An Optimal Battery-Free Approach for Emission Reduction by Storing Solar Surplus in Building Thermal Mass

An Optimal Battery-F ree Approac h for Emission Reduction b y Storing Solar Surplus in Building Thermal Mass Mic hela Boffi a, ∗ , Jessica Leoni a , F abrizio Leonforte a , Mara T anelli a , P aolo Oliaro a a Polite cnic o di Milano, Piazza L e onar do da Vinci, Milano, 20133, Milano, Italy Abstract Decarb onization in buildings calls for adv anced con trol strategies that co or- dinate on-site renew ables, grid electricit y , and thermal demand. Literature approac hes t ypically rely on demand side management strategies or on ac- tiv e energy storage, like batteries. Ho wev er, the first solution often neglects carb on-a ware ob jectiv es, and could lead to grid o verload issues, while bat- teries entail environmen tal, end-of-life, and cost concerns. T o o v ercome these limitations, we prop ose an optimal, carb on-aw are op- timization strategy that exploits the building’s thermal mass as a passiv e storage, a voiding dedicated batteries. Sp ecifically , when a surplus of renew- able energy is a v ailable, our strategy computes the optimal share of surplus to store b y temp orarily adjusting the indoor temp erature setp oint within comfort b ounds. Th us, by explicitly accounting for forecasts of building en- ergy consumption, solar pro duction, and time-v arying grid carb on intensit y , our strategy enables emissions-a ware load shifting while main taining comfort. W e ev aluate the approach by simulating three TRNSYS mo dels of the same system with differen t thermal mass. In all cases, the results show consisten t reductions in grid electricit y consumption with resp ect to a baseline that do es not leverage surplus renewable generation. These findings highligh t the p oten tial of thermal-mass-based control for building decarb onization. ∗ Corresp onding author Email addr esses: michela.boffi@polimi.it (Michela Boffi), jessica.leoni@polimi.it (Jessica Leoni), fabrizio.leonforte@polimi.it (F abrizio Leonforte), mara.tanelli@polimi.it (Mara T anelli), paolo.oliaro@polimi.it (P aolo Oliaro) Keywor ds: Optimal control, Decarb onization, Photo voltaics, Smart buildings, Passiv e thermal storage, Energy flexibility 1. In tro duction The construction and building sector contributes significantly to global energy-related CO 2 emissions. A ccording to data reported in the Global Status Rep ort for Buildings and Construction 2024/2025, in 2023 buildings w ere resp onsible for approximately 32% of global energy demand and 34% of CO 2 emissions, mainly asso ciated with space heating and cooling, domestic hot w ater pro duction, ligh ting, and other end uses, whic h reac hed a record of 9.8 GtCO 2 [1]. Despite the progress made in 2024, represen ted by greater adoption of renewable energy and increased electrification, the sector is still not aligned with the climate neutralit y targets set for 2050. In fact, as highligh ted by the global buildings climate track er, b et ween 2015 and 2023, CO 2 emissions asso ciated with buildings increased b y 5.4%, compared to the required reduction of 28.1% [1]. As a consequence, the observ ed progress remains insufficient to meet the targets of the P aris Agreemen t [1]. Figure 1: CO 2 Emissions from the building sector from 2010 to 2023 (left) and the share of buildings in global energy- and pro cess-related emissions in 2023 (right). Source: re- pro duced from [1]. Therefore, practical decarbonization solutions are required, and impro v- ing en velope and system efficiency alone is often insufficient. In this regard, a promising direction is given by the design of strategies aimed at explic- itly increasing the utilization of on-site renewable generation, predominantly 2 solar. Ho wev er, photo voltaic (PV) output is intermitten t and often p o orly aligned with building energy demand, so surplus electricity frequen tly o ccurs when it cannot b e consumed directly . T o manage the in termittency of energy pro duction from PV systems, tw o strategies are t ypically adopted: feeding the generated energy into the grid and using electro chemical storage systems. Ho wev er, b oth solutions come with some dra wbacks. Indeed, in the first case, under a scenario of full electrification of the built environmen t, a large-scale injection of electrical energy into the grid ma y lead to o ver-v oltage issues, o verloads, and congestion in distribution lines, particularly in the presence of old electrical net works [2, 3]. Consequently , an excessive reliance on the electrical grid ma y become critical for the stabilit y and reliabilit y of the system. Considering batteries, instead, it must b e noted that they are tech- nically effectiv e but not fully sustainable. In fact, some studies show that a non-negligible share of the en vironmental fo otprint is related to battery man- ufacturing and end-of-life processing, with outcomes strongly dependent on assumptions regarding chemistry , lifetime, depth of disc harge, and recycling path wa ys [4, 5]. Moreo ver, although recycling technologies are adv ancing, they are still complex and energy-in tensive, and their viability dep ends on logistics and recov ered material v alue, hindering b oth sustainability and cost at scale [4, 6, 7]. These limitations hav e motiv ated growing in terest in battery-free alter- nativ es. In this context, the most promising solutions aim at increasing re- new able self-consumption b y exploiting in trinsic storage within the building. This p ersp ective naturally connects to the concept of building energy flexibil- it y , defined as the capability of a building to mo dulate demand and/or gener- ation in resp onse to climate, o ccupants’ needs, and grid requirements [8, 9]. Energy flexibility can b e provided through dedicated storage (electrical or thermal) or, importantly , through passive storage enabled by the thermal capacit y of env elop e comp onen ts [8]. In this con text, several studies high- ligh t thermal inertia as a promising alternative to activ e storage. Sp ecifically , these works analyze ho w to engineer the building env elope so that it can store and release heat, shifting Heating, V en tilation, and Air Conditioning (HV A C) op eration and effectiv ely acting as a “virtual battery” [10, 11]. How ev er, muc h of the existing literature emphasizes env elop e design and retrofit measures as a passive mean to enhance thermal storage capacit y , rather than a to ol that can b e real-time managed by a proper control framew ork. Bey ond storage tec hnologies, the strategy used to regulate the wa y in whic h they absorb and release energy must also b e considered. In this re- 3 gard, is indeed key to note that man y building con trol strategies aim at minimizing energy use or electricit y cost. Ho wev er, these ob jectives are not generally equiv alent to minimizing CO 2 emissions. In fact, as electricity- related emissions dep end on the time-v arying grid carb on intensit y , the same energy sav ed at different times can lead to markedly different emission out- comes. Therefore, not only an alternative to battery storage is required but also a dedicated control strategy that explicitly account for carb on in tensity , rather than treating energy or cost minimization as a proxy for decarb oniza- tion. T o address these issues, in this work, we prop ose an optimal battery-free con trol strategy to reduce carb on emissions b y storing the surplus of solar energy in the building’s thermal mass. This av oids battery-related en viron- men tal and end-of-life impacts and mak es the solution easier to implemen t, also reducing costs. Sp ecifically , w e design a control strategy that, consid- ering the forecasts of real-time carb on emission in tensit y , PV generation, external temp erature, and building energy consumption, computes the op- timal fraction ( α ( k )) of a v ailable surplus solar energy to be stored in to the building’s thermal mass. Th us, it shifts the indo or temp erature setpoint up ward in winter and do wnw ard in summer, while maintaining o ccupants’ comfort. In doing so, our strategy stores solar energy when it is av ailable and reduces subsequen t reliance on grid electricity , thereby lo wering near- term CO 2 emissions. T o ev aluate the effectiveness of the proposed strategy , w e consider three case studies in which we analyze the b eha vior of the ro om, but with differen t thermal mass, i.e., with low, medium, and high thermal ca- pacit y . F or each case, w e sim ulate its thermal dynamics with and without the prop osed con trol strategy , enabling a direct comparison of its impact across differen t env elop e c haracteristics. In all the scenarios, the results sho w that our strategy yields considerable CO 2 emissions reduction, while maintaining o ccupan ts’ comfort. F urthermore, as a side effect, it also allo ws for reducing the consumption of grid electricity , thus fav oring cost savings. The remainder of this pap er is organized as follo ws: Section 2 better details the state of the art on building energy managemen t tec hniques and on the use of the building en velope for passive thermal storage. Then, Section 3 details the prop osed metho d and its implemen tation, also pro viding insights in to the theoretical rationale that supp orts it. Next, Section 4 describ es the case study and the models used to ev aluate our strategy , while Section 5 presen ts and discusses the obtained results. Finally , Section 6 commen ts on the main con tributions of the w ork and outlines its p ossible future directions. 4 2. Related W ork This Section summarizes the state of the art in building energy manage- men t. T o this end, w e first review the most effectiv e strategies prop osed in the literature, then fo cus on approaches that use the building’s thermal mass as passiv e storage. The goal is to outline their b enefits and current limita- tions, to effectively p osition our w ork and highlight its no v el con tributions. 