Core KPI Specification and Calculation¶

Core KPIs¶

The following KPI definitions constitute the core KPIs to be calculated in every test case, and documentation of the KPI considered during the development phase is provided in the Appendix (See Appendix: Additional KPI Specification and Calculation). During the IBPSA expert meetings, these core KPIs have been selected as the most representative and relevant indicators to compare different control approaches for buildings. Additional KPIs may be calculated and used for specific purposes, but the core KPIs are considered the basis for assessing the performance of a controller. The definitions consist of a description, mathematical formula for quantification, and KPI tagging notation. Note that floor areas used for normalization are calculated according to the definitions of the Commercial Buildings Energy Consumption Survey (see https://www.eia.gov/consumption/commercial/terminology.php) and Residential Energy Consumption Survey (see https://www.eia.gov/consumption/residential/reports/2015/squarefootage/).

Thermal discomfort in a given period of time¶

The thermal discomfort is the integral of the deviation of the temperature with respect to a predefined comfort range during a given period of time averaged over all zones. The units are $K.h/zone$ and is quantified as:

\[D(t_0, t_f) = \frac{\sum_z^N \int_{t_0}^{t_f} \left \|s_z (t) \right \| dt}{N}\]

Where $D(t_0, t_f)$ is the total discomfort between the initial time $t_0$ and the final time $t_f$; $z$ is the zone index out of $N$ zones in the building; $s_z(t)$ is the deviation (slack) from the lower and upper set point temperatures established in zone $z$.

Energy use in a given period of time¶

This KPI is the measure of the site HVAC energy use in $kWh/m^2$ when accounting for the sum of all energy vectors present in the test case HVAC system. Each test case determines the energy vectors and conversion factors necessary for HVAC (heating, cooling, fans, pumps). The mathematical formulation for this KPI is the following:

\[E(t_0, t_f) = \frac{\sum_{i\in \xi} \int_{t=t_0}^{t=t_f}\ P_i(t) dt}{A}\]

Where $E(t_0, t_f)$ is the total amount of energy use from the initial time $t_0$ up to the final time $t_f$; $\xi$ denotes the set of equipment in the system with an associated energy use of any type; finally, $P_i$ is the instantaneous power used by the energy vector $i$; $A$ is the total floor area of the building.

Peak electricity demand in a given period of time¶

This KPI is the measure of the site HVAC peak electricity use in $kW/m^2$ when accounting for the sum of all electrical equipment present in the test case HVAC system. The mathematical formulation for this KPI is the following:

\[P_E(t_0, t_f) = \frac{\max_{15}[\sum_{i\in I} P_i(t)]}{A}\]

Where $P_E(t_0, t_f)$ is the peak electricity demand from the initial time $t_0$ up to the final time $t_f$; $I$ denotes the set of equipment in the system with an associated energy use of electricity; $P_i$ is the instantaneous power used by the equipment $i$; $A$ is the total floor area of the building; and $max_{15}[]$ indicates the maximum value after taking the average of each 15 minute interval.

Peak gas demand in a given period of time¶

This KPI is the measure of the site HVAC peak gas use in $kW/m^2$ when accounting for the sum of all gas equipment present in the test case HVAC system. The mathematical formulation for this KPI is the following:

\[P_G(t_0, t_f) = \frac{\max_{15}[\sum_{i\in I} P_i(t)]}{A}\]

Where $P_G(t_0, t_f)$ is the peak gas demand from the initial time $t_0$ up to the final time $t_f$; $I$ denotes the set of equipment in the system with an associated energy use of gas; $P_i$ is the instantaneous power used by the equipment $i$; $A$ is the total floor area of the building; and $max_{15}[]$ indicates the maximum value after taking the average of each 15 minute interval.

