DOI: 10.3303/CET24114112 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 23 May 2024; Revised: 10 August 2024; Accepted: 6 December 2024 
Please cite this article as: Polyvianchuk A., Petruk V., Polyvianchuk N., Yurii K., Semenenko R., Arsenyeva O., 2024, Approach for Optimal 
Selection of Innovative Actions for Residential Heating Systems, Chemical Engineering Transactions, 114, 667-672  
DOI:10.3303/CET24114112 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 114, 2024 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Petar S. Varbanov, Min Zeng, Yee Van Fan, Xuechao Wang 

Copyright © 2024, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-12-0; ISSN 2283-9216 

Approach for Optimal Selection of Innovative Actions for 

Residential Heating Systems 

Andrii Polyvianchuka, Vasyl Petruka, Natalia Polyvianchuka, Kovalenko Yuriib, 

Roman Semenenkoa, Olga Arsenyeva*,c 

aVinnytsia National Technical University, Department of Ecology, Chemistry and Technologies of Environmental Protection, 

 95 Khmelnytske shose, 21021, Vinnytsia, Ukraine 
bO.M. Beketov National University of Urban Economy in Kharkiv, Department of Engineering Ecology of Cities, 17 Marshal 

 Bazhanov str., 61002, Kharkiv, Ukraine 
cPaderborn University, Chair of Fluid Process Engineering, 100 Warburger str., 33098, Paderborn, Germany 

 olga.arsenyeva@upb.de 

Urban housing is the largest consumer of energy in European countries, representing approximately 43 % of 

total energy consumption. The objective of a sustainable society is to enhance the energy efficiency of buildings 

and domestic heating systems, with the goal of achieving zero-energy buildings that rely on renewable energy 

sources for their energy supply. To accomplish this, the current buildings must be effectively renovated. This 

study presents a method for upgrading household heating systems when there are limited finances available for 

investment. The proposed mathematical model is derived from the analysis of the building's energy system and 

combines the thermal energy producer and consumer into a unified system. It allows for the analysis of the 

building's condition using energy, environmental, and economic key indicators while also suggesting appropriate 

innovative measures. A proposed approach is to pick effective creative measures for the analysed building and 

optimise investment in time. The case study for the education building in Ukraine showed that the 

implementation of such an approach enables significant savings of up to 60-85 % of energy and fuel resources 

spent on building heat supply with a simultaneous reduction of environmental emissions by 39 % from the initial 

state. 

1. Introduction 

The International Energy Agency's report (IEA, 2022) states that the world is currently in a crucial period for the 

development of energy systems, which should be more safe, sustainable and cost-effective. Within the 

European Union, the buildings utilise 43 % of energy and release 36 % of greenhouse gases during energy 

generation. Ensuring the sustainability of cities requires the renovation of buildings and their energy systems, 

together with the implementation of innovative technologies that utilise renewable energy sources to generate 

energy for heating and hot water supply demand. 

To decrease energy usage for residential heating and cooling, the building’s energy demand should be 

decreased. It can be done by the building energy system retrofit, which will inevitably depend on the energy 

level of the building envelope, making the retrofit of the building itself the important measure of all the 

innovations. In the review paper by Fahlstedt et al. (2022), the various approaches used to decrease carbon 

emissions by improving the building envelope in order to achieve zero-energy buildings were examined. Wu et 

al. (2017) discuss the utilisation of building refit and enhancement of the energy supply system, with an 

emphasis on cost reduction and the reduction of greenhouse gas emissions. An examination of various energy 

sources in terms of their cost and environmental impact on non-residential buildings in Ukraine was conducted 

by Polyvianchuk et al. (2023a). The study conducted by Sarmouk et al. (2022) investigated the most efficient 

incorporation of solar energy and gas boilers for heating systems in commercial buildings. 

There is a limited number of studies that have been carried out to identify the optimal investment in building 

retrofit, and ongoing research is being undertaken at present. It is crucial to include the complete time span of 

667



building life cycles when doing optimisation, as highlighted by Richarz et al. (2022). This enables the 

identification of more practical approaches to constructing decarbonisation, when the investment choices are 

possible at various points over the building's lifespan and are flexible. The study conducted by Wirtz et al. (2023) 

examined the activities required for the transition to the 5th generation district heating system. Two investment 

strategies were employed: advance planning scenario and step-by-step implementation. Both techniques 

demonstrated cost savings in comparison to a single investment. The scenario that used the optimal investment 

pathway resulted in even greater savings, amounting to 17 % of the costs. The integrated approach, combining 

the selection of optimal building energy system renovation strategy and its investment in time using data-driven 

modelling, was proposed by Pedone et al. (2023). 

