Role of Losses in Design of DC Cable For Solar PV Applications
Role of Losses in Design of DC Cable For Solar PV Applications
Role of Losses in Design of DC Cable For Solar PV Applications
size will reduce the energy losses due to lower resistance, and
vice versa. However, this will only occur at the expense of 8760
higher investment cost. Therefore, an optimal trade-off
between the cost of losses and the investment cost can be opt ⎛ β +1 ⎞
ρ ∑ I (t )
t =1
2
ep(t )
I cap = ⎜⎜ ⎟⎟
sought within a Life Cycle Assessment (LCA) framework [13]. ⎝ β ⎠ 1
The following sections of this paper present the methodology ⎛ 1 ⎞β
K ⋅ β ⋅⎜ ⎟
and the relevant case study applications that illustrate the ⎝α ⎠
prominent role of losses in determining the optimal cable rating (7)
for Solar PV application. This is followed by analysis of the
results and finally the conclusions. The optimal utilization of the cable, Uopt can be described
by Equation (8) which defined as the ratio of the peak current
II. METHODOLOGY circulating in the circuit to the optimal capacity determined
The methodology used in formulating the optimization from (7). The utilization value can be used as a useful indicator
problem is based on the life-cycle methodology as described in to compare between the available capacity headroom of
[13]-[15]. The optimal capacity of the cable (Icap) is determined different cable design strategies.
by minimizing the sum of the annual cost of losses and the
annuitized capital cost as shown in (1): I max
U opt = opt
× 100%
I cap
min
I cap
[∑ (CC + CL )] (8)
(1)
In case the costs of maintenance and the cost of cable
From the equipment datasheet, a correlation analysis has
installation are available, a more holistic system level study can
been carried out in order to establish the relationship between
be carried out to evaluate the cost breakdown of the respective
the cross sectional area of circuit (A) and its current-carrying
components. Thus, giving a better insight into the proportion of
capacity. In particular, power-type correlations have been
various costs involved.
found to fit very well with the given data. It can be expressed
as in (2): III. CASE STUDY APPLICATIONS
8760
CL = R ⋅ ∑ I (t ) 2
⋅ ep(t )
t =1 (4)
ρ⋅L
R=
A (5)
Substituting (5) into (4) and solving the optimal cable
current-carrying capacity as expressed in (6), gives the closed
form solution of the optimization problem as shown in (7). Figure 1. Correlation of cable ampacity versus cable cross-sectional area.
∂ (CC + CL)
=0
∂I cap (6)
Australasian Universities Power Engineering Conference, AUPEC 2014, Curtin University, Perth, Australia, 28 September – 1 October 2014 3
4,500 2000
4,000 1800
1600
3,500 Sunny Day
1400
3,000 Cloudy Day
1200
2,500 1000 Normal Day
2,000 800
y = 12.399x - 356.43 600
1,500 R² = 0.997
400
1,000
200
500
0
0:00
1:00
2:00
3:00
4:00
5:00
6:00
7:00
8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
18:00
19:00
20:00
21:00
22:00
23:00
0
0 50 100 150 200 250 300 350 400
Ampacity, A Time, hour
Figure 2. Correlation of annuitized capital cost versus cable ampacity. Figure 3. Solar PV power generation profiles on March 23, 26 and 29,
2014.
TABLE I. SOLAR CABLE ELECTRICAL AND COST DATA
Cable Size, Ampacity, Cost, Resistance, C. Heuristic versus Analytical Model
mm² A RM/km Ω/km
Under the Malaysia FiT scheme, the 2014 FiT rates varies
2.5 41 2,200 7.400 from RM 1.0411/kWh for PV installation up to and including 4
4.0 55 4,400 4.610 kW to RM 0.5440/kWh for 10 MW-30 MW solar farm. For the
6.0 70 5,500 3.080 sake of simplicity, highest FiT rate of RM 1.0411/kWh has
been considered [16]. In addition, the average electricity price
10.0 98 9,200 1.830 of RM 0.3583/kWh (end consumer electricity bill rate) [17] is
16.0 132 14,000 1.150 also considered in the study to illustrate the sensitivity of
2x10 176.4 18,400 0.915 electricity prices to the design of optimal solar cable. The
analysis is carried out assuming solar cable lifespan of 21
2x16 237.6 28,000 0.575 years, consistent with the 21 years FiT period in Malaysia. A
3x16 336.6 42,000 0.383 7% discount rate is also assumed to calculate the annuitized
solar cable capital cost. This study further assumes a safety
factor of 25% for peak-driven cable selection approach.
B. Solar PV Generation Data Figure 4 and Figure 5 show the parametric analyses by
The weather condition in Malaysia is non-seasonal and utilizing heuristic approach to determine the optimal solar
relatively ‘stable’ throughout the year as compared to the cable size for a 3x8 array configuration with 250W module for
countries with four seasonal changes. As a result, a month of the considered FiT rate and electricity price, respectively.
