VỀ một GIẢI PHÁP điều KHIỂN QUÁ TRÌNH TRAO đổi NĂNG LƯỢNG hãm của tàu điện ĐƯỜNG sắt đô THỊ VIỆT NAM tiếng anh

1 INTRODUCTION 1, The urgency of the thesis: Electric transportation with outstanding advantages is the ability to transport large passengers, reduce environmental pollution, reduce traffic congestion [63,78] In Vietnam, the planned urban railway network in the near future has routes deployed in Hanoi city routes in Ho Chi Minh city However, the energy required to operate urban railway is up to billions of kWh Therefore, the goal of energy saving on train operation is a very urgent issue, with high scientific and practical significance, but so far, no research group in Vietnam has proposed energy saving solutions operate urban electric trains Therefore, the author selected the topic with the name: "About a solution to control the energy exchange process of Vietnam urban railway electrified trains" with the aim of saving energy by a solution for regenerative braking energy when the train operates in braking mode and in combination with the optimal theory of determining the optimal train speed profile Research objectives: Introducing energy saving solutions in electrified train operation Thereby, proposing solutions suitable to the characteristics and conditions of Vietnam's urban railways; and applying these solutions for Cat Linh-Ha Dong urban railway to assess saving energy Research objects: Urban electric trains have traction drive system integrated with supercapacitor energy storage device Research content: The thesis structure consists of chapters - Chapter 1: Overview of braking energy recuperation solutions: Synthesizing, analyzing previously published works, thereby proposing research directions, research objects, and developing solutions to solve research problems - Chapter 2: Implementation of modeling of electric train and supercapacitor energy storage system - Chapter 3: Strategies for optimal control of train operation energy with trains integrated supercapacitor energy storage system (SCESS) - Chapter 4: Verification of the correctness of theoretical research through simulation results on Matlab software with parameters of Cat Linh - Ha Dong urban electric train line, and an experimental part of Interleaved DC -DC converter in SCESS - Finally, some conclusions and further research directions of the thesis are presented in the conclusions The novelty of the thesis:  Proposing SCESS on board integrated with traction motor drive system via Interleaved bidirectional DC-DC converter and designing supercapacitor control according to the operation characteristics of a railway vehicle  Applying Pontryagin's maximum principle to find optimal transfer points of operating modes, determine the optimal speed profile of train operation using supercapacitors on board 2 CHAPTER OVERVIEW OF SOLUTIONS FOR BRAKING ENERGY RECUPERATION 1.1 The announced researches on solutions for braking energy recuperation 1.1.1 Domestic research This is a very new field in Vietnam, so there are very few studies on optimizing the energy of urban electric train operation [60] 1.1.2 Overseas research Energy -efficient operation of electrified train Regenerative braking energy Energy -efficient driving Optimal speed profile Eco-driving tools: ATO, DAS Energy storage device Energyoptimised timetables Hình 1.7 Strategies for effective management of train operation energy Studies have shown that there are two groups of solutions with higher energy-saving percentages: Regenarative recuperation solutions and energy efficient driving solutions [31] 1.1.2.1 Research on regenrative braking energy recuperation a) Regenerative braking energy recuperation by energy storage device The supercapacitor energy storage system (SCESS) is installed onboard, at the traction substations, or at points along the train track to recover regenerative braking energy when the train operates in traction mode [9, 12, 21, 25, 44, 45, 46, 53, 58, 66, 68, 69, 72, 73, 75] b) Reversible substations Traction substations use active rectifiers for bidirectional energy flow to recuperate braking energy up to 18% [86], [22] c) Braking energy recuperation by timetable optimization: This solution does not require additional investment in infrastructure of the route, with the idea of using regenerative braking energy from a train operating in the braking mode to switch to trains operating in accelerating mode Typically, Subin Sun (2017) [71] combines the operation of two trains in the same station, recuperating the regenerative braking energy represented by the power q(t ) in dv = u f f (v) + q(t ) / v - ubb(v) - r (v) - g(x ) dx ì ï t < tb ï ï With braking mode occuring in interval [tb, tc], q(t ) = íq (t ) tb £ t £ tc ï ï ï ï ỵ0 tc the motion equation: v 1.1.2.2 Energy - efficient driving a) Determining the