Techno-Economic Analysis of Alternative PV Orientations in Poland by Rescaling Real PV Profiles

Abstract

This paper presents factors affecting the effectiveness of photovoltaic (PV) plants and issues occurring in the distribution system network due to the high penetration of conventionally designed PV plants. Factors analyzed in this paper are shading, distance between panels, location of PV plants, European grid code requirements, and network constraints. Their impacts on the effectiveness of the PV power plant are presented one by one. Furthermore, the 1-year power profile of a real PV plant is rescaled to different orientations, and the energy effectiveness of different variants is compared. Finally, the economic aspects are considered by multiplying the energy produced by the energy prices. At the end, final conclusions are given and further research is outlined.

1. Introduction

The extensive growth of renewable energy sources often has a negative impact on power system networks [1,2]. More and more often, renewable power sources have to be curtailed to avoid overloads and voltage violations in a power system [3]. One of the main reasons is the large number of PV plants and the simultaneity of the production of photovoltaic energy since traditional photovoltaic (PV) plants are oriented south. The current situation in the power system is already difficult, but unfortunately will be worse due to the construction of power plants for which connection conditions have been issued, e.g., one of the biggest operators in Poland informs about ~750 renewable energy sources with issued connection conditions but without a grid connection agreement [4]. The number of energy sources connected will definitely increase over the years, even though the number of rejections of connection conditions is very high and increasing, as shown in Figure 1. The literature, data, and opinions of experts in the field clearly indicate that changes to the power system are needed.

New research indicates that different orientations may be more beneficial for the power system network, e.g., in the context of peak load shaving [6]; however, the literature does not describe all relevant factors. This paper addresses local power system network conditions, which are typically missing in the literature. This paper addresses misunderstandings between energy engineers, investors, and power engineers and presents the methodology for similar analysis. What is more, it highlights the impact of changing network and market conditions on decisions regarding power plant design. This paper proposes a modification of the photovoltaic plant design in order to reduce stress on the power system network and to help reduce the usage of fossil fuels by extending the period of availability of PV power plants. The modification is connected with the proper orientation of PV plants.

Photovoltaic plants consist of PV panels, cabling, protection and control, inverters, and a power output system [7]. Typically, photovoltaic panels in Poland are facing south because it ensures the biggest possible energy production. Practically, only PV rooftop installations are facing west or east because, according to common knowledge, the energy production is much lower—according to a simplified analysis presented in the literature; west/east produce up to 80% of the energy produced in a south-oriented PV plant [8]. Further, according to common belief, the area required for alternatively oriented PV plants is significantly larger than that required for conventionally oriented PV plants. A conventional 1 MW south-oriented PV plant in Poland requires approximately 1.5 hectares [9]. According to the authors’ investigations, the presented drawbacks are real; however, significant differences are noticed after performing the detailed analysis—particularly in the context of the PV plant area.

Among the factors analyzed, one can mention the technical progress, changes in the power market, and network situation, which require constant analysis of factors affecting the effectiveness of PV plants. In order to address the changing situation, the real generation profiles of the PV plant should include the inverter clipping effect, shadow, dirt, or snow deposit, grid code requirements, and power network problems (e.g., negative prices of energy on the stock market, which occurred on 11 June 2023 in Poland, or a 2.2 GW reduction of PV power in Poland on 23 April 2023) [8,10,11,12].

The mentioned technical factors are analyzed one by one. After the relevant technical factors are explained, the economic aspects are analyzed by combining the electricity prices with the generation profiles of alternatively oriented PV plants. The obtained results allowed for gaps in the current rules, which allowed for the formulation of the concept of modified energy source connection rules and the modification of the billing system.

2. Situation

2.1. Real PV Generation

Often, for the analysis of a PV plant’s design, only the sun’s potential is used. This is because of the limited data regarding shading and different particles such as snow or dust on PV panels [13]. Some advanced simulation software is able to consider the mentioned factors, e.g., PVSOL software allows for the analysis of shading; however, one needs to be aware that predictions may differ from reality. Furthermore, the deposit-related factor is only considered a reduction factor given manually by the user [14]. The deposit-related factors are important because theoretically, the sun potential over winter is still significant; however, due to freezing, snow deposits, dust, etc., there are significant differences between the calculated sun potential and the generated power. Therefore, there is a need to carefully analyze winter profiles, preferably by using real profiles obtained by advanced metering infrastructure—AMI installed in power plants or in the power system network [15].

