In this section we present a methodology for the definition of the thermal storage potential in Switzerland from the results that Stadler et al. obtained when they analysed the deployment of model predictive control (MPC) systems for energy systems in buildings. The results and the methodology that Stadler et al. employed are discussed in [202].
3.4.1 Available results of the deployment of MPC systems in Switzerland
The energy system of a building can be composed of several technologies: boiler, HP, PV panels, thermal storage tank, etc. MPC systems optimize the building energy system operation strategy, taking into consideration parameters such as temperature and radiation forecast, or expected electricity prices. Stadler et al. [202] propose a MILP formulation to reproduce the MPC problem. The developed formulation describes the thermo-economic behavior of a building energy system allowing the optimisation of its design (CAPEX) and OPEX. It offers a third optimisation objective, the pseudo generation multiple (GM). The GM grades the level of grid-friendliness of the solution. The formulation of the GM indicator is available in [203]. It evaluates the smoothness of the interaction between the building and the electricity grid, since it compares the daily absolute net grid-building power flow to its daily average.
In [202], Stadler et al. explore the potential of MPC for building energy systems in Switzerland. For that purpose data on the Swiss building stock is required. As mentioned in section 3.5, this information is obtained from the RegBL database [204]. In Switzerland, the buildings stock contains 1.7 millions elements by ends 2016 [205], hence it is not feasible to solve the problem for each of the buildings due to a lack of data and calculation time constraints. Stadler et al. classifies the buildings by their type (single family, multi-family and mixed-usage) and by their age category.
In addition, they apply a dual spatial and temporal clustering. The data to perform the clustering comes from weather data from 40 national weather stations. Prior to the clustering a design reference year (DRY) is calculated [206]. The spatial clustering reduces the number of weather stations to eight. The temporal clustering decomposes the DRY into 6 typical days plus 2 extreme peak periods to capture the peak demand hours. Hence the methodology presented in [202] calculates the Swiss potential of MPC by solving the 120 optimisation problems obtained when the options of each of the columns in table 3.3 are combined.
Table 3.3 – Combinations of elements classifying the buildings.
Buidlings type Weather station Construction period
Single family Genève-Cointrin 1920
Multi-family La Chaux-de-Fonds 1970 Mixed-usage Lugano 1980 Ulrichen 2005 Zürich-SMA 2020 Montana Bern-Liebefeld Davos
For each of the building type / weather stations / construction period (BWC) combination 15 solutions are generated. The fifteen solutions correspond to the combination five possible upper limits for the CAPEX with three possible upper limits for the GM. each of the solutions defines the mix of installed technologies and their operations strategy for each of the typical days.
3.4.2 Integration of the results into the model for determining the thermal storage po- tential
The results Stadler et al. obtained from the analysis of the implementation of MPC systems serve as basis to define the thermal storage potential of the building stock in Switzerland. each of the 15 generated solutions for each BWC combination has a space heating profile determined by the optimiser. The optmised profile respects the imposed indoors temperature bounds (15°C≤ Tin≤ 30°C). The building thermal behaviour, i.e. the space heating demand (QSh(t) [kW]), is calculated with a first-order resistance-capacity model [202], which is described in Eq. 3.33, whose parameters are listed in table 3.4. The HOURS set contains the hours of each typical day. The time duration of the time steps (top) is one hour, measured in hours.
Table 3.4 – Parameter list with description from Eq. 3.33. The parameters are specific to each type of building.
Parameter Units Description
U [kW/(°C·m2)] Building heat transfer coefficient. C [kWh/(°C·m2)] Building heat capacity coefficient.
A [m2] Building reference area.
Q+Gains(t) [kW] Heat gains from the building usage (e.g. users and appliances).
QSh(t )=−e
-top*U/CTin(t )− (1 − e-top*U/C)T
ext(t )+ Tin(t+ 1)
1− e-top*U/C (U∗ A) −Q
+
Gains(t )−Q+Solar(t )
∀t ∈ HOURS (3.33) In addition to the 15 optimized space heating profiles for each BWC combination generated by Stadler et al., we calculate a 16thprofile considering that the heating is controlled by a thermostat at 20°C, hence Tin(t) is constant at 20°C. The comparison between the optimized and the thermostat- controlled heating profiles gives the thermal storage capacity for each BWC combination and for each typical day. The thermal storage capacity is calculated as the maximum accumulated heat supply difference between the two profiles.
