Solar Potential in Saudi Arabia for Flat-Plate Surfaces of Varying Tilt Tracking the Sun

Abstract

The objective of the present work is to investigate the performance of flat-plate solar panels in Saudi Arabia that continuously follow the daily motion of the sun. To that end, the annual energy sums are estimated for such surfaces at 82 locations covering all Saudi Arabia. All calculations use a surface albedo of 0.2 and another one with a near-real value. The variation of the solar energy sums on annual, seasonal, and monthly basis is given for near-real ground albedos; the analysis provides regression equations for the energy sums as function of time. A map of the annual inclined solar energy for Saudi Arabia is derived and presented. The annual energy sums are found to vary between 2159 and 4078 kWhm⁻²year⁻¹. Finally, a correction factor, introduced in a recent publication, is used; it is confirmed that the linear relationship between the correction factor and the ground-albedo ratio is general enough to be graphically representable as a nomogram. A discussion regarding the differences among solar systems on horizontal, fixed-tilt, 1-axis, and 2-axis systems is presented.

1. Introduction

Installations with tilted solar panels for exploiting the (renewable) energy of the sun have long been available in the market as commercial products. Solar flat-plate panels are nowadays widely used for converting solar energy into electricity (PV installations). These systems consist of solar modules receiving solar radiation by flat-plate surface(s) that (i) operate at a fixed-tilt angle with southward orientation in the northern hemisphere or northward orientation in the southern hemisphere, (ii) continuously track the sun at a fixed-tilt angle rotated on a vertical axis, and (iii) continuously track the sun at a varying tilt angle fixed on a system with two axes (one vertical and one horizontal); this makes the receiving surface to always be normal to the solar rays. Installations of mode (i) are known as fixed-tilt systems and are widely used because of lower cost for the supporting frame. Installations of mode (ii), also known as 1- or single-axis systems, provide higher solar energy on the inclined surface, but have slightly higher cost because of the need to maintain the moving parts. Installations of mode (iii) are considered the most effective and are known as 2-, double-, or dual-axis systems. They provide higher efficiency, but, on the other hand, they are associated with higher maintenance costs because of more moving parts. The first type of solar system is also called stationary or static, while the other two are dynamic, because of their sun-tracking ability. Farahat et al. [1] examined the mode (i) static systems for the performance of fixed-tilt flat-plate solar systems with southward orientation in Saudi Arabia, while Farahat et al. [2] investigated the mode (ii) dynamic systems receiving solar energy on fixed-tilt flat-plate solar panels that rotate on a vertical single-axis structure and track the sun continuously. This work is a continuation of the previous two as it investigates the mode (iii) dynamic systems for the solar energy received by flat-plate solar systems with continuously variable tilt angle of the inclined surface and mounted on 2-axis sun trackers across the country.

Static solar systems are widely used nowadays in solar energy production throughout the world because of their simple construction and low maintenance cost; therefore, they have received major attention from researchers (i.e., for estimating the solar potential or solar availability) at a certain location or region, e.g., [3,4,5]. A second preference has been given to dynamic mode (ii) solar systems because of their relatively higher performance in terms of the solar energy received, e.g., [6]. The dynamic mode (iii) solar systems have started being used in the last 20 years or so because of their higher performance in comparison to that of the other two types, e.g., [7,8]. Much effort has been invested in improving both the moving and electronic parts for the sun-tracking sensors [9,10]. Nevertheless, despite the technology development, the performance of such systems must be evaluated against solar radiation measurements at first hand. However, the scarcity of solar radiation measuring stations around the world has triggered studies to use solar radiation modelling, e.g., [11,12,13], in order to derive the optimum tilt angle and orientation for obtaining maximum solar energy on flat-plate solar panels. Other methods use a combination of ground-based solar data and modelling, e.g., [14], or utilise solar data from international data bases, e.g., [15,16]. Recently, a new method was presented by [17] for Greece and was applied in two recent studies for Saudi Arabia [1,2]. The proposed method [17] is able to find the maximum solar energy received by flat-plate solar systems with southward (northward) orientation in the northern (southern) hemisphere. The idea behind this methodology is applied in the present study for solar modules continuously tracking the sun.

Some studies similar to the present work have already been conducted for Saudi Arabia. El-Sebaii et al. [4] computed the global, direct, and diffuse solar radiation components on horizontal and tilted surfaces at Jeddah. Kaddoura et al. [15] estimated the optimal tilt angle for maximum energy reception by PV installations at 7 sites in the country. They suggested that the PV panels should be adjusted six times in a year for maximum performance, a conclusion that triggers extra installation and maintenance costs because of the moving parts involved. Zell et al. [18] performed solar radiation measurements at 30 stations in Saudi Arabia in the period October 2013–September 2014 (1 year) to assess the solar potential at these sites. The World Bank [19] has derived a Global Solar Atlas, which includes Saudi Arabia. This solar map provides the distribution of the three solar radiation components over the country and is based on calculations during the periods 1994, 1999, and 2007–2018. Finally, Almasoud et al. [20] has provided a study about the economics of solar energy in Saudi Arabia.

