APPLICATION NOTE ECONOMIC CABLE SIZING IN PV SYSTEMS: CASE

Transcription

1 APPLICATION NOTE ECONOMIC CABLE IZING IN PV YTEM: CAE TUDY Lisardo Recio Maillo July 017 ECI Available from

2 Document Issue Control heet Document Title: Publication No: Application Note Economic cable sizing in PV systems: case study Cu0167 Issue: 03 Release: Public Content provider(s) / Author(s): Editorial and language review Content review: Lisardo Recio Maillo, Eduard Bullich Massagué, Mònica Aragüés Peñalba, Andreas umper Bruno De Wachter (editorial), Noel Montrucchio (English language) Hans De Keulenaer, Creara Document History Issue Date Purpose 1 October 009 Initial publication June 013 Publication in the framework of the Good Practice Guide 3 July 017 Reworked after review Disclaimer While this publication has been prepared with care, European Copper Institute and other contributors provide no warranty with regards to the content and shall not be liable for any direct, incidental or consequential damages that may result from the use of the information or the data contained. Copyright European Copper Institute. Reproduction is authorized providing the material is unabridged and the source is acknowledged. Issue Date: July 017 Page i

3 CONTENT ummary... 1 Introduction... General remarks... ystem description... 3 PV plant features... 3 Characteristic curves of the PV array... 5 Calculating the cable cross-section according to the standards... 8 Design to maximum allowed current... 8 Design to maximum allowed voltage drop Calculation of the most economic cable cross-section Layout Layout... 0 Optimal Layout... 4 Conclusions... 5 References... 6 Issue Date: July 017 Page ii

4 UMMARY When sizing electric cables for PV installations it is a common practice to select cabling that meets the minimum regulatory requirements. This is done to minimize upfront costs. However, choosing a larger cable cross section than legally required reduces energy losses. The purpose of this paper is to establish the optimal cable cross-section for a PV installation that will minimize its life cycle cost. In some countries, the allocated price for electricity generated by PV systems is higher than the market price thanks to the feed-in tariff or green certificates. When this is the case, energy losses become even more costly. In other words, reducing the energy losses of a PV plant by increasing the cable cross-section leads to an even bigger financial return than in other electrical installations. The PV installation layout is one of the determining factors for establishing the length and minimum crosssection of each cable. A careful study of all the lay-out options can significantly lower the life-cycle cost of the installation. Issue Date: July 017 Page 1

5 INTRODUCTION The annual installed PV capacity is steadily growing around the world. Environmental concerns, fossil fuel price variability, PV technology advances and cost reductions are making this type of renewable electricity generation increasingly competitive. This paper presents an analysis on how to select of the optimum cable size for a PV system. The analysis is illustrated with an actual business case study. The first chapter provides a detailed description of all the relevant characteristics of the PV system under study. The second chapter is devoted to the calculation of the minimum cable size to comply with current regulations and technical requirements. It serves to illustrate the common practice for selecting the cable cross-section, which results in minimum upfront costs. The third chapter evaluates the economic benefit of selecting a larger cable cross-section than the minimum that is legally required. It demonstrates that in a large majority of cases the financial optimum lies at a larger cross-section than what the standard prescribes. If Feed-in-Tariffs (FITs) or other financial incentives for PV generated electricity apply, energy losses become even more costly and the economically optimal cable crosssection will even be larger. It is demonstrated that the PV installation layout is an important factor in reducing its life-cycle cost. GENERAL REMARK The methodology that has been used when sizing the PV plant cables is generic, but the results are specific to the particular case study analyzed in this document and cannot be generalized to cases with other conditions. It is especially important to mention that these results can be affected by the location of the PV plant. The benefits of oversizing the cables come from the power loss reduction that compensates for the initial investment. If the PV plant is placed in an area with a lower irradiation profile than the one considered in this study, the loss reduction will be lower and as a result, the optimal cable cross-section will be smaller. For the same reason, the optimal cable cross-section will increase with increasing irradiation levels, e.g. through PV panels that can change their orientation based on the data provided by solar trackers. In the present analysis, it is assumed that the PV plant is installed in a country that benefits from feed-in tariffs. Feed-in tariffs are policy mechanisms designed to promote investment in renewable energy technologies. However, they are country dependent and evolve over time. Furthermore, they are different for each technology and installation size. Feed-in tariffs are currently being phased-out and replaced by more market-oriented mechanisms (e.g. tenders) in many countries. In this application note, the over-sizing of cables refers to the practice of choosing a larger cable cross-section than what is strictly required by the technical standards. Issue Date: July 017 Page

