Economy/regularity fuzzy-logic control of DC railway systems using event-driven approach

C.S.Chang Y.H. Phoa W.Wang B.S.Thia

Indexing terms: Electrical railway operation, Event-driven approach. Firing angle and tap adjustment, Fuzzy logic, Performance indices

Abstract: A methodology for predictive fuzzy control in an event-driven environment for multiobjective decision making on DC railway systems is presented. Railway operation is assessed by a set of performance indices, and the aim of fuzzy control is to score the best performance among these indices. In particular, the paper addresses regenerative braking in DC railways. The proposed methodology is implemented in two control loops: on each traction station and on each train dwell time at passenger stations.

List of symbols

V = voltage I = current E = energy R = regularity index ER = energy index G = nodal conductance matrix P = active power (2 = reactive power B” = network susceptance matrix used in fast decou- pled loadflow B’ = as B” but with all shunt branches and tap-chang- ing transformer representation deleted a = line receptivity p = firing angle p = membership value CO = vertex of membership function

1 introduction

A fuzzy control algorithm [I] was proposed for emer- gency conditions for reformulating and rejection of train reschedules from their terminating stations. Using the event-driven approach, the only decision to be made at a proposed reschedule time will be whether or 0 TEE, 1996 IEE Proceedings online no. 19960204 Paper first received 22nd March 1995 and in revised form 18th July 1995 The authors are with the Department of Electrical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 051 1

IEE Proc-Electr. Power Appl.. Vol. 143, No. 1, January 1996

not to dispatch each train. Due to its simplicity, the proposed methodology is fast enough to be imple- mented for online train operation, and has been extended for dwell time adjustment at intermediate sta- tions.

Using the approximate train and passenger models, the algorithm applies fuzzy performance indices for predicting the effects of a reschedule decision. These performance indices are each formulated in terms of a control target, a preferred direction of control, and a fuzzy membership function which gives an indication of how well a train reschedule proposal would achieve in improving each requirement. To provide a compre- hensive coverage of all railway operating requirements during the emergency state, nine performance indices were incorporated [I] in the control algorithm to meas- ure the effects of rescheduling in terms of 0 quality of passenger service

traffic and signalling requirements regularity, and electrical loading.

During normal conditions other performance indices have to be considered. For a railway system to be attractive to passengers in the normal state it must offer sufficiently frequent train services during busy hours to cope with peak passenger flows. During less busy periods, the reduced train frequency must be such that waiting on each platform does not become exces- sive. To derive full economic benefits from railway sys- tems, it is often desirable to run trains at high acceleration and braking, and to adhere as closely as possible to the speed restrictions and comfort con- straints. This minimises journey time, making the train service more attractive, but incurring high energy costs [2]. On the other hand, sizable cost savings can be achieved on energy consumption with the use of coast- ing controlhegenerative braking provided that this does not lead to acquiring more rolling stock and losing unacceptable running time.

To ensure safety on a railway system, the signalling system is designed to ensure a minimum operating headway between trains. For consistent operation, it is important to operate successive trains with similar speed-distance trajectories since irregularities bring about uneven time gaps between trains and energy wastage in train operation. The regularity aspect is thus an important requirement of train operation. Not only is it directly related to the quality of train services but it also represents a sound operation which eliminates

9

conflicts between trains in the normal running state. In this paper, the event-driven approach is intro-

duced into underground DC railway systems equipped with both regenerative and rheostatic braking. Special attention has been drawn to energy and regularity aspects of the operation, although the approach is well suited for considerations of all aspects. Performance indices measuring how much electrical energy is recov- ered during regenerative braking have been examined.

An important characteristic arising from this approach is a common framework for optimising mul- tiobjective functions and for dealing with conflicting constraints which are part of the complex operation of a railway system. Without the use of complicated opti- misation techniques, this paper shows how the fuzzy set theory [3] may be applied in such framework to weigh the various controls to provide a comprehensive treat- ment of all operating requirements. Using the proposed methodology, the original problem is decomposed into several subproblems each dealing with one specific requirement. This enables a best-suited mathematical or heuristic technique to be applied to each subprob- lem.

The proposed methodology is supported by a data- base which is made up of approximate models of pas- senger flow, train movement and consumption. These approximate models are mapped into each train sched- uling/rescheduling subproblem, for predicting and for assessing the effects of relaxing one operating require- ment against the others.

