In this section, we demonstrate the properties of the framework through three scenarios. The aim of these results is to demonstrate the versatility of the framework for future case studies. We focused our attention on the capability of the framework to address different scenario requirements and on its flexibility. Scenarios include a few households and results are shown for one single household to prove that the strategy or behaviour implementation works properly. In particular:
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(i)
Case study 1 provides an example of the working principle of the framework, i.e. select the desired level of interest and test a simple strategy;
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(ii)
Case study 2 proves the capability of the agent-oriented framework to work in a co-simulation environment and the re-usage of different modules;
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(iii)
Case study 3 proves the flexibility of the framework, which can also be used to implement implicit demand response strategies. In other terms, the simplified behavioural model presented here can be substituted with more complex modules that model the change of behaviour of the user.
Case study 1
Case study 1 considers a simple Home Energy Management System (HEMS) that optimally schedules certain appliances that can be shifted in time, i.e. washing machine and dishwasher (if present), under a variable tariff. Thus, the HEMS efficiently manages the usage of appliances inside the single house.
For this reason, Case study 1 requires a stand-alone configuration involving only two levels, i.e. four Household agents, ten User agents and as additional modules the “Appliance” and the ”Optimisation” modules (the block in red under the Household agent in Fig. 4). The “Optimisation” module acts as the HEMS. The simulation time of the scenario has been set to one day with a time resolution of 10 min, i.e. 144 time steps in a day.
Since the HEMS needs to know in advance the desire of the user for turning on an appliance the day after, we need to simulate the initial intention of the household for the next 24 h, i.e. n equal to 144 time-steps in the future (Fig. 2, “Initial-intention”). This consumption pattern is the baseline against which the change can be observed. Instead, the “change” block (Fig. 2) is implemented, as already explained, by the “Optimisation” module. Thus, the energy consumption of the appliances that can be shifted in time is optimally allocated. In this scenario, for demonstration purposes, the Household agents allow shifting the appliance at any time during the day.
The mechanism underlying the model that generates the consumption was validated in Bottaccioli et al. (2019), thus we will only show the behaviour, i.e. the baseline and the modified consumption, for a single household with a housewife, a full-time worker and their kid. For each person, the corresponding transition probability matrices where obtained from the Italian Time Use Survey provided by the Italian National Institute of Statistics (ISTAT 2022).
For this scenario, the HEMS will determine the best time slots for the appliances considering the day-ahead prices. The day-ahead prices used in this scenario are shown in Fig. 5. We picked the day-ahead prices of a random day in 2013 provided by the Italian Power Exchange—(NORTH) (GME). We then added system and network charges (ARERA 2018) and fees (excise tax and VAT (Masci)).
However, to evaluate the implication for the Energy Provider Agent in presence of many customers equipped with a HEMS, we performed a second simulation with 2000 Household agents and 4000 User agents (random composition of families). We considered the same day-ahead prices, but we decided to limit the allowed shifting of the appliance to (i) \(\pm {3}\) h and (ii) \(\pm {5}\) h from the initial desired starting time, as long as the shift is performed inside the same day the users wanted to the appliance.
Results for Case study 1
For the first scenario, Fig. 6 shows when the Household agent wanted to turn on the washing machine (light-blue), i.e. when the user initially desired to use the appliance, and when it has been shifted according to the optimisation together with the rest of the consumption pattern (turquoise). The washing machine was initially scheduled around 1 p.m. However, since the electricity was cheaper for a longer period in the morning, the washing machine had been turned on at 9 a.m. Thus, we do not only observe the optimal schedule according to the HEMS but also the “initial-intention” for every single household. This allows us to make deeper considerations when considering a limited time window for the shift.
For the second scenario, in Fig.7 it is possible to observe the effects from the point of view of the Energy Provider Agent when \(\pm {3}\) h of shift from the desired starting time is allowed. The shiftable appliances with an initial start around noon are anticipated and scheduled in the best time slots, as for the household example visible in Fig. 6. Those appliances scheduled around 8 p.m. are postponed after the highest prices since they cannot be shifted many hours in advance.
Running again the simulation for the case in which \(\pm {5}\) h of shift is accepted, we observe the results shown in Fig. 8. Since more time is allowed for the shift, a secondary peak has been created. Indeed, more appliances have been shifted in the best time slots. The appliances scheduled in the evening are anticipated since it is more convenient.
Thus, this case study allows us to understand the benefits for a single household but also the possible threats for the Energy Provider Agent if no power limit is introduced.
