the development of a prosumer modelling tool

the development of a prosumer modelling tool

5 Results

5.1 Introduction

Although the main objective of this thesis is the development of a prosumer modelling tool (generation and demand profiles), rather than power system analysis itself, two study cases are included in this Chapter to illustrate possible applications of the developed model. Case Study A assesses the performance of a single rooftop PV system located in Edinburgh. The example illustrates:

• How the developed prosumer model can be used to determine the impact of the ambient temperature on the PV system power output and annual energy production.
• How the tilt angle of the PV modules can alter the system’s maximum power output and the monthly energy yield throughout the year.
• The determination of the optimal PV tilt angle maximizes the rooftop PV system’s annual energy production.
• The developed model can be used to identify the most typical scenarios in terms of power output and daily energy generated.

Case Study B illustrates how the prosumer model can provide the generation and demand profiles (time series) for N number of households defined by the user. The example analyses the low voltage network’s performance before and after the connection of the distributed generation (PV systems and micro wind turbines).

5.2 Case Study A

The improvement has influenced the growth of PV technology in manufacturing cost and efficiency of modules during the last decade [1]. It is well known that the performance of crystalline silicon panels is affected by the ambient temperature. Hence, this case study aims to analyse the impact of the ambient temperature and the solar panel tilt angle on the peak power output and energy production. A household located in Edinburgh (geographic coordinates defined in Chapter 3) was selected for the analysis. The installed capacity of the rooftop solar power system is 5 kW. The high performer monocrystalline Sharp NU-AC310 photovoltaic panel was chosen because crystalline silicon technology is the most common all over the world currently [1]. The manufacturer’s technical specifications for standard test conditions and nominal operating cell conditions are reported in Table 5.1. Whereas the mechanical data and temperature-correction factors are listed in Table 5.2 (see Appendix A.3 for the complete datasheet).

Table 5.1 Manufacturer electrical data specifications

Table 5.2 Manufacturer mechanical and thermal data specifications

5.2.1 The effect of ambient temperature on PV systems performance

The power output time-series profiles obtained from the Python model developed in this project were processed to determine the impact of the ambient temperature. First, the maximum monthly power output was calculated when the temperature correction factor is equal to 1 (neglecting the ambient temperature). Then, the temperature correction power factors were obtained from Eq. (3.2) and applied to the power profiles. Figure 5.1 shows a comparison of the maximum power output per month. It was found that the power output is reduced during the summer and spring due to temperature losses. On the other hand, between October and February (Winter and Autumn), the temperature correction factor is higher than 1. Accordingly, the performance of the PV system is improved due to the low temperatures. To visualize the relationship between ambient temperature and maximum power output, Table 5.3 presents the monthly average temperature and the power variation caused by the temperature correction factor. In general, it is observed that the power output is increased by up to 7% in the winter, whilst there is a power output reduction of 5% in the summer. It should be noted that the analysis was carried out from 5-minute resolution data for the year 2019. Long term historical data would give more accurate results for the performance assessment of PV systems in Edinburgh.

Figure 5.1 Effect of temperature on maximum power output

Table 5.3 Variation of maximum power output due to air temperature effect

A similar analysis was carried out in terms of monthly energy generated. Figure 5.2 displays the annual energy production profile for both cases (considering and neglecting the temperature correction factor in the calculations). Whereas the monthly average temperature and the energy production variation caused by the temperature-correction factor are presented in Table 5.4. No significant energy yield variations were found between April and September. This is because although the highest temperatures are recorded in the summer, the time the PV system operates at maximum power is deficient (as seen in the previous Chapter). Therefore, the monthly sum of energy is not significantly altered by the effect of temperature. As a result, the maximum monthly energy reduction due to temperature effect is around 1% in June.

On the other hand, the ambient temperature effect is more pronounced in winter, with an increase in energy production. The maximum energy increase corresponds to January, where the variation reaches up to 7%. It is because, during the winter, the air temperature is low throughout the day, which improves the performance of the crystalline silicon technology.  However, it should be kept in mind that solar radiation is the most economical during the winter. Consequently, even when there is an increase of 7% in energy production due to the temperature correction, January’s energy is the lowest of the year.

