Component and material needs

The Nmod number of PV modules are calculated from the Ninv number of inverters, the Np number of strings per inverter and the Ns number of modules in a string:

𝑁_𝑚𝑜𝑑 = 𝑁_𝑖𝑛𝑣𝑁_𝑝𝑁_𝑠 (3.137)

The total installed DC and AC power of the PV plant is calculated as follows:

𝑃_{𝑖𝑛𝑠𝑡,𝐷𝐶} = 𝑁_𝑚𝑜𝑑𝑃_𝑆𝑇𝐶 (3.138)

𝑃_{𝑖𝑛𝑠𝑡,𝐴𝐶} = 𝑁_𝑖𝑛𝑣𝑃_{𝐴𝐶,𝑚𝑎𝑥} (3.139)

where PSTC is the power of one module at STC, and PAC,max is the maximum AC power of one inverter. If the installed capacity of the plant is known, these equations can also be used to calculate Nmod and Ninv.

The Al,mod land area occupied by the PV modules on the mounting structure lines, including the inter-row spacing, is calculated by:

𝐴_{𝑙,𝑚𝑜𝑑} = 𝑑𝑁_𝑚𝑜𝑑𝐴_𝑚𝑜𝑑 (3.140)

where d is the relative row spacing, and Amod is the surface area of one module. The total Aland

land area is estimated by multiplying Al,mod by an aland land extension factor, accounting for the extra land required by the inverters, transformers, roads, and ditches, and by adding an Al,0

constant term covering the land occupied by the main control building:

𝐴_{𝑙𝑎𝑛𝑑} = 𝐴_𝑙,0+ 𝑎_{𝑙𝑎𝑛𝑑}𝐴_{𝑙,𝑚𝑜𝑑} (3.141) The material need for the mounting structure is considered according to the geometry visualized in Fig. 3-8. Many different structures exist in practice with different geometries;

therefore, the presented model is only one general example, which gives a realistic estimation of the effect of the tilt angle and structure size on the amount of raw material in the lack of more specific data. The Lst total length of the mounting structure lines is calculated as:

𝐿_𝑠𝑡 =𝑁_𝑚𝑜𝑑

𝑁_𝑚𝑝𝑙 𝐿_𝑚𝑜𝑑 (3.142)

where Nmpl is the number of modules along the width of a structure line, and Lmod is the length of a module.

Fig. 3-8 Schematic of the considered support structure geometry

The structure can be decomposed into repeating segments, each consisting of one tilted spar with a length of W, one vertical spar for every Wstand width of the structure, and horizontal spars on the two sides of the structure and between each module rows. Considering a pile foundation with H0 extra length for each vertical spar measured from the lowest part of the modules, the Lsp,v total length of vertical spars is:

𝐿_{𝑠𝑝,𝑣} = ceil ( 𝑊

𝑊_{𝑠𝑡𝑎𝑛𝑑}) (𝐻₀+𝑊 sin 𝛽

2 ) (3.143)

The mst total mass of the mounting structure is calculated as:

𝑚_𝑠𝑡 = 𝜌_{𝑠𝑡𝑒𝑒𝑙}𝐿_𝑠𝑡[𝐴_{𝑠𝑝,𝑣}𝐿_{𝑠𝑝,𝑣}+ 𝑊

𝐿_𝑠𝑒𝑔 + 𝐴_{𝑠𝑝𝑎𝑟,ℎ}(𝑁_𝑚𝑝𝑙 + 1)] (3.144)

seg

H₀

Vertical spars Tilte r

W

L

where ρsteel is the density of steel, Lseg is the length of one segment, and Asp,v and Asp,h are the cross-section of the vertical and tilted, and the horizontal spars, respectively (the horizontal spars are typically thinner than the vertical and tilted ones).

The length of the DC and AC cables depend on the type of inverters used in the PV plant.

The string inverters are typically placed close to the modules, which results in shorter DC but longer AC cables. The central inverters are closer to the transformers, which leads to longer DC but shorter AC cables. The assumptions presented below apply for string inverters, as this is the most commonly used inverter type in Hungary. In this case, the strings connecting to the same inverter are typically placed in the same mounting structure line to avoid underground cable ducts. In our detailed shading analysis study presented in [174], we concluded that the modules at the same vertical position should be connected to the same string to minimize the shading losses. This string arrangement is visualized in Fig. 3-9.

Fig. 3-9 String layout for DC cable length calculation

The adjacent modules are connected by their own cables (blue cables in Fig. 3-9); therefore, the DC cables should only cover the distance between the inverters and the first and last module of each string (red cables in Fig. 3-9). The Lc,DC average length of the DC string cables are calculated as:

𝐿_{𝑐,𝐷𝐶} = 𝐿_{𝑐0,𝐷𝐶} +𝑁_𝑠𝐿_𝑚𝑜𝑑

𝑁_𝑝 ∑ [2 ceil ( 𝑖

2𝑁_𝑚𝑝𝑙) − 1]

𝑁_𝑝

𝑖=0 (3.145)

where Lc0,DC is the basic length of the cables, accounting for vertical height differences and margins.

The Ac,DC cross-section of the cable is calculated using its average length and resistance [46]:

𝐴_{𝑐,𝐷𝐶} =𝑟_𝐶𝑢𝐿_{𝑐,𝐷𝐶}

𝑅_{𝑐,𝐷𝐶} (3.146)

where rCu is the resistivity of copper, and the average Rc,DC resistance can be calculated from the desired nominal voltage drop by (3.131).

The low-voltage (LV) AC cables connect the inverters to the transformer. Their length is estimated using two assumptions: the cables run only parallel or perpendicular to the mounting structure lines, and the inverters are placed in a square around the transformer according to Fig.

3-10 [54]. The Lc,AC average length of a low-voltage AC cable is calculated as:

𝐿_{𝑐,𝐴𝐶} = 𝐿_{𝑐0,𝐴𝐶}+1

2√𝐴_{𝑙,𝑚𝑜𝑑} 𝑃_1𝑡𝑟

𝑃_{𝑛𝑜𝑚,𝐴𝐶} (3.147)

where P1tr is the nominal power of one LV/MV transformer and Pinst,AC is the total installed AC power.

39

Fig. 3-10 Inverter layout for AC cable length calculation

The Ac,AC cross-section of one conductor of the three-phase AC cable is calculated from its length and resistance:

𝐴_{𝑐,𝐴𝐶} =𝑟_𝐶𝑢𝐿_{𝑐,𝐴𝐶}

𝑅_{𝑐,𝐴𝐶} (3.148)

where the average Rc,AC resistance, similarly to the DC cables, can be calculated from the nominal AC voltage drop by (3.132). The length of the medium-voltage (MV) cables is not modeled in detail as it is typically significantly lower compared to the low-voltage cables, and it depends on many local factors that are hard to generalize.

The mCu total mass of copper in the DC and the four-wire low-voltage AC cables are calculated by:

𝑚_𝐶𝑢 = 𝜌_𝐶𝑢(𝑁_𝑝𝐿_{𝑐,𝐷𝐶}𝐴_{𝑐,𝐷𝐶}+ 4𝐿_{𝑐,𝐷𝐶}𝐴_{𝑐,𝐷𝐶})𝑁_𝑖𝑛𝑣 (3.149) where ρCu is the density of copper.

The transformers and medium-voltage switchgears are simply characterized by the Pinst,AC

nominal AC power, and not modeled in detail as they depend more on local factors than the design parameters of the plant.