Energy saving in metro systems: Simultaneous optimization of stationary energy storage systems and speed profiles

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Energy saving in metro systems: Simultaneous optimization of stationary energy storage systems and speed profiles Saeed Ahmadia, Ali Dastfanb,∗, Mohsen Assilib a

Department of Electrical and Computer Engineering, Faculty of Montazeri, Khorasan Razavi Branch, Technical and Vocational University (TVU), Mashhad, Iran Department of Electrical and Robotic Engineering, Shahrood University of Technology, Shahrood, Iran

b

A R T IC LE I N F O

ABS TRA CT

Keywords: Energy saving Optimal speed profile Metro Urban railway Stationary energy storage system Supercapacitor Optimization

High electric energy consumption is one of the main challenges of metro systems, which the operators deal with. Among several energy saving methods, this paper focuses on the simultaneous application of speed profile optimization and energy storage systems, to efficiently utilize regenerative braking energy. With this approach, a substantial reduction in energy was achieved for the case study of Mashhad LRT Line 1. In addition, because of the simultaneous utilization of the schemes, the required capacity of stationary energy storage systems was decreased in comparison with the case of normal (not optimized) speed profile. To demonstrate the validity of the proposed method, two procedures were done. First, the optimization of stationary supercapacitor energy storage systems was performed by using experimental results (real world, not optimized speed profiles) so that the total input energy would be minimized. In the second procedure, the optimal speed profiles were determined and optimum energy storage was recomputed. The results show a significant reduction of energy in the latter procedure, as well as lower energy storage system costs.

1. Introduction Urban electric rail transportation is developing in big cities because of features such as safety, high energy efficiency, high capacity, accuracy, punctuality and low environmental pollution. High energy consumption of this system is one of the challenges that has attracted many researchers. Two best measures to raise energy efficiency in these systems, especially the traction energy are first, energy saving, which in most of the previous researches has been equivalent with economic driving. The second solution is recovery of the regenerative braking energy of trains, which can be provided by trains' timetable adjustment, use of reversible substations to return the energy to upstream network and energy storage systems (ESSs) (Martinisa and Gallob, 2013), (Gonzalez Gil et al., 2014). In recent years, many studies have been performed on energy saving by optimal train driving. Most of these studies were conducted in single train systems. The optimal control theory and Pontryagin's maximum principle were used in (Scheepmaker and Goverde, 2015). Genetic algorithm (GA), simulated annealing (SA), ant colony optimization (ACO), decision theory and expert systems methods were also utilized for this purpose (Kim and Chien, 2011; Lu et al., 2013; Domínguez et al., 2011; Yin et al., 2014). In all of the above studies, travel time was assumed constant and it was attempted to optimize the movement of trains and minimize energy consumption by greater use of coasting mode. A single train system with multi-objective functions was considered and

∗

Corresponding author. E-mail address: [email protected] (A. Dastfan).

https://doi.org/10.1016/j.jrtpm.2018.03.003 Received 18 October 2017; Received in revised form 11 March 2018; Accepted 12 March 2018 2210-9706/ © 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: Ahmadi, S., Journal of Rail Transport Planning & Management (2018), https://doi.org/10.1016/j.jrtpm.2018.03.003

