CN104346525B - Method for calculating accumulated power of multiple trains of traction substation of electricity supply system of urban rail transit - Google Patents

Abstract

The invention relates to a method for calculating the accumulated power of multiple trains of a traction substation of an electricity supply system of an urban rail transit. The method comprises the following steps: obtaining the power distribution of a train through simplified traction calculation, and obtaining the power distribution of n trains through permutation and combination; obtaining the number of the trains driven by the traction substation and the probability thereof through the electricity supply radius of the traction substation, the average travelling speed of the trains, the departure interval and a number probability integer method; obtaining the power distribution of the traction substation by combining the power distribution of the n trains and the number of the trains driven by the traction substation and the probability thereof. The method disclosed by the invention only uses as few as basic parameters which are easy to obtain, so that complicated tide calculation of mixed alternating and direct currents of the traction substation is avoided, at the same time, the largest power distribution, 95% of power distribution, and the average power of the traction substation are obtained, and the error of a calculation result is within an allowable scope, so that the method is suitable for the practical application of engineering. The power of the traction substation, which is obtained through calculation by the method disclosed by the invention, is used, and the harmonic assessment knowledge is combined, so that the level of the harmonic emission of the traction substation can be assessed.

Description

City rail traffic electric power system traction substation multiple row train number integral power calculates method

Technical field

The present invention relates to the city rail traffic in a kind of assessment for Harmonics of Urban Mass Transit System emission level is powered and is The computational methods of system traction substation (traction becomes) multiple row train number integral power distribution.

Background technology

Urban passenger terminals are served in urban track traffic, are handed over freight volume is big, speed fast, safety is punctual, alleviate ground Logical crowded the advantages of.The trip for developing into people of urban track traffic is provided a great convenience, flourishing, real to promoting city Existing economic sustainable development plays an important role.

There are a large amount of non-linear power loads in urban track traffic, including power rectifier, inverter, variable voltage variable frequency Device.Harmonic wave in city rail electric power system be mainly derived from locomotive traction power-supply rectifying system, Vehicular inverter and All kinds of power electronic equipments at station.These nonlinear-loads generate substantial amounts of harmonic wave and inject electrical network, make the voltage of electrical network Current waveform produces distortion, and the quality of power supply is reduced, and the various electrical equipments of city public electric wire net and urban track traffic are produced Different degrees of impact and harm.

Multidigit scholar point out, trailer system is the first big harmonic source of City Rail Transit System, the harmonic wave point of trailer system Cloth situation causes the attention of numerous scholars.When carrying out Harmonic Assessment, the accurate calculating of power distribution is particularly important.Open When the circuit of logical operation carries out Harmonic Assessment, the power of traction substation is obtained by surveying；Circuit is not opened, for traction becomes Electricity process have two kinds：The first is that current scholars carry out trailer system Harmonic Assessment in the design planning stage and mainly use Method：By assuming the load factor of tractive transformer, the power of traction substation is determined；Document [1] is calculating traction substation During AC harmonic wave, the power of traction substation is its peak hour peak load at a specified future date, for each traction substation For be a fixed value；Second is emulated from special traction generator simulation software, and user only needs input Parameter or data, these large softwares by the modeling tool founding mathematical models of itself, and can carry out simulation calculation output Simulation result, so that obtain the power of traction substation.Document [2] is based on the Multiple-population Genetic Algorithm of Matrix real-coded The train operation simulation module of city rail traction power supply analogue system is established, based on drawing and calculate, Rectification Power Factor is adopted With many broken line external characteristics models, a kind of many wire direct-current traction power supply emulation moulds for considering stray current collection net are proposed Type.Based on 12 pulse wave rectifier unit ac-dc conversion models, using Newton Algorithm trend, urban rail traction power supply is established The unified traction power supply computing module of the alternating current-direct current of system.By setting up the probability distribution of train position, departure interval, with traction Power supply calculation algorithm is combined, and proposes a kind of city rail tractive power supply system Probabilistic Load Flow algorithm based on Monte Carlo simulation, Obtain the power of traction substation.The functions such as several systems TOM, RAILSIM and TPC systems of foreign study exploitation are completeer It is kind, by being input into train, circuit relevant parameter, the physical quantitys such as node power can be obtained.

