Strategies for Multigeneration in Residential Energy Systems: An Optimization Approach

Abstract

With the energy transition, energy supply trends indicate more autonomy for the final consumer, with a more decentralized, intelligent, and low-carbon scenario. Multigeneration technologies offer substantial socioeconomic and environmental advantages by enhancing the efficient utilization of energy resources. The main objective of this study is to develop a flexible, easy-to-use tool for the optimization of multigeneration systems (configuration and operation), focused on obtaining minimal annual costs. C++ was used for the implementation of the optimization problem, which was solved using IBM’s ILOG CPLEX Optimization Studio solver. The case study is a residential consumer center, with energy demands encompassing electricity (including electric vehicles), sanitary hot water, and coolth (air conditioning). The optimal economic solution indicates the installation of 102 photovoltaic modules and the use of biomass to produce hot water. When compared with a conventional solution, where all energy demands are met conventionally (no renewables nor cogeneration), the optimal economic solution reduced annual costs by 27% despite presenting capital costs 42% higher.

1. Introduction

Discussions on energy transition and the use of renewables have advanced worldwide [1] and are associated with significant changes in the structure of the global primary energy matrix. The new energy supply scenario is a more decentralized, intelligent, low-carbon model offering the final consumer more autonomy. There has been growing interest in developing reliable and adaptable energy integration systems [2], while addressing the challenge of balancing power generation and consumption remains particularly complex when renewables are present [3].

In this energy transition context, the building sector is responsible for 30% of global final energy consumption and contributes to 27% of total energy-related emissions worldwide [4]. In Brazil, the building sector (comprised of residential, commercial, and public consumers) accounts for approximately 1/6 of energy and 50% of electricity consumption [5]. In the USA, these figures amount to 40% of total energy use, including 75% of national electricity consumption and 35% of emissions [6].

Considering technological innovations and the efficient use of energy resources, the development and application of high-performance multigeneration technologies (combined energy production) should be the focus of this new energy scenario. The transition to sustainable and more renewable energy alternatives is increasingly critical to address and mitigate the escalating environmental challenges [7]. Multigeneration can employ conventional (fossil-fuel-based) and renewable energy sources and supports hybridization [8].

Multigeneration technologies offer significant socioeconomic and environmental benefits by enabling the efficient utilization of energy resources [9]. Overall system efficiency can be substantially enhanced through the optimized system design and effective integration of subsystems. Furthermore, the utilization of alternative fuels can enhance resource efficiency through appropriate fuel switching or blending with conventional fuels [10]. Implementing multigeneration systems is still a complex problem and is often restricted to studies in academic environments or implementation in isolated systems. Although the optimization of the energy supply is frequently adopted when there is a wide variety of energy resources available, the possibility of energy conversion within the energy system creates the need to optimize the design while considering internal energy flows. The number of parameters, variables, and restrictions involved results in high computational complexity. Among the convex optimization methods available for optimization, Mixed-Integer Linear Programming (MILP) is the most widely utilized approach due to its simplicity, convex nature, and capability to handle diverse energy flow scenarios [11]. Wirtz et al. [12] reported that the lowest total annual costs were achieved using MILP models with part-load efficiencies (despite reaching the highest computation times).

Souza et al. [13] employed MILP within the synthesis and optimization of an energy supply system for a set of nine buildings in Italy. The optimization model considered the possibility of sharing energy flows between the buildings (self-produced and imported electricity from the grid, as well as heating and cooling). The optimal solution reduced 31.9% of the total annual costs. Algieri et al. [14] focused on synthesizing and operating a multigeneration energy system for a residential complex in northern Italy, including solar photovoltaic (PV) modules and thermal energy storage units. A MINLP (Mixed-Integer Nonlinear Programming Model) was formulated with a bi-objective function (economic and environmental). All suggested optimal multigeneration configurations reduced total costs and carbon emissions compared to a conventional energy system. In addition, primary energy savings of over 19.7% were achieved, with payback times between 3.8 and 8.1 years.