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optimization was done by using multi-objective optimization methods such as particle swarm optimization (PSO) and evolutionary algorithm (Chevrier et al., 2013; Domínguez et al., 2014; ShangGuan et al., 2015; Fernández-Rodríguez et al., 2015; Liu et al., 2015). The general goal was that in addition to minimizing the energy consumption, traveling time was also lowered. In other words, the energy-time Pareto front was determined. In all of the above researches, regenerative energy was not considered. In (Su et al., 2014), (Goodwin et al., 2015), which have studied multi-train systems, regenerative braking energy issue was not taken into account. An algorithm was presented for train trajectory optimization problem as a multi-phase optimal control model, which considered signaling, time and speed constraints (Wang and Goverde, 2016). Afterwards, a multi-train trajectory optimization method was proposed to minimize energy consumption and reduce delays (Wang and Goverde, 2017). Although operational constraints have been met, but the regenerative braking energy has not been considered. In (Su et al., 2015; Li and Lo, 2014; Zhao et al., 2017) while train speed profiles were optimized, recovery of regenerative braking energy was also maximized by timetables adjustment. An optimization method for multi-train network with regenerative braking system was proposed to solve the energy saving problem, and showed that by only minimizing traction energy of the trains, one cannot minimize the energy usage in whole system (Tian et al., 2017). A comprehensive review was done in (Yang et al., 2016), (Scheepmaker et al., 2017) on energy-efficient train operation methods, which could be used in driver advisory systems (DAS) or automatic train operation (ATO) systems. A complete comparison was made between direct and heuristic methods. Finally, it was concluded that the methods must be used with a trade-off between energy efficiency and traveling time in future researches. In the last studies, which are often known as energy-efficient train operation, although the issue of regenerative energy has been paid attention to, only acceleration and braking synchronization capability of trains were used. In relation to the use of ESSs, numerous studies were conducted, some of which such as (Devaux and Tackoen, 2014) compared different methods of reusing regenerative energy and a variety of ESSs. Stationary and onboard ESSs were compared in (Barrero et al., 2010). Control methods for charge and discharging of ESSs and their effect on raising energy efficiency were investigated, moreover, improving power quality parameters such as voltage fluctuations and the peak of substations power, were considered (Iannuzzi and Tricoli, 2012; Ciccarelli et al., 2012, 2014, 2016, 2017; Gao et al., 2014). Determination of the optimal size and location of the stationary ESSs was also studied. An analytical optimization method was proposed to determine an optimal design for stationary Lithium-ion Capacitor (LiC) ESSs in light electrical transportation systems (Ciccarelli et al., 2013). A method was introduced to predict the maximum instantaneous regenerative energy in each substation. Based on these values of regenerative energy, the appropriate stationary supercapacitor (SC) ESSs was determined for energy saving (Teymourfar et al., 2012). A method based on both power and capacity constraints of SC ESSs was introduced and showed that this approach could realize effective recovery of whole absorbed braking energy and have high energy-saving/weight ratio (Shen et al., 2012). A DC railway power flow algorithm was developed, considering stationary ESSs to calculate the optimal power and capacity of ESSs (Lee et al., 2011). Mixed integer linear programming was used to optimize the size of hybrid ESSs consist of batteries and SCs (de la Torre et al., 2015). The objective function was the minimization of total investment operating costs. SA GA optimization method was proposed for SC ESSs locating and sizing (Wang et al., 2014). The objective functions were energy saving rate, regenerative braking cancelling rate and installation costs. A cost-benefit analysis was done to determine the recovery rate of costs. An optimization method based on GA was proposed to optimize energy management, location and size of stationary SC ESSs simultaneously in order to obtain the best economic efficiency and voltage profile (Xia et al., 2015). In researches related to ESSs, the energy efficiency was increased, only by using recovery regenerative braking energy. In this study, for the first time, ESSs and optimal speed profiles were used simultaneously for energy efficiency increasing. In other words, by combining energy savings with regenerative braking energy recovery, while the energy consumption of the entire network was reduced, the capacity of ESSs decreased as well. For this purpose, first for the network with normal train speed profiles, the optimum capacity of stationary ESSs was calculated, then the same calculation was performed for optimum speed profiles and it was shown that in the latter case, both total input energy and ESS capacity were reduced. It is worth recalling that in all of the previous studies done in the field of computing or optimization of energy storage capacity, normal speed profiles or speed profiles corresponding to the minimum travel time (flat out) were considered. This has led to calculating a large capacity of energy storage that may not be used completely. 2. Rail transit system simulation Urban electric railway network includes traction substations, power lines, and rails as feeders of network and the trains as electric loads. ESSs are integrated as additional equipment to the network for increasing energy efficiency. Modeling of each part is expressed in the following briefly. 2.1. Train modeling The operation of train is expressed according to mechanical equation (Vuchic, 2007):

M . a = FT (v ) − RT (v )

(1)

Where M is the total mass of the train and passengers, a is the acceleration of the train, and v is the velocity of the train. FT is the traction effort of the train and RT is the total train resistance. The train resistance is determined according to the physical characteristics of the track and for the specified acceleration, the amount of required tractive effort could be determined from the characteristic of train. The amount of electric power consumed by the train Pcons in motor mode and regenerative braking power Pregen 2

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Fig. 1. A typical speed profile with four motion regimes and feasible ranges of decision variables.

in generator mode are determined from (2) and (3).