Whether first method is mainly used in the feasibility of proof scheme, not to traction substation actual motion power Illustrate, for the circuit of actual motion only has reference significance, can not assess exactly and open circuit trailer system Harmonics level；The dedicated emulated software price of second method is expensive, and calculating process is complicated, and major part is opened by railway interests Send out, be applied to city rail, main emphasis train operation arrangement, automatically control, the aspect such as energy saving optimizing operation.Using In the software of the calculating traction substation power of power system, need to carry out detailed traction calculating, need substantial amounts of basic number According to, and in terms of being also not applied to Harmonic Assessment.

The content of the invention

The technical problem to be solved, is just to provide a kind of one city rail traffic electric power system of simply calculating and leads Draw electric substation band difference train, under the conditions of the different departure interval integral power method, on this basis, with reference to fairing And knowledge in terms of harmonic wave, obtain the individual harmonic current value of traction substation AC, it is possible to realize traction substation harmonic wave The assessment of emission level.

Above-mentioned technical problem is solved, the technical solution used in the present invention is：

A kind of city rail traffic electric power system traction substation multiple row train number integral power calculates method, it is characterized in that including with Lower step：The calculating of S1, n train power distribution

S1-1, a train power calculation

By the characteristic curve with reference to traction electric machine, i.e. train speed and its corresponding pull strength respectively with train operation distance Relation, as shown in figure 1, by train operation be divided into traction, coasting, braking three phases, by load-carrying and the technical parameter of train, A power distribution during train operation is sought, calculation procedure is as follows：

S1-1- 1. distraction procedures：

The peak power of one train distraction procedure is：

In formula, P_AFor the maximum electric power of train traction process, F_t(v_A) it is that train speed is v_APull strength, v_AFor train Corresponding speed when operating in A points, η₁、η₂The respectively efficiency of motor and inverter, Δ P_eIt is regenerative braking to traction power Influence amount；

Distraction procedure is P except other stage train operation mean powers in invariable power area_BCan be written as：

In formula, v_B、v_CRespectively train operation corresponding speed, t in B, C point_1aFor permanent torque end of extent time, t_1bFor Invariable power end of extent time, t_1cFor the natural characteristic end of extent time；

S1-1- 2., coasting process：

Train operationally only absorbs electrical power needed for auxiliary equipment operation from electrical network：

P=P_f(3-3)；

In formula, the electrical power that P is obtained from electrical network for train operation, P_fFor the electricity that the operation of train auxiliary equipment is obtained from electrical network Power；

S1-1- 3., braking procedure：

Impact of the regenerative braking to train is to decline traction power, and decrement is：

ΔP_e=0.3 α P_av(3-4)；

In formula, α is to regenerate capacity usage ratio, P_avIt is the mean power in distraction procedure；

Consider that regenerative braking is affected on traction power, the actual electrical power absorbed from electrical network of train in distraction procedure

P=P_e-ΔP_e(3-5)；

In formula, P_eIt is to disregard train traction power when regenerative braking affects；

4., when stopping, train is that auxiliary equipment runs power demand from the power that electrical network absorbs to S1-1-；

P_C=P_f(3-6)；

In formula, P_CIt is train is absorbed from electrical network when stopping power；

5., a train power distribution is calculated S1-1-

To sum up, obtain a traction substation power distribution situation during train operation：

In formula, P₁It is power that train is obtained from Traction networks, t₁For drawing used time in stage, t_tThe time used by a cycle, P_AIt is train traction maximum electric power, P_BBe train obtain from electrical network mean power, P_CIt is least work that train is obtained from electrical network Rate；

Train, in running, is constantly to repeat said process, so probability distribution P' of the power of 1 train₁Can It is written as：

In formula, P'_1A、P'_1B、P'_1CPeak power, mean power and most are obtained from electrical network when representing a train operation respectively The corresponding probability of small-power；

S1-2, many train power combination situations are calculated

Because being independent same distribution per the power in train travelling process, related to permutation and combination know with reference to being independently distributed Know, obtain the power distribution during n train operations such as 2,3,4；

If P_nRepresent all possible power value condition of n trains, P_n' it is its corresponding probability distribution,