Although being successfully on a moderately sized and simplified system, the algorithm as described in this paper should be applicable to large systems with a variety of train types and services. This is because the methodology was formulated to perform predictive rea- soning on one train schedule at a time, and for a gen- eral rather than a specific railway system.

given event

retr ieval of data

predictive fuzzy \ control

system I I

implementation of predetermined

timetable

cycle to next

Fig. 1 Framework o j event-dreiven model

2 reschedu I i n g

In the simulation of dynamic systems there are two fundamentally different methods, namely: the time- domain model and the event-driven model. For online

Event-driven approach for online train

train rescheduling, the event-driven model (Fig. 1 [l]) is preferred since the calculation is extremely fast, involving only simple processes such as data retrieval, matching and addition. All inter- and intra-event sys- tem dynamics are represented by previously calculated performance values, and additional adjustments can be made for specific traffic and loading conditions. Oper- ating constraints due to train interactions (e.g. head- way, loading, regularity, passengers, etc.) are entered only if they are related to an event occurring or about to occur.

In the context of this paper, an event would be to dispatch a train from either a terminal or an intermedi- ate station (dwell time control). Should an event cause any violation of the constraints, the calculation will be backtracked to the previous state for reconsideration of that event for a modified dispatch time. Due to simplic- ity of the approach, trains are rescheduled online in a predictive mode on an event-by-event basis.

2. I Brief description of object-oriented railway sim ula tion program The simulation algorithm developed for this work was written on a SUN workstation using X-Motif, an object-oriented programming language in the X-Win- dow environment. Using such language, a simple graphical interface was developed to view train per- formance during simulation. Runtime information about any trains, passenger and traction stations can be obtained by clicking the mouse cursor onto a box representing the respective area. Also available on the command panel are functions for requesting clock dis- plays, termination, pausing and running the simulation with specific study options. Further development of the simulation algorithm has included compilation and storing of attributes and behaviour of signalling devices and train - station controls for subsequent retrieval and simulation.

UP 3

d 2 " section 1 section 2

Fig. 2 Network configuration 8 circuit breaker -track I . 3. 4 and 6 rectifiedinv. station 2 and 5 rectifier station

3 Modelling of train networks

The study system: Case studies are performed on a typ- ical two-track (up/down) system (Fig. 2), which is divided into two sections connected through a circuit breaker and with parallel connections between the two tracks at several locations. The railway line has an overall length of 6.6km, six passenger stations, six rec- tifier or rectifiedinverter traction stations. Each trac- tion station receives AC supply at 66kV, and supplies the line at a nominal DC third-rail voltage of 750V. The study system uses 4 6 GTO (four quadrants, gate turn off) chopper controlled trains which are equipped with a continuous blending of regenerative, rheostatic and air braking [5]. Other data of the study system are attached in the Appendix.

IEE Pioc -Electr Poivev App1 Yo1 143, No 1 January 1996 10

Train movement and power consumption: In the online event-driven model [ 11, typical plots [6] were obtained beforehand. These plots store and approximate each train’s running time, speed, control and electrical power consumption against displacement (Figs. 3 and 4). To develop a comprehensive database for online control purposes, many of these plots are created to model each train’s performance in each interstation run. The general nature of these plots allows for fur- ther improvement in accuracies using new information from detailed simulations, manufacturer’s characteris- tics, or site measurements.

velocity acceleration coasting deceleration,

volts

inverter operation rectifier operation

I I I I I *

regenerative current powering current Fig. 5 Traction station characteristics

time

inverter rectifier Fig. 6 Rectifier and inverter models

&ion k staj ion k + l Fig. 3 Speed-distance profile of train and time-distance profile of train squf passenger station

power c

cceleration profile

I 1 * distance 9 deceleration

profile stat ion k + l

t station k

Fig. 4 Power-distance profile of train squ passenger station

To a first approximation, each train’s speed, acclera- tion, coasting, and braking (Fig. 3), and therefore its consumption during motoring and braking (Fig. 4), are assumed to depend solely on its position between stations. Under all operating conditions, the power consumption plot (Fig. 4) is mapped for all trains and between all stations, the collective current supplied for each rectifier and/or inverter station is evaluated by DC/AC loadflow (Section 4.5).

Such a train model should be general enough to include the supply voltage sensitivities. Approximating functions may be developed to represent the system voltage variations for different traffic conditions. Appropriate coefficients and scaling factors from these functions may be retrieved from lookup tables to mod- ify each train’s consumption, so as to represent effects of the supply voltage variations [l]. The overall per- formance systemkrain performance may then be evalu- ated in the DC/AC loadflow as outlined in Section 4.5.