From the short review above, key findings emerge:

• In terms of maximum power, the temperature effect reduces the maximum power output by up to 5% in the summer. At the same time, power is increased by up to 7% in the winter.
• In terms of energy, the production is reduced by around 1% in the summer, and there is an increase of up to 7% in the winter. Therefore, the annual balance is positive. The temperature effect increases the annual energy production from 4.674 MWh to 4.726 MWh (1.11% increase). It can be concluded that the ambient temperature throughout the year in Edinburgh is suitable for PV systems.

Figure 5.2 Effect of temperature on monthly energy

Table 5.4 Variation of energy production due to air temperature effect

5.2.2 The effect of panel tilt angle on PV systems performance

The analysis shown previously corresponded to a horizontal PV system. However, in the northern hemisphere, it is common to adopt a panel tilt angle equal to the latitude of the location to maximize the energy yield [2].  This is not genuinely viable in real scenarios because the slope of the rooftop defines the tilt angle. Only to validate the effects of the tilt angle on the maximum power output and monthly energy production, an analysis similar to that presented above was carried out for the same photovoltaic system, but with a tilt angle equal to 55° (Edinburgh latitude).

Figure 5.3 shows a comparison of the monthly maximum power output for both cases (horizontal and tilted PV system). It can be seen that the maximum power output reached each month of the year is increased when the PV system operates at a tilt angle equal to 55°. The power increase is remarkable, especially between October and March (Winter and Autumn). There is an interesting finding, the maximum power output of a horizontal panel occurs in June, while the tilted panel maximum power is shifted to April. This behaviour is in accordance with the theory reported in the literature [3]. However, it is not possible to draw any definite conclusions from this because only 1-year data were analysed. The tilt angle is not the only factor that influences the PV power output. As seen in the previous section, the ambient temperature also plays an essential role in the maximum power reached. Besides, the ratio diffuse to global irradiance varies between locations and has an impact on the performance of the PV system.

A summary of the variation in the maximum power output per month due to the panel tilt angle is presented in Table 5.5. Special attention has been paid to the winter because of the highest power increase (up to 182%). The horizontal panel reaches 1.3 kW in January, which is around 26% of the PV system’s installed capacity. In comparison, the tilt panels get to operate at 3.7 kW (approximately 74% of the rated power). It is worth mentioning that the maximum power calculations correspond to 5-minute resolution data. It means that the solar PV system reaches that power value, but the percentage of time the system operates at those power values may be very low. It is defined by the global irradiance variation, which was analysed in Chapter 3.

Figure 5.3 Comparison of maximum power output

Table 5.4 Variation of power output due to a panel tilt angle

Despite the significant changes in maximum power output reached when the PV system is tilted, relatively small differences were found in terms of annual energy production. Figure 5.4 shows the annual energy production profile for both cases (horizontal and tilted at 55°). It can be seen that between April and August, the tilted panels’ energy production is lower than the production of the horizontal panels. Conversely, the tilt panels’ winter energy production is higher than the energy obtained from the horizontal PV system. These results agree well with the study carried out by Hartner et al. [3], which concluded that steeper tilt angles could shift the energy production from summer to winter. To visualize the variation in monthly energy production between horizontal and tilted panels, Table 5.3 presents a summary of the results per month. In general, it is observed that the energy production is reduced to 13.56% during the winter, while there is an increase of up to 86.35% during the winter.

From the examination, key findings emerge:

• In terms of maximum power, there is a substantial increase in the maximum power output reached by the tilt PV system throughout the year, especially during the winter.
• In terms of energy, the tilt panels’ energy production is lower in the summer, but it is much higher than the horizontal panels during the winter. Therefore, the annual balance is positive. The 55° tilted PV system increases the annual energy production from 4.726 MWh to 4.973 MWh (5.23% increase). However, an economic assessment must determine if the increase in annual energy produced by the tilt panels justifies the investment.

Figure 5.4 Comparison of energy production throughout the year for horizontal and tilted PV system

Table 5.5 Variation of monthly energy production between horizontal and tilted panels

5.2.3 Optimum PV tilt angle for Edinburgh

There exists pervasive literature on the topic of optimum tilt angle for fixed mounted PV panels [4], [2]. There is one angle of inclination that maximizes the annual energy production of the PV system. As a rule of thumb, a tilt angle equal to the latitude is the optimum for maximizing the annual yield [3]. However, that rule assumes that the atmosphere is entirely transparent to solar radiation (no scattering effect). Actually, the optimal tilt angle mainly depends on the site latitude, irradiance levels, and the clearness index [5]. Thus, the calculation of the optimum tilt angle should be done for each location independently. It is worth mentioning that the tilt angle described here may not be the optimum from an economic perspective.