Pcons =

FT × v η

(2)

Pregen = FT × v × η′

(3)

Equation (2) applies to all modes where FT ≥ 0; that is, acceleration, cruising and coasting. Equation (3) applies when FT < 0; that is when braking. ?? is the motoring mode overall efficiency (encapsulating motor (??mot), gearbox (??gear) and inverter (??inv) systems) and ??' is the overall efficiency of the set of generator (??gen), gearbox and inverter in regenerative mode. In other words,

η = ηmot × ηinv × ηgear

(2a)

η′ = ηgen × ηinv × ηgear

(3a)

An optimal speed profile with regenerative braking should consist of five operating regimes: maximum acceleration (MA), cruising (CR), coasting (CO), regenerative braking (RB) and maximum braking (MB) (ShangGuan et al., 2015). In metro lines with short inter-station distances and normal slopes, partial braking (regenerative braking mode) could occur in cruising regime. It is important to note that in speed profile optimization process, regenerative braking was considered. So a simplified typical speed profile is shown in Fig. 1 consisting of four operating regimes, accelerating, cruising, coasting and braking. To obtain the different speed profiles, two decision variables were used, the speed of trains entering to the constant velocity (Vcr) and the switching moment from cruising to coasting mode (tcr). Vcr can vary between two margins, the minimum allowance comfortable speed, Vmin and the maximum operational speed limit, Vmax. Vm1, Vm2, Vm3 are different speed limits in an inter-station which are often lower than Vmax. Complete equations of train, resistance relationships, how to simulate them, are given in (Ahmadi and Dastfan, 2016), (Ahmadi et al., 2017). 2.2. Stationary ESS modeling In recent years, the use of ESSs for improving the performance of the rail transport system is becoming increasingly important. The main goals are improving energy efficiency, reducing the voltage fluctuations and maximum current of substations. For this purpose, both stationary and onboard ESSs were used (Gonzalez Gil et al., 2014). Common types of ESSs include battery, flywheel and supercapacitor. Due to the large number and high-rate acceleration and braking of trains, ESSs must have the proper characteristics of power density, energy density and a high life cycle. Among the existing technologies, SCs are the most suitable option. Since this study was done on a pre-built network, stationary types that had less installation and operation constraints were implemented. The ESS is composed of two main parts; first, the storage element that is SC. Since the rated voltage of SCs is low and about 2.5 V, manufacturing companies usually build ready modules by putting them into series. According to the rated voltage of the network, appropriate number of these modules could be put into series and form a string. Depending on the required power and energy, a sufficient number of these strings are paralleled to each other. The second part of an ESS is the DC/DC converter, which is used to connect the ESS to the network. It is a bi-directional converter which in braking mode works as a buck converter and stores energy in the SCs and in accelerating mode, returns the stored energy in SCs to the network as a boost converter. A sample stationary ESS consisting of SC modules and converter is shown in Fig. 2. 3

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Fig. 2. A sample stationary ESS connected to metro network.

The operation of converter is very important and a power flow management system is needed to control the charging and discharging procedure of SCs. As mentioned earlier, many studies were done on how to control the converter and thereby maximize the efficiency of ESS. The control algorithm used in the simulation is similar to the method used in (Barrero et al., 2010). In transition from charging and discharging to standby and vice versa, a sudden jump in the current of SC occur, which reduces the lifetime of SCs. To avoid this in the paper, the maximum rate of change of current limitation was considered. Charging, discharging and standby modes are determined with feedback from the three parameters: the network voltage, the state of charge (SOC) of SCs and the current of ESS in the most recent moment. This set could be modeled by using a controlled current source, shown in urban railway network Fig. 4. The SC served as a constant power load in DC power flow. First, based on the amount of voltage of the network and SOC of the SC, it was decided that capacitor should be in either charging, discharging or standby mode. Then, by using the previous iteration voltage, the current of SC was calculated, DC network power flow was performed and the new amount of SC voltage was determined. At each simulation time step ti+1, the amount of energy of ESS, Ei+1, is derived from (4): Ei+1 = Ei + Pi.Δt

(4)

Where Ei and Pi are the energy and power of the ESS in iteration i respectively. The simulation interval [ti, ti+1] is sufficiently small and Δt = ti+1- ti

(5)

The SOC is calculated from (6):

SOCi =

Ei Emax

(6)

Emax is obtained from nominal characteristic of the utilized SC. It should be noted that in this paper, the ESS efficiency is assumed to be 100%, and the internal losses of SCs and convertors are neglected. Although this approximation could modify the numerical results slightly, it does not affect the final conclusion of the paper.

