Integration of Photovoltaic Plants and Supercapacitors in Tramway Power Systems

energies

Article Integration of Photovoltaic Plants and Supercapacitors in Tramway Power Systems

Flavio Ciccarelli 1 ID , Luigi Pio Di Noia 2 and Renato Rizzo 2,* 1 University of Naples Federico II, 80125 Naples, Italy; ﬂ[email protected] 2 Department of Electrical Engineering and Information Technologies, University of Naples Federico II, 80125 Naples, Italy; [email protected] * Correspondence: [email protected]; Tel.: +39-081-768-3231

Received: 18 January 2018; Accepted: 7 February 2018; Published: 9 February 2018

Abstract: The growing interest in the use of energy storage systems to improve the performance of tramways has prompted the development of control techniques and optimal storage devices, displacement, and sizing to obtain the maximum proﬁt and reduce the total installation cost. Recently, the rapid diffusion of renewable energy generation from photovoltaic panels has also created a large interest in coupling renewable energy and storage units. This study analyzed the integration of a photovoltaic power plant, supercapacitor energy storage system, and railway power system. Random optimization was used to verify the feasibility of this integration in a real tramway electric system operating in the city of Naples, and the beneﬁts and total cost of this integration were evaluated.

Keywords: optimization; photovoltaic; supercapacitor; tramway

1. Introduction The substantial increase in the use of electrified collective transport systems, which has occurred in recent years in large urban centers, has made it necessary to increase the vehicle frequency rate and capacity of convoys in terms of transportable passengers. This has been reflected in the use of vehicles with more propulsion power, as well as lower time displacement, with consequent voltage variations, which are critical factors in the proper operation of the transport system. Maintaining the line voltage within certain limits is in fact dictated by the need to properly power the input bus of the electrical traction drive, which is currently the most popular propulsion system in metropolitan, tram, and tramway trains. Major voltage drops in the line occur mainly at the acceleration stages of the convoys and are therefore directly related to the number of vehicles simultaneously operating on the line and to the total power required. During the braking phases, however, the kinetic energy of a convoy is converted into electrical energy and, if possible, supplied to the other accelerating convoys. In this context, the use of braking energy recovery storage systems located along the contact line or near the passenger stations could result in significant energy savings, compensating for the costs incurred for their installation. The stored energy could also help to support the contact line during consecutive congestion restarts, thus reducing voltage drops and energy dissipation. Among the different rail transport systems, a solution with energy storage systems can be particularly effective and beneficial if applied to metropolitan, suburban, and tramway systems. In fact, these are characterized by operating convoy sets that accelerate and brake in short time intervals. In such applications, the placement of the energy storage system in the station is optimal because of the availability of space and therefore may be preferable to on-board installation. This solution also enables recovery and re-use for other convoys passing near the same station. Energy storage systems are essentially made up of components for energy storage and static energy converters that regulate the incoming and outgoing energy flows, ensuring high reliability and