Then：

k₁,k₂,k₃,…,k_n∈ { A, B, C }, k_n≥k_n-1≥…k₃≥k₂≥k₁；

P'_n=f (n) P'_1k1P'_1k2P'_1k3…P'_1kn, wherein f (n) is variable coefficient；

N=2：If k₁=k₂, f (n)=1；

If k₁≠k₂,

N=3：If k₁=k₂=k₃, f (n)=1；

If k₁≠k₂≠k₃,

Other situations,

N=4：If k₁=k₂=k₃=k₄, f (n)=1；

If wherein only three are equal,

If wherein have two groups two it is equal,

Other situations,

To sum up, obtain the power distribution situation of n trains；

S2, traction substation band train number and its probability calculation

S2-1, traction substation band train number are calculated

The DC feeder of traction substation is respectively connected to upcoming contact net and descending contact net, and a traction substation is simultaneously Uplink and downlink train power supply is given, same section of contact net is by its two neighboring traction substation two-side feeding, whole piece circuit Each traction substation power between influence each other so that the power for accurately asking for independent traction substation is highly difficult；With The power calculation of the traction substation for the purpose of Harmonic Assessment, and complete and accurate power distribution is required no knowledge about, because humorous Ripple is with its 95% probit as evaluation criteria；

So doing hypothesis below：The radius of electricity supply of one traction substation is all adjacent net-fault overall length powered by it 1/2nd；The train number of one traction substation band is the train number of all directly connected contact net bands / 2nd of (including uplink and downlink)；

The departure interval of the power supply distance and train of known traction substation just can determine that this traction substation band Train number；The train number that one traction substation is capable of band be towed electric substation's radius of electricity supply, train Average Travel Speed and The impact of departure interval, traction substation band train number can be written as：

In formula, S is the radius of electricity supply of a traction substation, and unit is m,

v_avFor the Average Travel Speed of train, unit is m/s, and Δ t is the departure interval, and unit is s；

S2-2, draws variable speed train number probability distribution

The train number tried to achieve by the radius of electricity supply of traction substation, train Average Travel Speed and departure interval can Can be decimal, it is also possible to integer, but in actual motion, the train number of traction substation band can only be integer, so using When above method calculating acquired results are decimal, by decimal probability integer method, above-mentioned result of calculation is converted into whole Number；Note is designated as n and n+1 respectively apart from two n' nearest integers, and a probability of the traction substation with n trains is designated as P' N (), the probability with n+1 trains are designated as P'(n+1), then above variable meets following relational expression：

One probability of the electric substation with n trains：

Probability with n+1 train operations:

Above-mentioned result of calculation combines the power distribution of different trains, and rate of citing sb. for meritorious service combination corresponding with probability obtains determination and dispatches a car The corresponding power distribution situation of traction substation under interval.

Principle of the invention explanation：The power distribution of one train is calculated by simplified traction, n is obtained by permutation and combination The power distribution of train；By radius of electricity supply and the Average Travel Speed of train of a traction substation, departure interval, number are general Rate integer method, so that obtain traction substation band train number and its probability；By the power distribution of n trains and traction variable speed Car number and probability combine the power distribution for obtaining a traction substation.

Beneficial effect：The inventive method is applied only for as far as possible few when the power distribution of city rail traction substation is calculated Underlying parameter, the underlying parameter of needs is readily available, it is to avoid the trend meter of numerous and diverse traction substation alternating current-direct current mixing Calculate, at the same obtained drawing become maximum, 95%, and mean power, and error calculated is within allowed band, is suitable for In practical implementation.Using the calculated traction substation power of the inventive method, with reference to Harmonic Assessment knowledge, Ke Yishi The now assessment to traction substation harmonic emission level.

Description of the drawings

Fig. 1 is the curve of traction characteristics figure of traction electric machine；

Fig. 2 is urban track traffic tractive power supply system structure chart；

Fig. 3 is traction substation line and contact net band car operation schematic diagram；

Fig. 4 is a traction substation power calculation block diagram.

Specific embodiment

Below in conjunction with the accompanying drawings and subway circulation example the invention will be further described with explain.

Power department focus are that can user's injection PCC individual harmonic currents meet national standard requirement.But it is main Electric substation and traction substation belong to metro operation division management, and the harmonic emission level of whole system to be carried out is commented Estimate, need substantial amounts of basic data, the such as detailed load-carrying parameter of train motor, technical parameter, traction braking characteristic etc., draw, Controller switching equipment capacity and the mode of connection, and the urban rail internal system method of operation etc. is relevant.These data belong in subway Portion's data.In the case where basic data obtains difficulty, it is critically important to carry out rational estimation.