From the above, it is clear that no attempt has been made thus far to construct a solar map for Saudi Arabia to show the solar potential on inclined flat-plate surfaces that continuously track the sun. This gap is bridged in the present study and includes two innovations. (i) For the first time, solar maps for Saudi Arabia showing maximum energy on inclined flat-plate surfaces tracking the sun are derived. (ii) The notion of the (ground-albedo) correction factor introduced in [1,2] is also used.

The structure of the paper is as follows. Section 2 describes the data collection and data analysis, Section 3 deploys the results of the study, Section 4 provides a comparison among the various fixed and moving solar systems, Section 5 gives the guidelines for using the results deployed, and Section 6 presents the conclusions and main achievements of the work. Acknowledgements and references follow.

2. Materials and Methods

2.1. Data Collection

Hourly values of H_b,0 (direct horizontal solar irradiance in Wm⁻²) and H_d,0 (diffuse horizontal solar irradiance in Wm⁻²) were downloaded from the PV—Geographical Information System (PV-GIS) tool [21] using the latest Surface Solar Radiation Data Set—Heliostat (SARAH) 2005–2016 database (12 years) [22,23]. This platform provides solar radiation data through a user-friendly tool for any location in Europe, Africa, the Middle East including Saudi Arabia, Central and Southeast Asia, and most parts of the Americas. Nevertheless, the platform provides solar maps for Europe, Africa, Turkey, and Central Asia only. The methodologies used for estimation of solar radiation from satellites by the PV-GIS tool are described in various works [24,25,26].

For the purpose of the present work, a set of 82 sites was arbitrarily chosen in order to cover the whole territory of Saudi Arabia.

Table 1. The 82 sites arbitrarily selected over Saudi Arabia to cover the whole area of the country; φ is the geographical latitude, and λ the geographical longitude in the WGS84 geodetic system. The “unnamed” sites refer to those away from known locations. This table is a reproduction of Table 1 in [1,2]. N = North, E = East.

#	Site	φ (Degrees N)	λ (Degrees E)
1	Dammam	26.42	50.09
2	Al Jubail	26.96	49.57
3	Ras Tanura	26.77	50.00
4	Abqaiq	25.92	49.67
5	Al Hofuf	25.38	49.59
6	Arar	30.96	41.06
7	Sakaka	29.88	40.10
8	Tabuk	28.38	36.57
9	Al Jawf	29.89	39.32
10	Riyadh	24.71	46.68
11	Al Qassim	26.21	43.48
12	Hafar Al Batin	28.38	45.96
13	Buraydah	26.36	43.98
14	Al Majma’ah	25.88	45.37
15	Hail	27.51	41.72
16	Jeddah	21.49	39.19
17	Jazan	16.89	42.57
18	Mecca	21.39	39.86
19	Medina	24.52	39.57
20	Taif	21.28	40.42
21	Yanbu	24.02	38.19
22	King Abdullah Economic City	22.45	39.13
23	Najran	17.57	44.23
24	Abha	18.25	42.51
25	Bisha	19.98	42.59
26	Al Sahmah	20.10	54.94
27	Thabhloten	19.83	53.90
28	Ardah	21.22	55.24
29	Shaybah	22.52	54.00
30	Al Kharkhir	18.87	51.13
31	Umm Al Melh	19.11	50.11
32	Ash Shalfa	21.87	49.71
33	Oroug Bani Maradh Wildlife	19.41	45.88
34	Wadi ad Dawasir	20.49	44.86
35	Al Badie Al Shamali	21.99	46.58
36	Howtat Bani Tamim	23.52	46.84
37	Al Duwadimi	24.50	44.39
38	Shaqra	25.23	45.24
39	Afif	24.02	42.95
40	New Muwayh	22.43	41.74
41	Mahd Al Thahab	23.49	40.85
42	Ar Rass	25.84	43.54
43	Uglat Asugour	25.85	42.15
44	Al Henakiyah	24.93	40.54
45	Ar Rawdah	26.81	41.68
46	Asbtar	26.96	40.28
47	Tayma	27.62	38.48
48	Al Khanafah Wildlife Sanctuary	28.81	38.92
49	Madain Saleh	26.92	38.04
50	Altubaiq Natural Reserve	29.51	37.23
51	Hazem Aljalamid	31.28	40.07
52	Turaif	31.68	38.69
53	Al Qurayyat	31.34	37.37
54	Harrat al Harrah Conservation	30.61	39.48
55	Al Uwayqilah	30.33	42.25
56	Rafha	29.63	43.49
57	Khafji	28.41	48.50
58	Unnamed 1	21.92	51.99
59	Unnamed 2	21.03	51.16
60	Unnamed 3	22.33	52.53
61	Unnamed 4	23.42	50.73
62	Unnamed 5	21.28	48.03
63	Unnamed 6	31.70	39.26
64	Unnamed 7	32.02	39.65
65	Unnmaed 8	31.02	42.00
66	Unnamed 9	30.63	41.31
67	Unnamed 10	29.78	42.68
68	Unnamed 11	28.68	47.49
69	Unnamed 12	28.41	47.97
70	Unnamed 13	28.05	47.53
71	Unnamed 14	27.97	47.88
72	Unnamed 15	27.15	48.98
73	Unnamed 16	27.21	48.56
74	Unnamed 19	27.15	48.02
75	Unnamed 18	27.66	48.52
76	Unnamed 19	24.74	48.95
77	Unnamed 20	28.34	35.17
78	Unnamed 21	26.27	36.67
79	Unnamed 22	21.89	43.06
80	Unnamed 23	18.76	47.54
81	Unnamed 24	21.38	53.28
82	Unnamed 25	19.24	52.79