In order to minimize the uncertainty of PV profile prediction, the paper utilizes measured profiles combined with the rescaling factors. The direction factors express the ratio of power produced by panels oriented south and in different directions. The direction factors are calculated as the ratio of sun potential for alternatively oriented PV plants in relation to south-oriented PV plants. The direction factors are obtained from the quasi-dynamic simulation module of PowerFactory 2022 software [16]. The exemplary relations between different PV panel orientations are given in Figure 2. The solid lines present sun potential; the orange dashed line presents the measured profile of conventional PV south-oriented plants; and other dashed lines present the south profile rescaled to different directions using the direction factor. The rescaling procedure is very straightforward. However, there is a need to pay attention to generating proper rescaling factors by adapting the shape of the sun potential with the shape of the profile being rescaled since the sun potential of a PV plant does not consider many technical details connected with the real PV power plant, even though the calculation method is very complex [17]. There are many different parameters required for the calculation of direction factors, for example, GPS coordinates, time, zone, or method of solar calculation. The parameters are adopted so the envelope of the normalized sun potential is in line with normalized measured PV profiles—100% of the sun potential is connected with 100% of measured—generated power; and the beginning of the measured profile is in line with the beginning of the sun potential. The normalization is needed to make sure that the sun potential reproduces the real profile properly and that the resulting rescaling factors are proper. The performed analysis allowed for a proper fit, which resulted in the proper rescaling of profiles, as shown in Figure 2. Unfortunately, even the proper adaptation of the sun potential may cause improper results, particularly during the winter, since very high differences between recorded values and the sun potential are observed. Even though the winter time is characterized by small PV generation (e.g., in Germany, the energy produced during the winter months is approximately 20–30% of the energy produced during the summer months), it may have a significant impact on calculation errors [18]. In order to cope with worse convergence of profiles in winter, the sun potential and the generated power were manually analyzed, and small time shifts between profiles were added so the proper rescaling factor would be used at the proper time.

The calculation of the output power of a PV module includes several factors: its nominal parameters, metrological conditions (ambient temperature or wind speed), and solar radiance recalculated for the tilt and azimuth of the module. The simplified Equation (1) for the calculation of PV power is presented below [19]. Detailed calculation methods may be found in manuals [17].

$$bullets{P}_i=N·S·G_i·\frac{{\eta }_{STC}}{100}·\left[1+\frac{\mu }{{\eta }_{STC}}·\left(t_{o,i}-t_{STC}\right)+\frac{\mu }{{\eta }_{STC}}·\left(t_{NOCT}-t_{o,NOCT}\right)·\frac{G_i}{G_{NOCT}}·\frac{9.5}{5.7+3.8·v_i}\right]$$

(1)

where, P_i—power at moment i (W), N—number of modules in plant, S—surface of a module (m²), G_i—solar radiance at moment i (W/m²), η_STC—efficiency of a module at standard test conditions (%), μ—temperature coefficient of power (%/°C), t_o,i—ambient temperature at moment i (°C), t_o,STC—ambient temperature at standard test conditions (°C), t_o,NOCT—the ambient temperature at normal operating cell temperature conditions (°C), t_NOCT–normal operating cell temperature (°C), G_i—solar radiance at normal operating cell temperature conditions (W/m²), v_i—wind speed at moment i (m/s).