Fig. 1 is traction electric machine characteristic curve used by city railway vehicle, using velocity close-loop control, realizes motor successively Constant moment of force, invariable power and natural characteristic, and traction acceleration, three processes of coasting and braking deceleration of rail traffic vehicles.

Fig. 2 is the simple schematic diagram of urban track traffic tractive power supply system.110kV inlet wires are introduced to main transformer electricity from electrical network Institute, main transformer station export 35kV or 10kV Jing after blood pressure lowering, form middle-voltage network and power to traction substation, two in traction substation Platform transformator forms equivalent 24 pulse wave rectifier by phase shift, and outlet is DC1500V, is powered to subway train.

Fig. 3 is the schematic diagram of line and Traction networks to train power supply of traction substation.The inlet wire of traction substation From middle-voltage network, contact net is connected to Jing after step-down rectifier output, subway train obtains electricity by pantograph from Traction networks Can, electric energy is provided to train.

Fig. 4 is traction substation power calculation flow chart.The power distribution situation of a train is calculated first, with reference to arrangement Combination relevant knowledge, obtains the power distribution of traction substation during different train operations, then to a traction substation institute band Train number and corresponding probability calculated, with reference to the power distribution of n trains, obtain drawing power transformation under certain departure interval Power distribution situation.

Specific implementation step is as follows：

(1) n trains power calculation

1) a train power distribution is calculated

Think that train acceleration is approximately constant in permanent torque area and natural characteristic area, it is believed that traction power is linearly to increase 's.Each scholar's research obtains the energy of train regenerative braking generation and accounts for the 30% of haulage capacity or more, wherein by other trains The energy for utilizing accounts for 20%～80% (according to the different and different of departure interval and zone distance).Different times (just, closely, far) The value of utilization rate α of train braking energy is respectively 40%, 50%, 60%.Think that train is inhaled from electrical network in braking simultaneously The electrical power of receipts is auxiliary electric power.Thereby determine that Δ P_eValue.

Train speed at the end of the acceleration of known each operating mode and operating mode, tries to achieve the time used by each operating mode, Know F_tFor tractive force of train, train speed v, permanent torque end of extent time t_1a, invariable power end of extent time t_1b, natural characteristic area knot Beam time t_1c.After train model determines, these parameters may be considered fixed.

By the characteristic curve with reference to traction electric machine, i.e. train speed and its corresponding pull strength respectively with train operation distance Relation, as shown in figure 1, by train operation be divided into traction, coasting, braking three phases, by load-carrying and the technical parameter of train, A power distribution during train operation is sought, calculation procedure is as follows：

Distraction procedure：

The peak power of one train distraction procedure is：

In formula, P_AFor the maximum electric power of train traction process, η₁、η₂The respectively efficiency of motor and inverter, Δ P_eFor Influence amount of the regenerative braking to traction power；

Distraction procedure is P except other stage train operation mean powers in invariable power area_BCan be written as：

In formula, v_B、v_CRespectively train operation corresponding speed in B, C point,

Coasting process：

Train operationally only absorbs electrical power needed for auxiliary equipment operation from electrical network：

P=P_f(3-3)；

In formula, the electrical power that P is obtained from electrical network for train operation, P_fFor the electricity that the operation of train auxiliary equipment is obtained from electrical network Power；

Braking procedure：

Impact of the regenerative braking to train is to decline traction power, and decrement is：

ΔP_e=0.3 α P_av(3-4)；

In formula, α is to regenerate capacity usage ratio, P_avIt is the mean power in distraction procedure；

Consider that regenerative braking is affected on traction power, the actual electrical power absorbed from electrical network of train in distraction procedure

P=P_e-ΔP_e(3-5)；

In formula, P_eIt is to disregard train traction power when regenerative braking affects；

When stopping, train is that auxiliary equipment runs power demand from the power that electrical network absorbs；

P_C=P_f(3-6)；

In formula, P_CIt is train is absorbed from electrical network when stopping power；

One train power distribution is calculated：

To sum up, obtain a traction substation power distribution situation during train operation：

In formula, P₁It is power that train is obtained from Traction networks, t₁For drawing used time in stage, t_tThe time used by a cycle, P_AIt is train traction maximum electric power, P_BBe train obtain from electrical network mean power, P_CIt is least work that train is obtained from electrical network Rate；

Train, in running, is constantly to repeat said process, so probability distribution P' of the power of 1 train₁Can It is written as：