Energies 2018, 11, 410; doi:10.3390/en11020410 www.mdpi.com/journal/energies Energies 2018, 11, 410 2 of 14 high efficiency. These controlled converters have to be installed between the feeding lines and storage components in order to manage bi-directional flow of electrical energy. Supercapacitors (SC) are a good alternative to electrochemical batteries in applications where it is necessary to quickly compensate for the discontinuous power absorption of electric loads. A proper storage capacity design allows the use of SCs in different practical applications. In the recent past, the scientific community has been paying growing attention to the different uses of these technologies in urban and suburban railway traction systems (streetcar, light rail transit, and mass rapid transit) [1,2]. In fact, it has been widely demonstrated that their use enables both the under sizing of the power supply plant in the project stage or a more intensive use of existing subsystems without major modifications (e.g., the repowering of electrical substations and the increase of the cross-sectional area of contact wires), and besides it definitely allows to improve the overall energy efficiency thanks to the recovery of the braking energy and its subsequent release in the starting phase of the traction motors. Moreover, their intervention involves the benefit of avoiding overvoltages on the overhead contact line which become more receptive. Practical employments of storage units can be either stationary or mobile [3–5]. In the first case, they can be used to reduce the energy demand of the whole system and to stabilize the supply network voltage at weak points (e.g., the voltage drops typically associated with end of lines) with the potential elimination of additional feeding substations [6]. In addition, this solution can greatly contribute to the peak shaving action of traction power during the acceleration of vehicles, as the storage unit is capable of recovering energy from several braking vehicles at the same time with any limitation in terms of weight and required space for installation. In mobile applications, the storage units are installed on-board and, hence, are used for the shaving of power peaks demanded during the acceleration of vehicles, which leads to reduced energy costs, limitation of voltage drops, and minimum resistive losses in the supply line and improves efficiency by recovering mechanical energy during braking [7,8]. The management of the regenerated energy is simpler, since the control is independent of traffic conditions and the action could be also useful to have a certain power autonomy, e.g., in emergency catenary free operation. In the literature, remarkable attention has been devoted to the efficiency of the energy storage unit operating mainly as a support system for the contact lines voltage in urban and suburban railway traction networks, because this practical application can be useful for problems that arise today, especially in many large cities, when new generation vehicles are put in operation on feeding lines not modified or correctly executed according to the increase of the absorbed current. This, together with the stringent need to increase the passenger carrying capacities as well as the vehicle’s frequencies during the day, can cause overloading of the contact lines, with consequent operating voltage drops and probable intervention of minimum voltage protection relays. To avoid this situation, a quick and effective solution to improve supply line performance and prevent unwanted voltage drops without further modification in the existing feeding infrastructure is the use of SC stations allotted along contact line sections [9]. Naturally, the achievement of these targets is closely linked to the proper design of SC sets in terms of size and capacitance, the number and locations of the stations, and the control strategies of the power electronic devices [10,11]. In order to achieve a satisfactory braking energy recovery, it is necessary to consider that the amount of energy that can actually be recovered during vehicle braking and reuse is only a part of the kinetic energy owned by the vehicle itself at the start of braking. This part is smaller than the power losses incurred in converting the kinetic energy into electric energy and transferring it to the storage components. In practice, the efficiency of the electrical traction motor during generator operation is very high. The leaks in static converters are very low, because of their high efficiency. Joule leakage losses in the conductors between the storage systems and contact lines increase considerably with the distance between the storage device and the point where the vehicle brakes, because braking is a short-term phenomenon and is generally constrained to deceleration values that are easily acceptable to passengers. Consequently, the power and current values involved are relevant. These losses can, Energies 2018, 11, 410 3 of 14 therefore, also counteract the energy recovery benefits. Therefore, the use of energy recovery storage systems for tramcars can only be effective with the on-board installation of the systems themselves. Their arrangement along the contact lines may be useful when they are used to support contact line voltages. In our opinion, this last goal can be achieved, together with an optimal recovery of braking energy, by integrating the recharge of stationary SC energy storage sets with energy from local photovoltaic (PV) sources appropriately installed along the rail path. There have been a few recent papers that have dealt with the application of PV sources to urban railway networks. In [12], the authors investigated the performance of solar PV modules mounted on the roof of a rail coach to quantify the reduction in diesel consumption of the end-on generation system that powered the electrical load in the new generation coaches. A roof coach installation of the panels was proposed in [13], which introduced a technical scheme for the auxiliary power supply system of a passenger train based on PV and battery energy storage. This auxiliary power has to be injected into the direct current (DC) power supply system in order to obtain an annual output power payback, energy conservation, and emissions reduction [14,15]. Moreover, Becherif et al. [16] presented the concept of an embarked power source using SCs that were charged by means of a combination of a roof-placed PV source and an aero generator, which supplied power to the DC link of the main traction drive. The design and energy management strategies were applied to a miniature train in the laboratory. In [17,18], the potentials, peculiarities, and prospects of using solar power generation systems on the platform roofs of railway stations were analyzed for power injection into the main electrical grid. The prospects for realizing a solar generation system with lithium ion batteries for a local station, called a “zero-emission station”, were also shown to realize a more eco-friendly traction power supply system [18]. Ultimately, in [19–21], the feasibility and application modes of a fixed PV generation system with an auxiliary SC or battery storage equipment were studied for urban rail transit. The alternating current (AC) grid-connected mode and DC grid-connected mode were presented, and the grid-connected topology and energy management strategy were developed. The intrinsic capability of saving regenerative energy with a consequent increase in the energy savings of the systems and reduction in the voltage drop was highlighted. This paper proposes a procedure for the optimal integration of PV power plants, SC storage systems, and railway power systems. The PV modules are installed on the available surfaces of shelters positioned along the track. In order to use a modular approach for the storage systems, each shelter is also provided with SC units. The modular distribution of storage systems makes it possible to improve the discharge phase, reduce the losses in the connection to the railway power system, and improve the control because it is possible to act in a different manner in the various nodes of the railway systems. The approach utilized for the optimal integration is based on the use of a random optimization procedure. This is based on a minimization cost function that takes into account the cost of the entire system and can solve the mathematical problems with integer variables. Some simulations were performed taking into account the case of a tramway of Naples (Italy) and using the software Matlab© and Simulink© (R2017a, Mathworks, Natick, MA, USA).

2. The Photovoltaic Power Plant The considered tramway track, which is shown in Figure1, is approximately 1.8 km long and has five stops placed 300 m apart. The total time needed to pass over this track is about 300 s. A yellow circle in Figure1 indicates the presence of one shelter, while the green circles correspond to two shelters. The green circles are also positioned at the initial and final stops of the track. At each shelter, it is possible to install five PV panels with the characteristics reported in Table1. The maximum power generated by a plant assembled on a single shelter is about 1 kWp. Considering the total number of shelters, it is possible to install 12 kWp of PV panels along the entire track. The electrical power generated by this power plant can be utilized by connecting the PV Energies 2018, 11, 410 4 of 14 panelsEnergies directly2018, 11, xto FOR the PEER low-voltage REVIEW power system through an inverter to exchange electrical energy4 with of 14 the power system, or by linking the panels to a storage system based on SCs and using the energy power system, or by linking the panels to a storage system based on SCs and using the energy during during the tramway operation. the tramway operation.

