonlinear, the traction network state space model after the arc is introduced is a time-varying nonlinear state space model, and the discretization processing of the prior research is as follows:
G＝eAt
the state equation after the discretization process is expressed as:
for this method, since the traction network modeling is related to the arc occurrence location, i.e., the order of the state equation is affected by the parameter n. With the increase of the value of n, the state equation variables are increased, and in the equation solving iteration process, the high-order matrix A, B needs to be discretized again according to the formula once per iteration, so that the calculation is complex and the operability is not high.
In order to simplify the calculation steps and reduce the iteration difficulty, the embodiment first operates the traction network state equation and the equivalent arc dynamic resistance model according to the following discrete processing method:
the arc model selected in this embodiment is a Habedank model, and the mathematical model representation manner thereof is as follows:
wherein g is the instantaneous arc conductance of the Habedank equation; i is the instantaneous arc current of the Habedank equation; gcTransient conductance which is part of the entire arc equation Cassie; gMInstantaneous conductance, which is part of the overall arc equation Mayr; v is train speed; tau is0Is an initial time constant; α, γ, β are all correlation constants that affect arc dynamics.
Discretizing the electric arc to obtain:
where Δ t is the step size, tkK Δ t, denotes tkThe time of day.
Consider 0 ≦ tk≤tendWherein t iskK Δ t, denotes tkAnd the time, taking the step length h as delta t, and the integral iteration number is tendH is used as the reference value. Let us assume at tk<t≤tkWithin + delta t time, the system matrix A and the input matrix B are continuous, and all the state variable values x at the momentkAre all known, then tk+1The state response at a time may be expressed as:
the above formula can be simplified in the following simplified form:
in the formula (I), the compound is shown in the specification,
iterative solution of the nonlinear time-varying state equations is equivalent to solving a non-homogeneous linear equation set for each step.
The traction network state model is processed according to the three formulas to obtain a discrete state equation tk、tk-1And (5) expressing the time parameters, substituting the time parameters into an arc discrete model expression, and obtaining a traction network loop discrete state model.
And step 3: traction network voltage calculation considering multiple arcing of pantograph-catenary of motor train unit
The method for carrying out repeated arcing electromagnetic transient iteration solving by using a numerical analysis method comprises the following steps:
(1)tkstarting at time 0, substituting the initial parameters to solve the arc equation and then performing the first state equation solution.
(2) The result of the previous calculation versus the time parameter tk+1＝tk+ Δ t, state variable parameter xkAnd arc parameter gkUpdating is carried out, and the system matrix A needs to be continuously corrected every time of iteration until the iteration time limit t is metk>tendAnd stopping calculation until the time, and finally realizing the solution of the nonlinear state equation.
(3) And (3) considering the re-arcing condition after the arc is extinguished, correcting the voltage value of the traction network according to the waveform parameter of the head voltage of the pantograph for the nth time, and iterating again to obtain the voltage waveform change of the traction network after the pantograph is ignited for the (n + 1) th time, wherein the specific algorithm flow is shown in figure 2.
The initial state variable value of the algorithm influences the iteration number, so that the initial variable of the state equation needs to be properly assigned, and the parameters are set as follows:
(1) when the train normally operates, the voltage values of all parts of the traction network can be basically considered to be equal, namely, if the initial voltage phase angle of the substation is equal
When the initial power supply voltage is 90 degrees (the initial power supply voltage is zero), the initial values of the voltage and the current on the contact network circuit are considered to be zero;
(2) in order to simplify calculation, the arc dynamic resistance adopts an equivalent distribution principle, and because the arc resistance is smaller and the Mayr arc model and the Cassie arc model adopt series equivalence, the two parts of resistance are obtained according to the bisection of the whole arc resistance.
According to the above analysis method, arc characteristic waveforms at three loads can be obtained as shown in fig. 3-1, 3-2, and 3-3.
And (3) carrying out multiple arcing analysis on the phenomenon of uninterrupted re-ignition after the primary arcing is extinguished, taking twice arcing as an example, storing each state variable result of the primary arcing according to the above process, substituting the result as the initial value of the secondary arcing, and solving again to obtain the secondary arcing traction network pressure waveform, such as the primary arcing of fig. 4-1 and the secondary arcing traction network pressure result of fig. 4-2. Comparing fig. 4-1 and 4-2, it is analyzed that one arcing event will distort, but not significantly, the traction network pressure; if the electric arc is re-ignited again, the voltage distortion of the traction network is increased, more harmonic current is injected into the traction network, and the internal equipment of the vehicle body and the whole traction network are damaged. And due to sequential consideration, the voltage distortion of the traction network is more serious due to repeated arc blowout and arc burning.