The PV plant’s power calculation requires the use of several factors: tilt β (°), azimuth of a module γ (°), azimuth of the sun γ_s (°), angle of incidence of solar radiation on a flat surface θ (°), and both beam G_b and diffuse radiation G_d. The Equation (2) for the calculation of solar radiance for given conditions is presented below [19].

$$G_i=G_{b,i}·\frac{{\cos \mathsf{\Theta }}_{z,i}·cos\beta +{\sin \mathsf{\Theta }}_{z,i}·sin\beta ·\cos \left({\gamma }_s-\gamma \right)}{{\cos \mathsf{\Theta }}_{z,i}}+G_{r,i}$$

(2)

In order to properly rescale output power, there is a need to include the abovementioned factors, such as shading or dust/snow deposits. The rescaled profiles are analyzed in the context of the energy produced in different months. As can be seen, analysis of the sun’s potential only leads to the conclusion that the south direction is much better in the context of energy effectiveness; however, considerations or technical factors reduce the difference between conventional and south-oriented panels, as shown in the next paragraphs. Despite the energy effectiveness, the energy density—MW/ha—has to be considered—the area required for the production of the same power. Alternative orientations of PV panels are connected with different shadows and, as a result, different distances between panel rows. Unfortunately, the PowerFactory software is not equipped with shading analysis tools, and therefore, some analyses are performed in specialized photovoltaic software—PVSOL 2023. The software allows for simple generation of 3D models of PV panels and simple analysis by visualization of the results (Figure 3). For simplicity, only the 30° tilt angle is considered, which is the optimum for Poland. However, panels oriented east or west can have higher effectiveness for lower tilts (+3% effectiveness for a 10° tilt angle) [20]. Unfortunately, the higher potential efficiency of PV plants is connected with a higher risk—the lower tilt angle worsens the self-cleaning properties of the PV panel surface [21]. As a result, the efficiency of PV panels could drop. In order to minimize the problem, one can choose PV panels with better self-cleaning properties; however, detailed analysis is required, and therefore, for the time being, the variants are excluded from the analysis.

The average yearly shading factor is read in the middle of the second row of PV panels placed in the same direction to obtain typical shading in uniformly constructed PV plants. It should be noticed that shading is not even on the whole surface of the row—the part of the row placed closer to ground level is shaded more often than the part located higher from the ground. Therefore, to minimize the impact of shadow, bypass diodes should be considered in proper orientation according to the position of panels (vertical or horizontal) and number, as well as a proper connection of PV strings—preferably one string should be limited to one row [22,23]. It is also important to ensure proper maintenance strategies, e.g., cleaning the surface and monitoring the condition of the PV plant [24].

The shadow resulting from different distances (expressed as a ratio of distance to height of PV panels) between panels is given in

Table 1. Results for average shadow analysis.

Orientation	Distance/Height of PV Panels	Rrzeszow		Suwalki		Swinoujscie		Wroclaw
		Shadow in 1st Row [%/Year]	Shadow in 2nd Row [%/Year]	Shadow in 1st Row [%/Year]	Shadow in 2nd Row [%/Year]	Shadow in 1st Row [%/Year]	Shadow in 2nd Row [%/Year]	Shadow in 1st Row [%/Year]	Shadow in 2nd Row [%/Year]
S	1	8.3	0.3	10.2	0.5	10.1	0.5	8.9	0.3
	1.5	3.4	0.2	5.3	0.3	5.2	0.3	3.9	0.2
	2	1.3	0.1	2.8	0.2	2.7	0.2	1.6	0.2
	2.5	0.7	0.1	1.4	0.2	1.3	0.2	0.9	0.1
	4	0.3	0.1	0.5	0.1	0.5	0.1	0.4	0.1
E	1	9.9	0.9	11.3	1.1	11.7	1.8	9.9	0.9
	1.5	5.3	0.5	6.1	0.6	6	0.6	5.4	0.5
	2	3.2	0.3	3.8	0.4	3.7	0.4	3.4	0.3
	2.5	2.2	0.2	2.6	0.3	3.6	1	2.3	0.2
	3	1.6	0.1	1.9	0.2	2	0.2	1.8	0.1
	4	1	0	1.3	0	1.3	0	1.1	0
W	1	10.4	1.6	11.8	1.8	11.2	1.1	10.8	1.6
	1.5	6.1	1.2	6.9	1.4	6.9	1.4	6.3	1.3
	2	4.1	1	4.7	1.1	4.7	1.1	4.3	1
	2.5	3.1	0.9	3.6	1	3.6	1	3.2	0.9
	3	2.5	0.8	2.9	0.9	2.9	0.9	2.6	0.8
	4	1.9	0.6	2.2	0.7	2.2	0.7	2	0.6
E/W	1	3.2/4.1	0.3/1	3.8/4.7	0.4/1.1	3.8/4.7	0.4/1.1	3.4/4.2	0.3/1.0
	1.5	2.2/3.1	0.2/0.9	2.7/3.6	0.3/1	2.6/3.6	0.3/1	2.4/3.2	0.2/0.9
	2	1.6/2.5	0.1/0.8	2.0/2.9	0.2/0.9	2.0/2.9	0.2/0.9	1.8/2.6	0.1/0.8
	2.5	1.3/2.2	0/0.7	1.5/2.5	0.1/0.8	1.5/2.5	0.1/0.8	1.4/2.3	0.1/0.7
	3	1.0/1.9	0/0.6	1.3/2.2	0/0.7	1.3/2.2	0/0.7	1.1/2	0/0.6
	4	0.6/1.5	0/0.6	0.8/1.7	0/0.6	0.8/1.7	0/0.6	0.7/1.6	0/0.6