provides the names and geographical coordinates of the sites; Figure 1 shows their location in the map of the country. The selection of the sites was based on the “inhabited” criterion (i.e., urban areas, 57 out of 82), while the additional 25 sites out of the 82 are uninhabited and have no name (marked as “unnamed” in Table 1). For this reason, the distribution of the 82 sites is not uniform within Saudi Arabia. It must be mentioned that the downloaded hourly solar horizontal radiation values refer to those for an unobstructed horizon.

2.2. Data Processing and Analysis

To process the data used in this work, we followed the following 5 steps:

Step 1. The downloaded hourly data from the PV-GIS website were transferred from universal time coordinate (UTC) into Saudi Arabian local standard time (LST = UTC + 3 h). It must be mentioned that the PV-GIS solar radiation values were provided at different UTC times for the 82 sites considered, e.g., at hh:48 or hh:09, where hh stands for any hour between 00 and 23.

Step 2. The hourly global horizontal solar radiation, H_g, values were estimated at all sites as the sum H_g = H_b + H_d.

Step 3. The routine SUNAE introduced by Walraven [27] was used to derive the solar azimuths and elevations. The original SUNAE algorithm has, however, been renamed to XRONOS (meaning time in Greek, X is pronounced CH) because of added modifications due to the right ascension and atmospheric refraction effects [28,29]. XRONOS ran for the geographical coordinates of the 82 sites in the period 2005–2016 to derive the solar altitudes, γ, at all LST times calculated in step 1.

Step 4. All solar radiation and solar geometry values were assigned to the nearest LST hour (i.e., values at hh:48 LST or hh:09 LST were assigned to hh:00 LST). This was done in order to have all values in the data base as integer hours.

Step 5. Only those hourly solar radiation values greater than 0 Wm⁻² and corresponding to γ ≥ 5° (to avoid the cosine effect) were retained for further analysis. Moreover, the criterion of H_d,0 ≤ H_g,0 was required to be met at the hourly level.

For estimating global solar irradiance on an inclined plane that continuously tracks the sun, H_g,t (in Wm⁻²), the isotropic model of Liu-Jordan [30] was adopted (the subscript t stands for “tracking”). The isotropic model was used to estimate the ground-reflected radiation from the surrounding surface, H_r,t (in Wm⁻²), received on the inclined plane. This model was adopted in the present study because of its simplicity and effectiveness in comparison to other anisotropic models in providing the tilted total solar radiation in many parts of the world; the good performance of the isotropic model has been verified by various studies (e.g., [31,32,33,34,35]).

Figure 2 provides a schematic for a tilted surface receiving solar radiation. Deliberately, the tilted surface is not aligned along the direction of the sun in order to show the various angles formed, i.e., the tilt angle of the surface, β; the solar altitude, γ; the solar zenithal angle, θ_z; the incidence angle, θ (the angle between the normal to the surface and the direction toward the sun); the solar azimuth, ψ; and the azimuth of the tilted plane, ψ’. In this graph, the sun lies in the N-S plane that is normal to the local horizon (therefore, ψ = 180°). In the case of a surface tracking of the sun, it is easy to conclude that θ = 0° (the solar rays are normal to the tilted surface), β = 90° − γ, and ψ = ψ’.

For a sun-tracking surface, the received total solar radiation is given by the following well-known expression:

H_g,t = H_b,t + H_d,t + H_r,t,

(1)

where the subscript t implies “tracking” the sun by the receiving surface. According to Liu-Jordan (L-J) [30]:

H_d,t = H_d,0·R_di,

(2)

H_r,t = H_g,0·R_r·ρ_g0, (or H_g,0·R_r·ρ_g)

(3)

R_di = (1 + cosβ)/2 = (1 + sinγ)/2,

(4)

R_r = (1 − cosβ)/2 = (1 − sinγ)/2,

(5)

H_b,t = H_b,0 · cosθ/sinγ = H_b,0 · cos0/sinβ = H_b,0/cosγ

(6)

where θ = 0° and β = 90° − γ because the inclined surface is always normal to the solar rays (see Figure 2). R_di and R_r are the isotropic sky-configuration and ground-inclined plane-configuration factors, respectively. In the L-J model, the ground albedo usually takes the value of ρ_g0 = 0.2 (Equation (3)). This value was used in the present study. Apart from using ρ_g0 in the calculations, values of ρ_g close to reality were also adopted in this study as in [1,2]. To retrieve such values for the 82 sites, we made use of the Giovanni portal [36]; pixels of 0.5° × 0.625° spatial resolution were centered over each of the 82 sites for which monthly mean values of the ground albedo were downloaded in the period 2005–2016. Annual mean ρ_g values were then computed and were used to re-calculate H_g,t.