Claims (2)
1. A method for calculating traction network pressure for calculating multiple off-line arcing of a pantograph-catenary of a motor train unit is characterized by comprising the following steps of:
step 1: establishing a traction network distribution parameter equivalent model comprising n series-connected pi-type equivalent models for the high-speed railway AT traction network, introducing a mathematical model of bow net off-line electric arc into the traction network distribution parameter equivalent model to establish an electric arc model, and establishing a traction network loop state space model considering nonlinear dynamic arcing based on a state space theory;
step 2: carrying out discretization processing on the traction network loop state space model by using a numerical analysis method;
and step 3: according to a traction network loop state space model subjected to discretization processing, solving pantograph bow voltage waveforms for accounting for primary arcing of the pantograph nets, saving each state variable result solved by the arcing, taking each state variable result as a secondary arcing state variable initial value, and carrying out iterative solution until traction network voltage waveforms for accounting for multiple offline arcing of the pantograph nets of the motor train unit are obtained;
the arc model is obtained by combining a Habedankl equivalent arc model with a Mayr arc model and a Cassie arc model and modifying, and the mathematical model expression mode is as follows:
wherein g is the instantaneous arc conductance of the Habedank equation; i is the instantaneous arc current of the Habedank equation; gCTransient conductance which is part of the entire arc equation Cassie; gMInstantaneous conductance, which is part of the overall arc equation Mayr; v is train speed; tau is0Is an initial time constant; alpha, gamma and beta are all relevant constants influencing the dynamic characteristic of the electric arc;
in the step 1, the traction network distribution parameter equivalent model has 2n-1 state variables, a system matrix A of a (2n-1) x (2n-1) order state equation is solved, and a matrix B is input to obtain a state equation of the system:
wherein x (t) is a state variable, u (t) is an input vector; selecting the state variable x (t) as:
x(t)＝[is(t) u(t) i1(t) u1(t) i2(t) u2(t) … in(t) un(t) im(t)]
the input vector u (t) is:
u(t)＝[uS(t)]
in the formula uS(t) is the bus voltage of the traction substation,phi is an initial phase angle;
solving a state equation:
wherein R ism、LmLoad equivalent resistance and inductance; rS、LSRespectively representing equivalent impedance of a transformer of the traction substation; the system matrix A is a (2n-1) × (2n-1) order tri-diagonal matrix, Rarc(t) is an arc nonlinear dynamic resistance; state variable ij(t), j ═ 1,2, …, n, traction network currents at different distances from the traction substation; u. ofi(t), i ═ 1,2, …, n, traction network voltages at different distances from the traction substation, where u isn(t) is also the voltage of the pantograph head of the motor train unit roof; i.e. im(t) is the arc current, i.e. the load current; the arc voltage is expressed as:
uarc(t)＝im(t)Rarc(t)
selecting proper n according to the length of the contact network line and the arc generation position to obtain the characteristic waveform of the arc and the voltage waveforms of all positions on the traction network;
the method specifically comprises the following steps of carrying out discretization processing on the traction network loop state space model:
1) the expression of the arc model after discretization is as follows:
where △ t is the step size, tkK △ t, representing tkTime of day;
2) discrete processing of a traction network loop state space model:
if t is not less than 0k≤tendThat is, when the initial state is 0, the selected reference time is tendWhen the step h is △ t, the overall iteration number is tendH; at tk<t≤tk+ △ t, the system matrix A and the input matrix B are continuous, and all the state variable values x at that momentkAre all known, then tk+1The state response at the time is expressed as:
the above formula is simplified to the following simplified form:
in the formula (I), the compound is shown in the specification,
obtaining a discrete state equation from tk、tk-1And (5) time parameter expression is substituted into the arc discrete model expression to obtain a traction network loop discrete state model.
2. The method for calculating the traction network voltage considering multiple off-line arcing of the pantograph-catenary of the motor train unit according to claim 1, wherein the specific steps in the step 3 are as follows:
1)tkstarting at the moment of 0, substituting the initial parameters to solve an arc equation to solve a first state equation;
2) the result of the previous calculation versus the time parameter tk+1＝tk+ △ t, state variable parameter xkAnd arc parameter gkUpdating, and continuously correcting the system matrix A once per iteration until an iteration time limit t is metk>tendStopping calculation until the calculation is finished, and finally realizing the solution of the nonlinear state equation;
3) and for the re-arcing condition after the arc is extinguished, correcting the voltage value of the traction network according to the output nth pantograph bow voltage waveform parameter, and iterating again to obtain the voltage waveform change of the traction network after the n +1 th pantograph bow-type arc is ignited.
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