The voltage-dependent characteristics and control of train braking are covered in Section 3.1.

IEE Proc.-Electr. Power Appl., Vol. 143, No. 1, January 1996

Traction station characteristics (Fig. 5): As shown in the equivalent circuit of Fig. 6, the rectifier and inverter models are

and

where Vr and Vi represent the terminal voltages across the rectifier and inverter; R, and Ri represent the recti- fier and inverter equivalent internal resistances; p r and pi are the firing angles of rectifier and inverter; Vro and Vi, represent the rectifier and the inverter no-load volt- ages which are interfaced with the AC supply through a tap-changing transformer.

3.1 regenerative braking During regenerative braking, the energy released from braking should be fully utilised either by returning it to the AC supply through inverter stations or by nearby trains for acceleration. Line receptivity is essentially a measure of the amount of the energy recovered by these two means. Line receptivity is time varying, and depends on the DC voltage profile which is a function of train positions and power demands and AC supply loading conditions. Mathematically,

where Ebr represents the energy released from all brak- ing trains. E,, and E,,, represent the portion of energy absorbed by the AC source and nearby trains. is the portion of energy loss which has three components: the first component in lines and tracks, the second component in rheostatic resistors that are inserted dur- ing regenerative braking to avoid overvoltages (see (i) following), and the third component in power devices and any other elements of the drive systems. The first two loss components depend on the train and system conditions and the amount of rheostatic resistance

Vr = Vro COS pT - RrIT

v, = v,, cos pi + RZIi

(1)

(2)

Receptivity and its restrictions on train

Ebr gin, E a c c i- Eloss ( 3 )

11

inserted during regenerative braking. In this work, it is assumed that the third component is voltage independ- ent and remains constant. The line receptivity a may be defined as

(E,,, $. E a c c ) / E b r (4) Eqn. 4 has a theoretical value of 1 should the trains be supplied from an infinitely strong source with zero net- work impedances where all energy released from brak- ing will be absorbed. During regenerative braking, there is a tendency for the nearby voltages to rise, which could sometimes become excessive causing dam- ages to railway equipment unless the following meas- ures are taken: (i) trains under regenerative braking: by blending or switching in braking resistors (rheostatic braking) when the filter capacitor voltage exceeds a certain level [5] so as to bypass some of the surplus energy (ii) rectfier stations: lowcring V, by changing the con- trol angle pi and/or the transformer tap position (iii) inverter stations: lowering V i by the same means as in (ii) and/or clamping the voltage across the inverter to Vinvmax (Fig. 5 )

Should (i) be taken, a in eqn. 4 will fall short of 100%. Effects due to measures (ii) and (iii) are more complex. Preliminary investigation (Section 5) has how- ever confirmed the advantage of having some form of adaptive control on (ii) and (iii). Adaptive rectifier/ inverter control is capable of reducing all DC voltages below Vinvmnx and Vrrmax, so as to increase both the receptivity and the energy recovered to nearly 100%. In this paper, however, another form of dynamic control is investigated: (iv) Fuzzy dwell time control: During regenerative brak- ing, the departure times of nearby trains could be brought forward or backward so as to recover the sur- plus energy for acceleration. Such dwell time adjust- ment calls for sophisticated communications and co- ordination between trains, and gives rise to competition against other performance indices. In particular, regu- larity of train service could suffer because of such dwell-time adjustment. In the following Section, a scheme is presented for multiobjective dwell-time adjustment.

train reaches station scheduled dwell time I E

t, tg . t, t , dwell time

1

power ver-time profile i twn ctntinns

i L

c/dwelI time v time

6 Fig. 7 Basic idea behind dwell time control and train energy usage predic- tion (1) Train currently here (11) Time scheduled to reach station (in) Time scheduled to leave station