2.3. DC network modeling Power supply system is usually DC with nominal voltages 600, 750, 1500 or 3000 V. In Iran 750 V DC is used currently. Power transformers from the upstream network deliver traction supply voltage, then the DC supply voltage is provided by 12-pulse diode rectifier systems. This rectifier is used for harmonic reduction in DC network. The upstream AC network is connected to a Δ-Δ and a ΔY transformer to obtain 30° phase-shift between the secondary windings. The secondary of each transformer is connected to a sixpulse diode-rectifier. The outputs of the rectifiers are parallel and feed the DC network. The complete structure of this rectifier was shown in Fig. 3. The trains are supplied through substation output feeders and overhead lines or third rail network. In network analysis, substations were modeled by a DC voltage source with internal resistance and a series diode. Ohmic resistances modeled power lines and rails. Trains were also modeled by current sources that their position are changed. The model of a typical urban train network with stationary ESSs is shown in Fig. 4.

3. Proposed optimization algorithm The main objective of this research is to minimize electrical energy consumption. Therefore, the problem was defined as minimization of total input energy from traction substations, which is shown in (7) 4

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Fig. 3. The complete model of 12-pulse diode-rectifier.

Fig. 4. Metro network model with stationary ESSs. Nsub T

min Ein − tot =

∑ ∫ Vsub (k)·Isub (k)·dt k=1

(7)

0

Since the trains' movement is periodic, based on energy conservation law, the amount of net energy exchanged between the ESS and the network in each cycle should be zero (total energy intake and delivered energy of each ESS should be equal in a period). In other words, to repeat the same cycle, the super-capacitors should be in the same state of charge at the beginning and the end of the cycle. This condition applies when the integral of the power absorbed by the ESS over a cycle is zero (the losses of ESS was neglected for simplicity). This constraint is shown in (8). T

∫ VESS (k). IESS (k). dt = 0 , k = 1,2, ..., Nsub

(8)

0

Where Ein-tot is the total input energy of network in a period of work. Nsub is the number of traction substations, Vsub(k), Isub(k) are the voltage and current of the kth substation, VESS(k), IESS(k) are the voltage and current of the ESS in kth substation and T is the period of trains' movement or the time distance between two successive trains (Headway). Since the headway of trains is assumed constant in a specific time interval, the overall behavior of the network is the same in all periods. Therefore, to simulate and calculate the energy of the system, the same value of T is chosen as the simulation time. However, other mechanical constraints such as speed, acceleration and jerk limitations are met in speed profile optimization. The electric constraints such as voltage and current limitations in power supplies, trains, ESSs and DC network are considered in DC power flow analysis. More detailed explanations were given in (Ahmadi and Dastfan, 2016), (Ahmadi et al., 2017). The capacity of ESSs must be calculated in a way that the total energy consumed in the period be minimum. ESS requires a certain location to install the SCs and related equipment. Due to space limitations, it was assumed that ESSs be installed only at stations with traction substations. So the number of ESSs is equal to the number of traction substations Nsub. The number of series SC modules in each string ns is fixed and it could be selected according to the rated voltage of the network. The variable parameter is the number of parallel branches np in each ESS. This number could vary between zero and the maximum possible value np-max. np = 0 for a substation means that, there is no ESS. np-max have been calculated based on the maximum negative power in (Teymourfar et al., 2012), by assuming reversible substations. The above approach may not always provide the right answer because, in some cases, the maximum instantaneous power is large, but the average power is small and the large capacity of ESS is not used completely. The maximum number of parallel strings np-max were determined according to space limitations in (Xia et al., 2015). In present study, both the peak and average negative power in a period were used. In all of the previous studies done in the field of calculation of ESSs capacity or optimizing their size, the ESS capacity was determined for normal speed profile or speed profile with minimal travel time (flat out specification) in which the cost of buying ESSs 5

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Fig. 5. Procedure of minimization the total input energy by ESS size and location optimization.

is high and under many circumstances their maximum capacity might not be used. The main feature of this research is that, by optimizing the speed profiles at no cost, ESS capacity requirements also declined. In addition, other benefits were observed such as reduced depreciation associated with trains. To achieve this goal, the simulation was done in 2 groups and 10 scenarios. First, total energy consumption in normal condition was calculated, and then optimum size and location of ESSs were determined. At the end, ESSs optimization for optimum speed profiles was worked out. To simulate the entire network, first, the movement of train was simulated in each inter-station (IS) by using single train simulator (Ahmadi and Dastfan, 2016) and ESS simulation was done according to the explanations given in section 2.2. then DC power flow on the multi train network was done to determine the energy of each substation and total input energy eventually. Afterwards, optimization process consisting of objective function evaluation and ESS configuration improvement was done to minimize Ein-tot. The block diagram of the procedure of minimizing total input energy is shown in Fig. 5. The results are analyzed in detail in the next sections. Genetic algorithm is used for optimization, which includes the modeling the problem and evaluation of objective function and genetic manipulation. The process is described as follows: 3.1. Integer genetic algorithm Integer programming with GA involves several modifications of the basic algorithm. For integer programming Special creation, crossover, and mutation functions enforce variables to be integers (Deep et al., 2009). 3.1.1. Problem encoding The configuration of ESSs (number of parallel strings npk) in traction substations could be encoded by X chromosome which presents an individual from population. X = [x1, x2, …,xk, …, xn]