PV generation data may consider as sufficient to provide some Despite the minimum design requirement of 2.5 mm2 for a
strategic insight into as how the losses may affect the optimal 6kW (3x8x250W) PV array solar cable (assume satisfies
design of cable. As a result, 31 days (March 2014) of 5-minutes voltage drop limits), it is interesting to observe that the optimal
resolution PV generation data is collected from a 2 kW grid- solar cable sizes are much larger, i.e. 6 mm2 for the assumed
connected PV system installed at UTeM. These data are used average electricity price and 10 mm2 for the FiT rate. It is also
in the analysis considering the annual PV generation data is not important to highlight the very high proportion of losses
yet available from the current installed system. However, it is incurred (and the associated cost) for smaller, i.e., 2.5 mm2 and
important to highlight the need to use the annual PV generation 4 mm2 cable sizes. Given the higher role of losses for the
data (when it becomes available) to provide more accurate considered FiT rate (RM 1.0411/kWh) as compared to the
results. Figure 3 below shows three different day types’ average electricity price of RM 0.3583/kWh, the larger
samples of daily PV generation profiles, namely sunny day, conductor size of 10 mm2 instead of 6 mm2 is selected as the
normal day and cloudy day in March 2014. optimal ones.
Australasian Universities Power Engineering Conference, AUPEC 2014, Curtin University, Perth, Australia, 28 September – 1 October 2014 4
Cost of Losses
3,500
Capital Cost results are as shown in Table II and Table III, respectively. It is
3,000 interesting to highlight that the optimal utilization for solar
2,500 cable is quite low particularly for the case of FiT rate. For
example, the optimal utilization of a 2 kW PV array is 26% as
2,000
shown in Table II below. In addition, the optimal utilization of
1,500 solar cable increases when the PV array power increases. This
1,000 is due to the fact that the role of losses becomes less prominent
when the required cable rating increases. For example, the
500
optimal cable utilization of a 10 kW PV array is approximately
0 42% as compared to 17% for a 2 kW PV string as shown in
2.5 4 6 10 16 2*10 2*16 3*16 Table III. It is important to note that the peak-driven design as
Cable Size, mm²
shown in the Table II and Table III have factored in the
Figure 4. Overall cost of DC array cable for 3x8 array configuration at RM additional 25% headroom, but does not consider the other
0.3583/kWh. design requirement such as voltage drop limit. Hence, the
4,500 design may change considerably if very stringent voltage drop
4,000
limit is applied to the peak-driven design. It is expected that the
optimal solar cable design proposed in this paper is likely to
Annuitized Total Cost, RM/ km.year
Cost of Losses
3,500
Capital Cost meet both thermal and voltage drop limit criterion given its
3,000 very low cable utilization.
TABLE II.
2,500 OPTIMAL CABLE DESIGN FOR DIFFERENT PV ARRAY POWER AT
ELECTRICITY PRICE OF RM 0.3583 /KWH
2,000
Array Power
Peak-Driven Optimal Optimal
1,500 for Multiple of
Design, mm² Design, mm² Utilization (%)
2kW string
1,000
2 2.5 2.5 26
500
4 2.5 4 39
0
2.5 4 6 10 16 2*10 2*16 3*16 6 2.5 4 50
Cable Size, mm² 8 2.5 6 59
Figure 5. Overall cost of DC array cable for 3x8 array configuration at RM 10 4 6 67
1.0411/kWh.
12 4 6 74
E. Example of Real Case Application a result, when designing the solar cable, both losses and
An example of a 6kW real case residential rooftop PV voltage drop limit will need to be considered simultaneously.
system is considered here to exemplify the effectiveness of the
ACKNOWLEDGEMENT
proposed model. The system consists of 20 polycrystalline
modules of 250 Wp each with Imp = 7.96 A and Vmp=31.41V. The authors would like to thank Mr. Tan Pi Hua from Sharp-
The inverter rating is 5kW with two separate MPPTs. Given Roxy Malaysia for his valuable suggestions. The funding
the number of solar modules, the inverter characteristic and the support provided by The Ministry of Malaysia under research
rooftop directions, two strings (Np = 2) with 12 modules each grant FRGS/2012/FKE/TK02/02/1/F00121 is also gratefully
(Ns=12) is considered as the optimal configuration. The acknowledged.
distance (L) from the rooftop solar module to inverter is
REFERENCES
approximately 10 meter. Assuming a voltage drop design limit
of 2.5%, the minimum required DC cable size (A) can be [1] P. Denholm, R. Margolis, T. Mai, G. Brinkman, E. Drury, M. Hand,
M. Mowers, "Bright Future: Solar Power as a Major Contributor to
calculated as follow which give 0.36 mm2. Table I shows that
the U.S. Grid," IEEE Power and Energy Magazine, vol.11, no.2,
the minimum commercially available solar cable size is 2.5 pp.22-32, 2013.
mm2, also as the minimum size required by the MS1837 [18]. [2] K. Ogimoto, I. Kaizuka, Y. Ueda, T. Oozeki, "A Good FiT: Japan's
Therefore 2.5 mm2 shall be selected as the designed cable size. Solar Power Program and Prospects for the New Power System,"
It also satisfies the thermal limit. IEEE Power and Energy Magazine, vol.11, no.2, pp.65-74, 2013.
