**3. Methodology**

Following the initial concept for the development of a quantitative approach on a building scale, the below outlined methodology aims at upscaling the concept to a bigger dimension. The numerical model-based approach provides an assessment of whole districts (or even larger entities) based on their overall energy storage capacity, load shifting potential and their ability to actively interact with the energy grids. With this methodology, districts or larger conglomerates of buildings can be rated and subsequently categorized with a single indicator per energy type. In addition, the resulting CO2 savings potential compared to an equivalent non-interactive system can be defined, which in turn highlights the probable benefits of the load shifting. This last aspect is of particular importance for future funding schemes or other incentives tied to CO2 emission savings. Since load shifting increases the efficiency of the overall system and subsequently the efficient use of renewable energy, the equivalent savings should be calculated and highlighted. Subsequently the proposed methodology aims at providing an answer to the following questions:

"What is the potential of the district to take energy from the grid, store it over a certain period of time and again dispatch it back to the grid? What are the potential CO2 emission savings associated with the load shifting potential of the district?"

In a first step, the previously published methodology is improved based on stakeholder feedback. Based on the adapted equations, the approach is enlarged from the single building to multiple buildings thus allowing the application on a whole district or any bigger logically connected series of buildings. The last sub-section finally provides an estimation for the equivalent CO2 savings, which might be of particular importance for the communication of the benefits of increasing the load shifting capabilities in buildings.

#### *3.1. Adaptation of the Previously Published Methodology*

Following the publication of the initial methodology on the quantitative assessment of the load shifting potentials in buildings [16], a series of discussions were held with relevant stakeholders to gain insight related to the usefulness and potential application of the methodology. Whilst the overall approach to provide a simplified numerical assessment has been positively acknowledged, it has been critically reviewed, that the proposed calculation does not require minimum efficiency standards related to the storage system. It was noted that this could essentially mean that a series of highly inefficient (and potentially environmentally adverse) storage technologies could result in an equally good SRI as highly efficient (and less ecologically detrimental) systems. This could be of particular importance if the SRI is used in future application for any funding mechanisms. Thus, in order not to favor cheap and inefficient storage technologies via the definition of the SRI, the original approach has been extended by a simple extension to include a barrier in regard to minimal efficiency related to the storage type and system.

The preceding equation with the variables as outlined below has been originally published [16] and reads as follows:

$$SRI = \frac{A\mathcal{C}}{\left(1 + e^{-6\left(\left(\frac{S\mathcal{C}}{E\mathcal{D}} \* \eta\_{S\mathcal{C}}\*(1-\zeta\_{S\mathcal{C}})\right) - 1\right)}\right)}\tag{1}$$

where *ED* refers to the energy demand of the building per energy source for the selected time period τ, *SC*, the storage capacity of the respective storage in the building, and η*SC*, the efficiency factor of the storage capacity (here the efficiency for loading as well as unloading the storage must be considered). η*SC* = η*C* \* η*D*. η*C* denotes the efficiency factor of the storage capacity for charge. η*D* refers to the efficiency factor of the storage capacity for discharge, ζ*SC*, the storage loss during the selected period in full storage (e.g., through self-discharge or associated heat losses), and *AC* the activity coefficient for the building.

Depending on the activity of the building, four different activity coefficients have previously been distinguished: (1) no grid available n/a; (2) no interaction with the grid, the activity coefficient is 0; (3) passive interaction with the grid, the activity coefficient is 1; (4) active interaction with the grid the activity coefficient is 2. (" ... In this context "no interaction with the grid" means that no storage or load shifting potential is available, the building is a simple consumer. A "passive interaction with the grid" requires the building to offer storage and/or load shifting potential to the grid. The load shifting is however only one-directional from the grid to the building. The "active interaction with the grid" stands for an energy flexible building that provides storage and/or load shifting capabilities and offers bi-directional load shifting from the grid to the building as well as from the building to the grid. This building would be able to produce as well as consume energy and consequently be a prosumer ... ") [16].

From this equation the required characteristics for the SRI methodology can be achieved. An initial validation of the methodology has also been described in the previous publication [16]. Following the comments for improvements as outlined above, a function has been added to regulate the SRI regarding the storage efficiency. The following variables are necessary for the amendment of the equation:

*AF*: Attenuation Factor to regulate the SRI related to storage efficiency.