For every site, hourly values of H_g,t were estimated twice from Equation (1); the first time by using computations with ρ_g0 = 0.2 in Equation (3), being considered as reference value in solar modelling, and a second time by using calculations with ρ_g equal to the ground-albedo value retrieved from the Giovanni platform. From the hourly H_g,t values, annual, seasonal, and monthly solar energy sums (in kWhm⁻²) under all-sky conditions were estimated for all sites and both ground-albedo values.

3. Results

3.1. Annual Energy Sums

Annual solar energy sums were derived from the appropriate database of each site by utilising both ground albedos, ρ_g0 and ρ_g, in Equation (3). The annual solar energy sum (or yield) at each location was estimated by aggregating (summing up) all hourly solar radiation values within the period of 2005–2016.

Table 2. Maximum annual solar energy sums for the 82 sites in Saudi Arabia for flat-plate solar collectors that are: horizontal (H_g,0), mode (i) static (H_g,β,S/ρg), mode (ii) dynamic (H_g,β,t/ρg), and mode (iii) dynamic (H_g,t/ρg) derived by using a ground albedo of ρ_g, under all-sky conditions in the period 2005–2016. The H_g values are rounded integers in kWhm⁻²year⁻¹.

Site #	Hg,0	Hg,β,S/ρg	Hg,β,t/ρg	Hg,t/ρg
1	2237	2359	2846	2938
2	2239	2374	2873	2932
3	2206	2320	2782	2893
4	2275	2409	2925	2972
5	2286	2409	2925	2985
6	2214	2409	2993	3033
7	2279	2470	3081	3136
8	2359	2544	3173	3283
9	2256	2443	3022	3076
10	2318	2452	2991	3058
11	2271	2415	2955	3034
12	2220	2298	2804	2857
13	2260	2406	2944	3015
14	2284	2423	2953	3016
15	2300	2462	3035	3113
16	2344	2436	2917	3029
17	2301	2192	2767	2903
18	2339	2432	2909	3020
19	2374	3503	3021	3161
20	2316	2420	2931	3053
21	2392	2517	3053	3186
22	2349	2453	2940	3066
23	2480	2568	3128	3250
24	2267	2342	2803	2920
25	2446	2549	3086	3212
26	2422	2543	3109	3169
27	2407	2528	3103	3171
28	2699	2980	4078	4245
29	2349	2478	3043	3101
30	2434	2603	3314	3471
31	2460	2567	3132	3200
32	2400	2522	3069	3126
33	2455	2559	3131	3193
34	2405	2512	3062	3146
35	2381	2501	3050	3128
36	2363	2491	3046	3110
37	2346	2480	3028	3101
38	2277	2414	2956	3019
39	2365	2492	3025	3127
40	2418	2539	3091	3197
41	2383	2503	3037	3173
42	2279	2423	2967	3036
43	2335	2479	3033	3131
44	2382	2519	3076	3211
45	2286	2443	3008	3111
46	2348	2513	3111	3202
47	2369	2566	3228	3287
48	2290	2472	3058	3123
49	2378	2556	3181	3248
50	2261	2450	3056	3153
51	2188	2393	3004	3042
52	2179	2381	3692	3972
53	1560	1763	2365	2445
54	2228	2411	2980	3048
55	2219	2401	2964	2998
56	1520	1724	2324	2387
57	2163	2275	2696	2821
58	2401	2530	3100	3144
59	2418	2538	3097	3156
60	2391	2523	3091	3137
61	2356	2487	3042	3081
62	2413	2527	3069	3142
63	2138	2350	2892	3033
64	2157	2308	2926	2988
65	2130	2354	2913	2966
66	2170	2396	2922	2961
67	2221	2396	2978	3021
68	1529	1721	2553	2737
69	2168	2333	2827	2864
70	2201	2321	2833	2865
71	2187	2351	2821	2868
72	2212	2374	2859	2881
73	2233	2421	2863	2921
74	2229	2397	3067	3149
75	2235	2397	2945	3005
76	1464	1613	2159	2226
77	2316	2521	3002	3030
78	2353	2517	3125	3279
79	2377	2533	3086	3248
80	2416	2578	3078	3170
81	2474	2511	3170	3216
82	2383	2537	3051	3141

