Railway Power Network Simulation and Optimisation Dr Zhongbei Tian - PowerPoint PPT Presentation

Railway Power Network Simulation and Optimisation Dr Zhongbei Tian Email: z.tian@bham.ac.uk

Background  Good transport is critical to the economic growth and the success of cities;  Energy consumption is becoming a significant concern for modern railway operation;  There is an opportunity to improve the energy consumption of the system through analysis, simulation and optimisation of both static and dynamic design parameters.

Contents  Energy flow in DC rail systems  Simulation development - Mathematical modelling  Using the simulator:  1. Understand the rail power systems  2. Energy evaluation  3. Energy optimisation

System Energy Flow Chart

Simulation structure

Train movement simulation d 2 𝑡 𝑁 𝑓 d𝑢 2 = 𝐺 − 𝑁𝑕sin 𝛽 − 𝑆 n o i t c e r i D F 𝑁 𝑓 = 𝑁 𝑢 × 1 + 𝜇 𝑥 + 𝑁 𝑚 R α 2 𝑆 = 𝐵 + 𝐶 d𝑡 d𝑢 + 𝐷 d𝑡 + 𝐸 d𝑢 𝑠 Mg

Train movement simulation 𝐺 𝑤 < 𝑤 1 𝑛 v 1 F m 𝐺 𝑛 × 𝑤 1 𝑤 1 < 𝑤 < 𝑤 2 𝐺 𝑤 = 𝑤 𝐺 𝑛2 × 𝑤 2 2 𝑤 2 < 𝑤 < 𝑤 3 𝑤 2 𝐺 𝑛2 = 𝐺 𝑛 × 𝑤 1 v 2 F m2 𝑤 2 v 3 Zone 1 Zone 2 Zone 3 𝑄 𝑛𝑓_𝑛𝑏𝑦 = 𝐺 𝑛 × 𝑤 1

Train movement simulation Motoring Coasting 𝐺 > 𝑁𝑕sin 𝛽 + 𝑆 Cruising speed point 𝑏 = 𝐺 − 𝑁𝑕sin 𝛽 − 𝑆 ൞ Cruising 𝑁 𝑓 point Braking speed Cruising ቊ 𝐺 = 𝑁𝑕sin 𝛽 + 𝑆 Braking 𝑏 = 0 point 𝐺 = 0 Coasting 𝑏 = −𝑁𝑕sin 𝛽 − 𝑆 ቐ 𝑁 𝑓 𝐺 < 0 Braking 𝑏 = 𝐺 − 𝑁𝑕sin 𝛽 − 𝑆 ቐ 𝑁 𝑓

Power network simulation

Rectifier substation V 𝑡𝑣𝑐 = V no−load − R × I 𝑡𝑣𝑐

Rectifier substation circuit Contact line system R sub V sub Contact line system Return rails R sub V sub R big Return rails Contact line system R sub V sub Return rails

Traction train current limit I train_max I max Under-voltage Normal traction traction No traction Zone 1 Zone 2 Zone 3 I aux V train V min2 a × V n V max2 𝐽 𝑏𝑣𝑦 𝑗𝑔 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑊 𝑛𝑗𝑜2 𝑊 𝑢𝑠𝑏𝑗𝑜 − 𝑊 𝑛𝑗𝑜2 + 𝐽 𝑏𝑣𝑦 𝑗𝑔 𝑊 𝑛𝑗𝑜2 < 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑏 × 𝑊 𝑜 𝑠 𝐽 𝑢𝑠𝑏𝑗𝑜_𝑛𝑏𝑦 = 𝑢𝑠𝑏𝑑_𝑓𝑟 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒_𝑛𝑏𝑦 𝑗𝑔 𝑊 𝑢𝑠𝑏𝑗𝑜 > 𝑏 × 𝑊 𝑜 𝑊 𝑢𝑠𝑏𝑗𝑜