4 controller

Formulation of predictive fuzzy dwell-time

Railway performance indices are mostly competitive [l]. In this paper, only two of the most contradicting ones (good regularity and high energy recovery) are included for highlighting the basic characteristics of the proposed controller. The algorithm makes use of fuzzy rule-based reasoning to achieve compromise between good regularity and high energy recovery. The decision could be (i) train dwell-time adjustment: each train is allowed to vary dynamically its departure time at each station by taking one of the discrete departure time deviations within a given range (Fig. 7 top); and (ii) firing angle and tap-position adjustment: This could be carried out dynamically together with (i). In this paper, settings at each rectifieriinverter station are preselected. These settings are varied for each case study to give an insight into the interactive effects of one decision variable against the others. Fuzzy rule- based reasoning is made up of four standard processes, namely: normalisation (Section 4. l), fuzzification (Sec- tion 4.2), decision making (Section 4.3), and defuzzifi- cation (Section 4.4). In the event-driven environment, inputs to these processes are the proposed event (depar- ture time deviation), and the predicted system status on regularity and energy. Output from the reasoning proc- ess is the overall performance index due to each pro- posed event, which compares such event against the others. To assess system status changes due to each proposed event, fast predictive simulations are carried out. For effects on regularity this simply calls for map- ping each typical train’s time-distance profile, accord- ing to the original schedules and the proposed departure time deviation. To assess effects on energy, this requires mapping of the plots of train time-distance and power consumption-distance, as well as DC/AC loadflow (Section 4.5).

4. I Normalisation This converts results from the fast predictive simulation into performance indices for a common basis of com- parison: Regularity: This performance index R is given by

R = kR(T - T,) if R 2 LR then R = LR

(54 (5b)

where T is the proposed departure time for the train under consideration, T, is the original departure time, k , is the scaling factor, and L, is a hard limit on R. Eqns. 5a and b stand for two ways of treating R: the first being unconstrained, and the second plays down the importance of regularity w.r.t. other performance indices. Energy: As shown in Fig. 7, this is evaluated by run- ning the fast predictive simulation for a period ahead of the present time TPr (typically 20 s). As shown in Fig. 8 and Section 4.5, the fast predictive simulation is essentially a process of numerical integration in the time domain. Appropriate controls (Sections 3.1 and 4.5.1) are implemented to remove any overvoltage detected. During the forward control period T,,, the overall energy input through rectifiers E,,, and the energy fed back through inverters E,, are obtained by numerical integration. The energy supplied to the DC railway during the period Tpy is thus

E s u p p l z e d = E r e , - Etnu (6) IEE Pvoc -Elem Power Appl , Vol 143, No I , January 1996 I L

Esupphed represents the sum of the energy used by all the trains, the three energy loss components as mentioned earlier, during the period Xpy: Taking the subscript i to denote a certain departure time deviation in the given range (Fig. 7) and m to denote the original time sched- ule (no deviation), the extra energy for implementing the ith departure time deviation represents the varia- tions of energy loss components in lines and tracks, and in rheostatic resistors inserted during regenerative braking. This is represented by the following energy performance index:

ERt = ~ E R ( E Z ~ ~ ~ ~ ~ ~ - ELppized) (7a)

(7b) if ERz 2 LER then ER2 = LER where kER and L, are chosen to ensure that ER' is always actively represented in the membership function (Section 4.2). Similar to regularity (eqns. 5a and b), eqns. 7a and b stand for the unconstrained and con- strained forms of the energy performance index.

electrified railway model i I model ! I I ' I I I I simulation AC I DC I

load f low I analysis I

* status --C, of rai lway I

I I I I

operation

strategies control

Fig. 8 Model of electrified railway operation

4.2 Fuzzification In fuzzy set theory, performance indices R and ER are generic elements in the universe of concourse R and ER. Each value of performance indices is related to a corresponding linguistic level through a membership function to show the level of belonging in the respec- tive level. Linguistic levels of R and ER are contained in two fuzzy sets {early, good, late} and {poor, OK, good}. After decision making (Section 4.3)' the result- ing overall performance is represented with five linguis- tic levels {very poor, poor, OK, good, very good}. Typical memberships in the work are shown in Fig. 9.

membership value

I t

membership value

I t

- 1 O l R - 1 0 1 E regularity energy

Fig. 9 Membership ,functions for regularity and energy

4.3 Decision making This process involves reading rules from the rule base, matching rules, and inferring the overall performance by employing fuzzy implication. Typical fuzzy rules have the form

IEE Proc -Elect? Power A p p l , Vol 143, No I , January 1996

Rule 1: IF energy is bad AND regularity is early, THEN overall performance is very poor. Rule 2: IF energy is good AND regularity is okay, THEN overall performance is very good.

and 'poor', the fuzzy rules may be rewritten as: Using symbols V, G, and P to represent 'very', 'good'

R I : ~ v r i = ~ E o n n E = min(~E, 7 P ~ E 1 (8)

where pvpl and kvc2 are membership values for the fuzzy set overall performance 'very poor' and 'very good'; and pEC are membership values for energy 'bad' and 'good'; and pRE and pRo are membership val- ues for the regularity 'early' and 'OK, respectively.