optimal train journey on the route - The research team of the University of South Australia including Howlett, Benjamin, Pudney, Albrecht, Xuan has determined the optimal speed profile through finding the optimal transfer points with control rules taking into account the actual conditions on the route such as the slope, the speed limit, etc., it is possible to find the optimal time and distance at each train operation mode Comment: The research team of the University of South Australia in published studies does not mention the problem of train running on time Hai Nguyen (2018) [2] applied PMP to trains with long-distance diesel locomotives, found the optimal speed profile corresponding to the lines with different slopes, and in the objective function also mentioned to the station problem on time Comment: In his thesis, Hai Nguyen does not mention the problem of recovering braking energy 1.2 Selecting the research direction and the tasks solved of the thesis Through analysis of published works, there are no works that combine both the regenerative braking energy recuperation solution by ESS and the optimal speed profile determination with the on-board ESS while ensuring fixed trip time Therefore, the author proposes the selected structure for research Braking energy recuperation Technology Energy converter system - DC-AC converter - DC-DC converter Traction substation Control stratergies - Control charge/ discharge of supercapacitor - PMP for train with Onboard SCESS, finding optimal speed profile DC Link ESS VSI Voltage source inverter IM Train Wheel Fig 1.14 The selected structure for research  Technology: Learning about technology of electric train operation in some urban railway lines in Vietnam; namely, urban railway of Cat Linh - Ha Dong line  Energy conversion system on electric trains: focusing on studying Interleaved DC-DC converter in an effort to ensures energy exchange between supercapacitor and traction drive system  Control strategies: Proposing the control method for Interleave DC-DC converter ensures the charging-discharging mode of supercapacitors suitable for train running characteristics Proposing PMP to determine the optimal speed profile for train operation Conclusion of chapter By synthesizing and analyzing a number of domestic and foreign research works on energy saving solutions, the author has analyzed and selected the research object as an urban electric train integrated on-board SCESS and proposed independent control strategies for each train; proposed to control regenerative braking energy recuperation by managing the charging / discharging mode of supercapacitors; using Pontryagin's maximum principle to optimize train operation energy with hybrid power systems These suggestions will be verified by MATLAB simulation software The summary content of Chapter has been published by the author in the work [3] CHAPTER MODELING ELECTRIC TRAIN AND SUPERCAPACITOR ENERGY STORAGE SYSTEM The accuracy and characteristics of the mathematical model is the core factor determining the quality of the system So in Chapter centralized modeling system including:  Modeling lectric train  Modeling supercapacitor enregy storage system Rday iday Overhead contact line Pantograph Substation DC-DC converter Etdk iinv iC Rtdk Usc i LL RL rbr ibr VSI Csc IM IM Fig 2.1 Electrical drive configuration equipped with SCESS 2.1 Modeling electric train and SCESS 2.1.1 Modeling electric train Modeling the train needs to calculate the forces affecting train motion, the traction motor drive system to make the wheel movement 2.1.1.1 The forces act on the train The forces acting on the train include: The main resistance force including wind resistance (Fwind), rolling friction resistance (Froll); slope resistance (Fgrad) 5 The third rail, 750 VDC Feeder Air resistance force Train Wheel Gear Traction force IM Motor torque railway Friction force 𝛂 Gravity Fig 2.9 Diagram of forces acting on electric train [1] Traction / braking force: Fig 2.11 Traction force /01 motor Fig 2.13 Traction force regression/ 01 motor Fig 2.12 Electric braking force/01 motor Fig 2.14 Electric braking force regression/ 01 motor Resistance forces: FTr Faero mgsinα Froll α mg Fig 2.16 Forces acting on train a The main force W0 : The main resistance force (also known as basic resistance force) includes wind resistance and friction force W0 = Fwind + Froll (1.1)  The wind resistance force depends on train speed, size and shape, represented by the formula [93]: Fwind = Where:       rC d Af v - vwind = rC d Af v - v wind cos(v wind , v ) 2 { r } (1.2) is the air density; Cd is the air drag coefficient, determined by train shape; Af is the largest section of the train; v is train speed; vwind is wind speed; b is the sharp angle created by the direction of the wind velocity with the movement of the