6 YTEM DECRIPTION An actual case study is used to explain the principles of optimal cable sizing however the same method can be applied to other PV system types and/or sizes. PV PLANT FEATURE The system under study is a 100 kw PV plant located in Valencia, pain. It consists of 3 PV arrays of 39 kw at standard conditions (5 0 C and 1,000 W/m ). Each array is composed of 11 strings of 16 PV modules connected in series. The PV array configuration is shown in Figure 1. Based on this configuration, the maximum output of each PV array at the above mentioned standard conditions and operation at the maximum power point is as follows: U dc-array = V I dc-array = A P array = kw The PV inverter has a rated power of 100 kw. We shall analyze two configurations: In the first configuration (Figure ), the output cables of the three junction boxes are joined at the inverter input. Consequently, these cables must be sized following the PV array rating. In the second configuration (Figure 3), the output cables are connected at the output of the junction boxes. This results in a shorter cable length, but requires a higher current rating for the PV inverter cable. Note that the PV inverter is rated at 100 kw, while the total PV power at standard conditions is x 3 = kw. Figure 1 PV Array Configuration. Issue Date: July 017 Page 3

7 Figure PV Plant Layout. Configuration 1. Finally, Table 1 summarizes the PV plant data. Figure 3 PV Plant Layout. Configuration. Issue Date: July 017 Page 4

8 Location Valencia, pain Active power At MPP Panel installation mode Fixed, tilted 30 0, facing south Current at MPP PV plant general characteristics Maximum ambient temperature Minimum ambient temperature Rated power 50 0 C 0 0 C 100 kw PV array characteristics (at 5 0 C and 1,000 W/m ) Voltage at the maximum power point (MPP) hort circuit current Number of parallel strings Number of series modules per string kw A V A Nominal power Current at MPP PV module characteristics (at 5 ºC and 1,000 W/m ) Voltage at MPP hort circuit current W 7.44 A 9.84 V 7.96 A Table 1 General PV Plant Characteristics. CHARACTERITIC CURVE OF THE PV ARRAY The purpose of the following study is to enable the optimal design of the conductor cross section for those cables interconnecting the junction boxes with the PV inverter. To do so, the current and voltages of the PV arrays must be studied beforehand. The characteristics of the PV modules and the array layout are summarized in Table. The characteristic voltage-current and voltage-power curves are shown in Figure 4 and Figure 5. If these curves are not available, they can be obtained from Table, which applies the equations explained in [1] Development of generalized photovoltaic model using MATLAB imulink. PV module Number of series connected cells 60 Nominal Power (W) MPP voltage (V) 9.84 MPP current (A) 7.44 Open circuit voltage (V) 36. hort circuit current (A) 7.96 hort circuit current temperature coefficient (%/ 0 C) 0.03 Open circuit voltage temperature coefficient (%/ 0 C) PV array Number of series modules per string 16 Number of parallel strings per array 11 * PV MODULE CHARACTERITIC ARE AT 1,000 W/M AND 5 0 C Table PV array characteristics used for modeling the characteristic curves. Issue Date: July 017 Page 5

9 As shown in Figure 4, the short circuit and the maximum power point (MPP) currents vary proportionally with the irradiance while the MPP and open circuit voltages remain nearly constant. In contrast, Figure 5 reveals that the MPP and short circuit currents do not depend on the temperature while the voltages increase linearly with the temperature decrease. Figure 4 I-V and PV characteristic of the PV array as a function of the irradiation (T=5 0 C). Figure 5 I-V and PV characteristic of the PV array in function of the temperature (G=1,000 W/m ). It can be concluded from Figure 4 and Figure 5 that the maximum MPP voltage, which is at the minimum considered temperature of the area, is 533 V and the maximum MPP current (corresponding to the higher irradiation) is A. In accordance with these values, the maximum currents and voltages for the two layouts are summarized in Table 3, where CCGx-CCGy refers to the cables that interconnect the junction box x to the junction box y (see Figures and 3) and CCGx-Inverter refers to the cable connecting the junction box x to the inverter. Issue Date: July 017 Page 6

