Research on capacity optimization of new energy hybrid energy storage system of high-speed railway

With the fast expansion of electrified railways, the need for energy is growing. Thus, improving railway coupling and interconnection, new energy, and energy storage is critical to support low-carbon and green railway development. Therefore, this paper proposes an optimal configuration method for the access capacity of wind power generation system (WPGS), photovoltaic power system (PVPS), and hybrid energy storage system (HESS) in the traction power supply system (TPSS) of high-speed railways. Firstly, the HESS’s mathematical model is developed, then the high-speed railway TPSS’s economic optimization operating model is built, and a HESS energy management approach is presented, taking the energy management strategy parameters and model capacity configuration parameters as the optimization variables. The mixed integer linear programming approach is used to resolve the actual example with the least daily operational cost of the high-speed rail system as the optimization goal, and the optimal capacity of WPGS, PVPS, and HESS is obtained. Finally, through comparison and analysis, it is verified that the economic benefit is the highest when the distributed complementary energy system covering WPGS, PVPS, and HESS is connected to the traction substation, and 10.47% of the daily expenditure is saved.


Introduction
The railway industry has developed rapidly in recent years and is a major energy consumption position.To reduce carbon emissions, introducing new energy power generation units into electrified railway facilities has become an urgent need to encourage the development of green and low-carbon railways.
During the operation of electrified trains, in addition to using a large amount of energy from the traction network, there will also be a significant quantity of regenerative braking energy produced [1].The addition of energy storage devices is the most efficient way for regenerative braking energy recovery and usage [2] while taking into account that regenerative braking energy exhibits both big power and large energy characteristics [3].A HESS composed of lithium-ion batteries and supercapacitors will be used to participate in the scheduling and operation of high-speed rail systems, maximizing the complementary advantages of the two kinds of energy storage [4].There are few studies on new energy access capacity in high-speed railway TPSS.The optimal configuration of energy storage for TPSS including photovoltaics is studied, and PVPS's potential as well as its use and energy storage in the railway industry are demonstrated [5][6].An optimal operation model is established for railway systems, to obtain the optimal output of new energy and energy storage [7].Although the research considered the distribution of energy storage capacity, they did not consider the optimization of new energy capacity.Most of them use a given new energy installed capacity or are based on a typical new energy output curve to study the optimal scheduling operation of trains, without considering the joint optimization of new energy and energy storage capacity.
In summary, this paper proposes an optimal configuration method for the access capacity of WPGS, PVPS, and HESS in high-speed railway TPSS.This method considers the capacity configuration of WPGS and PVPS when solving the optimal capacity of HESS and proposes a HESS energy management approach, with the energy management strategy parameters and system capacity configuration parameters as optimization variables.With the lowest daily operating cost of high-speed rail systems as the optimization goal, the optimal capacity configuration of WPGS, PVPS, and HESS is completed.We compare the capacity configuration results with scenarios without WPGS, PVPS, and HESS, as well as scenarios with only HESS, and select the economically optimal capacity configuration scenario to evaluate the viability and excellence of the proposed scheme.

Structure of high-speed railway TPSS including new energy and HESS
The distributed complementary energy system covering WPGS, PVPS, and HESS is connected to the high-speed railway traction substation [8], as shown in Figure 1.TPSS includes traction transformer, autotransformer (AT), catenary, train, etc.The system converts 110/220 kV three-phase alternating current into 27.5 kV single-phase alternating current through a V/v traction transformer to provide electric energy for the train.PVPS and WPGS are connected to the TPSS through the corresponding converter, which can supply power to both sides of the bus at the same time.HESS can not only recover the train's regenerative braking power and the excess energy of the WPGS and PVPS but also discharge the energy it has accumulated to power the train's traction load.

Mathematical model of HESS
In this paper, the HESS composed of lithium-ion batteries and supercapacitors is used, and its mathematical model is as follows: where SOC is the energy storage device's state of charge; SOCBa (0) is the SOC of the battery at the beginning of a scheduling cycle; SOCsc (0) is the SOC at the start time of the supercapacitor; T refers to the system scheduling cycle; m is the number of batteries put into operation; n is the number of input supercapacitors; EBa and Esc are the capacities of the battery and supercapacitor unit devices; XBa (t) and YBa (t) are the charging and discharging states of the battery; PBach (t) and PBadis (t) are the battery charging and discharging power; Pscch (t) and Pscdis (t) are the supercapacitors charging and discharging power; ηBa refers to the charging and discharging efficiency of the battery; ηsc is the efficiency of the supercapacitor.