train  Rolling resistance force Froll For simplicity, consider rolling frictional force only on hard track and consider the ideal case that all wheels have the same conditions At this time, rolling friction (1.3) force can be calculated as follows [93]: Froll = fr mg cos a where fr is rolling resistance coefficient b Gradient resistance force F gra d : When the train operates on the slope, the gradient resistance force is calculated according to the formula [93]: Fgrad = mg sin(a ) (1.4) where: sin(a) = sin(arctan(ik )) ik (‰)is the ratio of slope height to slope, a is the slope of the track 2.1.1.2 Dynamic equation of the train The motion equation of the train is often transformed into its own form of impact force converted into the mass unit of the train as follows: ì ï dt ï = ï ïdx v í ï dv ïv = utr ftr (v ) - ubr fbr (v ) - w (v ) - fgrad (x ) ï ï ï ỵ dx In the (2.7): utr ubr are control variables: utr = (2.7) Ftr (v ) F (v ) ; ubr = br , and Ftr max (v ) Fbr max (v ) utr Ỵ [0,1], ubr Ỵ [0,1] ; The unit main resistance force (also called the unit basic resistance force) is represented by the David equation: w = a + bv + cv (2.8) The a,b,c coefficients are supplied by the Manufacturer 2.1.1.3 Motion equation of tractive electrical motor Tel -TL = J d wr ; dt J = J m + J eq (2.9) m ổỗ Dwh ửữ ç ÷÷ The inertia torque of the train is calculated [59]: Jeq = N ỗỗố t ữứ Load torque when the motor operates in engine mode [59] (2.10) TL = Ftr DWh D Wh = KmFtr với K m = 2thmor hmech 2thmor hmech (2.11) Load torque when the motor operates in generating mode [59]: Fbr DWh hgen TL = 2thmech = KG Fbr với KG = DWh hgen (2.12) 2thmech 2.2 Supercapacitor energy storage device modeling Modeling energy storage device includes supercapacitor modeling and Interleave DCDC converter modeling 2.2.4 Supercapacitor modeling Supercapacitors replaced by equivalent electrical circuit model include many parallel branches [32] Two RC branches provide two time constants to describe the fast and slow dynamics iL I iP Ci v sc R P R Ci0 Ii R I d R d i i Ci1 Cd Vi Ci C i0 i Ci1 (a) (b) Fig 2.22 Simple equivalent supercapacitor circuit As the above analysis, supercapacitor dymamic is considered for a short period of time, ignore the Rd ,C d branch (with a minute time constant) and the branch containing RP (characteristic for long-term leakage current in self-discharge) as shown in Figure 2.22b See the two capacitors with equivalent capacitance Ci depending on the voltage ui in relation: C i (u i ) = C i + C i = C i + k v u i (2.21) Given Ci=Csc, ui=usc, Ri=Rsc The mathematical model of supercapacitor is shown as follows: ì ï du (t ) ï isc (t ) = Csc (usc ) sc ï ï dt ï ï ï u ( t ) = R i ( t ) + usc (0) sc sc í sc ï ï usc (0) = Usc,max ï ï ï p (t ) = usc (t )isc (t ) ï ï ỵ SC (2.22) 2.2.5 Interleaved DC-DC converter modeling Non-isolated bidirectional DC-DC converter consists of parallel branches (also called Interleave DC-DC converter) suitable for high-power, high-voltage drives 2.2.5.1 Power circuit structure of Interleaved DC-DC converter with three switch branches Supercapacitor performs the process of energy charging / discharging through the Interleaved DC-DC converter with three switch branches as shown in Figure 2.24 8 Rectifier Electric  Source Induction motor Inverter AC DC Wheel Gear IM RD DC AC SCESS Converter DC SC DC HB1 SBK1 SBK2 SBK3 DBS1 iL SC HB3 HB2 DBS2 DBS3 RL1,L1 RL2,L2 UDC-link CDC Csc RL3,L3 esr RSC usc SBS1 SBS3 SBS2 DBK1 DBK2 DBK3 Fig 2.24 Power circuit structure of Interleaved DC-DC converter The configuration of Interleaved DC-DC converter includes half-bridges (HBs) in parallel, as shown in Figure 2.24 with three parallel H-bridge halves: HB1, HB2, HB3 In order to SCESS charges/discharges according to the train characteristics, the Interleaved DC-DC converter needs to work in two modes: Boost mode, Buck mode 2.2.5.2 Modeling bidirectional DC-DC converter with one switch branch The Interleaved DC-DC converter operates with assumptions: IGBTs are ideal, converter operates in continuous current mode; conventionally, current positve direction flowing through the inductance coil regards as charge state of SC, and vice versa regards as discharge state, the current mode of Interleaved DC-DC converter is equivalent with the current mode of DC-DC converter with one switch branch as shown in Figure 2.30a and apply the small - signal averaged method to model Interleaved DC-DC converter The averaged representation of the bi-directional switching power-pole in fig.2.30a is an ideal transformer shown in fig.2.30b with a turns -ratio 1:d(t), where d(t) represents the duty-ratio of IGBT Boost Buck + D BS RL,L S BK iL C RL UDC- + link S BS D BK q = -q q Fig.2.30a Average dynamic model of the switching power-pole with bi-directional power flow In fig.2.31, applying the Kirchhoff's