shows these annual H_g,t sums. It should be noted here that the reference value of ρ_g0 is used for grassland areas (and widely used in the L-J model), while surfaces with different vegetation or no vegetation (such as tundra, desert, and snow-covered area) may have different reflectance far from 0.2 [25]. Figure 3 shows the variation of the annual solar energy yields on horizontal as well as on inclined flat-plate surfaces for all three solar system types (static and dynamic) across all 82 sites. The difference in the mean values between the mode (iii) and (ii) systems is only 4.2%, and between the mode (i) and horizontal cases only 6.4%. At first glance, these small differences imply a preference to use mode (ii) solar systems with constant tracking-the-sun ability instead of the more sophisticated mode (iii) ones, or to use horizontal surfaces instead of mode (i) inclined ones with constant tilt towards the South. As shown in Figure 4, the above difference of 4.2% is equivalent to 11,883 kWhm⁻²year⁻¹, and the second difference of 6.4% to 10,353 kWhm⁻²year⁻¹. Indeed, the first difference is equal to 3.81 times the average annual solar energy sum for a mode (iii) solar system, i.e., 3.81 × 3120 kWhm⁻²year⁻¹ = 11,887 kWhm⁻²year⁻¹, or 3.97 times the average annual solar energy sum for a mode (ii) solar system, i.e., 3.97 × 2994 kWhm⁻²year⁻¹ = 11,886 kWhm⁻²year⁻¹. The second difference is equal to 4.27 times the average annual energy sum for a mode (i) solar system, i.e., 4.27 × 2422 kWhm⁻²year⁻¹ = 10,342 kWhm⁻²year⁻¹, or 4.55 times the average annual solar energy sum for a horizontal surface, i.e., 4.55 × 2277 kWhm⁻²year⁻¹ = 10,360 kWhm⁻²year⁻¹. Therefore, these solar energy differences cannot be ignored as they correspond to sites producing 3.81 (3.97) more energy than mode (iii) ((ii)) solar systems or corresponding to sites deriving 4.27 (4.55) more energy than mode (i) (horizontal) solar systems. On the other hand, it is clear about what type of solar system to use if one has to choose between the first group with modes (ii) and (iii) systems and between the second group with horizontal and mode (i) systems, as the gap between the two groups was found to be rather high (i.e., 707 kWhm⁻²year⁻¹ = (3120 kWhm⁻²year⁻¹ - 2994 kWhm⁻²year⁻¹)/2 − (2422 kWhm⁻²year⁻¹ − 2277 kWhm⁻²year⁻¹)/2, see Figure 3). Nevertheless, the choice of the solar system type depends upon the cost-benefit criterion. This criterion is discussed in Section 4.

As a summary, Table 2 reports the total annual solar energy sum per site for all cases of possible installation modes of solar collectors in Saudi Arabia.

Contrary to the recent works by Farahat et al. [1,2], where three solar energy zones (SEZs) with three different tilt angles for the solar installations were defined and adopted, the present work is independent from these SEZs because the tilt angles of the inclined surfaces are not constant but continuously variable. As far as other similar works to the present one are concerned, the study by Zell et al. [18] is worthy of mention. That study divided the country into five geographical regions (central, eastern, southern, western, and western inland) for the purpose of analysing the solar radiation data from [19]. However, the partitioning by Zell et al. did not follow any solar radiation criteria, and, therefore, it is of limited practical value.

Another study by Kaddoura et al. [15] estimated 12 optimal angles β for the 12 months of the year for Tabuk (#8 in Table 1), Al Jawf (#9), Riyadh (#10), Jeddah (#16), and Abha (#24). These angles were derived from modelling and, therefore, have a purely theoretical value, since it is not practical at all to change the tilt angle of the solar panel frame every month. From the international literature, no other work has appeared in relation to modes (ii) or (iii) solar systems for Saudi Arabia.

3.2. Monthly Energy Sums

The intra-annual variation of H_g,t/ρg for all sites is shown in Figure 5. It is seen that the variations of almost all sites are very close to each other, creating a bundle, a zone. There are, however, two sites that present exceptional monthly yields and, therefore, lay above the bundle (i.e., sites #28, and 52). Site #28 lies in the very southeastern part of Saudi Arabia and receives high solar insolation throughout the year. On the contrary, site #52 lies in the very northern part of the country, and lower solar insolation would be expected; this unevenness could probably be attributed to local climatology with very clear skies occurring most time of the year or miscalculation of the ground albedo at the Giovanni platform or inaccurate estimation of solar radiation by the PV-GIS tool or a combination of them. The exceptional performance of solar energy at these two sites is also depicted in Figure 3.