2.1. Building ener gy management Building energy managemen t strategies can b e broadly group ed into three categories, each with distinct strengths and limitations. A first research line fo cuses on demand side managemen t. These approac hes aims at reshap- ing in telligen t device scheduling and user b ehavior through load shifting, p eak reduction, and price-based op eration. Representativ e examples include reinforcemen t learning-based sc hedulers for residen tial devices and aggrega- tions [12, 13], game-theoretic or negotiation-based co ordination sc hemes [14], and heuristic optimization, mainly emplo y ed in industrial applications [15]. Despite promising results, demand side management strategies dep end heav- ily on the av ailabilit y of sufficien tly flexible loads and on user acceptance, and their p erformance degrades when short-term demand forecasts are inac- curate. A second family of approaches includes mo del-based control strategies, where a predictive mo del is used to optimize HV A C setp oints and op erating v ariables o ver a receding horizon [16, 17]. Compared to o ccupancy- or air qualit y-driven modulation, these metho ds explicitly exploit forecasts of ex- ogenous disturbances and op erating conditions to anticipate system b ehavior and adjust the plant accordingly . Their effectiv eness, ho w ev er, strongly de- p ends on the a v ailabilit y of accurate predictiv e mo dels. T o this end, in many con tributions, mo dels are learned via mac hine- or deep-learning metho ds, whic h pro ve to b e less computationally in tensiv e, despite pro viding simi- lar accuracy p erformance. Ho w ev er, they also come with drawbac ks, e.g., c hanges in operating conditions or o ccupancy patterns ma y lead to incor- rect predictions, thereby requiring frequent re-calibration [18]. Con v ersely , ph ysics-based mo dels yield more generalizable predictions but lead to com- putationally demanding optimization problems that may b e difficult to solve in real time on embedded con trollers. Similar limitations characterize the last category of literature approac hes, whic h includes works based on deep reinforcemen t learning [19, 20], as w ell 5 as metaheuristics and sw arm intelligence [21, 22], or ev en broader deep- learning-enabled frameworks [23, 24] for HV AC control and comfort enforce- men t. While these metho ds can handle complex, nonlinear dynamics and high-dimensional state spaces, they are t ypically sample-inefficient, sensitiv e to reward design, and difficult to deploy safely without extensiv e training. Moreo ver, the lack of in terpretabilit y limits user trust and regulatory accep- tance, which are critical factors for real-w orld adoption. All three categories share a common limitation: they are primarily de- signed to minimize energy consumption or cost, without explicitly accoun ting for the carb on intensit y of the grid. New strategies are therefore required that go b ey ond con ven tional energy reduction by explicitly targeting decarb oniza- tion. This means that they should not b e designed to use less energy , but to use energy at the righ t time, i.e., when the grid is cleaner and renew- able a v ailabilit y is higher. A c hieving this goal requires integrating real-time carb on intensit y signals in to the energy management decision-making pro- cess, which remains largely absent from the existing literature. Bey ond that, t wo additional limitations also emerge. First, practical deplo y ability: many state-of-the-art approac hes rely on deep learning or reinforcemen t learning, whic h are sensitive to changes in plant configuration and op erating condi- tions, p o orly interpretable, and computationally complex. Therefore, more in terpretable, light w eight solutions are needed to promote adoption and trust. Last, giv en the w ell-known limitations of electro c hemical batteries in terms of cost, degradation, and en vironmental impact, there is a clear need for strategies that enable renewable surplus management through battery-free alternativ es. 2.2. Building thermal mass as a p assive stor age system Considering the latter limitation, i.e., the need for battery-free strate- gies, sev eral solutions hav e b een prop osed in the literature. One of the most promising research line uses the thermal mass of the building as a passiv e means to store thermal energy . Such a solution is effective, as it enables the absorption of heat when av ailable in excess and its gradual release when needed, thereby stabilizing indo or temp eratures, reducing p eak energy de- mand, and enhancing building energy flexibilit y [25, 26, 8]. Suc h approaches can b e categorized in to three groups: sensible heat stor- age through a high-inertia en velope materials, which attenuate indo or tem- p erature peaks [26, 27]; laten t heat storage via Phase Change Materials, whic h exploit phase transitions at nearly constan t temp erature, ac hieving 6 storage capacities from 5 to 14 times higher than sensible materials [28, 29, 30]; and active exploitation of the building en velope as a thermal battery , in tegrated with photov oltaics and heating systems to supp ort energy man- agemen t and emission reduction [10]. In this work, we fo cus on the third approach. Sp ecifically , we build up on existing literature in the field, which can b e organized along three main ob jec- tiv es: cost reduction, p eak demand reduction, and PV self-consumption max- imization. Considering cost reduction, a reference work in the field prop oses a v ariable setp oint strategy — 21 . 5 ◦ C during lo w-price p erio ds and 19 ◦ C during high-price perio ds — applied to a Nordic m ulti-apartmen t building. This strategy yielded ann ual cost savings of 5.2% in 2015 and 7% in 2022 [31]. A similar approach prop oses a floating setp oin t pre-co oling s trategy to re- duce electricity imp ort costs, achieving a reduction of approximately 6.1% through temp oral load shifting [32]. Considering approaches aimed at reduc- ing HV A C energy use, [33] shows that raisi ng the co oling setp oin t from 24 ◦ C to 26 − 28 ◦ C can reduce air-conditioning load by up to 40% in the t wo hours follo wing a demand resp onse even t. F urthermore, [34] shows that hysteresis- based setp oint con trol within a 0.5–4 K band reduces heat pump energy use b y 28–41% ov er a four-mon th heating perio d. Comparisons betw een ligh tw eigh t and hea vyweigh t buildings show that higher thermal mass re- duces co oling demand b y 67–75% during heat wa v es [35]. Finally , [36] shows that, in district heating contexts, pre-heating strategies can render 5.5–7.7% of total heating demand temp orally flexible. Finally , considering temp erature mo dulation approac hes aimed at increasing the self-consumption of lo cally pro duced energy , several b enefits hav e b een rep orted. In the presence of PV surplus, pre-heating or pre-cooling strategies with v ariable setp oints exploit the bu ilding thermal mass b y shifting the indo or temperature to ward the limits of the comfort range ( 20 − 23 ◦ C instead of a constant 21 ◦ C ). Sim- ulations show a reduction in electricity imp orted from the grid of 45–80%, an increase in renew able self-consumption of 29–43%, and a reduction in ev ening p eak demand of 55–85%, while maintaining acceptable comfort con- ditions [37]. Similarly , in high-performance residen tial buildings equipp ed with PV systems and mo dulating heat pumps, a rule-based strategy mo d- ulating the indo or temperature setpoint b y approximately ± 2 ◦ C relativ e to the nominal v alue reduces electricit y purc hased from the grid by up to 17% and increases PV self-consumption by 22% [38]. Despite the breadth of these con tributions, t wo critical gaps p ersist in the literature. As previously mentioned, none of these w orks explicitly targets 7 CO 2 emission reduction as the primary ob jective of the designed strategies. In fact, even when using thermal storage, the presen ted strategies optimize cost or energy consumption, implicitly assuming that reducing energy use is equiv alent to reducing emissions. Second, mo del complexit y , in terpretability , and computational cost are rarely rep orted, making it unclear whether pro- p osed strategies can b e realistically adopted in day-to-da y building op eration. Therefore, in this w ork, we prop ose an optimization strategy that exploits building thermal mass as a battery-free thermal storage supp ort, and ex- plicitly targets CO 2 emission reduction, while also accoun ting for o ccupants’ comfort. T o this end, unlike existing approac hes, w e explicitly consider the real-time grid carb on intensit y signal, ensuring that energy is consumed when the grid is cleaner and not just in smaller amounts. F urthermore, we rely on in terpretable and light w eight mo dels to simulate the system thermal b eha v- ior and to perform the optimization, obtaining an approac h that it suitable for practical, large-scale deplo yment. 3. Metho dology As introduced in Section 1, our approach is based on a simple y et nov el idea: minimizing the emissions asso ciated with building energy use b y lever- aging the building’s thermal mass as a passiv e storage resource. T o this end, w e design a control strategy that, at each time step k , based on the time- v arying carb on intensit y v alue of the National Grid, computes the optimal fraction α ( k ) ∈ [0 , 1] of the av ailable renewable surplus which should b e con- v erted into thermal energy to b e stored in the building mass. It is imp ortant to note that this approach requires no mo difications to the existing temp er- ature control system. Instead, the prop osed strategy virtually increases or decreases the temp erature setp oint for a sp ecific interv al to store the surplus energy . In this wa y , the strategy pre-c harges the building’s thermal mass, and th us reduces future grid demand, as the indo or temp erature remains near the user-defined setp oint using the stored energy . In this framew ork, α serv es as the decision v ariable to optimize the amount of energy stored while ensuring the ro om temp erature do es not deviate excessively from the user’s actual comfort settings. More in detail, to achiev e this goal, at eac h time step k , we optimize a sin- gle scalar decision α ( k ) and up date it in a receding-horizon fashion; forecasts o ver the next m steps of building energy consumptions, solar energy pro duc- tion, indo or and external temp erature, and grid carb on intensit y are used 8 only to compute α ( k ) , which is then applied to the current con trol action. As previously men tioned, α ( k ) is c hosen to reduce near-term grid electricit y consumption and the asso ciated CO 2 emissions, while also accoun ting for o ccupan ts’ comfort. Please note that, a key con tribution of this w ork is go- ing b ey ond aggregate CO 2 metrics; in fact, we explicitly consider temp oral dynamics by using time-v arying carb on intensit y , a voiding av erage con ver- sion factors that, although widely used in the literature [39], can mask when emissions