Optimized Sizing and Scheduling of Hybrid Energy Storage ... - MDPI

energies Article

Optimized Sizing and Scheduling of Hybrid Energy Storage Systems for High-Speed Railway Traction Substations Yuanli Liu 1 , Minwu Chen 1, *, Shaofeng Lu 2 1 2

*

ID

, Yinyu Chen 1

ID

and Qunzhan Li 1

School of Electrical Engineering, Southwest Jiaotong University, Chengdu 611756, China; [email protected] (Y.L.); [email protected] (Y.C.); [email protected] (Q.L.) Department of Electrical and Electronic Engineering, Xi’an Jiaotong-Liverpool University, Suzhou 215123, China; [email protected] Correspondence: [email protected]; Tel.: +86-028-6636-6930

Received: 23 July 2018; Accepted: 18 August 2018; Published: 22 August 2018

Abstract: The integration of hybrid energy storage systems (HESS) in alternating current (AC) electrified railway systems is attracting widespread interest. However, little attention has been paid to the interaction of optimal size and daily dispatch of HESS within the entire project period. Therefore, a novel bi-level model of railway traction substation energy management (RTSEM) system is developed, which includes a slave level of diurnal HESS dispatch and a master level of HESS sizing. The slave level is formulated as a mixed integer linear programming (MILP) model by coordinating HESS, traction load, regenerative braking energy and renewable energy. As for the master level model, comprehensive cost study within the project period is conducted, with batteries degradation and replacement cost taken into account. Grey wolf optimization technique with embedded CPLEX solver is utilized to solve this RTSEM problem. The proposed model is tested with a real high-speed railway line case in China. The simulation results of several cases with different system elements are presented, and the sensitivity analyses of several parameters are also performed. The obtained results reveal that it shows significant economic-saving potentials with the integration of HESS and renewable energy. Keywords: railway traction substation energy management; hybrid energy storage systems; mixed integer linear programming; bi-level model; battery degradation

1. Introduction The dramatic increase of carbon emissions is driving global climate change and poses risks for human and natural systems [1,2], and a worldwide consensus on reducing atmospheric greenhouse gases (GHGS) has been reached [3,4]. As for China, the government committed a reduction of carbon emission intensity by 18% during the 13th Five-Year Plan period (2015–2020) [5]. A joint report from the International Energy Agency (IEA) and the International Union of Railways (UIC) shows that the transport sector accounted for 24.7% of global carbon emissions and the rail sector accounted for 4.2% of total transport carbon emission in 2015, while the corresponding proportion in China is 10.6% and 15.3% [6]. Most noteworthily, the railway-related energy consumption and carbon emissions per passenger-km increased by 44.1% and 96.8% between 2005 and 2015 in China respectively, largely as a result of the rapid expansion of the high-speed railway (HSR) network [6]. Consequently, energy savings in railway systems and in HSR systems have received considerable critical attention. A few approaches provide insights for energy saving, such as the use of regenerative braking energy and renewable energy techniques. Due to the high speed and colossal traction power Energies 2018, 11, 2199; doi:10.3390/en11092199

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of high-speed trains (HSTs) with pulse width modulation-based four-quadrant converters [7], considerable regenerative braking power (RBP) is produced in their braking mode. For instance, the maximum braking power of a CRH-380AL electric multiple unit (manufactured by China Railway Rolling Stock Corporation, Qingdao, China) can be up to 20 MW. Therefore, there is a growing application of energy storage systems (ESSs) in railway systems to store this massive braking energy [8]. Currently, industrial applications of onboard ESS for braking energy recovery include the Sitras SES of Siemens, the MITRAC energy saver of Bombardier and the STEEM project of Alstom [9–11]. However, the limitations of size and weight have presented an obstacle to the application of onboard ESSs in HSRs. By comparison, wayside ESSs can be a better solution. Moreover, the intersections of railway networks and renewable energy sources (RES) are propitious to the utilization of local renewable energy. For instance, the Lanzhou-Xinjiang HSR line crosses the north-western regions of China with rich solar and wind energy, while there is no access to local RES consumption. With regard to the way that RBP and RES are used, aside from supplying to the HSTs, they can also be utilized to charge the energy storage devices, e.g., HESS, for further usage. Therefore, increasing the utilization rate of RBP and RES via HESS helps achieve the energy saving goals. Moreover, cost savings for rail operators can also be implemented from another point of view. In the current railway power systems, the dramatic stochastic volatility of traction loads and the harsh requirements for overload capacity of traction transformers result in the extremely low utilization rate of traction transformers and high demand charge. Besides, the RBP fed back to the grid contains a large number of harmonic components and negative sequence components because of the single-phase asymmetry of traction loads, seriously jeopardizing the safety and stabilization of the utility power system [12]. Consequently, a resulting penalty bill is charged. To this end, there is great potential for cost saving through the application of HESS and management of energy flows. Smart grid technologies present the potential of energy management in railway power supply systems. The battery sizing and energy management in smart grids have been extensively studied in recent years, such as grid-tied photovoltaic (PV) systems [13,14], wind farms [15], active distribution systems [16] and microgrids in stand-alone mode or grid-connected mode [17–22]. However, the characteristic of traction loads differ significantly from conventional loads. Therefore, the sizing and dispatch strategy of HESS need to be re-examined when applied to electrified railway systems. Numerous researchers have focused on solving the above problems in the railway systems. Khayyam et al. [23] developed a railway energy management system (REM-S) architecture by coordinating loads, regeneration, storage, and distributed energy resources for optimal energy use. It offers the inspiration of applying the research achievements of smart grids to railway systems. Generic hybrid railway power substation (HRPS) architectures for DC and AC systems were proposed in [24] by integrating RES and storage units with railway systems. Based on the HRPS system in [24], corresponding fuzzy logic energy management strategies were developed in [25,26] for feasibility analysis. However, the battery degradation and replacement were ignored. A hierarchical structure, including on-route trains energy consumption optimization and traction substation energy flows management, was identified in [27,28] to minimize the electricity bill. However, no capital cost of storage devices was considered. In [29] a smart railway station energy management system model was formulated for the utilization of braking energy, and the initial state of charge (SOC) was highlighted in particular as the uncertain factor. Unfortunately, it merely concentrated on the reduction of electricity bill of power consumption and paid little attention to the comprehensive cost analysis. In [30] an optimization model of battery energy storage system (BESS) operation strategy was developed for the maximization of owner’s net benefit. However, the evaluation of degradation cost was off-line, i.e., it was not included in the optimization model. Furthermore, regenerative braking energy of metro trains was not considered. In [31] the author proposed a methodology for optimal dispatch of railway ESS with RES and braking energy, while the investment cost was not taken into consideration. In [32] the optimal sizing of HESS for braking energy utilization was studied, yet the battery lifetime was

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Energies 2018, 11, x based FOR PEER of 29 estimated simply onREVIEW the cycles, and the depth of discharge (DOD) of each cycle was3 ignored, thus the estimation of battery lifetime and daily cost need to be further improved. aforementioned studies and many other studies not referred here give approaches to sizing TheThe aforementioned studies and many other studies not referred here give approaches to sizing of energy storage devices or energy management in railway systems from different perspectives, of energy storage devices or energy management in railway systems from different perspectives, while the comprehensive cost study within the time scope of project period is ignored, and a more while the comprehensive cost study within the time scope of project period is ignored, and a more accurate on-line methods for battery lifetime estimation are not considered. Accordingly, this paper accurate on-line methods for battery estimation are not considered. this paper aims at addressing this problem. Thelifetime highlights of this paper can be outlined asAccordingly, follows: aims at addressing this problem. The highlights of this paper can be outlined as follows:

• •

•

•

The interaction of HESS sizing and daily scheduling of HESS within the time scope of project

Theservice interaction HESS sizing anddegradation daily scheduling of HESSvia within the model. time scope of project periodofconsidering battery are formulated a bi-level service period considering battery degradation are formulated via a bi-level model. • The electricity bill for rail operators is largely reduced through peak shaving of traction loads, of bill braking power and the mitigation bill penalties for power back to the utility grid. Theutilization electricity for rail operators is largelyofreduced through peakfed shaving of traction loads, •utilization The impact of different electricity pricing schemes,of length of project service period initial of braking power and the mitigation bill penalties for power fedand back to the SOC of HESS are also analyzed. utility grid. TheThe impact of this different pricing schemes, length of project and initial rest of paper electricity is structured as follows: Section 2 introduces the service general period architecture of RTSEM system and descriptions of all the elements included. Sections 3 and 4 present the problem SOC of HESS are also analyzed.