Pinto et al. [15] proposed an approach for the design of multigeneration systems for residential buildings based on a MILP model that considered different constraints that allowed the energy system to function as a microgrid. The substitution of batteries with alternative energy storage systems to achieve more cost-effective solutions was emphasized. Pina et al. [16] evaluated the influence of legal conditions on the integration of renewable energy technologies in multigeneration systems for buildings. The optimization model incorporated various regulatory conditions, such as energy exchange mechanisms, subsidies and surcharges on energy prices, and investment costs, as well as a complete prohibition on fossil fuel usage. The model was applied to a Brazilian hospital, taking into account the current net energy metering framework established by Brazilian legislation. Natural gas cogeneration emerged as an effective solution to meet the hospital’s energy requirements, both with and without an electricity export to the grid. It was verified that the compensation scheme adopted by Brazilian legislation, by itself, is not enough to guarantee the deployment of renewable energy.

Pinto and Amante [17] focused on optimizing a polygeneration system for a building energy system retrofit, using MILP and maximizing the Net Present Value of the system. Different technologies were available in the superstructure, with the optimal solution including 2nd-life Li-Ion batteries, PV panels, and cogeneration modules. Martin et al. [18] highlighted the versatility of MILP in addressing comprehensive optimization models that tackle complex retrofit challenges and used a MILP model with a French open database to optimize retrofit solutions for different buildings. The study stresses accelerating building renovations to meet progressively more stringent environmental goals.

The study presented herein develops a MILP in C++, using the CPLEX solver to optimize the annual cost of a generic multigeneration system installed in a residential building. The configuration with the lowest yearly costs is obtained based on commercially available technologies and resources. This study goes further than existing studies by presenting an interface, which the end users of multigeneration systems can operate. Solar PV panels and collectors are available to produce electricity and hot water. The energy system accommodates electricity demand for electric vehicles and informs the excess photovoltaic electricity produced. There is also the possibility of using a fuel cell to produce electricity. The system is analyzed within Law 14,300 [19], which establishes the legal framework for distributed microgeneration and minigeneration, the Electric Energy Compensation System, and the Social Renewable Energy Program in Brazil.

2. Material and Methods

2.1. Energy Demands

The case study focuses on a 30-story residential building located in João Pessoa, Northeast Brazil. The building’s energy demands include electricity, hot water, and cooling (air conditioning). The characterization of electricity demands was conducted following the Brazilian standard ABNT NBR 5410:2004 [20], which specifies lighting loads based on room area, electrical outlet dimensions based on the room perimeter, and active power requirements for equipment such as elevators, pool pumps, and water reservoirs. Demand factors were applied in accordance with the guidelines of the local electricity utility [21]. Hot water demands were determined based on the daily useful energy requirements (kWh/day), following Brazilian standard ABNT NBR 15569:2021 [22]. Cooling loads were estimated using the degree-day method [23], assuming daily air-conditioning usage in apartment units from 9 pm to 7 am (on both weekdays and weekends). The reception area (front desk) maintained 24 h air-conditioning operation, while the party room required cooling only between 4 p.m. and 10 p.m. on weekends. An electric vehicle charging station was also included in the analysis, operating 24 h a day with the capacity to charge two vehicles simultaneously, twice daily, at a rate of 22 kW per charge.

The analysis was conducted using two representative days per month: one for weekdays and one for weekends/holidays. Each day was divided into 24-hourly periods, resulting in a total of 576 hourly periods. The building’s annual energy demands were calculated as 747.74 MWh/year for electricity, 330.34 MWh/year for hot water, and 85.37 MWh/year for cooling.

2.2. Superstructure and Equipment Specification

The superstructure includes all possible technologies, available energy resources, and their interactions. Equipment is included in the superstructure based on the energy demands of the residential building, considering commercially available technologies. Figure 1 illustrates the superstructure considered herein. A positive node indicates energy production (supply), and a negative node indicates consumption. Horizontal lines refer to physical distribution systems into which the equipment (the vertical lines) can supply or consume.

On the left side of Figure 1, the green box indicates the energy resources available for purchase. For example, EE is Electricity, which can be produced (+) or consumed (−) by equipment. Also, on the left side of Figure 1, the orange box indicates the energy demands of the building. The upper section of Figure 1 shows the available resources and equipment. Electricity generated by the PV system can be exported to the electric grid, following Brazilian law [19].

Table 1. Utilities and energy demands.

