Aggregated Use of Energy Flexibility in Office Buildings

Abstract

Due to climate change consequences, all Member States of the European Union signed an agreement with the goal of becoming the first society and economy with a neutral impact on the planet by 2050. The building sector is one of the highest energy consumers, using 33% of global energy production. Given the global increase for energy demand, implementing energy flexibility strategies is crucial for a better integration of renewable energy sources and a reduction of consumption peaks arising from the electrification of energy demand. The work described in this paper aims to develop an optimization algorithm to use the existing aggregated energy flexibility in office buildings to reduce both the electric energy costs of each office, considering the tariffs applied at each moment and the total power peak, aiming to reduce the entire building’s cost of the contracted power, considering the Portuguese context. The obtained results conclude that it is possible to reduce both the costs associated with electric energy consumption and contracted power. Nevertheless, since the cost of contracted power has a lower impact on the overall energy bill, it is more beneficial to focus only on the reduction of costs associated with electric energy consumption in the considered case study.

1. Introduction

The carbon dioxide (${\mathrm{CO}}_2)$ released from the combustion of fossil fuels for energy is considered to be the main contributor to the increase of the greenhouse effect [1]. According to NASA’s Goddard Institute for Space Studies, the planet’s average temperature has been rising decade after decade, also increasing the rate of occurrence of natural disasters and extreme weather phenomena, and these same phenomena and disasters serve as an alert for the impact of Humanity’s behavior on the environment [2,3]. To change this current trend, it is imperative for humankind to find and implement effective strategies aiming at reducing the emission of greenhouse gases (GHG).

With the ambition to become the first climate-neutral society and economy by 2050, all the European Union Member States signed the Paris Agreement, committing to comply with the strategies presented in order to reduce carbon emissions of the European Union by 2030 by at least 55% compared to emissions recorded in 1990 [4]. As a member state of the European Union, Portugal has set several targets under the Plano Nacional de Energia e Clima for the 2021–2030 horizon with the aim of being at the forefront of the energy transition [5]. By 2030, in addition to increasing energy efficiency by 35%, reaching 15% renewable energy in interconnections between member states and 20% in transport, and reducing ${\mathrm{CO}}_2$ emissions between 45% and 55% in relation to the values recorded in 2005, Portugal committed to meeting 47% of the gross final consumption of energy with renewable energy sources.

Since the demand for energy is increasing across the planet, as it is essential for the development of any economy, renewable energy sources are considered fundamental to avoid the destruction of the planet and its inhabitants [6]. Even so, the energy supply from renewable sources such as the sun and wind are not constant, and it is usually impossible to continuously satisfy the energy needs of a building using only renewable energy sources. Consequently, it is essential to find a solution that reduces the impacts caused by the misalignment between consumption and demand to improve the use of these sources. This solution may involve the integration of energy flexibility usage in these systems, which consists of the ability to adapt a system’s energy consumption or generation without violating technical restrictions or compromising the users’ comfort level [7]. The most common method to add flexibility to a building’s energy demand is storage, through the use of batteries for electrical energy or through the use of a building’s thermal mass for thermal energy [8,9].

Since the building sector consumes around 33% of the global energy produced, the use of the energy flexibility provided by these infrastructures plays a key role in reducing carbon emissions through the integration of renewable energy sources and reduction of consumption peaks arising from the electrification of energy demand [10]. In this context, a recent study carried out by ADEME within the scope of the Odyssee-Mure project in 2019, indicates that office buildings located in Portugal have an average annual consumption of 3411 kWh per employee [11].

Despite the need for a greater use of energy flexibility, information and research on this subject is still scarce in the Portuguese context when compared to other countries. Naim Majdalani et al. [12] assessed the potential of energy flexibility of a space heating and cooling system in a typical household under different geographical conditions in Portugal and concluded that energy flexibility depends on the geographical location of the houses, among other factors. Even if separated by only a few kilometers, there are locations in the Portuguese territory that are more conducive to the use of energy flexibility than others. Daniel Aelenei et al. in [13] investigated the potential for energy flexibility in an office building in Portugal that had two different renewable energy sources installed (a building integrated photovoltaics (BIPV) system and a photovoltaics (PV) system). In this study, the authors resorted to the integration of battery energy storage systems (BESS), with the objective of increasing self-consumption and improving the performance of the interaction with the distribution grid. The results showed that the proposed objectives are achieved, and that the integration of BESS is economically viable for a period of 10 years when the existing energy flexibility is used to increase self-consumption of renewable energy sources.

Internationally, there is more information regarding not only the exploitation of energy flexibility in general but also in the specific context of office buildings. In [14], Fei Lu et al. investigated the energy flexibility of a cooling system using the thermal mass of a nearly zero-energy office building located in northern China and concluded that a rule-bases control can reduce the peak power and the energy consumed during the peak period by 55.6% and 54.0%, respectively, as compared to a reference scenario. Mingzhe Liu et al. in [15] evaluated the potential for energy flexibility of a nearly zero-energy office building located in Denmark under the influence of different control strategies. Due to the increase in energy consumption and the high transmission and tax costs, despite achieving a reduction of around 0.005 $\mathrm{kW}/{\mathrm{m}}^2$ in power demand during peak hours, the authors concluded that it would be more profitable not to use the energy flexibility of the building. Jingfan Hu et al. [16] sought to optimize the operation of the heating, cooling, and air conditioning system to reduce the energy consumption and operating cost of an office building located in China. By combining a rule-based control model with an artificial neural network (ANN), they showed that it is possible to reduce operating costs by 39.22% and 44.41% in summer and winter, respectively.