formulations of the master level and slave level respectively. In Section 5, a grey wolf optimization The rest of this paper is structured as follows: Section 2 introduces the general architecture of approach with CPLEX solver embedded is proposed. In Section 6 the case study is performed and RTSEM system and descriptions ofthe allconclusions the elements relevant results are given. Finally areincluded. reached inSections Section 7.3 and 4 present the problem

formulations of the master level and slave level respectively. In Section 5, a grey wolf optimization approach with CPLEX solver embedded is proposed. In Section 6 the case study is performed and 2. System Description relevant results are given. Finally the conclusions are reached in Section 7. 2.1. Block Diagram of the System and Model

2. System Description

In conventional electrified railway systems, the 25 kV traction network supplies single-phase AC at the power frequency for HSTs. As the phases of adjacent power supply sections are different, 2.1. Block Diagram of the System and Model all sections must be kept strictly isolated to prevent the risk of mixing out-of-phase supplies, which isInachieved by neutral sections.railway In this study, a scheme RTSEM system is illustrated in single-phase Figure 1, conventional electrified systems, the 25ofkV traction network supplies which is based on the architecture of hybrid railway power substation proposed in previous AC at the power frequency for HSTs. As the phases of adjacent power supply sections arestudies different, [24,27]. must The power direction corresponding are presentedsupplies, as well. which The is all sections be kept strictly and isolated to prevent symbol the risk convention of mixing out-of-phase RTSEM system sections. is mainlyIn composed utilityofgrid, PV system generator, battery in storage achieved by neutral this study, aofscheme RTSEM is illustrated Figuresystem, 1, which is ultracapacitor (UC) storage system and HSTs. It is important to highlight that HSTs have dual based on the architecture of hybrid railway power substation proposed in previous studies [24,27]. properties of “load” and “power source”, depending on whether the train is in traction mode or The power direction and corresponding symbol convention are presented as well. The RTSEM regenerative braking mode. This special feature of HSTs differs from conventional power load system is mainly composed of utility grid, PV generator, battery storage system, ultracapacitor (UC) greatly, increasing the diversity of operation mode and the complexity of energy management storage system and HSTs. It is important to highlight that HSTs have dual properties of “load” and though, yet nevertheless showing quite economic-saving potentials. “power source”, depending on whether the train is in traction or regenerative mode. Note that a study of the entire HSR line containing plentymode of traction substations braking (TSSs) and Thispower special feature of HSTs differs from conventional power load greatly, increasing the diversity supply sections may lead to a large-scale problem. As different power supply sections of an of operation mode and the complexity of energy management though, nevertheless showing quite HSR line are electrically disconnected via neutral sections, this paperyet concentrates on each power economic-saving supply section potentials. individually. Power Flow

Communication Flow

Pt ,pvs > 0

DC bus

PV Generator

~ = Utility Grid

,dis Pt bat >0 ,s

Pt ,grid >0 s

=

Pt ,fed s >0

=

… ,ch Pt bat >0 ,s

Battery HESS

,dis Pt uc >0 ,s

Meter = Traction Substation

B

A

C

Control Center ~

β

α

=

= ,ch Pt uc >0 ,s

Ultracapacitor

Signal Tower

Pt load >0 ,s

Pt brake >0 ,s

Neutral Section

Traction mode

Regenerative braking mode

Figure 1. Structure diagram of the RTSEM system. Figure 1. Structure diagram of the RTSEM system.

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Note that a study of the entire HSR line containing plenty of traction substations (TSSs) and power supply sections may lead to a large-scale problem. As different power supply sections of an HSR line are electrically disconnected via neutral sections, this paper concentrates on each power supply section individually. Figure 2 illustrates the block diagram of the bi-level model proposed in this paper. The upper blocks of computer simulation and scenarios are the pretreatment process, which offers input parameters for the following model. In this study, the sizing of HESS and comprehensive cost calculation are implemented within the time scope of the project service period. A bi-level model is thus proposed in order to reflect the close association between the total project cost and diurnal scheduling of HESS. The master level model concentrates on the optimal sizing of HESS and the slave level model involves the diurnal scheduling of HESS. As the decision variables of master level model, the power rating and capacity of battery and UC are regarded as the boundary parameters of slave level model. Battery lifetime, HESS operation hours and daily electricity cost calculated in the slave level model are returned to the master level model for the assessment of certain types of cost Energies 2018, 11,The x FOR PEER REVIEW 5 of 30 accordingly. diurnal operation of HESS is regarded as repeated within the project service period.

Figure Figure2.2.Overview Overviewof ofproposed proposedbi-level bi-levelmodel modeloptimization. optimization.

2.2. 2.2.Traction Traction Load Load and and Regenerative Regenerative Braking Braking Power Power As Asthe theinput inputparameters parametersof ofthe theproposed proposedmodel, model,railway railwaytraction tractionload loadand andRBP RBPprofile profileshould should be bedetermined determinedin inan anaccurate accurateand andefficient efficientway. way. Two Two common common methods methodsfor for traction tractionload loadprediction prediction include include[31]: [31]: • •

Computer simulation method based on traction and power supply calculation. Statistical model or sampling method based on measurement data from the meter installed in the traction substation. For ease of the analysis of different operation conditions, the computer simulation method is

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Computer simulation method based on traction and power supply calculation. Statistical model or sampling method based on measurement data from the meter installed in the traction substation.

For ease of the analysis of different operation conditions, the computer simulation method is adopted here. A lot of parameters of HSTs and HSR lines are required in advance in the computer simulation method, e.g., the traction force, running resistance and braking force of HSTs, slope, curve radius and speed limitation of HSR lines, and the equivalent impedance and admittance of traction power systems [31]. Normally, these required parameters can be obtained from the railway investigation and design institutes. Benefitting from the great advances of simulation software for the load processes of traction power supply systems, forecasting of railway traction loads and regenerative braking power can be easily implemented based on the aforementioned parameters and timetables preset by railway operators. In this study the traction simulation is performed via the commercial software ELBAS WEBAnet v3.121 (SIGNON Group, Berlin, Germany) [33]. On account of the computational resource limitations and for saving computation time, sampling and processing of the simulation results should be designed appropriately. The sampling time interval in [29] is determined as 1 min considering the short braking time. A time period reduction method is applied in [31,32] via combining short 30 s time periods to form longer time periods, yet with the defect of unequal duration between different time periods. The sampling time of power profile and the scheduling time interval of HESS are determined as 1 min in this study, based on the fact that power profiles of traction load and HESS do not change much during this short period. 2.3. Uncertainty Representation of PV Generation When we focus on the sizing configuration and long-term planning of HESS within the time scope of project period, the stochastic characteristics of weather conditions have to be included. Typically, a series of scenarios and corresponding probabilities are used to describe the stochastic process and data process [34], thus the scenario-based technique is adopted in this section. Renewable energy represented by PV generation is taken into account in this paper for the nearby consumption of renewable energy. With regard to the scenarios generation, in order to describe the uncertainty of PV generation as far as possible, the annual solar irradiance profile is used here to generate 365 different scenarios. Significant computational resources and time cost are required when all the scenarios are included in the stochastic bi-level model, thus a tradeoff between the solution accuracy and computation speed should be achieved [35–37]. Aiming at dealing with the contradiction of computational complexity and time limitation, scenario reduction method is developed in previous studies [34,38,39]. In [34] the scenario reduction algorithms reject the low-probability scenarios and aggregate those that approximate to each other in light of probability metric, forming a scenario subset that represents a relatively good approximation to the initial scenario set in terms of statistic metric: s ∈ {1, 2, 3, 4}

(1)

Various algorithms can be applied for scenario reduction, including the fast backward method, fast backward/forward method and fast backward/backward method [34,38]. In view of the different computation performance and accuracy between these algorithms, they are applicable for different occasions, such as the problem size and target precision [35,40,41]. For example, the forward method provides the best solution accuracy with the largest computational resource consumption, while the fast backward method requires the least computational effort at the cost of lower accuracy [35,41]. Therefore the forward method is utilized to generate four representative scenarios for scenario reduction in this study, as shown in Equation (1), considering a small number of scenarios need to be reduced.