In formula, P'_1A、P'_1B、P'_1CPeak power, mean power and most are obtained from electrical network when representing a train operation respectively The corresponding probability of small-power；

2) n trains power calculation

On same circuit, the model of subway train is identical, on each fixed position, the motion shape of train State, the power obtained from electrical network are construed as approximately equalised, to be pointed out by the inventive method combined method, applying equation 3- 7,

k₁,k₂,k₃,…,k_n∈ { A, B, C }, k_n≥k_n-1≥…k₃≥k₂≥k₁；

P'_n=f (n) P'_1k1P'_1k2P'_1k3…P'_1kn, wherein f (n) is variable coefficient；

N=2：If k₁=k₂, f (n)=1；

If k₁≠k₂,

N=3：If k₁=k₂=k₃, f (n)=1；

If k₁≠k₂≠k₃,

Other situations,

N=4：If k₁=k₂=k₃=k₄, f (n)=1；

If wherein only three are equal,

If wherein have two groups two it is equal,

Other situations,To the power point of n trains can be obtained after the arranged combination of power of different operating modes Cloth Pn.

(2) variable speed train number and probability calculation are drawn

The characteristics of by metro traction load, when one timing of departure interval, the train number of a traction substation band can only be Two adjacent integers, such as 3-9 formulas result of calculation are 3.4, then the train number of this traction substation band can only be 3 row and 4 row Two kinds of situations, probability of the traction substation with 3 trains and 4 trains and be 1, probability with 3 trains is 0.6, with 4 trains Probability is 0.4, i.e., be assigned to 0.6 weight to 3 trains, and 4 trains are assigned to 0.4 weight, just obtains this traction substation average band Train number be 3.4.Radius of electricity supply S of traction substation always, train Average Travel Speed v_av, departure interval Δ t, with Row are various to ask traction variable speed train number and its probability.Wherein n and n+1 are distancesNearest two positive integers.

Traction substation band train number can be written as：

In formula, S is the radius of electricity supply of a traction substation, and unit is m,

v_avFor the Average Travel Speed of train, unit is m/s, and Δ t is the departure interval, and unit is s；

But in actual motion, the train number of traction substation band can only be integer, so being calculated with above method When acquired results are decimal, by decimal probability integer method, above-mentioned result of calculation is converted into into integer；Note is nearest apart from n' Two integers, be designated as n and n+1 respectively, a probability of the traction substation with n trains is designated as P'(n), with the general of n+1 trains Rate is designated as P'(n+1), then above variable meets following relational expression：

One probability of the electric substation with n trains：

Probability with n+1 train operations:

In sum, according to the inventive method, with reference to the power distribution of different trains, can just obtain between different dispatching a car Under, the power distribution of one traction substation run time different.

The application autonomous emulation platform write of document [2] obtains the mean power of the traction substation of different times and most It is high-power.Sweep spacing is 1s, and it uses linear electric motors in simulations, and 4 classification types, the power of motor are relatively wide at present The general alternating current generator for using is little.In the period of different, peak power and mean power have certain ratio corresponding relation.It is initial stage, near Phase, ratio at a specified future date are respectively 2.33,1.97,1.87.95% value and average power ratio of the power that said method is obtained be 2.18、2.08、1.99.This is the maximum for being Monte Carlo simulation, being under a kind of random case due to document [2], and It is not maximum truly, it is believed that 95% value and his peak power of calculated power in aforementioned manners Corresponding is rational.Two kinds for the error of peak power and the ratio of mean power is within 7%.So calculate traction becoming Electricity power distribution be rational.

The inventive method is primarily adapted for use in the assessment of Harmonics of Urban Mass Transit System emission level.Easy power calculation Method can not accurately calculate the power distribution situation of a train, also cannot be accurate by the probabilistic combination of different trains The power distribution of one traction substation of description.But in Practical Project, for the assessment of harmonic wave,《The quality of power supply _ common electrical Net harmonic wave》In point out, harmonic data should take its 95% probit, used as judging that whether harmonic wave exceed the foundation of permissible value.It is humorous 95% probit of ripple is referred to and is arranged in order the harmonic data of acquisition descending, gives up above 5% big value, take remaining real Maximum in measured value.So only needing to be calculated 95% probit of traction substation power.By a train Power distribution combines the inventive method, disclosure satisfy that requirement.