Traction train power limit P train_max P train_demand_max Under-voltage Normal traction traction No traction Zone 1 Zone 2 Zone 3 P aux V train V min2 a × V n V max2 𝑄 𝑗𝑔 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑊 𝑏𝑣𝑦 𝑛𝑗𝑜2 (𝑊 𝑢𝑠𝑏𝑗𝑜 −𝑊 𝑛𝑗𝑜2 ) × 𝑊 𝑢𝑠𝑏𝑗𝑜 + 𝑄 𝑗𝑔 𝑊 𝑛𝑗𝑜2 < 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑏 × 𝑊 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑛𝑏𝑦 = 𝑏𝑣𝑦 𝑜 𝑠 𝑢𝑠𝑏𝑑_𝑓𝑟 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒_𝑛𝑏𝑦 𝑗𝑔 𝑊 𝑢𝑠𝑏𝑗𝑜 > 𝑏 × 𝑊 𝑜

Traction train circuit limit V train R sub R catenary I train 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒 = 𝑄 𝑢𝑠𝑏𝑗𝑜 = 𝐽 𝑢𝑠𝑏𝑗𝑜 × 𝑊 𝑢𝑠𝑏𝑗𝑜 P train V sub I train V train 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒 > 𝑄 𝑢𝑠𝑏𝑗𝑜 = 𝐽 𝑢𝑠𝑏𝑗𝑜 × 𝑊 R sub R catenary 𝑢𝑠𝑏𝑗𝑜 r trac_eq I aux 𝐽 𝑢𝑠𝑏𝑗𝑜 = 𝐽 𝑏𝑣𝑦 + 𝑊 𝑢𝑠𝑏𝑗𝑜 − 𝑊 V sub 𝑛𝑗𝑜2 V min2 𝑠 𝑢𝑠𝑏𝑑_𝑓𝑟

Braking train current limit V max1 V max2 V n V train Zone 1 Zone 2 I regen_over_max overvoltage Normal regen regen I train_max 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒_𝑛𝑏𝑦 𝑗𝑔 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑊 𝑛𝑏𝑦1 𝑊 𝑢𝑠𝑏𝑗𝑜 𝐽 𝑢𝑠𝑏𝑗𝑜_𝑛𝑏𝑦 = 𝑊 𝑢𝑠𝑏𝑗𝑜 − 𝑊 𝑛𝑏𝑦2 𝑗𝑔 𝑊 𝑛𝑏𝑦1 < 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑊 𝑛𝑏𝑦2 𝑠 𝑐𝑠𝑏𝑙𝑓_𝑓𝑟

Braking train power limit V n V max1 V max2 V train Zone 1 Zone 2 P train_demand_max Overvoltage Normal regen regen P train_max 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒_𝑛𝑏𝑦 𝑗𝑔 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑊 𝑛𝑏𝑦1 (𝑊 𝑢𝑠𝑏𝑗𝑜 − 𝑊 𝑛𝑏𝑦2 ) × 𝑊 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑛𝑏𝑦 = ൞ 𝑢𝑠𝑏𝑗𝑜 𝑗𝑔 𝑊 𝑛𝑏𝑦1 < 𝑊 𝑢𝑠𝑏𝑗𝑜 ≤ 𝑊 𝑛𝑏𝑦2 𝑠 𝑐𝑠𝑏𝑙𝑓_𝑓𝑟

Braking train circuit V train R sub R catenary I train 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒 = 𝑄 𝑢𝑠𝑏𝑗𝑜 = 𝐽 𝑢𝑠𝑏𝑗𝑜 × 𝑊 𝑢𝑠𝑏𝑗𝑜 P train V sub I train V train 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒 > 𝑄 𝑢𝑠𝑏𝑗𝑜 = 𝐽 𝑢𝑠𝑏𝑗𝑜 × 𝑊 𝑢𝑠𝑏𝑗𝑜 R sub R catenary r brake_eq 𝐽 𝑢𝑠𝑏𝑗𝑜 = 𝑊 𝑢𝑠𝑏𝑗𝑜 − 𝑊 𝑛𝑏𝑦2 V sub V max2 𝑠 𝑐𝑠𝑏𝑙𝑓_𝑓𝑟

Equivalent circuit

Traditional power flow solver V train (𝑊 𝑓𝑟 −𝑊 𝑢 )  𝑄 𝑢 = × 𝑊 r eq 𝑢 I train 𝑠 𝑓𝑟 V eq  𝑄 𝑢 is known P train  𝑊 𝑢 ?  Newton-Raphson iterative method  Point-Jacobi method  Zollenkopf’s bifactorisation  Incomplete Cholesky Conjugate Gradient