From Figure 5, one can detect the energy yield per site. Nevertheless, this task is not very informative for solar energy engineers and entrepreneurs, as they would like to have a “compass” that would show them an (even approximate) estimate of the monthly solar energy yield. For this reason, the average monthly energy sums for all sites were estimated, and their intra-annual variation for all Saudi Arabia is shown in Figure 6. It might have been anticipated that all curves (mean and mean ± 1σ) in Figure 6 would be smoother than those actually derived because of the continuous normality of the solar rays on the inclined flat-plate surface. Nevertheless, the differentiation in the ground-albedo values across the whole territory of Saudi Arabia and the variation in local climatology provided the shapes seen in Figure 6. The mean + 1σ curve shows a peak in August and a secondary one in October. Since this statistic is related to the dispersion of the 82 H_g,t values within some limits (i.e., the band of mean ± 1σ), the upper limit (mean + 1σ) corresponds to the dispersion of the higher solar energy values and the lower limit (mean − 1σ) to the dispersion of the lower solar energy values. In other words, the red line in Figure 6 denotes the weighting of the higher values in the whole sample of the 82 H_g,t values, while the blue line is weighted towards the lower values in the same sample. This implies that the upper limit is dominated by the high H_g,t values in the south of the country (i.e., SEZ-A, Figure 3 in [2]), while the lower limit by the low H_g,t values that occurred in the northern part of Saudi Arabia (i.e., SEZ-C, Figure 3 in [2]). Therefore, the upper limit is influenced by a solar energy pattern with maximum in the summer (August), and the lower limit by a solar energy pattern with a main peak in the summer (June, July) and minor peaks in April and September. These observations are justified by Figure 5 in [2].

Table 3. Regression equations for the best-fit curves to the monthly (seasonal) mean H_g,t,β/ρg sums averaged over all 82 sites in the period 2005–2016, together with their R² values; s is month in the range 1–12; 1 = January,…,12 = December (season in the range 1–4; 1 = spring, 2 = summer, 3 = autumn, 4 = winter).

Time Scale	Regression Equation	R2
Months	Hg,t/ρg = 0.005$·$s6 − 0.186$·$s5 + 2.712$·$s4 − 19.668$·$s3 + 71.696$·$s2 − 100.840$·$s +264.580	0.96
Seasons	Hg,t/ρg = 37.983$·$s3 − 325.370$·$s2 + 780.750$·$s + 318.820	1

provides the expression for the monthly H_g,t values over all Saudi Arabia as function of the month number, s (s = 1,…,12); the regression equation has a very high R² equal to 0.96, implying an almost perfect fit to the data.

3.3. Seasonal Energy Sums

Minimum and maximum possible energies received by solar energy systems occur during the winter and summer months, respectively, as anticipated. Therefore, this Section is devoted to analszing the seasonal solar energy sums, i.e., during spring (March–April–May), summer (June–July–August), autumn (September–October–November), and winter (December–January–February). The seasonal energy values at each site were calculated by the summation of all hourly solar radiation values in each season.

As in the case of the intra-annual variation of the H_g,t/ρg levels, Figure 7 presents the seasonal variation of the solar energy values; each individual data point in the graph is the average seasonal energy yield for the specific site over the period 2005–2016. To find an overall expression for the received seasonal energy sum in Saudi Arabia, as done for the monthly case, we averaged the energy values for each season from all sites over the period 2005–2016 under all-sky conditions; Figure 8 presents the results. Table 3 provides the regression equation for the curve that best fits the mean seasonal values. The fit is ideal (R² = 1).

3.4. Maps of Annual Energy Sums

Figure 9 shows the solar potential over Saudi Arabia in terms of the annual H_g,t,β/ρg sums. A gradual increase in the annual solar potential in the direction NE–SW for the sun-tracking inclined flat planes is observed. Very similar patterns to that in the present study are given in the Solar Radiation Atlas for Saudi Arabia [37]. The interpretation for this gradient is attributed to two reasons. (i) Latitude: the higher the latitude, the lower the solar radiation levels received on the surface of the earth. (ii) Meteorology: more frequent precipitation is observed in the north-eastern part of the country, which is related to the precipitation occurring in southern Iraq and Iran [38].

3.5. Evaluation of the PV-GIS Tool

There have been various validation studies for the solar radiation PV-GIS satellite-derived estimates in the literature (e.g., [24,25,26]). The reported differences between the estimated values and those derived by PV-GIS were found to vary between −14% and +11%. Furthermore, Farahat et al. [1,2] demonstrated such a comparison by taking monthly mean H_g values measured at the Actinometric Station of the National Observatory of Athens (ASNOA, 37.97° N, 23.72° E, 107 m above sea level) and corresponding values from the PV-GIS platform in the period 2005–2011. Figure 10 presents this comparison, which shows an excellent agreement (R² = 0.99). Although the PV-GIS-estimated values seemed to overestimate the measured H_g ones by +10%, this figure is within the acceptable range (−14%, +11%). For this reason, the PV-GIS data were accepted for use in the present study.