for four different locations. Locations express roughly the corners of Poland (the limitation of the meteoroidal database in PV SOL) in order to show that the results presented in the paper are not universal and should be considered as an example. The most important results are also presented in Figure 4—one can see that for the same distance between panels oriented west or east—shadow losses are roughly 2–3% higher. Moreover, the west direction is slightly more shadowed than the east direction. The east/west direction is connected with more than two times lower shadow losses than a conventional south-oriented plant when the relative distance is 1. With the rise of the relative distance, the advantage of the west/east configuration is decreasing, and when the relative distance is 2, the shadow factor is comparable with other orientations.

Analysis of the results presented in Table 1 allows us to conclude that the distances between rows should be bigger if panels are oriented west or east. However, shading losses are, in general, small and have a limited impact on energy effectiveness. Moreover, in some cases, e.g., west or east slope PV panels can be placed much closer or only with minimal distance between them. The consideration of alternative-oriented PV plants clearly allows for the use of terrain, which was often considered useless for photovoltaic. Other examples are agro-photovoltaic plants, which are characterized by large distances between panels so the crops can grow [25]. Additionally, the west/east construction is considered in the shadow analysis. In this case, the losses due to shading are similar to the losses of panels directed south.

2.2. Grid Code

Commission Regulation (EU) 2016/631 of 14 April 2016 established a network code about requirements for grid connection of generators. According to the grid code, the real power generated by power plants has to be reduced to a level that allows for the generation of the required level of reactive power. The grid code specifies different requirements for different types of power plants, which are categorized based on voltage level, power level, and technology (

Table 2. Classification of maximum power-generating modules in Poland.

Maximum Power Threshold Limit from Which a Power-Generating Module Qualifies as:
Type B	Type C	Type D
0.2 MW	10 MW	75 MW

) [26]. Furthermore, the local transmission operator specifies the general requirements for different types of plants, which may differ significantly in nearby countries (Figure 5) [27]. However, in some cases, the operator may specify individual requirements within the limits given in the grid code. Reactive power regulation capabilities are essential for the stable and effective operation of a power network. Only low-voltage installations are allowed to operate without constraints since the requirements regarding reactive power are specified in relation to the nominal power [28], whereas bigger PV installations have to reduce the nominal power to the level of P_max, which allows for the generation of the required reactive power level.

The required reduction of the nominal power depends mostly on the type of inverter and its reactive power regulation capability, but also on the power output system since it is built out of non-ideal elements that have some induction or capacitance [29]. As a result, the reactive power capabilities of a point of coupling are shifted towards the side of one of the reactive power types. The point of coupling is important since the requirements are specified not for the energy source but for the power generation unit, which includes the power output system. A similar approach is common in power systems, e.g., requirements connected with power quality parameters are specified for the point of coupling [30].

The regulation capabilities may differ significantly depending on the type of inverter. In general, the reactive power capabilities of inverters have increased over the years. In the new inverters, there is a need to reduce maximum power to approximately 90% of the nominal power to comply with NC RFG grid code requirements, whereas the reduction factor in older inverters is approximately 0.8. Figure 6 presents an exemplary output current (measured at the secondary side) and flattening of the PV power profile. The reactive power capabilities and control of inverters are still under research; therefore, further progress may be expected [31].