o ccur. Delving into the d etails of the approach, the steps follow ed for the de- v elopment and implementation are outlined b elo w. T o facilitate a clearer understanding, a flow c hart illustrating these steps is pro vided in Figure 2. O ff l i ne O nli ne T RN SYS e ne rg y m odel STEP 1 Thermal dynamic ident ification M A TL A B M A TL A B M A TL A B MA T L A B st at e - sp ace mode l STE P 2 H yper pa r ameter s fine - tun ing α ( k) STEP 3 Real - time s tr ateg y ap plica tion Figure 2: Flow chart illustrating the step wise developmen t, implementation, and applica- tion of the prop osed optimization strategy . It consists of 3 main steps, hereafter describ ed: • STEP 1: thermal dynamic iden tification.The first step, described in detail in Section 4, consists of identifying an in terpretable and simple mo del to describ e the thermal b eha vior of the system of in terest. This can b e ac hieved by using data pro duced through detailed thermal sim- ulations or collected from a physical building. In this case study , we use 9 TRNSYS high-fidelit y mo del to simulate the data required to iden tify a simplified state-space mo del of the system dynamics. Therefore, the TRNSYS mo del is used for initial iden tification and v alidation, while the reduced-order state-space model is the one actually used in the optimization strategy for real-time consumption forecasting. • STEP 2: The energy consumption predicted by the reduced-order state- space mo del, com bined with a forecast of solar energy pro duction and time-v arying grid carb on intensit y data obtained from the Electricity Maps platform [40], is used to form ulate the optimization problem and compute the optimal fraction α ( k ) of surplus solar energy to store in the building’s thermal mass at each time step. The ob jective is to minimize emissions while enforcing comfort constrain ts. As discussed later, the strategy dep ends on a set of hyperparameters that m ust be tuned for the sp ecific system, namely the w eigh t ω , the sampling time t s , and the prediction horizon m . This step is therefore devoted to the tuning of these h yp erparameters via a P areto-based pro cedure, whic h also clarifies ho w the chosen w eights shap e the comfort–emissions trade- off. • STEP 3: real-time strategy application to the actual system. Once the optimal hyperparameters are iden tified, the strategy can b e used. Th us, giv en the iden tified state-space mo del, the num b er of o ccupants, solar energy generation forecast, and CO 2 in tensity trends, the strategy determines how to adjust the temp erature setp oint to reduce emissions b y storing energy in the building’s thermal mass when renew able gen- eration is av ailable, thereby reducing reliance on the grid at times of higher carb on intensit y . As rep orted in Section 5, in this w ork, we apply these steps to three different high-fidelit y TRNSYS mo dels. Suc h mo dels are referred to the same ro om with v arying thermal masses. Thus, for eac h case, w e first build the TRN- SYS mo del, and we then use it to generate the data required to iden tify the corresp onding light w eigh t reduced-order mo del, used during optimization. Then, the optimal set of h yp erparameters is computed for eac h ro om con- figuration, and the strategy is applied to a new scenario. F or each case, the strategy results are compared against a baseline in whic h no thermal stor- age is performed, in terms of b oth CO 2 emissions reduction and o ccupan ts’ comfort. 10 3.1. Optimization str ate gy Delving in to the details of the strategy implemen tation, α ( k ) is com- puted according to a receding-horizon pro cedure that accoun ts for the fore- casts of building energy consumption ( E pred ( k ) ), the solar energy pro duction ( E solar ( k ) ), and time-v arying grid carb on intensit y ( C I ( k ) ). Therefore, the ob jectiv e function consists of t w o terms: • CO 2 emissions cost. T o minimize this term, the con trol strategy should fa vor larger v alues of α ( k ) when the carb on in tensit y i s exp ected to increase in the next hours, so that more solar energy surplus is stored and less grid energy is needed later. • Thermal comfort. This term is in tro duced to penalize temp erature deviations from the reference setp oin t; therefore, α ( k ) is reduced when the induced temp erature shift b ecomes to o large. A ccordingly , the optimization problem is form ulated as J = J CO 2 | {z } C O 2 emissions + J comfort | {z } thermal comfort . (1) In the following, we detail ho w J CO 2 and J comfort ha ve b een formulated. 3.1.1. CO 2 Emission Cost This cost is in tro duced to reduce the energy drawn from the grid when the related carb on intensit y is high. T o this end, let m b e the length of the prediction horizon considered to p erform the optimization. In the baseline case, where there is no surplus storage and the solar energy is only used instan taneously , the grid energy required o ver the horizon is: E grid , 0 = m X i =1 max  E pred ( i ) − E solar ( i ) , 0  , (2) where E pred ( i ) is the predicted building energy consumption at step i and E solar ( i ) is the a v ailable PV energy at the same step. The corresp onding baseline CO 2 emissions are then J CO 2 , 0 = m X i =1 max  E pred ( i ) − E solar ( i ) , 0  · C I ( i ) , (3) 11 with C I ( i ) denoting the time-v arying grid carb on intensit y signal. Please note that, as previously men tioned, the c hoice of accoun ting for the temp oral dynamics of the carb on intensit y factor is a k ey contribution of this w ork, and is rarely addressed in the literature, which usually considers an a verage Europ ean factor. The rep orted relations dep end on E pred ( i ) , E solar ( i ) , and C I ( i ) . While the last tw o measures can b e obtained from historical datasets (e.g., assuming cyclic b ehavior ov er a year) or forecasted using metho ds a v ailable in the liter- ature [41, 42, 43, 44, 45], estimating E pred ( i ) requires a mo del of the building thermal b eha vior in b oth heating and co oling op eration, whic h can b e identi- fied from measured data or from physics-based simulations of the system. In this work we consider as a case study a room, whose complete b eha vior, as discussed in Section 4, has b een mo deled using TRNSYS soft ware. How ev er, as it was unnecessarily complex, w e then mo del only the thermal b eha vior of in terest using a state-space mo del, identified using ad-ho c simulated dataset from TRNSYS. This simplified mo del has then b een used to predict the en- ergy consumption of the ro om ov er time, which, along with solar energy and carb on intensit y trends, hav e b een used to implemen t our strategy . Therfore, w e are able to compute in real-time the actual emission cost, with our strategy implemen ted, which requires an additional term to be in- cluded with resp ect to the baseline formulation J CO 2 , 0 . Sp ecifically , this term is related to the amount of energy sa v ed thanks to the thermal storage. T o deriv e it, we first compute the solar energy surplus as: ∆ E solar ( i ) = max  E solar ( i ) − E pred ( i ) , 0  . (4) Then, w e accoun t that thanks to the con trol strategy , a fraction α ( k ) of this surplus is stored in the building thermal mass, pro viding an additional thermal energy input that can b e computed as: ∆ Q ( i ) = γ α ( k ) ∆ E solar ( i ) , (5) where γ is the efficiency factor for the conv ersion from solar energy to thermal storage, which we set equal to γ = 1 in the simulations. T o obtain a closed-form control la w, we adopt the simplifying appro xi- mation that the stored thermal energy offsets future grid imp orts uniformly o ver the prediction horizon. A ccordingly , the actual CO 2 -related cost can b e 12 computed as: J CO 2 = m X i =1 max max  E pred ( i ) − E solar ( i ) , 0  − α ( k ) m m X j =1 ∆ E solar ( j ) , 0 ! C I ( i ) , (6) where ∆ E solar ( i ) and ∆ Q ( i ) are defined as in the CO 2 cost formulation. 3.1.2. Thermal Comfort Cost The thermal comfort cost, instead, is introduced to penalize an y devi- ations of the indo or temp erature from the reference setp oin t. As a conse- quence, it limits the temp erature c hange induced b y storing solar energy surplus in the thermal mass. Starting from (5), the temp erature v ariation due to the thermal storage at step i can b e approximated as: ∆ T ( i ) = η ∆ Q ( i ) C th = η γ α ( k ) ∆ E solar ( i ) C th , (7) where C th is the equiv alen t thermal capacitance and η = ( +1 , heating mo de (temp erature increase) , − 1 , cooling mo de (temp erature decrease) . (8) Consisten tly with the approximation used in (6), the ov erall induced shift o ver m steps is ∆ T tot = η γ α ( k ) P m i =1 ∆ E solar ( i ) C th . (9) A ccordingly , we can define the comfort cost as: J comfort =  ∆ T tot  2 = α ( k ) 2  γ P m i =1 ∆ E solar ( i ) C th  2 . (10) 3.1.3. Close d-F orm Solution By combining (6) and (10), we can rewrite (1) as: J = E grid , 0 − α ( k ) m m X i =1 ∆ E solar ( i ) ! m X i =1 C I ( i ) + + ω α ( k ) 2  γ P m i =1 ∆ E solar ( i ) C th  2 , (11) 13 where ω > 0 is a weigh t introduced to balance emissions reduction and ther- mal comfort. It can b e tuned via a P areto analysis to explore the comfort– emissions trade-off, and then selected according to application requirements. Since J is a conv ex quadratic function of α ( k ) , the minimizer is obtained b y setting d J d α ( k ) = 0 : d J d α ( k ) = − 1 m m X i =1 ∆ E solar ( i ) ! m X i =1 C I ( i ) ! + +2 ω α ( k )  γ P m i =1 ∆ E solar ( i ) C th  2 . (12) Solving for α ( k ) leads to a closed-form solution: α ⋆ ( k ) = C 2 th 2 ω m γ 2 P m i =1 C I ( i ) P m i =1 ∆ E solar ( i ) . (13) If P m i =1 ∆ E solar ( i ) = 0 , we set α ⋆ ( k ) = 0 . Finally , the actuation is saturated to satisfy α ( k ) ∈ [0 , 1] : α ( k ) = min  1 , max(0 , α ⋆ ( k ))  . (14) Please note that achieving this closed-form solution is a key adv an tage of this form ulation as this considerably reduces the computational complexity requried to get optimal α ( k ) v alue at eac h step. 4. Application to the Case Study This section describ es the simple yet high-fidelit y reference system, con- sisting of a small office ro om mo deled in TRNSYS, which has b een considered to ev aluate the effectiveness of our approac h. Sp ecifically , three versions of the ro om are designed, each with a different thermal capacit y . This allows us to demonstrate that the prop osed strat- egy is effectiv e regardless of the sp ecific thermal properties of the building, and can therefore b e