Figure 1. Map of possible installationinstallationof ofphotovoltaic photovoltaic power power plant plant in in a a part part of of Naples’ Naples’ tramway. tramway. Yellow circleYellow one circle shelter, one greenshelter, circle green two circle shelters. two shelters.

Table 1. Electrical data of photovoltaic panels. Table 1. Electrical data of photovoltaic panels. Quantity Values MaximumQuantity Power 212 Values W MaximumOpen circuit Power Voltage 36.2 212 V W OpenShort circuit circuit Voltage Current 7.93 36.2 A V Short circuit Current 7.93 A ModuleModule efﬁciency efficiency 16.1% 16.1%

In recent years, because of the large development of distributed generation, the management of powerIn systems, recent years, particularly because low-voltage of the large developmentsystems, has been of distributed affected by generation, new problems the management related to the of powervoltage systems, drop along particularly the line and low-voltage the sorting systems, of the locally has been generated affected energy. by new Therefore, problems relatedthe necessity to the voltageof integrating drop along storage the systems line and in the the sorting power ofsyst theem locally continues generated to grow. energy. Another Therefore, important the necessityproblem ofintroduced integrating by storagethe integration systems of in distributed the power genera systemtion continues in the power to grow. system Another is the important random behavior problem introducedof renewable by energy the integration sources. of The distributed feasibility generation of PV power in the plants power is system based ison the a study random of behaviorthe annual of renewablesolar radiation energy that sources. is typical The for feasibility a geographical of PV power location. plants Figure is based 2a shows on a studythe mean of the value annual of daily solar radiationglobal radiation that is in typical the case for considered a geographical in this location. paper [22] Figure in 2kWh/ma shows2. the mean value of daily global 2 radiationConsidering in the case the considered efficiency inof this the paper PV panels [22] in (T kWh/mable 1),. a power electronic converter global efficiencyConsidering of 0.96, the and efﬁciency the total of surface the PV panelsof the shel (Tableters,1), ait poweris possible electronic to compute converter the global mean efﬁciency value of ofenergy 0.96, (Figure and the 2b) total generated surface by of the the considered shelters, it PV is power possible plant. to compute the mean value of energy (FigureThe2b) mean generated value byof theachievable considered energy PV powerin a year plant. is approximately 26,000 kWh. Considering the high Thepower mean required value ofin achievabletraction applications, energy in athe year PV is power approximately plant cannot 26,000 be directly kWh. Considering coupled to the highrailway power lines, required so it is necessary in traction to applications, use an approp theriate PV powerstorage plant system, cannot i.e., beone directly based on coupled SCs, and to the to railwayintegrate lines, it in the so ittramway is necessary electric to usepower an appropriatesystem. The storageintegration system, of a PV i.e., power one based plant on in SCs,the railway and to integratesystem requires it in the an tramway appropriate electric analysis power of system. the distribution The integration of solar of radiation a PV power during plant a in day the to railway avoid systemoversizing requires the storage an appropriate system. Solar analysis radiation of the is distribution quite variable of solar during radiation the day. during Thus, a forecasting day to avoid is difficult, and it is usually evaluated using statistical data. A correct knowledge of the radiation permits the optimal sizing of the storage systems. Figure 2c,d reports the average values of solar radiation [23] in the summer and winter months for the case considered in this paper.

Energies 2018, 11, 410 5 of 14 oversizing the storage system. Solar radiation is quite variable during the day. Thus, forecasting is difﬁcult, and it is usually evaluated using statistical data. A correct knowledge of the radiation permits theEnergies optimal 2018, 11 sizing, x FOR of PEER the storageREVIEW systems. Figure2c,d reports the average values of solar radiation5 [of23 14] in the summer and winter months for the case considered in this paper. Figure 22c,dc,d shows the the obvious obvious and and substantial substantial difference difference between between winter winter and summer, and summer, which whichmust be must taken be into taken account into account for the forcorrec thet correctsizing of sizing the energy of the energystorage storage systems. systems. The choice of a storage system with a capacity capacity equal to the the maximum maximum recovery recovery energy in summer is oversizedoversized with respectrespect toto thethe energyenergy availableavailable inin winter.winter. Thus, it is necessary to considerconsider the possibility of storing only a part of the energy obtainableobtainable by the PV power plant and exchanging the other part with the distributiondistribution power system. Th Thee energy storage depends on the behavior of the electrical load in the considered railway systems. The The total total duration duration of of a a single single track track is is about 300 s, with ﬁvefive stops, and the total energy that can be storedstored in 300 s isis veryvery low.low. Thus, it is necessary to consider a longer interval (more tramway rides) to obtain a reasonable amount of energy and increase the life of the storage systemsystem byby reducingreducing thethe numbernumber ofof chargecharge andand dischargedischarge cycles.cycles.