Utilities	Description
EE	Electricity
GN	Natural gas
DI	Diesel
BM	Biomass
AR	Cooling water
AA	Ambient air
Demands	Description
EE	Electricity
AQ	Hot water
AG	Chilled water

and

Table 2. Technologies available.

Equipment	Description
RDEE	Electric grid
SIFV	Photovoltaic system (panels + inverters)
GDGN	Natural gas generator
GDDI	Diesel generator
CADI	Hot water boiler that consumes diesel
CAGN	Hot water boiler that consumes natural gas
CABM	Hot water boiler that consumes biomass
CAEE	Hot water boiler that consumes electricity
CHAQ	Single-effect absorption chiller
CHEE	Mechanical chiller
TRAR	Cooling tower
TCAQ	Heat exchanger (hot water − cooling water)
CCOM	Fuel cell
SITS	Thermosolar system (solar collectors + boiler)

summarize the utilities and technologies available on site.

Technical parameters of the equipment were obtained from equipment data sheets and are displayed in

Table 3. Technical production coefficients and costs of equipment.

Technical Coefficients										Equipment
	EE	DI	BM	GN	AQ	AG	VA	AR	AA	Investment Cost Cinv (103 BRL)	O&M (BRL/h)	Nominal Power (MW)
RDEE	1.00									0.00	0.00	0.07
SIFV	1.00									13.36	0.50	0.45
GDGN	1.00			−3.70	2.95			2.12		158.10	3.69	0.17
GDDI	1.00	−2.03			1.45			1.48		73.05	1.70	0.33
CADI		−1.09			1.00					49.30	1.15	0.38
CAGN				−1.09	1.00					49.30	1.15	0.38
CABM			−1.25		1.00					56.52	1.32	0.37
CAEE	−1.10				1.00					28.20	0.66	0.35
CHAQ	−0.01				−1.26	1.00		2.23		150.00	3.50	0.10
CHEE	−0.32					1.00		1.32		145.00	2.61	0.06
TRAR	−0.01							−0.98	1.00	23.99	0.56	0.36
TCAQ					−1.10			1.00		7.40	0.17	0.40
CCOM	1.00			−2.75	1.03					3500.00	81.67	0.20
SITS					1.00					10.52	0.50	0.02

, along with costs. Appendix A presents detailed equipment data. Capital costs were obtained from consultation with manufacturers, and operation and maintenance (O&M) costs were obtained from the Brazilian National Research System on Civil Construction Costs and Indices [24].

Direct price surveys were carried out to obtain the tariffs for the energy services. The location used as a reference for the case study was the city of João Pessoa. For biomass (sugarcane bagasse), the value of Delgado et al. [25] was used (BRL 78/MWh), and, for diesel, the value used was BRL 743.46/MWh [26].

The electricity tariff for the residential consumer unit is BRL 356.61/MWh, a conventional flat tariff throughout the day [27]. For natural gas, the tariff is BRL 451.38/MWh [28], which is also a flat tariff.

2.3. Modeling and Programming

The model was implemented using C++, a high-performance programming language chosen for its ability to handle complex calculations and large data volumes efficiently, as the proposed problem requires. In energy optimization, using C++ offers advantages such as enabling the development of customized algorithms and direct integration with optimization libraries like CPLEX, facilitating the resolution of highly complex problems.

The flowchart in Figure 2 presents the required steps and the sequence of the modeling of the multigeneration system, as well as the requirements for programming and optimization.

IBM^® ILOG^® CPLEX^® Optimization Studio v20.1 [29] was employed, a decision optimization software for building and solving complex optimization models. The solution provides the results of an economic analysis, specifying the optimal configuration, including the type and quantity of equipment to install, as well as the operational strategy required to achieve minimal annual costs. All input data were organized into spreadsheets, with separate sheets for energy demand, a list of technical coefficients, investment, maintenance, and operational costs, and a third sheet for tariff information.

