Modelling of operation of a stationary energy storage device in metro rail transport for selection of its parameters

The paper presents a Simulink model of a DC metro traction supply system with a stationary energy storage device (SESD). The simulation model consists of traction substations, a train model, and an energy storage device (ESD) with supercapacitors (SC). A new energy management strategy considering the line voltage and current, SC state of charge (SOC) and SC charging and discharging current is proposed. This method can improve the energy savings and manage the remaining energy. Simulation results provided in this paper justify the control method. The proposed model can be used with different ESD, such as batteries.


Introduction
In 2014, energy needed for transportation was around 24 % in the United States of the overall energy consumption [1]. Nowadays most of the electrical vehicles have the capability to return the braking energy to the traction system [2]. Reutilizing the vehicle braking energy can reduce the transportation costs, power needed for the traction system and the carbon footprint. The key to saving more energy is the optimal design for the energy storage devices including: selection of an appropriate type, location, size and energy management strategy.
During the last few years, a large number of energy management strategies were proposed in different papers for example: adaptive fuzzy logic strategy [3], real time optimization [4], global optimization [5], rule based strategy [6], genetic algorithm strategy [7] and load power strategy [8,13]. The energy management strategies can theoretically lower the energy consumption up to 20 % and reduce the size of the energy storage devices [9,10]. Experimental tests with ESD have justified their application in urban transport [14]. On the other hand, these methods have several drawbacks, e.g. the complexity of the solution and the input data needed obtained from additional costly equipment in the vehicle for its location, velocity etc. In this paper a new management strategy is presented and tested on a simulation model build in Matlab / Simulink for the SESD on metro transport.

Matlab / Simulink model of a traction supply system with SESD
A simulation model was built in Matlab / Simulink, for a light rail power supply system which includes 15 kV AC power supply source, 750 V DC traction substations with transformer -rectifier, trains and SESD with SC.

Traction substation model
In Poland the power to the metro traction supply is provided from District Point Supply (RPZ -Rejonowych Punktow Zasilania). The transformer rectifier substations convert the 15 kV, 50 Hz to 750 V DC which is supplying the metro cars by third rail. The metro supply is "dual feed" on AC and DC side to provide backup power in the event of a fault. Figure 1 presents the polish metro supply configuration. In table 1 is given the assumed specification for the power supply model.

Line model
The running rail and the third rail are simulated by linear resistance and considered pure resistive. The running rail has an assumed resistance of 35.7 mΩ/km and the third rail has an assumed resistance of 11.7 mΩ/km.

Train model
A simplified model of a train was built using a controlled current source and the input signal for the source is provided with a Signal Builder. In the Signal Builder the values of the assumed train current with respect to time is provided. Real values of the train current can be provided to the model. Figure 2 shows the assumed train currents used for the simulation purposes. For the train model all 3 stages were considered: acceleration, coasting, braking with regeneration. A simulation time of 200 s was proposed to verify the Simulink model. If the train is braking with regeneration and there is no other train or SESD to absorb the energy the voltage in the third rail will increase and exceed the limits. European Standard (EN) 50163 [11] regulates the maximum and minimum allowable voltage for the 750 V DC system as below: • Un = 750 V DC -nominal voltage; • Umin1 = 500 V DC -lowest permanent voltage; • Umax1 = 900 V DC -highest permanent voltage; • Umax2 = 1000 V DC -highest non-permanent voltage; To prevent the overvoltage, a braking system with braking resistor was implemented for the train. A control system using Matlab Function and compliant to the EN 50163 standard was designed. The input values are the train voltage values measured by a voltage meter. The output consists of control signals to ideal switches which in turn switch OFF or ON different braking resistance (Rb) according with third rail voltage as per table 2. The 1 means that the braking resistor is switched ON and the 0 means that is switched OFF.  The SC voltage values need to be between 40 % (300 V) and 100 % (750 V) of the nominal value in order to maintain converters operation. The SC state of charge was set between 40 % and 100 % for the simulation and the maximum SC charging / discharging current has to be kept below 6 kA in order to protect it.
An energy management control system considering the third rail voltage and current, regenerated power, load power, SC SOC, SC charging current and SC discharging current was designed and presented in figure 3.