Considering the work already developed in the Portuguese and international contexts, this study aims to develop an optimization algorithm that uses the existing aggregated energy flexibility in an office building to reduce the total peak power as well as the electric energy costs of each office, considering the tariffs applied at each moment, so that the cost of contracted power for the entire building is reduced. The reduction of total peak power and the electric energy costs play a key role in reducing the energy bill since both are considered in Portugal.

In order to demonstrate the effectiveness of the developed algorithm, a simulation analysis is conducted on an office building located in the Porto region, Portugal. The building has 3 stories with more than 10 individually controlled spaces consisting of both offices and meeting rooms. Three different scenarios are considered in the simulation: a reference scenario, where the HVAC system is subject to a rule-based control; a scenario where a single objective version of the developed algorithm is applied, which only optimizes energy consumption costs; and finally, a scenario where the developed multi-objective algorithm is applied, optimizing both energy costs and the total peak power.

2. Proposed Solution

The proposed solution consists of a genetic algorithm, chosen considering its applicability in this type of problems and the experience of the authors from previous works [12,17,18], paired with RC models that will create, modify, and test several sequences of thermostat settings in order to find the solution that reduces both the electricity costs of each individual office and the total peak load of the building. This optimization algorithm requires a set of inputs: outside temperature, interior temperatures inside each office, accurate estimation of internal heat gains, and solar radiation considering the different orientations of the building spaces. The inputs are used by the optimization algorithm to establish the optimal operation to be applied to the HVAC system of each office. Figure 1 describes the interactions between offices, optimization algorithm and HVAC system.

To provide the best possible set of outputs, the interaction between the offices and the optimization algorithm is fundamental since it involves the offices sharing information with the optimization algorithm. This shared information is used in order to find the optimal behavior to apply to the different considered thermostats. The process used to find this behavior will be covered later in this chapter.

2.1. Modeling The Thermal Behavior of A Building

A model of the resistor-capacitor type is used to model the thermal behavior of the building; this type of model can capture the thermal dynamics of buildings with acceptable accuracy, while being faster than models obtained through detailed simulation tools such as EnergyPlus [12]. For this reason, there is a need to find the values of the equivalent resistors and capacitors, and the parameters of the heat sources that better capture the behavior of the offices. To select these values, the thermal behavior of the building under analysis was modelled with a software tool accredited by the ASHRAE 140 standard [19]. EnergyPlus was chosen considering the amount of information available, its wide usage, and its plugins, which proved to be fundamental in simplifying the modelling process.

A second-order resistor capacitor (R2C2) circuit is considered in this paper, similarly to the one used by Rouchier et al. [18]. The circuit is composed of two equivalent resistors and capacitors, along with two heat sources. It seeks to model the behavior of the envelope and the interior of a given thermal zone as a function of the exterior temperature, the solar radiation, and internal gains [20,21,22].

Based on the work described in [20,21], it is possible to obtain the circuit presented in Figure 2. Variables ${\mathrm{T}}_{\mathrm{o}}$, ${\mathrm{T}}_{\mathrm{e}},$ and ${\mathrm{T}}_{\mathrm{i}}$ denote the outdoor, envelope, and indoor temperatures of the thermal zone, respectively; ${\mathrm{R}}_{\mathrm{e}}$ ($\mathrm{K}/\mathrm{W}$) represents the thermal resistance between the envelope and outdoor temperature, and ${\mathrm{R}}_{\mathrm{i}}$ ($\mathrm{K}/\mathrm{W}$) is the thermal resistance between the indoor temperature and the envelope; ${\mathrm{C}}_{\mathrm{i}}$ and ${\mathrm{C}}_{\mathrm{e}}$ ($\mathrm{J}/\mathrm{K}$) represent the heat capacities of the interior and the envelope, respectively; ${\mathsf{\Phi }}_{\mathrm{h}}$ ($\mathrm{W}$) represents the indoor heating and cooling power applied to the thermal zone during a given timestep by the HVAC system; ${\mathsf{\Phi }}_{\mathrm{G}}$ ($\mathrm{W}$) represents the internal gains; and finally ${\mathsf{\Phi }}_{\mathrm{s}}$ ($\mathrm{W}$) represents the global horizontal solar irradiance, with ${\mathrm{A}}_{\mathrm{e}}$ and ${\mathrm{A}}_{\mathrm{i}}$ (${\mathrm{m}}^2$) being its coefficients for the internal and envelope solar gains, respectively.