What is important is that the NC RFG specifies requirements regarding energy sources. However, there are different grid codes, e.g., NC DC, which specify requirements regarding the distribution system operator. According to general requirements, distribution system operators are obliged to provide more reactive power [32], so if the energy source is close to the point of common coupling, it may cause a significant tightening of requirements [26], so the reduction factor of real power would increase up to approximately 0.8. At the same time, in the case of the DSOs, specific requirements defined by the transmission system operator are more common. Therefore, the situation requires individual analysis.

Theoretically, it is possible to provide additional reactive power sources. However, this is rarely the case because of the high investment cost. The high investment cost is the result of the complex structure of reactive power sources. It is not enough to provide the proper amount of reactive power. There is a need to provide many regulatory steps. The step change of reactive power—Q—has to be below 5% of maximum reactive power or 5 MVA—depending on what occurs first. Reactive power control methods have to be carefully analyzed and adapted to the voltage level and network conditions [32,33]. The general requirements regarding control strategies are given in the Network Operation Manual provided by the system operator [28].

3. Analysis of the Energy Generation in the Context of Grid Code Requirements

3.1. Grid Code

To consider the grid code requirements, the power generation profiles are trimmed to specified reduction factors: 0.95, 0.9, 0.85, and 0.8. The resulting generation profiles are compared in the context of the energy produced. Results are given in

Table 3. Sun potential for different PV panel orientations.

	Yearly Production (% of Nominal) as a Function of Reduction of Pnom (%)
	5	10	15	20
Sun potential S	98.54%	97.02%	95.05%	92.65%
Sun potential W	75.25%	74.69%	73.72%	72.37%
Sun potential E	75.25%	74.69%	73.72%	72.37%
Sun potential E/W	75.37%	75.37%	75.36%	75.01%
Sun potential 120% W	86.53%	84.77%	82.71%	80.35%
Sun potential 120% E	86.53%	84.77%	82.71%	80.35%
Sun potential 120% E/W	89.89%	89.05%	87.85%	86.30%

. It can be observed that the differences in energy production are reduced in favor of the alternative direction of photovoltaic panels since the reduction of Pmax caused a 3% energy reduction instead of a 6% reduction in conventional south-oriented plants. The exemplary sun potential and rescaled profiles for different PV panel orientations are presented in Figure 7 and Figure 8. The Figures present two variants of PV power plants—with the same number of PV panels as a south-oriented PV plant or 120% of PV panels. The increase in PV panel number is often possible (if the resulting voltage rise of the strings does not exceed the limits [34]), since it does not increase the power capacity of the PV plant if the inverter power remains the same. Moreover, the short circuit power cannot rise above the maximum inverter power since the inverter is protected against the overcurrent to avoid destruction of the inverter [35].

Relative power P_i,rel (%) for both sun potential and rescaled profile are calculated according to Equation (3). Yearly production E_i,rel (%) for these cases was calculated according to Equation (4).

$$P_{i,rel}=100\%\frac{P_{i,var}}{P_{i,S}}$$

(3)

$$E_{i,rel}=100\%\frac{\sum P_{i,var}/h}{\sum P_{i,S}/h}$$

(4)

where P_i,var—power calculated for any variant (kW), P_i,S—power calculated for the base case of south-oriented panels (kW), and h—number of calculations per hour (1/h).

Table 4. Rescaled profile.

	Yearly Production (% of Nominal) as a Function of Reduction of Pnom (%)
	5	10	15	20
S	98.99	98.15	97	95.51
W	79.26	79.05	78.6	77.9
E	79.13	78.88	78.42	77.72
E/W	79.31	79.31	79.27	79.11
120% W	90.04	89.23	88.16	86.83
120% E	89.83	89.04	88.01	86.72
120% E/W	91.10	90.86	90.39	89.67

presents the same results as Table 3; however, for rescaled PV profiles, which include the power reduction factor due to any issues, e.g., shadow. The interesting thing is that in the case of rescaled PV profiles, the reduction factor is significantly reduced since the number of days, in which maximum power is produced is relatively low. In the case of a conventionally oriented plant, the effect is approximately two times lower than for the sun potential; however, it is significant—in the range of 3.5% energy reduction for a 20% reduction of the nominal power of a south-oriented PV plant and 1.3% for a west oriented PV plant.