10 Layout configuration 1 Cable Maximum MPP current (A) Maximum hort Circuit current (A) Maximum MPP voltage (V) Length (m) CCG1-Inverter CCG-Inverter CCG3-Inverter Layout configuration Cable Maximum MPP current (A) Maximum hort Circuit current (A) Maximum MPP voltage (V) Length (m) CCG1-CCG CCG3-CCG CCG-Inverter Table 3 Maximum currents and voltages in the cables. Issue Date: July 017 Page 7

11 CALCULATING THE CABLE CRO-ECTION ACCORDING TO THE TANDARD Due to its location, the installation must comply with the REBT 00 (panish Low Voltage Electrotechnical Regulation) and particularly with the ITC-BT 40 (Complementary Technical Instruction Low voltage generation systems ). When designing installations for other countries, their specific regulations must be considered. In this case, the afore-mentioned legislation establishes two design criteria for the minimum cable section: maximum current allowed and maximum voltage drop. DEIGN TO MAXIMUM ALLOWED CURRENT According the ITC-BT 40, the cable current must be sized for a current no lower than 15% of the maximum generator current. This current corresponds to the short circuit current at the maximum irradiation and maximum temperature. The cable temperature will reach 50 0 C As specified in the UNE tandard for outdoor installations, a correction coefficient of 0.9 must be applied at 50 0 C. Taking into account that the cable will be exposed to the sun, an additional correction factor of 0.9 is applied. Table 4 shows the result of applying the above mentioned correction factors to obtain the minimum admissible current of the different cables. Layout configuration 1 Cable Maximum hort Circuit current, I sc-max (A) Minimum admissible current: I sc-max 1.5/( ) (A) CCG1-Inverter CCG-Inverter CCG3-Inverter Layout configuration Cable Maximum hort Circuit current, I sc-max (A) Minimum admissible current: I sc-max 1.5/( ) (A) CCG1-CCG CCG3-CCG CCG-Inverter Table 4 Minimum admissible current for selection of the cable cross section. The cable lies on a grill-type rack (Category F in Table 5). The insulation type used on the Tecsun (PV) (A) cable is XLPE. Based on Table 4 and Table 5, the minimum cross section for a copper conductor is shown in Table 6. Issue Date: July 017 Page 8

12 Conductor numbers with types of insulation A1 PVC3 PVC XLPE3 XLPE A PVC3 PVC XLPE3 XLPE B1 PVC3 PVC XLPE3 XLPE B PVC3 PVC XLPE3 XLPE C PVC3 PVC XLPE3 XLPE E PVC3 PVC XLPE3 XLPE F PVC3 PVC XLPE3 XLPE Cu Al Required cross section mm² Maximum current after temperature correction (A) 1, , , , , ,5 18, , , , Table 5 Maximum allowed current in function of the cross section, insulation and installation configuration. Issue Date: July 017 Page 9