Based on the previous circuit, it is possible to obtain Equations (1) and (2) for this model. Regarding the envelope temperature, it is important to note that it is associated with the thermal mass of opaque surfaces, not representing just a specific point.

$${\mathrm{C}}_{\mathrm{i}}{\mathrm{dT}}_{\mathrm{i}}=\frac{1}{{\mathrm{R}}_{\mathrm{i}}}\left({\mathrm{T}}_{\mathrm{e}}-{\mathrm{T}}_{\mathrm{i}}\right)\mathrm{dt}+{\mathsf{\Phi }}_{\mathrm{h}}\mathrm{dt}+{\mathsf{\Phi }}_{\mathrm{g}}\mathrm{dt}+{\mathrm{A}}_{\mathrm{i}}{\mathsf{\Phi }}_{\mathrm{s}}\mathrm{dt}$$

(1)

$${\mathrm{C}}_{\mathrm{e}}{\mathrm{dT}}_{\mathrm{e}}=\frac{1}{{\mathrm{R}}_{\mathrm{i}}}\left({\mathrm{T}}_{\mathrm{i}}-{\mathrm{T}}_{\mathrm{e}}\right)\mathrm{dt}+\frac{1}{{\mathrm{R}}_{\mathrm{e}}}\left({\mathrm{T}}_{\mathrm{o}}-{\mathrm{T}}_{\mathrm{e}}\right)\mathrm{dt}+{\mathrm{A}}_{\mathrm{e}}{\mathsf{\Phi }}_{\mathrm{s}}\mathrm{dt}$$

(2)

Based on Equations (1) and (2), it is possible to obtain Equations (3) and (4), where the interior temperature and the temperature of the envelope at time t + 1 depend on variables at time t [20]. Since at this stage the influence of the air conditioning system has not yet been considered, one must consider ${\mathsf{\Phi }}_h=0$.

$${\mathrm{T}}_{\mathrm{i}}^{\left(\mathrm{t}+1\right)}={\mathrm{T}}_{\mathrm{i}}^{\left(\mathrm{t}\right)}+\frac{\mathrm{dt}}{{\mathrm{C}}_{\mathrm{i}}}{\left(\frac{1}{{\mathrm{R}}_{\mathrm{i}}}\left({\mathrm{T}}_{\mathrm{e}}-{\mathrm{T}}_{\mathrm{i}}\right)+{\mathsf{\Phi }}_{\mathrm{h}}+{\mathsf{\Phi }}_{\mathrm{G}}+{\mathrm{A}}_{\mathrm{i}}{\mathsf{\Phi }}_{\mathrm{s}}\right)}^{\left(\mathrm{t}\right)}$$

(3)

$${\mathrm{T}}_{\mathrm{e}}^{\left(\mathrm{t}+1\right)}={\mathrm{T}}_{\mathrm{e}}^{\left(\mathrm{t}\right)}+\frac{\mathrm{dt}}{{\mathrm{C}}_{\mathrm{e}}}{\left(\frac{1}{{\mathrm{R}}_{\mathrm{i}}}\left({\mathrm{T}}_{\mathrm{e}}-{\mathrm{T}}_{\mathrm{i}}\right)+\frac{1}{{\mathrm{R}}_{\mathrm{e}}}\left({\mathrm{T}}_{\mathrm{o}}-{\mathrm{T}}_{\mathrm{e}}\right)+{\mathrm{A}}_{\mathrm{e}}{\mathsf{\Phi }}_{\mathrm{s}}\right)}^{\left(\mathrm{t}\right)}$$

(4)

The estimates at any timestep depend on the previous timestep, so it is necessary to calculate the envelope temperature at t = 0. For this, and based on [22], the following equation is considered:

$${\mathrm{T}}_{\mathrm{e}}^{\left(0\right)}=\frac{\left({\mathrm{R}}_{\mathrm{i}}{\mathrm{T}}_{\mathrm{o}}{}^{\left(0\right)}+{\mathrm{R}}_{\mathrm{e}}{\mathrm{T}}_{\mathrm{i}}{}^{\left(0\right)}\right)}{\left({\mathrm{R}}_{\mathrm{i}}+{\mathrm{R}}_{\mathrm{e}}\right)}$$

(5)

With the model equations defined, it is necessary to find the optimal parameters (${\mathrm{C}}_{\mathrm{i}}$, ${\mathrm{R}}_{\mathrm{i}}$, ${\mathrm{A}}_{\mathrm{i}}$, ${\mathrm{C}}_{\mathrm{e}}$, ${\mathrm{R}}_{\mathrm{e}}$, and ${\mathrm{A}}_{\mathrm{e}}$) that represent the thermal dynamics of the different considered offices with acceptable accuracy. Different values are used for the different conditions imposed by the different seasons of the year. The values are defined through a program developed in MATLAB^© such that they minimize the sum of squares error (SSE) between the internal temperature predicted by the model (${\mathrm{T}}_{\mathrm{i}}$) and obtained through the simulation performed using EnergyPlus (${\mathrm{T}}_{\mathrm{indoor}\mathrm{simulated}})$, as described in Equation (6).

$$\mathrm{SSE}={\displaystyle \sum }_{\mathrm{i}=0}^{\mathrm{t}}{\left({\mathrm{T}}_{\mathrm{i}}-{\mathrm{T}}_{\mathrm{indoor}\mathrm{simulated}}\right)}^2$$

(6)

2.2. Optimization Algorithm

In addition to the environmental and internal gain inputs, the optimization algorithm also considers the electricity tariffs, and the power of the air conditioning systems present in each office under analysis. A genetic algorithm is used for this optimization; thus, an initial population is also provided for refinement of the results, despite not being mandatory. This population is made up of a set of chromosomes, which in turn are made up of a set of genes [23]. In this case, each gene in the chromosomes represents the state of the HVAC system of a specific office for 15 min, with values limited to integers between 0 and 10. The use of this interval is intended to allow the air conditioning system to work at different power levels where a gene of value 0 means that the air conditioning system is off, and a value of 10 means that the equipment is working at 100% of its maximum power.