The optimum tilt angle was not expected to be equal to Edinburgh’s latitude angle for two reasons. First, places located at high latitudes tend to have an optimum tilt angle smaller than the location’s latitude [5]. Second, the diffuse to global radiation ratio (analysed in Chapter 4) is very high in Edinburgh. Therefore, a sensitivity analysis was carried out to validate the hypothesis. The same 5-kW PV system explained in previous sections was considered for the examination. Figure 5.5 shows the variation in the annual energy yield due to the tilt angle. It was found that the maximum annual energy yield is 5.186 MWh, and it corresponds to an optimum tilt angle equal to 34°. Figure 5.6 displays a comparison of the yearly energy production profiles for 3 cases: horizontal panels, tilted angle equal to latitude (55°), and optimum tilt angle (34°). It can be observed that the optimum tilt angle PV system has a better performance than the 55° tilt angle system during the summer.

The optimum angle result obtained was compared with the Global Photovoltaic Power Potential by Country report published by the World Bank [6], which determined that the optimum tilt angle for the United Kingdom is 39°. Since the calculations were limited by the irradiance data (only one-year data provided by SOLCAST), the optimum tilt angle found in this project can not be generalized. However, it was demonstrated that the generation modelling tool develops in Python can calculate the power time-series profiles and energy production for any tilt angle and installed capacity. The quality of the irradiance data is vital to obtain accurate results. Finally, Table 5.6 summarises the performance of the PV system for the 3 cases analysed. Generally, the capacity factor of PV systems is in the range of 10-25% [7]. Since the capacity factor values obtained for the 3 cases (horizontal, 55° tilt, and 34°tilt) are in the range of 10-12%, it can be concluded that Edinburgh is not the best location for high energy yield of PV systems. Moreover, the increase of energy obtained when the panels are tilted at 34° is 9.73%. The results lead to the conclusion that due to the high ratio diffuse to global irradiance and the high latitude of Edinburgh, optimizing the tilt angle of the PV systems does not significantly improve the annual performance of the panels.

Figure 5.5 Sensitivity analysis of annual energy yield

Figure 5.6 Comparison of annual energy production profiles

Table 5.6 Performance Comparison of PV systems

5.2.4 Identification of energy scenarios

So far, the focus of the analysis has been the performance of the PV system in terms of maximum power and annual energy production. The impact of the ambient temperature and the tilt angle has been exposed. However, the high penetration of distributed renewable generation (wind and solar) causes inadvertent stress on the distribution network [8]. During peak solar hours or maximum wind speeds, the production is higher than the local demand, and then the power flows are reversed in the low voltage network (bi-directional power flows). As a result, there exist some issues in the distribution network such voltage fluctuation, unbalance, overloads in feeders, harmonics, malfunction of relays, reliability, islanding, and security [9]. Therefore, it is necessary to identify the most representative daily energy scenarios to carry out regular simulations and analyse the network’s performance.

Since the solar and wind resource data used in this project is a 5-minute time step for a whole year, the prosumer modelling tool produces power time-series profiles made up of 105120 points. The selection of the most typical scenarios was based on maximum and minimum power generation. For the same 5 kW PV system analysed in previous sections, the top 10-day energy generation and bottom 10-day energy production were identified, Figures 5.7 and 5.8, respectively. It can be observed that the best days in terms of energy yield correspond to the summer and spring, being the 27^th of June the day of maximum energy production (around 39 kWh). On the other hand, the lowest daily energy production occurs in Winter, being the 5^th of January the worst day (approximately 0.8 kWh energy production). Accordingly, if an electrical study were required to analyse the implementation of energy storage devices, the power time-series profiles corresponding to the 27^th of June and 5^th of January would be exported to the power system software to carry out the study.