3.2. Expected Grid Constraint

Results presented until now indicate that even though the negative limiting factors affect conventional, south-oriented PV plants more, the energy production effectiveness is much better. However, the amount of energy produced depends on the time of production because the production of electricity at the same time causes serious technical issues—overloads of lines and violations of voltage level—which cause premature aging and increase the risk of a failure of the power system network elements [36]. As a result, there is a need to pay particular attention to the diagnostic and monitoring of elements of modern power systems [37,38]. Moreover, according to a typical contract between plant owner and operator, when the violation level is unacceptable and there is no other solution, the transmission or distribution system operator may order to reduce the power of power plants. If it is possible, the power from the distribution network can be sent to the transmission system, from which it could be transferred to neighboring countries using international. Nevertheless, one needs to underline that the transmission of high power over long distances is connected with higher transmission losses—simplifying—proportional to the square root of current and impedance. The higher losses and technical issues with transmission of the energy over long distances are not economically effective; therefore, many different initiatives connected with load demand management and the energy market have been introduced [39]. Alternative-oriented PV plants allow for similar effects to demand-side management.

The risk of voltage level violation may be assessed based on the analysis of a voltage profile at the point of connection. Thanks to an advanced metering infrastructure, practically all medium voltage (MV), high voltage (HV), and extra high voltage (EHV) lines in Poland are monitored. MV lines are typically analyzed within a 15 min period, whereas HV and EHV lines are recorded with a higher resolution for up to 1 min. In the future, it is planned to increase the resolution of measurements [40]. However, it is rather unlikely that it will happen soon due to technical issues; the amount of data, compression, computation power, etc. [41].

After simplification, the voltage rise—“a” caused by the PV plant is given by the formula 5 [42]:

$$\begin{gathered} a=\frac{\sqrt{3}\mathsf{\Delta }I·R·cos\phi +\surd 3 \Delta I·X·sin\phi +}{U}=\frac{\mathsf{\Delta }P}{U^2}R+\frac{\mathsf{\Delta }Q}{U^2}X \\ =\frac{\mathsf{\Delta }Scos\phi }{U}·\frac{1.1U^2}{S_{kQ}^{″}}cos\psi +\frac{\mathsf{\Delta }Ssin\phi }{U}·\frac{1.1U^2}{S_{kQ}^{″}}sin\psi = \\ 1.1\frac{\mathsf{\Delta }S}{S_{kQ}^{″}}cos\phi ·cos\psi +1.1\frac{\mathsf{\Delta }S}{S_{kQ}^{″}}sin\phi ·sin\psi =1.1\frac{\mathsf{\Delta }S}{S_{kQ}^{″}}\cos \left(\psi -\phi \right) \end{gathered}$$

(5)

where:

• φ—the angle between real and apparent power,
• ψ—the angle that describes the impedance of the supply line,
• S″_kQ—short circuit power,
• ∆I/∆S—change of consumed or generated current/power.

For simplification, it is assumed that a typical 1 MW PV plant is connected to a feeder with high penetration of south-oriented PV plants at a distance of 10 km. It is assumed that the feeder mains are made of typical 3 × 120 mm² Al core cable. As can be seen in Figure 9, the addition of the next south-oriented PV plant is connected with a higher risk of achieving the maximum allowable voltage under normal operating conditions (110%) at the point of common coupling between 10 and 14 o’clock, which is becoming a more and more pressing issue in MV and HV lines. Moreover, the higher the length of the feeder and the resulting impedance, the higher the voltage level and the higher the risk of exceeding the voltage limit.

