*2.4. Seasonal Flexibility Analysis*

Seasonal flexibility offered by a building integrated sorption storage is evaluated based on its ability to use grid electricity in summer during charging and to reduce electricity demand in winter during discharging of the storage. Electricity is not stored seasonally but rather the potential to reduce electricity demand in winter/heating season. The electric load shift achieved is referred to as the virtual battery effect as it acts similarly to storing this part of electricity over the season. The seasonal energy flexibility must be separated in two parts, i.e., the additional electricity absorbed during charging (negative flexibility) and the electricity savings in discharging (positive energy flexibility). These energy flexibilities are quantified with reference to the regular heat pump operation without sorption storage integrated. The electricity consumed by the heat pump is calculated as the energy provided by the heat pump divided by its coefficient of performance (COP). The COP is calculated as the ideal Carnot COP based on thermal reservoir temperatures multiplied by a fixed isentropic efficiency (η*isen*) of 0.5.

Negative energy flexibility provided with storage is equal to the electricity utilized by the heat pump to charge the storage, given a certain time (Δ*texcess*) with excess electricity available from the electricity grid (Equation (1)). During charging, the heat pump must provide the entire temperature lift between the HMX desorber and condenser and sensible heat stored in the charged, concentrated sorbent is lost (η*charging*). The temperature of the desorber is fixed at 55 ◦C and the saturation pressure of water vapor at this temperature and a targeted sorbent concentration of 50 wt.% determines the condensation temperature needed in the HMX. The inlet to the condenser of the HMX provided by the evaporator of the heat pump then needs to be lower by the amount of the temperature difference between the absorbate and the heat transfer fluid (Δ*Thx,HMX*) and an additional temperature difference of the heat transfer fluid across the HMX condenser (Δ*THMX,ev*). The evaporation temperature of the heat pump is then below the inlet temperature on the HMX condenser by <sup>Δ</sup>*Thx,hp*. In the condenser of the compression heat pump there is no temperature difference assumed between condensation temperature and temperature of the heat transfer fluid leaving the condenser. This assumption is justified because of the desuperhating taking place in the condenser, allowing even for secondary fluid temperatures above condensation temperature at the outlet of a counterflow-type condenser. This affects Equations (2) and (4) where condensation temperature of the heat pump is equal to the HMX desorber inlet temperature (*Tdesorption* + Δ*Thx,HMX*) and *Tsupply* of the space heating, respectively.

$$E\_{flex,charging} = P\_{el,lp,charge} \Delta t\_{\text{excess}} = \eta\_{\text{charge}} \frac{Q\_{lp,\text{ desorption}}}{COP\_{hp,\text{charging}}} \Delta t\_{\text{excess}} \tag{1}$$

$$\text{COP}\_{\text{hp,charging}} = \eta\_{\text{isen}} \frac{T\_{\text{desorption}} + \Delta T\_{\text{lx},H\text{MX}}}{\left(T\_{\text{desorption}} + \Delta T\_{\text{lx},H\text{MX}}\right) - \left(T\_{\text{sat},p\_{\text{deswb}}} - \Delta T\_{\text{lx},H\text{MX}} - \Delta T\_{\text{HMX},\text{cv}} - \Delta T\_{\text{lx},\text{hp}}\right)} \tag{2}$$

In discharging, the energy flexibility is calculated as the difference in electricity consumed during heating season (Δ*theating*) by the single-stage and double-stage heat pump including storage respectively (Equation (3)). In case a sorption storage is included the temperature lift is to be provided by the compression heat pump is reduced, thus increasing its COP.

$$E\_{\text{flex,dischargeing}} = (P\_{\text{el,ref,heating}} - P\_{\text{el,stong},\text{dischargeing}})\Delta t\_{\text{heating}} = Q\_{\text{heating}} \left(\frac{1}{\text{CO}\_{\text{nf},\text{heating}}} - \frac{1}{\text{CO}\_{\text{sl,avg,dischargeing}}}\right)\Delta t\_{\text{heating}} \tag{3}$$

In standard operation without storage installed, the heat pump COP (*COPref,heating*) is calculated based on supply temperatures ( *Tsupply*) of the space heating system and the evaporation temperature (Equation (4)). The latter is determined by the ambient air temperature reduced by the temperature di fference between the air inlet of the water/air heat exchanger and the water outlet of the heat pump evaporator ( Δ *Tair*) and the temperature di fference between the water and refrigerant ( Δ *Thx,hp*) in the evaporator.

$$\text{COP}\_{ref,\text{haiting}} = \eta\_{\text{lisen}} \frac{T\_{\text{supply}}}{T\_{\text{supply}} - (T\_{amb} - \Delta T\_{air} - \Delta T\_{\text{lux},hp})} \tag{4}$$