To ensure the efficient allocation of investments over time for enhancing a building's energy system, a new 

method for optimising a multi-period investment strategy is necessary. The present work is based on previous 

research, utilising key performance indicators to estimate the effectiveness of each proposed innovation 

(Polyvianchuk et al., 2020), and integrates multi-objective optimisation to define the best strategy based on 

economic and environmental criteria (Polyvianchuk et al., 2023b). A new method for the optimal selection of the 

most efficient multi-period investments for the chosen innovation actions is proposed. This technique is 

particularly applicable in situations where financial resources are limited. A case study of a university building is 

provided, demonstrating the advantages of the multi-period investment technique over a lump-sum investment 

strategy. 

2. Mathematical model of multi-period investment in retrofit of the building energy system 

Accurate determination of the most effective combinations of refurbishment actions for a building's energy 

system based on their efficiency and prioritising their sequence and optimal timing requires a comprehensive 

mathematical model, which allows account for a thorough assessment of investment required with optimal pay-

back periods. The proposed strategy is founded on the concurrent examination of the renovations from the 

perspectives of economics, environment, and energy. 

The proper estimation of the optimal combinations of refurbishment actions for building energy systems 

according to their efficiency needs comprehensive mathematical modelling. The methodology of the proposed 

approach is summarised in Figure 1. It is based on the estimation of the initial condition of the building’s energy 

system performed by the energy audit. The proposed energy retrofit measures are divided into three groups. 

The actions which can be done for thermal modernisation of the building envelope, such as insulation of the 

envelope walls, roof and windows, and improvement of the ventilation system, are included in the 1st group. 

The control system of climatic conditions in the rooms and the improvement of the insulation of all the connection 

tubes are in the 2nd group. The changes in the heating subsystems and implementation of renewable energy 

sources and heat pumps are related to the 3rd group. During the modelling, the highest priority is allocated to 

the 1st group of actions, then 2nd and 3rd, which allocates the sequence of the retrofit measures in time. These 

priorities will provide a systematic order of actions for the modernisation of the building. The first step will be to 

renovate the enclosing structures, followed by assessing the subsequent steps for reducing heat consumption 

in the building while avoiding unnecessary expenses. 

Based on the existing state of the building, its thermal energy performance ∆𝑞0 is estimated. For each retrofit 

measure proposed for the observed building, three performance indicators are estimated (Polyvianchuk et al., 

2020). The energy performance indicator 𝐸𝑃𝐼1 is defined as the ratio between current energy consumption and 

the value after implementing the retrofit action ∆�̅�. The cumulative 𝐸𝑃𝐼1 value includes the energy savings 

resulting from the modernisation of the building construction 𝑞𝑐𝑜𝑛𝑠 and fuel consumption 𝑉𝑓𝑢𝑒𝑙 . The 

environmental performance indicator 𝐸𝑃𝐼2 is determined based on the quantity of carbon dioxide emissions 

𝑚𝐶𝑂2, kg and the reduced level of pollution due to innovative measure ∆𝑚𝐶𝑂2. The economic performance 

indicator 𝐸𝑃𝐼3 is derived from the investment funds available, denoted as 𝐶𝑖𝑛, and the calculation of potential 

cost savings, represented as ∆c, throughout a single innovation period and in total, denoted as ∆𝑐. The priority 

of the performance indicators during the optimisation are set as weight coefficients when applying multi-objective 

optimisation (Polyvianchuk et al., 2023a). The primary objective of the present study is to determine the optimal 

allocation of investment capital over time. 

To determine the optimal multi-period investment function, it is necessary to estimate the total investment costs 

throughout time, 𝐹Σ−ін(𝑇). These expenses include the expenses generated from completed retrofit measures, 

𝐹𝑓−ін(𝑇), as well as the running costs associated with unfinished measures, which will be implemented later, 

𝐹т−ін(𝑇). The relationship between the costs is depicted as follows: 

𝐹𝛴−ін(𝑇) = 𝐹𝑓−ін(𝑇) + 𝐹т−ін(𝑇) (1) 

668



The revenue of completed measures is estimated based on the overall possible pay-back cost and is determined 

as the difference between the total amount of the resources needed 𝐹𝑓−Σ(𝑇) and operating costs for the energy 

building system when part of the planned retrofit measures were not done yet 𝐹(𝑓−e)(𝑇): 

𝐹𝑓−ін(𝑇) = 𝐹𝑓−𝛴(𝑇) − 𝐹(𝑓−е)(𝑇) (2) 

The total amount of required investment 𝐹𝑓−ін(𝑇) for the multi-period retrofitting will allow to maximise the 

investment cost 𝐹𝑓−Σ(𝑇) through the introduced financial effect of the multi-period investment ∆𝐹𝛴 defined as 

follows: 

∆𝐹𝛴 = ∆𝐹ін − ∆𝐹(−е) (3) 

where ∆𝐹ін is the reduction in investment due to earlier financing and associated pay-back revenue; ∆𝐹(−е) is 

the surcharge for energy supply throughout the funding period 𝑇𝐵, which is part of the overall investment period. 