fisrt, describled as follow: RSC Csc usc - L iL i1 (t ) i2 (t ) - u2 (t ) d(t):1 + iinv uDC -link + u1 (t ) ic - C - Fig 2.31 Equivalent electrical circuit of one switch branch bidirectional DC-DC converter averaged model second law; the state equation of converter is ì ï di (t ) R ï L = - L i (t ) + d (t )u ï (t ) - u (t ) ï L DC link ï L L L SC (2.24) í dt ï du (t ) ï ï i (t ) = ic (t ) + i2(t ) = DC -link - d (t )i (t ) ï L dt C ï ỵ inv Detail control design of Interleaved DC-DC converter is shown in chapter Conclusion chapter The content of Chapter presents the problem of modeling electric train and supercapacitor energy storage system (SCESS) In train modeling: Analysis of the forces acting on the train, regression of traction, electric braking force characteristics, building motion equation of train, motion equation of motor, calculating load torque In SCESS modeling, performing supercapacitor and Interleaved DC-DC converter modeling with switch branches The content of chapter presented in the work [6] under the list of published works of the author CHAPTER OPTIMAL CONTROL OF ENERGY CONSUMPTION OF ELECTRIFIED TRAIN INSTALLED SUPERCAPACITOR In chapter 3, the control structure of train operation energy is proposed with the goal of saving energy: Designing Interleaved DC-DC converter control enables SCESS to recuperate regenerative braking energy Using optimal algorithm determines train speed profile when train has integrated SCESS Traction substation B traction substation A Traction substation Voltage source inverter Braking resistor Electric source AC UDC-link DC IM AC wm,v Tm , v Wheel TL Resistance forces DC-DC Interleave DC Csc K usc FR Froll Fgrad esr RSC RU uDC-link PSC RD SC u*DC-link Traction motor DC iL* DC iL RI Traction motor drive PWM POWER MANAGEMENT SYSTEM ( USING OPTIMAL CONTROL THEORY ) Traction, resistance,braking forces Parameters of train, speed, distance, running time Fig 3.1 The overall control structure of train operation energy 10 3.1 Control DC-DC Interleaved DC-DC converter * uDC -link + ‐ u iL* PI + 1/3 ‐ iL1 PI + _ + CARRIER ‐ iL2 120 deg phase delay + _ ‐ iL3 PI + _ CARRIER SBK2 SDK2 CARRIER + 240 deg phase delay PI SBK1 SDK1 CARRIER DC -link SBK3 SDK3 Fig 3.6 Two -loop cascaded control structure for Interleaved DC-DC converter Designing control law for Interleaved DC-DC converter structure according to average current mode, with PI controllers both inner-loop and outer-loop 3.1.1 Design of current - loop controllers The goal is to design the controllers so that the average current flowing through the inductance coil iL tracks a certain reference iL* Designing the inner-loop is in three steps Step 1: Determine the state equation of the bi-directional DC-DC converter in the average model rewritten as follows: ìïdi (t ) ïï L = - RL i (t ) + d(t )u (t ) - uSC (t ) L DC link ï dt L L L í ïïduDC -link (t ) 1 = - d (t )iL (t ) + iinv (t ) ïï dt C C ïỵ (3.1) Step 2: Determine the operating points by giving the left derivative of equation (3.1) equal to zero and the quantities are in the steady state ì ï -RL U ï 0= I Le + U DC -link e D - SC ï ï L L L (3.2) í ï i inv ï 0= I D+ ï ï C Le C ï ỵ Solving equation (3.2) finds operating points (I Le,U DC -link e ) corresponding to measured voltage of supercapacitor U SC and duty-ratio D Step 3: Linearize the first equation of equations (3.1) Since the model (3.1) is nonlinear, it is recommended to design the controllers according to linearization method around the operating point The transfer function between the inductor current and the duty-ratio considered on the small-signal domain is calculated as follows: i (s ) U DC -linke / RL kC G dd (s ) = L = = d (s ) L TC s + ( s + 1) RL (1.5) 11 Where: kC = U DC -linke L ; TC = RL RL Beacause the transfer function (3.6) has a first-order, the PI controller may be effectively used to ensure both zero steady-state error and controlled bandwidth With the PI set, the controller is described as follows: Rdd (s) = k pC (1 + Gkin _ dd (s ) = TIC s )= k pC (1 + TIC s ) TIC s G dd (s )Rdd (s ) + TIC s = + G dd (s )Rdd (s ) TICTC s + TIC (1 + )s + k pC kC k pC kC (3.7) (1.6) ì ï L ï TIC = ï ï RL k pC ,TIC can be found : ïí ï L ⋅ 104 ï k pC = ï ï ⋅U DC -linke ï ỵ 3.1.2 Design voltage-loop - control UDC-link * Designing the voltage-loop is to control the voltage uDC -link sticking value uDC with -link * uDC being constant by the nominal working voltage according to the traction power -link standard EN 50163 and IEC 60850 Designing control is the same current loop; the transfer function between DC-link voltage and inductor current is: Gda (s ) = where: kV = uDC -link (s ) kV = iL (s ) TV s + (1.7) U SC CU DC -link ;TV = I inve I inve Similar to current-loop, designing PI controller for voltage-loop is in the form: k (1 + TIV s ) ) = pV (1.8) Rda (s) = k