The voltage level can be reduced by activating the reactive power consumption mode in an inverter (e.g., Q(U) regulation). However, reactive power regulation is associated with higher losses and may cause coordination problems with other voltage regulation methods/devices. One of the problems is a tap changer, where the abovementioned power control could cause an increased number of tap changer operations, e.g., reactive power reduces the voltage in a 110/15 substation. It results in a change in the tap changer position to compensate for the voltage change. As a result, the voltage in the feeder is reduced but not as strong as needed. Furthermore, the operation of a tap changer causes increased flicker due to the step change of voltage in the range of 150 V for a typical tap changer in a 110/MV transformer [43]. On the other hand, it is important to underline that the new PV plants can provide reactive power for the whole day and also during the night, which may be used to improve the situation in the power network (e.g., reduce the stress during switching operations [44,45].

3.3. Profits

The overproduction of energy causes the abovementioned issues in the power system, which results in higher operational costs for the power network. To limit the overproduction of energy and control the generation units, the day market was created. The price of electricity is given for every day and every hour [46]. When the amount of generated power in the power system is high, prices of electricity are typically lower, and when the amount of generated power is low, prices are higher. As a result, from an economic perspective, it may be more beneficial to produce less energy during a higher demand period than to produce more energy during overproduction. To assess the impact of electricity prices, the recorded south-oriented and rescaled PV profiles are multiplied by the prices of electricity for a 1-year period (2021). Exemplary financial benefits for one day (the same day as in Figure 1) are presented in Figure 10. As can be seen, the financial benefits for a given day are comparable.

The resulting financial incomes calculated for a 1-year perspective are presented in

Table 5. Economic effectiveness.

PV Panels Power	S	W	E	W/E
100%	100.00%	79.00%	78.20%	78.60%
120%		94.79%	93.84%	94.32%

. For the base case—without reducing Pnom to Pmax—the financial benefits are very similar to the amount of energy produced. Statistically speaking, the impact of changing prices on economic effectiveness, at least for 2021, is limited. As can be seen, economic benefits are also very similar to energy effectiveness when the number of alternatively oriented PV panels is increased to 120%. Even though the economic effectiveness of alternatively oriented PV panels is lower, the risk of power reduction due to local power network constraints is much lower, as shown in the paragraphs above. The very similar results may be explained by the scale of the power market, which considers the global needs of the power system but does not consider local constraints. In order to consider local problems with energy prices, the system needs to be modified. The next paragraph presents the concept of modifications.

3.4. Concept of Modification of Energy Integration and Accounting Rules

The presented analysis allows for the formulation of guidelines for power system development and the modification of current rules for new energy source integration [47]. According to the guidelines, short circuit capabilities, power quality parameters—harmonics; flicker (only for wind farms); and voltage changes—as well as the loading of the 110/15 transformer are analyzed in the context of defined limits. If any of the parameters exceed the limits, the decision about the connection of a new source is negative. As a result, assuming the value of 100% in Figure 7 is connected with the limit, one can conclude that the power network can accept 100% of conventional south-oriented power plants (orange line) or alternatively, 125% of installed power oriented west and east (red, dashed line). Further, one can notice that the total amount of energy produced will be significantly larger (due to a longer generation period), so emissions of greenhouse gases can be significantly reduced, and at the same time, the consumption of fossil fuels, which are becoming more expensive, is also reduced. Despite the fact that the production of PV energy using alternative-oriented plants is more beneficial for power systems, its economic effectiveness is lower. As a result, investors decide to connect more and more south-oriented plants until the possibility of further power source connections is exhausted. Some of the above-mentioned parameters are connected with the simultaneity of power production:

-

the maximum loading of transformers or lines,

-

the maximum voltage rise,

-

the maximum allowable power quality degradation.