13 Cable Layout configuration 1 Minimum admissible current (A) Minimum cross section (mm ) CCG1-Inverter CCG-Inverter CCG3-Inverter Layout configuration 1 Cable Minimum admissible current (A) Minimum cross section (mm ) CCG1-CCG CCG3-CCG CCG-Inverter Table 6 Minimum cross section for the different cables studied. DEIGN TO MAXIMUM ALLOWED VOLTAGE DROP In compliance with the Tecsun (PV) (A) cable specifications, the maximum permissible operating voltage in direct current (DC) systems is 900/1800 V. In this case study, the maximum voltage of the installation (533 V) does not exceed this value. Therefore, the cable insulation is appropriate. The maximum allowed voltage drop is checked for all cables. The ITC-BT 40 is used for the maximum allowable voltage drop calculation: the voltage drop between the generator and the point of connection to the Public Distribution Network or indoor installations shall not exceed 1.5% at the nominal current. It is important to note that in the system analyzed, there is a power converter connected between the generator and the point of connection to the public network. This requirement does not include any specification regarding what happens if there is a voltage transformation between the generator and the connection point. Nevertheless, as specified above, when applying the technical requirements established in [] (Technical specifications for gridconnected systems) the maximum voltage drop in DC cables turns out to be 1.5 and (referred to the MPP voltage and current at 5 0 C and 1,000 W/m [3] (Technical handbook. The installation of ground photovoltaic plants over marginal areas). Assuming that the main DC lines are responsible for 1% of the total DC voltage drop and the remaining 0.5% corresponds to the rest of the cabling, the voltage drop can be obtained (TC sub index refers to standard ambient conditions): MPP voltage: V V mpp@ TC Maximum allowed voltage drop: V V max 0 V TC Maximum current for voltage drop calculation (single array): I 84A TC 81. Maximum current for voltage drop calculation (three arrays): I TC 45.5 A L 1 Cable resistance: R Issue Date: July 017 Page 10

14 Where: L is the total cable length (positive + negative) is the cross section 46.8m / mm is the cooper conductivity at 70 0 C Note that the maximum current corresponds to the maximum short circuit current which is at 50 0 C The voltage drop at each cable is shown in Table 7: Layout configuration 1 Cable (A) mpp TC Cross section (mm ) L positive + negative (m) R (Ω) Voltage drop V R (V) I TC CCG1-Inverter CCG-Inverter CCG3-Inverter Layout configuration Cable (A) mpp TC Cross section (mm ) L positive + negative (m) R (Ω) Voltage drop V R (V) I TC CCG1-CCG CCG3-CCG CCG-Inverter Table 7 Voltage drop calculation at each cable. As shown in Table 7 all cables exceed the maximum voltage drop (note that for configuration, the total voltage drop is V). Hence, the cross section must be increased. For configuration 1, the cables are in parallel. This means that the minimum cross section can be calculated as follows (note that L is the total cable length, positive + negative): min L I mpp@ TC V max Table 8 shows the minimum cross section and the cable selection for configuration 1: Issue Date: July 017 Page 11

15 Layout configuration 1 Cable I mpp@ TC (A) L positive + negative (m) Minimum cross section (mm ) Cable selection according to Table 5 (mm ) CCG1-Inverter CCG-Inverter CCG3-Inverter Table 8 Minimum cross section for cables of configuration 1 and the corresponding cable selection. In contrast, configuration has cables in series. In this case the CCG1-CCG-Inverter or CCG3-CCG-inverter paths have to be studied. The voltage drop will be: V VCCG1 CCG VCCG inverter VCCG3 CCG VCCG inverter Path CCG1-CCG-inverter is considered. o, the voltage drop can be written as: V L CCG1CCG I CCG1CCG mpp@ TC CCG1CCG L CCG inverter I CCG inverter CCGinverter mpp@ TC The length L is equal for both cables, and the current of CCG-inverter is three times that of the current of the CCG1-CCG. o, the voltage drop can be re-written as: V L I CCG1CCG mpp@ TC 1 CCG1CCG 3 CCG inverter 4.6 V The condition has been found to comply with the voltage drop: 1 3 CCG1CCG CCG inverter 0.07mm As can be observed, there are many options to choose among the cross sections. Finding the minimum amount of cable is imperative, in order to minimize the total volume of cable. As the cable CCG3-CCG is equal to the cable CCG1-CCG: Vol LCCG1 CCG CCG1 CCG LCCG inverter CCG inverter As the cable length is equal for all cables, in our case: Vol L CCG 1CCG CCG inverter A simple optimization problem can be formulated: - Objective function: min f Vol Issue Date: July 017 Page 1