applied without requiring an y structural mo dification. Eac h ro om mo del serv es as the ground-truth represen tation of the thermal b eha vior of the corresp onding configuration. Based on data collected in ad- ho c p erformed simulations, w e then iden tify a predictive discrete-time state- space represen tation of the system, which captures only the sp ecific thermal 14 dynamics of interest f or our control strategy . A ccordingly , we obtain a sim- ple and interpretable model that is accurate enough to predict the heating and co oling p ow er, while av oiding the computational complexit y of the orig- inal TRNSYS counterpart, which is impractical for the optimization routine (STEP 1 in Figure 2). Please note that, although the chosen system is in- ten tionally simple, the prop osed workflo w is general and can b e applied to more complex buildings, including using real op erational data. Indeed, the iden tification step can b e p erformed on an y system to obtain a reduced-order state-space mo del linking the relev ant exogenous v ariables to the heating and co oling p ow er required. This separation betw een data source and control mo del makes the strategy flexible and system-independent. Bac k to our considered case study , eac h ro om consists of an office lo cated within a larger single-story building, situated in Milan. It has a net flo or area of 30 m 2 (6 × 5 m ) and a net internal height of 3 m . Three w alls are adjacen t to other spaces, whereas the remaining side is exp osed outdo ors. In Figure A.10 of App endix A, the space represen tation in plan and section (along the AA’ axis) is rep orted. T o inv estigate the effect of thermal mass on the strategy p erformance, three configurations are considered: light-, medium-, and hea vy-weigh t mass. Their main characteristics are summarized in T able 1, whic h shows that all three configurations share the same thermal transmittance, but differ in their dynamic thermal properties, e.g., the decremen t factor, the phase shift, the surface mass, and the internal areal heat capacit y . In this study , particular atten tion is giv en to this last parameter, denoted as C m , which represen ts the effectiv e thermal capacity of eac h case study [46]. In fact, this is the main parameter determining the amplitude of the setp oin t v ariation resulting from storing a fraction of the solar energy surplus in the thermal mass, as a func- tion of the parameter α . Sp ecifically , it has b een computed as the sum of the in ternal areal heat capacities of the individual env elop e components, whic h has b een determined according to the dynamic thermal formulation pro vided b y [46]. A ccording to [47], it is calculated through the global heat transfer matrix of each building comp onent, obtained b y com bining the transfer ma- trices of the individual la y ers across the construction. T o this end, w e start from the thermal transfer equation:  ˆ θ 2 ˆ q 2  =  Z 11 Z 12 Z 21 Z 22  ·  ˆ θ 1 ˆ q 1  (15) Here, ˆ θ 1 and ˆ θ 2 represen t the complex amplitudes of temp erature on the 15 in ternal and external sides of the comp onent, resp ectively , while ˆ q 1 and ˆ q 2 denote the corresp onding heat fluxes. The co efficients Z ij are the elements of the thermal transfer matrix and describ e the dynamic relationship b etw een temp erature and heat flux across the construction under p erio dic conditions. F rom that equation, we then derive κ i , which represen ts the internal areal heat capacity of the comp onen t ov er a considered p erio d T , that is, by stan- dard set to 24 hours: κ i = T 2 π     Z 11 − 1 Z 12     (16) Then, the in ternal heat capacity of the three case studies is determined b y summing the in ternal heat capacities of all construction comp onents, as de- fined b efore, each multiplied by its corresp onding surface area: C m = X j κ ij · A j . (17) Bac k to the sp ecific configuration, eac h ro om includes a glazed vertical elemen t consisting of a windo w frame with double lo w-emissivity glazing, separated by a gas-filled argon cavit y . Its solar heat gain co efficien t (g-v alue) is 0.62, the visible light transmittance is 0.78, and the thermal transmittance is 1.1 W /m 2 K . In each model, we consider a single thermal zone represen ted b y an air no de, corresp onding to the volume of air assumed to ha v e a uniform temp era- ture. The adjacent ro oms are assumed to share the same thermal conditions, while the outdo or-facing façade is oriented north and features three windows, eac h measuring 120 × 140 cm. The b oundary conditions used in the mo deling are summarized in T able 2. Instead, Figure 3 shows the TRNSYS implementation of the energy plan t implemen ted in each ro om, whic h will no w b e detailed. As rep orted, it con- sists of several blo cks, defined T yp es, which corresp ond to a sp ecific element of the plant and embed the resp ective go verning equations. T o provide a b etter o verview of this plant, the comp osing types can b e se- man tically group ed in to six main circuits, represented using differen t colors. F rom a system p ersp ectiv e, the mo del represen ts a h ybrid system for indo or climate con trol. Heating (red circuit) is provided by a high-temp erature air- to-w ater heat pump (Type 941) for thermal generation and b y a radiator (T yp e 1231) for heat distribution within the space. Co oling (blue circuit) is supplied by an air-to-air multi-split heat pump system (T yp e 954a), con- 16 T able 1: Building en velope c haracteristics. This table rep orts the main prop erties of the building en velope based on the stratigraphy adopted for the design of the building hosting the considered office ro om, for each configuration analyzed in the case study . The stratigraph y lab els are referred to Figures A.11,A.12,A.13 of App endix A. Building Classification Configuration Stratigraphy Thickness Thermal Surface Atten uation Phase In ternal Areal Heat Thermal Env elop e Subfigure [ cm ] T rans. [ W/m 2 K ] Mass [ k g/m 2 ] Shift [ h ] Capacity [ kJ/m 2 K ] Capacity [ kJ /K ] LIGHT-WEIGHT External 3130.83 opaque W all External (a) 20.9 0.206 49 0.608 5.39 24.3 enclosure Internal vertical W all Boundary (b) 12.5 1.563 45 0.960 1.58 21.7 enclosure Horizontal flat Ro of External (c) 44.05 0.203 55 0.904 3.30 27.3 enclosure Horizontal enclosure Floor Boundary (d) 58.2 0.235 327 0.236 11.46 31.8 against ground MEDIUM-WEIGHT External 6531.77 opaque W all External (a) 39 0.207 228 0.267 9.84 50.7 enclosure Internal vertical W all Boundary (b) 15 1.572 144 0.768 4.19 51.4 enclosure Horizontal flat Ro of External (c) 46.5 0.198 335 0.215 11.07 68.9 enclosure Horizontal enclosure Floor Boundary (d) 37.9 0.260 559 0.120 12.15 44.7 against ground HEA VY-WEIGHT External opaque W all External (a) 44 0.210 428 0.087 13.49 59.4 8182.05 enclosure Internal vertical W all Boundary (b) 21 1.547 306 0.380 7.97 66.5 enclosure Horizontal flat Ro of External (c) 44.5 0.204 597 0.146 11.36 92.4 enclosure Horizontal enclosure Floor Boundary (d) 48.3 0.253 785 0.048 15.52 48.4 against ground T able 2: Boundary conditions. This table rep orts the v alues used for the modeling of heating and co oling con trol, natural ven tilation, infiltration, and internal gains, which are shared across the three implemented ro oms. Parameter Type V alue Internal gain Artificial lighting 6 W/m 2 , active during working hours (09:00–19:00) Occupancy 130 W per person (ASHRAE standard for mo derately active office work [29]). During working days (09:00–19:00), the num b er of occupants v aries b etw een 0, 2, or 4; w eekends: 0. Control and op eration Hourly air change rate 0 . 6 AC H (infiltration and natural ven tilation) Heating setpoint (temp erature) Stepwise profile ranging b etw een 20 ◦ and 22 ◦ Cooling setp oint (temp erature) Stepwise profile ranging b etw een 25 ◦ and 27 ◦ sisting of an outdo or unit connected to indo or unit. Indo or comfort is main- tained b y a control system (gra y circuit) based on t w o separate mo dulating PID con trollers (Type 23). The controllers regulate the heating p o wer of the air-to-w ater heat pump, the circulation pump p o wer, and the co oling p o wer of the m ulti-split system, based on the indo or air temp erature and the refer- ence setp oint. Effects of the thermal temp erature and o ccupancy are instead 17 Legend Heating system Cooling system Control system Photovoltaic system E xt e r na l t e m pe r a t ur e ef f ect Occupancy schedules Environment effect Figure 3: Plant of each TRNSYS mo del. This Figure provides an ov erview of the energy plan t implemented in each TRNSYS ro om. describ ed using the orange and light blue circu it, resp ectively . Regarding on- site generation (green circuit), considering the single-store configuration of the building, a mono crystalline PV mo dule with a nominal p ow er of 445 W is assumed. A ccordingly , w e design a system comp osed of 4 mo dules to provide a total p eak p o wer of 1.78 k W p . The PV system sizing was p erformed in ac- cordance with Directive (EU) 2018/2001 (RED I I) [48] on renewable energy , meeting the requiremen ts applicable to existing and new buildings. Overall, in the sizing of the comp onen ts considered, some parameters w ere customized to ensure consistency with the design conditions. The main configurations adopted for each Type are rep orted in T able A.5 in the App endix A. 18 4.1. Thermal dynamic identific ation Once the TRNSYS mo dels are implemen ted, the next step is to identify a simplified yet reliable surrogate that still c haracterizes the room’s ther- mal resp onse while b eing less computationally complex. This reduced-order mo del is used in the optimization pro cess, while the TRNSYS counterpart is only used as a high-fidelity reference for mo del identification and v alidation. It is w orth noting that, since the appro ximated mo del is iden tified from data, whether sim ulated or collected from a real system, the same workflo w can b e applied to other buildings and to real op erational measurements. As discussed in Section 1, existing literature generally usually p erform the iden ti- fication step in tw o differen t w ays. On the one hand, data-driven approaches use regression predictors, e.g., gradien t-b o osted trees or recurrent neural net- w orks, trained on environmen tal data, control v ariables, and o ccupancy pro x- ies to forecast consumption. On the other hand, grey-b o x approaches mo del the ro om as a lo w-order R C (resistance-capacitance) net work and estimate energy consumption