Figure 5.7 Top 10-day energy production

Figure 5.8 Bottom 10-day energy production

In like manner, the top 10-day maximum power and bottom 10-day power output were identified in Figure 5.9 and Figure 5.10, respectively. It can be observed that the best days in terms of power correspond to the summer and spring, being 10^th of June the day of maximum power output (around 4.03 kW, which represents 80% of the installed capacity). It proves the fact that not necessarily the days of maximum energy yield (27^th of June) and maximum power output (10^th of June) are coincident. The reasons were explained in the previous sections). Although, due to the high solar irradiance during the summer, both of them occur in June.

On the other hand, the poorest power output occurs during the Winter, being the 5^th of January the worst day (around 0.2 kW, which represents less than 5% of the installed capacity). In this case, the days of minimum energy yield and power output are coincidental. But it is not necessarily the same each year. Therefore, if it were required an electrical study to analyse the voltage fluctuations (overvoltage and Undervoltage), and unbalances due to the distributed generation, the power time-series profiles corresponding to the 10^th of June and 5^th of January would be exported to the power system software to carry out the study.

Figure 5.9 (a) Top 10-day maximum power output (b) Best day power profile

Figure 5.10 (a) Bottom 10-day maximum power output (b) Worst day power profile

This section has illustrated the importance of high-resolution power time series profiles in identifying the most representative energy and power scenarios for the subsequent electrical power system studies. Since the generation Python model can calculate power time series profiles for any number of points (the solar resource data define the time horizon), it facilitates selecting the critical scenarios that allow us to study the distribution network performance under the most necessary conditions.

5.3 Case Study B

The primary purpose of Case Study B is to illustrate how the developed modelling tool can provide generation and demand time-series profiles for a prosumer community group to analyse the impact on the low voltage network performance. The software selected for the electrical power system study is OpenDSS. The chosen location corresponds to an urban area of Edinburgh (geographic coordinates defined in Chapter 3). The prosumer community is made up of 30 households (Figure 5.11). The houses with rooftop PV systems are highlighted in green colour, whereas the homes with micro wind turbines are highlighted in blue colour. Table 5.7 and Table 5.8 summarizes the range of parameters of each household used by the prosumer modelling tool to calculate the photovoltaic and wind-based generation profiles, respectively. It is worth mentioning that the Python model provided 5-minute time step power time-series for 2019. Since the objective was to carry out a daily simulation on OpenDSS, selecting the worst-case scenario (maximum generation and minimum load) was necessary. The method to identify the day was the same as that explained in the previous case study (Section 5.2.4). As most households have PV systems (only four houses have micro wind turbines), the day selected corresponds to the summer. This step is essential because it allows us to analyse the scenario where the voltages lie outside the allowed operating limits (+10/-6%). In other words, when the distributed generation is high, and the load demand is low, the power flows are reversed, and overvoltage problems are remarkable.

The technical specifications of the PV panels are the same as those exposed in Case Study A; the complete datasheet provided by the manufacturer is presented in Appendix A.3. The orientation of most of the panels is towards the south and east. The convention adopted for the azimuth angle is traditional; the angle is designated as positive when it is westward from true south [10]. The installed capacity of each household is in the range of 2.79-4.96 kW. The orientation and tilt angle of each PV system were obtained from Google Earth. It is worth mentioning that the input data quality plays a vital role in generation profiles modelling. Regarding the wind-based generation, only the technical characteristics required by the Python model are presented in Table 5.8. The datasheets of each micro wind turbine are provided in Appendix A.3.

Figure 5.11 Prosumer community group

Table 5.7 Assumed parameters of rooftop PV systems

Table 5.8 Assumed parameters of micro wind turbines

5.3.1 Network configuration and components

Typically, a distribution transformer (11/0.4 kV) connects the medium and low voltage networks in the United Kingdom. There are 3-phase trunk feeders that supply a certain number of customers (households) [11]. It should be noted that residential customers are connected to the low voltage network (0.4 kV) by single-phase cables. Consequently, unbalances should be considered in the analysis of the network. Since an urban area of Edinburgh was selected for this project, it is assumed that the 3-phase feeders and the single-phase cables of the low voltage network are underground cables. In the UK, the statutory voltage limits for distribution networks are +10%/-6%. The network analysis was carried out in OpenDSS using a typical low voltage network model of the UK. Figure 5.12 displays the distribution model adapted from [12]. The 500 kVA transformer supplies electricity to 190 single-phase households, which have typical residential loads. The prosumer community (30 homes) described above was allocated to the second feeder of the network (red circle in Figure 5.12).