[3] Malaysia Prime Minister, 15th Conference of Parties, 2009.
[4] Tenth Malaysia Plan (10th MP), www.epu.gov.my.
2 × LDC _ cable × I DC × ρ copper [5] Renewable Energy Act 2011, seda.gov.my
ADC = (9)
%Vdrop × Vstring [6] Handbook on the Malaysian Feed-in Tariff for the Promotion of
Renewable Energy, Ministry of Energy, Green Technology and
Water Malaysia, 2011.
Next, the optimal model (7) is used to design the optimal [7] F. Muhammad-Sukki, S.H. Abu-Bakar, A.B. Munir, S.H.M. Yasin,
cable for the case described above. The calculated optimal R. Ramirez-Iniguez, S.G. McMeekin, B.G. Stewart, R.A. Rahim,
current is 76.5 A for FiT rate electricity price of RM 1.0411/ Progress of feed-in tariff in Malaysia: A year after, Energy Policy,
vol. 67, pp. 618-625, 2014.
kWh. This means 10 mm2 cable should be selected as the
[8] SEDA Malaysia Grid-Connected Photovoltaic Systems Design
optimal designed cable. The result is consistent with the result Course, 2014.
as discussed in Section III.D. This also confirms the proposed [9] A. Richter, M. Hermle, S.W. Glunz, "Reassessment of the Limiting
optimal model is able to satisfy both the voltage drop and Efficiency for Crystalline Silicon Solar Cells," IEEE Journal of
thermal limits. Photovoltaics, vol.3, no.4, pp.1184-1191, 2013.
[10] K.L. Lian, J.H. Jhang, IS. Tian, "A Maximum Power Point Tracking
IV. CONCLUSION Method Based on Perturb-and-Observe Combined With Particle
Swarm Optimization," IEEE Journal of Photovoltaics, vol.4, no.2,
This paper presents an optimization approach to determine pp.626-633, 2014.
the optimal rating of DC cable in a PV system taking into [11] S. Saridakis, E. Koutroulis, F. Blaabjerg, "Optimal Design of
account the total cost of cable and losses across the lifespan of Modern Transformerless PV Inverter Topologies," IEEE
the PV system. The aim is to determine the optimal rating of Transactions on Energy Conversion, vol.28, no.2, pp.394-404,
the solar cable, (and the size) for PV system applications. 2013.
[12] K.-N.D. Malamaki, C.S. Demoulias, "Minimization of Electrical
Thirty days of five minutes resolution real PV generation data
Losses in Two-Axis Tracking PV Systems," IEEE Transactions on
in Malaysia were considered in this study. The results of the Power Delivery, vol.28, no.4, pp.2445-2455, 2013
proposed optimal model are validated against the heuristic [13] S. Curcic, G. Strbac and X.-P. Zhang, “Effect of losses in design of
approach for different electricity price rates. In addition, peak- distribution circuits”, IEE Proc.-Gener. Transm. Distrib., Vol. 148,
driven design is also considered and compared with the optimal 2001, pp. 343-349.
design. The results suggest the prominent role of losses in [14] P. Mancarella, C.K. Gan, and G. Strbac, “Optimal design of low
voltage distribution networks for CO2 emission minimisation. Part I:
designing the solar cable with optimal utilization of below 50%
Model formulation and circuit continuous optimisation,” IET Gener.
for PV array of up to 12 kW when FiT rate is considered. This Transm. Distrib., vol. 5, 2011, pp. 38-46.
implies that the PV installer should consider to oversize the [15] P. Mancarella, C.K. Gan, and G. Strbac, “Optimal design of low
designed cable considerably in order to minimize the losses voltage distribution networks for CO2 emission minimisation. Part
cost-effectively in the long run. Finally, a real case example II: Discrete optimisation of radial networks and comparison with
was considered to demonstrate the application of the proposed alternative design strategies,” IET Gener. Transm. Distrib., vol. 5,
2011, pp. 47-56.
model. The results suggest that cable designed from the
[16] "FiT Rates for Solar PV". Source: www.seda.gov.my, Jan.1, 2014
proposed optimal model is able to satisfy both the voltage drop [June. 14, 2014].
and thermal limits. However, it is also important to highlight [17] Suruhanjaya Tenaga (Energy Commission): Peninsular Malaysia
that for large scale solar PV farm application, the distance from Electricity Supply Industry Outlook 2013, 1st ed. Putrajaya,
the PV array junction box to the inverter room may become Malaysia 2013.
considerable. Hence, design may be become voltage-driven. As [18] Malaysia Standard (MS) 1837:2010, “Installation of Grid-
Connected Photovoltaic (PV) System (First revision)”, Department
of Standards Malaysia, 2010.