The economic objective function is the minimization of total annual costs (C_total), comprising fixed annual costs (C_fix, capital costs) and variable costs (C_var), which include the costs of purchasing of energy resources and O&M costs, as shown in Equations (1)–(3).

$${\mathrm{Min}\mathrm{C}}_{\mathrm{total}}={\mathrm{C}}_{\mathrm{fix}}+{\mathrm{C}}_{\mathrm{var}}$$

(1)

$${\mathrm{C}}_{\mathrm{fix}}=[\mathrm{frc}·\left(1+\mathrm{fci}\right)·{\displaystyle \sum }_{\mathrm{t}\in \mathrm{T}}{\mathrm{i}}_{\mathrm{t}}{\mathrm{y}}_{\mathrm{t}}]+\mathrm{SisFV}+\mathrm{SisTS}$$

(2)

$${\mathrm{C}}_{\mathrm{var}}={\displaystyle \sum }_{\mathrm{m}\in \mathrm{M}}{\displaystyle \sum }_{\mathrm{r}\in \mathrm{R}}{\displaystyle \sum }_{\mathrm{h}\in \mathrm{H}}{\displaystyle \sum }_{\mathrm{t}\in \mathrm{T}}({\mathrm{c}}_{\mathrm{t}}{\mathrm{x}}_{\mathrm{mrht}}+{\mathrm{cm}}_{\mathrm{t}}{\mathrm{x}}_{\mathrm{mrht}})-{\displaystyle \sum }_{\mathrm{m}\in \mathrm{M}}{\displaystyle \sum }_{\mathrm{r}\in \mathrm{R}}{\displaystyle \sum }_{\mathrm{h}\in \mathrm{H}}{\displaystyle \sum }_{\mathrm{t}\in \mathrm{T}}{\displaystyle \sum }_{\mathrm{n}\in \mathrm{N}}{\mathrm{c}}_{\mathrm{n}}{\mathrm{Q}}_{\mathrm{mrhnt}}$$

(3)

The fixed costs consider the capital recovery factor (frc = 0.13) and an indirect cost factor (fci = 0.15). i refers to the capital cost and y to the number of installed equipment. t is the type of equipment. SisFV and SisTS refer to the capital costs of the solar PV and thermal systems.

Within the variable costs, m, r, and h refer to, respectively, month, representative day, and hour. c_t refers to the cost of technology t in reais (Brazilian currency), and x_mrht indicates the use of technology t during month m, day r, and hour h (measured in hours). ${\mathrm{cm}}_{\mathrm{t}}$ is the cost of technology maintenance cost t in reais (Brazilian currency), and Q_mrhnt is the excess of utility n used by technology i during month m, day r, and hour h (measured in hours).

The operational limits of the system are implemented as restrictions in production, capacity, and energy balance equations. For each time period, energy production is restricted to the installed capacity, and an energy balance must be followed for each utility n, as shown in Equation (4).

$${\mathrm{S}}_{\mathrm{mrhn}}+{\mathrm{P}}_{\mathrm{mrhn}}-{\mathrm{E}}_{\mathrm{mrhn}}-{\mathrm{C}}_{\mathrm{mrhn}}-{\mathrm{D}}_{\mathrm{mrhn}}-{\mathrm{W}}_{\mathrm{mrhn}}=0$$

(4)

In Equation (4), S, P, E, C, D, and W represent Purchase, Production, Excess, Consumption, Demand, and Waste, respectively, for utility n in month m, day r, and time h.

The restriction expressed by Equation (5) guarantees that all energy demands are met because production must be greater than the sum of demand and consumption. ${\mathrm{A}}_{\mathrm{tn}}$ indicates the production of utility n by technology t.

$${\displaystyle \sum }_{\mathrm{t}\in \mathrm{T}}{\mathrm{x}}_{\mathrm{mrht}}{\mathrm{A}}_{\mathrm{tn}}\ge {\mathrm{D}}_{\mathrm{mrhn}}+{\mathrm{C}}_{\mathrm{mrhn}},\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H},\forall \mathrm{n}\in \mathrm{N}\mathrm{e}\forall \mathrm{t}\in \mathrm{T}$$

(5)

The restriction shown in Equation (6) indicates that the excess of a utility in a specific hour is the difference between the production and consumption of equipment.

$$\begin{gathered} {\displaystyle \sum }_{\mathrm{t}\in \mathrm{T}}{\mathrm{x}}_{\mathrm{mrht}}{\mathrm{A}}_{\mathrm{tn}}-\left({\mathrm{D}}_{\mathrm{mrhn}}+{\mathrm{C}}_{\mathrm{mrhn}}\right)={\mathrm{E}}_{\mathrm{mrhn}},\hspace{1em}\forall \mathrm{m}\in \mathrm{M}, \\ \forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H},\forall \mathrm{n}\in \mathrm{N}\mathrm{e}\forall \mathrm{t}\in \mathrm{T} \end{gathered}$$