Then, using the objective function, the elements of the population are analyzed and selected based on the quality of their response. The best elements will then be selected as parents to produce better descendants for the next generation. This reproductive process consists of two phases: crossover and mutation. Crossover is a process in which elements defined as parents exchange their genetic material, generating descendants. Later, these descendants are altered through mutations. The application of mutations plays a fundamental role in the search for the optimal solution since it introduces randomness, guarantees diversity, and prevents premature convergence, thus preventing the algorithm from finding only local optimal solutions [23]. The elements obtained through crossover and mutation constitute the next generation. These steps are successively repeated until the stopping conditions are met, meaning that the optimal solution of the problem has been reached [23].

Since the algorithm seeks to solve two problems simultaneously, the optimization scheme follows an iterative approach, as described in Figure 3.

The for loop is needed because the optimization algorithm intends to optimize not only one space, but several spaces belonging to the same building, with the number of loop iterations performed being equal to the number of offices. The process performed by the for loop consists of three phases. In the first phase of this cycle, the selection of inputs corresponding to the office under optimization is made. In the second phase, the genetic algorithm is applied to find the optimal functioning of the air conditioning system of the respective space. Depending on the iterations that have already been carried out, since a genetic algorithm is being used, the behavior of the offices is modelled using either the initial population or its offspring if an interaction has already taken place. Since at this stage the influence of the air conditioning system is considered, the term ${\mathsf{\Phi }}_{\mathrm{h}}$ is reintroduced in Equation (3), and its value comes from the genes of the chromosomes belonging to the population. After this step where, through the RC model, the variation of the interior temperature is modelled considering the state of each air conditioning unit coming from the genes, it is necessary to evaluate their quality. For this, an objective function is used. The correct definition of this function while formulating the problem is crucial since the optimal solution will be achieved based on it. The objective function used in the scope of this paper is divided into two phases: a first phase, where the cost of air conditioning of the space is calculated based on tariffs and the total peak power; and a second phase, where a penalty is imposed if the temperature limits are not respected as described in Equations (7)–(9). In those equations, ${\mathrm{Energy}}_{\mathrm{HVAC}}\left(\mathrm{t}\right)$ refers to the energy consumed by a specific office during a 15 min resolution timestep; ${\mathrm{Power}}_{\mathrm{Total}\mathrm{Peak}}$ is the building’s peak load during the horizon of analysis (from ${\mathrm{t}}_1$ to ${\mathrm{t}}_2$); ${\mathrm{Tariff}}_{\mathrm{Energy}}\left(\mathrm{t}\right)$ is the energy tariff applied at each timestep; ${\mathrm{Tariff}}_{\mathrm{Contracted}\mathrm{Power}}$ is the tariff associated with contracted power, ${\mathrm{T}}_{\max /\min }$ corresponds to the defined limits of the inside temperature comfort zone; and α refers to a coefficient that emphasizes the weight of the penalization in the cost function (a value of 1000 was considered). Within the scope of this paper, these limits were defined based on the Portuguese law Portaria n.° 349-D/2013, which defines that interior temperatures must be between 20 °C and 25 °C [24].

$$\mathrm{Costs}={\displaystyle \sum }_{\mathrm{t}={\mathrm{t}}_1}^{{\mathrm{t}}_2}\left({\mathrm{Tariff}}_{\mathrm{Energy}}\left(\mathrm{t}\right){\ast \mathrm{Energy}}_{\mathrm{HVAC}}\left(\mathrm{t}\right)\right)+\max \left({\mathrm{Power}}_{\mathrm{Total}\mathrm{Peak}}\right){\ast \mathrm{Tariff}}_{\mathrm{Contracted}\mathrm{Power}}$$

(7)

$$\{\begin{array}{c}\mathrm{Penalization}={\displaystyle {\displaystyle \sum }_{\mathrm{t}={\mathrm{t}}_1}^{{\mathrm{t}}_2}}{\left({\mathrm{T}}_{\mathrm{i}}-{\mathrm{T}}_{\max /\min }\right)}^2,{\mathrm{if}\mathrm{T}}_{\mathrm{i}}>{\mathrm{T}}_{\max }{\mathrm{or}\mathrm{T}}_{\mathrm{i}}<{\mathrm{T}}_{\min }\\ \mathrm{Penalization}=0,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{if} {\mathrm{T}}_{\min }<{\mathrm{T}}_{\mathrm{i}}<{\mathrm{T}}_{\max }\end{array}$$

(8)

$$\mathrm{Objective}\mathrm{Function}=\mathrm{Costs}+\mathsf{\alpha }\ast \mathrm{Penalization}$$

(9)

Finally, the selection of the individuals that obtained the best results is made and the crossover between them and the mutation is carried out, giving rise to a new population. When the optimal functioning for the HVAC system of a particular office is found, it is stored in a n column matrix. When the loop goes through and optimizes all the offices, this matrix is complete and ready to be analyzed.

This analysis is performed outside the for loop, but inside the while loop, where the n optimal performances are added in order to obtain the total peak power per timestep. This analysis is carried out based on a defined stopping criteria that must be suitable for the problem. In this paper, the following was defined: continue to optimize as long as (while) the total peak power does not remain constant during 11 iterations, considering a 20% error margin. When the stopping criteria are reached, the algorithm returns one or more solutions, depending on the number of offices considered. If for some reason these criteria were not met, a re-optimization procedure is considered.