Therefore, the distribution of the production allows for a reduction in the stress on the power system. Voltage has often the highest amplitudes between 11 and 14, which is the result of power generation in conventional south-oriented PV plants. Figure 9 allows us to notice that the voltage rise for alternatively oriented PV plants is roughly 20% lower, which ensures a higher safety margin if an alternatively connected PV plant is connected. The safety margin is very important because the power system is constantly evolving, e.g., due to prosumers who are allowed to connect small energy sources based on simple registration (connection capabilities analysis may also be performed); however, the number of installations may be large, therefore total power may be significant [48]. The authors believe that further connection analysis should promote trend analysis and solutions that allow for a higher safety margin for essential power system parameters. The authors propose to extend trend analysis and at the same time warn against potential issues with data quality, e.g., missing or extra data, that disturb the trends. The extended trend analysis method considers not only the real power trend, which is state-of-the-art, but also the analysis of the voltage trend and THDu. The mentioned trends are recorded by AMI meters and, therefore, can simply be provided by the power system operator [49]. The real power is analyzed according to the state of the art in order to verify if the 110/15 transformer or another element is overloaded. The voltage and THDu trends are summed with the predicted voltage rise (as explained in Section 3.2, Figure 9) and the predicted THDu rise. The predicted THDu rise is calculated using PQ software based on the power system model obtained from the operator (what is essential to consider potential resonances, etc.) and technical data about harmonics obtained from the inverter manufacturer [50,51]. The technical documentation of inverters contains information about harmonic share in relation to the fundamental component (50 Hz) for different operating points of the inverter, e.g., 10% of power, which allows for simulation and the prediction of the rise of THDu. Further, the transformation matrix—THDu rise characteristic for generated power range—is created. Finally, trends presenting the expected voltage rise and THDu rise for different orientations of PV panels are compared. The whole trend is analyzed in order to find the week characterized by the worst violation of parameters, since one week is the time period specified in PQ norms [52]. Further analysis of the reduction of the safety margin and limit defined in norms is conducted using the penalty factor, which is calculated based on a linear function according to Figure 11. Finally, the sum of penalties for different PV orientations is compared and transformed into an energy price correction factor. The energy price correction factor can have different values depending on the conditions in the analyzed network. The introduction of a price correction factor would improve the economic effectiveness of the proposed alternative-oriented PV plants and mitigate stress on the power system. The price correction factor is proposed to be the ratio of the penalty factor for the best-oriented plant to the worst-oriented plant. The proposed solution would allow for the minimization of the very high investment cost for power quality improvement in the future.

In the future, the proposed penalty factors would be tabulated so the industry could perform a simplified analysis effectively. It will be possible to overwrite penalty factors if a similar analysis is provided to the operator, e.g., due to further development of inverters.

The proposed concept is adjusted to the limits of the current AMI systems; however, can also be analyzed based on PQ meters. Moreover, in the future, the impact of PV power plants on flicker, which is currently not practiced in Poland, even though the impact may be significant [43].

4. Conclusions

The presented analysis allows us to conclude that the amount of energy produced in alternatively oriented PV plants is significantly lower than in conventional, south-oriented PV panels. However, it is shown that it is possible to utilize different areas, such as west- or east-oriented slopes, for PV panels. The energy and economic effectiveness of alternatively oriented PV plants with an increased number of PV panels (120%), calculated for 2021, are only a little lower than in the base scenario. It is expected that in the future, the alternative orientation of PV panels will be more beneficial due to further network constraints and possible modifications of the energy market, e.g., subareas of the energy market or methods considering local network conditions in the price of generated electricity. Furthermore, there is a need to consider the changing prices of photovoltaic power and different technical aspects, e.g., power quality issues. In general, the lower the sum of PV power at the moment, the better the power quality; therefore, the distribution of the generation has a positive impact and, in some cases, may reduce the investment cost for PQ-improving devices.

The proposed modification of photovoltaic power plants may utilize the rescaled PV profile to maximize PV production under cable pooling conditions and on different hybrid and microgrid systems [53]. Different variants could be analyzed, e.g., any angle between west and east orientation or inclination angle. Adjustment of photovoltaic panels’ orientation can have similar effects on load demand response [54]. Moreover, the procedure may be further used to verify different configurations, e.g., complex roofs or floating power plants [55].

The presented research presents the methodology for the assessment of PV effectiveness in changing network and market conditions over the years. The authors verified data rescaling and performed extensive analysis. However, further research connected with verification in real-life conditions and comparative analysis based on measurements is planned. Furthermore, optimization of alternatively oriented plants is required, e.g., the mentioned issues with cleaning for low tilts in the range of 10°. Finally, there is a need to be aware that typically HV PV plants are characterized by more stable output power than small-scale MV plants; therefore, it is recommended to use a similar-sized PV plant as a base for rescaling.

At the end of the paper, the innovative concept of modification of the PV energy integration and accounting rules is presented.