7 3000

6 2500

5 2000

2 4

1500 kWh

kWh/m 3

1000 2

1 500

0 0 Gen Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Gen Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Month (a) (b) December July 0.18 0.35

0.16 0.3

0.14 0.25 0.12

0.1 0.2

0.08 0.15

0.06

kWh for each shelter for kWh each shelter for kWh 0.1 0.04

0.05 0.02

0 0 06:00 09:00 12:00 15:00 18:00 06:00 09:00 12:00 15:00 18:00 Time Time (c) (d)

Figure 2. Photovoltaic (PV) power plants solar radiation typical for the considered geographical Figure 2. Photovoltaic (PV) power plants solar radiation typical for the considered geographical location: (a) Mean value of daily global radiation (kWh/m2); (b) Mean value of generated energy per location: (a) Mean value of daily global radiation (kWh/m2); (b) Mean value of generated energy per month (kWh); (c) Daily distribution of energy in December (kWh); and (d) Daily distribution of month (kWh); (c) Daily distribution of energy in December (kWh); and (d) Daily distribution of energy inenergy July (kWh).in July (kWh).

Energies 2018, 11, 410 6 of 14

3. The Photovoltaic Power Plant The integration of the SCs in the railway power system is modular. The modularity of the storage systems involves the installation of multiple SCs near the shelters along the track, which increases the system reliability, prevents the complete exclusion of the storage systems during maintenance, Energies 2018, 11, x FOR PEER REVIEW 6 of 14 introduces some optimal strategies for reducing losses, and minimizes the installation cost. The electric scheme of the railway power system with the PV modules and SCs is shown in Figure3. voltage in the different nodes of the net can vary in the range of 600–900 V. The output of the bridge The railway power system is fed by a transformer with a primary voltage of 20 kV. The secondary side rectifier is linked to the catenary of the power system. Table 2 reports some data of the railway power includes a bridge rectifier that outputs a voltage of 750 V. During its performance, the voltage in the system [24]. different nodes of the net can vary in the range of 600–900 V. The output of the bridge rectifier is linked In the literature, some AC schemes are used for the integration of renewable energy sources in to the catenary of the power system. Table2 reports some data of the railway power system [24]. power systems [25,26]. In particular, this scheme can be optimized through the use of a reversible In the literature, some AC schemes are used for the integration of renewable energy sources in optimal power flow, which also avoids the use of storage systems and permits the regulation of power systems [25,26]. In particular, this scheme can be optimized through the use of a reversible energy price in the market and some ancillary services. Considering the scheme of Figure 3, it is not optimal power flow, which also avoids the use of storage systems and permits the regulation of possible to recover energy through the Medium Voltage (MV) substation, because this implies a high energy price in the market and some ancillary services. Considering the scheme of Figure3, it is not economic investment for the replacement of the rectifier diode (usually coupled with three windings possible to recover energy through the Medium Voltage (MV) substation, because this implies a high transformers) with a bidirectional rectifier; for this motivation, the recovery and the use of energy economic investment for the replacement of the rectifier diode (usually coupled with three windings from the tram braking or from the PV installed on the shelters can be done by means of an energy transformers) with a bidirectional rectifier; for this motivation, the recovery and the use of energy from storage system. Due to the high value of current necessary during the acceleration (or charge current the tram braking or from the PV installed on the shelters can be done by means of an energy storage available during the deceleration), a supercapacitor is the most suitable technology for the system. Due to the high value of current necessary during the acceleration (or charge current available application. during the deceleration), a supercapacitor is the most suitable technology for the application. The PV modules are connected to the storage systems through a buck converter. In the same The PV modules are connected to the storage systems through a buck converter. In the same way, way, the storage systems are linked to the railway power system with a buck converter. A storage the storage systems are linked to the railway power system with a buck converter. A storage system system can be installed at the end of the track to recover the energy generated by the train during can be installed at the end of the track to recover the energy generated by the train during braking. braking. The electric layout of the system can be modeled as shown in Figure 4. The electric layout of the system can be modeled as shown in Figure4. Table 2. Parameters of the electrical railway system. Table 2. Parameters of the electrical railway system. Quantity Value SubstationQuantity Power 1150 Value kVA SubstationLength Power 1.8 1150 km kVA CatenaryLength resistance 0.15 1.8Ω/km km CatenaryNominal resistance Voltage 0.15 750 ΩV/km Nominal Voltage 750 V NumberNumber of of stations stations 5 5

Figure 3. ElectricElectric layout layout of of the the railway power system for the consideredconsidered track:track: integration of photovoltaic modules and of storagestorage systems in the circuit.

RE 1 R1 2 R2 3 R3 4 R4 5 R5 6 R6 7 R7 8 R8 9 R9 10

i isc,1 isc,2 isc,3 isc,4 isc,5 isc,6 isc,7 isc,8 isc,9 sc,10 E i i tr,1 itr,2 itr,3 itr,4 tr,5

Figure 4. Model of the electric scheme shown in Figure 6.

The output of the transformer is considered constant, and both the train and storage system units are considered to be current generators. RE is the resistance between the substation and the first node of the net, and Rj (j = 1, …, 9) are the line resistances between the different nodes. The stops are

Energies 2018, 11, x FOR PEER REVIEW 6 of 14

voltage in the different nodes of the net can vary in the range of 600–900 V. The output of the bridge rectifier is linked to the catenary of the power system. Table 2 reports some data of the railway power system [24]. In the literature, some AC schemes are used for the integration of renewable energy sources in power systems [25,26]. In particular, this scheme can be optimized through the use of a reversible optimal power flow, which also avoids the use of storage systems and permits the regulation of energy price in the market and some ancillary services. Considering the scheme of Figure 3, it is not possible to recover energy through the Medium Voltage (MV) substation, because this implies a high economic investment for the replacement of the rectifier diode (usually coupled with three windings transformers) with a bidirectional rectifier; for this motivation, the recovery and the use of energy from the tram braking or from the PV installed on the shelters can be done by means of an energy storage system. Due to the high value of current necessary during the acceleration (or charge current available during the deceleration), a supercapacitor is the most suitable technology for the application. The PV modules are connected to the storage systems through a buck converter. In the same way, the storage systems are linked to the railway power system with a buck converter. A storage system can be installed at the end of the track to recover the energy generated by the train during braking. The electric layout of the system can be modeled as shown in Figure 4.