16 - Voltage drop constraint: 1 3 CCG1CCG CCG inverter - Thermal constraints (maximum current limitation): 0.07mm CCG1 CCG 5mm CCG inverter 150mm olving the optimization problem: CCG1 CCG. 4 8 mm CCG inverter mm Now, appropriate cable sections can be selected using Table 5. CAE A The CCG-inverter cable section is fixed at CCG inverter 40mm, as it is the next possible eligible value in Table 5 for this section. As this value is greater than the minimum required value for the section, the cable size associated with the other section can be reduced while still maintaining the voltage drop under its threshold value. The optimization problem is now solved again but with the added constraint: CCG inverter 40mm o, the minimum section for cable CCG1-CCG that satisfies the thermal and voltage drop constraints is found: CCG1 CCG 69mm o, according to Table 5, the section that will be chosen is: CAE B CCG1 CCG 70mm The CCG1-CCG cable section is fixed at CCG1 CCG 95mm, as it is the next possible eligible value in Table 5 for this section. As this value is greater than the minimum required value for the section, the cable size associated with the other section can be reduced while still maintaining the voltage drop under its threshold value. The optimization problem in now solved again but with the added constraint: CCG1 CCG 95mm o, the minimum section for cable CCG-inverter that satisfies both the thermal and voltage drop constraints is found: CCG inverter 18.1mm o, according to Table 5, the section that will be chosen is: CCG inverter 185mm Issue Date: July 017 Page 13

17 REULT FOR CONFIGURATION In this case, option B produces the solution with the minimum amount of cable volume, involving a total volume of m 3 (in comparison with option A that involves m 3 1 ) as summarized in Table 9. Note that as cables are placed in series, when considering the total voltage drop constraint, the minimum cross section of cables CCG1-CCG and CCG3-CCG depends on the cross section of the cable CCG-Inverter and vice versa (see 4 th column in Table 9). Layout configuration Option b. Cable I mpp@ TC (A) L positive + negative (m) Minimum cross section (mm ) Cable selection according to Table 5 (mm ) CCG1-CCG CCG3-CCG CCG-Inverter Depends upon the other cables Depends upon the other cables Depends upon the other cables Table 9 Cable selection for configuration. The next chapter will demonstrate that minimizing the total cable conductor material will not minimize the life-cycle cost of the installation. When it comes to the life-cycle cost, the added energy losses have a far bigger weight than the cost of the conductor material. 1 Option A: ( ) =0.034 m 3 Option B: ( ) = m 3 Issue Date: July 017 Page 14

18 CALCULATION OF THE MOT ECONOMIC CABLE CRO-ECTION In the previous chapter, the minimum required cable sections were calculated. In this chapter we will carry out an economic study to obtain the optimal cable cross-section and cable lay-out from the point of view of the life-cycle cost. The instantaneous power losses of a cable can be calculated as: Where: P loss ( t) R( t) I ( t) (W) R(t) (positive + negative cable) is expressed in Ω I(t) is expressed in A R(t) can be considered constant without significant error. We take values of R at 70 0 C, so the energy lost is obtained as: E R I loss ( t) dt (J) When simplifying the equation, we may consider the current as constant during time period Δt (expressed in hours), the energy loss can be approximated as: E loss R I i t i (Wh) If all time intervals are of one hour, the total energy loss is: E R loss I i (Wh) From Figure 4 and Figure 5, it can be observed that the MPP current is approximately directly proportional to the irradiation. Using the reference MPP current at 5 0 C and 1,000 W/m (I mpp = A per PV array), so the current can be written as: I G G Impp G G 1000 ref 81 (A) Where: G is the irradiation in W/m. The energy loss in kwh can be expressed as: E loss R G i (kwh) 1000 Then, the cost of losses (energy lost and not sold at the applicable feed-in tariff (FIT)) can be expressed as: C loss E FIT ( ) loss Issue Date: July 017 Page 15