(6)

Equation (7) guarantees that the total amount of an internally used utility (consumption and demand) cannot be higher than the excess produced. ${\mathrm{Q}}_{\mathrm{mrhnt}}$ indicates the used excess of utility n in month m, day r, and hour h by technology i.

$${\displaystyle \sum }_{\mathrm{t}\in \mathrm{T}}{\mathrm{Q}}_{\mathrm{mrhnt}}\le {\mathrm{E}}_{\mathrm{mrhn}},\hspace{1em}\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H},\forall \mathrm{n}\in \mathrm{N}\mathrm{e}\forall \mathrm{t}\in \mathrm{T}$$

(7)

Equation (8) limits the excess used by a piece of equipment. ${\mathrm{U}}_{\mathrm{nt}}$ is how much, proportionally, technology t uses of n.

$${\mathrm{Q}}_{\mathrm{mrhnt}}\le {\mathrm{U}}_{\mathrm{nt}}{\mathrm{x}}_{\mathrm{mrht}},\hspace{1em}\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H},\forall \mathrm{n}\in \mathrm{N}\mathrm{e}\forall \mathrm{t}\in \mathrm{T}$$

(8)

Equation (9) indicates that the maximum number of equipment installed must be equal or higher than the amount of equipment used at any time. ${\mathrm{Y}}_{\mathrm{t}}$ is the maximum amount of technology t used.

$${\mathrm{Y}}_{\mathrm{t}}-{\mathrm{x}}_{\mathrm{mrht}}\ge 0,\hspace{1em}\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H},\mathrm{e}\forall \mathrm{t}\in \mathrm{T}$$

(9)

The restrictions shown in Equations (10)–(14) define the nature of the decision variables.

$${\mathrm{x}}_{\mathrm{mrht}}\ge 0,\hspace{1em}\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H},\mathrm{e}\forall \mathrm{t}\in \mathrm{T}$$

(10)

$${\mathrm{E}}_{\mathrm{mrhn}}\ge 0,\hspace{1em}\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H}\mathrm{e}\forall \mathrm{n}\in \mathrm{N}$$

(11)

$${\mathrm{Q}}_{\mathrm{mrhnt}}\ge 0,\hspace{1em}\forall \mathrm{m}\in \mathrm{M},\forall \mathrm{r}\in \mathrm{R},\forall \mathrm{h}\in \mathrm{H}\mathrm{e}\forall \mathrm{n}\in \mathrm{N}\forall \mathrm{t}\in \mathrm{T}$$

(12)

$${\mathrm{Y}}_{\mathrm{t}}\ge 0,\hspace{1em}\forall \mathrm{t}\in \mathrm{T}$$

(13)

$$Y_t\in Z,\hspace{1em}\forall t\in T$$

(14)

3. Results and Discussion

A reference system is defined to serve as a basis for comparison in which the optimization is restricted. No renewable energy sources or combined energy scheme can be installed in the reference system. The only technologies and utilities allowed are conventional: electric grid, natural gas and diesel boilers, heat exchangers, mechanical chiller, and cooling tower.

The optimal economic system is determined through unrestricted optimization, utilizing all the utilities and technologies available within the superstructure. The optimization results are presented in

Table 4. Economic optimization results for the residential building.

Equipment/Utility	Economic Optimization
	Reference System	Optimal System
Electric grid	1 (300 kW)	1 (300 kW)
Natural gas boiler	1 (385 W)	-
Biomass boiler	-	1 (370 kW)
Mechanical chiller	1 (60 kW)	1 (60 kW)
Cooling tower	1 (360 kW)	1 (360 kW)
PV panels	-	102 panels (0.455 kW)
Energy flows (MWh/year)
Imported electricity	824.66	641.04
Purchase of natural gas	238.83	-
Purchase of biomass	-	345.32
Annual Costs (BRL/year)
Capital costs	27,702	47,510
O&M	25,974	29,575
Purchase of electricity	294,294	228,620
Purchase of natural gas	107,806	-
Purchase of biomass	-	26,935
Total Annual Cost (BRL/year)	455,776	332,640

.