Table 2. Parameters of the electrical railway system.

Quantity Value Substation Power 1150 kVA Length 1.8 km Catenary resistance 0.15 Ω/km Nominal Voltage 750 V Number of stations 5

EnergiesFigure2018, 113., 410Electric layout of the railway power system for the considered track: integration of7 of 14 photovoltaic modules and of storage systems in the circuit.

RE 1 R1 2 R2 3 R3 4 R4 5 R5 6 R6 7 R7 8 R8 9 R9 10

i isc,1 isc,2 isc,3 isc,4 isc,5 isc,6 isc,7 isc,8 isc,9 sc,10 E i i tr,1 itr,2 itr,3 itr,4 tr,5

Figure 4. Model of the electric scheme shown in Figure 6. Figure 4. Model of the electric scheme shown in Figure 6. The output of the transformer is considered constant, and both the train and storage system units are consideredThe output to of be the current transformer generators. is considered RE is the constant, resistance and between both the the train substation and storage and the system first unitsnode areof the considered net, and to R bej (jcurrent = 1, …, generators. 9) are the RlineE is resistances the resistance between between the the different substation nodes. and The the ﬁrststops node are of the net, and Rj (j = 1, ... , 9) are the line resistances between the different nodes. The stops are positioned along the track at nodes 1, 3, 5, 7, and 10. The mathematical model can be used for the following systems:  V (t) − R I − V (t) = 0  e E E 1 Vh(t) − Rh Ih − Vh+1(t) = 0 h = 1, . . . , 8 (1)   V9(t) − R9 I9 − V10(t) = 0  Vsc,1(t)  Isc,1(t) ( ) + IE(t) − [Itr,1(t)S1(t) + I1(t)] = 0  V1 t ( ) Vsc,h(t) + ( ) − ( ) = = Isc,h t V (t) Ih−1 t Ih t 0 h 2, 4, 6, 8, 9 . (2)  h  Vsc,h(t)  Isc,h(t) + Ih−1(t) − [Itr,h(t)Sh(t) + Ih(t)] = 0 h = 3, 5, 7, 10 Vh(t)

Function Sh(t) is a function that has values of 0 when the train does not start from node h and 1 when the train starts from the considered node. The model obtained with relations (1) and (2) is valid considering a quasi-stationary performance of the system [27]. In fact, the regulation transient of the chopper is considered to be very fast, and choosing an adequate stepping time for the simulation makes it possible to neglect the dynamic of the chopper and consider the output voltage to be constant.

4. Random Searching Optimization Problem The optimal integration of PV plant and SC energy storage systems in the railway power systems is carried out by means of an optimization procedure based on a random searching algorithm. This procedure is suitable for performing the minimization of an objective function, usually depending on integer variables, starting from a set of possible solutions of unknown variables and using an iteration procedure that calculates the new value of cost functions using a random uniform distribution of unknown variables. After a certain number of iterations, the minimum (or maximum) obtained value of the objective function determines the optimal solutions. In the case considered in this paper, the optimization variables are the number of series (nsh) and parallel (nph) SCs used on each shelter (it is supposed that the numbers of SCs are equal in the intermediate shelters and different at the ﬁrst and last stops) and the number of complete track sections performed by the train (nt) during which the energy obtained by the PV cells is stored in the SCs. The last random variable utilized is the discharge power Pd of the SCs in the discharge process (divided into Pd1 and Pd3 for the ﬁnal and initial shelters, respectively, and Pd2 for the intermediate shelters). All of the variables are strictly related to the electrical optimization of the net, because they determine the improvement of the total power dissipated in the railway system. The optimization problem is resumed in the following system: min (c1 − c3)∆E · ns1np1 + ns2np2 + ns3np3 + ...... + c2Eloss − c3Epv,p subject to (3) Vmin ≤ Vh(t) ≤ Vmax Isc,h(t) ≤ Imax Energies 2018, 11, 410 8 of 14

In (3), c1, c2, and c3 are weight parameters in Euro/kWh related to the cost of the SCs (∆E is the energy stored in a single SC unit), the cost of the energy losses (Eloss), and the cost of the energy generated by the PV cells (Epv,p) and exchanged to the power system. The optimization procedure Energiestakes into 2018 account, 11, x FOR the PEER solution REVIEW of a complete track section for the train with all the stops, along with8 of the 14 calculation and evaluation of the cost functions for each combination obtained by the procedure (Figure5). TheThe time time dependence of variables Vh andand Isc,h,h isis directly directly considered considered because because the the optimization optimization procedureprocedure simulates simulates the the complete complete railway railway track. track. The The minimum minimum and and maximum maximum voltage voltage limits limits for for the the consideredconsidered electric electric system system are are 6 60000 V V and and 900 900 V, V, respectively, respectively, whil whilee the maximum discharge discharge current current dependsdepends on on the the type type of of SC SC adopted. adopted.