pV (1 + TIV s TIV s The closed-loop transfer function becomes: G da (s )Rda (s ) + TIV s = Gkin _ da (s ) = + G da (s )Rda (s ) TIVTV s + TIV (1 + )s + k pV kV k pV kV k pV ,TIV ì ï CU DC -linke ï TIV = ï ï I inve can be found: ïí ï CU DC -linke ⋅ 103 ï k pV = ï ï 2U SC ï ï ỵ (1.9) 12 3.1.3 Verifyting the design of the Interleaved DC-DC converter Through simulation results figures 3.7, 3.8, and 3.9 having validated the design of the two control loops of charge-discharge modes of supercapacitors according to the operating characteristics of train The train's trip time from Cat Linh to La Thanh station is 68s, when the train operates in accelerating mode from to 28s, the current on supercapacitors is positive, it shows that the supercapacitors are discharging to support the train in traction mode; from 28 to 48s supercapacitor current is equal to zero, respectively, the train operates in coasting mode; from 48 to 68s train operates in the braking mode, the current on supercapacitors is negative SOC% 80 79 78 77 10 20 30 40 50 60 68 Time(s) 700 Usc IL [A] 600 500 400 300 10 20 30 40 50 40 50 60 68 Time(s) 1000 isc 500 Time(s) -500 -1000 10 20 30 Time(s) 60 68 Fig.3.7 Values of current iL in each Fig.3.8 State of charge, voltage, current of a SC module in a process of running branch and total current train Fig 3.9 Charge-discharge of supercapacitor when train integrates SCESS With different train operation speeds, psc (t ) obtained in charge-discharge mode also has different values 3.4 Designing a problem of optimal control of train motion according to Pontryagin' maximum principle Using Pontryagin's maximum principle determines optimal speed profile, thereby determining the saving energy compared to the speed control profile without control 13 3.4.1 Optimal control of train operation energy according to PMP 3.4.1.1 Performing motion equations and objective function In the case of a train using On-board SCESS, the train's equation of motion is shown again as follows: ìï dt ïï = ïdx v í ïï dv p (v, t ) = utr ftr (v ) - ubr fbr (v ) + sc - w (v ) - fgrad (x ) ïïv v ïỵ dx (3.54) In equation (3.54), psc depends on the speed and trip time However, in order to design the optimal control for running energy consumption easily, psc only represents the time state variable t: psc (t ) With train specifications, and route survey, boundary conditions are defined: ìï0 £ v(x ) £ V (x ) ïï ïí0 £ t (x ) £ T d ïï ïï0 £ x £ x f ỵ ìv(0) = 0; v(x ) = (3.55) ï f ï í ïït(0) = 0; t(x f ) = Td ỵ (3.56) Constraints: ì ï 0£u £1 ï tr ï ï0 £ u £ í br ï ï u > or u > Either ï ï tr br ỵ (3.57) Speed profile comprises of modes: Accelearating  Coasting  Braking Where: V x - the maximum allowable speed, x f - length of distance () (3.58) v (0) - speed at the beginning, v (x f ) - speed at the end of the route Td - Duration of the trip is also given by the timetable Limits of traction and braking force: £ Ftr (v) £ Ftr max (v); £ Fbr (v) £ Fbr max (v) (3.59) supercapacitor power per ìï P (t ) ïï-e sc ïï m psc (t ) = íï ïï ïï Psc (t ) ïïe ïỵ m unit mass psc (t ) is given: t1 £ t £ t2 (Discharge time) t2 < t £ t (Coasting time) t3 < t £ t4 (Charge time) * (3.60) * Problem set: Find optimal control variables utr , ubr and optimal motion trajectories * * of the train v (x ) , t (x ) , according to the state equation (3.48) to ensure the optimal standard of train operation energy Ae is minimal with boundary conditions (3.49), (3.50); constraints (3.51), (3.52); limit control forces (3.53) 14 In case of ensuring the trip time in the station is Td (known in advance), calling the actual trip time is Ta , we have to add the boundary condition of the objective function: (Ta -Td )  (3.61) To ensure the fixed trip time, adding Lagrange multiplier, we have the objective function to consider regenerative energy recuperation: x x é é ù p (t ) l ù l J = ò êutr ftr (v ) + ú dx + ò psc dx = ò êêutr ftr (v ) + sc + úú dx  (3.72) ê v úû v v vû 0 ë ë When applying the Lagrange multiplier method, it is necessary to combine the objective function with the boundary conditions to transfer the problem of non-binding optimization, then there must be more conditions: xf f f ¶J = hay Ta -Td = ¶l Ta ò dt -T d =0 (3.73) In equation (3.73), l does not appear explicitly, so it cannot be solved directly from this equation Therefore, the algorithm to determine Lagrange multiplier will be presented in the next section 3.4.2.2 Speed trajectory optimality of a train based on PMP The Pontryagin's maximum principle is applied to solve energy efficient operation problems by finding the optimal transfer points of operating modes from which the energy optimal operating trajectory of the train is obtained Figure 3.11 shows the train running cycle with three modes: Accelerating  Coasting  Braking vt(km/h) vh vb Accelerating Braking