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2.4. Hybrid Energy Storage Systems Energy storage systems play a key role in the cost-saving benefits of RTSEM by means of discharging during peak traction load periods and charging during regenerative braking periods. Two types of widely applied energy storage systems include the high energy density type, represented by batteries, and high power density type represented by UC. Batteries have good performance in terms of high energy density and mature manufacturing process, whereas lifetime cycles and power density are limited [42]. By contrast, UC have advantages of high power density, fast response, lower maintenance cost and extremely long cycle life [8], while low energy density and quite high energy capacity cost are the main obstacles to the spread application of UC. HESS is proposed with the intention of combining the batteries and UC to obtain both high energy and power density, and thus has an obvious advantage over the single type of energy storage system, especially for the application of peak load shaving and regenerative braking power absorbing in the high-speed railway system. In general, the UC’s advantage of long cycle life and fast response make it suitable to capture the railway power peaks and valleys in high frequency, while batteries are more suited for low frequency operation [31,32]. Accordingly, HESS is adopted in this study for the better energy saving performance. 3. Master Level: HESS Sizing Problem Formulation 3.1. Battery Degradation Analysis When applied into the electrified railway systems, HESSs are operated to coordinate with the traction loads, a kind of shock load with dramatic stochastic volatility. It is assumed that UC can serve for the entire project period and the batteries degradation analysis is considered, as a result of the fact that the lifetime of UC is less affected by the cycles, while batteries are more likely to suffer from the frequent fluctuations and plenty of cycles of traction load in view of the limited life cycles [42]. As the key connection between the master and slave level model, battery lifetime indicates the fact that the diurnal operation strategies of HESS have a great impact on the replacement cost, thus an optimal balance should be achieved between the performance of HESS and the replacement cost, and that is the problem this paper tries to solve. The disadvantage of limited lifetime cycles results in a more severe aging of batteries during the operation of HESSs, thus an appropriate method should be utilized to evaluate the aging rate of batteries within the considered time scope. There are lots of approaches for batteries lifetime estimation, in which the number of battery cycles calculation method is utilized in this study. Generally, battery cycles can be divided into two types, including full cycles and partial cycles [43]. A full cycle is defined as a combination of a charge half cycle and a discharge half cycle with equal starting SOC and ending SOC. Accordingly, a partial cycle is defined as a charge or discharge progress with unequal starting SOC and ending SOC. By means of the rainflow counting method, full cycles and half cycles can be extracted from a series of charge or discharge sequences. For further knowledge of counting methods readers may refer to [44]. The flow chart of the rainflow counting method is presented in Figure 3. The functions of this method include the extraction of two types of cycles and the determination of corresponding DOD of each cycle. According to manufacturer’s data, number of battery cycles to failure as a function of depth of discharge D is presented in Equation (2), by applying interpolation with least square method. The coefficient α1 , α2 , α3 and α4 are 24,090, −9.346, 6085 and −1.319 respectively in this study according to [45]: NC ( D ) = α1 eα2 · D + α3 eα4 · D (2) Each cycle corresponds to an aging rate. In order to establish the association between the lifetime and aging rate of each cycle, accumulated aging rate AR is derived in Equation (3) by adding up the total aging rate based on the total cycles (Ntotal ) of batteries within a day, where 1/[αi · NC ( Di )] is the aging rate for each cycle i. Coefficient αi is 1 when cycle i is a full cycle and 0.5 when cycle i is a half

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cycle, since it is regarded that the effect of a half cycle is the half of a full cycle. Therefore the expression of lifetime in years can be derived in Equation (4): Ntotal

AR =

∑

i =1

1 αi · NC ( Di )

(3)

Tbat = 1/(365A R )

(4)

Note that according to [45], an adverse effect is on the lifetime once the operating temperature is over 20 ◦ C. A constant operating temperature of 20 ◦ C is assumed in this study for the sake of Energies 2018, 11, x FOR PEER REVIEW 7 of 29 simplicity and the related cost is included in the Balance of Plant (BOP) cost that is introduced in Energies 2018, 11, x FOR PEER REVIEW 7 of 29 Section 3.2.1. Cycle counting algorithm startCycle counting algorithm

Input profile Input profile

SOC profiles of batteries from the optimal scheduling in the slave SOC profilesmodel of batteries from the optimal scheduling in the slave model Peaks and valleys extraction from the considered profilefrom Peaks and valleysSOC extraction

Rainflow counting Rainflow method counting method

the considered SOC profile

Full cycles and half cycles counting Full cycles and half cycles counting

start Read 3 successive points of peak and valley from starting point S Read 3 successive points of peak and valley from starting point S X denotes the considered peakvalley range X denotes the considered peakvalley range Y denotes the previous peakvalley range adjacent to X Y denotes the previous peakvalley range adjacent to X

Yes Yes

|X| x max j j   xi,j , else

(64) 16 of 29

Start Update the position of each search agent by Equation (61) Read all input data of traction load, PV Generation and price signal

Adjustment operation for variables beyond the lower/upper bounds by Equation (64)

Give the number of search agents (N), Max number of iterations (It max)

Additional operation by Equation (63) to maintain each component of search agents accounts to fixed decimal places

Initialize the wolf population Xi (i=1,2,…,N) by Equation (62)

Update a, A and C by Equation (53) and (54)

Initialize

a, A and C by Equation (53) and (54)

Transfer the position of each search agent to the slave model, obtain Ce via embedded CPLEX solver and update the fitness (total cost per day)

Update Xα, Xβ, Xδ Transfer the position of each search agent to the slave model, obtain Ce via embedded CPLEX solver and calculate the fitness (total cost per day)

Iteration index t = t + 1

If t >= It max ? Xα, Xβ, Xδ denote top three best search agent positions

Iteration index t =1

No

Yes Output Xα as optimal HESS sizing, corresponding fitness as optimal total cost per day

End

Figure 5. Flowchart of GWO with CPLEX solver embedded. Figure 5. Flowchart of GWO with CPLEX solver embedded.

6. Case Study 6. Case Study To validate the feasibility of proposed HESS sizing approach, an HSR line with a length of 710 To validate the feasibility of proposed HESS sizing approach, an HSR line with a length of 710 km km at the design phase in Xinjiang province is considered for case study. In this section the total cost at the design phase in Xinjiang province is considered for case study. In this section the total cost of of different cases within the project service period are compared and the effects of electricity pricing different cases within the project service period are compared and the effects of electricity pricing strategies, length of project service time and initial SOC of HESS are also analyzed. strategies, length of project service time and initial SOC of HESS are also analyzed. 6.1. Cases Description and Input Parameters As the diurnal operation of HESS is regarded as repeated within the project service period, the simulation period for case study is one day and TSS 2 of the HSR line is selected as an example for detailed cases analysis. Four different scenarios are proposed and they are presented as follows: • • • •

Case 1: conventional railway system with no HESS nor PV generation, as the base case; Case 2: conventional railway system with HESS only; Case 3: conventional railway system with battery energy storage systems only; Case 4: conventional railway system with both HESS and PV generation.

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6.1. Cases Description and Input Parameters As the diurnal operation of HESS is regarded as repeated within the project service period, 17 of 29 the simulation period for case study is one day and TSS 2 of the HSR line is selected as an example for detailed analysis. of Four different scenariossources are proposed and they are presented asItfollows: For cases the utilization RES, PV generation are included in RESEM system. is assumed

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1000 2200 800

400

TSS12 (DK 645.71km)

Tunnel 600

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Position in the line (km) TSS8 (DK 419.5km)

TSS12 (DK 645.71km)

TSS11 (DK 603.21km)

350

TSS10 (DK 541.8km)

TSS9 (DK 481km)

Figure 6. Longitudinal profile of HSR line for case study. Figure 6. Longitudinal profile of HSR line for case study.