 

Figure 1: The flowchart of research methodology for estimation of the optimal multi-period investment in building 

energy system retrofit 

For the optimisation of the ∆𝐹𝛴 function (Eq.(3)), the amount of required investment in time 𝐹𝑓−𝛴(𝑇) should be 

defined. It is proposed to determine the 𝐹𝑓−𝛴(𝑇) based on the division of funding periods on number of multi-

periods 𝑇𝐵 according to: 

𝐹𝑓−𝛴(𝑇) = 𝐶𝑒
𝛴 ∙ (

𝑇

𝑇𝐵
)

𝑎

 (4) 

where the unknown parameter 𝑎 needs to be approximated throughout the optimisation process. The number 

of implementation periods, Тв should be optimised as well. The parameters 𝑎 and 𝑇𝐵. in the proposed technique 

are defined based on discrete values in the following ranges: 𝑎 = 0.25 … 1.0;  𝑎 ranges from 0.25 to 1.0, while 

𝑇𝐵 = 0,1,2, … 10. When 𝑇𝐵 = 1 y, it corresponds to two stages of investment (initial and at the end of the year). 

The total investment required for retrofitting the building energy system 𝐹(𝑓−е)(𝑇)  is defined by integration over 

the time period of the efficiency function of capital investment 𝑓е
2, which presents the functional dependence on 

the financial resources allocated to the retrofitting over time 𝐹𝑓−𝛴(𝑇): 

𝐹(𝑓−е)(𝑇) = ∫ 𝑓е
2(𝐹𝑓−𝛴(𝑇))𝑑𝑇

𝑇

0

 (5) 

The expenses associated with compensating for the non-implemented actions 𝐹т−ін(𝑇)  are calculated based 

on the overall investment potential for all proposed retrofit measures 𝑓𝑒
𝛴 in each time period, excluding the 

revenue saved as a result of completed modernisation: 

𝐹т−ін(𝑇) = 𝑓е
𝛴 ∙ 𝑇 − 𝐹(𝑓−е)(𝑇) (6) 

669



 

Figure 2: The flowchart of the optimisation algorithm for the optimal multi-period investment 

By determining the maximum value of the target function presented in Eq.(3) within the specified range of 

parameters 𝑎 and Тв, one can achieve the most favourable allocation of investment over time for the suggested 

retrofit measures. The mathematical model defined by Eqs. (1)-(6) was realised in Excel spreadsheets using 

VBA to accomplish the spreadsheets used for energy audits of the buildings. The general flowchart of the used 

optimisation method is presented in Figure 2. The proposed approach can be used for the estimation of the 

optimal investment strategy for retrofitting insufficient energy systems of buildings based on performance 

indicators for proposed retrofit measures, and its application is presented in the case study. 

3. Case study 

The building of the Vinnytsia National Technical University, presented in Figure 3a, was investigated. The 

building was built in 1986 and is a 3-story building with a total heated area equal to 2,282.0 m2. The building 

uses the following types of fuel and energy resources: thermal energy in the form of hot water for heating needs; 

electricity is used to meet the needs of hot water supply and internal lighting. The existing heating system of the 

building is connected to the centralised district heating system operating on natural gas. Inside the building, the 

heating system is a two-pipe design with a lower distribution of the heat carrier and is equipped with iron 

sectional heating radiators without thermostats.  

Table 1: Estimation of the key performance indicators representing the effectiveness of the building 

 𝐸𝑃𝐼1 𝐸𝑃𝐼2 𝐸𝑃𝐼3 

𝑞𝑐𝑜𝑛𝑠, 

(kW·y)/m2 

𝑉𝑓𝑢𝑒𝑙,  

103 m3 

𝑚𝐶𝑂2, 

103 kg 

𝑓е
Σ, 

103 EURO 

Initial state 168.9 38.7 20.6 23.2 

After proposed retrofit measures 67.4 10.6 5.6 6.3 

670



The indoor heating system is designed to work at a temperature range of 95-70 °С; the actual temperature 

range in recent years has been close to 80-60 °С. The actual annual volume of thermal energy consumption by 

the building averaged over the last 3 y, is 385.5 MW·h. The actual average annual specific energy consumption 

per 1 m2 of total area is 168.9 W/m2. The calculated key performance indicators for the initial state of the building 

are presented in Table 1. 

(a) (b) (c) 

 

  

Figure 3: Retrofitting measures with optimised multi-period investment for the investigated building: (a) building 

photo; (b) distribution of the retrofit actions in time; (c) resulting investment parameters for the proposed time 

After the analysis of the initial state of the building, the recommended retrofitting measures were proposed, and 

their effectiveness was calculated. To choose the most efficient measures, the priority was given to the economic 

(𝐸𝑃𝐼3) and energy (𝐸𝑃𝐼1) indicators, considering the pay-back period. Each of the possible retrofitting measures 

was classified according to the 1st, 2nd or 3rd group for proper allocation of the different steps of retrofit in time. 

