Renewable electricity generation is progressively improving in EU countries. In particular, investments in photo-voltaic (PV) systems for self-consumption are getting larger and at the end of 2012 Germany and Italy were the top two countries in terms of cumulative installed solar PV capacity with 32 Gigawatts (GW) and 17 GW, respectively (Brown, 2013). The European Union solar photo-voltaic market picked up in 2015 after three successive years of decline. It registered 3% growth over the twelve-month period, by installing 7226 MW, which took Europe’s installed capacity to date to 94.6 GW. The global market soared by comparison, gaining 25% year-on-year and connecting at least 50 GW, which took global PV capacity past the 227-GW mark EuroObserver (2016).

Many incentive schemes allowed for attractive returns for the consumer during the past years, but nowadays and in the future only PV self-consumption provides significant benefits, which directly impacts capability to meet ambitious climate protection and energy policy targets. In fact, the European Union has established binding renewable energy targets with the goal of having the entire EU derive 20% of total energy consumption from renewable sources by 2020 and self-consumption can provide significant impetus to meet this target. The self-consumption of solar energy refers to the proportion of energy which is used directly in the building where a photo-voltaic (PV) system is located. It is calculated as the ratio of directly consumed energy to generated energy.

But to improve the efficiency of energy management it is necessary to develop, implement, and evaluate novel energy management concepts and strategies. The increasing of such a decentralized production of green energy is affecting the current energy management scheme both at the grid and at the user level. In fact, the integration of energy production systems such as PV (photo-voltaic) systems is changing residential buildings from passive energy consumers to active prosumers (producer/consumer). At grid level the amount of energy that is not consumed locally must be transported to the next consumer or stored somewhere. These energy flows introduce transfers peeks and energy loss along the lines, which must be addressed by greater investment at grid infrastructure level. Many issues are related to the fact that the amount of consumed electricity and production by photo-voltaic systems vary over the course of the day, from season to season and depending on the weather conditions. Users may not have the opportunity to switch-on their appliances when the PV is producing because they do not know when or because they are outside or simply because they do not need those appliances at that time. For this reason there is no alignment along the day between production and consumption. At the user level, this limits the optimal utilization of green energy and affects the budget spent. In fact, the feed-in tariff is lower than what people pay for the purchase of electricity. That means it is not convenient for the prosumer to sell energy to the General Companies.

A battery storage inside each household could appear a trivial solution, but the cost of these battery systems, and the environmental effects due to the disposal issues, is a deterrent so a self-adaptation mechanism is needed.

The CoSSMic project1 proposed an intelligent scheduling of user’s consumptions within a neighbourhood in order to exploit the flexibility of a community of collaborating users which are available to share their energy and to adapt their behaviours. The main goal was to enable the collaboration among households in a way that the energy produced by PV plants are consumed by the neighbour that is able to do it. An autonomic system, implemented by software agents, was able to shift in time the loads in each neighbourhood, according to users’ constraints and preferences, so that the use of renewable energy is optimized. Appliances (refrigerators, washing machines, driers, dishwashers, water heaters, air conditioners) equipped with intelligent controllers are represented by software agents negotiating energy exchanges according to availability, demand, user’s preferences and constraints. The energy negotiation between agents will return rewards to local producers.

To obtain the maximization of self consumption, a predictive approach was considered, but prediction of PV production and learning of consuming profiles are affected by many errors. Prediction is affected by limited accuracy and precision of weather forecast. Consumption of appliances can depend on environmental conditions and not all devices can be monitored and controlled independently.

The original contribution of this paper is a hybrid approach that complements the CoSSMic predictive schedule with a reactive solution to compensate the prediction error on PV production. We aim at controlling continuously running appliances such as water heaters, heat pumps and air conditioners, in order to increase self-consumption of single households without compromising the collaborative strategy and the global optimum at neighbourhood level. The computation of the optimal set of control signals is formulated as a linear optimization problem and the solution has been implemented by an open source solver for mixed integer linear programming. We also demonstrate, using real data which have been collected from 12 German trials, the feasibility and the improvement by the reactive correction when freezers, fridges, heat pumps, air conditioners are interrupted under different constraints.