b y mapping thermal loads using simplified equipmen t mo dels. In this work, we lev erage a reduced-order state-space representa- tion mo del, as more interpretable and ligh tw eigh t than the machine-learning coun terpart. Sp ecifically , we identify six mo dels, tw o for each of the three TRNSYS mo dels, one for heating and one for co oling b eha vior. Eac h mo del has b een iden tified using the MA TLAB ssest function [49] and discretized at the controller sampling time ts for b eing integrated in the optimization framew ork. Although the designed TRNSYS models provide man y signals, w e select a reduced input set based on b oth correlation analysis results and practical measurability in real deplo yment. Therefore, the selected regressors are: • the setp oin t temp erature T ref ( k ) ; • the o ccupancy level n occ ( k ) (used as an internal-gains proxy); • the external temp erature T ext ( k ) ; while the output v ariable is the related heating and cooling required pow er P ( k ) . T o ensure that the identified mo dels capture the full range of thermal dynamics, for each TRNSYS ro om mo del we generated training datasets for t wo distinct seasonal perio ds: heating (Octob er 15 – April 15) and co oling (April 15 – October 15). In eac h scenario, w e sp ecify the time-series trends 19 for the ro om setp oint T ref ( k ) , o ccupancy coun t n occ ( k ) , external temp era- ture T ext ( k ) (based on Milan Brera meteorological data), and the resulting heating and cooling p ow er required p ow er P ( k ) . Please note that, to iden- tify the system dynamics accurately , it is essen tial to sub ject the mo del to large v ariations and diverse step conditions. Consequen tly , we applied v ary- ing setp oint profiles: in the win ter scenario, a stepwise profile ranging from 20 ◦ C to 22 ◦ C w as adopted, whereas in the summer scenario, the pro- file ranged from 24 ◦ C to 26 ◦ C . In b oth scenarios, the o ccupancy profile v aries ov er the course of the day: no o ccupants are present during night-time (00:00–08:00 and 20:00–24:00), tw o o ccupants are present during 08:00–12:00 and 16:00–20:00, and four o ccupants are present from 12:00 to 16:00. It is w orth noting that, although high-excitation conditions w ere necessary for mo del iden tification, the resulting mo del is fully general and can predict the ro om’s thermal b ehavior under arbitrary inputs. It is therefore used in the optimization strategy to forecast heating and co oling energy consumption across scenarios that differ from those used during iden tification. Therefore, at the end of this iden tification pro cess, we obtain a state-space mo del capa- ble of accurately predicting the heating and co oling p o wer of our ro om while a voiding the prohibitive computational o v erhead of TRNSYS, which would otherwise make real-time optimization infeasible. T o select the optimal order for the state-space mo dels and verify their abilit y to accurately repro duce the TRNSYS reference b ehavior, mo dels of order 1 through 3 are iden tified and compared using t wo metrics, mostly used in the literature: • the co efficien t of determination ( R 2 ), R 2 = 1 − P N t i =1 ( y v al , true ( i ) − y v al , pred ( i )) 2 P N t i =1 ( y v al , true ( i ) − ¯ y v al , true ) 2 , ¯ y v al , true = 1 N t N t X i =1 y v al , true ( i ); (18) • the normalized mean absolute error ( nM AE ), normalized with resp ect to the maximum true output v alue, nMAE = 100 · 1 N t P N t i =1 | y v al , true ( i ) − y v al , pred ( i ) | max i | y v al , true ( i ) | . (19) In more detail, the ev aluation is conducted on a dedicated TRNSYS- generated dataset, generated for each ro om in the conditions rep orted ab o ve 20 and split in to an identification and a v alidation subset. Each mo del is iden ti- fied on the former and ev aluated on the latter by computing R 2 and nM AE considering the true TRNSYS output y v al , true ( i ) and the mo del prediction y v al , pred ( i ) . Results consisten tly sho w that a second- or third-order mo del pro vides the b est accuracy across b oth heating and co oling conditions and for all three room configurations. First-order mo dels fail to capture the dominan t transient dynamics, while higher-order mo dels yield only marginal accuracy improv emen ts at the cost of increased complexit y and reduced in- terpretabilit y . The aggregated results obtained when ev aluating the b est mo dels identified for eac h ro om are rep orted in T able 3, while a represen- tativ e comparison b etw een the temp oral trends of TRNSYS and surrogate mo dels predictions o ver 5 days of v alidation data is shown in Figure 4. Ov er- all, the iden tified mo dels repro duces the reference thermal dynamics with go o d accuracy , th us supp orting its use as the predictive mo del in the opti- mization pro cedure. The figure also highlights sp ecific asp ects of the ro om’s thermal b eha vior that will b e relev an t when analyzing the results of the pro- p osed strategy . In particular, the required p o wer is generally higher as the building thermal capacit y decreases, since lighter structures are less able to store heat and therefore resp ond more rapidly to external temp erature v ari- ations. Consequen tly , the ligh t configuration exhibits the highest demand, while the heavy configuration, thanks to its greater thermal inertia, shows the low est. This b ehavior is more evident in summer simulations, where solar gains and temp erature fluctuations are more intense, but it also c haracterizes the winter results, although to a lesser extent. T able 3: Iden tification p erformance. This table rep orts, for each ro om configuration, the R 2 and nM AE metrics ac hieved on the v alidation set b y the surrogate heating and co oling mo dels identified from the TRNSYS sim ulation. Surrogate Light-w eigh t Medium-w eight Hea vy-w eight Mo del R 2 nM AE R 2 nM AE R 2 nM AE Win ter 0.77 10.24 0.64 13.73 0.60 14.00 Summer 0.90 6.10 0.76 10.52 0.70 12.24 21 15-Dec 16-Dec 17-Dec 18-Dec 19-Dec 20-Dec 0 10 20 30 40 T emperatur e [°C] T e x t ( k ) T r e f ( k ) (a) Winter: T emp eratures ( T ref , T ext ) 15- Aug 16- Aug 17- Aug 18- Aug 19- Aug 20- Aug 0 10 20 30 40 T emperatur e [°C] (b) Summer: T emperatures ( T ref , T ext ) 15-Dec 16-Dec 17-Dec 18-Dec 19-Dec 20-Dec 0 1 2 3 4 P eople [-] (c) Winter: People ( n occ ) 15- Aug 16- Aug 17- Aug 18- Aug 19- Aug 20- Aug 0 1 2 3 4 P eople [-] (d) Summer: P eople ( n occ ) 20-Dec 21-Dec 22-Dec 23-Dec 24-Dec 25-Dec 0 500 1000 1500 P ower [W] (e) Winter: Heating Po wer ( P , P pred ) - Ligh t Configuration 20- Aug 21- Aug 22- Aug 23- Aug 24- Aug 25- Aug 0 500 1000 1500 P ower [W] P ( k ) P p r e d ( k ) (f ) Summer: Co oling Po wer ( P , P pred ) - Ligh t Configuration 20-Dec 21-Dec 22-Dec 23-Dec 24-Dec 25-Dec 0 500 1000 1500 P ower [W] (g) Winter: Heating Po wer ( P , P pred ) - Medium Configuration 20- Aug 21- Aug 22- Aug 23- Aug 24- Aug 25- Aug 0 500 1000 1500 P ower [W] P ( k ) P p r e d ( k ) (h) Summer: Co oling Po wer ( P, P pred ) - Medium Configuration 20-Dec 21-Dec 22-Dec 23-Dec 24-Dec 25-Dec 0 500 1000 1500 P ower [W] (i) Winter: Heating Po wer ( P, P pred ) - Heavy Configuration 20- Aug 21- Aug 22- Aug 23- Aug 24- Aug 25- Aug 0 500 1000 1500 P ower [W] P ( k ) P p r e d ( k ) (j) Summer: Co oling Po wer ( P , P pred ) - Heavy Configuration Figure 4: Heating and co oling mo del identification. This figure shows tw o representativ e v alidation p erio ds, with win ter data on the left and summer data on the righ t. The first tw o rows report the mo del’s inputs, common to the three ro om configurations. The remaining rows compare the heating and co oling p ow er predicted by the TRNSYS mo del ( P ) with that predicted by the corresp onding surrogate mo del ( P pred ). 22 5. Results and Discussion No w that w e hav e iden tified an efficien t surrogate mo del for each TRNSYS ro om that accurately predicts the energy consumption (STEP 1 in Figure 2), our strategy can b e applied. In fact, other information, such as the time series of grid carb on intensit y C I ( k ) and a v ailable solar energy E solar ( k ) can b e retriev ed from measured data. Sp ecifically , as we assumed that our office is lo cated in Northern Italy , w e considered hourly data on grid carb on intensit y C I ( k ) (kgCO 2 /k Wh) from the Electricity Maps platform [40], referring to the y ear 2024. The outdoor temp erature profile, instead, w as derived from the climatic data recorded at the Milano Brera meteorological station. Last, the solar energy pro duction of the PV system w as estimated through sim ulations carried out using the room mo del developed in TRNSYS with the same climatic data. The sim ulation, conducted ov er an ann ual time horizon, allo ws the calculation of the electrical energy generated b y the PV system, assuming a constant panel efficiency . Please note that the c hoice of using 2024 data has been made as w e assume comparable seasonal patterns across y ears. Ho wev er, as later discussed in the limitations subsection, if this assumption is considered not reliable, the same framework can b e applied using an y forecasting metho d from the literature to predict these v ariables in real-time. With this setup, the prop osed strategy is ev aluated on each of the three ro om configurations ov er a full-year sim ulation spanning Jan uary 1 to Decem- b er 31, 2024. During the heating season, the indo or temp erature setp oint w as set to 20 ◦ C during w orking hours (08:00–19:00) and 18 ◦ C during off- hours and w eek ends. Similarly , in the co oling season, we assume a setpoint of 26 ◦ C during w orking hours (08:00–19:00) and 28 ◦ C during off-hours and w eekends. Considering the o ccupation, during working hours, t w o p eople w ere considered to b e consisten tly presen t in the office. 