(9)

Where xk = npk, k = 1, 2, …, Nsub

(10)

There are two limits for npk, one is that by increasing the number of SCs, the cost of ESSs rises and the second is the limitation of installation space. Therefore, the maximum number of npk in each substation must be limited to np-max. The sum of all parallel strings in all substations is: Nsub

sumnpk =

∑ npk

(11)

k=1

In the case study, the preliminary value for np-max was selected 10, due to space limitations (each series string, which consists of six modules specified In Table 3, needs a space of about 1 m3). However, its appropriate value was calculated 6, according to the maximum amount of negative power in substations and traffic conditions. 3.1.2. Objective function In this paper, the main objective is the minimization of total input energy from upstream network Ein-tot. The normalized representation of objective function is:

ObjV [X ] =

Ein − tot Einmax − tot

(12)

Einmax − tot is

Where the maximum value of Ein-tot related to normal driving strategy (normal speed profiles) without any ESS. As predicted, the simulation revealed that, if no restriction other than np-max is not considered, the result tends to np-max, although there is 6

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not much improvement in energy optimization. Therefore, to consider npk more effectively and to reduce costs, a violation function V was defined as:

V=

sumnpk max sumnpk

−1 (13)

The violation function could be replaced by a simple penalty factor. However, by doing simulation for all modes of uniform distribution of ESSs for npk = 1 to npk = 10, the results showed that for npk greater than 6, total input energy does not decreased significantly. Therefore npk = 6 was chosen for all ESSs as a proper threshold value. max The sumnpk for case study has been selected 66 from the scenario Norm.3 in which almost all of the regenerative energy delivered to the network and the blocked energy is nearly zero. This number was chosen as the base, a lower number is better due to the lower cost. Therefore, the ultimate objective function is:

E − tot min Z = ⎜⎛ inmax + wV ⎞⎟ ⎠ ⎝ Ein − tot

(14)

The weighting coefficient w is selected proportionally to sum of npk, i.e. the cost effect. It can be said that total cost function includes energy and ESSs prices. Therefore, determining the value of the coefficient w, requires the exact quantities of energy price and the cost of SCs and related equipment. Since the above values were not available, optimization was performed with different values of the coefficient 0 < w < 1. Finally, with the value of 0.05, both the total input energy and the number of SCs were minimized. This is further explained in Section 4.2 scenario Norm.5. 3.1.3. Genetic manipulation Three basic steps of Genetic manipulation are selection, crossover and mutation, which have been described in (Deep et al., 2009). Thus, no detailed introduction will be made about genetic manipulation in this paper. 4. Analysis of simulation results 4.1. Specification of case study network Line 1 of Mashhad urban railway was selected as case study. The network specifications are listed in Table 1. Total traveling time in all simulation scenarios were assumed constant and equal to 87 min. The fleet size in action was 18 trains with 5-min headways. Height profile of the track, location of station and traction substations were illustrated in Fig. 6. Each train consists of two vehicles. Specifications of each vehicle are summarized in Table 2. Further characteristics were specified in (Ahmadi and Dastfan, 2016). Since in manual operating, the use of the maximum acceleration was not possible, the amounts 1.05 and 0.8, for acceleration and deceleration rates have been considered respectively. A string consisting of six series modules of Maxwell SCs with the nominal voltage 750 V and continuous maximum power 180 kW were selected as the minimum ESS capacity, connected to DC network via a DC/DC bi-directional converter. The specification of SC modules are summarized in Table 3. 4.2. Comparing the results of different scenarios To simulate the entire network, first, the movement of train was simulated in each inter-station (IS) by using single train simulator. Because the actual speed profile in manual driving depends heavily on the behavior of drivers, the stored data in the trains Event Recorder (ER) were used for modeling the real mode. Various Speed profiles in different working conditions were drawn, then the nearest samples to the scheduled travel time were selected and simulated as real speed profiles. Real and simulated speed profiles for one downhill and an uphill IS were shown in Fig. 7. The same procedure was performed for all ISs. Finally, with DC power flow for the entire network, all electrical parameters including voltage, current, power of all substations and trains and total input energy of network were calculated. The section of speed profile optimization has not only been validated by real data, but is also currently being implemented as a practical approach to the network under study. In the process of optimizing the location and size of the ESSs, since the supercapacitor was not obtainable, only specification of the SC available in the market was used in simulation. The simulations were done in two groups, Norm. (normal speed profiles) and Opt. (optimum speed profiles) and the results are Table 1 Metro network characteristics. Parameter