Figure 5.12 Typical Urban Low Voltage distribution network in the UK [12]

The distribution network consists of 7 types of underground cables, which can be identified by an uppercase letter. Table 5.9 contains the electrical parameters used to model the distribution lines (underground cables). Bear in mind that all the electrical parameters of the network were adopted from [12].  In regard to the substation, the parameters adopted for the 500 kVA distribution transformer are listed in Table 5.10. It should be noted that the resistance and reactance in per-unit are calculated own base. The connection of the 11/0.4 kV transformer is delta-star.  In the subsequent sections, a brief analysis of voltage variations, unbalances, power losses, and energy flows are carried out to describe some of the impacts of distributed generation on the low voltage network performance.

Table 5.9 Assumed parameters of underground cables [12]

Table 5.10 Assumed parameters to model the distribution transformer [12]

5.3.2 Load demand profiles

As shown in Figure 5.12, the distribution network is made up of 190 customers (households), grouped into 19 groups. It was allocated an identification code (from U1 to U19) to each group of customers to facilitate the construction of the model in OpenDSS. U14 and U15 are the groups’ identifiers corresponding to the 30 prosumer households analysed in this case study. It is worth mentioning that the DEXIMAX model created the demand curves (Active and Reactive power profiles) for each of the 190 households. Each daily power time-series profile is made up of 1440 points (1-minute time step). Figure 5.13 displays the aggregated demand corresponding to the whole low voltage network (190 households). It can be seen that the load shape is similar to the typical residential load curve characterised by the peak time around 20:00.

In the case study, the demand profiles were aggregated in 19 groups. Figure 5.14 shows the active and reactive power profiles corresponding to the group (U14), consisting of 15 households. It can be observed that the load curve does not have the same shape as the typical load curve obtained in the aggregated demand previously. That is why it is crucial to work with detailed load models that allow an accurate representation of the loads to carry out power system studies.  Figure 5.15 displays the demand profile corresponding to the group (U15), which is made up of 15 households as well. The main conclusion is that the consumer’s behaviour defines the shape of the load curve. The intermittency of residential loads due to switching on/off makes the variability of the demand be challenging to model. Accordingly, adopting typical load curves does not allow us to represent the loads accurately. When it comes to low voltage power system studies, it is vital to use detailed load models.

Figure 5.13 Aggregated load profiles

Figure 5.14 Daily demand profile group U14

Figure 5.15 Daily demand profile group U15

5.3.3 Generation profiles

From the data presented in Table 5.7 and Table 5.8, the Python modelling tool calculated the solar PV and wind-based power time-series, respectively. The prosumer community is made up of 30 households allocated to the second feeder. In other words, the prosumer community represents sixteen percent of the total number of homes of the low voltage network analysed. In like manner to the residential loads, the generation profiles were grouped into two groups (U14 and U15) to facilitate the construction of the model in OpenDSS. Group U14 is made up of 12 rooftop PV systems and three micro wind turbines, while group U15 is made up of 14 PV systems and one micro wind turbine. As expected, the shape of the aggregated profiles is very similar to that of a photovoltaic system since there are only three micro wind turbines in the prosumer community.

The day selected for the daily simulation is the 18^th of June because of the maximum generation identified. Figure 5.15 shows the daily generation profile corresponding to the group (U14). Since group U14 has four households facing east directly, the generation curve is shifted to the morning hours. It can be observed that the maximum power output occurs at around 10:30 am.  Another aspect to be taken into account is the low contribution of energy generated by the micro wind turbines. It can barely be seen that between midnight and 2 am; the power output is less than 1 kW. It is because the rated power of the rooftop micro wind turbines selected is deficient. However, if pole-mounted small turbines (around 5 kW) were installed instead of rooftop micro wind turbines, the power output would increase significantly during the night.

Figure 5.16 displays the daily generation profile corresponding to the group (U15). The shape of the curve is similar to that of the group U14. It is slightly less shifted to the morning hours than the group U14 because the orientation of most rooftops is south and southeast. The main conclusion of the power time-series obtained is the utmost importance of distributed generation modelling. The variability of both demand and generation requires high-resolution power profiles for the subsequent low voltage network performance assessment.