3. Case Study

The considered office building was built in 2015 for S&P Portugal (Figure 4). It is located at one of the industrial areas of the Moreira parish, Maia council, 14 km from the city of Porto (Portugal). The building consists of three stories with a total usable area of approximately 725 ${\mathrm{m}}^2$ and an average ceiling height of 3 m. The ground story has a different layout that the upper stories, which are intended for administrative activities.

Considering the definition of thermal zone provided by Michaël Kummert et al. [25], 35 thermal zones are identified in this building, as shown in Figure 5. Of these 35 thermal zones, it was considered that only the zones referring to offices, cabinets, and meeting rooms are under influence of a HVAC system.

The building is provided with a VRV-based HVAC system (Daikin RXYQ8T), which has a heating power of 25 kW, a cooling power of 22.4 kW, and a coefficient of performance (COP) and an energy efficiency ratio (EER) of 4.54 and 4.30, respectively. However, for simplification, the EnergyPlus modelling was carried out assuming the ideal system object available. This approach allows to match the operation of the VRV air conditioning system using a simplified computational model, while obtaining identical results. Typical heating and cooling power are considered for the indoor units, considering the size and use of the spaces.

A building has two types of thermal gains: through internal loads (occupancy, lighting, and electrical equipment) and through incident solar radiation. The parameters used to describe each of these gains are detailed below.

• Occupancy
  • For simulation purposes, four types of spaces are considered in the building: offices, cabinets, meeting rooms, and the staff room.
  • Regarding office occupancy, the reference values considered by the Portuguese Legislation (Decreto-Lei n.° 79/2006) are used: $15{\mathrm{m}}^2/\mathrm{occupant}$ for this type of space, from 9 am to 5 pm and with a one-hour lunch break starting at 1 pm [26]. Cabinets follow the same principle both for the occupation considered and for the hours of occupation.
  • Finally, a temporary occupation is assumed for both the meeting rooms and the staff room. In the case of the meeting rooms, a daily meeting of four to five people is considered between 4 pm and 5 pm. For the staff room, an occupancy of six people is assumed during the lunch break.
  • The total thermal load released by each occupant is set to $120\mathrm{W}/\mathrm{occupant}$, following the reference value considered by ASHRAE in relation to an office activity.
• Lighting
  • The luminosity values adopted consider the recommendations given by the Chartered Institution of Building Services Engineers (CIBSE). A value of $500\mathrm{lux}$ is assumed for the meeting rooms and offices and $300\mathrm{lux}$ for the staff room. For the remaining spaces $100\mathrm{lux}$ are considered. The usage profiles are set based on the Decreto-Lei n.° 79/2006 for offices [27]. The considered consumptions are $3.75\mathrm{W}/{\mathrm{m}}^2$ following [26].
• Electrical Equipment
  • To calculate the thermal loads associated with electrical equipment, the values established by the Decretal-Lei n.° 79/2006 are also used. Those are 15$\mathrm{W}/{\mathrm{m}}^2$ for offices, cabinets, and meeting rooms, and $200\mathrm{W}/{\mathrm{m}}^2$ for the staff room [27].
• Solar Radiation
  • The EPW type file relating to the climate in the Porto region is used to consider the variation of solar radiation [28].

Since the influence of tariffs in optimizing the operation of air conditioning systems in spaces is under analysis in this paper, three different types of time-of-use tariffs are considered: single tariff, where the consumer pays the electric energy at the same price regardless the period of the day; double tariff, where the consumer pays for the electric energy according to the period of consumption, with two periods with different prices; and triple tariff, similar to the double tariff, but with three periods of consumption.

Table 1. Energy tariffs considered [29,30].

Active Energy Price	Time Period	Schedule		€/kWh
		Winter	Spring, Summer and Autumn
Single Tariff	-	-		0.1742
Double Tariff	Off-peak	00:00 h to 08:00 h and 22:00 h to 24:00 h		0.1994
	Peak	08:00 h to 22:00 h		0.1058
Triple Tariff	Peak	09:00 h to 10:30 h and 18:00 h to 20:30 h	10:30 h to 13:00 h and 19:30 h to 21:00 h	0.3161
	Half-peak	08:00 h to 09:00 h, 10:30 h to 18:00 h and 20:30 h to 22:00 h	08:00 h to 10:30 h, 13:00 h to 19:30 h and 21:00 h to 22:00 h	0.1702
	Off-peak	00:00 h to 08:00 h and 22:00 h to 24:00 h		0.1058

presents the costs associated with each tariff and their respective schedules. The costs related to the contracted power are also considered, which are presented in

Table 2. Costs related to contracted power [29].

Contracted Power (KVA)	Cost (€/day)
1.15	0.0791
2.3	0.1315
3.45	0.1662
4.6	0.2163
5.75	0.2661
6.9	0.3160
10.35	0.4656

. The values presented in Table 1 and Table 2 do not consider additional applicable taxes.

To make the best possible analysis, several simulation periods are considered in this paper taking into account the different seasons of the year. Although in [31] it is mentioned that RC models should only be used to make predictions within a maximum period of 12 h, Rouchier et al. present accurate results even considering a period of 96 h [20]. Thus, to find the best simulation period, five different simulation periods are tested (12, 24, 48, 72, and 96 h).