When combined with the sorption storage the evaporation temperature of the heat pump remains the same but the condensation temperature of the heat pump being the inlet temperature of the HMX evaporator ( *THMX,ev,in*) changes, leading to a di fferent COP (*COPstorage,discharging*) as expressed in Equation (5). The inlet temperature to the evaporator side of the HMX provided by the compression heat pump as the first stage shown in Equation (6) is determined by the required supply temperature (*Tsupply*) of the space heating and the available temperature lift from the sorption storage ( Δ *T50,max*) between the maximum sorbent temperature and the evaporation temperature. Further, there is the temperature di fference of the heat exchanger, once between the sorbent and heat transfer fluid (Δ *Thx,HMX*) and once between the absorbate and the heat transfer fluid ( Δ *Thx,HMX*) and the temperature di fference across the evaporator of the HMX ( Δ *THMX,ev*). The temperature lift provided by the sorption storage ( Δ *T50,max*) depends on the maximum sorbent concentration of 50 wt.% as shown in Figure 3. In this analysis, a departure from ideal equilibrium condition is assumed, leading to a reduction of the effectively provided temperature lift.

$$\text{COP}\_{\text{storage, discharging}} = \eta\_{\text{isen}} \frac{T\_{\text{HMX,av,in}}}{T\_{\text{HMX,cv,in}} - (T\_{\text{amb}} - \Delta T\_{\text{air}} - \Delta T\_{\text{lux,hp}})} \tag{5}$$

with

$$T\_{\rm HMX,\varphi\upsilon,in} = T\_{\rm supply} + \Delta T\_{\rm lx,fMIX} - \Delta T\_{\rm 50,max} + \Delta T\_{\rm lx,fMIX} + \Delta T\_{\rm HMX,\varphi\upsilon} \tag{6}$$

**Figure 3.** Ideal temperature lift provided between HMX evaporator temperature (TEout) and the maximum HMX absorber temperature by the sorption storage depending of maximum sorbent concentration. Adapted from [20].

The positive energy flexibility provided during discharging is depending on the amount of energy stored. This amount is determined during the charging phase. Maximum energy storage capacity is determined by the installed heat pump capacity multiplied by the time with available excess

electricity from the electricity grid ( Δ*texcess*). In discharging mode, the fraction of space heating demand that can be covered by the stored energy is determined in order to identify the system operating in double-stage mode. When storage capacity is exhausted it switches to standard single-stage operation mode. This way the positive energy flexibility o ffered with limited storage capacity is calculated and confronted with the ideal case of unlimited storage capacity.

In order to determine the volumetric energy density of the sorption storage with reference to the diluted sorbent and the volume required to store the calculated energy, terminal sorbent concentrations were evaluated based on system temperatures. Specifically, for the HMX evaporator temperature, the saturation pressure of water vapor is calculated, determining the achieved terminal concentration in the HMX absorber based on absorber inlet temperatures. These temperatures are determined by the return temperatures from the space heating system plus a temperature di fference *(*Δ *Thx,HMX*) between the heat transfer fluid and the sorbent. An average terminal sorbent concentration is then calculated over the heating period in order to calculate the sorbent mass needed to store the energy provided during charging. For this purpose an energy balance, a species mass (NaOH), and total mass balance over the HMX absorber is applied resulting in an expression for the inlet mass of concentrated sorbent depending on the known ratio of inlet to terminal concentration and the specific enthalpies of concentrated (*hsorbent,in*) and diluted (*hsorbent,out*) sorbent, respectively, and enthalpy of condensation for water (*hlg*) given in Equation (7).

$$M\_{\text{sorbent},in} = \frac{Q\_{\text{heating}}}{h\_{\text{sorbent},in} + \left(\frac{c\_{\text{sorbent},in}}{c\_{\text{sorbent},out}} - 1\right)l\_{l\bar{\xi}} - \left(\frac{c\_{\text{sorbent},in}}{c\_{\text{sorbent},out}}\right)l\_{\text{sorbent},out}}\tag{7}$$

The outlet mass of diluted sorbent then becomes

$$M\_{\text{sorbent},\text{out}} = \left(\frac{c\_{\text{sorbent},\text{in}}}{c\_{\text{sorbent},\text{out}}}\right) M\_{\text{sorbent},\text{in}} \tag{8}$$

The volumetric energy density of the sorption storage is calculated dividing the leaving sorbent mass ( *Msorbent,out*) by the sorbent density at the terminal concentration (*csorbent,out*) assuming a fixed temperature of 25 ◦C, representing the average absorber inlet temperature.

In Table 2, parameter values used for the evaluation of energy flexibility are summarized.

**Table 2.** Parameter values used for evaluation of energy flexibility provided with the building integrated sorption storage.