The centre-of-gravity method [3] is used for inferring the rules:

n

2 = 1 P v P = n

1 PVF,+? P P Z + k P O K , + k PO.+& P V G , 2 = 1 2=1 z = 1 2=1 2 = 1

(10) where II is the total number of rules in the rule base, pVp, p p , poK, pG and pvG are membership values for overall performance corresponding to linguistic level VP, P, OK, G and VG, respectively.

4.4 Defuzzification This involves mapping fuzzy output values into an overall performance index D:

where mVP, mP, mOK, we and mVG are the vertices of fuzzy sets for overall performance corresponding to lin- guistic levels VP, P, OK, G and VG. The overall per- formance D reflects the railway performance due to a proposed departure time deviation. The fuzzy dwell- time controller cycles through all time deviations in the given range (Fig. 7), and recommends the best depar- ture time deviation with the highest D.

4.5 DC/AC loadflow This is made up of two iterative components, namely: the AC and the DC loadflows, and an iterative inter- face (Fig. lo).

4.5.1 DC loadflow: Network equation of the DC system is

where 1, is the vector of busbar injected currents which can either be a train current, a rectifier output or an inverter input (Fig. 6); Vd is the vector of train termi- nal or busbar voltages; and G is the nodal conductance matrix of the DC system. Each train's current is calcu- lated from the typical power consumption ~ distance

I d = GVd (12)

plot: It, = p,","/v,r (13)

where Ilr, P,, and V,, are the train's injected current, power consumption and terminal voltage respectively; and the superscript sp stands for a specified or known quantity. A powerful method [7] was developed to refer all train currents to their nearest busbars andlor trac-

13

tion stations, and thus eliminate all trains from the net- work equation. This so called 'train load referral' process maintains the structure of the nodal conduct- ance matrix G which needs to be reconfigured and inverted once only unless there is a major change of the railway network configuration.

By inserting high-resistance links, the structure of G is preserved after each temporary change or switching operation. Mode changes of rectifieriinverter stations are modelled by varying the shunt branches attached to the respective busbars (Fig. 6). Such changes are incor- porated into the inverse of matrix G' using a tech- nique such as the matrix inversion lemma [7].

Having obtained the network solution, one then uses interpolation [7] to evaluate the voltages supplied to each train from voltages of the nearest fixed buses. Should there be any overvoltage detected in the load- flow results, rheostatic braking (control 1, Section 3.1) is progressively blended to remove the overvoltages. Braking currents are reduced, and eqns. 12 and 13 are resolved. 4.5.2 AC loadflow: The standard method of fast decoupled loadflow with sparsity technique [8] has been used. AC sources are represented by an equivalent cur- rent source and reactance for the grid short-circuit MVA. Tap-changing transformers and power-factor compensation devices have also been modelled.

initialise AC and DC system, obtain 0' and 13".

obtain G and inverse G

t. i

obtain Vtwith A C eqns.

obtain Vd, Pt (dc). Qi(dc ) wi th DC eqns.

output results

Fig. 10 Flow chart of AC/DC loadflow

4.5.3 Combined solution of DC/AC loadflow: The basic algorithm (Fig. 10) modifies the AC network status using results from DC loadflow. For each trac- tion station, the following active and reactive power mismatches are

LIP, = P,"P - P,"" - P,"" (14) AQZ = Q f p - Q,"" - Q,""

where P and Q represent the busbar active and reactive power, and the superscripts ac and de represent the AC and DC quantities, respectively. Active and reactive power supplied to the DC side of each traction station are given by [8]

P,"" = klaV,I, cos$

Qtc = klaV,I, sin q5 (15)

where a, Vi, Ii, $ and kl are, respectively, the trans- former off-nominal turns ratio, the rectifier or inverter terminal voltage, the station injected current, the power factor angle, and a constant associated with a certain rectifieriinverter configuration.

5 Factors affecting firing angle and dwell time

The algorithms and data, as described, have been implemented. Results presented here are to substantiate various claims made in preceding Sections, and to pro- vide insight into key characteristics of the proposed scheme.