4. Results and Discussion

The analysis of the results for different time periods show that more accurate results are obtained for shorter simulation times. Even so, only the results obtained for 72 and 96 h are not very accurate and consequently unusable within the scope of this paper. The 12, 24, and 48 h simulation periods present good results. Therefore, since it is advantageous for the optimization algorithm to have a longer simulation period to exploit and benefit from thermal inertia, a simulation period of 48 h is considered.

For this simulation period, the determination of the different parameters of the model is carried out to find the combinations that best portray the thermal dynamics of the various zones under analysis. By looking into the optimal parameters for each zone, it is possible to observe that only the coefficients for the internal and envelope solar gains (${\mathrm{A}}_{\mathrm{e}}$ and ${\mathrm{A}}_{\mathrm{i}},$ respectively) should vary from season to season since the values of ${\mathrm{R}}_{\mathrm{e}}$, ${\mathrm{R}}_{\mathrm{i}}$, ${\mathrm{C}}_{\mathrm{e}}$, and ${\mathrm{C}}_{\mathrm{i}}$ represent the physical constitution of the building, which should always remain the same. Through an analysis of the obtained results, it is found that a single RC model is not able to model the behavior of a zone for all seasons. Therefore, a different RC model is considered for each season (

Table A1. Parameters obtained for the winter RC model.

Zones	${\mathbf{C}}_{\mathbf{i}}$	${\mathbf{R}}_{\mathbf{i}}$	${\mathbf{A}}_{\mathbf{i}}$	${\mathbf{C}}_{\mathbf{e}}$	${\mathbf{R}}_{\mathbf{e}}$	${\mathbf{A}}_{\mathbf{e}}$
Z1_1	115817.7	0.040107	0.157969	26628991.8	1.848667	6.665796
Z1_2	88049.73	0.049642	0.162183	46409254.7	1.626257	14.387339
Z1_3	65800.02	0.032577	0.115207	100949790.	3.572689	15.585181
Z1_7	39799.44	0.101603	0.103805	47936649.9	5.015017	15.441295
Z1_8	37928.78	0.099807	0.122932	15907569.7	4.995903	4.344319
Z1_12	83636.5	0.045308	0.186124	72626904.4	3.224278	15.693726
Z2_1	102106.2	0.041621	0.104512	63656330.5	2.806462	15.670239
Z2_2	70376.44	0.047844	0.052287	54013723.3	4.205719	15.699841
Z2_3	70536.56	0.062066	0.111844	58826705.4	1.854434	14.884222
Z2_4	40596.43	0.070450	0.026637	31889831.1	5.004427	4.794063
Z2_5	23580.92	0.074909	0.038493	18797929.3	5.035396	2.530044
Z2_13	62621.42	0.047394	0.186124	77504640.1	3.553191	10.78246

,

Table A2. Parameters obtained for the spring RC model.

Zones	${\mathbf{C}}_{\mathbf{i}}$	${\mathbf{R}}_{\mathbf{i}}$	${\mathbf{A}}_{\mathbf{i}}$	${\mathbf{C}}_{\mathbf{e}}$	${\mathbf{R}}_{\mathbf{e}}$	${\mathbf{A}}_{\mathbf{e}}$
Z1_1	201713.9	0.05678	0.000342	95934828.9	1.90041	4.081978
Z1_2	141552.7	0.066541	0.039061	87927162.5	2.046976	4.338496
Z1_3	128360.6	0.017753	0.186119	216915823	4.030443	9.783983
Z1_7	76482.8	0.058847	0.154619	91881157.5	3.507424	6.152563
Z1_8	59334.4	0.089815	0.072892	240510881	5.433061	14.59317
Z1_12	130693.7	0.033229	0.186122	163762507	3.433841	8.254729
Z2_1	189695.2	0.048883	0.000991	322900122	3.17159	15.70631
Z2_2	216096.3	0.057558	0.000549	1685586706	7.652105	15.61594
Z2_3	100652.7	0.094881	9.04E-05	425480687	3.611368	15.06941
Z2_4	64221.2	0.049417	0.036794	354963272	43.73521	15.71811
Z2_5	38767.3	0.050619	0.04846	38586653.8	25.59372	1.625303
Z2_13	38767.3	0.050619	0.04846	38586653.8	25.59372	1.625303

,

Table A3. Parameters obtained for the summer RC model.

Zones	${\mathbf{C}}_{\mathbf{i}}$	${\mathbf{R}}_{\mathbf{i}}$	${\mathbf{A}}_{\mathbf{i}}$	${\mathbf{C}}_{\mathbf{e}}$	${\mathbf{R}}_{\mathbf{e}}$	${\mathbf{A}}_{\mathbf{e}}$
Z1_1	662750.7	0.0105170	1.333157	78659563.6	0.415830	12.661040
Z1_2	470841.7	0.010444	1.852617	73122035.1	0.503852	15.656180
Z1_3	96067.6	0.016937	0.186118	140850519.1	4.998125	9.697990
Z1_7	116621.1	0.009232	1.598011	3741158.4	0.474585	0.618964
Z1_8	149428.2	0.008249	1.833341	8466209.5	0.503475	0.007803
Z1_12	105790.3	0.031658	0.186107	84942867.2	3.257322	11.343427
Z2_1	671959.5	0.006797	1.571484	45008325.3	0.450924	4.673582
Z2_2	939172.5	0.005767	1.847074	132833113.9	0.503832	14.828370
Z2_3	400804.9	0.009737	1.852830	49889879.4	0.503824	9.098063
Z2_4	56578.2	0.043655	0.053515	193349801.5	5.037983	11.22223
Z2_5	31633.6	0.048044	0.055719	3226269.8	4.488279	0.034942
Z2_13	83714.3	0.038669	0.184269	125803025.1	2.513791	15.714175

and

Table A4. Parameters obtained for the autumn RC model.

