In the solar farm, PV-modules (“modules” below) are exposed by rows where modules are installed side by side in parallel. Usually there are several rows, one behind the other. Evidence of how the hindered row is shaded by the first one has been analyzed in the literature [2, 3]. We focused on the co-operation and mutual shading of two-positionally tracked neighbor modules in a

row. Most of the modules perform inside the farm and are surrounded by neighbors from both sides. Performance of such a module defined as an “inner” module was analyzed first. A module at the end of the row, which has a neighbor on one side only, is defined an “outer” module. Peculiarities of their performance will be described later.

In the theoretical analysis, a simplification has been made: the PV-module (or its column on the roof) is considered being infinitely long. It means that we will ignore edge effects on the top of the inner column. At these limitations the gain has its minimal value as the edge effects increase the illumination. Figure 1 shows the 2-D model of a row of modules deflected eastward in the morning with the deflection angle -%, which shows the view from the top along the axes around which the modules are rotated (deflected) twice per day. Around the noon (exact time is not critical) the modules are triggered into the westward position with the deflection angle +%. The processes in the afternoon are the mirror reflection of those in the morning and were not subjected to detailed analysis.

Each module with a width WC has its axis parallel to the basis. The basis may be ground with the zero tilt angle p0=0, a roof with a free tilt angle 0<р0<л /2 or wall p0=n /2. To simplify the analysis we suggest that the tilted basis is looking south with the azimuth y0=0, but that is not obligatory. The inner modules are installed at the distance DR from each other, the outer module is installed on the distance DC from the edge of the base (roof, wall). An important parameter in the analysis below is the relative distance (density) dR= DR /WC. Illumination on the upper (outer) edge of the inner module appears when the sun has reached the position characterized by the clock angle юF. Then the sun is shining along the plane of a virtual envelope, parallel to the basis, it joins together all the upper edges of the farm. At the clock angle ®G, the whole area of the inner module is illuminated and after that ю >®G the module performs like a tracked stand-alone module. During a transient shading process, characterized by the angle ^=(®G ^F ), the shadow of the neighboring module will move across the module. Converted solar energy E from the direct component is proportional to the share of the illuminated area AC (ю). As AC (®)<AC, the tracked module inside the farm produces always less energy than the stand-alone tracked module. Consequently, the gain of a solar farm with the two-positional tracking will be somewhat lower, compared to that of the two-positionally tracked stand-alone module.

2. Approach

The task of the study is to calculate the hourly, daily, monthly or seasonal energy yield for a module exposed in the two-positional regime. This calculated (and experimentally measured)

energy yield will be compared with the energy yield of a fixed module, which is installed in optimal conditions. Improved efficiency, i. e. the profit (“gain”), is defined as the ratio of the energy produced in (two) deflected positions to the energy produced by the collector that is optimally exposed and fixed in this position. This is a south-faced collector with the tilt angle that warrants the most uniform energy yield during the season. For the latitude around 60° N, the tilt angle should be 45°<p <60°. We refer to the value of 45°.

Gain may be defined for an hour as follows: hourly gain = hourly energy yield of the deflected collector ETx divided by the hourly energy yield ET of the fixed collector, kWh/kWh.

Also, gain may be defined as the ratio of the corresponding irradiances kWm-2/kWm-2.

Gain = GTxj GT, (1)

where GT is the irradiance on the tilted module and GTx is the same in the deflected position.

Daily gain = energy yield in the two-position deflected collector per day divided by the energy

yield of the fixed collector per day, kWh/kWh.

Monthly and seasonal gains are defined analogously to the daily gain. The main goal is to maximize the seasonal energy yield, although the hourly gain is also of interest, considering co­operation of solar PV farms with the grid.

Gain is the function of several variables: geographical location due to the latitude Ф, season due to the changing declination 5, solar clock angle ю, initial tilt angle p0, initial azimuth y0, deflection angle x, and solar radiation that varies by site and time. In view of these circumstances, a general analytical solution would hardly be possible especially due to the radiation data presented as table functions. Therefore, calculations must be performed by help of computer simulation. Radiation data of the beam Gb and the diffuse Gd component have to be considered separately as they are absorbed by the module in the farm differently. In the analysis of a PV-farm performance, in addition, we have to consider the variable dR characterizing the density of the modules in the farm. Geographical (Ф ) and constructional data (p0, yo, x) can be considered as constant for each analysis, radiation data Gb and Gd are tabular functions, 5 and ю are continuous variables sampled for each step of the calculation. Auxiliary variables in the computation process are presented as functions of the independent time variable ю.