3.6. The Correction Factor

Farahat et al. [1] introduced the notion of the correction factor, CF, which, for the purpose of the present work, is defined as: CF = H_g,t/ρg/H_g,t/ρg0. CF is, therefore, the ratio of the annual H_g,t sum at each site of the 82, calculated twice, once for ρ_g0 = 0.2 and a second time for ρ_g = actual value. The practicality of using CF is that it corrects the solar energy incident on an inclined surface under the influence of a ground albedo equal to 0.2 to that which is under the influence of a near-real ground-albedo value. Despite the variation of CF as function of β for all 82 sites in [1,2], the present analysis of the H_g,t values does not depend on this parameter at all because of the ever varying tilt angle of the receiving flat-plate surface during the operation of a mode (iii) system. Therefore, a different graph was prepared, i.e., a graph of CF as function of the ground-albedo ratio, ρ_r = ρ_g0/ρ_g. Figure 11 shows this dependence, which is linear: CF = 0.0203$·$ρr + 0.9797 with R² = 0.98 at the 95% confidence level; similar dependence was firstly found by Farahat et al. [1,2]. The two lines CF = 1 and ρ_r = 1 in Figure 11 cross each other at the site #24, which has a ground albedo ρ_g = ρ_g0 = 0.2, and, therefore, H_g,t/ρg = H_g,t/ρg0. The blue and red bands show the confidence and prediction intervals around the best-fit line, respectively. It is seen that many sites are within the blue zone, but most of them are accommodated in the red band. Only four sites lie outside the prediction interval. This observation means that some of the sites (i.e., their CF-ρ_r data pairs) that lie within the confidence interval are significant at the 95% level, while others that are within the prediction zone will be significant at the 95% level in the future (i.e., they will tend to be significant), and those four sites that are outside the prediction zone will be non-significant at the 95% level anyway.

Further, by defining the ratio of the annual solar energy sum differences, RΔH_g = (H_g,t/ρg − H_g,β,S/ρg)/(H_g,t/ρg − H_g,β,t/ρg), we derived two more plots. Figure 12a shows the dependence of CF on RΔH_g, and Figure 12b the dependence of ρ_r on RΔH_g. Both plots show the mean RΔH_g (black lines) and the (mean RΔH_g + 1σ, mean RΔH_g − 1σ) zone; this zone includes most of the 82 sites, a fact that is interpreted as meaning that most of the RΔH_g values are statistically significant at the 95% level in relation to those of CF vs. ρ_r (Figure 11). The other 24 sites outside the band (as #24 for which CF = ρ_r = 1) can be characterised as reflecting a loose dependence of CF or ρ_r on RΔH_g; this may occur because of the following reasons: (i) inaccurate estimation of ρ_g at the Giovanni platform, (ii) inaccurate estimation of H_g by the PV-GIS tool, or (iii) both.

4. Comparison of the Three Configuration Modes

This section is devoted to a comparison of static and dynamic solar systems in terms of cost–benefit. To achieve this goal, we searched for works published in the international literature.

A study for the USA by Drury et al. [39] showed that 1-axis tracking systems can increase power generation by 12–25% in relation to fixed-tilt ones, and 2-axis tracking systems by 30–45%. These researchers estimated the installation cost at 0.25 $W⁻¹, 0.82 $W⁻¹, and 1.23 $W⁻¹ for fixed-tilt, 1-axis, and 2-axis systems, respectively. In the same way, their operation and maintenance costs were estimated at 25 $kW⁻¹year⁻¹, 32 $kW⁻¹year⁻¹, and 37.5 $kW⁻¹year⁻¹, respectively.

Another study in Spain by Eke and Senturk [40] concluded that a double-axis solar system may result in an increase in electricity by 30.7% compared to a fixed-tilt system.

Hammad et al. [41] compared the performance and cost between fixed-tilt (static) and double-axis (dynamic) systems in Jordan. They found 31.29% more energy produced by the 2-axis system in comparison with the static one. Further, they estimated the payback period to be 27.6 and 34.9 months for the dynamic and static systems, respectively, with corresponding electricity costs of 0.08 $kWh⁻¹ and 0.10 $kWh⁻¹.

Lazaroiu et al. [42] found a 12–20% increase in the energy produced by a dual-axis solar system in comparison to a fixed-tilt one.

Michaelides et al. [43] studied the performance of solar boilers for Athens, Greece, and Nicosia, Cyprus, by considering 1-axis, seasonal-tilt, and fixed-tilt systems. They found that the solar fractions (the normalised difference between the hot water energy provided by the sun and the auxiliary one supplied by electricity) were 81.4%, 76.2%, and 74.4% for Athens, and 87.6%, 81.6%, and 79.7% for Nicosia in the case of a single-axis, a seasonal-tilt, and a fixed-tilt solar system, respectively.

As far as Saudi Arabia is concerned, the results of the present study (see Figure 3) lead to increases shown in

Table 4. Increase (in %) in the annual solar energy sums from all 82 sites in Saudi Arabia when using horizontal, mode (i) static, and modes (ii) and (iii) dynamic configurations.

Definition of Ratio	Increase (%)
Hg,t/ρg/Hg,β,t/ρg (mode (iii)/mode (ii)) ∙ 100	4.22
Hg,t/ρg/Hg,β,S/ρg (mode (iii)/mode (i)) ∙ 100	28.81
Hg,t/ρg/Hg,0 (mode (iii)/horizontal) ∙ 100	37.00
Hg,β,t/ρg/Hg,β,S/ρg (mode (ii)/mode (i)) ∙ 100	23.60
Hg,β,t/ρg/Hg,0 (mode (ii)/horizontal) ∙ 100	31.47
Hg,β,S/ρg/Hg,0 (mode (i)/horizontal)∙100	6.36

.