Problem stated and background is summarized in Section 2. Related work is discussed in Section 3. Section 4 describes the CoSSMic prediction solution. In Section 5 we introduce real trials and related studies that have been used to profile energy sources, consuming devices and user habits. Section 6 formulates the modelling approach. A proof of concepts is defined in Section 7 and some preliminary performance analysis are discussed in Section 7.4. Finally conclusion is due.

Our goal is the improvement of self-consumption by a smart scheduling that shifts the consuming loads to match the production profile in order to maximize the self-consumption, that will also minimize the amount of energy reversed into the grid, while satisfying user’s constraints. The problem we address is the optimal distributed schedule of appliances in order to align energy consumption to PV production during the day. Exploiting the users’ flexibility, the problem is to find the best start time of consuming appliances.

In Fig. 1, the power profiles of different devices are shown. In particular, the blue series represent the power production of a solar panel during the day. Red series represent the average power consumption of a household during the day. Consumer1 (C1) and Consumer2 (C2) represent the power consumed by two different appliances. They can be shifted by the scheduler within the time-window defined by the user. In Fig. 2 the yellow area above the average consumption represents the current power that was not used by the household and flowed to the grid. The blue area represents the self-consumed energy. A limited improvement of the self consumption is observed in Fig. 2(b) when the power profiles are shifted toward the peak of PV production.

Even if the improvement does not result very relevant we must consider that in a micro-grid there will be many devices and other PV plants. The new schedule has moved the consumption in a time slot where the probability of consuming green energy from neighbours is higher. The red peek over the yellow area could contribute to improve the self-consumption of the neighbourhood, meanwhile the reduced consumption at the end of the day will surely reduce the needs of dirty energy, so providing green energy to other appliances. Within the same neighbourhood a benefit would be also a reduced energy flow between different sections of the power grid.

Much effort has been spent on the investigation about the self-consumption of local generated electricity and the related optimization. Castillo-Cagigal et al. (2011) present, using simulated and real experiments, the effects of storage and Active Demand-Side Management (ADSM) in a house equipped with Photo-Voltaic (PV) generation and grid connection. The objective is the self-consumption maximization, reducing the use of the grid and supplying the highest amount of demanded electrical energy from the local sources. Results have shown the house electrical energy balances in daily and yearly studies, activating and deactivating the ADSM system and modifying the battery capacity. The use of both techniques increases the energy management considerably and allows the implementation of different electric behaviours in order to achieve a specific energy objective. But the number of possible cycles and calendar life makes the utilization of storages expensive and not environment-friendly Mulder et al. (2010). In Matallanas et al. (2011) self-consumption possibilities of the local electricity generated in a grid connected to low voltage PV system are analysed. This contribution focuses on theoretical and simulated studies of the energy flows and exchanges that take place within the system and the influence that Demand-Side Management and storage systems have. EPOS Pournaras et al. (2008) is a self-adaptation mechanism developed to aggregate energy plans devised by TCA software agents, to minimize fluctuations in demand, acquiring stability, minimizing oscillations in a global energy network. Self-optimization emerges through coordination of plans by agents. For self-adaptation, EPOS combines the effects of convergence in the cumulative plans over the tree overlay and the memory of previous plans. Mohamed and Mohammed (2013) propose an effective algorithm for optimizing distribution system operation in a smart grid, from cost and system stability points of view, that aims at controlling the power available from different sources. They try to satisfy the load demand at the lowest cost while giving the highest priority to renewable energy sources. In case of deficiency in the power, a fuzzy system was proposed to control the sharing of the power between the grid and the battery system so using storage as a buffer for the predicted large loads to increase the stability of the system and reduce voltage dips. Chabaud et al. (2013) focus on a multi-criteria approach for energy resources management in buildings equipped with energy production and storage systems. This approach takes into account the way the building and the electricity grid interact. The aim of the strategy is to improve energy self-consumption while minimizing the negative impact of the local production on the electricity grid. Energy and economic criteria are proposed to evaluate the strategy. A software is used to model the thermal behaviour of a single-story house, inhabited by four persons and equipped with photo-voltaic solar panels, a vertical-axis windmill and batteries for electricity storage. The results obtained in simulation prove that it is possible to design in an optimal way the systems and find interesting configurations. Silva et al. (2012) propose a short-term energy resource management methodology for smart grids where short-term scheduling is used to reschedule the previously obtained schedule taking advantage of the better accuracy of short-term wind forecasting in order to obtain more efficient resource scheduling solutions. The used optimization is based on a Genetic Algorithm (GA) and the feasibility of the obtained solution is technically validated using realistic power system simulation. In Mohsenian-Rad et al. (2010), the use of optimization algorithms to achieve end-consumer energy management has been explored. A powerful convex optimization (linear programming) technique was proposed to schedule the power of individual appliances. Nevertheless, it is not suitable for all appliances in practice because some appliances have a fixed power consumption pattern, which means that once the appliance is scheduled for operation, it has to operate according to its own power consumption pattern until the task is finished. The power consumption during the operation of the appliance is not under the control of the optimizer, so only the starting time can be optimized. A conceptual Mixed-Integer Linear Programming (MILP) model, showing typical trade-offs in energy planning is presented in Moret et al. (2016). Authors demonstrate that, in the uncertain domain, investing in more efficient and renewable technologies can be economically optimal.