Figure 5. Flow chart of the optimization procedure. Figure 5. Flow chart of the optimization procedure. 5. Optimization Results 5. Optimization Results The optimization procedure is applied to the considered railway track, and the mechanical The optimization procedure is applied to the considered railway track, and the mechanical power power and speed profile of a train traveling on the railway are respectively represented in Figure and speed profile of a train traveling on the railway are respectively represented in Figure6a,b. As can 6a,b. As can be noted, the profiles are typical of light railway power and speed profiles, with be noted, the profiles are typical of light railway power and speed profiles, with numerous accelerations numerous accelerations and stops; this also shows that the current absorption presents numerous and stops; this also shows that the current absorption presents numerous peaks, which can influence peaks, which can influence the behavior of the power electronic converter installed in the power the behavior of the power electronic converter installed in the power system. The power stored in system. The power stored in the SCs is supplied during the acceleration phases in order to reduce the the SCs is supplied during the acceleration phases in order to reduce the total power absorbed by the total power absorbed by the substation. The optimization procedure was implemented considering SCs with the features reported in Table 3. The random optimization procedure was carried out with 17 iterations, fixing c1 = 30,000, c2 = 0.2, and c3 = 0.1. Figure 7a,b shows the parallel and series SCs that must be installed at the initial and terminal stops (blue) and in the intermediate shelters, while Figure 8 shows the normalized cost function with various interval recharge times for the SCs, and Figure 9 shows the distribution of the cost function values as a function of the discharge power.

Energies 2018, 11, 410 9 of 14

substation. The optimization procedure was implemented considering SCs with the features reported Energiesin Table 20183., 11, x FOR PEER REVIEW 9 of 14 The random optimization procedure was carried out with 17 iterations, ﬁxing c1 = 30,000, c2 = 0.2, 500 70 and c3 = 0.1. Figure7a,b shows the parallel and series SCs that must be installed at the initial and

terminal400 stops (blue) and in the intermediate shelters,60 while Figure8 shows the normalized cost function with various interval recharge times for the SCs, and Figure9 shows the distribution of the 300 50 cost function values as a function of the discharge power. 200The results obtained through the optimization procedures40 are reported in Table4. The optimal value100 of the cost objective function is approximately 19930 kEuro, which was practically determined by Power (kW) Power the high0 cost of the storage unit systems and could be (km/h) Speed 20 reduced by the improvement and production of new SCs. The positive role of the SC is also inherent to the reduction of the peak power required for -100 10 Energiesthe distribution 2018, 11, x FOR power PEER systems. REVIEW Figure 10 shows the new trend for the power required by the train.9 of 14 -200 0

500 70 -300 -10 0 50 100 150 200 250 300 0 50 100 150 200 250 300 400 Time (s) 60 Time (s) (a) (b) 300 50 Figure 6. Mechanical power and speed profile of a train traveling on the railway: (a) Mechanical 200 40 power necessary by the train; and (b) Train speed along the track. 100 30 Power (kW) Power Table0 3. Datasheet of Maxwell BMOD0063 P125 B08 (Max (km/h) Speed 20 well Technologies, San Diego, CA, USA).

-100 Quantity10 Value

-200 Rated capacitance 0 63 F Rated voltage 125 V -300 -10 0 50 100 150 200 250 300 0 50 100 150 200 250 300 Time (s) Stored Energy 140 Wh Time (s) (a) Nominal Voltage 750 V (b) Number of passenger stations 5 Figure 6. Mechanical power and speed profile of a train traveling on the railway: (a) Mechanical Figure 6. Mechanical power andMaximum speed proﬁle series of a voltage train traveling 1500 on the V railway: (a) Mechanical power power necessary by the train; and (b) Train speed along the track. necessary by the train; and (bAbsolute) Train speed maximum along the current track. 1900 A

Table 3. Datasheet of Maxwell BMOD0063 P125 B08 (Maxwell Technologies, San Diego, CA, USA).

1 Quantity1 Value Rated capacitance 63 F First and terminal shelters 0.8 0.8 Rated voltage 125 V Intermediate shelters Stored Energy 140 Wh 0.6 Nominal Voltage0.6 750 V Number of passenger stations 5 0.4 Maximum series voltage0.4 1500 V Absolute maximum current 1900 A 0.2 0.2 Normalized value of cost functions cost of value Normalized Normalized value of cost functions cost of value Normalized First and terminal shelters Intermediate shelters 1 1 0 0 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 Number of parallel supercapacitors Number of series supercapacitors First and terminal shelters 0.8 0.8 (a) (b) Intermediate shelters

Figure 7. Supercapacitors that must be installed at the initial and terminal stops: (a) Number of 0.6Figure 7. Supercapacitors that must be installed at the initial0.6 and terminal stops: (a) Number of parallel parallel supercapacitors (SC) for the first and terminal shelters (blue) and the intermediate shelters supercapacitors (SC) for the ﬁrst and terminal shelters (blue) and the intermediate shelters (red); and (red); and (b) Number of series SC for the first and terminal shelters (blue) and the intermediate 0.4(b) Number of series SC for the ﬁrst and terminal shelters0.4 (blue) and the intermediate shelters (red). shelters (red).