TSS13 (DK 691.71km)

Traction substation

TSS7 (DK 357.8km)

TSS6 (DK 297.10km)

TSS4 (DK 180.51km)

TSS2 (DK 47km)

300

TSS5 (DK 239.80km)

200 TSS3 (DK 141.2km)

1600

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350

TSS13 (DK 691.71km)

Altitude curve

100

2000 1800

TSS11 (DK 603.21km)

TSS10 (DK 541.8km)

TSS9 (DK 481km)

TSS8 (DK 419.5km)

TSS7 (DK 357.8km)

TSS6 (DK 297.10km)

TSS4 (DK 180.51km)

TSS2 (DK 47km)

TSS3 (DK 141.2km)

TSS1 (DK 47km)

Altitude (m)

TSS5 (DK 239.80km)

that PV generation sources are connected to the traction substations. As for PV panels, ηpv = 12%, Apv • Case 1: conventional railway system with no HESS nor PV generation, as the base case; = 104 m2. PV converter capacity Spv = 1 MVA. The annual profile of solar irradiance can be obtained • Case 2: conventional railway system with HESS only; from [56] and four representative scenarios after using forward reduction algorithm are illustrated in • Case 3: conventional railway system with battery energy storage systems only; Figure 9b. • With Case 4:regard conventional railway system withbatteries both HESS PVare generation. to HESS, lead-acid (LA) andand UCs considered in this study. All parameters associated with HESS are presented in Table 2 [31,32,47,57]. is assumed that the service As an illustration, the longitudinal profile of considered HSR lineItand the location of traction period of this project years6.and the HESS-related devices can serve for km/h. the entire project Energies 2018, 11, x FOR PEERisREVIEW 17 of out 29 substations are outlined in20Figure Theall designed maximum speed is limited at 250 It turns period except for batteries. The lifetime estimation of LA batteries can be obtained according to the that there are high altitude drops between several adjacent TSSs, which is in favor of the production For the utilization of RES, PV generation sources are included in RESEM system. It is assumed method of RBP. introduced in previous sections. that PV generation sources are connected to the traction substations. As for PV panels, ηpv = 12%, Apv = 104 m2. PV converter capacity Spv = 1 MVA. The annual profile of solar irradiance can be obtained Altitude curve 2200 Tunnelalgorithm are illustrated in from [56] and four representative scenarios after using forward reduction Station 2000 Figure 9b. Traction substation With regard to1800 HESS, lead-acid (LA) batteries and UCs are considered in this study. All parameters associated 1600with HESS are presented in Table 2 [31,32,47,57]. It is assumed that the service period of this project is 20 years and all the HESS-related devices can serve for the entire project 1400 period except for batteries. The lifetime estimation of LA batteries can be obtained according to the 1200 method introduced in previous sections.

1400 CRH-3 HST (manufactured by6600kW China Railway Rolling Stock Corporation, Qingdao, China) is 300 300 (75% of traction) considered in this HSR line. Physical parameters of CRH-3 HST are listed in Table 1 and the traction 250 250 1200 4400kW and braking characteristics are presented in Figure 7. In regard to6000kW timetable, the departure time interval (50% of traction) 200 200 1000 of traction) of trains is3.0%30 min for both traveling2200kW directions. Based on the(75% above parameters of the trains and the 150 150 (25% of traction) 800 4000kW HSR line,2.0% the speed and power consumption of each400 train along the line are obtained by means of 100 200 300 500 600 700 (50% of traction) 100 100 1.2% in the line (km) results of upward trains are shown in the computer simulation software WEBAnet.Position The simulation 2000kW 0.6% 50 (25% of traction) Figure 850 and downwardFigure trains6.are processed profile in the of same Longitudinal HSRmanner. line for case study. Level track 0

0

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Braking Force (kN)

Traction Force (kN)

Wheel (half worm): 0.830m

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(75% of traction)

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(a)

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Power comsuption (MW)

Traction Force (kN)

(half worm): 0.830m 250 250 high-speed train: (a) Traction curve; (b) Figure 7. TractionWheeland braking characteristic of CRH-3 Wheel (half worm): 0.830m 4400kW (50% of traction) Braking curve. 200 200 6000kW


15 50 10 5

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-5

50 Traction and braking characteristic of CRH-3 high-speed train: (a) Traction curve; (b) Figure 7. -10 Figure 7. Traction and braking characteristic of CRH-3 high-speed train: (a) Traction curve; Braking curve. 0 -15 (b) Braking curve. 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 300

Position of the train (km)

25

(a)

20

250


(b)

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r comsuption (MW)

Speed (km/h)

Figure 8. Dynamic speed and power consumption of upward trains versus position: (a) Speed curve; 15 200 consumption curve, where the negative values indicate regenerative braking power. (b) Energy 10 5 0

Figure 6. Longitudinal profile of HSR line for case study. 350

350


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200


150

4000kW Table 1. Parameters of CRH-3 HST. (50% of traction)

2.0% 1.2%

50 0.6% Level track

0

300


250

Braking Force (kN)

Traction Force (kN)

300

Parameters

100

2000kW

50

Value

(25% of traction) Parameters

Value

0

100 150 200 250 300 350 50 power 100 150 200 250 300 350 Unloaded weight 479.36 t Max.0 traction 8800 kW Train Speed (km/h) (km/h) Average load 56.64 t Max. braking power Train Speed 8000 kW (b) 408 kW Power factor(a) (traction) 0.98 Auxiliary power Power factor (braking) 0.9 Max. acceleration (traction) 0.65 m/s2 Figure 7. Traction and braking characteristic of CRH-3 high-speed train: (a) Traction 2curve; (b) Transmission efficiency 0.9 Max. acceleration (braking) 1.2 m/s Braking curve. 0

50

25

300

20

Power comsuption (MW)

Speed (km/h)

250

200

150

100

50

0

15 10 5 0 -5 -10

0

100

200

300

400

500


(a)

Energies 2018, 11, x FOR PEER REVIEW

600

700

-15

0

100

200

300

400

500

600

700


(b)

18 of 29

Figure 8. Dynamic speed and power consumption of upward trains versus position: (a) Speed curve; Figure 8. Dynamic speed and power consumption of upward trains versus position: (a) Speed curve; negative values indicate (b) Energy consumption curve, where Table the 1. Parameters of CRH-3 HST.regenerative braking power. (b) Energy consumption curve, where the negative values indicate regenerative braking power.

Parameters Value Parameters Value For the utilization of RES, PV generation are included in RESEM system. Unloaded weight 479.36 tsourcesMax. traction power 8800 kWIt is assumed that PV generationAverage sourcesload are connected to tthe traction As for PV panels, 56.64 Max. substations. braking power 8000 kW η pv = 12%, Apv = 104 m2 . Power PV converter MVA. The annual profile of solar irradiance can be obtained factor capacity (traction)Spv = 10.98 Auxiliary power 408 kW 2 from [56] and Power four representative scenarios0.9 after using reduction algorithm are illustrated in factor (braking) Max. forward acceleration (traction) 0.65 m/s Figure 9b. Transmission efficiency 0.9 Max. acceleration (braking) 1.2 m/s2

(a)

(b)

Figure9.9.Initial Initialand andreduced reducedscenarios: scenarios: (a) (a) Annual Annual data data of of solar solar irradiance; irradiance; (b) (b) Typical Typicalscenarios scenariosof of Figure solar irradiance after scenario reduction. solar irradiance after scenario reduction. Table 2. Parameters of hybrid energy storage systems.

With regard to HESS, lead-acid (LA) batteries and UCs are considered in this study. All parameters Unit It is assumed LA Battery UC associated with HESS areParameters presented in Table 2 [31,32,47,57]. that the service period of this costs CNY/kW 2838 2050period except for project is 20 years and allPCS the HESS-related devices can serve for the entire project Energy capacity CNY/kWh 4640 198,000 batteries. The lifetime estimation of costs LA batteries can be obtained according to the method introduced CNY/kWh 1292 0 in previous sections. Replacement costs BOP costs CNY/kW 674 674 O&M costs (fixed) CNY/kW/year 25.5 0 O&M costs (variable) CNY/MW/h 2.78 0 Efficiency (charge/discharge) 80%/80% 95%/95% SOC range 20~80% 0~100% Initial SOC 50% 50% Self-discharging rate /mon 5% 0 Depreciation coefficient 0.7 0.7

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Table 2. Parameters of hybrid energy storage systems. Parameters

Unit

LA Battery

UC

PCS costs Energy capacity costs Replacement costs BOP costs O&M costs (fixed) O&M costs (variable) Efficiency (charge/discharge) SOC range Initial SOC Self-discharging rate Depreciation coefficient