Value

Parameter

Value

Nominal Voltage Number of Traction Substations Catenary resistance Length of line in each direction

750 V DC 11 0.036 Ω/km 19 km

No load substation voltage Number of passenger stations Rail resistance Headway

840 V DC 22 0.022 Ω/km 5 min

7

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Fig. 6. Height profile of the track, location of station and traction substations in Line 1 Mashhad Urban Railway.

Table 2 Each vehicle characteristics. Parameter

Value

Parameter

Value

Vehicle mass (AW0) Rotating mass Maximum acceleration Jerk limitation

43 tonnes 3.7 tonnes 1.3 m/s2 1 m/s3

Maximum passenger mass (AW3) Motor, inverter and gear box efficiency Maximum deceleration Auxiliary power consumption

18.9 tonnes 86% 1.2 m/s2 42 kW

Table 3 Specification of SC energy storage module. Parameter

Value

Parameter

value

Rated Voltage Maximum continuous Current Capacitance of each Cell Number of cells

125 V 240 A 3000 F 48

Rated Capacitance Maximum continuous Power Maximum Stored Energy Stored energy of each Cell

63 F 30 kW 0.137 kWh 3.0 Wh

Fig. 7. Real, simulated, and optimal speed profiles for a sample IS.

summarized in 10 scenarios in Tables 4 and 5. The scenarios Norm.1 through Norm.5 were considered with npk = 0, 10, 6, the calculated value obtained from (15), and the optimum number of npk respectively. The scenarios Opt.1 to Opt.5 are similar to the scenarios Norm.1 - Norm.5, except for the optimum speed profiles being used. The results of the simulation of the real operation (normal driving) are shown in the first rows of Tables 4 and 5 as the baseline scenario (Norm.1). As can be seen, the total input energy consumption is 301.7 kWh. By using the maximum number of SCs Based on space limitations, in scenario Norm.2, Ein-tot has decreased to 265.9 and 12% energy saving has been achieved. A main drawback of this scenario is using too many capacitors, which eventually increases the costs. This disadvantage can be seen from a different 8

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Table 4 ESSs configuration and network energies in different scenarios. Scenario

npk

Norm. (Normal Speed Profile)

Opt. (Optimum Speed Profile)

1 2 3 4 5 1 2 3 4 5

np1

np2

np3

np4

np5

np6

np7

np8

np9

np10

np11

Sum npk

Ein-tot (kWh)

0 10 6 5 1 0 10 6 4 1

0 10 6 5 3 0 10 6 4 0

0 10 6 6 7 0 10 6 5 2

0 10 6 6 5 0 10 6 5 3

0 10 6 5 5 0 10 6 5 7

0 10 6 5 2 0 10 6 6 2

0 10 6 4 4 0 10 6 3 8

0 10 6 4 1 0 10 6 3 0

0 10 6 4 2 0 10 6 5 4

0 10 6 4 6 0 10 6 4 3

0 10 6 5 2 0 10 6 6 5

0 110 66 53 38 0 110 66 50 35

301.7 265.9 264.8 266.6 266.7 260.1 238.5 239.3 240.8 241.4

Table 5 Outputs of the network analysis in different scenarios. Scenario

Energy (kWh)

Norm. (Normal Speed Profile)

Opt. (Optimum Speed Profile)