Objective function
This paper takes the minimum daily operating cost of high-speed railway TPSS as the optimization objective.The objective function is: where Cgrid is the high-speed railway's daily electricity purchase cost; Ce is the basic daily electricity fee for high-speed railway; CBa is the battery's daily input cost, which includes the daily investment cost as well as the daily operating and maintenance cost; Csc is the daily input cost of the supercapacitor; Cwt is the total daily cost of WPGS, including daily investment cost and daily operation and maintenance cost; Cpv is the total daily cost of PVPS.
grid buy buy 1 () where cbuy is the electricity price per kilowatt hour; Pbuy (t) is the power purchased during the t period.where co is the basic electricity price; Emax is the maximum power requirement of traction load.
where m is the number of batteries put into operation; CBaint is the unit device cost of the battery; ρ is the discount rate; LBa is the battery's useful life; CBaope refers to battery operation and maintenance costs.(1 ) ( ( ) ( )) 365 (1 ) 1 where n is the number of supercapacitors; Cscint is the unit cost of supercapacitors; Lsc is the service life of the supercapacitor; Cscope is the cost of operation and maintenance for supercapacitors.
wt wt wt wt wt wt wt 1 1 (1 ) () 365 (1 ) 1 where Pwt (t) is the wind power during the t period; Kwt is the cost coefficient of WPGS; Lwt is the service life of WPGS; Cwt is WPGS's investment cost per unit capacity; Vwt is the installed capacity of WPGS.
pv pv pv pv pv pv pv 1 1 (1 ) () 365 ( 1) where Ppv (t) is the photovoltaic power during the t period; Kpv is the cost coefficient of PVPS; Lpv is the service life of PVPS; Cpv is PVPS's investment cost per unit capacity; Vpv is the installed capacity of PVPS.

Constraint condition
where Pload (t) is the traction load of a high-speed railway during the period t.
where wt' is the normalized processing value of wind power output; wt is the predicted wind power curve data value; wtmax is the maximum value of the wind power curve; wtmin is the minimum value of the wind power curve.

P t V pv t pv t pv pv t pv pv
where pv' is the normalized value of photovoltaic output; pv is the data value of the photovoltaic predicted power; pvmax is the maximum value of the photovoltaic power curve; pvmin is the minimum value of the photovoltaic power.

6)
Maximum capacity limit of WPGS and PVPS connected to the traction side: where V max wt and V max pv are the upper limits of the capacity of the WPGS and PVPS on the traction side.

Energy management strategy for HESS
When the power of WPGS and PVPS is greater than the traction load, the energy storage device enters the charging stage, with the help of the characteristics of the large capacity of the battery.It is given priority to work when its maximum charging power cannot meet the requirements for recovering the excess power of the traction network, and the charging operation of the supercapacitor is conducted to supplement it.When the power of WPGS and PVPS is less than the traction load, energy storage enters the discharge stage, and the fast charging and discharging characteristics of the supercapacitor are used to discharge it first.Before the next charge, we should make sure that the supercapacitor has enough storage space.When its discharge power cannot meet the traction load demand, the battery is discharged to supplement.

Simulation scenario
This article aims to optimize the access capacity of WPGS, PVPS, and HESS in the TPSS by using the example of a domestic high-speed railway traction substation.The measured data curve of traction load is shown in Figure 2. New energy forecast power curves are shown in Figure 3.The unit sampling time in each curve is 1 minute, and the total duration is 1 day.This paper uses the YALMIP toolbox and the CPLEX solver to solve the model.Table 1 shows the unit energy storage element parameters and other equipment utilized in the constructed model [9][10].

Simulation result
This paper studies and analyses the following three cases: Case 1: The high-speed railway system does not use WPGS, PVPS, and HESS.Case 2: The highspeed railway system only uses HESS.Case 3: The high-speed railway system adopts WPGS, PVPS, and HESS.The corresponding simulation results in three cases are shown in Table 2. From the table, using only HESS for high-speed rail systems can save 1.11% of the total daily cost compared to scenarios without using WPGS, PVPS, and HESS.The HESS can recover the regenerative braking energy of the train to reduce the peak load of the traction substation, reduce the capacity of the traction transformer, reduce the daily basic electricity cost of high-speed rail, reduce the power consumption of the train, and reduce the entire daily cost of high-speed rail.We consider connecting WPGS, PVPS, and HESS to traction substations, saving 10.47% of the total daily cost compared to scenarios where WPGS, PVPS, and HESS are not used.From the analysis, adding WPGS and PVPS to the high-speed railway system can more effectively reduce the peak traction load and significantly reduce the total daily cost of the system compared to adding only energy storage.Figure 4 shows the change in traction load before and after adding HESS to the TPSS.For a clearer display, the curve from 11:00 to 13:00 is enlarged.Due to the role of HESS, high-speed train regenerative braking energy is effectively recovered, while reducing the peak traction load.Figure 5 shows the change in traction load before and after adding WPGS, PVPS, and HESS to the TPSS.Due to the addition of WPGS and PVPS, the effect of reducing train traction load has been significantly improved, greatly reducing the purchase of power for trains and the capacity of traction transformers, and effectively saving costs.

Conclusion
The optimal access capacities for WPGS and PVPS are 4, 229 kW and 1, 500 kW, respectively.The optimal access capacities for HESS include 107 batteries and 188 supercapacitors.When a distributed complementary energy system covering WPGS, PVPS, and HESS is connected to a traction the economic benefits are highest, and the total daily cost is saved by 10.47%.

Figure 1 .
Figure 1.Structure of the traction power supply system of high-speed railway.

Figure 2 .
Figure 2. Load curve of traction substation.Figure 3. New energy forecast power curve.

Figure 3 .
Figure 2. Load curve of traction substation.Figure 3. New energy forecast power curve.

Figure 4 .
Figure 4.The change of traction load before and after hybrid energy storage.

Figure 5 .
Figure 5. Traction load changes before and after adding new energy and hybrid energy storage.
unit device of the battery.Considering that the battery will not be in the charging or discharging stages at the same time, the charging and discharging state constraints are increased.To avoid overcharging or discharging of the battery, charging and discharging power constraints and SOC constraints are also added.