5.1. Str ate gy hyp erp ar ameters fine-tuning Before applying our strategy , its hyperparameters m ust b e prop erly tuned for each ro om. As detailed in Section 3, they include the weigh t ω , balancing the CO 2 -related and the comfort ob jectiv es, and the forecasting parameters, namely the sampling time ts and the prediction horizon m , which together determine the temp oral resolution and lo ok ahead windo w of the optimizer. T o prop erly set their v alues, tw o approaches are p ossible: if prior knowledge or appl ication-driv en constrain ts are av ailable, the parameters must b e set 23 accordingly . Alternativ ely , as in this case, a sensitivity analysis can b e p er- formed to identify the most suitable ones. T o this end, prediction horizons of 12, 18, 24, and 48 hours are considered; for eac h horizon, sampling times of 30, 60, 120, 180, and 240 minutes are ev aluated. F or eac h ( m, ts ) pair, ω is swept ov er a logarithmically spaced range from 1 to 1 e 15 , and the full one- y ear scenario is sim ulated. F or eac h v alue of ω , the resulting CO 2 emissions and comfort deviation define a p oint on the Pareto frontier; the optimal ω for that pair is then selected as the one that maximizes emission reduction while k eeping comfort within acceptable b ounds. Finally , the ( m, ts ) com bination that b est achiev es this ob jectiv e across the full sim ulation is selected. The iden tified optimal hyperparameters are then used to simulate the strategy on each of the three ro om configurations. The results are ev aluated with resp ect to a baseline scenario, in which the same b eha vior of the same ro om is simulated without any thermal storage, i.e., setting α equals 0. Therefore, in the baseline case, we exp ect that ∆ T is also 0, as the energy supplied to the ro om is exactly that required to meet the setpoint, while an y a v ailable solar surplus is not used. On the other hand, for the same reason, the CO 2 emissions are exp ected to b e higher than those measured when applying our strategy . Therefore, to ev aluate our strategy , we measure tw o indicators: • CO 2 emissions reduction, measured as the a verage grams sav ed p er da y and the ov erall p ercentage sa vings o ver a year, b oth computed relativ e to a baseline in which no thermal storage is applied; • T emp erature setp oint deviation, measured as the av erage and maxi- m um deviation from the user-defined setp oint, relative to the baseline scenario in which the setp oin t is follo wed exactly as no thermal storage is applied. The optimal h yp erparameter settings for eac h of the three ro om configura- tions are rep orted in T able 4. The results sho w that the optimal prediction horizon m scales as the configuration go es from ligh t to hea vy . This outcome is ph ysically in tuitive; in fact, the hea vy configuration has greater thermal inertia. Therefore, the heat stored or released propagates more slo wly through the structure. As a result, the strategy requires a larger horizon to an ticipate c harging and disc harging decisions. The optimal sampling time ts , instead, ranges b et ween 30 and 60 min utes, while longer v alues decrease the p erformance. Also, the optimal weigh t ω consistently assessed around 10 6 , suggesting that the 24 trade-off b et ween emissions reduction and thermal comfort is go verned by the problem scaling rather than the sp ecific thermal prop erties of the ro om. Considering sa vings and temperature deviations measured in these opti- mal configurations, some considerations should b e made. In terms of emis- sions reduction, the medium and heavy configurations achiev e substan tially larger sa vings than the light-w eigh t one, with annual reductions of approxi- mately 25% compared to 10%. This confirms that greater thermal mass pro- vides more storage capacit y , enabling the strategy to shift a larger share of energy demand to w ard p erio ds of low-carbon solar generation. Accordingly , temp erature deviations also increase in medium and heavy configurations. Nev ertheless, even when considering the hea vy configuration, the av erage daily deviation remains low er than 0 . 4 ◦ C , with a maxim um of 1 . 2 ◦ C , con- firming that the strategy achiev es significan t emissions reductions without compromising o ccupant comfort. T able 4: Optimal h yp erparameters set. The table rep orts the v alues of prediction horizon m , sampling time ts , and weigh t ω iden tified via grid search, along with the CO 2 emission reductions and setp oin t deviation. Configuration Hyperparameters Emissions Reduction Setpoint deviation m [h] ts [min] ω [-] a vg per day [g/day] tot per year [%] avg p er da y [ ◦ C ] max in a day [ ◦ C ] Light-w eight 12 30 10 6 19.67 9.88 0.1 0.5 Medium-weigh t 24 60 10 6 52.30 25.37 0.3 0.9 Heavy-w eight 48 30 10 6 46.06 24.77 0.4 1.2 Figure 5, further extends the results in T able 4, providing insigh ts into ho w the yearly CO 2 reduction and the maximum daily ∆ T v aries as a func- tion of the sampling time ts and prediction horizon m for the b est-p erforming v alue of ω in the three different configurations analyzed. These trends b etter highligh t the in trinsic trade-off that c haracterizes our strategy: hyperpram- eteres set that allow for obtaining higher CO 2 emissions reductions also pro- duce larger deviations from the temp erature setpoint. Indeed, reducing the CO 2 cost requires increasing α , whic h in turn increases the ro om temp era- ture. As previously men tioned, this trend is more eviden t for the medium and heavy configurations, where the thermal inertia affects the heating and co oling dynamics of the system. W e also note that, in general, longer hori- zons (1 or 2 days) lead to greater CO 2 emissions reduction. This means that, as exp ected, higher lo ok-aheads ov er surplus a v ailabilit y and carb on- in tensity tra jectories enable more effective temp oral shifting of grid imp orts. A dditionally , across all ro om configurations, higher actuation frequency , i.e., smaller ts , generally impro ves p erformance by allowing the controller to more 25 50 100 150 200 250 t s [ m i n ] 0 5 10 15 20 25 30 C O 2 r e d . p e r y e a r [ % ] (a) A verage Emissions Reduction [ g /day ] - Light Configuration 30 60 120 180 240 t s [ m i n ] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 m a x T p e r d a y [ ° C ] H = 12 h H = 18 h H = 24 h H = 48 h (b) A verage Setp oint V ariation [ ◦ C /day] - Light Configuration 50 100 150 200 250 t s [ m i n ] 0 5 10 15 20 25 30 C O 2 r e d . p e r y e a r [ % ] (c) A verage Emissions Reduction [g/day] - Medium Configuration 30 60 120 180 240 t s [ m i n ] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 m a x T p e r d a y [ ° C ] H = 12 h H = 18 h H = 24 h H = 48 h (d) A verage Setp oint V ariation ( ◦ C /day] - Medium Configuration 50 100 150 200 250 t s [ m i n ] 0 5 10 15 20 25 30 C O 2 r e d . p e r y e a r [ % ] (e) A verage Emissions Reduction [g/day] - Heavy Configuration 30 60 120 180 240 t s [ m i n ] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 m a x T p e r d a y [ ° C ] H = 12 h H = 18 h H = 24 h H = 48 h (f ) A verage Setp oint V ariation [ ◦ C /day] - Heavy Configuration Figure 5: Sensitivity analysis on hyperparameters. This figure sho ws how total y early emissions reduction (left) and maximum daily setp oint deviation (right) c hange as a func- tion of the sampling time and the prediction horizon for eac h ro om configuration. Optimal h yp erparameters set is marked b y a yello w star. effectiv ely exploit the building’s thermal mass. Finally , regardless of the sp ecific h yp erparameters, the a v erage daily deviation from the user tem- p erature setp oin t alwa ys remains b elow ± 1 . 5 ◦ C , which is definitely within acceptable b ounds to maintain a comfortable indoor en vironmen t. Larger deviations are observ ed for the heavy mo del configuration, whereas ligh ter configurations reduce emissions without introducing significant temp erature v ariations. Overall, this analysis sho ws that, although the optimal set of h yp erparameters dep ends on the sp ecific application requiremen ts, a go o d general choice is to employ mo derate-to-long prediction horizons, ab out 1 or 26 2 days, com bined with a reduced sampling time, of approximately 30 minutes. In the remainder of this section, more detailed results obtained by apply- ing our strategy to eac h ro om configuration under the best hyperparameter settings, i.e., those rep orted in T able 4 will b e presented. Baseline Strategy 0 10 20 30 40 50 60 70 80 C O 2 E m i s s i o n s [ k g ] 72.62 65.44 75.22 56.14 67.68 50.92 Configuration light medium heavy (a) CO 2 Emissions [kg] Baseline Strategy 0 50 100 150 200 250 300 350 E n e r g y [ k W h ] 330.27 296.75 346.21 256.39 312.04 233.12 Configuration light medium heavy (b) Energy Consumptions [k Wh] Figure 6: Strategy p erformance: annual results. This figure compares in all the considered ro om configurations the yearly aggregated CO 2 emissions (left) and energy consumption (righ t) for the baseline scenario ( α ( k ) = 0 ) and the prop osed strategy . 5.2. Str ate gy p erformanc e Once the optimal set of h yp erparameters has b een iden tified (STEP 2 in Figure 2), our strategy can b e online applied (STEP 3) and its b enefits can b e in vestigated. T o this end, a first commen t can b e made based on the results in Figure 6, which, for each ro om configuration, compares the ann ual CO 2 emissions and energy consumption pro vided by our strategy , with resp ect to the baseline scenario in which no thermal storage is applied. The results sho w that our strategy yields an annual CO 2 emissions sa ving with resp ect to the related baseline case of appro ximately 9 . 88% , 25 . 37% , and 24 . 77% , for the ligh t-, medium- and heavy-w eigh t configurations resp ectively . This corresp onds to 7 . 18 kg, 19 . 09 kg and 16 . 76 kg of CO 2 sa ved in a year. In addition, although this is not the main ob jectiv e of our strategy , w e also highligh t that it results in an annual energy saving with resp ect to the re- lated baseline case of 10 . 15% , 25 . 94% , and 25 . 29% , corresp onding to 33 . 52 k Wh, 89 . 81 k Wh, and 78 . 92 k Wh for the light-, medium-, and hea vy-weigh t configurations resp ectively . Beside CO 2 reduction, thermal comfort must also b e considered. T o this end, we used the Predicted Mean V ote (PMV) index, as defined b y the UNI EN ISO 7730 standard [50, 51] to ev aluate ho w comfort v aries when applying our strategy . Please note that, to compute this indicator, in accordance with 27 ISO 7730:2005, metab olic rate and clothing insulation v alues were defined for b oth the summer and winter seasons, while additional parameters used for PMV calculation are rep orted in T able A.6 of App endix A. With this setup, the results demonstrate that our strategy ac hieves thermal comfort levels comparable to the baseline. Specifically , while the baseline PMV is − 0 . 31 in win ter and 0 . 33 in summer, our approach yields similar v alues. This is further confirmed b y the w orst-case setp oint deviation, whic h remains limited to a PMV v alue of − 0 . 05 in winter and − 0 . 