1 2 3 4 5 1 2 3 4 5

Ein-tot

EESS

Econs-tot

Eregen-tot

Eblock

Eloss

β

ΔE%

ΔVmax %

Mean SOCmax

301.7 265.9 264.8 266.6 266.7 260.1 238.5 239.3 240.8 241.4

0.0 83.3 85.3 79.8 68.1 0.0 55.5 57.6 53.6 41.5

396.2 388.8 388.6 388.8 388.9 317.2 315.8 315.9 315.9 315.9

109.8 137.8 138.7 137.2 137.3 68.9 88.7 87.9 86.5 86.1

36.5 1.2 0.2 1.8 1.8 20.6 0.0 0.3 1.7 2.1

15.4 14.9 14.9 14.9 15.1 11.8 11.3 11.3 11.4 11.6

0.75 0.99 1.00 0.99 0.99 0.77 1.00 1.00 0.98 0.98

0.0 11.9 12.2 11.7 11.6 13.8 21.0 20.7 20.2 20.0

13 12 13 12 12 13 11 11 12 14

0 68 91 95 100 0 62 89 95 98

viewpoint in the right column of Table 5. The average value of the SOCmax for all SCs is 68%. In other words, the total capacity of ESSs is not used. In scenarios Norm.3 and Norm.4, first, like previous studies, the required ESS capacity for reducing the energy consumption of the entire system in normal condition (real operation) was calculated. To estimate the approximate maximum capacity of ESSs, assuming reversible substations, power flow was done and the instantaneous negative power in all substations were obtained. A sample of instantaneous power of a traction substation in studied network is shown in Fig. 8. The np-max in each substation were calculated from (15), whereP neg max is the maximum negative power in the substation. The rated power of each ESS string is 180 kW. The factor 0.75 were used in (15) due to the fact that to extend the life cycle of SCs in practice, the SOC is not allowed to be less than 0.25, therefore a part of the capacity is not usable.

np − max =

P neg max 0.75 × 180kW

(15)

By using (15), np-max was calculated 6. Thus the simulation was performed in scenario Norm.3, by assuming an equal npk = 6 for

Fig. 8. Instantaneous power in TS05 traction substation, assuming reversible substation.

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Fig. 9. Maximum instantaneous negative power in traction substations.

all ESSs. The results of this scenario were summarized in rows 3 of Tables 4 and 5 The energy saving is nearly equal to that of scenario Norm.2, except for the sumnpk having been reduced significantly from 110 to 66 (40%). The average of SOCmax of ESSs was increased from 68 to 91 percent. In other words, at a lower cost, the same amount of saving of Scenario Norm.2 was achieved. In scenario Norm.4, based on the maximum negative power in each traction substation in Fig. 9, and using (15), npk was calculated for all ESSs. The results were illustrated in Fig. 10. The simulation results were given in row 4 of Tables 4 and 5 In scenario Norm.5, optimization of the size and location of the ESSs was done. Despite a significant decrease in sumnpk from 66 to 38, energy saving only decreased less than 1 percent, which is very important economically. Different values were chosen For the coefficient w. Since the main objective was reducing energy, w value was chosen so that in extended objective function (Z) optimization, energy saving be maximum 1 percent less than its best value. As a result, the best value of w = 0.05 was considered for the violation function. The main parameters of GA are: population size, length of individual, maximum evolution generation, crossover rate, mutation rate, and generational gap, which were eventually chosen as, 40, 11, 50, 0.8, 0.015, and 0.95 respectively. The objective function evaluation results respect to Generation were illustrated in Fig. 11 for normal and optimum speed profiles. In the scenarios of the second group, optimal speed profiles were used. As previously mentioned, the aim of this article is to show the positive effect of the optimum speed profile on ESS optimization. In Scenario Opt.1, by using the algorithm presented in (Ahmadi and Dastfan, 2016) and using the decision variables of cruising speed Vcr and cruising time tcr – previously mentioned, optimal speed profiles were achieved for all ISs, while the ISs travel time and total route planning and other physical constraints were met. Optimum speed profile for the mentioned ISs were determined by using the proposed algorithm as shown in Fig. 7. Then, by performing power flow, total input energy was calculated and the results were illustrated in row 6 of Tables 4 and 5 As expected, speed profile optimization alone caused significant reduction in total energy consumption and about 14 percent energy saving. By using optimum speed profiles, other parameters have been significantly changed. Total consumed energy of all trains (Econs-tot) were reduced from about 390 to 316 kWh. The sum of regenerated energy (Eregen-tot which is successfully delivered to network plus Eblock which is often wasted in braking resistors) decreased from 140 to about 90 kWh. In spite of this, wasted energy (Eblock) is still high and must be reduced. The main reason for reduction of above energies is the maximum use of coasting mode in optimal driving. Due to the reduction of regenerative braking energy, normally less ESS capacity will be needed. In scenario Opt.2, the use of maximum

Fig. 10. Maximum number of parallel Strings of ESSs (np-max) in each substation.

