In this section a detailed description of each studied scenario is provided.

No demand side flexibility. Scenarios A1, A2 and B1 consider configurations without flexibility on the demand side:

• Scenario A1 [conventional supply (natural gas and electricity)] ‒ In scenario A1, the household’s DHW needs are supplied by a natural gas boiler and the electric demand is supplied by the photovoltaic installation and the grid;

• Scenario A2 (natural gas and electricity, with battery storage) ‒ In scenario A2, the DHW needs are supplied by natural gas, as in the previous scenario. However, the use of a battery is introduced to understand the impact of energy storage from both energy and economic point of view. The battery is designed to charge when there is PV surplus, and to discharge when there is demand and no PV production;

• Scenario B1 (all demand electrified) ‒ In scenario B1, a total electrification of household’s energy demand was considered. Since the gas boiler was replaced by an electric one, all the energy loads can be supplied by the PV installation, or the grid when PV power is not available.

The overall electric profile is the sum of the initial electric demand and the electrified DHW demand. The remaining amount of PV, when PV production exceeds consumption, is sold back to the grid.

With demand side flexibility. Scenarios B2 and B3 aim to improve the DHW loads of scenario B1, considering the same system components, while introducing demand side management of DHW loads through two different approaches: genetic-algorithms and heuristic optimization:

• Scenario B2 (DHW loads optimization with genetic-algorithms) The development of a genetic-algorithm is proposed in order to optimize the electrified DHW demand. The genetic-algorithm used was implemented in MATLAB^®, in similarity to the study conducted by Neves et al. [4].

  For the specific problem addressed in this study, the chromosomes have 24 genes (accounting for daily number of hours) and the values for each gene represent the DHW demand for each hour of the day. The objective function is given by the minimization of cost for the household owner, considering the balance between energy purchases and sales. The fitness given to each individual on the evaluation phase is the combination of the cost and the penalties that are assigned to them. The penalties are used to guarantee that the chosen chromosomes have specific characteristics. In this case, the penalties are applied to assure the satisfaction of the DHW needs. The algorithm used builds the annual consumption through the optimization of each day individually, saving the chromosome with the lower fitness for each day independently.

  The number of individuals and generations used for this optimization was 50 and 100, respectively. The crossover and mutation probability was assumed to be 70% and 5%, respectively;

• Scenario B3 (DHW loads optimization with heuristic method) ‒ The heuristic method developed for this scenario is similar to the one implemented in scenario A2, albeit using a DHW tank. The excess PV production is stored in the hot water tank as thermal energy, and when the tank is completely full, but still there is PV production, this energy is sold to the grid. The tank energy is used preferably before the use of grid energy, constraining the minimum energy in the tank at 10% of its maximum capacity.

Figure 1 presents a summarized schematic configuration of each scenario abovementioned.

Figure 1.

Schematic configuration of the considered scenarios

A typical Portuguese household at Lisbon, with three inhabitants (two adults and one child), was used as case study. The hourly electricity demand data for a year was accessed [15], resulting in a yearly demand of 3,381 kWh, peak demand of 2.95 kW and average daily demand of 9.3 kWh. Originally the house had a gas fired boiler for DHW and the electricity demand was exclusively supplied by the electric grid.

The DHW needs were estimated according to the current regulation for Portugal, that assumes a consumption of 40 L/day of hot water per person [16]. As such, a consumption of 120 L/day was assumed and distributed throughout the day to establish an hourly profile of hot water consumption. Then, this hot water profile was converted to thermal energy, assuming an initial and final temperature of 15 °C and 50 °C^†, respectively, which represents 5.5 kWh/day. When considering hot water storage equipment, a final temperature of 60 °C was assumed^‡. Also, the efficiency of the DHW equipment was taken into consideration (84% for the gas boiler and 97% for the electric boiler [17]) and the DHW profile was assumed constant along the year.

The DHW profile (using a gas fired boiler) and electric profile of an autumn typical week is represented in Figure 2. As an example, the PV production for this typical week for a PV system with 1.0 kW_p capacity is also presented in Figure 2 [18]. The PV production that exceeds the electric demand is mentioned throughout this work as the ‘Excess PV’.

Figure 2.

PV production (1.0 kW_p system), electric and DHW demand for an autumn typical week using a gas fired boiler

An economic analysis was performed regarding both the electricity and natural gas disbursements. For the scenarios with non electrified DHW (i.e., use of a gas-fired boiler), the natural gas costs were calculated according to its current retail price^§ and the associated fixed costs (fixed cost per day and soil use and occupation fee for Lisbon) [19], [20].

Regarding the electrical bill, a contracted power of 4.6 kVA was assumed and both simple and Time Of Use (TOU) tariffs were simulated. The electricity prices and fixed costs considered were the 2016 regulated tariffs^** [21].