04 in summer. Th us, w e can conclude that PMV v alues fall within the limits defined b y ISO 7730:2005, b oth for existing buildings (-0.7 < PMV < 0.7) and for new or reno v ated buildings (- 0.5 < PMV < 0.5). Therefore, the prop osed control strategy applies to b oth existing and new constructions, represen ting a v alid to ol to reduce emissions while meeting comfort constrain ts. T o b etter detail the outcomes of our strategy , Figures 7 and 8 sho w the trends of the relev an t input and output v ariables defining our ev aluation scenario ov er t wo representativ e zo omed windows. Those windows ha ve b een selected from the full-y ear simulation and span from the 15 th to the 30 th No vem ber for the winter perio d and from the 15 th to the 30 th July for the summer one. Please note that these sp ecific windo ws ha ve b een rep orted as represen tative; the observed trends are, indeed, consistent across the rest of the year. Sp ecifically , Figure 7 sho ws the input v ariables defining the scenario, i.e., the external temp erature T ext ( k ) , the setp oint temp erature of the ro om T ref ( k ) , the num b er of p eople n occ ( k ) , the solar energy av ailable E solar ( k ) , and the grid carb on intensit y C I ( k ) . Figure 8, instead, sho ws the output of our strategy . In particular, in the first ro w, it reports the trends of the optimal surplus allo cation factor α ( k ) , i.e., the fraction of PV surplus that is sug- gested to store in the building thermal mass. In the middle ro w, instead, the trends of the related CO 2 emissions reductions are rep orted. These v alues ha ve b een computed, according to the surrogate emission mo del in tro duced in Section 3, as: ∆ CO 2 ( k ) = max  E pred ( k ) − E solar ( k ) , 0  − α ( k ) m m X i =1 ∆ E solar ( i ) ! C I ( k ) , (20) i.e., as the difference of the grid-related emissions obtained in the baseline case, when α = 0 , and those asso ciated with the case in which the pro- p osed strategy is applied. Similarly , on the last row, the trends of the 28 15-Nov 16-Nov 17-Nov 18-Nov 19-Nov 20-Nov 21-Nov 22-Nov 23-Nov 24-Nov 25-Nov 26-Nov 27-Nov 28-Nov 29-Nov 30-Nov 0 10 20 30 T emperatur e [°C] T e x t ( k ) T r e f ( k ) (a) Winter: T emp eratures ( T ref , T ext ) 15- Jul 16- Jul 17- Jul 18- Jul 19- Jul 20- Jul 21- Jul 22- Jul 23- Jul 24- Jul 25- Jul 26- Jul 27- Jul 28- Jul 29- Jul 30- Jul 0 10 20 30 T emperatur e [°C] T e x t ( k ) T r e f ( k ) (b) Summer: T emperatures ( T ref , T ext ) 15-Nov 16-Nov 17-Nov 18-Nov 19-Nov 20-Nov 21-Nov 22-Nov 23-Nov 24-Nov 25-Nov 26-Nov 27-Nov 28-Nov 29-Nov 30-Nov 0 1 2 3 4 P eople [-] (c) Winter: People ( n occ ) 15- Jul 16- Jul 17- Jul 18- Jul 19- Jul 20- Jul 21- Jul 22- Jul 23- Jul 24- Jul 25- Jul 26- Jul 27- Jul 28- Jul 29- Jul 30- Jul 0 1 2 3 4 P eople [-] (d) Summer: P eople ( n occ ) 15-Nov 16-Nov 17-Nov 18-Nov 19-Nov 20-Nov 21-Nov 22-Nov 23-Nov 24-Nov 25-Nov 26-Nov 27-Nov 28-Nov 29-Nov 30-Nov 100 200 300 C O 2 I n t e n s i t y [ g / k W h ] (e) Winter: Grid Emissions Intensit y ( C I ) 15- Jul 16- Jul 17- Jul 18- Jul 19- Jul 20- Jul 21- Jul 22- Jul 23- Jul 24- Jul 25- Jul 26- Jul 27- Jul 28- Jul 29- Jul 30- Jul 100 200 300 C O 2 I n t e n s i t y [ g / k W h ] (f ) Summer: Grid Emissions Intensit y ( C I ) Figure 7: Simulated scenario: input parameters. This figure shows the trend of the input v ariables in a zo omed window of the defined scenario. temp erature v ariation are reported. These v alues ha ve b een computed as ∆ T ( k ) = η γ α ( k ) ∆ E solar ( k ) C th (with γ = 1 in our simulations), i.e., as the tem- p erature deviation induced by the con trol action with resp ect to the baseline case ( α = 0 ). Analyzing these trends, we can deriv e some considerations. First, the lim- ited thermal mass of the ligh t-weigh t ro om hinders the capabilit y of storing significan t amoun ts of thermal energy . As a result, whenever surplus solar energy is a v ailable, our strategy sets α close to 1 in b oth win ter and summer, th us storing nearly all excess p ow er. How ev er, due to the low thermal inertia, the ro om temp erature rises rapidly , causing α to drop shortly after, as further storage w ould lead to high setp oint deviations. This b ehaviour pro duces an 29 oscillatory temp erature profile, whic h nonetheless remains within ± 0 . 5 ◦ C of the setp oint, and yields small CO 2 sa vings. In con trast, the medium- and heavy-w eigh t configurations exhibit a smoother α profile, reflecting the slo wer thermal resp onse of the ro om. This also results in a more regular temp erature evolution, but also in sligh tly larger deviations from the set- p oin t, which are, how ev er, b ounded within ± 1 ◦ C . Also, we can note that in win ter, our strategy suggests storing most of the solar energy surplus across all configurations. In summer, instead, low er p ercentages of this energy are stored, esp ecially considering the medium- and hea vy-w eigh t configuration. This is reasonable, as summer is characterized by larger solar surplus, so only a fraction of the a v ailable excess energy can b e stored thermally to prev en t excessiv e temp erature increases. As a last comment, it is w orth noting that the results discussed so far refer to the optimal configuration in T able 4. Sp ecifically , their refer to the optimal ω v alue, whic h pro vides the b est balance betw een CO 2 emissions reduction and temp erature setp oint deviation. How ev er, dep ending on the sp ecific ap- plication, a different trade-off may b e desirable. T o b etter understand the impact of this parameter on the strategy p erformance, Figure 9 illustrates, for eac h ro om configuration, ho w b oth ob jectiv es v ary as a function of ω , k eeping the prediction horizon and sampling time fixed to their optimal v al- ues. It is possible to note that, decreasing ω places greater emphasis on emissions reduction, allowing larger temp erature deviations; conv ersely , in- creasing this parameter enforces adherence to the user-defined setp oin t at the cost of reduced sa vings. This flexibility mak es the prop osed approach adaptable to a wide range of op erational requirements, from comfort-critical en vironments to applications where emissions minimization is the primary ob jectiv e. It is indeed p ossible to observe that, b y forcing the weigh t tow ard a lo wer v alue, in order to induce a greater v ariation of the setp oin t and increase the amoun t of solar surplus stored in the thermal mass, thus reducing emissions, an ann ual CO 2 sa ving of 27 . 29% , 30 . 04% , and 29 . 97% can b e achiev ed for the ligh t-, medium-, and heavy-w eigh t cases, resp ectively , compared to the baseline case. These p ercentages corresp ond to reductions of 19.71 kg, 22.41 kg, and 20.43 kg of CO 2 . How ev er, this increased sa ving also leads to a larger deviation of the setp oint and greater o ccupant discomfort, with maxim um ∆ T v alues of 2 . 6 ◦ C 2 . 3 ◦ C , and 1 . 3 ◦ C , resp ectively . 30 15-Nov 16-Nov 17-Nov 18-Nov 19-Nov 20-Nov 21-Nov 22-Nov 23-Nov 24-Nov 25-Nov 26-Nov 27-Nov 28-Nov 29-Nov 30-Nov 0.00 0.25 0.50 0.75 1.00 [ - ] (a) Winter: Surplus F raction to Storage ( α ) 15- Jul 16- Jul 17- Jul 18- Jul 19- Jul 20- Jul 21- Jul 22- Jul 23- Jul 24- Jul 25- Jul 26- Jul 27- Jul 28- Jul 29- Jul 30- Jul 0.00 0.25 0.50 0.75 1.00 [ - ] (b) Summer: Surplus F raction to Storage ( α ) 15-Nov 16-Nov 17-Nov 18-Nov 19-Nov 20-Nov 21-Nov 22-Nov 23-Nov 24-Nov 25-Nov 26-Nov 27-Nov 28-Nov 29-Nov 30-Nov 0 5 10 15 20 C O 2 [ g ] (c) Winter: CO 2 Emission Reduction ( ∆ CO 2 ) 15- Jul 16- Jul 17- Jul 18- Jul 19- Jul 20- Jul 21- Jul 22- Jul 23- Jul 24- Jul 25- Jul 26- Jul 27- Jul 28- Jul 29- Jul 30- Jul 0 5 10 15 20 C O 2 [ g ] (d) Summer: CO 2 Emission Reduction ( ∆ CO 2 ) 15-Nov 16-Nov 17-Nov 18-Nov 19-Nov 20-Nov 21-Nov 22-Nov 23-Nov 24-Nov 25-Nov 26-Nov 27-Nov 28-Nov 29-Nov 30-Nov 1 0 1 T [ ° C ] Light Medium Heavy (e) Winter: T emp erature V ariation ( ∆ T ) 15- Jul 16- Jul 17- Jul 18- Jul 19- Jul 20- Jul 21- Jul 22- Jul 23- Jul 24- Jul 25- Jul 26- Jul 27- Jul 28- Jul 29- Jul 30- Jul 1 0 1 T [ ° C ] Light Medium Heavy (f ) Summer: T emp erature V ariation ( ∆ T ) Figure 8: Sim ulated scenario: output v ariables. This figure shows the trend of the output v ariables in the defined scenario, referred to a zoomed window of tw o w eeks. Please note that ∆ CO 2 and ∆ T are computed with resp ect to the baseline scenario in which no strategy is applied, i.e., ( α = 0 ). 1 0 1 1 0 3 1 0 5 1 0 7 1 0 9 [ - ] 58000 60000 62000 64000 66000 68000 70000 72000 J C O 2 J C O 2 J c o m f 0 500 1000 1500 2000 2500 J c o m f (a) Light Configuration 1 0 1 1 0 3 1 0 5 1 0 7 1 0 9 [ - ] 55000 60000 65000 70000 75000 J C O 2 [ k g ] J C O 2 J c o m f 0 250 500 750 1000 1250 1500 1750 J c o m f [ C 2 ] (b) Medium Configuration 1 0 1 1 0 3 1 0 5 1 0 7 1 0 9 [ - ] 50000 55000 60000 65000 J C O 2 J C O 2 J c o m f 0 2000 4000 6000 8000 J c o m f (c) Heavy Configuration Figure 9: ω fine-tuning. This figure shows the trends of annual CO 2 emissions reduction and av erage daily temp erature deviation with resp ect to the weigh t ω . 31 5.3. Limitations Despite the impressiv e results, it m ust b e ackno wledged that it is a pro of-of-concept v alidation, and several simplifying assumptions ha ve b een adopted. Still, the scop e of this work w as to provide a preliminary insight in to the p oten tial of our control strategy to minimize CO 2 emissions through the exploitation of the building’s energy flexibilit y pro vided by its thermal storage capacity . Therefore, it m ust b e noted that none of the following limi- tations undermines this p otential; rather, they p oin t to clear extensions that can further improv e robustness and applicability . The first limitation is that the con troller is ev aluated using historical datasets to estimate solar energy pro duction and external temp erature, while a dataset from 2024 is used for the grid carb on intensit y . In real deploymen ts these signals m ust b e forecast, and prediction errors may reduce the attain- able savings. Nev ertheless, the proposed con trol la w only requires short- horizon trends and is computationally light w eight, making it straigh tforward to integrate standard forecasting pip elines. Second, we assume that the energy offset induced b y thermal storage is uniformly distributed ov er the prediction horizon. In other w ords, the amoun t of renew able surplus effectively shifted to the thermal mass is mo d- eled as a constant reduction of grid energy across the next m steps. This simplification is introduced to k eep the problem analytically tractable and to preserve the closed-form solution for α ( k ) , while still capturing the main effect of in terest. In practice, the true impact of a setp oint shift on the energy tra jectory ma y b e non-uniform. Therefore, the uniform-allo cation as- sumption can b e relaxed in future w ork b y considering other profiles for the surplus distribution. Third, the in ternal heat capacity is mo deled as a 24-hour p erio dic signal, as required b y the standard. This assumption is supp orted by the limited amplitude of its in tra-day v ariations, which remain relatively small and re- p eat consistently ov er time. Therefore, the p erio dic approximation do es not significan tly affect the accuracy of the mo del and can b e considered a rea- sonable simplification rather than a restrictiv e assumption. Last, the prop osed con trol strategy was v alidated in a simulated environ- men t. F uture w ork will inv olv e its application to a real-world case. Still, these limitations do not reduce the relev ance of the approach; they rather indicate that the rep orted sa vings should be in terpreted as a conser- v ative low er b ound obtained under simplified but realistic assumptions. 