It is opportune to recap the two loops of the pro- posed control scheme, namely: for each train dynamic fuzzy dwell time adjustment, and for each rectifier/ inverter predetermined settings on firing angles and transfomer tap positions. The algorithm permits addi- tional control rules, such as adaptive rectifier/inverter control, to be added with ease to best suit other levels of operation sophistication.

Sensitivity studies are carried out individually to investigate performance of each control loop (firing angle or dwell time). With the regularity performance index deactivated, characteristics of the energy per- formance index is investigated over a range of parame- ter settings to establish its preferred direction of control.

Afterwards, the regularity performance index is reac- tivated, characteristics of the fuzzy dwell-time control- ler on both regularity and energy are evaluated and highlighted in Section 6.

5. I The two components of energy loss in DC systems: in lines and tracks and in rheostatic resistors during regenerative braking, each has a different pattern of variation with railway controls. The objective of con- trol here is to minimise the overall energy supplied to the DC railway by reducing the first to a low value and the second to zero. As stated in Section 5, the firing- angle control is allowed to take only preset values. For each set of preset values, the DC system performance is studied for different configurations: Configuration 1: this is the base case (Fig. 2) corre- sponding to the normal feeding condition, with all the six traction stations fully on, and the sectioning CB open. Configuration 2: this also corresponds to the normal feeding condition; but with traction station 1 off, and the sectioning CB open. Configuration 3: this corresponds to the emergency feeding condition; with traction station 1 off, and the sectioning CB closed. Configuration 4: this corresponds to the normal feeding condition; with the sectioning CB open, and traction stations relocated (see Appendix).

With the dwell-time adjustment deactivated, a train dispatch frequency of 3 min in both the up and down directions, the simulation was run for 2526s, and the total energy consumed by all trains is 6988.55MWs. In each simulation, each traction station is given a com- mon preset firing angle. Simulation results on the four configurations are shown in the DC energy supplied/ firing angle plots as in Fig. 11.

As expected, configuration 1 requires the least DC

Factors affecting firing-angle control

14 IEE Proc-Elect?. Power Appl., Vol. 143, No. 1, January 1996

energy supplied. Since there is sufficient energy sink in each isolated section, no train has undergone any rheo- static braking. With only the line and track loss in the DC system, the DC energy supplied is the lowest at zero firing angle.

r

71 60 !--A

0 5 10 15 20 25 30

72200% Ib 1i io G~ firing angle, deg.

0 5 10 15 20 25 30

0 5 10 15 20 25 30 f ir ing angle, deg

~~

Fig. 11 Energy supplied to DC railway against firing angle

In contrast, the rheostatic loss during regenerative braking is not zero in configuration 2. Half of the energy sink in the LHS section (traction station 1) has been taken off. Overvoltages have been detected. As a result, rheostatic braking has been employed and the DC energy plot is no longer monotonic. The lowest value occurs at p, = 15".

In configuration 3, the sectioning CB has been closed to provide extra energy sink in the LHS section. As compared with configuration 2, the DC energy sup- plied is smaller for lower firing angles (0 - 10"). Beyond this range, the DC energy supplied is larger than that of configuration 2 because of a higher line and track loss over a longer feed.

In configuration 4, traction stations are relocated. As compared with configuration 1, the energy sink is halved in each isolated section, and the DC energy sup- plied is thus higher as a result.

Summing up, there appears in each case an optimum firing angle by considering the energy alone and with- out activating the dwell-time control. However, the line and track loss and the rheostatic energy loss during regenerative braking do not have a fixed pattern of variations. To take full advantage of energy recovery, there seems to be a strong case for dynamic control of firing angle and transformer tap which should be adap- tive with system configurations as well as operating conditions.

5.2 Factors affecting dwell-time control The objective of this part of the work is to find out how the DC energy supplied may be reduced by the dwell time adjustment alone, and regularity is not con- sidered as part of the decision making. A simplified DC network is used in the study (see Appendix). Using a nominal train dispatch frequency of 3 min, the total energy used by all trains is 3839.53MWs for a simula- tion time of 1984s.

To begin the analysis, a base case with no control is established with a high DC energy supplied of 4116.58MWs. Next, five study cases have been simu- lated. In each case study a different number of discrete departure time deviations nJtep is used (nstep = 3, 5, 7, 9 or 1 I , Fig. 7), and the step size tstep is 2s for all the five cases. Using a forward control period TPr of 20s and a

1EE Pioc -Electr Power A p p l , Vol 143 'Vo I , January 1996

firing angle of 0" for all traction stations, Fig. 12 shows how the dwell time adjustment reduces the DC energy supplied. Since no requirement is placed on reg- ularity, larger values of nstep provide more freedom and better returns for the controller.