CNY/kW CNY/kWh CNY/kWh CNY/kW CNY/kW/year CNY/MW/h /mon -

2838 4640 1292 674 25.5 2.78 80%/80% 20~80% 50% 5% 0.7

2050 198,000 0 674 0 0 95%/95% 0~100% 50% 0 0.7

Two different electricity pricing schemes, including fixed tariff and time-of-use (TOU) tariff are considered here. The fixed tariff is 0.782 CNY/kWh for all time periods. As for TOU tariff, electricity price varies at different time periods. The price is 1.252 CNY/kWh for peak time periods of 8:00–11:00 and 18:00–21:00, 0.370 CNY/kWh for valley time periods of 0:00–6:00 and 22:00–0:00, 0.782 CNY/kWh for the rest time periods. The penalty charge price equals to the electricity price. Moreover, the demand charge price is 1.2 CNY/kW and the annual discount rate r0 is 5%. It is assumed that the upper and bat ∈ [1, 3] MW, Ebat ∈ [5, 10] MWh, lower bounds of decision variables of master level model are Prate rate uc uc Prate ∈ [10, 20] MW and Erate ∈ [0.1, 0.5] MWh. The GWO with CPLEX solver embedded approach is implemented under a MATLAB environment on a computer with Intel Core i5-4210M CPU at 2.6 GHz and 8 GB RAM. In GWO the number of search agents is 50 and the maximum number of iterations is 50. CPLEX solver is performed with YALMIP toolbox [58] for the convenience of describing variables and constraints easily and selecting different solvers. 6.2. Cases Results Analysis 6.2.1. Case 1 As the base case, Case 1 demonstrates the scenario of conventional railway system at present, i.e., no HESS, RES considered. Toward this end, the total cost per day equals to the daily electricity cost. The results are listed in Table 3 and the composition of electricity cost is presented in Figure 10. Table 3. Results of different cases. Cases

Case 1

Case 2

Case 3

Case 4

Pricing Schemes

Fixed Tariff

TOU Tariff

Fixed Tariff

TOU Tariff

Fixed Tariff

TOU Tariff

Fixed Tariff

TOU Tariff

bat /MW Prate bat /MWh Erate uc /MW Prate uc /MWh Erate Tbat /year Ce /k CNY HESS /k CNY Ccap bat /k CNY Crep HESS Com /CNY Csal /k CNY Ctotal /k CNY

88.70 88.70

99.98 99.98

2.9 5.0 13.0 0.43 5.47 40.84 26.72 3.57 202.60 0.57 70.76

2.2 5.0 11.6 0.43 3.26 45.42 25.75 7.14 153.70 1.43 77.02

2.9 5.1 1.21 70.38 6.22 19.42 202.60 0.83 95.39

3.0 5.1 1.1 75.83 6.29 21.84 209.60 1.48 102.69

2.7 5.0 16.7 0.49 3.95 31.31 30.18 5.95 188.63 1.55 66.08

2.7 5.0 14.5 0.48 2.84 33.14 28.98 8.33 169.52 1.60 69.04

Battery cycles per day (full/half cycles)

-

-

16/4

21/3

75/4

73/3

25/3

32/5

Electricity Cost Savings

-

-

53.96%

54.57%

20.65%

24.16%

64.70%

66.85%

Total Cost Savings

-

-

20.22%

22.96%

−7.54%

−2.71%

25.50%

30.95%

Com /CNY Csal /k CNY Ctotal /k CNY Battery cycles per day (full/half cycles) Electricity Cost Savings Energies 2018, 11, 2199 Total Cost Savings

88.70

99.98

202.60 0.57 70.76

153.70 1.43 77.02

202.60 0.83 95.39

209.60 1.48 102.69

188.63 1.55 66.08

169.52 1.60 69.04

-

-

16/4

21/3

75/4

73/3

25/3

32/5

-

-

53.96% 20.22%

54.57% 22.96%

20.65% −7.54%

24.16% −2.71%

64.70% 25.50%

66.85% 19 of 29 30.95%

125

Electricity cost per day (k CNY)

Energy consumption charge

Denmand charge

Penalty charge

99.98

100 88.70 75

70.38

50

40.84

75.83

45.42 31.31

33.14

25

0

Fixed Tariff TOU Tariff




Case 1

Case 2

Case 3

Case 4

Figure Figure 10. 10. Electricity Electricity cost cost and and composition composition in in different different cases. cases.

The obtained results are 88.70 k CNY and 99.98 k CNY under fixed tariff and TOU tariff The obtained results are 88.70 k CNY and 99.98 k CNY under fixed tariff and TOU tariff respectively. It shows that rail operators can benefit more under fixed tariff from the perspective of respectively. It shows that rail operators can benefit more under fixed tariff from the perspective of daily cost, which is in line with current situation that fixed tariff is adopted in Chinese railway systems. daily cost, which is in line with current situation that fixed tariff is adopted in Chinese railway systems. 6.2.2. Case 2 6.2.2. Case 2 In this case, HESS is included compared to Case 1. By applying proposed bi-level model In this case, HESS is included compared to Case 1. By applying proposed bi-level model combining combining HESS sizing and daily scheduling, the optimized sizing results are shown in Table 3. It is HESS sizing and daily scheduling, the optimized sizing results are shown in Table 3. It is interesting interesting that there are electricity cost savings of 53.96% under fixed tariff and 54.57% under TOU that there are electricity cost savings of 53.96% under fixed tariff and 54.57% under TOU tariff, and the tariff, and the corresponding percentage for total cost saving are 21.78% and 24.12%, owing to the corresponding percentage for total cost saving are 21.78% and 24.12%, owing to the operation of operation of charging at valley time period with low price and discharging at peak time period with charging at valley time period with low price and discharging at peak time period with high price high price under TOU tariff. under TOU tariff. Another significant difference we need to pay close attention to is the battery lifetime. As shown Another significant difference we need to pay close attention to is the battery lifetime. As shown in in Table 3, the battery lifetime of 3.26 years under TOU tariff is apparently shorter than that of 5.27 Table 3, the battery lifetime of 3.26 years under TOU tariff is apparently shorter than that of 5.27 years under fixed tariff, primarily arising from the fact that battery performs with a broader range of SOC and larger DOD of cycles so as to take advantage of the pricing signal and minimize the electricity cost under TOU tariff. In order to demonstrate the operation status of system components in detail, a time horizon of 2 h and a half from 8:00 to 10:30 is highlighted, as shown in Figure 11. As we can observe from Figure 10a, the effects of peak traction load shaving and RBP absorption are significant with the application of HESS compared to case 1, which gives an explicit explanation of the remarkable reduction of electricity cost. The frequent energizing of UC and relatively smooth energizing of LA battery depicted in Figure 11b,c reveal that, UC takes the responsibility of responding to power peaks rapidly, while LA battery plays the role of storing massive energy.

h and a half from 8:00 to 10:30 is highlighted, as shown in Figure 11. As we can observe from Figure 10a, the effects of peak traction load shaving and RBP absorption are significant with the application of HESS compared to case 1, which gives an explicit explanation of the remarkable reduction of electricity cost. The frequent energizing of UC and relatively smooth energizing of LA battery depicted 11b,c reveal that, UC takes the responsibility of responding to power 20 peaks Energies 2018,in11,Figure 2199 of 29 rapidly, while LA battery plays the role of storing massive energy. power of utility grid in Case 2

power of utility grid in Case 1

40 20 0 -20

(a)

(b)

(c) Figure 11. Results demonstration of Case 1 and Case 2: (a) Power of utility grid in Case 1 and Case 2, Figure 11. Results demonstration of Case 1 and Case 2: (a) Power of utility grid in Case 1 and Case 2, where positive values indicate power imported from grid and negative values indicate power fed where positive values indicate power imported from grid and negative values indicate power fed back back to grid; (b) Charge and discharge power of LA battery and UC in Case 2, where positive values to grid; (b) Charge and discharge power of LA battery and UC in Case 2, where positive values indicate indicate discharge power and negative values indicate charge power; (c) SOC of LA battery and UC discharge power and negative values indicate charge power; (c) SOC of LA battery and UC in Case 2. in Case 2.

6.2.3. Case 3 6.2.3. Case 3 In this section we consider the base case with BESS, for the comparison with the performance of In this section we consider the base case with BESS, for the comparison with the performance of HESS. All parameters of LA battery are same with HESS in Case 2. The power and SOC of LA battery HESS. All parameters of LA battery are same with HESS in Case 2. The power and SOC of LA battery during aa time of 22 hh and Energies 11, horizon xhorizon FOR PEER 21 of 29 during2018, time ofREVIEW and aa half half are are illustrated illustrated in in Figure Figure12. 12.