0.2 0.2 Normalized value of cost functions cost of value Normalized Normalized value of cost functions cost of value Normalized The results obtained through the optimization procedures are reported in Table 4. The optimal First and terminal shelters value of the cost objective functionIntermediate is approximat shelters ely 199 kEuro, which was practically determined by 0 0 the high0 cost1 of the2 storage3 4 unit5 systems6 7and 8could9 be reduced0 1 by the2 im3 provement4 5 and6 production7 8 9 Number of series supercapacitors of new SCs. TheNumber positive of parallel role supercapacitorsof the SC is also inherent to the reduction of the peak power required for the distribution power(a) systems. Figure 10 shows the new trend for the(b )power required by the train. Figure 7. Supercapacitors that must be installed at the initial and terminal stops: (a) Number of parallel supercapacitors (SC) for the first and terminal shelters (blue) and the intermediate shelters (red); and (b) Number of series SC for the first and terminal shelters (blue) and the intermediate shelters (red).

The results obtained through the optimization procedures are reported in Table 4. The optimal value of the cost objective function is approximately 199 kEuro, which was practically determined by the high cost of the storage unit systems and could be reduced by the improvement and production of new SCs. The positive role of the SC is also inherent to the reduction of the peak power required for the distribution power systems. Figure 10 shows the new trend for the power required by the train.

Energies 2018, 11, x FOR PEER REVIEW 10 of 14 EnergiesEnergies 20182018, ,1111, ,x 410FOR PEER REVIEW 1010 of of 14 14

In the proposed procedure, the SCs are controlled to keep the power used during the discharge process In the proposed procedure, the SCs are controlled to keep the power used during the discharge process and trainTable acceleration 3. phases constant, but it is also possible to completely discharge the SCs in a limited time, and train accelerationDatasheet phases of Maxwell constant, BMOD0063 but it is also P125 possible B08 (Maxwell to completely Technologies, discharg Sane the Diego, SCs in CA, a limited USA). time, which corresponds to the maximum value of power required. which corresponds to the maximum value of power required. Quantity Value Table 4. Results of the optimization procedure. TableRated 4. Results capacitance of the optimization procedure. 63 F RatedQuantity voltage Values 125 V StoredQuantity Energy Values 140 Wh np1, ns1 (2, 6) Nominalnp1 Voltage, ns1 (2, 7506) V Number of passengernp2, ns2 stations(1, 2) 5 np2, ns2 (1, 2) Maximum seriesnp3, n voltages3 (2, 1500 6) V Absolute maximumnp3, ns3 current(2, 1900 6) A nt 8 nt 8 Pd1 460 W Pd1 460 W In the proposed procedure, the SCs arePd controlled2 to keep970 the W power used during the discharge Pd2 970 W process and train acceleration phases constant,Pd3 but it is also possible460 W to completely discharge the SCs Pd3 460 W in a limited time, which correspondsValue of to objective the maximum function value 199 of power kEuro required. Value of objective function 199 kEuro

1 1

0.8 0.8

0.6 0.6

0.4 0.4

0.2

Normalized value of cost functions cost of value Normalized 0.2 Normalized value of cost functions cost of value Normalized

0 0 2 4 6 8 10 12 2 4 Number6 of track8 cycles 10 12 Number of track cycles Figure 8. Number of time interval of 15 min utilized for the recharge of supercapacitors. FigureFigure 8. 8. NumberNumber of of time time interval interval of of 15 15 min min utilized utilized for for the the recharge recharge of of supercapacitors. supercapacitors.

Figure 9. Power available for the control of SC in the discharge process. Optimal values: Yellow FigureFigure 9. 9. PowerPower available available for for the the control control of of SC SC in in the the discharge discharge process. Optimal values: Yellow circle circle (first and terminal shelter), Purple circle (intermediate shelters). circle(ﬁrst and(first terminal and terminal shelter), shelter), Purple Pu circlerple circle (intermediate (intermediate shelters). shelters).

Energies 2018, 11, 410 11 of 14

Table 4. Results of the optimization procedure.

Quantity Values

np1, ns1 (2, 6) np2, ns2 (1, 2) np3, ns3 (2, 6) nt 8 Pd1 460 W Pd2 970 W Pd3 460 W Value of objective function 199 kEuro Energies 2018, 11, x FOR PEER REVIEW 11 of 14

Figures 11 and 12 show the trend of voltage and current in node 10 during a typical winter day. The voltage proﬁle highlights500 that the maximum and minimum values of voltage are respected; also, the current respects the imposed400 constraints; the maximum value of current is reached when the tram passes through the last stop. In the previous instant, the current of node 10 is about 1 A (this behavior 300 permitsEnergies 2018 also, 11 the, x reductionFOR PEER REVIEW of Joule losses along the tramway power system). 11 of 14 200

500 100

Power (kW) Power 400 0

300 -100

200 -200 Required power Required power with supercapacitor integration 100 -300 0 50 100 150 200 250 300 350 Time (s) Power (kW) Power 0

Figure 10. New power-100 profile with integration of SC charged with photovoltaic modules.