5. Discussion

Three innovations appeared in the present study. (i) For the first time, solar maps for Saudi Arabia of the solar energy received on inclined flat surfaces continuously tracking the sun were derived. (ii) A universal curve (nomogram) of CF in relation to ρ_r was derived for this case, as in [1,2]. (iii) Accommodation of most sites within the mean RΔH_g ± 1σ band was found in both relations CF vs. RΔH_g and ρ_r vs. RΔH_g; the last two statements remain to be confirmed at other locations in the world to constitute universality.

On the basis of the adopted methodology, we here provide some guidelines for interested solar energy scientists and/or solar energy entrepreneurs. The steps of the guidelines are the following.

• If a solar radiation station exists in the area, hourly or daily values of the solar global horizontal radiation are collected for a climatological period of 10 years at least.
• If no solar radiation exists, then data from relevant websites (e.g., BSRN, GEBA, PV-GIS, ARM) are obtained.
• In the extreme case that this option is not possible, use of a solar energy model can be made to derive the anticipated data from other available variables (e.g., from meteorological parameters as the Meteorological Radiation Model-MRM does [44]).
• Transposition of the selected data from horizontal to inclined planes that track the sun takes place by setting the tilt angle always equal to 90° − γ. The transposition is achieved by selecting the desired model (the L-J model is sufficient). It is recommended that a near-real ground-albedo value is used in these calculations; if knowledge of this value is not available for the site, use of the nomogram of Figure 11 is made to correct the solar energy values derived.
• Annual solar energy sums for the inclined planes are calculated.
• Monthly solar energy sums are estimated, and a regression line can be derived that serves as guideline for estimating the expected solar energy on flat planes.
• The last step is repeated for the seasonal solar energy sums and the derivation of best-fit curves.

The significance of the results of the present study as far as the solar industry and society of Saudi Arabia are concerned can be summarised in the following. The solar engineering society now has a map with fresh knowledge about the solar potential for mode (iii) solar systems across Saudi Arabia. This knowledge may prove useful for designing such systems. On the other hand, actions from governmental policies may have indirect benefits to the society, if these policies promote renewable energy sources in Saudi Arabia (and especially solar energy sources), because of the new knowledge gained through the present work.

6. Conclusions

The present study investigated the solar potential across Saudi Arabia on flat-plate solar panels that vary their tilt angle in order to receive solar radiation normally to their surfaces during the day. The main objective was to find the annual energy available in this configuration type under all-sky conditions. This was achieved by calculating the annual energy sum on flat-plate surfaces with varying tilt angles that track the sun across Saudi Arabia; the solar availability on a horizontal plane was also included for reference purposes. For this reason, hourly solar radiation data in the period 2005–2016 were downloaded from the PV-GIS platform for 82 sites in the country. The calculations for the energy received on the tilted surfaces were performed for a ground albedo equal to 0.2 (as a reference value) and also for a near-real ground albedo. The latter values were retrieved from the Giovanni website.

The main result of the work was that the annual solar energy received by such (dynamic) mode (iii) systems varied between 2267 and 4319 kWhm⁻²year⁻¹ within Saudi Arabia. Along with the annual energy sums, monthly solar energy values averaged over all locations and over the mentioned period were estimated under all-sky conditions. A regression equation was provided as best-fit curve to the monthly mean energy sums that estimates the solar energy potential at any location in Saudi Arabia with great accuracy (R² = 0.96). This expression may prove very useful to architects, civil engineers, solar energy engineers, and solar energy system investors in order to assess the solar energy availability in Saudi Arabia for sun-tracking flat-plate solar systems throughout the year.

Seasonal solar energy sums were also calculated. They were averaged over all sites and over the period 2005–2016 under all-sky conditions. A new regression curve that best fits the mean values was estimated with absolute accuracy (R² = 1). Maximum sums were found in the summer (882 kWm⁻²), and minimum ones in the winter (667 kWm⁻²), as expected.

Although unified curves were presented for the monthly and seasonal solar energy yields in all territory of Saudi Arabia numerically expressed in Table 3, individual monthly and seasonal curves for all 82 sites were given in Figure 6 and Figure 8, respectively, in order for the interested scientist or engineer to see the individual solar energy yield variation.

The correction factor, CF, introduced in [1], was also used in this work. A graph of CF as function of ρ_r showed a linear dependence with increasing CF values as ρ_r increased. Such a behaviour was claimed to be considered universal (i.e., representable as nomogram). Nevertheless, this universality remains to be confirmed at other locations in the world with different climate and terrain characteristics. Two more plots were also prepared: (i) a graph of CF vs. RΔH_g, and (ii) a graph of ρ_r as function of RΔH_g. In both cases, 58 of the 82 sites were found to be accommodated within the ±1σ band around the mean RΔH_g value of 5.57. The other 24 sites remained outside the band, thus indicating a loose dependence of CF (ρ_r) on RΔH_g. These two graphs may be used as criteria for a strong (weak) dependence of CF (ρ_r) on the received solar energy, but this conclusion remains to be confirmed at other sites worldwide with different climate and terrain characteristics.