19 where FIT is the feed-in tariff expressed in /kwh. In case no feed-in tariffs apply, this term should be replaced by an estimation of the average price at which the PV electricity is sold to the grid, or the average cost of avoided grid electricity consumption through PV energy self-consumption ( /kwh). Once the cost of losses for a specific cable section and length C s1-l1 is found, the cost for any cable cross section can be easily obtained as: C sk L L C ( ) k 1 k s 1 L1 L k 1 LAYOUT 1 Firstly we calculate the cost of the losses in all cables and their minimum cross section. For this purpose, the annual irradiation profile is obtained. Table 10 shows the irradiation profile, the calculation of energy losses and the associated cost for the CCG-inverter cable. Cable CCG-inverter (positive + negative): L= 45 m, =50 mm, total R= Ω 1h d i G i G (W/m ) hour J F M A M J J A O N D d i =Num. days of E loss month i (0,08184 /1000) R G i It corresponds to Cost 1 FIT=0,3 /kwh Cost FIT=0,44 /kwh G i for 1 year at each daytime kwh ,0 0,0 0, ,1 0,0 0, ,6 0,5 0, ,0 3,0 4, ,7 8,0 11, ,5 14, 0, ,5 19,6 8, ,3,3 3, , 1,4 31, ,7 17,0 5, ,0 10,8 15, ,7 5,3 7, ,1 1,8, ,1 0,3 0, ,1 0,0 0, ,0 0,0 0,0 TOTAL (annual values) ,6 14,4 18,4 Table 10 Cost of energy loss calculation for CCG-inverter cable; layout 1. The annual cost of energy losses for any cable section and length can be obtained: 35 L L - For FIT=0.3 /kwh: C1 E loss ( ) L L - For FIT=0.44 /kwh: C E loss ( ) 90 Considering an annual interest rate of i, the net present value (NPV) for 30 years of cable lifetime is obtained as: NPV Inv min Inv 30 CF k1 1 1 i k Issue Date: July 017 Page 16

20 In which Inv min Ps min L and Inv Ps L represents the initial investment (P is the cost of a cable of section in /m shown in Table 11). CF is the cash flow calculated as C loss for the minimum section minus C loss for the section under study. Cable cross section (mm ) P s ( /m) Table 11 Price of cables. For the CCG-inverter cable, the results are shown in Figure 6 and Figure 7 and summarized in Table 1. The performance for the CCG1-inverter and CCG3-inverter cables is shown in Figure 8, Figure 9 and Table 13. Figure 6 NPV for different cable sections and different interest rate. FIT=0.3 /kwh. CCG-inverter Cable; layout 1. Issue Date: July 017 Page 17

21 Figure 7 NPV for different cable sections and different interest rate. FIT=0.44 /kwh. CCG-inverter Cable; layout 1 FIT=0.3 /kwh FIT=0.44 /kwh Interest rate (p.u) Optimal section (mm ) NPV ( ) Payback (years) Optimal section (mm ) NPV ( ) Payback (years) Table 1 Economic performance for the CCG-inverter cable election; layout 1. Issue Date: July 017 Page 18

22 Figure 8 NPV for different cable sections and different interest rate. FIT=0.3 /kwh. CCG1-inverter and cable CCG3-inverter Cables; layout 1. Figure 9 NPV for different cable sections and different interest rate. FIT=0.44 /kwh. CCG1-inverter and CCG3-inverter cables; layout 1. Issue Date: July 017 Page 19

23 FIT=0.3 /kwh FIT=0.44 /kwh Interest rate (p.u) Optimal section (mm ) NPV ( ) Payback (years) Optimal section (mm ) NPV ( ) Payback (years) Table 13 Economic performance for the CCG1-inverter cable and for the CCG3-inverter cable election; layout 1. These results show that sizing the cables as required by the minimum standards does not minimize the cost. In other words, oversizing power cables can be advantageous from an economic point of view. The lower the interest rate, the larger the optimal cross section because lower interest rates lead to higher benefits for energy loss reduction. As a result, the investment cost for oversizing the cables is compensated further by the loss reduction. Moreover, the benefits produced by the loss reduction increase with an increasing FIT, resulting in a greater optimal cross section. In the case study, over-sizing is beneficial for the CCG-inverter cable. For the longer CCG1-inverter and CCG3- inverter cables, oversizing is only profitable in the event of low interest rates. In the present study, the total savings from applying the most economic sections for the whole PV plant is between 59 and 5,5 depending on the FIT and the interest rate. LAYOUT For this layout, the annual cost of energy loss for CCG1-CCG and for CCG3-CCG1 cables can be evaluated with the same formulas shown in section 6.1 because the currents are the same. These formulas are as follows: 35 L L - For FIT=0.3 /kwh: C1 E loss ( ) L L - For FIT=0.44 /kwh: C E loss ( ) 90 Issue Date: July 017 Page 0