41 20 r

4000 t t

I

3 5 7 9 11 "step

3960

Fig. 12 Energy supplied to DC railway against n,Ttep

6 controller

Characteristics of the fuzzy dwell-time

Key parameters affecting firing angle and dwell-time control have been identified in Section 5. By varying these parameters and the weights attached to each per- formance index, some form of fuzzy rule tuning has been carried out for achieving a robust performance from the fuzzy controller. By looking after both energy and regularity, decision making in the controller is now fuzzy and multiobjective. A value of five is chosen for nYtep and tstep is 2s. Taking a typical value of 20s for a nominal dwell time, the chosen data have given rise to a minimum and maximum dwell time of 20 - 2 x 2 (= 16) and 20 + 2 x 2 (= 24)s, respectively. Computational time required by the controller is linearly proportional

Another important parameter of the controller is the forward control period Tpr. Fuzzy controller gives rise to a local optimum, and is based on predictive simula- tion within Tpr. Since it is somewhat uncertain how the system would behave outside Tpr, care should be taken in the choice of TPr to extend the control effectiveness beyond the local optimum. One way of choosing TFy is by conducting sensitivity studies. From the typical speed-displacement plot (Fig. 3), the startup accelera- tion of each train is 1.0m/s2 lasting for about 19 s. Hence, it would be reasonable to choose TPr in the neighbourhood of 19s. From Fig, 13, it is seen that the

to Itstep.

"""1 4008 1- I

10 15 20 25 30 35 40

Tpr.

Fig. 13 Energy supplied to DC railway againat TpF

15

optimum Tpr is 20s as the best compromise between both performance indices. This confirms the validity of the earlier choice of 20s as the appropriate value for

6.1 weight adjustment In the basic performance index equations (eqn. 5b and eqn. 7b), kR and kER are used to weigh between regu- larity and energy during decision making. The purpose of a tuning process is to keep the two performance indices both in its own active range, and to ensure robustness of the controller. The best values of kR and kER are determined heuristically through extensive sim- ulations. Generally speaking, larger values of KR put more emphasis on regularity and thus cause the DC energy supplied to rise. On the other hand, as the value of K E R increases, the DC energy supplied decreases. Typical performance plots of these parameters are given in Figs. 14 and 15. KR and K E R are assigned val- ues of 20 x and 0.01 x respectively.

Tpr.

Tuning fuzzy dwell-time controller by

4083

4083

f - 4082

21 P a, ' 4082 .2

0.25 8.3 25 33 50 100 4081 .8

K ~ . 1 o - ~ Fig. 114 Energy supplied to DC railway against KR

4086 r

4081 4082 0004 3 0005 0010 0015 0 0 2 5 0 1

K ~ , xi 0-3

Fig. 15 Energy supplied to DC railway against KER

6o r

4060 4040 0 > 5 10 15 20 25 30

f i r ing angle, deg. Fig. 16 Energy supplied to DC railway against firing angle after optimis- ing performance weights k R and kER

16

6.2 Performance of fuzzy dwell-time controller Using the values of nstep, Tpr, and the performance index weights kR and kER as determined in Sections 5.2, 6 and 6.1, the controller is applied to make a multiob- jective decision on seven values of the preset firing angle. Fig. 16 provides a plot of the DC energy sup- plied after optimising both performance indices, and the optimum firing angle is 10".

301

* O t

10 15 20 25 30 firing angle, deg.

-1 "I 0 Fig. 17 Time delay for all trains in roundjourney against firing angle

A plot of regularity against firing angles is shown in Fig. 17. Since nStep and tstep are 5 and 2s (Section 6), the maximum possible deviation of each train at each intermediate station is f (5 - 1)/2 x 2 = +4s (early or late). Since there are ten trains and three intermediate stations each way (upidown), the maximum possible time deviation of all trains at all intermediate stations is thus f10 x 3 x 4 = f120s each way or k240s in the round journey. As shown in Fig. 17, the regularity per- formance of the proposed control has been more than satisfactory, although some compromise (time delay i 15 s) has been to allow for optimum energy recovery.