As we can observe from Table 3, battery lifetime are 1.21 year and 1.10 year under fixed tariff and TOU tariff in case 3, which is much shorter than that in case 2, and the replacement cost in Case 3 is consequently much larger than that in Case 2. Moreover, negative total cost savings of −10.86% and −1.31% under these two pricing schemes are achieved, which means that the daily total cost is even larger than initial electricity cost in Case 1. In order to explain the difference of battery lifetime in detail, the SOC curve of LA battery in Case 2 and (a) Case 3 are illustrated in Figure 12. As0.8Figure 13 shows, the SOC curve of LA battery in Case 3 contains more fluctuating components and micro-cycles. For instance, in Figure 13a, SOC of LA battery in Case 2 contains merely a half cycle 0.6 in a fixed time horizon of two hours. By contrast, SOC of LA battery in Case 3 has five half cycles and 0.4 seven full cycles, resulting in a significant reduction of battery lifetime and degradation of system 0.2 applicability. As 8:15 a result, 8:30 compared of battery only perform in 8:00 8:45 to BESS, 9:00 a combination 9:15 9:30 9:45 and UC 10:00cannot 10:15 10:30 Time (hr) a more flexible manner, but also help prolong the battery lifetime and reduce relevant replacement cost. (b) Figure 12. Power and SOC of LA battery in Case 3 under TOU tariff: (a) Charge and discharge power, Figure 12. Power and SOC of LA battery in Case 3 under TOU tariff: (a) Charge and discharge power, where positive values indicate discharge power and negative values indicate charge power; (b) SOC. where positive values indicate discharge power and negative values indicate charge power; (b) SOC. Cycles identification of LA battery SOC in case 2 0.4

Value

① As we can observe from Table 3, battery lifetime are 1.21 year and 1.10 year under fixed tariff 0.38 and TOU tariff in case 3, which is much shorter than that in case 2, 0.36 and the replacement cost in Case 3 ② 0.34 is consequently much larger than that in Case 2. Moreover,①negative total cost savings of −10.86% 1(h) 0.32 and −1.31% under these two pricing schemes are achieved, which0.3 means that the daily total cost is

Upper Limit

peaks and valleys of SOC signal

0.28

0

1

Number of peaks and valleys

Cycles identification of LA battery SOC in case 3 0.38

11(h) 9(h)

0.36 6(f)

Lower Limit

②

alue

0.34 0.32

4(f)

5(f)

12(h) 10(h)

7(f)

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(a)

0.8

even larger than initial electricity cost in Case 1. In order to explain the difference of battery lifetime in 0.6 detail,0.4the SOC curve of LA battery in Case 2 and Case 3 are illustrated in Figure 12. As Figure 13 shows, the SOC curve of LA battery in Case 3 contains more fluctuating components 0.2 and micro-cycles. in8:45Figure 9:00 13a, SOC9:15 of LA battery in9:45 Case 2 contains merely a10:30 half cycle 8:00 8:15 For instance, 8:30 9:30 10:00 10:15 Time (hr) in a fixed time horizon of two hours. By contrast, SOC of LA battery in Case 3 has five half cycles (b) and seven full cycles, resulting in a significant reduction of battery lifetime and degradation of system applicability. As a result, compared to BESS, a combination battery and UCand cannot only power, perform in a Figure 12. Power and SOC of LA battery in Case 3 under TOUoftariff: (a) Charge discharge more flexible manner, but also help prolong theand battery lifetime and reduce relevant replacement where positive values indicate discharge power negative values indicate charge power; (b) SOC. cost. Cycles identification of LA battery SOC in case 2 0.4

①

0.38

② Value

0.36

①

0.34 1(h)

0.32 0.3

Upper Limit


0.28

0

1



11(h) 9(h)

0.36 6(f)

Lower Limit

②

Value

0.34 0.32

1(h)

SOC of LA battery in case 2 SOC of LA battery in case 3

5(f)

4(f) 2(f)

0.3

12(h) 10(h)

7(f)

3(f)

0.28 0.26


8(h)

0

5

10

15

20


(a) Cycles identification of LA battery SOC in case 2 0.8

①

②

1

①

Value

0.79

0.77

Upper Limit

0.8

1(f)

0.78

2(f)

3(h)


0.76 0

0.6

1

2

3

4

6

7

SOC


0.4

1(h) 8(f)

0.79

②

SOC of LA battery in case 2 SOC of LA battery in case 3

0

4

8

Value

Lower Limit

0.2

6(f)

0.77

5(f) 4(f)

0.76

3(h)

0.75

12

16

20

24

Time (hr)

0.74

10(f)

2(f)

0.78

0

5


9(f) 12(h)

11(h) 0

5

7(f) peaks and valleys of SOC signal

10

15

20


(b) Figure curve of of LALA battery andand cycle identification in Case 2 (HESS) and and CaseCase 3 (BESS): (a) Figure13. 13.SOC SOC curve battery cycle identification in Case 2 (HESS) 3 (BESS): b ) Under TOU tariff, where (f) denotes full cycle and (h) denotes a half cycle. Under fixed tariff; ( (a) Under fixed tariff; (b) Under TOU tariff, where (f) denotes full cycle and (h) denotes a half cycle.

6.2.4. Case 4 6.2.4. Case 4 For the utilization of renewable energy sources, PV generation as well as HESS are included in For the utilization of renewable energy sources, PV generation as well as HESS are included in this case. The power and SOC of LA battery and UC over a time horizon of 2 h and a half are presented this case. The power and SOC of LA battery and UC over a time horizon of 2 h and a half are presented in Figure 14. The obtained results show that there are 27.07% and 32.39% of total cost savings under in Figure 14. The obtained results show that there are 27.07% and 32.39% of total cost savings under two price schemes, with marked improvements compared to Case 2. two price schemes, with marked improvements compared to Case 2.

difference of LA battery SOC with or without PV integrated occurs at the daytime, particularly from 10:00 to 18:00. Generally, at daytime LA battery SOC curve in Case 4 stays at a higher level, while contains more cycles with larger DOD. Energies x FOR PEER 22 of to 29 As2018, PV 11, generation isREVIEW considered here, batteries tend to charge and discharge more frequently make full use of the available renewable energy and reduce the energy demand from utility grid so Energies 2018, 11, 2199 22 of 29 is noteworthy that the batteryaccelerates lifetimes of and 2.84 years in this case are as to However, reduce theitelectricity cost, which inevitably the3.95 aging of batteries. evidently decreased compared to the 5.47 and 3.26 years in Case 2. As shown in Figure 15, the difference of LA battery SOC with or without PV integrated occurs at the daytime, particularly from 10:00 to 18:00. Generally, at daytime LA battery SOC curve in Case 4 stays at a higher level, while contains more cycles with larger DOD. As PV generation is considered here, batteries tend to charge and discharge more frequently to make full use of the available renewable energy and reduce the energy demand from utility grid so as to reduce the electricity cost, which inevitably accelerates the aging of batteries. (a)

(a) (b) Figure 14. Power and SOC of LA battery and UC in Case 4 under TOU tariff: (a) Charge and discharge Figure 14. Power and SOC of LA battery and UC in Case 4 under TOU tariff: (a) Charge and discharge power, where positive values indicate discharge power and negative values indicate charge power; power, where positive values indicate discharge power and negative values indicate charge power; (b) SOC. (b) SOC.

However, it is noteworthy that the battery lifetimes of 3.95 and 2.84 years in this case are evidently Upper Limit decreased compared to the 5.47 and 3.26 years in(b) Case 2. As shown in Figure 15, the difference of LA battery SOC with or without PV integrated occurs at the daytime, particularly from to 18:00. Figure 14. Power and SOC of LA battery and UC in Case 4 under TOU tariff: (a) Charge and 10:00 discharge Generally, at daytime LA battery SOC curve in Case 4 stays at a higher level, while contains power, where positive values indicate discharge power and negative values indicate charge power;more cycles ) SOC.larger DOD. (bwith Lower Limit Upper Limit

Figure 15. Comparison of LA battery SOC between Case 2 (without PV integrated) and Case 4 in scenario 2 (with integrated PV). Lower Limit 6.2.5. Convergence Performance of GWO

As GWO algorithm is utilized to solve the master level problem, a comparison of convergence performance between GWO, differential evolution (DE), simulated annealing (SA) optimization and particle swarm optimization (PSO) is conducted, as shown in Figure 16. Note that in this section, Figure 15. Comparison of LA battery SOC between Case 2 (without PV integrated) and Case 4 in 15. Comparison LA batteryCPLEX SOC between 2 (without PVthe integrated) theseFigure four algorithms with of embedded solver Case are used to solve problemand in Case Case 42 in under scenario 2 (with integrated PV). fixedscenario tariff. 2 (with integrated PV). 6.2.5. Convergence Performance of GWO As PV generation is considered here, batteries tend to charge and discharge more frequently to algorithm is utilized to solve the and master level problem, a comparison of convergence makeAs fullGWO use of the available renewable energy reduce the energy demand from utility grid so as performance between GWO, differential evolution (DE), simulated annealing (SA) optimization and to reduce the electricity cost, which inevitably accelerates the aging of batteries. particle swarm optimization (PSO) is conducted, as shown in Figure 16. Note that in this section, 6.2.5. Performance of GWO these Convergence four algorithms with embedded CPLEX solver are used to solve the problem in Case 2 under fixed tariff. As GWO algorithm is utilized to solve the master level problem, a comparison of convergence performance between GWO, differential evolution (DE), simulated annealing (SA) optimization and particle swarm optimization (PSO) is conducted, as shown in Figure 16. Note that in this section, these four algorithms with embedded CPLEX solver are used to solve the problem in Case 2 under fixed tariff.