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Fig. 11. Objective function evaluation.

ΔE%max =

301.7 − 241.4 × 100 = 20% 301.7

(16)

allowance npk = 10 for all ESSs, reduced Ein-tot to 238.5 kWh (21% energy saving). However, as mentioned in Norm.2, the number of SCs is very large. In scenario Opt.3, with the use of uniform distribution npk = 6 for all ESSs, Ein-tot reduced to 239.3 kWh (20.7% energy saving). The energy saving was similar to npk = 10, but the usage of capacity of ESSs has increased. The scenario Opt.4 is similar to Norm.4, which used npk obtained from (15). In this scenario, energy saving increased to 20.2%. The average of SOCmax increased to 91 percent, however, sumnpk decreased to 50, which totally, it is more desirable than the previous scenarios. In the last scenario (Opt.5) with optimal speed profiles, a simulation similar to scenario Norm.5 was done and the optimum size and location of ESSs for minimizing total energy consumption was calculated. The results are shown in row 10 of Tables 4 and 5 As it could be seen, the energy saving in scenario Opt.5 is significantly higher than Scenario Norm.5; in addition, the number of required SCs is less. The total energy saving (reduction of total input energy) is calculated in (16). The results show that more energy could be reduced by first, optimizing speed profiles and then calculating the ESS size. Moreover, according to the need for fewer SCs, the investment costs could be reduced. In scenario Opt.5, despite the reduction of sumnpk from 110 to 35, energy saving is reduced only less than 1% of the maximum possible amount. The result is of economical significance. The efficiency of ESSs has been increased and average SOCmax of all ESSs reached one. The SOC curves of a sample ESS (ESS05) in different scenarios were shown on Fig. 12. As can be seen, the optimized scenarios Norm.5 and Opt.5 have the best SOC characteristics. Other results which are listed in Table 5, are EESS, Eloss, Eblock and β. EESS is the amount of delivered or absorbed energy by all ESSs in a period. By using optimal speed profiles, the amount of exchanging ESSs energy reduced from 68.1 to 41.5 kWh in each period, which could lead to a reduction in network losses. For analysing the receptivity of regenerative energy in multi-train system, regenerative energy recovery rate (RERR) β is defined in the whole network as:

β=

Eregen − tot Eregen − tot + Eblock

(17)

Eregen-tot is the total regenerated energy by all trains which is successfully delivered to the network. Eblock is the part of regenerated energy (for all trains) that is not absorbed by other trains and is often wasted by braking resistors. Since usually the network receptivity of regenerated energy is not 100%, Eregen-tot is less than the sum of regenerated energy (Eregen) by all trains.

∑

Eregen = Eblock + Eregen − tot

(18)

All trains

Eloss is the total electrical losses in power supply network, which determined by DC load flow analysis on the whole system. On the other hand:

Fig. 12. SOC of a sample ESS in different scenarios (ESS05).

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Ein − tot = Econs − tot−Eregen − tot + Eloss

(19)

With speed profile optimization, since consumed energy of the trains reduces, electrical network losses decrease too. However, the stationary ESSs alone have no impact on the amount of losses. Firstly, because by installing the ESSs, the current flow in the lines does not change. In other words, the required currents of trains, is drawn from the ESSs instead of the power sources at some times. The second reason is that we have assumed the internal losses of ESSs to be zero. As expected, due to the use of ESSs, receptivity of network was improved and β was reached to its maximum value 1. The other result in Table 5 is ΔVmax, which represents the maximum amount of voltage fluctuations in ESSs and substations. With proper selection of the threshold voltages in charge and discharge control process of ESSs, the fluctuations in different scenarios are kept in the acceptable range. If the purpose is to improve the voltage fluctuations, it can also be considered as a part of the objective function. However, as it has been shown in previous studies, for this purpose, it is better that ESSs are placed between substations. 5. Conclusion In this paper, total input energy of metro network was minimized by using optimal speed profiles and stationary ESSs simultaneously. The results show that if the optimal capacity of ESSs is determined with normal speed profiles, 11.6% energy saving is provided (Norm.5), while if optimal speed profiles are determined first and then the optimal capacity of ESSs are calculated (Opt.5), energy saving increases significantly to 20.% and the total capacity of ESS is less than previous case (Norm.5). It is obvious that speed profile optimization reduces the consumed energy of trains and network losses, although stationary ESSs have not significant effect on losses. 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