According to the Portuguese legal framework, a prosumer is able to sell its excessive production to the grid at 90% of the monthly daily average of the Iberian Electricity Market (OMIE) price for Portugal [22]. The calculation of the energy sales to the grid considered the information of OMIE market for 2015, the average sellback price being approximately 5 cEUR/kWh.

The investment regarding the electric boiler for the scenarios with electrified DHW was considered as the difference between the annualized acquisition cost of an instantaneous gas fired boiler and an electric boiler with a tank of 150 L (representing the additional cost that had to be covered). The useful lifetime and investment of each equipment is presented below in Table 1, along with the scenarios where they are included. All the equipment costs presented below do not consider VAT.

The LCoE and the solar fraction were calculated to understand the behaviour of each scenario according to the installed PV capacity.

The LCoE curves for simple and TOU tariffs (Figure 3 and Figure 4, respectively) show a minimum for each scenario, which reports the optimal sizing of PV power installation.

Figure 3.

LCoE according to the installed PV power for simple tariff

Figure 4.

LCoE according to the installed PV power for TOU tariff

Figure 5 presents the solar fraction of each scenario as an indicator of the self-consumption penetration. Even though a detailed discussion is provided later, these figures have been presented here since the individual analysis of each scenario is described, in the following section, for its optimum PV sizing.

Figure 5.

Solar fraction according to the installed PV power

Besides the LCoE and the solar fraction, other parameters can be relevant when analysing the performance of different system configurations. One of these parameters is the maximum peak power of the grid purchases which, when reduced, can provide benefits both to the consumer, since it allows the reduction of contracted power, and the distribution network operator, by smoothing the load diagram. As reported in Table 2, scenario A2 shows a reduction on the maximum peak due to the use of a battery. For electrified DHW scenarios, scenario B3 (heuristic) presents the highest reduction of the maximum peak power (11.2%).

Hereafter, an individual analysis of each scenario is presented for the optimum PV power capacity showed in Figure 3 and Figure 4.

In scenario A1, the electric demand is 3,381.2 kWh/year (Table 3). The minimum LCoE occurs at a PV power of 1.0 kW_p and 1.25 kW_p for simple and TOU tariffs, respectively. With a PV installation of 1.0 kW_p (Figure 2), 68.1% of the PV production is used for self-consumption, which leads to a grid purchase of 2,363 kWh/year. The solar fraction for this sizing is 19.7% and the LCoE for simple tariff is 15.11 cEUR/kWh. Considering TOU, the PV sizing increases to 1.25 kW_p, decreasing the LCoE to 14.81 cEUR/kWh and increasing the solar fraction to 22.2% (Table 3).

In scenario A2, when a storage battery is considered, the optimum sizing for the system is 2.0 kW_p, for both tariffs. In the following figure (Figure 6), the PV sales to the grid are represented as negative values.

Figure 6.

PV sellback, PV production (2.0 kW_p system), electric demand and grid purchases in an autumn typical week (scenario A2)

The system does not need to purchase energy from the grid until achieving the bottom limit of the battery (20%). As for the PV sales to the grid, it only occurs when there is excess PV production and the battery is full (which occurs at the 6^th day for the presented typical week). The use of a battery promotes self-consumption, providing a fraction of PV use of 79.0% and a solar fraction of 45.8%. The energy purchased from the grid (904 kWh/year) decreases significantly compared to scenario A1, despite the increase on LCoE for both tariffs (Table 3).

For scenario B1, the electric demand is 5,744 kWh/year, which is higher than in the previous scenarios, due to the electrification of the domestic hot water with the use of an electric water heater (Figure 7). Higher electric demand leads to higher PV power sizing. Thus, for this scenario the optimum sizing is 1.25 kW_p and 1.75 kW_p for simple and TOU tariffs, respectively (Figure 3 and Figure 4).

Figure 7.

PV production (1.0 kW_p system) and electric demand for an autumn typical week for scenario B1

The grid purchases are 4,498 kWh/year and the self-consumption accounts for 66.6% of the PV production. The solar fraction and the LCoE obtained are 22.0% and 17.19 cEUR/kWh. When considering the TOU, the PV sizing increases by 0.5 kW_p, which is due to the fact that the energy price during the day is higher, thus an increase on PV production leads to savings on the cost of energy (Table 3).

The optimum sizing results for the genetic-algorithms optimization (scenario B2) yielded a 1.75 kW_p PV system for simple tariff and 2.0 kW_p for TOU. The genetic-algorithm allows a more uniform distribution of the energy requirements throughout the day. The peaks decrease significantly as it can be seen in Figure 8. The percentage of total energy consumption provided by renewable sources (PV), i.e., the solar fraction, is 39.7% and 41.4% for simple and TOU tariffs, respectively (Table 3).

Figure 8.

Initial and optimized DHW demand and excessive PV production (1.75 kW_p system) for simple tariff in an autumn typical week (scenario B2)

The TOU tariff presents less grid purchases, mainly during daytime. The grid purchase for TOU is 3,398 kWh/year, while for simple tariff is 3,490 kWh/year. Even though the difference is not very clear, the LCoE for the optimum sizing for TOU (14.47 cEUR/kWh) is lower than for simple tariff (15.76 cEUR/kWh). This difference can be justified not only by the higher PV capacity installed but also with a better usage of the grid, purchasing more energy in off-peak periods than in peak hours.