The reference system relies on purchasing electricity from the grid to directly meet the electricity demands. Hot water and cooling demands are also satisfied by grid electricity through the use of an electric boiler and mechanical chiller.

The optimal economic solution recommends the installation of 102 PV panels but excludes the use of thermosolar collectors for hot water. Additionally, fuel cells are not incorporated into the system. Biomass is purchased to produce hot water in a boiler due to its low cost.

Although the optimal system requires a higher initial investment in equipment (41.69% higher capital costs), it results in a 27.02% reduction in total annual costs compared to the reference system (which separately produces energy services). The installation of PV panels leads to a 22.27% reduction in electricity imported from the grid.

Considering that the overarching aim of the program was to provide flexibility and ease of use, the optimization model can also provide other information. It is possible to visualize the hourly and monthly operation of the system (which equipment operates, the consumption of utilities, O&M costs, etc.). The graph in Figure 3 presents the monthly costs associated with the purchase of utilities throughout one year for the reference and optimal systems of the residential building.

It is also possible for the user to know which pieces of equipment are operating and the hourly associated costs, as shown in the graphs of Figure 4 and Figure 5. This presentation enables a more specific analysis and helps to decide O&M conditions, such as the replacement of equipment or maintenance stops.

Figure 4 shows that the PV system does not fully meet the energy demands of the optimal economic solution. This is represented by the blue bars that only appear between 6 a.m. and 6 p.m., with a small contribution. Electricity must still be purchased from the electric grid (brown bars) throughout the day.

The graph in Figure 5 shows that from 5 p.m. to 10 p.m., the hourly cost of equipment and utilities is higher, coinciding with the peak of demand and the absence of PV solar energy generation after 6 p.m.

3.1. Sensitivity Analysis

Some uncertainties and external influences can affect the multigeneration system, which is subject, for example, to fluctuations in equipment and fuel prices, increases in the energy demands of the consumer center, and changes in the regulatory model.

In this context, sensitivity analyses can simulate scenarios where changes occur in the variables representing the uncertainties.

The sensitivity analyses verify the impacts of changes in electricity tariffs, fuel prices (natural gas, diesel, and biomass), and increases in energy demands.

3.1.1. Electricity Demands

This sensitivity analysis considered an increase in electricity demands. This analysis is based on the Brazilian ten-year energy expansion plan 2032 [30], which predicts an average annual growth of 3.2% between 2022 and 2032 for electricity consumption in the residential sector.

Table 5. Optimization results for variations in residential electricity demands.

Progress Report	Year
	2022	2023	2024	2025	2026	2027	2028	2029	2030	2031	2032
Solution (s)	0.47	0.55	0.47	0.56	0.66	0.81	0.83	0.85	0.59	0.73	0.71
Interactions	1421	1444	1403	1418	1453	1429	1379	1397	1439	1432	1419
GAP	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
Economic Optimization
Equip.	Number of Equipment
RDEE	1	1	1	1	1	1	1	1	1	1	1
CABM	1	1	1	1	1	1	1	1	1	1	1
CHEE	1	1	1	1	1	1	1	1	1	1	1
TRAR	1	1	1	1	1	1	1	1	1	1	1
SIFV	102	104	108	111	115	117	122	126	128	133	137
Annual Energy Flows (MWh/year)
Imported electricity	641.04	661.16	680.96	704.27	724.66	748.52	771.33	797.30	822.28	847.41	874.49
Purchase biomass	345.32	345.32	345.32	345.32	345.32	345.32	345.32	345.32	345.32	345.32	345.32
Annual Costs (BRL/year)
Capital costs	47,509.81	47,877.05	48,611.51	49,162.36	49,896.82	50,264.05	51,182.13	51,916.60	52,283.83	53,201.91	53,936.37
O&M	29,574.64	29,586.16	29,609.20	29,626.48	29,649.52	29,661.04	29,689.84	29,712.88	29,724.40	29,753.20	29,776.24
Purchase electricity	228,599.51	235,965.51	242,838.51	251,150.51	258,421.51	266,928.51	275,065.51	284,325.51	293,321.51	302,194.51	311,852.51
Purchase biomass	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90	26,934.90
Annual Cost (BRL/year)	332,618.86	340,363.61	347,994.11	356,874.24	364,902.75	373,788.50	382,872.38	392,889.88	402,174.63	412,084.51	422,500.02

presents the optimization results for variations in the energy demand of the residential unit. It must be highlighted that the only parameter that changed in the optimization model was the electricity demand.