Coasting tc,xc ta,xa xh tb,xb xb x (m) Fig 3.11 Running Characteristic of a train Combined (3.48) to (3.54) Hamiltonian function is written: psc (v, t ) l + ) v v æ u f (v ) + psc (v, t ) / v - ubr fbr (v ) - w (v ) - fgrad (x )ữử +p1 + p2 ỗỗỗ tr tr ữữữ ỗố v v ữứ where p1, p2 are adjoint variables H = -(utr ftr (v ) + (3.74) 15 Adjoint variable differential equations are reformed: dp1 dp (v, t ) ¶H dpsc (v, t ) p2 ổỗdpsc (v, t )ửữ ữữ = (1 - p) sc == - ỗỗ ảt dx v dt v ỗố dt ứữ v dt (3.75) ộ ảf dp2 p lù p ¶H == êêutr tr - sc2 - úú + 21 dx v v û v ¶v ë ¶v p + 22 éëêutr ftr (v ) + psc (t ) / v - ubr fbr (v ) - w (v ) - fgrad (x )ùûú v p é ¶f p ¶f ¶w ùú - êêutr tr - sc2 - ubr br v ë ¶v v ¶v ¶v úû (3.76) Substitute p = p2 , so p ⋅ v = p2 v ì ï dp2 ¶H ï =ï ï dx ¶v ï ï í p (t ) ï utr ftr (v) + sc - ubr fbr (v) - w (v) - fgrad (x ) ï dv ï v = ï ï v ï ỵdx d(p ⋅ v) dv dp dp2 =p +v = dx dx dx dx dp dp2 dv v = -p dx dx dx (1.10) (1.11) (1.12) Hamiltonian function is reformulated as: H = (p - 1)utr ftr + (p - 1) psc l p - pubr fbr - p(w + fgrad ) - + v v v (3.80) Hamilton function reachs maximum value according to two control variables utr , ubr , the components that not contain utr , ubr can be removed, then only: H ' = (p - 1)utr ftr - pubr fbr = utr (p - 1)ftr + ubr (-pfbr ) ¾¾¾ ¾  max u ,u tr br (3.81) Two control variables utr , ubr found for the maximum H function will be: utr £ p £1 p 1 { } max {0, - sgn( f )} max {0, - sgn( f )} max 0, - sgn( ftr ) ubr max {0, - sgn( ftr )} tr max {0, - sgn( ftr )} tr max {0, - sgn( ftr )} From the above analysis, five optimal control laws are designed:  Full power (FP): utr = 1, ubr = when p >  Partial power (PP): utr Ỵ [0,1] , ubr = when p =  Coasting (C): utr = 0, ubr = when < p <  Full braking (FB): utr = 0, ubr = when p < 16  Partial braking (PB): utr = , ubr Ỵ [0,1] when p = Substitute Error! Reference source not found., (1.11) in (1.12) finding the differential equation for p (p - 1) dp (1 - p) p p l p1 ¢ ¢ ( ) ( ) ( ) = utr ftr¢(v ) + p t + u f v + w v (3.83) sc dx v v3 v br br v v3 v3 Full power mode: p > 1, ubr = 0, utr = 1, finding accelerating time ta , accelerating distance x a , multiplier l Using equation Error! Reference source not found (p - 1) dp (1 - p) p l p = ftr¢(v ) + psc (t ) + w 0¢(v ) - - 31 dx v v v v v From (3.48) determining x a , ta : ì ï dx v2 ï = ï ï v ⋅ utr ftr (v ) + psc (t ) - v ⋅ w (v ) - fgrad (x ) ⋅ v ïdv í ï dt v ï =ï ï v ⋅ utr ftr (v ) + psc (t ) - v ⋅ w (v ) - fgrad (x ) ⋅ v ï ỵdv (3.84) (3.85) With initial conditions: x(0)=0; t(0)=0 Partial power mode: p = 1, ubr = 0, < utr < , so dp = 0, findinf Lagrange dx multiplier l Using equation (3.83): l p w 0¢(v ) - - 31 = v v v dp1 = 0, easily, p1 is chosen by 0, so From (3.75), then dx l = v 2w0¢ (3.86) (3.87) Therefore, l = v (b + 2cv ) If l (3.88) is chosen previously, solve (3.88) to find the hold -speed vh Coasting mode: utr = 0, ubr = 0, < p < , finding braking speed vb, coasting time tc, coasting distance xc Coasting speed vb is calculated as following [41,88] vb = y(vh ) j ¢(vh ) (3.89) Where: j = v ⋅ w0 (v), y = v ⋅ w0¢(v) From (3.54) finding xc,tc 17 ì ï dx v ï = ï ï -w (v ) - fgrad (x ) ïdv í ï dt ï =ï ï w (v ) + fgrad (x ) ï ỵdv With t (v = vh ) = ta ; x (v = vh ) = x a (3.90) Partial braking mode (PB): utr = 0, < ubr < 1, p = finding l Using equation (3.83) - l p1 ( ) p t - =0 v sc v3 v3 (3.91) Therefore, l = -psc (t ) - p1 (3.92) Full braking mode (FB): utr = 0, ubr = 1, p < 0, finding braking time tb, braking distance xb Using equation (3.84) dp (p - 1) p p l p = psc (t ) + fbr¢(v ) + w 0¢(v ) - - 31 dx v v v v v (3.93) From (3.54) finding tb, xb ì ï dx v2 ï = ï ï -v ⋅ ubr fbr (v ) - v ⋅ w (v ) + psc (t ) - v ⋅ fgrad (x ) ïdv í ï dt ï = ï ï ubr fbr (v ) - w (v ) + psc (t ) / v - fgrad (x ) ï ỵdv with t (v = vb ) = tb , x (v = vb ) = x b (3.94) Conclusion chapter In Chapter 3, designing the control structure of the Interleaved DC-DC converter ensures the charge-discharge process of supercapacitors, applying the Pontryagin's maximum principle to find the optimal switch points; from there, finding the optimal speed profile The results of chapter are presented in [1,2,4,5, 6,7,8,9] in the list of published works of the author CHAPTER SIMULATION AND EXPERIMENT RESULTS The simulation results on MATLAB/Simulink software will be presented in this chapter to verify the theoretical research results:  Effectiveness of SCESS in energy recuperation in braking mode;  Comparison energy efficiency of train operation with /without PMP;  Experimental results verify the working capability of the Interleaved DC-DC converter 18 (m/s) 4.1 Off-line simulation The simulation results of the control design mentioned in chapters and have two problems 4.1.1 Simulation Program of the electric train system installed On-board SCESS on Cat Linh-Ha Dong line