Energies 2018, 11, x FOR PEER REVIEW 7.6

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104

total(CNY) cost per day (CNY) Best fitness of Best total fitness cost perofday

Energies 2018, 11, 2199 Energies 2018, 11, x FOR PEER REVIEW 7.5

7.6 7.4

23 of 29 23 of 29

GWO DE PSO SA

104

GWO DE PSO SA

7.5 7.3 7.4 7.2

X=29 Y=7.0783e+04

X=41 Y=7.0844e+04

7.3 7.1 X=12 Y=7.0760e+04

7.2 7 0

X=16 Y=7.0760e+04

10

20

30

X=29 Y=7.0783e+04

40

X=41 Y=7.0844e+04

50

Iteration

7.1

X=12 X=16 Figure 16. Convergence characteristics of grey wolf optimizer, differential evolution, simulated Y=7.0760e+04 Y=7.0760e+04 7 annealing optimization and particle swarm optimization for under fixed 0 10 20 30 Case 2 40 50 tariff.

Iteration

Capital cost

20

Total cost saving (%)

Replacement cost

19.0 20.0

30 15

18.5 19.5

25 10

18.0 19.0

20 5

17.5 18.5

15 0 10 5

19.5 20.5

20

30

40

50

60

Initial SOC (%)

70

80 18.0

(a)

15 50 30

Capital cost

25 Total cost saving (%) 10

Replacement cost

20 5

40 20

15 0 10 -5

30 10

20 0

5 -10 10

11

12

13

14

15

16

17

18

19

20

0

Project service period (year) 10

(b)

-5 -10

17.5 0 Figure 17. studies: (a) The impact of cost saving; ((b) b) The impact 11 on 12 total 13 14 15 16 17 18 19 20 Figure 17.30Sensitivity Sensitivity studies: of initial initial SOC SOC of of10HESS HESS on total cost saving; The impact 20 40 50 60(a) The 70 impact 80 Project service period (year) Initial SOC (%) of project service period on total cost saving. of project service period on total cost saving.

0

(a)

Total cost savingTotal (%) cost saving (%)

35

Cost per day (k CNY) Cost per day (k CNY)

25

Total cost savingTotal (%) cost saving (%)

Cost per day (k Cost CNY)per day (k CNY)

Figure 16 shows that the optimal solution of GWO equals to that of DE (70.760 k), both of which Figure 16. Convergence characteristics of grey wolf optimizer, differential evolution, simulated Figure 16. PSO Convergence of k). grey wolf optimizer, differential evolution, are better than (70.783 k)characteristics and SA (70.844 Besides, the optimal solutions of GWO,simulated DE, PSO and annealing optimization and particle swarm optimization for Case 2 under fixed tariff. annealing optimization and particle swarm optimization for Case 2 under fixed tariff. SA are achieved at the 12th, 16th, 29th and 41th iterations, respectively, which indicates that GWO algorithm better that convergence performance othertoalgorithms for solving theofRTSEM Figurehas 16 shows the optimal solution of than GWOthe equals that of DE (70.760 k), both which Figure 16 shows that the optimal solution of GWO equals to that of DE (70.760 k),PSO both of problem in this paper. Therefore, the results validate the effectiveness of GWO technique with are better than PSO (70.783 k) and SA (70.844 k). Besides, the optimal solutions of GWO, DE, and which are better than PSO (70.783 k) and SA (70.844 k). Besides, the optimal solutions of GWO, DE, embedded CPLEX solver. SA are achieved at the 12th, 16th, 29th and 41th iterations, respectively, which indicates that GWO PSO and SA achieved at the 12th, 16th, 29ththan and the 41thother iterations, respectively, which algorithm hasare better convergence performance algorithms for solving theindicates RTSEM 6.3. Sensitivities Analysis that GWO algorithm has better convergence performance than the other algorithms for solvingwith the problem in this paper. Therefore, the results validate the effectiveness of GWO technique RTSEM problem in this paper. Therefore, the results validate the effectiveness of GWO technique with embedded As theCPLEX defaultsolver. project service period and daily initial SOC of HESS are set as 20 years and 50% embedded CPLEX solver. in previous cases analysis, in this section, the sensitivities analysis concerning daily initial SOC of 6.3. Sensitivities Analysis HESS and project service period are performed to evaluate the impact of these two parameters on 6.3. Sensitivities Analysis total As costthe savings. default project service period and daily initial SOC of HESS are set as 20 years and 50% As for thethe default project service concerning period and dailyinitial initial SOCofofHESS, HESSboth are set 20 years As sensitivity LAas battery andand UC50% are in previous cases analysis,analysis in this section, thedaily sensitivitiesSOC analysis concerning daily initial SOC of in previous cases analysis, in this section, the sensitivities analysis concerning daily initial SOC of performed with theservice same initial that the considered SOC depends theparameters SOC rangeon of HESS and project periodSOC are so performed to evaluateinitial the impact of theseon two HESS and project service period are performed to evaluate the impact of these two parameters on total LA A series of initial SOC values of 20%, 30%, 40%, 50%, 60%, 70% and 80% are simulated totalbattery. cost savings. cost savings. with default project service periodconcerning under fixeddaily priceinitial tariffSOC and of relevant results shown in UC Figure As for the sensitivity analysis HESS, both LAare battery and are As for the sensitivity analysis concerning daily initial SOC of HESS, both LA battery and UC are 17a. As observed in Figure 17a, a maximum total cost saving of 20.22% is achieved with initial SOC performed with the same initial SOC so that the considered initial SOC depends on the SOC range of performed with the same initial SOC so that the considered initial SOC depends on the SOC range of of as a result of of allowing for a values more flexible LA50%, battery. A series initial SOC of 20%,SOC 30%,range. 40%, 50%, 60%, 70% and 80% are simulated LA battery.regard A series of initial SOC values of 20%, 30%,of40%, 50%,from 60%,10 70% and 80%are areconsidered simulated to the project service period, series integers to 20 years with With default project service period under fixeda price tariff and relevant results are shown in Figure with default project service period under fixed price tariff and relevant results are shown in Figure 17a. for sensitivity study with default initial SOC. Figure 17b reveals that total cost savings keep increasing 17a. As observed in Figure 17a, a maximum total cost saving of 20.22% is achieved with initial SOC As observed in Figure 17a, a maximum total cost saving of 20.22% is achieved with initial SOC of 50%, with theas extension of project service period, arisingSOC from a more sufficient utilization of UC. It’s worth of 50%, a result of allowing for a more flexible range. as a result of allowing for a more flexible SOC range. noting thatregard the project bounded by the cycle from lifetime. With to theperiod projectshould servicebeperiod, a series ofUC integers 10 to 20 years are considered for sensitivity study with default initial SOC. Figure 17b 50reveals that total cost savings keep increasing 20.5 35 Total cost saving (%) 25 Capital cost Replacement cost Total cost saving (%) Capital cost Replacement cost with the extension of project service period, arising from a more sufficient utilization of UC. It’s worth 20 30 20.0 noting that the project period should be bounded by the40 UC cycle lifetime.

(b)

Figure 17. Sensitivity studies: (a) The impact of initial SOC of HESS on total cost saving; (b) The impact of project service period on total cost saving.