Considering the percentage predicted by the Brazilian ten-year energy expansion plan, the gradual and linear increase in electricity demand in the residential building did not significantly change the configuration of the optimal system. There is an increase of 21.27% in the total annual cost of the system due to the installation of additional PV panels.

3.1.2. Electricity Tariff

This analysis considers a −20% to +20% variation in the electricity tariff (originally BRL 356.61/MWh). The most sensitive parameters to changes in the energy tariff are the electricity imported from the grid and the annual cost of electricity. The equipment installed in the optimal system remained, except for the PV system that is not installed when the electricity tariff is BRL 338.78/MWh. Additional PV panels are also required.

The sensitivity of the system was similar to when electricity demands increased. PV generation is installed when the electricity tariff is higher, benefitting from its low O&M costs.

3.1.3. Natural Gas and Diesel Tariffs

According to the Brazilian Ten-Year Energy Expansion Plan [30], the diesel tariff should decrease throughout 2023/2024 but remain at high levels throughout the ten-year period. The natural gas price projections estimated in the study do not foresee a significant increase in the price of natural gas.

When varying the tariffs of natural gas and diesel between −20% and +20% around the base case, there were no changes in the optimal solutions. The model did not include gas or diesel technology and maintained the structure presented in the optimal solution with the original tariff.

3.1.4. Biomass Price

The biomass price varied between −20% and +20% around the base case. The optimal system for the residential building is not very sensitive to variations in the cost of biomass for the range of values considered. The base price of biomass led to the installation of a biomass boiler instead of the solar thermal system for water heating. When biomass price reached BRL 225.00/MWh, which is a 65.33% increase in its price, the optimal configuration changed, and 70 solar collectors were installed to produce hot water.

3.1.5. Change in Equipment

This section considers that the biomass boiler is no longer available. The results of the optimization are shown in

Table 6. Results of the optimization with and without the biomass boiler.

Economic Optimization
	With biomass boiler	Without biomass boiler
Solution time	0.63 s	0.63 s
No. of interactions	1408	1594
GAP	0.00%	0.00%
Equip.	Number of equipment
Electric grid	1 (300 kW)	1 (300 kW)
Biomass boiler	1 (370 kW)	-
Electric boiler	-	1 (348 kW)
Absorption chiller	-	1 (100 kW)
Mechanical chiller	1 (60 kW)	1 (60 kW)
Cooling tower	1 (360 kW)	1 (360 kW)
PV system	102 modules (0.455 kW)	-
Thermosolar system		70 collectors (2 kW)
Annual Energy Flows (MWh/year)
Imported electricity	641.04	765.62
Purchased biomass	345.32	-
Annual Costs (BRL/year)
Capital costs	47,510	85,725
O&M	29,575	26,429
Purchase electricity	228,600	273,028
Purchase biomass	26,935	-
Annual Cost (BRL/year)	332,620	385,182

.

Table 6 shows that in the absence of the biomass boiler for hot water production, the economic optimization resulted in installing an electric boiler, a single-effect absorption chiller, and 70 solar collectors. In this configuration, the annual cost increases by 13.65%.

Comparing our results with those of Melo et al. [31], who did not consider renewable resources, it is observed that including commercially available equipment that uses renewable resources is interesting from an economic point of view. In [31], only traditional electrical equipment was installed, and herein the biomass hot water boiler and solar PV panels were installed to achieve an economic optimal solution. The system implemented by Melo et al. [31] did not allow new equipment and utilities to be inserted flexibly and dynamically.

Pinto et al. [15] addressed the synthesis and optimization of the operation of polygeneration systems for residential buildings in Spain, integrating renewable and thermal energy technologies and electricity storage. Given the critical conditions imposed by local regulations, economic and environmental aspects were the main objectives. A MILP model was explicitly developed to research these aspects, and thermoeconomic analysis was applied to analyze and uncover the synergies and interactions between the system components. The multi-objective optimization problem was solved by LINGO. Unlike the approach proposed herein, the analysis carried out focused on the economic viability of the multigeneration system as a microgrid functioning in two ways: connected to the conventional grid or autonomously. Legal and regulatory aspects were not considered herein.