Case study 2
To prove the capabilities of our solution in working in a co-simulation environment where the agent-oriented framework interacts with external and even third-party simulators, we developed the Case study 2. It considers a HEMS for prosumers by extending the previous Case study 1 including the PV generation. For this purpose, we exploited an external PV panel simulator developed in our previous work (Bottaccioli et al. 2018) and the Mosaik co-simulation framework, and its APIs, to couple this PV simulator with our agents (see Fig. 9) (De Vizia et al. 2022; Scherfke 2018). As for the Case study 1, Case study 2 considers the household and the user levels, the “Appliance” and the “Optimisation” modules, thus it uses the same configuration of the Case study 1 for the agents. The presence of the “PV panel simulator” slightly changes the MILP formulation, as described in section “The appliance module and the rule modules”. The PV production for a hypothetical cloudy day used in this scenario is illustrated in Fig. 10.
Moreover, we performed a second simulation for an entire week (time resolution of 10 min and same household selected for demonstration purposes in Case study 1) since certain patterns can be appreciated only by considering weekly habits. The 1st of January was Tuesday. Saturday and Sunday are clearly distinguishable since these are the 2 days with a lower consumption (and no appliances that can be shifted in time). The households installed a 3 kW PV system each, thus PV production changes depending on the day. \(Cpv_t\) has been set to 0.13 €/kWh according to IRENA (2018) and \(Cto_t\) to plausibly 0.1 €/kWh.
Results for Case study 2
Figure 11 shows an example of optimal scheduling for a single household in the Case study 2. The washing machine was initially scheduled during the evening when there is low or no PV generation. Thanks to the HEMS, the use of the appliance is anticipated in the morning, during high PV production, since the use of its solar energy is free of charge for the prosumer. For this scenario, we also check power balance in Fig. 12, which is clearly respected. In yellow, it is possible to observe the PV production. A good amount of it, i.e. the portion in green, is sold to the main grid, while the rest is used for self-consumption by the prosumer. During dark hours, instead, the electricity demand is satisfied by the main grid, i.e. the area in orange.
The results for the second simulations, visible in Fig. 13, highlight the tendency to anticipate the use of the appliances during daylight hours to save up. It can be also noticed that during nights the consumption of the household is very low as expected for a residential consumption pattern. Specifically, we simulated the first week of January 2013 in Fig. 13.
Case study 3
Case study 3 simulates a group of simple customers under Time of Use tariffs. Therefore, for Case study 3 a stand-alone configuration with all the three levels, i.e. Energy Provider Agent, Household Agent, User Agent is needed. As additional modules, the “Appliance” and “Behavioural” are used (see Fig. 14). In this scenario, the Energy Provider Agent exposes its customers to Time of Use tariffs. These have been taken taken from Carmichael et al. (2014): (i) High tariff, i.e. 67.2 pence/kWh (ii) Normal tariff, i.e. 11.76 pence/kWh and (iii) Low tariff, i.e. 3.99 pence/kWh.
Again, it is important to know the baseline, i.e. the hypothetical electricity consumption under a flat tariff, and the change in consumption under Time of Use tariffs modelled thanks to the “Initial-intention” mode. This time the “change” block is implemented through the “Behavioural” module (the block in red under the Household agent in Fig. 14). Thus, as already explained, the shift in time of the load is performed according to a probability p and the turning on of the appliance occurs at a random time during the Low tariff communicated by the Energy Provider Agent.
For this case study, we also performed a second simulation with 150 Household agents and 334 User agents (random composition of families) and a probability p of a change in the energy consumption equal to 0.5. Indeed, also in this case it is interesting to observe the effects from the Energy Provider Agent perspective. We simulated consumption for 1 week and we plot the average electricity consumption over the 24 h comparing the initial consumption of the households and the one obtained after the households are exposed to ToU tariffs.
Results for Case study 3
The result for the Case study 3 is plotted in Fig. 15. The curve in light blue displays the intentional behaviour of the user, while the turquoise curve represents the behavioural change of the user after the communication of the tariffs as explained in “The appliance module and the rule modules” section. Thus, under a flat tariff, the user would have used the dishwasher during the evening. However, since under the ToU tariff the moment of the turning on corresponds to a high tariff period, the user decided to anticipate from 9 p.m. to 10 a.m. the use of the dishwasher when it is more convenient for it during a low-tariff period.
It is clear that since the appliances are randomly allocated inside the low tariff period, we do not observe secondary peaks. Instead, if all loads are moved just before the beginning of the High Tariff, we would create new peaks (blue curve in Fig. 16). Results are visible in Fig. 16 where the x-axis represents the daily time slots and the y-axis the mean aggregated value of household consumption, normalised using the peak value. An in-between scenario with a two-rate ToU tariff was implemented by Vellei et al. (2020), where the shift of the loads was not exactly at the beginning or at the end of the off-peak hours, but based on an exponential distribution.
Therefore, it is important to be able to forecast the consequences of a DSM strategy considering different scenarios with different technologies involved, e.g. random behaviour of people or coordination of HEMSs to smooth the peak as opposed to individual greedy HEMS or similar technologies.
However, independently of the behaviour, the proposed framework would be able to include the corresponding module which is the focus of this work.