24 In contrast to this, the CCG-Inverter cable carries three times the current of the previous cables. As the energy losses are proportional to the square of the current, the annual energy loss cost for this cable is expressed as: - For FIT=0.3 /kwh: - For FIT=0.44 /kwh: C L L C1E loss ( ) L L ( ) E loss The benefits for all cables and all sections can now be computed. Figure 10, Figure 11 and Table 14 show the results for cables CCG1-CCG and CCG3-CCG. Cable oversizing is only profitable for a high FIT value. However, oversizing the main CCG-inverter cable leads to a considerable savings (Figure 1, Figure 13 and Table 15), even for lower FIT values. In this layout, the benefits of applying the economically optimal cross-section instead of the minimum cross-sections are between 0 and 1891 depending on the interest rate and the FIT. Figure 10 NPV for different cable sections and different interest rate. FIT=0.3 /kwh. CCG1-CCG and CCG3- CCG cables; layout. Issue Date: July 017 Page 1

25 Figure 11 NPV for different cable sections and different interest rate. FIT=0.44 /kwh. Cable CCG1-CCG and cable CCG3-CCG; layout. FIT=0.3 /kwh FIT=0.44 /kwh Interest rate (p.u) Optimal section (mm) NPV ( ) Payback (years) Optimal section (mm) NPV ( ) Payback (years) Table 14 Economic performance for the cable CCG1-CCG and for the cable CCG3-CCG election; layout. Issue Date: July 017 Page

26 Figure 1 NPV for different cable sections and different interest rate. FIT=0.3 /kwh. Cable CCG-inverter; layout. Figure 13 NPV for different cable sections and different interest rates. FIT=0.44 /kwh. Cable CCG-inverter; layout. Issue Date: July 017 Page 3

27 FIT=0.3 /kwh FIT=0.44 /kwh Interest rate (p.u) Optimal section (mm ) NPV ( ) Payback (years) Optimal section (mm ) NPV ( ) Payback (years) Table 15 Economic performance for the cable CCG-inverter; layout. OPTIMAL LAYOUT The previous results show that oversizing is more profitable for layout configuration 1. However, this does not imply that configuration 1 is the most profitable. To decide the optimal layout, the total life cycle costs of the optimal cables must be analyzed for both configurations. The total life cycle cost is the sum of the cable prices plus the cost of the yearly losses, taking into account the interest rate. Figure 14 shows a cost comparison between layout 1 and layout for a FIT=0.3 /kwh and proves that layout 1 is a better option than layout in this case. Issue Date: July 017 Page 4

28 Figure 14 Cost of the installation vs. interest rate and layout configuration. FIT=0.3 /kwh. Optimal cable size for each layout is considered. CONCLUION The following conclusions can be drawn from the results obtained in this report: From an economic point of view, sizing power cables according to the minimum standard requirements is rarely the best option. Performing an economic optimization analysis of the power cables is recommended to maximize the profit from PV installations. Most probably, this will lead to a larger cable cross-section than what is prescribed by the standards. The lay-out of power cables can also affect the economic performance of the PV system. Analyzing different possible lay-outs can result in a greater benefit. The optimal cable section can depend on factors such as the solar irradiance profile, the feed-in tariff (or other financial incentives for PV electricity), the PV plant lay-out and the length of the power cables. The larger the cable cross-section is chosen for a particular PV installation, the slower the ageing of the cable an additional benefit. Issue Date: July 017 Page 5

29 REFERENCE [1] Huan-Liang Tsai, Ci-iang Tu, and Yi-Jie u. Development of generalized photovoltaic model using matlab imulink, In Proceedings of the World Congress on Engineering and Computer cience, Oct 008 [] IDAE, Pliego de condiciones técnicas de instalaciones conectadas a red, 011. Available online, [accessed on ] [3] G Nofuentes, J Muñoz, D Talavera, J Aguilera, J Terrados, Technical handbook. The installation of ground photovoltaic plants over marginal areas, PVs in BLOOM Project a new challenge for land valorisation within a strategic eco-sustainable approach to local development, 011 Issue Date: July 017 Page 6