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With regard to the project service period, a series of integers from 10 to 20 years are considered for sensitivity study with default initial SOC. Figure 17b reveals that total cost savings keep increasing with the extension of project service period, arising from a more sufficient utilization of UC. It’s worth noting that 11, thex project period should be bounded by the UC cycle lifetime. Energies 2018, FOR PEER REVIEW 24 of 29 6.4. Cost Savings Savings Analysis Analysis of of TSSs TSSs in 6.4. Cost in the the HSR HSR Line Line Detailed TSS 22 have have been been performed performed in in the the previous previous sections. sections. Here Here we we concentrate concentrate Detailed case case studies studies of of TSS on the cost-saving study of remaining TSSs in the HSR line and try to evaluate whether on the cost-saving study of remaining TSSs in the HSR line and try to evaluate whether each each TSS TSS shows when thethe HESS is integrated. NoteNote that one the of twothe power shows satisfactory satisfactorycost-saving cost-savingpotentials potentials when HESS is integrated. thatofone two supply sectionssections that each TSS contains is selected for costfor savings analysis. power supply that each TSS contains is selected cost savings analysis. As observed from Figure 18, almost all TSSs shows different levels of economic-saving potentials potentials As observed from Figure 18, almost all TSSs shows different levels of economic-saving and 10, primarily primarily arising arising from from considerable and the the best best cost cost saving saving is is achieved achieved at at TSS TSS 10, considerable RBP RBP of of train train at at on on long and sharp grade. With regard to TSS 12 and TSS 13, high altitude and relatively gentle sloping long and sharp grade. With regard to TSS 12 and TSS 13, high altitude and relatively gentle sloping track result in in lower lower RBP RBP for for reuse reuse and and inconspicuous inconspicuous cost-saving cost-saving results. results. Toward Toward this TSSs with with track result this end, end, TSSs notable notable cost cost savings savings should should be be given given priority priority to to when when HESS HESS is is applied applied in in the the future. future. 40 With HESS and PV generation

With HESS

Total cost saving (%)

35 30 25 20 15 10 5 0

1

2

3

4

5

6

7

8

9

10

11

12

13

TSSs

Figure 18. Cost TSSs in in the the HSR HSR line. line. Figure 18. Cost saving saving results results of of TSSs

7. Conclusions 7. Conclusions This paper proposes a bi-level model combining long-term HESS sizing and short-term diurnal This paper proposes a bi-level model combining long-term HESS sizing and short-term diurnal HESS dispatch strategy for energy management in railway traction substations. The optimized sizing HESS dispatch strategy for energy management in railway traction substations. The optimized sizing of HESS involving power rating and capacity of LA battery and UC is formulated in the master level of HESS involving power rating and capacity of LA battery and UC is formulated in the master level model with the intention of minimizing the total cost throughout the project service period, with model with the intention of minimizing the total cost throughout the project service period, with battery battery degradation and replacement cost taken into account. While the diurnal HESS scheduling degradation and replacement cost taken into account. While the diurnal HESS scheduling strategy strategy is formulated as a MILP model in the slave level model. The proposed GWO with CPLEX is formulated as a MILP model in the slave level model. The proposed GWO with CPLEX solver solver embedded approach has been implemented successfully on TSSs of considered HSR line. The embedded approach has been implemented successfully on TSSs of considered HSR line. The case case study results reveal that there are significant cost savings with the integration of HESS and RES study results reveal that there are significant cost savings with the integration of HESS and RES under both fixed tariff (25.5%) and TOU tariff (30.95%). Besides, a combination of battery and UC, under both fixed tariff (25.5%) and TOU tariff (30.95%). Besides, a combination of battery and UC, namely HESS, helps prolong the battery lifetime and reduce replacement cost remarkably. namely HESS, helps prolong the battery lifetime and reduce replacement cost remarkably. Meanwhile, Meanwhile, the daily initial SOC of HESS and project service period are found to have significant the daily initial SOC of HESS and project service period are found to have significant impacts on total impacts on total cost savings, and the sensitivity analysis is performed. It is noteworthy that TSSs in cost savings, and the sensitivity analysis is performed. It is noteworthy that TSSs in the HSR line the HSR line present different cost-saving potentials under different line geometry, thus it is crucial present different cost-saving potentials under different line geometry, thus it is crucial to evaluate each to evaluate each TSS in advance so as to provide preferences for further application of HESS. TSS in advance so as to provide preferences for further application of HESS. Future work can incorporate the power flow calculation of traction networks into the Future work can incorporate the power flow calculation of traction networks into the optimization optimization model and figure out the optimal position and sizing of HESS and RES in the HSR line. model and figure out the optimal position and sizing of HESS and RES in the HSR line. Moreover, Moreover, HESS between adjacent power supply sections for power routing and negative sequence reduction deserves further study. Author Contributions: Y.L. and M.C. proposed the idea, developed the model, performed the simulation works and wrote the paper. S.L., Y.C. were in charge of review and editing. This work was conducted under the supervision of Q.L.

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HESS between adjacent power supply sections for power routing and negative sequence reduction deserves further study. Author Contributions: Y.L. and M.C. proposed the idea, developed the model, performed the simulation works and wrote the paper. S.L., Y.C. were in charge of review and editing. This work was conducted under the supervision of Q.L. Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 51877182) and the Science and Technology Plan Project of Sichuan Province (Grant No. 2018FZ0107). The APC was funded by the National Natural Science Foundation of China and the Science and Technology Plan Project of Sichuan Province. Acknowledgments: This research was supported by the China Railway Construction Co., Ltd. (CRCC) and the First Design and Survey Institute (FDSI) Group Co., Ltd. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature Abbreviations RTSEM HESS PCS BOP RBP UC LA PV MILP HSR HSTs DOD SOC Parameters Ptload Ptbreak T ∆t ρt,s pen ρt,s Apv πs pv st,s Tproj r0 Pbat , Pbat Ebat , Ebat Puc , Puc Euc , Euc bat , η bat ηdis ch uc , η uc ηdis ch εb,εc SOCbat min , SOCbat max SOCbat 0 SOCuc min , SOCuc max

Railway traction substation energy management Hybrid Energy storage systems Power conversion systems Balance of plant Regenerative braking power Ultracapacitor Lead-acid Photovoltaic Mixed-integer linear programming High-speed railway High-speed trains Depth of discharge State of charge Railway traction load at time interval t (MW) Regenerative braking power at time interval t (MW) Total number of operation time intervals during a day The discretization time interval (1 min) Electricity price for power imported from the utility grid (CNY/MWh) penalty charge for power fed back to the utility grid (CNY/MWh) Total area of PV panels (m2 ) Probability of PV generation scenario Solar irradiance at time interval t for scenario s (kW/m2 ) Project service period (year) Annual discount rate Upper and lower bounds of power rating of battery (MW) Upper and lower bounds of capacity of battery (MWh) Upper and lower bounds of power rating of UC (MW) Upper and lower bounds of capacity of UC (MWh) Discharge and charge efficiency of battery Discharge and charge efficiency of UC Self-discharging rate of battery and UC Minimum and maximum SOC limit of battery Initial SOC of battery per day Minimum and maximum SOC limit of UC

Energies 2018, 11, 2199

SOCuc 0

Initial SOC of UC per day Maximum limit for active power imported from the utility grid (MW)

grid

Plimit fed

Plimit Variables bat,dis bat,ch Pt,s , Pt,s uc,dis uc,ch Pt,s , Pt,s

Maximum limit for regenerative braking power fed back to the utility grid (MW)

Pt,s

grid

Power supplied by the utility grid at time interval t for scenario s (MW)

Pt,s pv Pt,s bat,stored Et,s ,

fed

Power fed back to utility grid at time interval t for scenario s (MW)

uc,stored Et,s ubat,dis , uuc,dis t,s t,s bat,ch uc,ch ut,s , ut,s bat,ope

ut,s

26 of 29

uc,ope

, ut,s

grid

ut,s Tbat bat , Puc Prate rate bat uc Erate , Erate bat , T uc Thr hr

Discharge and charge power of battery at time interval t for scenario s (MW) Discharge and charge power of UC at time interval t for scenario s (MW)

PV output power at time interval t for scenario s (MW) The energy stored in battery and UC at time interval t for scenario s (MWh) Binary variable: 1 if battery or UC are discharging at time interval t for scenario s, 0 otherwise Binary variable: 1 if battery or UC are charging at time interval t for scenario s, 0 otherwise Binary variable: 1 if battery or UC are in operation mode (charge/discharge) at time interval t for scenario s, 0 otherwise Binary variable: 1 if grid supplies power to trains, and 0 if braking power is fed back to grid. Battery lifetime (year), as an intermediate variable Rated power of battery and UC (MW) Rated capacity of battery and UC (MWh) Operation time of battery and UC per day (hour), as intermediate variables

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