Zones	${\mathbf{C}}_{\mathbf{i}}$	${\mathbf{R}}_{\mathbf{i}}$	${\mathbf{A}}_{\mathbf{i}}$	${\mathbf{C}}_{\mathbf{e}}$	${\mathbf{R}}_{\mathbf{e}}$	${\mathbf{A}}_{\mathbf{e}}$
Z1_1	154578.2	0.051167	9.48E-09	115721626.8	2.532311	13.351637
Z1_2	129297.9	0.052560	0.146755	88222870.49	2.535602	13.837722
Z1_3	95587.5	0.024586	0.166709	184306463.4	4.771323	13.460518
Z1_7	47553.5	0.137969	0.042630	158082.5	5.023292	0.192098
Z1_8	46480.6	0.107353	0.061751	61550019.2	5.038516	11.312383
Z1_12	104400.1	0.039789	0.185975	12818508.7	3.871203	1.315828
Z2_1	137083.3	0.047464	5.34E-05	76287406.1	3.946815	8.135855
Z2_2	133923.6	0.049509	0.000819	33377279.7	5.036977	3.98385
Z2_3	99104.3	0.066419	0.099093	30222527.3	5.026976	3.888611
Z2_4	49933.9	0.069179	0.006564	163735531.7	5.038525	12.50038
Z2_5	29694.5	0.068419	0.025585	9550086.4	4.769888	0.636558
Z2_13	167624.7	0.097382	0.184021	134594.2	32.29969	0.605458

).

4.1. Scenario 1

Scenario 1 is the reference scenario. The air conditioning system is not controlled by the optimization algorithm. It is called upon to intervene only when the indoor temperature falls outside the comfort range (20 °C to 25 °C) [25].

Since an office building has high internal gains, it is no surprise that the thermal zones under study remain within the comfort limits for most of the time during the winter season even without air conditioning. Thus, we use stricter limits for the winter season (i.e., an interval between 21 °C and 24 °C is used).

Considering what was reported, the building is simulated taking into account the two coldest days for the winter and the two hottest days for the remaining seasons. Based on the obtained results, the costs associated with each tariff per season were calculated and presented in

Table 3. Costs associated with Scenario 1.

	Tariff Type and Cost (€)		Total Power Peak (W)	Associated Cost (€/day)	Total Cost (€)
Winter	Simple	4.91	1295	0.13	5.17
	Double	3.39	1295	0.13	3.65
	Triple	3.44	1295	0.13	3.65
Spring	Simple	2.30	1953	0.13	2.56
	Double	2.63	1953	0.13	2.89
	Triple	3.11	1953	0.13	3.37
Summer	Simple	38.17	5907	0.27	38.70
	Double	43.69	5907	0.27	44.22
	Triple	47.07	5907	0.27	47.60
Autumn	Simple	1.37	870	0.08	1.53
	Double	1.52	870	0.08	1.69
	Triple	1.70	870	0.08	1.86

.

From the previous results it is possible to conclude that summer is the season with highest energy demand. Furthermore, the maximum electrical power for cooling is exceeded in this season—the maximum total peak power is 5.9 kW, greater than the 5.2 kW rated capacity of the VRV heat pump. This value is obtained by dividing the cooling power by the EER, which describes the cooling efficiency of the system. This means that, when supplying 5.2 kW to the HVAC system (i.e., the maximum that the machine supports) it manages to produce 22.4 kW of cold. The air conditioning system considered is not capable of responding to the day-to-day demands imposed by the scenario under analysis, and the consequence is that temperatures will be outside the considered range.

Finally, it is important to note that the already defined comfort bands will be used for the remaining scenarios, as well as the functioning of the HVAC systems found in Scenario 1, which will be used as the initial population of the genetic algorithm.

4.2. Scenario 2

In Scenario 2, an adaptation of the developed algorithm is used to reduce only the electricity costs of each office considering the applicable tariffs at each moment, ignoring the total peak power. The objective function is modified to consider office-to-office optimization individually (Equation (10)).

$$\mathrm{Objective}\mathrm{Function}={\displaystyle \sum }_{\mathrm{t}={\mathrm{t}}_1}^{{\mathrm{t}}_2}\left({\mathrm{Tariff}}_{\mathrm{Energy}}\left(\mathrm{t}\right){\ast \mathrm{Energy}}_{\mathrm{HVAC}}\left(\mathrm{t}\right)\right)+\mathsf{\alpha }\ast \mathrm{Penalization}$$

(10)

This objective function will lead the algorithm to always seek to use the HVAC system outside the periods when the tariffs are higher, thus trying to take full advantage of the thermal inertia to reduce the costs. The costs associated with each tariff and season are shown in

Table 4. Costs associated with Scenario 2.