7 Conclusions

The event-driven approach has been proposed for online control of normal railway operation. In particu- lar, predictive fuzzy set theory has been applied to achieve multiobjective decision making. The paper has addressed the energy-related performance index, and its interaction with the regularity-related performance index. The paper has presented a robust fuzzy dwell- time controller over a wide range of railway configura- tions and operating conditions, and has demonstrated strong economic incentives for developing an adaptive approach of traction station control for maximising line receptivity.

Further work is necessary to ensure consistency of fuzzy implication rules to minimise the possibility of contradiction between control rules, which are derived from different performance indices. Methods of online tuning of fuzzy implication rules should also be further investigated.

8 A c k n o w l e d ~ ~ e n t

The authors wish to thank Dr Y.C. Liang of the Department of Electrical Engineering, National Uni- versity of Singapore, for his advice and help in estab- lishing the necessary platform for developing the computer program.

IEE Proc -Electr Power A p p l , Vol 143, No I , January 1996

9 References 70.2 Data for configuration 4

1 CHANG C.S.: ‘AC train emergency fuzzy logic control using event-driven approach’, I E E Proc. B, 1993,140, (5), pp. 307-315.

2 MELLITT B., MOUNEIMNE Z.S. and GOODMAN C.J.: ‘Sim- ulation study of DC transit systems with inverting substations’, I E E Proc. B, 1993, 140, (2), pp. 38-50.

3 LEE C.C.: ‘Fuzzy logic in control systems: fuzzy logic controller - Pts 1 & 2’, ZEEE Trans., 1990, SMC-20, (2), pp. 404435.

4 CHANG C.S. and THIA B.S.: ‘Object oriented representation of signalling and train control system in railway operation’. 4th international conference on Computer-aided design, manufacture and operation in railway and other advance Mass transit systems, Madrid, Spain, September 1994 CHEW T.C. and KOYAMA S.: ‘4QIGTO chopper propulsion control system for Singapore MRT’. Proceedings of international conference on Mass rapid transit worldwide, 1986, pp. 425432

6 GONDO T., HOSHINO M. and SAWADA K.: ‘Electrical power system computer simulation’. Proceedings of international confer- ence on Mass rapid transit worldwide, 1986, pp. 377-396

7 CHANG C.S., CHAN T.T. and LEE K.K.: ‘AI applications and solution techniques for AC railway system control and simula- tion’, I E E Proc. B, 1992, 139, (l), pp. 1-12.

8 ARILLAGA, and J. ARNOLD, C.P.: ‘Computer analysis of power systems’ (Wiley, 1990)

5

10 Appendix

70. I Base case data of study system

Table 1: Position of passenger stations

ID Dist (m) 0 0 1 1000 2 1900

3 3000 4 4600 5 5400 6 6600

Nominal track voltage (V): 750 Nominal track resistance (G/km): 0.009

Table 2: Information about traction stations

ID Position Vnvmax p Type V, R, V, Ri 0 0 801 0 3 750 0.01 750 0.006 1 1400 801 0 1 750 0.01 750 0.006 2 3100 801 0 3 750 0.01 750 0.006 3 3100 801 0 3 750 0.01 750 0.006 4 4700 801 0 1 750 0.01 750 0.006 5 6600 801 0 3 750 0.01 750 0.006

type: 0: off 1: rectifier 2: inverter 3: rectifierhnverter

Table 3: Information about traction stations

ID Position V,,vmax p Type V, R, V, Ri 0 0 801 0 1 750 0.01 750 0.006

1 1400 801 0 3 750 0.01 750 0.006

2 3100 801 0 1 750 0.01 750 0.006

3 3100 801 0 1 750 0.01 750 0.006

4 4700 801 0 3 750 0.01 750 0.006

5 6600 801 0 1 750 0.01 750 0.006 type: 0: off 1: rectifier 2: inverter 3: rectifierhnverter

70.3 control

Data used in study of dwell-time

Table 4 Position of passenger stations

ID Dist (m) 0 0 1 1000 2 1900 3 3000 4 4600

Table 5: Dwell time of train in passenger stations

ID Dist (m) 0 25 1 15 2 15 3 20 4 25

Train despatch frequency ( s ) : 180

Table 6: Information about traction stations

ID Position vnvmax p Type V, R, 4, Rj 0 0 801 0 3 750 0.01 750 0.006 1 1900 801 0 0 750 0.01 750 0.006 2 4600 801 0 1 750 0.01 750 0.006

type: 0: off 1: rectifier 2: inverter 3: rectifiedinverter

IEE Proc.-Electr. Power AppL, Vol. 143, No. 1, January 1996 17