*EPmin*: Definition of the required minimal efficiency of the storage system. Substitute for the definition: *EPmin* := η*min*·(<sup>1</sup> − ζ*max*) with η*min* the minimal required efficiency factor and ζ*max* the maximal required losses.

Λ: Definition point of the minimal efficiency λ = 1/*EPmin*. At this point the Attenuation Factor (AF) is always 0.63.

*k*: defines how fast the SRI veers with a low efficiency towards 0. With a low *k* the SRI is slowly reduced. With a high *k* the AF (SRI will be cut off) is rapidly reduced with minimal efficiency from 1 to 0.

*EP*: Energy Performance, i.e., the efficiency of the system *EP* := η*SC*·(<sup>1</sup> − ζ*SC*).

$$AF = 1 - e^{-\left(\lambda \cdot EP\right)^k} \tag{2}$$

As shown in Figure 2 the pinch-off characteristics of *k* influence the overall energy performance as there is a vast difference if *k* = 5 or *k* = 100 as displayed in the figure. The graphic shows the main properties of the function used to calculate the Attenuation Factor (*AF*). The *x* shows the definition point for the minimum acceptable efficiency of the storage system. Based on this limit, the parameter *k* can be used to define how quickly the SRI approaches zero when the EP decreases. A version for a slow decline is shown for the curve *k* = 5. The curve with *k* = 100 shows a rapid decline of the SRI for a decreasing EP. That means with a large *k* a cut off of the SRI, by a continuous function, is achieved at the definition limit for the minimal EP. In this case, if the EP is greater than EPmin, the SRI remains the same as in the first definition and consequently the basic properties are retained. In Figure 2, Equation (2) has been applied.

**Figure 2.** Pinch-off characteristics relating to *k*.

Following this logic, the *SRI* including the above outlined function for the regulation of the storage efficiency can be derived as follows based on Equations (1) and (2):

$$SRI = \frac{AC \cdot e^{-\left(\frac{\eta\_{SC} \cdot (1 - \zeta\_{SC})}{\eta\_{\min} \cdot (1 - \zeta\_{\max})}\right)^{k}}}{\left(1 + e^{-6\left((\frac{\zeta\_{C}}{\frac{SC}{\Delta t}} \cdot \eta\_{SC} \cdot (1 - \zeta\_{SC})\right) - 1\right)}\right)}\tag{3}$$

Based on this adapted equation the required characteristics for the *SRI* methodology can be achieved. The new function now considers the regulation of the storage efficiency and thus avoids the use of potentially inefficient storage technologies.

Figure 3 below depicts the SRI curves based on the modified Equation (3) for the various activity coefficients. Graph (a) shows the SRI curves with the activity coefficient 1 and (b) shows the SRI curves with the activity coefficient 2. Both SRIs are calculated with a *k* = 100.

**Figure 3.** Pinch-off characteristics relating to k with Activity Coefficient 1 (**a**) and Activity Coefficient 2 (**b**).

It is shown that, with a high *k*, the curve with the EPmin (definition of the minimal efficiency and maximum losses, yellow curve) reaches a maximum exactly at 0.63 with the *AC* = 1 and 1.26 with the *AC* = 2. However, with the same *k*, an EP lower than EPmin results in a *SRI* = 0. Consequently, a bad storage efficiency cannot be compensated with a high storage capacity. In Figure 3, Equation (3) has been applied.

#### *3.2. Enlargement to the District Scale*

In order to enlarge the methodology to the district scale, the following variables are added:

*N* Number of buildings

*EDi* Energy demand of the building i per energy source for the selected time period τ.

*SRIi* SRI for the building i.

*EDDist* Energy demand for the whole district.

*SRIDist* SRI for the whole district.

$$SRI\_{Dist} := \sum\_{i=1}^{N} w\_i \cdot SRI\_i \tag{4}$$

With the weighting factor as follows:

$$
\omega\_i := \frac{ED\_i}{ED\_{Dist}} \tag{5}
$$

The weighting factor has been included in order to ensure a fair comparability of districts with different characteristics. Therefore, this does not represent an average of the district's SRI, but rather a weighted average based on the respective share of energy consumption in relation to the total energy consumption of the district. For example, if a commercial entity has a low SRI with a very high ED, then a single building with a high SRI and low ED does not compensate for this.