The most efficient measures were selected. They are listed according to the optimal sequence of implementation 

are presented in Table 2. The step-by-step distribution of the measures in time based on the efficiency function 

of capital investment from financial resources allocated for each retrofitting measure is demonstrated in Figure 

3b. The retrofitting measures RA1 and RA2 should be implemented in the beginning during the first investment 

period measures RA3-RA6 in the second, and RA7 in the 3rd investment period. 

Table 2: Estimated efficiency of the proposed retrofitting measures 

N Description of the innovative 

retrofitting action (RA) / group 

𝐸𝑃𝐼1 𝐸𝑃𝐼2 𝐸𝑃𝐼3 Investment 

cost, 

103 EUR 

Pay-back 

period, 

y 
𝑞𝑐𝑜𝑛𝑠, 

(kW·y)/m2 

𝑉𝑓𝑢𝑒𝑙,  

103 m3 

𝑚𝐶𝑂2, 

103 kg 

𝑓е
Σ, 

103 EUR 

RA1 Thermal modernisation of the 

attic floor /1st group 

23.0 5.26 2.80 3.16 10.03 3.2 

RA2 Thermal modernisation of the 

ventilation system /1st group 

22.5 5.16 2.75 3.09 15.33 5.0 

RA3 Installation of gas 

condensation boiler / 3rd 

group 

- 1.62 0.86 0.97 4.74 4.9 

RA4 Installation of smart control 

system for heating / 2nd group 

7.2 1.65 0.88 0.99 7.05 7.1 

RA5 Thermal modernisation of the 

entrance doors /1st group 

1.8 0.42 0.22 0.25 1.87 7.4 

RA6 Thermal modernisation of the 

walls /1st group 

47.0 10.77 5.73 6.46 56.07 8.7 

RA7 Installation of solar collectors 

/ 3rd group  

- 3.25 1.73 1.95 24.53 12.6 

Total  101.5 28.13 15.0 16.88 119.63 7.1 

Table 3: The resulting parameters of the optimised multi-period investment 

Measurement 

units 

Parameter 

𝐹𝑓−𝛴 𝐹(𝑓−е) 𝐹𝑓−ін 𝐹т−ін 𝐹𝛴−ін ∆𝐹ін ∆𝐹(−е) ∆𝐹Σ 

103 EUR 119.6 30.1 97.9 3.7 111.6 18.1 -3.7 14.4 

% 100 25.2 81.9 3.1 85.0 15.2 -3.1 12.1 

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The estimated parameters of the optimisation function are presented in Eq.(3), with the optimal values of the 

investment distribution over time (see Eq.(4)), where 𝑎 = 0.25 and 𝑇𝐵 = 2, corresponding to three investment 

periods, as shown in Figure 3c. The start of the 1st investment period concurs with the start of the retrofit, 2nd 

investment begins in 3.2 y, and 3rd in 3.3 y. The estimated payback period for the 1st investment period is 3 

years; for the 2nd, it equals 3.5 y and 4 y for the 3rd investment period. The resulting optimal parameters of the 

mathematical model of multi-period investment given in Eqs.(1)-(6) are listed in Table 3 in EURO and in %, 

compared to the full lump-sum investment strategy. The decrease in the cost for the observed period is 18,100 

EUR. It requires a longer retrofit period, which increases from 7.1 to 7.3 y compared to the lump-sum case. 

4. Conclusions 

The renovation of old buildings and their heating systems is required for the sustainable development of modern 

cities. The selection of modernisation actions should account for the efficiency of the measures, estimation of 

its cost, environmental impact and total consumption of energy. A mathematical model, which allows the 

estimate of the optimal multi-period investment in selected retrofit measures, is developed. The use of the model 

allows optimal distribution of the implementation of the proposed retrofit measures in time, reducing the total 

required costs. The application of the proposed approach for the retrofit of the University building allows to 

reduce heat energy consumption by 72.7 %. The implementation of optimal multi-period investment enables the 

decrease in the costs of investment resources by 15.2 % with the slightly increased retrofit period, which requires 

an additional 0.2 y compared to the strategy of lump-sum investment. A resulting positive integrated economic 

effect is equal to 12.1 %, which shows the benefits of the optimal investment strategy during the energy system 

retrofit. The adaptation of the current approach for building energy management systems integrated with 

electricity consumption and renewable energy sources is the subject of future work. 

Acknowledgements 

Olga Arsenyeva is grateful for receiving the Philipp Schwartz funding grant for threatened researchers from 

Paderborn University within the framework of the Philipp Schwartz Initiative of the Alexander von Humboldt 

Foundation. 

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