32 6. Concluding Remarks In this w ork, w e present a nov el building decarb onization strategy based on a battery-free setup. Sp ecifically , our idea is to store excess renew able en- ergy , when av ailable, in the building’s thermal mass, using it as a con trollable energy buffer. T o this end, w e design an ad-ho c optimization strategy that, whenev er a renew able surplus is a v ailable, computes the optimal fraction to store, trading off grid-related CO 2 emissions and o ccupants’ comfort. Under sp ecific assumptions, we sho w that a closed-form solution can b e derived, yielding a p olicy that is light w eigh t and suitable for real-time implemen ta- tion. T o assess the effectiveness of this approach, we consider a pro of-of-concept v alidation by designing a simplified yet high-fidelit y TRNSYS ro om mo del and iden tifying an in terpretable discrete-time mo del for describing its ther- mal b eha vior, which has b een then used for short-horizon energy consumption forecasting. The strategy is ev aluated across three configurations of the case study , represen ting buildings with low, medium, and high thermal mass. The results obtained by simulating our strategy p erformance o ver a year sho w a reduction in grid-related emissions of approximately 10% compared to the reference scenario without storage in the low thermal mass case, corresp ond- ing to annual sa vings of 7 kg of CO 2 . In the medium and high thermal mass cases, the reduction reaches 25% (appro ximatelly 18-20 kg of CO 2 ). These sa vings are achiev ed with maximum setp oint deviations of ± 0 . 5 ◦ C in the low thermal mass case, and ± 1 . 2 ◦ C in the medium and high thermal mass cases. A thermal comfort assessment based on the PMV index confirms that, de- spite these deviations from the reference setp oint, thermal comfort remains within the limits prescrib ed by the standard. F uture work will fo cus on real-building v alidation, in tegrating forecasting mo dels for solar energy and carbon intensit y . Overall, the presented re- sults supp ort the p oten tial of the prop osed in tuition, showing that the build- ing env elop e as a thermal storage can b e a lo w-cost alternativ e to batteries for increasing renewable self-consumption and reducing building-related CO 2 emissions. 33 App endix A. A dditional Details on TRNSYS Mo del In this App endix, further details on the TRNSYS mo del implementation and on the calculation of PMV for the differen t scenarios are rep orted. First, Figure A.10 sho ws the represen tation of the space in plan and section, carried out along the AA’ axis of the case study . In addition, Figures A.11, A.12 and A.13 illustrate the stratigraph y of the v arious env elop e comp onents used to mo del the office ro om. Second, T able A.5 pro vides further information into TRNSYS T yp e set- tings and functionality . Last, T able A.6 presents additionals details on the parameters adopted for the PMV calculation across the different scenarios considered. 34 120 140 5 m 6 m Office Area = 30 m 2 h = 3 m Volume = 90 m 3 b a b b A' A 120 140 120 140 (a) Plan 3 m c d (b) AA’ Section Figure A.10: Designed building section. This Figure shows the plant and the AA’ section of the building hosting the designed office ro om. 35 o ROCK WOOL INSULATION thickness 100 mm GYPSUM PLASTERBOARD thickness 12.5+12.5 mm i OSB PANEL thickness 15 mm ROCK WOOL INSULATION thickness 50 mm AIR GAP thickness 15 mm ALLUMINIUM CLADDING thickness 4 mm 20,9 10 2,5 1,5 5 1,5 0,4 (a) External opaque enclosure GYPSUM PLASTERBOARD thickness 12.5+12.5 mm ROCK WOOL INSULATION thickness 75 mm GYPSUM PLASTERBOARD thickness 12.5+12.5 mm i i 12,5 7,5 2,5 2,5 (b) Internal v ertical enclosure i o GYPSUM PLASTERBOARD thickness 12.5+12.5 mm STEEL BEAM thickness 100 mm PROFILED METAL SHEET thickness 1 mm VAPOUR BARRIER EPS INSULATION thickness 160 mm WATERPROOF BREATHABLE MEMBRANE PERFORATED STEEL PROFILE FOR VENTILATION thickness 60 mm PROTECTIVE STEEL PLATE thickness 2.4 mm 44,05 16 6 3,45 5,5 10 2,5 (c) Horizontal flat enclosure o i VENTILATED CRAWL SPACE thickness 250 mm CONCRETE BLINDING LAYER thickness 80 mm OSB PANEL thickness 18 mm AIR GAP thickness 80 mm XPS INSULATION thickness 120 mm VAPOUR BARRIER GYPSUM FIBREBOARD PANEL thickness 12.5+12.5 mm 58,2 2,5 8 0,6 12 25 8 LVT FLOORING thickness 6 mm 1,8 (d) Horizontal enclosure against ground Figure A.11: Ligh t-weigh t configuration stratigraphy . This Figure shows the stratigraphy of the main elemen ts constituting the ligh t-weigh t v ersion of the building hosting the designed office ro om. 36 o HOLLOW BRICK thickness 200 mm PLASTER thickness 15 mm i EPS INSULATION thickness 140 mm AIR GAP thickness 15 mm CERAMIC CLADDING FACADE thickness 20 mm 39 20 1,5 14 1,5 2 (a) External opaque enclosure HOLLOW BRICK thickness 120 mm PLASTER thickness 15 mm PLASTER thickness 15 mm i i 15 12 1,5 1,5 (b) Internal v ertical enclosure i o PLASTER thickness 15 mm REINFORCED CONCRETE AND HOLLOW BLOCK SLAB thickness 200 mm SLOPED LIGHTWEIGHT CONCRETE SCREED thickness 40 mm WATERPROOFING MEMBRANE EPS INSULATION thickness 160 mm NON-WOVEN FABRIC BALLAST LAYER IN GRAVEL thickness 40 mm 46,5 16 4 4 20 1,5 (c) Horizontal flat enclosure o i VAPOUR BARRIER MECHANICAL/ELECTRICAL CONCRETE SCREED thickness 60 mm LIGHTWEIGHT FINISHING SCREED thickness 40 mm LVT FLOORING thickness 20 mm XPS INSULATION thickness 120 mm REINFORCED CONCRETE SLAB thickness 150 mm 37,9 4 0,6 6 12 15 (d) Horizontal enclosure against ground Figure A.12: Medium-w eight configuration stratigraphy . This Figure sho ws the stratigra- ph y of the main elements constituting the medium-weigh t version of the building hosting the designed office ro om. 37 CONCRETE BLOCKS thickness 250 mm PLASTER thickness 15 mm EPS INSULATION thickness 140 mm AIR GAP thickness 15 mm CERAMIC CLADDING FACADE thickness 20 mm i o 44 25 1,5 14 1,5 2 (a) External opaque enclosure CONCRETE BLOCKS thickness 180 mm PLASTER thickness 15 mm PLASTER thickness 15 mm i i 21 18 1,5 1,5 (b) Internal v ertical enclosure i o PLASTER thickness 15 mm REINFORCED CONCRETE SLAB thickness 180 mm SLOPED LIGHTWEIGHT CONCRETE SCREED thickness 40 mm WATERPROOFING MEMBRANE EPS INSULATION thickness 160 mm WATERPROOFING MEMBRANE BALLAST LAYER IN GRAVEL thickness 40 mm 44,5 16 4 4 18 1,5 (c) Horizontal flat enclosure o i VAPOUR BARRIER MECHANICAL/ELECTRICAL CONCRETE SCREED thickness 80 mm LIGHTWEIGHT FINISHING SCREED thickness 60 mm CERAMIC FLOORING thickness 20 mm XPS INSULATION thickness 120 mm REINFORCED CONCRETE SLAB thickness 200 mm 48,3 6 2 8 12 20 (d) Horizontal enclosure against ground Figure A.13: Heavy-w eigh t configuration stratigraphy . This Figure shows the stratigraph y of the main elemen ts constituting the heavy-w eight version of the building hosting the designed office ro om. 38 T able A.5: Employ ed TRNSYS Types. This T able lists all the TRNSYS T yp es used to design the considered office ro om and rep orts their parameter settings. T yp e Definition Settings 941 Blo wer Po w er = 0.059 k W Air T o W ater T otal Air Flowrate = 1097.04 m 3 /hr Heat Pump Rated Heating Capacity = 1.04 k W Rated Heating Po w er = 0.246 k W 954a T otal Air Flowrate = 378 m 3 /hr Air to Rated Indo or F an Po w er = 0,035 k W Heat Rated Outdo or F an Po w er = 0,05 k W Pump Rated T otal Co oling Capacity = 1,3 Rated Co oling Po w er = 0,33 k W 114 Circulation Pump Rated Po wer = 32 W 1231 Design Capacity = 1200 W Design Surface T emp erature = 70 ◦ C Radiator Design Air T emp erature = 20 ◦ C Design Delta-T Exp onent = 1,3 Num b er of Pip es = 20 562f Photo vo ltaic Area = 7.73 m 2 P anel PV Cell Efficiency = 23% 23 Minim um Control Signal = 0 Maxim um Control Signal = 1 Co oling Gain Constant = -2 Con troller In tegral Time = 1 hr Deriv ative Time = 0 hr F raction of ySet for Prop ortional Effect = 1 23 Minim um Control Signal = 0 Heating Maxim um Control Signal = 1 and Gain Constant = 0.1 Pump In tegral Time = 1 hr Con troller Deriv ative Time = 0 hr F raction of ySet for Prop ortional Effect = 0.5 39 T able A.6: PMV calculation in different scenarios. The table summarizes the parameters used for the PMV calculation across the considered scenarios. Scenario Settings PMV Win ter scenario without α Air temp erature = 20 ◦ C Air sp eed = 0.1 m/s Relative humidit y = 50% PMV = -0.31 Metabolic rate = 1.2 (70 W /m 2 ) Clothing insulation = 1.1 (0.17 m 2 K/W ) Air temp erature = 21.2 ◦ C Air sp eed = 0.1 m/s Win ter scenario with α Relativ e humidit y = 50% PMV = -0.05 (maximum ∆ T = 1.2 ◦ C ) Metabolic rate = 1.2 (70 W /m 2 ) Clothing insulation = 1.1 (0.17 m 2 K/W ) Summer scenario without α Air temp erature = 26 ◦ C Air sp eed = 0.15 m/s Relative humidit y = 50% PMV = 0.33 Metabolic rate = 1.2 (70 W /m 2 ) Clothing insulation = 0.6 (0.095 m 2 K/W ) Air temp erature = 24.8 ◦ C Air sp eed = 0.15 m/s Summer scenario with α Relative humidit y = 50% PMV = -0.04 (maximum ∆ T = 1.2 ◦ C ) Metabolic rate = 1.2 (70 W /m 2 ) Clothing insulation = 0.6 (0.095 m 2 K/W ) 40 References [1] United Nations En vironmen t Programme, Global Alliance for Build- ings and Construction, Global status rep ort for buildings and construc- tion - b eyond foundations: Mainstreaming sustainable solutions to cut emissions from the buildings sector, United Nations Environmen t Pro- gramme (2024). doi: 10.59117/20.500.11822/45095 . 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