2.1. Critical Load
The US Department of Homeland Security defines resilience as the ability to resist, absorb, recover from, or successfully adapt to adversity or a change in condition [
17]. Resilience is an emerging concept and is defined based on the performance of a system under specific conditions and time frames. In the current work, the energy system’s resilience is defined in terms of the system’s robustness and the ability of the energy system to provide critical loads during power outages.
Critical load refers to the minimum load that needs to be supplied to emergency and uninterruptable functions to ensure their performance [
18]. Critical load is a percentage of the day-to-day demand [
18]. Depending on the system design, critical load could be estimated for both electricity and air conditioning (heating and cooling). In urban areas where space heating and cooling is provided by electricity, the air-conditioning critical load could be evaluated separately. This critical load refers to the load that needs to be supplied to provide the minimum habitable temperature for dwellings and prevent severe damage to buildings. Precise evaluation of this load needs detailed information regarding the number of occupants, construction material and isolation of the building, dimensions of penetrations, geographical location, weather conditions, etc. In the current method, simplified assumptions were considered, and the evaluation of critical load is proposed in four steps:
Step 1: To find the critical loads of a district, the first step is to list all the use types of the district. At a district scale, buildings might have different use types, from residential to commercial, schools, educational institutes, and medical centers. During a disruption, the level of importance of these use types and their loads are different.
Step 2: In the second step, after defining all the use types, they need to be ranked based on the criticality level. On a DOD document [
19], three levels of loads are defined as (1) uninterruptable loads which need to be supplied without a momentary disconnection, (2) essential loads, for instance, HVAC loads that can suffer short de-energized periods, and (3) non-essential loads, which can be de-energized for noticeable periods of times. Similar to the mentioned document, criticality levels of loads in a campus building are defined in three categories: loads with low criticality levels, e.g., gym; loads with medium criticality levels, for example, teaching labs; and loads with high criticality levels, for instance, IT and server rooms. Loads with a high level of importance need to be prioritized to the appropriate category of uses. In a time of disruption, the demand of these category of uses, such as server rooms, cannot be disconnected.
In building complexes, where detailed data about each category of demand are unavailable, an alternative way to define the load for each category could be identified based on the ratio of use-type area to the total area:
where
is the ratio of category
i to the total area,
is the area of the category
i (m
2), and
is the total area of the building (m
2), and in a building with
n different use-type categories:
Step 3: In this step, coefficients related to each use type used to estimate the critical load are defined. The critical load in each building is a portion of the day-to-day demand. Therefore, the coefficients are a number between 0 and 1, and are defined separately for electricity demand and air-conditioning systems as follows:
Step 3.1: Air-conditioning critical coefficient (CA)
For a building with a central air-conditioning unit, the critical load of the air-conditioning unit is impacted by working hours and seasons (summer and winter) to simplify the process. Therefore, the critical coefficient is defined based on these two parameters and then multiplied by the actual hourly load of the air-conditioning system. As shown in
Table 1, the value of the coefficients is defined based on the different time ranges during summer and winter.
shows the critical coefficient of the air-conditioning unit during the daytime, while
refers to the value of the critical coefficients during the nighttime in each season.
Step 3.2: Electricity critical coefficient (CE)
Electricity demand varies depending on the use type, and a critical coefficient is defined based on each use type. Considering the importance ranking of use types in Step 2, the loads with higher levels of importance have coefficients closer to one. Defining coefficients based on the working and closing states of the services is suggested to address the load curve pattern changes during the day and night.
Table 2 represents the structure of estimating the coefficients, where
and
are critical coefficients of use type
i during the day and night. The critical coefficient is defined based on professional judgment, which is directly correlated to the range of existing use-type categories in the building.
Step 4: In the final step, the total critical load is evaluated. The building’s air-conditioning critical load (
) is estimated using Equation (3):
where
, and
are air-conditioning critical load and actual load in time step
t, respectively.
is the air-conditioning critical coefficient that is divided into seasonal coefficients for day and night (
Table 1).
The hourly critical electricity load for each use type is calculated using Equation (4), where
and
are critical and actual electrical load demands in time step
t, respectively,
is ratio of category
i to the total area (%), and
is the critical coefficient, which is further divided into
and
coefficients.
The total critical electricity demand of the building
) is the summation of all the available use types’ critical loads and is assessed using Equation (5):