	Tariff Type and Cost (€)		Total Power Peak (W)	Associated Cost (€/day)	Total Cost (€)
Winter	Simple	3.37	1956	0.13	3.63
	Double	2.26	1784	0.13	2.52
	Triple	2.50	2035	0.13	2.76
Spring	Simple	2.18	1953	0.13	2.44
	Double	2.45	2019	0.13	2.71
	Triple	2.64	2028	0.13	2.90
Summer	Simple	19.21	5137	0.22	19.64
	Double	26.84	6981	0.32	27.47
	Triple	33.86	6884	0.27	34.39
Autumn	Simple	1.31	870	0.08	1.47
	Double	1.37	870	0.08	1.53
	Triple	1.36	966	0.13	1.62

.

The low tariff seeking behavior is illustrated in Figure 6, where the power obtained for Scenario 1 and Scenario 2 are simultaneously represented. A triple tariff during spring is considered. It is possible to verify, especially near the 34th hour of the simulation period, the effect of applying the optimization algorithm, where the space cooling is shifted from a more expensive period in Scenario 1 to a cheaper one in Scenario 2.

4.3. Scenario 3

The final scenario consists of the application of the developed algorithm, seeking to simultaneously reduce the electricity costs of each office, considering the applicable tariffs at each moment, and the total peak power, so that the cost of the contracted power of the entire building is also reduced. The costs associated with each tariff and season are presented in

Table 5. Costs associated with Scenario 3.

	Tariff Type and Cost (€)		Total Power Peak (W)	Associated Cost (€/day)	Total Cost (€)
Winter	Simple	3.44	1222	0.13	3.70
	Double	2.55	1222	0.13	2.81
	Triple	3.20	1242	0.13	3.46
Spring	Simple	2.25	1033	0.08	2.41
	Double	2.72	1302	0.13	2.98
	Triple	2.69	1116	0.08	2.85
Summer	Simple	22.83	4637	0.22	23.26
	Double	28.25	4744	0.22	28.68
	Triple	34.17	4791	0.22	34.60
Autumn	Simple	2.44	781	0.08	2.60
	Double	2.80	791	0.08	2.96
	Triple	2.76	721	0.08	2.92

.

4.4. Discussion

Through

Table 6. Comparison between the three scenarios under study regarding the costs associated with the electrical energy of each office and the total peak power during the summer.

	Tariff Type and Cost (€)		Total Power Peak (W)	Associated Cost (€/day)	Total Cost (€)
Scenario 1	Simple	38.17	5907	0.27	38.70
	Double	43.69	5907	0.27	44.22
	Triple	47.07	5907	0.27	47.60
Scenario 2	Simple	19.21	5137	0.22	19.64
	Double	26.84	6981	0.32	27.47
	Triple	33.86	6884	0.27	34.39
Scenario 3	Simple	22.83	4637	0.22	23.26
	Double	28.25	4744	0.22	28.68
	Triple	34.17	4791	0.22	34.60

it is possible to compare the results obtained for all the considered scenarios. It presents the costs due to the consumption of electric energy and to the total peak of power during the summer, which represents the season of greatest energy need.

Comparing the results obtained in Scenario 1 and Scenario 2, it is possible to observe that there is a considerable decrease in electric energy costs and a significant increase in terms of maximum power in the latter. This happens as the adapted objective function seeks only to reduce the electric energy costs of each office without a concern for the consequences at the aggregate level. In Scenario 2, the optimization algorithm seeks to shift the heating/cooling of spaces to periods where the double- or triple-tariffs are lower, reducing consumption during peak times. Therefore, most of the loads are moved to the same moment which results in an increase of the total peak power. In the case of the single tariff, since the applied tariff is always constant, there is an optimization of costs due to the simple search for the optimal operation, which consumes less energy without compromising the comfort of the occupants of the spaces.

By comparing the results obtained in Scenario 3 and the results obtained in Scenario 2, it is possible to observe that although both seek to reduce the costs associated with electricity, Scenario 3 does not present such significant reductions as the previous scenario. This is because the optimization algorithm developed and applied in Scenario 3, seeks to optimize the functioning of the systems of the different offices considering two objectives. In view of this, even though it does not have a reduction in energy costs (when comparing to the previous scenario), Scenario 3 does present the lowest maximum peak powers for all tariffs.

By observing the results obtained in each scenario for all seasons, it is possible to conclude that the optimization algorithm always reduces the energy cost and the total peak power. Even so, since the cost of the contracted power has a lower impact, it is possible to observe through Table 6 that Scenario 2 is the most advantageous in economic terms.

5. Conclusions

The work presented in this paper has, as its main motivation, the need to explore the energy flexibility of buildings. This need is seen as essential since buildings belong to a sector that consumes about 33% of global energy produced and also because energy demand is expected to increase as it is essential for the development of any economy.

The optimization algorithm developed seeks to explore the energy flexibility of office buildings, with the objective of reducing the costs associated with the consumption of electric energy in each office. It considers electricity tariffs and the total peak power at each moment, so that the cost of contracted power for the entire building is also reduced.

The study carried out considered three different cases: Scenario 1, which concerns the baseline behavior; Scenario 2, where only energy demand is optimized; and Scenario 3, where the developed algorithm is used to optimize both energy demand and total peak power. The results show that since the cost of the contracted power has a lower impact on the total cost, the most economically advantageous option for the building is to opt for Scenario 2.

The developed work offers a multi-objective optimization algorithm in order to reduce both the electric energy costs of each office, considering tariffs applied at each moment, and the total power peak, aiming to reduce the entire building’s cost of the contracted power, and the respective application to a case study under the Portuguese context. Further developments include the assessment of the referred algorithm to a real office-building in Portugal.