Current-vector iterative method V train  Step 1: Initialise all the train voltage r eq (0) = 𝑊 𝑊 I train 𝑢𝑠𝑏𝑗𝑜_𝑜 𝑡𝑣𝑐 V eq  Step 2: Calculate the train current at next iteration P train = 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑒𝑓𝑛𝑏𝑜𝑒_𝑜 (1) 𝐽 𝑢𝑠𝑏𝑗𝑜_𝑜 (0) 𝑊 𝑢𝑠𝑏𝑗𝑜_𝑜  Step 3: Update nodal voltages by nodal analysis 𝑊 (1) = 𝑍 −1 × 𝐽 (1) (1) (1) 𝑊 = 𝑊 𝑓𝑟_𝑜 − 𝑠 𝑓𝑟_𝑜 × 𝐽 𝑢𝑠𝑏𝑗𝑜_𝑜 𝑢𝑠𝑏𝑗𝑜_𝑜  Step 4: Calculate train power at this iteration (1) = 𝑊 (1) × 𝐽 𝑢𝑠𝑏𝑗𝑜_𝑜 (1) 𝑄 𝑢𝑠𝑏𝑗𝑜_𝑜 𝑢𝑠𝑏𝑗𝑜_𝑜  Step 5: Criteria check . If not, repeat the above steps.

Traction train power flow P train P=1/r eq × (V eq -V t ) × V t P=I × V P train_demand (2) P t (1) P t V train V (0) V (2) V (1) V eq

Braking train power flow P train P=1/r eq × (V eq -V t ) × V t V eq V train V (2) V (1) V (0) (2) P t P train_demand (1) P t P=I × V

Piecewise nonlinear circuit solver  Traction train model  Under-voltage traction  Normal traction  Regen train model  Normal regen  Over-voltage regen

Load solver structure start Data from STMS Power network data Formulate admittance matrix Load flow solver Change model All substations No switch on Converge? All braking trains Yes set to over-voltage Yes Over-voltage? No Yes Over-power? No Yes Under-voltage? No Yes Over-power? No Yes Substation? No End

Using the simulator  To apply the University of Birmingham Multi-Train Simulator at existing or expected rail routes to assist the understanding of the existing power supply network system performance ：  Normal operation;  Energy consumption;  Shut down a traction power substation (TPSS);  Short circuit;  The developed simulation will be further used to optimise the train driving and operation systems for energy saving or delay reduction.

SMRT East West MRT line  East West MRT line is a suburb commuter railway line;  Connecting from Boon Lay to Airport or Pasir Ris, total length 29km, 750V third-rail power supply system;  The line is equipped with 23 substations, 8 tie stations and 2 stations without DC-link connection

Speed trajectory Figure SMRT East-West Train Operation -East Bound-

Normal operation VS disturbed operation Train interaction Reduced service interval Minimum train voltage: 639 V. Please see Figure 10 for details Under-voltage

Under-voltage operation I train_max 645.3 V I max Under-voltage traction 1000 V No traction Normal traction 500 V Zone 2 I aux Zone 3 Zone 1 Under-voltage V train limitation: 645.3 V V min2 a × V n V max2 Figure 2. Current limitation of traction train Figure 1. Trains operated at under-voltage

Shut Down a TPSS  A traction power substation (TPSS) could be switched off when there is a fault current or in maintenance. The impact of TPSS outage on the network power consumption is evaluated in this section.  Simulation findings: 1. If one of TPSS is switched off, the energy consumption of this TPSS is zero. The energy consumption of TPSS around this fault TPSS increases. 2. The amount of energy consumption changing of working TPSS depends on the distance from the fault TPSS. The maximum variation happens on the nearest working TPSS. 3. If the fault TPSS supplied very large energy when it was on, the impact on the nearby TPSS will be significant when this fault TPSS is down.

Normal operation VS TPSS outage Network voltage decreases due to TPSS outage Figure 1 Network voltage against location Figure 3 Network voltage against location Figure 4 Train voltage against location Figure 2 Train voltage against location