-200 Required power Figures 11 and 12 show the trend of voltageRequired and power cuwithrrent supercapacitor in node integration 10 during a typical winter day. -300 The voltage profile highlights0 that the50 maximum100 150 and minimum200 250 values300 of350 voltage are respected; also, Time (s) the current respects the imposed constraints; the maximum value of current is reached when the tram passes through the last stop. In the previous instant, the current of node 10 is about 1 A (this behavior FigureFigure 10. 10.New New power power proﬁle profile with with integration integration of of SC SC charged charged with with photovoltaic photovoltaic modules. modules. permits also the reduction of Joule losses along the tramway power system). Figures 11 and 12 show the trend of voltage and current in node 10 during a typical winter day. The voltage profile highlights900 that the maximum and minimum values of voltage are respected; also, the current respects the imposed constraints; the maximum value of current is reached when the tram 850 passes through the last stop. In the previous instant, the current of node 10 is about 1 A (this behavior permits also the reduction800 of Joule losses along the tramway power system).

750

900 700

Voltage (V) 850 650

800 600

750 550

700 500 0 50 100 150 200 250 300

Voltage (V) Time (s) 650

FigureFigure 11.11.Voltage Voltage trend 600trend in in the the node node 10 10 during during the the movement movement of of the the tram tram along along the the track. track.

550

800 500 0 50 100 150 200 250 300 Time (s) 600 Figure 11. Voltage trend in the node 10 during the movement of the tram along the track. 400

800 200 Current (A)Current 600 0

400 -200

200 -400 0 50 100 150 200 250 300 350

Current (A)Current Time (s) 0 Figure 12. Current trend in the node 10 during the movement of the tram along the track. -200

-400 0 50 100 150 200 250 300 350 Time (s)

Figure 12. Current trend in the node 10 during the movement of the tram along the track.

Energies 2018, 11, x FOR PEER REVIEW 11 of 14

500

400

300

200

100

Power (kW) Power 0

-100

-200 Required power Required power with supercapacitor integration

-300 0 50 100 150 200 250 300 350 Time (s)

Figure 10. New power profile with integration of SC charged with photovoltaic modules.

Figures 11 and 12 show the trend of voltage and current in node 10 during a typical winter day. The voltage profile highlights that the maximum and minimum values of voltage are respected; also, the current respects the imposed constraints; the maximum value of current is reached when the tram passes through the last stop. In the previous instant, the current of node 10 is about 1 A (this behavior permits also the reduction of Joule losses along the tramway power system).

900

850

800

750

700

Voltage (V) 650

600

550

500 0 50 100 150 200 250 300 Time (s) Energies 2018,Figure11, 410 11. Voltage trend in the node 10 during the movement of the tram along the track. 12 of 14

800

600

400

200 Current (A)Current 0

-200

-400 0 50 100 150 200 250 300 350 Time (s)

FigureFigure 12. 12.Current Current trend trend in in the the node node 10 10 during during the the movement movement of of the the tram tram along along the the track. track.

6. Conclusions The integration of PV panels, SC energy storage systems, and railway power systems was analyzed in this paper. This study considered a real tramway track and simulated a real train operating on that track. Starting from the analysis of the available shelters and available surface, the PV energy was calculated, and the utilization of this energy in the railway power system was determined by means of an innovative random optimization procedure. An appropriate random optimization procedure was proposed and implemented using the data available for the production of electrical energy in the worst and best cases during the year in order to ﬁnd the optimal size of the energy storage system, the time needed to charge the SCs with the PV panels, and the reduction of the total losses in the net. The procedure found the optimal value of the cost functions and demonstrated the technical feasibility of integrating the PV power plant in order to supply a railway system.

Acknowledgments: This work was supported by Regione Campania in the frame of L.R. 5/2002, project “Stazioni fotovoltaiche di sostegno per la rete tranviaria di Napoli”. Author Contributions: All the authors equally contributed to this paper. Conﬂicts of Interest: Authors declare no conﬂict of interest.

Abbreviations c1 Parameter of cost function related to SC energy c2 Parameter of cost function related to losses c3 Parameter of cost function related to the energy exchanged with the distribution system Eloss Total loss energy Epv,p Total energy exchanged with the distribution system Ih Current in the node h Imax Maximum value of current during the discharge Isc,h Current in the SC allocated in node h Itr,h Current required by the tram in the node h np1 Number of parallel SC in the ﬁrst node np2 Number of parallel SC in the intermediate nodes np3 Number of parallel SC in the last nodes ns1 Number of series SC in the ﬁrst node ns2 Number of series SC in the intermediate nodes ns3 Number of series SC in the last nodes Energies 2018, 11, 410 13 of 14

Re Line resistance between the substation and the feeder Rh Line resistance between two consecutive nodes Ve Substation voltage Vh Voltage in the node h Vmax Maximum voltage value admissible in the nodes Vmin Minimum voltage value admissible in the nodes Vsc,h Voltage of SC energy system installed in the node h ∆E Energy of a single SC

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