CoSSMic (Collaborating Smart Solar-powered Micro-grids - FP7-SMARTCITIES-2013) is an ICT European project that aims at fostering a higher rate for self-consumption of decentralized renewable energy production by innovative autonomic systems for management and control of power micro-grids on users’ behalf. CoSSMic research partners are Stiftelsen Sintef, International Solar Energy Research Center Konstanz (ISC), Second University of Naples, Norges Teknisk-Naturvitenskapelige Universitet, University of Oslo, Sunny Solartechnik, Boukje.com Consulting. City of Konstanz in Germany and province of Caserta in Italy are project partners themselves and provided trial sites for experimental activities and validation of results.

The CoSSMic Architecture is described in Amato et al. (2014a) and Amato et al. (2014c). The CoSSMic Multi Agent System (MAS) is in charge of implementing a distributed task scheduler within the conceptual architecture of CoSSMic, using energy negotiation and shifting the loads (when it is possible) to minimize the energy exchange between the neighbour and the public power grid, as it is described in Amato et al. (2014b). Ideally, the pool is at the zero level when the energy production within the neighbourhood matches the consumption, and there is no exchange of energy with the grid.

The system provides also functionalities for the management of devices, like electric cars, allowing to switch them on/off by an interactive control or automatically, according to preferences and constraints set by user. For example, the system must allow the user to specify earliest and latest start time for appliance, charging policy for energy storages, etc. Autonomy and proactivity of software agents will allow for the automation of power management, while still leaving the user in control through the setting of simple parameters such as earliest and latest start time of appliances, as it is detailed in Amato et al. (2015).

Consuming profiles of appliances are predicted using a continuous learning algorithm that exploits monitoring information. PV production is based on the weather forecast data provided by third party services and PV plant configuration. Weather forecast service provides environmental parameters such as irradiation, temperature and humidity, over a time horizon of 8 hours.

The optimal schedule is computed by a one-to-one negotiation between consumer agents and producer agents. Consumer agents ask for the best starting time of their appliances according to a defined time-window and an energy profile. The producer agent returns the best starting time, if it has enough energy to satisfy the request. If there are not producers that can provide Green Energy, then the appliance consumes from the grid at the latest start time.

In our case the main issues are related to the complexity and the accuracy of the prediction model for the PV production and to the uncertainty about the weather forecast prediction. Moreover, the behaviour of consuming appliances can change each day according to a number of parameters. Let us consider the external temperature in the case of a refrigerator and an air conditioner, or the user’s needs for the electric cars or for the oven. They will affect both the starting time, the power profile and the amount of energy consumed by each appliance. Moreover, violations of the planned usage or simply some failures can occur.

In any case the system cannot predict in advance short term system fluctuations caused by system dynamics or component transients. For these reasons the utilization of a reactive approach for short term corrections is mandatory. To improve the CoSSMic predictive model, here we propose a complementary approach consisting in the reactive control of some devices which can be switched-off or switched-on without affecting their correct behaviour.