(1) power distribution of single traction substation in actual motion is calculated and is incorporated into city rail friendship by the inventive method In the harmonic wave distributional analysiss of way system, the harmonic emission level for more accurately assessing whole City Rail Transit System is provided Foundation.

(2) the inventive method is by the power distribution of a train that obtained, and traction substation radius of electricity supply, dispatches a car Several simple parameters such as interval, have obtained a mean number of the traction substation with train.The method parameter acquiring is simple, Engineer applied is convenient.

(3) the inventive method points out that number of the traction substation with train only has two in the case where the departure interval determines Plant possible, by number probability integer method, obtained a number of the traction substation with train and its probability.

(4) with leading to before the peak power of the calculated traction substation of this method and mean power and relevant scholar Cross and write value error that special analogue system obtains within 10%.The method is simple and easy to do, and desired data is few, it is adaptable to lead Draw electric substation's Harmonic Assessment.

List of references

[1] Li Jianmin, Yin Chuangui. urban track traffic Harmonic Analysis of Traction Power System [J]. urban track traffic is ground Study carefully, 2004,6:46.

[2] Liu Wei. urban railway transit train running optimizes and tractive power supply system dynamic simulation [D]. Chengdu:West Southern university of communications, 2009.

Claims (1)

1. a kind of city rail traffic electric power system traction substation multiple row train number integral power calculates method, it is characterized in that including following Step：

The calculating of S1, n train power distribution

S1-1, a train power calculation

By the characteristic curve of traction electric machine, train operation is divided into into traction, coasting, braking three phases, by train load-carrying and Technical parameter, seeks a power distribution during train operation, and calculation procedure is as follows：

S1-1- 1., distraction procedure：

The peak power of one train distraction procedure is：

$P_A=\frac{F_t\left(v_A\right)v_A}{{\mathrm{\η}}_1{\mathrm{\η}}_2}-{\mathrm{\ΔP}}_e---(3-1);$

In formula, P_AFor the maximum electric power of train traction process, F_t(v_A) it is that train speed is v_APull strength, v_AFor train operation The corresponding speed in A points, η₁、η₂The respectively efficiency of motor and inverter, Δ P_eFor impact of the regenerative braking to traction power Amount；

Distraction procedure is P except other stage train operation mean powers in invariable power area_BIt is written as：

$P_B=\frac{\frac{F_t\left(v_A\right)v_A}{2{\mathrm{\η}}_1{\mathrm{\η}}_2}\·t_{1a}+(\frac{F_t\left(v_A\right)v_A}{2{\mathrm{\η}}_1{\mathrm{\η}}_2}+\frac{F_t\left(v_A\right)v_B}{2v_C})\·(t_{1c}-t_{1b})}{t_{1a}+t_{1c}-t_{1b}}-{\mathrm{\ΔP}}_e---(3-2);$

In formula, v_B、v_CRespectively train operation corresponding speed, t in B, C point_1aFor permanent torque end of extent time, t_1bFor permanent work( Rate end of extent time, t_1cFor the natural characteristic end of extent time；

S1-1- 2., coasting process：

Train only absorbs electrical power needed for auxiliary equipment operation from electrical network：

P=P_f(3-3)；

In formula, the electrical power that P is obtained from electrical network for train operation, P_fFor the electrical power that the operation of train auxiliary equipment is obtained from electrical network；

S1-1- 3., braking procedure：

Impact of the regenerative braking to train is to decline traction power, and decrement is：

ΔP_e=0.3 α P_av(3-4)；

In formula, α is to regenerate capacity usage ratio, P_avIt is the mean power in distraction procedure；

Consider that regenerative braking is affected on traction power, the actual electrical power absorbed from electrical network of train in distraction procedure；

P=P_e-ΔP_e(3-5)；

In formula, P_eIt is to disregard train traction power when regenerative braking affects；

4., when stopping, train is that auxiliary equipment runs power demand from the power that electrical network absorbs to S1-1-；

P_C=P_f(3-6)；

In formula, P_CIt is train is absorbed from electrical network when stopping power；

5., a train power distribution is calculated S1-1-

$P_1=\left\{\begin{array}{cc}{P}_A& (t_{1a}\&le;t\&le;t_{1b})\\ P_B& (0\&le;t\&le;t_{1a})\&cup;(t_{1b}\&le;t\&le;t_1)\\ P_C& (t_1<t\&le;t_t)\end{array}\right.---(3-7);$