Peak district heating demand in a given period of time¶

This KPI is the measure of the site HVAC peak district heating use in $kW/m^2$ when accounting for the sum of all district heating equipment present in the test case HVAC system. The mathematical formulation for this KPI is the following:

\[P_{DH}(t_0, t_f) = \frac{\max_{15}[\sum_{i\in I} P_i(t)]}{A}\]

Where $P_{DH}(t_0, t_f)$ is the peak district heating demand from the initial time $t_0$ up to the final time $t_f$; $I$ denotes the set of equipment in the system with an associated energy use of district heating; $P_i$ is the instantaneous power used by the equipment $i$; $A$ is the total floor area of the building; and $max_{15}[]$ indicates the maximum value after taking the average of each 15 minute interval.

CO2 emissions in a given period of time¶

This KPI is the measure of the amount of source CO2 emissions in $kgCO_2/m^2$ when accounting for the sum of all energy vectors in the test case HVAC system, each using an emission factor profile based on the source of energy. The emission factors are to be related with the energy mix associated with the location of the test case building. According to this, the CO2 emissions are calculated as:

\[\epsilon (t_0, t_f) = \frac{\sum_{i\in \xi} \int_{t=t_0}^{t=t_f}e_i(t)P_i(t) dt}{A}\]

Where $\epsilon (t_0, t_f)$ is the equivalent total amount of CO2 emissions during the period of time between $t_0$ and $t_f$. $e_i$ is the emission factor of component $i$ and has units of $kgCO_2/kWh$; $A$ is the total floor area of the building.

Operational cost in a given period of time¶

This KPI is the measure of the HVAC operational cost in $\$/m^2$ when accounting for the sum of all energy vectors in the test case HVAC system, each using a price profile based on the source of energy and given tariff archetype. Three tariff archetypes are defined: constant, moderately dynamic (e.g. day/peak and night/off-peak pricing), and highly dynamic (e.g. real-time pricing).

\[C^\tau(t_0, t_f) = \frac{\sum_{i\in \xi}\int_{t=t_0}^{t=t_f}p_i^\tau(t) P_i(t) dt}{A}\]

Where $C^\tau(t_0, t_f)$ is the total cost during the period between time $t_0$ and $t_f$ with a tariff $\tau$; $p_i^\tau$ is the price profile of equipment $i$ with a tariff $\tau$ and has units of $\$/kWh$; $A$ is the total floor area of the building.

Indoor air quality violation¶

The indoor air quality violation is the integral of the deviation of the CO2 concentration above a predefined threshold during a given period of time averaged over all zones. The units are $ppm.h/m^2$ and is quantified as:

\[\Phi(t_0, t_f) = \frac{\sum_{z\in \mathbb{Z}} \int_{t_0}^{t_f} \phi_z(t) dt}{N}\]

\[\phi_z(t)=\gamma_z(t)-\gamma_{r,z}(t), \quad if \quad\gamma_z(t)>\gamma_{r,z}(t)\]

\[\phi_z(t)=0, \quad if \quad \gamma_z(t) \leq \gamma_{r,z}(t)\]

Where $\Phi$ is the total violation of carbon dioxide CO2 concentration in $ppmh$ between the initial time $t_0$ and the final time $t_f$. $z$ is the zone index out of $N$ zones in the building. $\phi_z$ is the deviation of measured zone CO2 concentration $\gamma_z$ from the zone CO2 concentration threshold $\gamma_{r,z}$.

Computational time ratio¶

The computational time at simulation step $k$, $t_c(k)$, is the real time required by the controller to compute the control inputs between simulation steps $k$ and $k-1$. It needs to be shorter than the duration of the simulation step of that iteration, $T_s(k)$. The ratio between $t_c(k)$ and $T_s(k)$ helps indicate the practicality of the controller as well as potential for increasing computational time. This is called the computational time ratio.

As the computational time and the simulation step duration may not be the same for every simulation step, an average of the computational time ratio from all of the simulation steps that take place between the initial time $t_0$ and the final time $t_f$ for which this KPI is calculated. Thus, the computational time ratio is computed as follows:

\[t(t_0,t_f) = \frac{\sum_{k=1}^{n}\frac{t_c(k)}{T_s(k)}}{n}\]

Where $n$ is the number of simulation steps that take place between $t_0$ and $t_f$.