In Figure 9 the daily energy cost is presented along with the fitness value for each day of the year. The fitness of the majority of the days is very close to the daily energy cost, which means that the chosen chromosomes are not violating significantly any of the imposed conditions. The cost presented is a balance between the purchases and sales of energy to the grid.

Figure 9.

Daily energy cost and fitness for each day and PV production for a PV capacity of 1.75 kW_p and for simple tariff (scenario B2)

In the middle of the year, when higher radiation occurs, the daily cost of energy assumes negative values. This is due to higher excessive PV production that leads to higher sales of photovoltaic energy to the grid. However, it is worth noting that the electricity purchases avoidance, due to self-consumption, contributes more to the reduction of the overall energy cost than the energy sales to the grid. This regards to the sellback price, established by the Portuguese regulation, which is significantly lower than the electricity purchase price. As it was expected, when lower values of radiation occur (winter) the cost of energy is higher and so is the daily balance of energy cost.

In scenario B3, the photovoltaic production that is not used for the electric demand is used to “charge” the DHW tank. The minimum LCoE for both tariffs occurs with a 2.5 kW_p PV system. Hereafter, the behaviour of the system can be observed (Figure 10).

Figure 10.

Initial and optimized DHW demand and PV excess in an autumn typical week for a 2.5 kW_p PV system (scenario B3)

The hot water tank is able to store the energy as thermal energy by heating up the water, when excessive PV production occurs. In Figure 10, one can observe that with the sizing presented (2.5 kW_p), the remaining PV production is very low and so are the energy sales to the grid (514 kWh/year). Almost all the energy produced is used for self-consumption (86.2%), as a consequence the energy purchases decrease to 2,518 kWh/year. As the optimum sizing is the same for both tariffs, the main difference is on the minimum LCoE: 14.63 cEUR/kWh and 14.11 cEUR/kWh for simple and TOU tariff, respectively (Table 3).

The use of the heuristic method can bring benefits regarding the peaks of energy that are no longer static, and as Figure 10 shows, they tend to decrease.

Regarding the LCoE, scenario A1 (gas boiler) provides the best energy supply solution up to 1.5 kW_p of installed PV (Figure 3 and Figure 4), mainly due to the reduced cost of natural gas, compared to electricity costs. When PV production becomes significant, scenario A1 is not able to take advantage of the increased PV production, since energy storage is absent in this scenario and the consumption peaks do not match the solar resource.

In scenario A2 (battery), the LCoE is the most expensive for both tariffs (Figure 3 and Figure 4). The second most expensive scenario for both tariffs is scenario B1, where the system configuration is not able to take advantage of the PV production for self-consumption, because of the decoupling between DHW demand and production profiles. In addition, the increased electricity purchase due to electrified domestic hot water penalizes this scenario, since natural gas is more affordable.

For genetic and heuristic algorithms scenarios (B2 and B3, respectively) the results showed that, for simple tariff, the LCoE is very similar between these two scenarios up to 1.25 kW_p of installed PV capacity (Figure 3). The PV production not used in instantaneous self-consumption (DHW and/or electric demand) is extremely reduced in these cases, which leaves a narrow space for improvements. For larger PV capacities, scenario B3 performs best since it aims to maximize the stored thermal energy, while scenario B2 focus on charging only the correspondent to the daily DHW needs.

When comparing the performance of both optimization scenarios considering TOU tariff (Figure 4), scenario B2 presents lower LCoE up to 1.75 kW_p of PV capacity. This may be explained by the fact that scenario B3 is not “tariff sensitive” and when PV production is not enough to fulfil the DHW needs, the system relies on grid electricity at the hour of the demand (peak hour) when energy is most expensive. Since, in scenario B2, a cost function optimization is performed using genetic algorithms, this scenario is pointed as the best solution for this range of PV powers.

It is interesting to compare the thermal storage (scenario B3) against the electrochemical storage (scenario A2), since the changing variables are the acquisition cost of the storage devices, their technical characteristics and the end use of stored energy. Due to the high cost of battery acquisition and the reduced amount of excessive PV production for smaller installed powers, scenario A2 represents the worst solution, while B3 clearly represents a better system configuration, having a lower LCoE for all PV powers, in both tariffs.

Regarding solar fraction (Figure 5), for smaller PV installation (0.25-0.5 kW_p) the results are very similar within the scenarios since reduced amount of PV production is almost totally used in electric demand. When the excess PV production becomes significant the performances of the considered scenarios differ notably, being scenario B3 the one that maximizes renewable energy self-consumption. Scenario A1 presented the lower solar fraction, but by adding a battery and an energy management strategy (scenario A2) the solar fraction nearly doubles.