In the case of a reactive solution the main issues are related to how fast the power produced and consumed by PV plants and appliances can change. In fact, we should be able to evaluate the current availability of energy in real-time and we must suppose that such information can be used to take a decision for the future. This means that the system must be able to collect data and to process them in a time slot that is so short that the measured power can be supposed constant.

The decentralized solution of CoSSMic, that is based on a distributed negotiation between software agents running in different households, could not satisfy real time constraints of the reactive approach. It would be neither feasible nor scalable. For this reason we will apply the reactive corrections only locally, at household level.

Before addressing the resolution of the problem it is necessary to classify different devices according to the power required for the operating cycle; frequency of use on a daily basis; type and duration of the operating cycle. We identified the following classes at the beginning of the CoSSMic project. Related work provided power profiles. For example, load profiles of major household appliances in the U.S are available at www.ari.vt.edu/research-data/. They include two clothes washers, two clothes dryers, two air conditioners, an electric water heater, an electric oven, a dishwasher, and two refrigerators. Their electrical power consumption data are provided in one-second or one-minute intervals. Data are represented as an ordered list of samples. The data were gathered from two houses in Virginia and Maryland in 2012.

The problem presented in the previous section is formulated here as a scheduling problem. The goal is to plan the time when appliances will be switched on or off, to use as much PV energy as possible during the period of production, according to user’s constraints and preferences.

The predictive scheduling is addressed for the full neighbourhood. We defined $de{v_{i}}$ a smart device with sensing and switching capability. It can produce, or consume energy. A storage will be represented by a couple of devices, a consumer and a producer. Of course not every device can be equipped with such kind of capability or can be controlled by an autonomic system. In fact, the usage of computer desktops or televisions will depend only on the user’s will. Moreover, devices which do not absorb a relevant amount of energy or which are simply not equipped with controlling capability will be included in a background load.

Let us introduce also the following definition:

The objective is the maximization of daily self-consumption of the all neighbourhood that corresponds to the minimization expressed in Eq. (1).

The set of assigned start times represents the task schedule that minimizes the total energy absorbed from the grid. The background load will include continuously running devices and will be split in different chunk, which correspond to single run devices whose run cannot be shifted (EST==LST). They are used to take into account the actual available PV energy. We do not provide additional details about the implementation, but the reader can refer to Amato et al. (2014a).

We introduce here the increment of self-consumption in the neighbourhood by the CoSSMic scheduler and demonstrate the improvement due to the reactive switching of continuously running devices, when the production is different from prediction.

We evaluated the utilization of a linear solver for the resolution of the reactive formulation introduced in Section 6.1, starting from the evaluation results of the CoSSMic project and using the data collected from trials. We used lpsolve software,5 which is a free Mixed Integer Linear Programming (MILP) solver. lpsolve is a free (see LGPL for the GNU lesser general public license) linear (mixed integer) programming solver based on the revised simplex method and the branch-and-bound method for the integers.

Smart management of energy demand is the key for improving self-consumption in smart grids. In fact PV plants do not always produce the energy at the time it is needed. CoSSMic is an ICT European project that aims at fostering a higher rate for self-consumption of decentralized renewable energy production by connecting up to household appliances and scheduling when to switch them on, according to users’ constraints and preferences, to use as much PV energy as possible during the period of production. In CoSSMic project, and in related work, prediction of PV production is based on the weather forecast data provided by weather service and on consuming profiles, which are built using a continuous learning algorithm that uses monitoring information. The objective is the planning of an optimal collaborative schedule of energy workloads within a neighbourhood. However, complexity of prediction of energy production and unforeseen causes of consumption may affect the planned strategy for smart energy management. To address in real time such unpredictable events we proposed here a reactive approach for short term corrections to complement the CoSSMic predictive model. We presented an original formulation of the problem and, after some preliminary hypothesis, its resolution using techniques for linear optimization. Simulation results were presented to demonstrate the feasibility of the approach in terms of performance to manage short terms for recovering energy mismatch which affect the planned optimal schedule. Improvement in terms of self-consumption are also estimated using original measures collected by the project trials integrating both predictive and reactive techniques. Those encouraging results can be used also to reduce the dimension of an energy storage that could filter and compensate all power fluctuations.