DC-DC charging converter
The DC-DC charging converter was built with ideal switches. A diode was used to make the current to flow from the braking train to the SESD. An inductor was designed for keeping the charging current stabile. The block marked "X" in figure 5 and figure 7 is used for multiplication of the logical values of "ESD charging / discharging" for all decision blocks.
The SESD charging control have been implemented as below: • The third rail voltage (UL) and current (IL) is measured. The regenerated power (PL) is calculated. The train braking with regenerations is detected when the third rail voltage is higher than 800 V and the power is lower than 100 W. The SESD is charging if the network demand power is negative (<0W) which means that the train is braking with regeneration. To avoid fluctuations in the control block the control power for SESD charging was selected arbitrary to be 100W.
• SESD current (ISESD) is measured and compared with the sum current of the running trains. This function allows the SESD to charge only from the regenerative energy and not from the substations.
• SESD current (ISESD) is measured and compared with the maximum allowable charging current 6 kA. This restrictions keeps the discharge current below the maximum value in order to protect the SC.
• SC state of charge (SOC) is measured and when reaches 100 % the SESD stops from charging.
If all conditions are met then SESD will charge from the third rail (SESD charging = ON). The energy management strategy flowchart for the charging control is shown in figure 5.

DC-DC load converter
A Cuk converter is used for the DC-DC load converter described and tested in [13]. The converter uses a closed loop cascade control with two PI regulators for load current and output voltage. The controller objective is to stabilize the current supplied by the SC during sudden changes in load current and keep the output voltage constant to 750 V.
The DC third rail voltage is measured and compared with the voltage threshold value 750 V. If the third rail voltage is lower than 750 V the SESD provides with the rest of the power. To prevent PI regulators saturation during the SESD charging, they are enabled by the energy management load control.
The SESD load control has been implemented as below: • The third rail voltage (UL) and current (IL) is measured. The load power (PL) is calculated and compared against the minimum value of 1 MW to protect the SESD from simultaneous charging and discharging. The minimum power value allow the SESD to provide with energy only on heavy demand load conditions.
• SESD current (ISESD) is measured and compared with the maximum allowable load current 6 kA. This condition keeps the load current below the maximum value to protect the SC.
• SC state of charge (SOC) is measured. The minimum SOC is set to 40 %.
If all conditions are achieved then the third rail will be fed by the SESD (SESD discharging = ON).
The energy management strategy flowchart for the load control is presented in figure 7.  To simulate different load for each substation a resistance was designed for third rail and running rail. The total length of the line is considered 2.1 km and the line resistance was designed according with the train distance from the substations. The location of the train is given in table 4. In figure 9 is presented the simulation results for the SESD installed within Substation 2 for a simulation time of 210 seconds and a step size of 0.5 seconds. During heavy demand of traction energy the SESD successfully provides the auxiliary energy for keeping the third rail voltage stable and under the limits. The maximum discharge current is 3 kA. During braking process the SESD stores the energy with maximum charging current up to 6 kA.
In figure 11 it can be observed that the substations voltage did not exceed the 1 kV voltage limit according with EN 50163 standard.
On figure 13 the SC SOC is charging / discharging according with the train powering or braking.    From figure 14 and figure 15 it can be observed that the control system for the braking system has a good time response and is able to suppress the overvoltage during train braking. The third rail voltage is below the 1kV maximum allowed non-permanent voltage limit. During braking process excessive part of the regenerated energy is lost on the braking resistors. This is due to lack of receptivity of power supply.

Study case
A study case was performed for a 8 km section of a metro line with a SESD installed in the mid-point between 2 traction substations (TS) distanced 3 km one from another. Traffic of metro trains was organized regularly with density dt = 90, 150, 180 and 240 s between trains on both directions. There were assumed 3 energy capacity of SESD with maximum charge / discharge current rated: 2.5 kA (minimum), 4 kA and 6 kA (maximum). For dt = 90 s 1 hour obtained energy savings were 0.32 MWh, 0.28 MWh and 0.18 MWh respectively for 6 kA, 4 kA and 2.5 kA SESD. The results of simulation of operation of SESD for traffic density dt = 90 s and dt = 240 s are presented in figure  15 -energy Es stored and current Is of SESD for 6 kA SESD having 42 MJ available energy capacity.   Measurements taken from supercapacitors SESD installed in II Warsaw Metro line shown week-day savings around 2 MWh. Similar results were reported in [14] for high power capacity battery type SESD installed in a TS in metro line in Washington USA, with practically double value of energy saved when this SESD was installed between 2 TS.

Conclusion
In this paper a simulation of a metro rail power supply system with SESD was presented. A new dynamic energy management strategy was proposed. The strategy uses the measurements of the third rail currents and voltage and the SC SOC. The simulation results in a study case performed shown influence of density of traffic and SESD capacity on amount of braking energy savings. The simulation tools could be used for designing of the SESD parameters and location to obtain high effectiveness of its installation.