The simulation results of operation modes of T1 train and T2 train are conducted with scenarios that fully demonstrate train operation situations on the following areas: Scenario 1: T1 train operates in braking mode t = 48s; T2 train begins operating in accelerating mode Speed profile of T1,T2 (m/s) 20 15 10 train train 00 20 40 20 40 1000 60 80 100 120 140 160 80 100 120 140 160 DC-link voltage [V] (V) 800 600 400 200 00 60 Time (s) Fig 4.5 Dynamic behavior of DC-link voltage when T1 braking and T2 accelerating Energy loss of braking resistor of T1 without SCESS(Wh) 150 100 100 75 50 25 50 -50 Energy loss of braking resistor of T2 without SCESS(Wh) 125 20 40 60 80 100 120 140 160 Energy consumption of line source supplied T1 without SCESS (Wh) 4000 3000 2000 1000 00 20 40 60 80 Time(s) 100 120 140 160 0 20 40 60 80 100 120 140 160 Energy consumption of line source supplied T2 without SCESS (Wh) 2500 2000 1500 1000 500 0 20 40 60 80 100 120 140 160 Time(s) Fig.4.6 Energy behaviors of T1 without Fig.4.7 Energy behaviors of T2 without SCESS, when T1 braking and T2 SCESS, when T1 braking and T2 accelerating accelerating Fig.4.5, fig.4.6, fig.4.7 show voltage behavior of DC-link fluctuating from 700 to 900VDC, and energy loss of braking resistors of T1 and T2 is 4,3% Scenario 2: Both T1 and T2 operate in accelerating mode Fig 4.8 shows that UDC-link fluctuates in the range of 490 VDC to 900 VDC compared to the scenario The loss on the braking resistor of T1 and T2 is: 450 (Wh) / 4700 (Wh) = 9.6% shown in Fig 4.9, Fig.4.10 19 Speed profile T1,T2 (m/s) 20 train 15 train 10 00 20 40 60 80 100 120 140 160 140 160 DC-link voltage [V] 1400 1200 1000 800 600 400 200 0 20 40 60 80 100 120 Time [s] Fig.4.8 UDC-link behavior when T1 and T2 accelerating 600 Energy loss of braking resistor of T1 without SCESS(Wh) 500 400 450 300 300 150 -200 200 100 20 40 60 80 100 120 140 0 160 20 40 60 80 100 120 140 160 Energy consumption of line source supplied T2 without SCESS (Wh) Energy consumption of line source supplied T1 without SCESS (Wh) 6000 6000 4500 4500 3000 3000 1500 1500 0 Energy loss of braking resistor of T2 without SCESS(Wh) 20 40 60 80 100 Time (s) 120 140 0 160 20 40 60 80 100 120 140 160 Time (s) Fig 4.9 Energy behavior of T1 when T1 Fig 4.10 Energy behavior of T2 when T1 and T2 are in accelerating mode and T2 are in accelerating mode Scenario 3: T1, T2 operate together in accelerating mode, the tration drive system integrated SCESS Fig.4.11 to Fig.4.13 show that U DC -link fluctuates in the range of 730 VDC to 770VDC, the loss on the braking resistor 12 (Wh) / 2400 (Wh) = 0.05% Thus, the regenerative braking energy part during braking mode was recovered by supercapacitors up to 9.6% Speed profile T1,T2 (m/s) 20 train train 15 10 0 20 40 60 80 100 120 140 160 120 140 160 DC-link voltage(V) 900 850 800 750 600 550 500 00 20 40 60 80 100 Time [s] Fig 4.11 UDC-link behavior when T1 and T2 accelerate and the train installs SCESS 20 Energy loss of braking resistor of T2 with SCESS(Wh) Energy loss of braking resistor of T1 with SCESS(Wh) 15 10 10 5 0 3000 20 40 60 80 100 120 140 160 Energy consumption of supply line supplied T1 with SCESS (Wh) 20 40 60 80 100 120 140 160 Energy consumption of supply line supplied T2 with SCESS (Wh) 3000 2000 2000 1000 1000 0 20 40 60 80 100 120 140 160 Time (s) 20 40 60 80 100 120 140 160 Time (s) Fig 4.12 Energy behavior of T1 when T1 Fig 4.13 Energy behavior of T2 when and T2 are in accelerating mode and T1 and T2 are in accelerating mode and integrated with SCESS integrated with SCESS 4.1.2 The optimal speed profile simulation program for train operation on Cat Linh - Ha Dong line applied PMP with electric train system integrated SCESS on-board Cat Linh-Ha Dong urban electric train line has 12 stations (corresponding to 11 areas), total length is 12.662 km, the train runs from the first station: Cat Linh, to the last station: new Ha Dong bus station a) A survey the train operation energy when the train does not have SCESS  A survey of energy consumption for running train from Cat Linh-La Thanh Fig 4.16 A comparison of optimal speed profile with original speed profile with/without PMP Fig 4.17 A comparison of distance versus time Fig 4.19 A comparison of energy consumption levels of train operation with/without PMP The survey of energy consumption for the next station is similar to the first station Fig.4.18 A comparison of speed versus time with/without PMP 21 Fig 4.60 A Comparison of optimal speed profile and original speed profile of 12 stations Fig 4.61 A Comparison of Optimal time profile and original time profile of 12 stations Table 4.3 Results of a comparison of energy consumption with / without energy optimization strategy PMP Inter-station length Actual Optimal Distance Pratical energy trip Optimal energy trip (m) consumption