The *EDDist* can subsequently defined as follows:

$$ED\_{Dist} := \sum\_{i=1}^{N} ED\_i \tag{6}$$

Out of the above equations, the load shifting potential for the whole district can be derived. Based on the calculation as outlined in the previous publication [16], the equation to estimate the storage potential reads as follows:

$$SP = \min\left(\frac{5}{2}, \max\left(0, -\frac{\ln\left(\frac{2}{SRI} - 1\right)}{6} + 1\right)\right) \tag{7}$$

The estimation of the storage potential of a building is derived from the SRI. The reverse function is based on the following assumption: The losses and efficiencies were already taken into account when calculating the SRI. For this reason, and the fact that the SRI is monotonically increasing in terms of storage efficiency a higher efficiency subsequently implies a higher SRI. The efficiency for the inverse was chosen with 1, thus the equation is defined as:

$$
\eta\_{\text{SC}^\circ}(1-\zeta\_{\text{SC}}) = 1 \tag{8}
$$

Subsequently the energy that can be taken from storage is calculated based on the time τ. Also, the storage potential of the building is defined with:

$$SP \coloneqq \frac{SC}{ED} \tag{9}$$

In order to maintain the properties of the SRI with regard to the building as consumer (one-directional) or prosumer (bi-directional) the activity coefficient for the inverse is set to 2 (*AC* = 2). This is following the assumption that a storage with an *AC* = 1 is expected to be less active in shifting loads than a storage with an *AC* = 2. Based on the definition of the SRI and the above assumptions:

$$SRI = \frac{A\mathbb{C}}{\left(1 + e^{-\Phi((\frac{S\mathbb{C}}{\mathbb{E}D} \cdot \eta \mathbb{S} \colon (1 - \zeta\_{\mathbb{S}}\mathbb{C})) - 1)}\right)} = \frac{2}{1 + e^{-\Phi(SP - 1)}}\tag{10}$$

Following these equations, the *SP* can be derived as follows:

$$SP = 1 - \frac{\ln\left(\frac{2}{\text{SRI}} - 1\right)}{6} \tag{11}$$

In the extreme areas of *SRI* = 0 and *SRI* = 2 the estimate obtained needs to be reasonably limited. This means that since the approach function is defined on R, it must still be restricted to R<sup>+</sup> 0 . Furthermore, due to rounding errors in the range of *SRI* ≈ 2, errors could occur which should be limited by an upper bound. As a suggestion 2.5 was chosen as the upper bound for this study. Based on these assumptions, the storage potential for buildings can be defined as follows:

$$SP = \min\left(\frac{5}{2}, \max\left(0, 1 - \frac{\ln\left(\frac{2}{SRI} - 1\right)}{6}\right)\right) \tag{12}$$

With the equation to calculate the storage potential for the whole district:

$$LP\_{Dist} := \sum\_{i=1}^{N} SP\_i \cdot ED\_i \tag{13}$$

With the individual coe fficients as follows:


The load shifting potential for the whole district serves as an approximation as derived from the SRI, the SP and the ED as outlined in the above equations and displayed in Figure 4 In this figure, in field 2 Equation (3) has been applied, in field 3 Equation (12) has been applied, and in field 4 Equation (13) has been applied.

**Figure 4.** Assessment of the load shifting potential of the whole district.

The general assumption is that only buildings with an activity coe fficient of 2 (active interaction) can fully and actively contribute to the load shifting potential in grids. An activity coe fficient of 1 (passive interaction) could only contribute to peak shaving but cannot be considered to be fully contributing to the load shifting potential of the district.


As outlined above, the SRI and its subsequent calculations are solely derived from planning data and does not include any monitoring or real time measured data. It gives decision making support in the planning phase and provides answers to the question of how much energy can be theoretically shifted from the grids to the building in addition to the district's own consumption in the time span τ. The calculation provides an approximate order to magnitude for planning purposes only. Thus, this assessment is intended to be applied for a preliminary load shifting analysis of whole districts in regard to their various networks (electrical, thermal, gas).

#### *3.3. Approximation of CO2 Savings Potential*

Whilst the load sifting potential (LP) provides a relevant number for the assessment of whole districts and cities, it will remain closely linked to infrastructure planning decisions. Arguably, load shifting alone does not necessarily increase e fficiency of the system. However, if it is linked with the potential to store and dispatch renewable energy, emissions related savings can evidently be made. Especially wind and solar energy is heavily dependent on current and regionally localized weather occurrences. Thus, at times there can either be too much or not enough renewable energy in the system, which would result in wind or solar system being switched o ff to prevent an overload for the former or fossil-based systems to substitute the remaining demand for the latter. As outlined in the background section, in this context, storage plays an existential role.

