## 2 Materials and Methods  
### PMC Configuration  
Main features of PMC households are summarized in Table 1[24; 27]. Ten out of twenty-two households owned a \(\upmu\)-CHP unit with a nominal power of 1 kW of electrical energy. Adding to that, a \(\upmu\)-CHP unit was able to produce 6 kW thermal energy to heat the house, using a hot water buffer of 210 L. Four of the households had rooftop PV installations with an area and nominal power given in Table 1. Through the local smart grid, 18 other households virtually shared a PV system on a farm located 2.3 km from Groningen, the actual location where this smart gird pilot is installed. Each household received a nominal power of 1590 W\({}_{\text{p}}\) from this farm.  
The smart appliances installed in this pilot were smart washing machines, smart dishwashers, and smart hybrid heat pumps (SHHP) with a condensing boiler. The SHHPs contained heat pump units with a thermal power output of 4.5 kW and a condensing boiler with a thermal power output of 20 kW. Additionally, a 210-L hot water buffer was used in these systems. In this pilot, the smart washing machines and smart dishwashers were programmable by time so that users could program it to their needs or comfort expectancies. Half of the households had been equipped with these two smart appliances. The expected outcome of experiments with PMC household smart energy systems matched the time of use of smart appliances with PV power production by a smart algorithm. Figure 1b shows the household consumption and production of a PMC household equipped with PV and \(\upmu\)-CHP in the winter, when irradiance levels are low. It gives an example of how PV and \(\upmu\)-CHP jointly produce electricity to meet the demand, aiming at minimizing the power flow from the grid.  
The activation of \(\upmu\)-CHP was organized by PowerMatcher, which not only took into consideration the self-sufficiency of the households but also the neighbors' demand, the dynamic price signal, and the heating requests. Moreover, we were able to see the help of \(\upmu\)-CHP in instantaneously counter-balancing high demands, especially visible in the evening, where usually peak hours occur in the Netherlands (example in Figure 1b is a weekday). The purchase from the grid was brought down  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Distributed Energy Sources** & **Details of PV Systems** & **PV Production** & **Smart App.** \\ \hline \multirow{4}{*}{10 Households with \(\upmu\)-CHP} & 2 Households: & 500 W\({}_{\text{p}}\), 4 m\({}^{2}\) & 150 kWh & No \\  & Rooftop PV & 2200 W\({}_{\text{p}}\), 18.7 m\({}^{2}\) & 1833 kWh & Yes \\  & 8 Households: & 1590 W\({}_{\text{p}}\), 11 m\({}^{2}\) (on average & 880 kWh (on & 4 Households out \\  & Virtual PV & per household) & average per & of 8 \\ \hline \multirow{4}{*}{12 Households with Hybrid Heat Pump (4.5 kWh & 2 Households: & 500 W\({}_{\text{p}}\),4 m\({}^{2}\) & 350 kWh & Yes \\  & Rooftop PV & 3840 W\({}_{\text{p}}\), 16 m\({}^{2}\) & 1858 kWh & No \\  & 10 Households: & 1590 W\({}_{\text{p}}\), 11 m\({}^{2}\) (on average & 880 kWh (on & 5 Households out \\  & Virtual PV & per household) & average per & of 10 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the smart grid pilot settings and photovoltaic (PV) energy production for 2012 in PowerMatching City.  
to less than 500W by \(\upmu\)-CHP, and the electricity plus including PV production was either delivered to the grid or served for smart appliances, heating, neighbors, etc. Therefore, our aim was to analyze the overall system performance, including DER and smart appliances.