For the implementation of the thermal storage for buildings in the national energy system (NES) model is necessary to have an annual hourly profile for the thermal storage capacity. However at this point of the methodology, we only have the hourly profile for the thermal storage capacity for the 6 typical days. In order to obtain an annual hourly profile (c) is necessary to find the best fitting typical day for each 24-hours period in the representative year used in the NES model. The selection is done based on the comparison of the outdoors daily average temperature for each of the weather stations.
The 20°C profile is also used to obtain the annual specific SH demand (q-Annual) of the BWC combi-
nation for the design reference year (DRY) used for the MPC calculations. For computing it, we take into consideration the frequency of each of the typical days in the DRY.
At this step of the methodology we know the thermal storage capacity for each of the solutions for each BWC combination. However the researched value is the Swiss thermal storage capacity offered by the building stock. Hence we need to be able to describe the future building stock as a combination of the solutions. Thus the next step consists in determining the square meters for each of the solutions in the future Swiss building stock. The square meters mix problem is added into the MILP formulation describing the NES. The daily national thermal storage capacity C is calculated using the square meters mix in Eq. 3.34.
Eq. 3.35 and 3.36 warranty that the square meter mix respects the mix of technologies defined at national level. The TECHS THS set contains the technologies that are considered to generate the MPC solutions: HPs, CHP, boiler and DEH. Eq. 3.37 ensures that the new area mix respects the expected increase in surface for each of the building types. That increase can only come from buildings with 2005 and 2010 contruction characteristics (Eq. 3.38), and the surface for buildings with 2020 standards cannot decrease (Eq. 3.39). Furthermore, the new surface mix must compile with the expected increase in buildings insolation (Eq. 3.40).
with their corresponding description.
Table 3.5 – Parameter list with description.
Parameter Units Description
pth(b,c,w,s,tech) [kW/m2] Technology specific thermal installed capacity for solution s
in the b,c,w combination.
q-Annual(b,c,w,s) [kWh/m2] Specific annual SH demand
the b,c,w combination in reference year.
ΔQ [-] Decrease of the annual national buildings heating demand
relative to the old surface heating demand.
SrefOld(b,c,w) [m2] Current square meters for the b,c,w combination.
ΔS(b) [-] Increase of the surface for building type
b relative to the old surface SrefOld.
c(b,c,w,s,t) [kWh/m2] Daily thermal storage capacity for solution s in the b,c,w combination.
Table 3.6 – Variables list with description.
Variable Units Description
SrefNew(b,c,w,s) [m2] New square meters for solution s in the b,c,w combination.
Q+Total [kW] Total installed thermal power.
C(t) [kWh] Daily total thermal storage capacity.
%DecMix(tech) [-] Ratio [0;1] tech installed capacity over total installed capacity.
C(t )= (1 − %Dhn)
i∈T Y PE,j∈MET EO,k∈Y E AR,l∈SOLUT ION
c(i , j , k, l , t )SrefNew(i , j , k, l ) ∀t ∈ T (3.34)
Q+Total=
i∈T Y PE,j∈MET EO,k∈Y E AR,l∈SOLUT ION,m∈TECHS THS
pth(i , j , k, l , m)SrefNew(i , j , k) (3.35)
%DecMix(t ech)Q+Total≥
i∈T Y PE,j∈MET EO,k∈Y E AR,l∈SOLUT ION
pth(i , j , k, l , m)SrefNew(i , j , k, l ) ∀m ∈ TECHS THS (3.36)
k∈Y E ARΔS(i)SrefOld
(i , j , k)=
k∈Y E AR,l∈SOLUT ION
SrefNew(i , j , k, l ) ∀i ∈ T Y PE,∀j ∈ MET EO (3.37)
SrefOld(i , j , k)≤
l∈SOLUT ION
SrefNew(i , j , k, l )
∀i ∈ T Y PE,∀j ∈ MET EO,∀k ∈ Y E AR \ {2005,2020} (3.38) SrefOld(i , j , 2020)≤
l∈SOLUT ION
i∈T Y PE,j∈MET EO,k∈Y E AR
SrefOld(i , j , k)q-Annual(i , j , k, 16)≥
i∈T Y PE,j∈MET EO,k∈Y E AR,l∈SOLUT ION
q-Annual(i , j , k, l )SrefNew(i , j , k, l ) (3.40)