time consumption(kWh) time (s) (kWh) (s) Cat Linh-La 931 19.5 66 18.59 Thanh La Thanh -Thai 902 10.94 79 9.7 Ha Thai Ha-Lang 1076 10.5 95 9.8 Lang-VNU 1248 9.9 124 9.5 VNU- Ring road 1010 17.4 77 15.4 Ring road 31480 17.4 105 15 Thanh Xuan Thanh Xuan-Ha 1121 17.6 86 15.7 Đong BS Ha Đong BS -BV 1324 19.6 98 16.6 Ha Đong BV Ha Đong -La 1110 17.8 83 15.7 Khe La Khe-Van Khe 1428 18.2 103 15.7 Van Khe-new Ha 1032 17.4 72 15.5 Dong BS Total: 12662 176.24 988 157.19 Total consumed energy when PMP is not applied: 176.24 kWh; 68 81 97 126 78 107 87 100 85 105 74 1010 22 Total consumed energy when PMP is applied: 157.19kWh; energy saving: 10.8%; But the trip time lasts additionally seconds b) Conducting a survey of energy consumption when electric trains integrate SCESS, and ensure the fixed trip time by changing the Lagrange multiplier In this problem, consider a station, from Cat Linh - La Thanh station with a distance of 931m, trip time 68s Total consumed energy when PMP is not applied: 19.5kWh Total consumed energy when PMP is applied: 18.57kWh (saving 4.6%) Total consumed energy when applying PMP and having SCESS is 16.53 kWh (saving 15.2%), see Figure 4.66 Fig.4.62 Discharge/charge power of supercapacitor energy storage system Fig.4.63 A comparison of optimal speed profile with original speed profile Fig 4.65 A comparison of energy consumption levels of train operation with/without PMP Fig 4.64 A comparison of speed versus time Fig.4.66 A comparison of energy consumption levels of train operation with/without PMP and onboard supercapacitor energy storage system 23 Comment: Depending on modes of train operation, survey of train schedule, number of passengers, infrastructure of the route , which selects appropriate energy saving solutions 4.2 Designing experimental model of SCESS Designing the experimental model of electric train with SCESS is very expensive and complicated, so the author only designs the Interleaved DC-DC converter with switch branches in the working modes: Buck (charge) - Boost (discharge) in order to verify advantages of this converter Fig 4.69 SCESS experimental system Fig.4.71 PWM with d=0.625 Fig.7.42 Conductance coil currents cảm Fig.7.45 Conductance coil current with d=0.33 with d=0.625 Conclusion chapter Off-line simulations have demonstrated SCESS's role in saving energy for train operation by recovering regenerative braking energy, and contributing to voltage stability on the DC bus, the ability to apply optimal theory in saving energy Theses simulations create a premise for the application of solutions to use energy efficiency for Vietnam urban railway trains in the coming time The results of chapter are presented in the project [7,8,9] under the list of published works of the author 24 CONCLUSIONS AND RECOMMENDATIONS The thesis is the first research in Vietnam to address the issue of energy saving for urban electric train operation In this section, the author summarizes the new contributions of the thesis as well as points out the next development direction of the thesis Novelty contributions of the thesis  To propose the use of SCESS on-board integrated with traction motor drive via bidirectional DC-DC converter and design supercapacitor control according to train running characteristics  Applying the Pontryagin's maximum principle finds optimal transfer points of operating modes, determining the optimal speed profile of trains intergrated with SCESS on-board Recommendations and further research directions Some issues can be researched further to complete the thesis  Researching and combining supercapacitor energy storage device with high energy density storage systems such as batterry, flywheel, to expand the capacity of energy storage suitable for many different control strategies  Applying other control methods such as dynamic programing, weighting function method with the multi-objective problem to determine the optimal speed profile  Developing optimal control algorithm regulates many trains running on the route  Optimal control of energy operation when the train goes on the routes with slope changes  Optimal control of train operation when the speed profile vs time has S-curve shapes in both acceleration and braking processes  ... 66 18.59 Thanh La Thanh -Thai 902 10.94 79 9.7 Ha Thai Ha-Lang 1076 10.5 95 9.8 Lang-VNU 1248 9.9 124 9.5 VNU- Ring road 1010 17.4 77 15.4 Ring road 31480 17.4 105 15 Thanh Xuan Thanh Xuan-Ha... Technology: Learning about technology of electric train operation in some urban railway lines in Vietnam; namely, urban railway of Cat Linh - Ha Dong line  Energy conversion system on electric trains:... sin(arctan(ik )) ik (‰)is the ratio of slope height to slope, a is the slope of the track 2.1.1.2 Dynamic equation of the train The motion equation of the train is often transformed into its own form