Subsequently the assumption is, that a widespread expansion of energy storage enables a higher proportion of renewable energy to be e fficiently used. In the area of thermal energy sources, it is also possible to use waste heat (i.e., low temperature heat from buildings or processes) through su fficient storage distribution in the network. Centered on this logic, the following procedure is recommended as a basis for presenting a possible CO2, saving potential based on the SRI. From the estimate of the load shift potential (*LP*), an estimate for the potential CO2 savings can be derived:

$$\text{CO2}\_{4} = \left(\text{CO2}\_{\text{Curr}} - \text{CO2}\_{\text{remw}}\right) \cdot \text{LP}\_{\text{Dist}} \cdot \frac{year}{\pi} \tag{14}$$

 sources.

With the individual coe fficients as follows:

*CO*2*Curr* Actual CO2 emissions per kWh. *CO*2*renew* CO2 emissions per kWh from renewable energy

*CO*2*a* Potential total CO2 savings per year.

The calculation follows the postulation that currently renewable energy production cannot be fully exploited due to limited storage capacities. Thus e.g., wind turbines must be switched o ff in times of energy overload in the grid. On the other hand, when there is no wind, the energy must be produced from conventional, mostly fossil-based sources. With a SRI > 0, the district can store renewable energy in the amount of *LPDist* if the grid cannot take up any more energy. If subsequently energy is in demand again, it can be re-loaded back from the districts to the grid. The extent of the potential total CO2 savings per year can thus be calculated based on the di fference between the CO2 amount of the type of energy produced multiplied by the amount of energy that can be additionally produced due to the storage capacities of the district.

It should be noted that, since the methodology is focused on load shifting, the resulting CO2 savings are equivalent to potential savings only. That means, without a corresponding renewable energy generation, there are obviously no CO2 savings in this context.

#### **4. Application of the Methodology in Theoretical District Use Case**

Following the testing of the previously published methodology on the building scale with the use of di fferent building types, the extended methodology has subsequently been applied to a whole district. The selected theoretical use case should include multiple buildings of di fferent size, type and age. For this purpose, a building block situated in the 12th district of the City of Vienna has been used as the SRI has also previously been tested on these buildings [55]. The small district includes nine buildings, di ffering in type and age, ranging from an erection date of the 1900s to a building constructed in 2010. One of the buildings is for o ffice use while the others are multi-family residential buildings. To simplify the assessment the inner courtyard buildings have been omitted (as no specific use could be determined for these edifices) and the retail areas on the ground floor have been left out. Figure 5 shows a partial land use plan of the City of Vienna, highlighting the selected district as well as an aerial view of the building block.

**Figure 5.** Partial land use map of the City of Vienna with the selected district highlighted in red (**a**) and aerial view of the selected district (**b**) [56,57].

#### *4.1. Description of Theorectical District Use Case*

The building data for this district has been derived from a series of publicly available data, such as the land use plan of the City of Vienna [56] and imagery derived from Google maps [57]. Data on typical energy usage depending on the type and age of the building as well as the assumptions on typical heating, cooling and ventilation systems have been based on the Tabula database [58]. It should be noted that, for planning purposes, actual building data derived from, e.g., the Energy Performance Certificate (EPC) or monitored data, should be given preference to proxy data derived from generic databases. However, for the purpose of this study, the accuracy of the energy figures for the base case are of lesser importance, as the aim is solely to assess, whether the proposed methodology can be applied for di fferent types of scenarios for whole districts.

For the assessment of the load shifting potential of the selected district, various scenarios have been defined to cover a wide range of possibilities. The selected options follow a previously carried out study on the SRI validation and are expanded in regard to the scenarios as well as the calculation for the whole district assessment as described in Section 3 above.


For Scenarios 3 and 4 a double and triple size of the original Base Scenario has been defined. This has been done in order to demonstrate the overall weighting of the SRI across the district. As outlined in Equations (4)–(6) above, a specific weighting factor has been integrated to ensure that districts with di fferent characteristics can be fairly compared. As the *SRIDist* is a single number it needed to be avoided that the SRI represents a simple average across all buildings but rather a weighted average based on the respective share of energy consumption in relation to the total energy consumption of the district.

In Table 1, a description of the energy related properties for the base case as well as subsequent scenarios is outlined.