Figure 5.15 Daily generation profile group U14

Figure 5.15 Daily generation profile group U15

5.3.3 Results OpenDSS simulation

This section presents the main results of the daily simulation carried out in OpenDSS. To clearly visualize the impact of distributed generation on the low voltage network, all the figures below show a comparison of the electrical parameters of the network before and after the connection of the renewable energy generation, which is made up of 26 PV systems and four micro wind turbines. Figure 5.16 displays the time-varying active power flow through the distribution transformer. It can be observed that when the distributed generation is connected, the power flow is reversed between 8 am and 3 pm. The production is higher than the residential loads in the summer day analysed (18^th of June). Consequently, the surplus generation is exported to the distribution network. However, it should be noted that the peak demand occurs at around 20 h, and the PV generation is practically zero at that time (except in the summer when the daylight is the longest). That is one of the biggest problems related to solar PV generation; the prosumer community will consume energy from the distribution network unless energy storage devices are implemented. Unfortunately, electrical storage technologies are not currently economically feasible [13].

As the residential loads are connected to the network by single-phase underground cables, voltages unbalance is another aspect analysed in this case study. Figure 5.17 shows the daily voltage profile corresponding to the 0.4 kV trunk feeder that supplies energy to the prosumer community. Once the distributed generation is connected, the unbalance of the load voltage distribution network increases. The phases to which the renewable generation is connected experience a voltage rise, especially when the maximum power output is reached, and the residential load is low (around 10:30). Nevertheless, the voltage on the 0.4 kV trunk feeder lies inside the allowed operating limits (+10/-6%) for both cases with and without a distributed generation.

Figure 5.16 Distribution transformer power flows

Figure 5.17 Voltage prosumer community 0.4-kV trunk feeder

However, the points of connection of distributed generation tend to experience overvoltage problems [14]. It was found that the voltage rise on the lateral spurs and the single-phase service cable are out of the statutory limits. Figure 5.18 shows the voltage values for the whole distribution network at 10:30 am (the worst-case scenario identified).  Before the connection of distributed generation, the voltage at each bus network lies inside the allowed operating limits (+10/-6%). Once the DG is connected, the feeder, lateral spur, and service cable that connect the prosumer community experience a voltage rise. Consequently, the voltage of the point of connection reaches 1.11 per-unit, outside the UK’s statutory limits.

Since the prosumer community is made up of 2 groups of households (U14 and U15), it was expected that the group of houses that are farther to the distribution transformer (Group U15) experience the highest voltage rise. To validate this, the voltage profiles of groups U14 and U15 were plotted in Figure 5.19 and 5.20, respectively.  It can be observed that the voltage rise on Group U14 remains inside the allowed limits, although it is very close to 1.1 per unit. Whereas the voltage on the point of connection of Group U15, which is 85 meters farther than Group U14, lies outside the statutory limit between 9 -12 h. The main conclusion from this section is that the voltage rise limits the level of distributed generation penetration. It should be noted, however, that exist some approaches to mitigate the voltage rise. Reactive power compensation, coordinated voltage regulation, curtailment of generation, and resistance reduction are the most common approaches to cope with the voltage rise [14].

Figure 5.18 Distribution network voltage profiles at the worst-case scenario (10:30 am)

Figure 5.19 Daily voltage profile Group U14

Figure 5.20 Daily voltage profile Group U15

Finally, an energy meter was located on the trunk feeder. The prosumer community is attached to quantify the reduction of energy supplied from the distribution network after the PV systems and wind turbines are connected. The results are given in Table 5.11. Before joining the 26 PV systems and four micro wind turbines, the net energy is -212.47 kWh (energy supplied by the distribution network). The energy losses represent 1.88% of the electricity imported from the network.

When the DG is connected, the daily amount of energy produced is higher than the residential loads. Thus, the net energy produced by the 30 households is 397.63 kWh (energy exported to the network). However, the losses increase to 31 kWh, representing 4.87% of the daily energy produced by the prosumer community. It is worth mentioning that it does not mean that the prosumer community stops consuming energy from the network. As shown above, the peak demand is not coincidental with the PV generation curve.

Figure 5.11 Daily Energy comparison (30 households)

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