Installation metrics¶

The installation metrics refer to the effort and cost required to get the controller settled and running. Many aspects play a role in this sense. They are intrinsically subjective and therefore require qualitative measures. Therefore, these metrics are provided by the controller developer in the form of a simple score according to the following categories. These categories may be refined in the future.

Installation Metrics¶
Associated Score	1	2	3	4	5	Given Score
Hardware Installation Time (measured in one person time and excluding staff training)	Less than one day	Between a day and a week	Between a week and a month	Between a month and three months	More than three months	To be added by Control Developer
Software Development and Installation Time (measured in one person time)	Less than one day	Between a day and a week	Between a week and a month	Between a month and three months	More than three months	To be added by Control Developer
Hardware Installation Cost (including extra-sensors and labor)	There is not any extra cost	There is a negligible initial extra cost	The extra cost is less than 1% of the actual value of the building	The extra cost is estimated between 1% and 3% of the actual value of the building	The extra cost is estimated to be larger than 3% of the actual value of the building	To be added by Control Developer
Software Development and Installation Cost (including any software licenses and labor)	There is not any extra cost	There is a negligible initial extra cost	The extra cost is less than 1% of the actual value of the building	The extra cost is estimated between 1% and 3% of the actual value of the building	The extra cost is estimated to be larger than 3% of the actual value of the building	To be added by Control Developer
Installation Expertise and Operator Training Requirements	Everyone can install the controller	Everyone can install the controller after a short training course of less than one day	Everyone can install the controller after a short training course of less than one week	Specific engineering knowledge is required like programming skills plus a short training course of less than one week	Only experts and very advanced engineers are able to install the controller	To be added by Control Developer
Intensity of Extra Excitations for Obtaining an Identification Dataset	There is not any need to excite the building because no monitoring data is required or the data can be gathered from the building working as business as usual.	Slight excitations are required. These excitations may have a minor influence in the energy use and there is no need to vacate the building during the training period.	Slight excitations are required that may have a noticeable influence in the energy use but there is no need to vacate the building during the training period.	Intense excitations are required. There is a considerable influence in the energy use and/or a need to vacate the building during the training period.	Intensive excitations are required that can only be obtained from detailed simulation models.	To be added by Control Developer
Required Length of Identification Dataset	There is no need of training from monitoring data.	Less than one day.	Between a day and a week.	Between a week and a month.	Several months.	To be added by Control Developer

Maximum allowed capital cost¶

The maximum allowed capital cost is the installation cost that would lead to a maximum payback period of 5 years. The reason to calculate the maximum allowed capital cost instead of the payback period directly is because of the subjectiveness associated with the installation metrics. The qualitative nature of the installation metrics could hamper the quantification of the payback period. On the contrary, the maximum allowed capital cost to obtain a fixed payback period of 5 years can be objectively quantified if a baseline controller is established as a reference. First, the operational savings per year are calculated as:

\[S_{1 year} = C_{1 year}^{old}-C_{1 year}^{new}\]

These savings are computed as the difference between the operational cost of the old controller (the baseline) and the new controller. Notice the way to calculate these costs is the same as defined in the total operational cost KPI defined before for a given time period of one year and the selected tariff. The maximum allowed capital cost for the controller to get a payback period of 5 years is then calculated as:

\[CAPEX_{max}^{5 years} = 5 S_{1 year}\]

The judgement of whether it is worth to install the new controller relies on the BOPTEST user, who can use the objective quantification of this KPI to take the decision.

Calculation Module¶

A KPI calculation module is implemented that calculates the core KPIs during the test case simulation by computing KPIs on the fly in order to provide feedback to the controller or only for informative purposes. Upon deployment of the test case, the module first use the KPI JSON (kpis.json) to associate model output names with the appropriate KPIs through the specified KPI annotations.