**Table 1.** Description of energy related properties for base case and scenarios, extended from [55].

#### *4.2. Results of Theoretical District Use Case*

The results of the theoretical use case comprising of the base case and four scenarios are displayed in the following figures. In Figure 6, the SRI is shown per building for each scenario. It can be seen that, whilst the base case, Scenario 1 and 2, is comprised of nine buildings in the district (*N* = 9), in Scenario 3, the district is doubled in size with 18 buildings (*N* = 18), and in Scenario 4, tripled with 27 buildings (*N* = 27). The *SRIi* for the base case is "0" as the activity coefficient is also "0" (i.e., no interaction with the grid, buildings are simple consumers). The SRI for all other buildings varies dependent on type, size, interaction potential and storage capacity. In Figure 6, Equation (3) has been applied.

**Figure 6.** Smart Readiness Indicator for the individual buildings (*SRIi*) per district for the Base Case and Scenarios 1–4.

In Figure 7 the *SRIDist* for the various scenarios is displayed on a district scale. Since the base case has an activity coefficient of "0" the SRI for the base case for the district is equally "0". Scenario 1 rates already better, however Scenario 2, with the optimized refurbishment option and active storage potential for both electrical and thermal provides the best result. The mix of base case and Scenario 1 which is displayed in Scenario 3 is obviously less good than Scenario 1 as the SRI is weighted across the district. With half the buildings in Scenario 3 being un-refurbished and offering no load shifting potential, the results are poorer. Scenario 4, which is a mix of the Base Case, Scenario 1 and Scenario 2 rates second best, as the base case takes up only a third of the overall scenario and the SRI is weighted across the district. The results highlight that the above described weighting factor does ensure an objective comparability across the various scenarios. In Figure 7, Equation (4) after Equation (5) after Equation (6) after Equation (3) have been applied.

The load shifting potential for the overall district is displayed in Figure 8. The *LPDist* represents, different to the *SRIDist*, a total figure. The results show, that Scenario 4 can provide with a total number of 27 buildings based on a mix of the base case, Scenario 1 and 2 the highest amount of load shifting in kWh. The base case obviously has no load shifting potential, as there is no interaction with the grid and the *SRIDist* as shown above is consequently "0". Scenario 1 and Scenario 3 have exactly the same load shifting potential, as they have the same amount of buildings that offer the same storage capacities, as the base case buildings in Scenario 3 do not contribute at all to the load shifting. Scenario 4 offers the best results due to the highest number of buildings in the district (*N* = 27) and the relatively high storage capacity due to the mix of Scenario 1 and 2 (the base case buildings in this scenario equally

do not contribute to the *LPDist*). In Figure 8, Equation (13) after Equation (12) after Equation (3) have been applied.

**Figure 7.** Smart Readiness Indicator District (*SRIDist*) for the Base Case and Scenarios 1–4.

**Figure 8.** Load Shifting Potential (*LPDist*) for the Base Case and Scenarios 1–4.

In Figure 9, the potential CO2 savings for the district are displayed. The results follow in tendency the results for *LPDist* as a higher load shifting potential results in increased CO2 savings. Similar to the above results, the Base Case does not save any emissions due to the lack of load shifting potential. Scenario 1 and Scenario 3 show the same results (as is also the case with *LPDist*) as they both feature the same load shifting potential and subsequently the same potential for emission savings. Scenario 2 and 4 also feature higher equivalent savings due to their higher storage capacity and improved activity (bi-directional connection).

**Figure 9.** CO2 equivalent savings (CO2 Dist) for the Base Case and Scenarios 1–4.

Evidently, these figures vary, depending on the actual emissions of the energy system (*CO*2*Curr*, actual CO2 emissions per kWh) and the emissions from renewables in the energy system (*CO*2*renew*, CO2 emissions per kWh from renewable energy sources) as outlined in Equation (14). Since this theoretical use case is based in Vienna, the figures for electrical and thermal energy have been taken from the Austrian standards [59] with a noted power mix of 417 g/kWh CO2 and district heating from highly efficient CHP (combined heat and power) with 73 g/kWh CO2. Emissions from renewables have been calculated with 0 g/kWh CO2. Since the emissions from the current power mix are substantially higher than the emissions from the current thermal sources, the savings on the electrical side subsequently exceed the savings from the thermal side, even though the thermal load shifting potential as outlined in Figure 8 is higher in all four scenarios than the electrical load shifting potential. In Figure 9, Equation (14) after Equation (13) after Equation (12) after Equation (3) have been applied.