The work of Mohammadi and Mohammadi [32] used MILP within MATLAB and considered different operating strategies, objective functions, and components. The optimization focused on technical and efficiency aspects. The results demonstrated that the optimal solution could reduce the total annual costs by up to 62.5%, with consequent reductions in emissions of 14. 9%, compared to separate conventional generation. The study did not include renewable resources, electric mobility demand, or analyses based on current regulatory models. Jeon and Bae [33] studied the integration of hybrid energy storage into renewable power systems in Korea. The authors used MILP to establish the optimal configuration and operation of the hybrid energy storage system while minimizing operation costs. The optimal solution achieved a reduction of at least 50% in operation costs, outperforming previous studies by the authors, particularly excelling in cost performance.

Considering that the model developed herein for the optimization problem aims to be more flexible than existing solutions, it was tested to generate other information with the optimal result to assist the end user in decision-making. For temporal analyses of the optimal conditions with a period of less than one year, the model enables the visualization of the hourly and monthly dynamics of the system (utility consumption, maintenance cost, equipment used, etc.).

Regarding the selection of CPLEX for optimization, although Gurobi is also a popular tool for solving optimization problems in energy systems, there are distinct advantages depending on the specific requirements of the task (e.g., computational performance, ease of use, or integration capabilities). CPLEX is renowned for its strong performance in Linear Programming (LP) and MILP problems, frequently employed in optimizing energy systems. CPLEX also provides a highly intuitive graphical interface that simplifies the model creation, debugging, and visualization of results. CPLEX offers seamless integration with the IBM Ecosystem, especially with IBM Decision Optimization. Finally, robust CPLEX licensing options exist for researchers and academic institutions, making it an attractive choice for academic energy system studies.

Some challenges arise in the search for the best way to use these multigeneration systems. In addition to the search for optimization, democratization and the intelligent use of data, given its complexity, are important parameters to consider.

In the energy transition process, although Brazil has a favorable energy matrix due to the wide availability of renewable resources, public policies have sought to encourage the use of more decarbonized sources, following a global trend. Some pillars that guide this transition are the sustainability of expansion, incentives for efficiency, and the search for the lowest overall cost [34]. In this context, multigeneration systems emerge to provide a versatile, efficient, and economical solution to meet the demands of different consumer centers.

4. Conclusions

The study presented herein focused on synthesizing and optimizing an energy supply system for a residential building in Northeast Brazil. The contribution of this study is the consideration of solar energy (PV panels and solar collectors), fuel cell, and biomass as available energy resources. Electricity demands for an electric vehicle were also present. Also, the optimization model was built as a stand-alone program that relies on spreadsheets.

The optimal economic system consumed electricity from the grid and installed 102 PV panels. A biomass boiler was also installed, along with a mechanical chiller. Compared with a conventional separate energy production, the optimal economic solution presented a reduction of 27.02% in the total annual cost. The capital costs were 41.69% higher, but 22.27% less electricity was imported from the grid in the optimal solution.

Regarding the sensitivity analyses, more PV panels were installed when the electricity tariff reached BRL 374.44/MWh. When the price of biomass skyrocketed to BRL 225.00/MWh, thermosolar collectors were finally installed to produce hot water. Changes in diesel and natural gas tariffs did not impact the optimal solution. Changes in energy demands (following predicted growth trends by the Brazilian government) did not significantly change the system’s configuration but caused an increase of 21.27% in the total annual cost of the system (in 2032) due to the installation of additional PV panels. When the biomass boiler was unavailable for installation, 70 thermosolar collectors and a single-effect absorption chiller were part of the optimal solution. In this configuration, the annual cost increases by 13.65%.

The optimization presented herein achieved a significant reduction in the system’s total cost, enabling the insertion of other technologies with renewable resources to meet the energy demands of the building. Suggestions for future work include considering energy storage technologies in the superstructure and formulating a scheme to accommodate the energy credits from surplus production, following Brazilian laws.