In formula, P₁It is power that train is obtained from Traction networks, t_1aFor permanent torque end of extent time, t_1bFor during invariable power end of extent Between, t_1cFor natural characteristic end of extent time, t₁For drawing used time in stage, t_tThe time used by a cycle, P_ABe train traction most Big electrical power, P_BBe train obtain from electrical network mean power, P_CIt is minimum power that train is obtained from electrical network；

Train, in running, is constantly to repeat said process, so probability distribution P' of the power of 1 train₁It is written as：

$\left\{\begin{array}{c}{P^{\&prime;}}_{1A}==\frac{t_{1b}-t_{1a}}{t_t}\\ {P^{\&prime;}}_{1B}==\frac{t_1-t_{1b}+t_{1a}}{t_t}\\ {P^{\&prime;}}_{1C}==\frac{t_t-t_1}{t_t}\end{array}\right.---(3-8);$

In formula, P'_1A、P'_1B、P'_1CPeak power, mean power and least work are obtained from electrical network when representing a train operation respectively The corresponding probability of rate；

S1-2, many train power combination situations are calculated

Because the power in per train travelling process is independent same distribution, with reference to being independently distributed and permutation and combination relevant knowledge, obtain Power distribution when the n train operations such as 2,3,4；

If P_nRepresent all possible power value condition of n trains, P_n' it is its corresponding probability distribution,

Then：

$P_n=P_{k_1}+P_{k_2}+P_{k_3}+...+P_{k_n}---(3-9);$

k₁,k₂,k₃,…,k_n∈ { A, B, C }, k_n≥k_n-1≥…k₃≥k₂≥k₁；

P'_n=f (n) P'_1k1P'_1k2P'_1k3…P'_1kn, wherein f (n) is variable coefficient；

N=2：If k₁=k₂, f (n)=1；

If k₁≠k₂,

N=3：If k₁=k₂=k₃, f (n)=1；

If k₁≠k₂≠k₃,

Other situations,

N=4：If k₁=k₂=k₃=k₄, f (n)=1；

If wherein only three are equal,

If wherein have two groups two it is equal,

Other situations,

To sum up, obtain the power distribution situation of n trains；

S2, traction substation band train number and its probability calculation

S2-1, traction substation band train number are calculated

If：The radius of electricity supply of one traction substation is 1/2nd of all adjacent net-fault overall length powered by it；

The train number of one traction substation band be the train number of all directly connected contact net bands two/ One；

The departure interval of the power supply distance and train of known traction substation determines the train number of this traction substation band；

The train number that one traction substation is capable of band is towed electric substation's radius of electricity supply, train Average Travel Speed and dispatches a car The impact at interval, is written as：

$n^{\&prime;}=\frac{2S}{v_{av}\mathrm{\&Delta;}t}---(3-10);$

In formula, S is the radius of electricity supply of a traction substation, and unit is m,

v_avFor the Average Travel Speed of train, unit is m/s, and Δ t is the departure interval, and unit is s；

S2-2, draws variable speed train number probability distribution

When being decimal with above method calculating acquired results, by decimal probability integer method, by above-mentioned result of calculation It is converted into integer；

Note is designated as n and n+1 respectively apart from two n' nearest integers, and a probability of the traction substation with n trains is designated as P' N (), the probability with n+1 trains are designated as P'(n+1), then above variable meets following relational expression：

$\left\{\begin{array}{c}{P}^{\&prime;}\left(n\right)+P^{\&prime;}(n+1)=1\\ {\mathrm{nP}}^{\&prime;}\left(n\right)+(n+1)P^{\&prime;}(n+1)=n^{\&prime;}\end{array}\right.---(3-11);$

One probability of the electric substation with n trains：

$P^{\&prime;}\left(n\right)=1-(\frac{S}{v_{av}\mathrm{\&Delta;}t}-\&lsqb;\frac{S}{v_{av}\mathrm{\&Delta;}t}\&rsqb;)---(3-12);$

Probability with n+1 train operations:

$P^{\&prime;}(n+1)=\frac{S}{v_{av}\mathrm{\&Delta;}t}-\&lsqb;\frac{S}{v_{av}\mathrm{\&Delta;}t}\&rsqb;---(3-13);$

Above-mentioned result of calculation combines the power distribution of different trains, and rate of citing sb. for meritorious service is corresponding with probability to be combined, that is, obtain between determination dispatches a car The corresponding power distribution situation of traction substation under.