Design and operational challenges of renewable-powered isolated microgrids: a zero-carbon approach

Abstract

This article investigates the characteristics, operation and challenges of zero carbon microgrids, including size, generation from renewable sources, energy balance, and costs. An isolated zero-carbon microgrid is powered exclusively by renewable energy sources. It utilizes energy storage technologies, such as long-duration batteries or hydrogen storage, to mitigate intermittency and ensure a reliable power supply, allowing it to meet demand even under conditions of low production or high variability. The temporal variability between generation and load has technical and economic implications for microgrid sizing. This mismatch can be mitigated by combining renewable sources with diverse intermittency profiles, affecting both the storage system and the size of the generating units to be installed. This article formulates the sizing problem of an isolated microgrid designed to meet all load requirements solely through renewable sources and storage. The implications of this objective are analyzed and discussed, and sensitivity analysis studies are conducted to explore potential load shedding agreements and their impact on the solution. Solar, wind, and tidal energy exhibit a good degree of complementarity and help reduce storage requirements. However, the high cost of storage makes the oversizing of renewable sources even more attractive to ensure 100% load supply. On the other side, it was observed that allowing a load shedding of only 2.5% results in an approximate 46% reduction in the total system cost. Although the studies are carried out on a small microgrid, the conclusions can be expanded to systems of any size.

Introduction

Intelligent microgrids represent the cornerstone of modern electrical systems, leading the way in the search for reliability, resilience, and cost reduction. Global demands for decarbonizing the economy have recently highlighted another important benefit of microgrids: zero emissions. Microgrids must rely solely on clean energy sources to meet their energy needs while maintaining performance standards. The technological implications for these challenges are significant and, although there are technologies capable of meeting these requirements, they are still maturing, especially in the efficient integration of various renewable energy sources and storage¹.

A zero-carbon intelligent microgrid exemplifies our vision of a sustainable global electrical system. Recent studies have highlighted the opportunities and challenges of operating microgrids powered exclusively by renewable energy sources. These studies collectively focus on the feasibility, energy management, control strategies, and techno-economic aspects of achieving 100% renewable microgrids, especially in isolated or mission-critical contexts.

Rousan et al.² discuss the design and operation of a 1 MW islanded microgrid, focusing on managing excess renewable generation through energy storage and generation curtailment strategies. They used a grid-forming battery energy storage inverter to balance load and generation, demonstrating the technical feasibility of operating with 100% renewable capacity while ensuring stability and reliability. Campagna et al.³ emphasize the challenges related to the green transition towards 100% renewable energy sources, addressing technical, economic, and policy aspects. They highlight the need for technological innovations, government policies, and social acceptance to address these challenges effectively. The authors also point out that achieving a complete transition involves overcoming traditional system limitations and adapting to innovative paradigms that include renewable energy sources and smart inverters.

In⁴, Bastos and Trevisan investigated the feasibility of microgrids for powering remote communities with renewable sources. Using an island on the coast of Maine as a case study, they analyzed the optimal sizing of solar PV and battery energy storage systems. Their results show that the island can primarily be powered by renewable sources, utilizing a 400 kW PV system and a 2 MWh battery energy storage system, thereby reducing dependence on backup diesel generators. In⁵ and⁶, Li et al. studied hydrogen-based storage systems for renewable microgrids. They proposed a model that includes hydrogen tanks, electrolyzers, and batteries to create a power station capable of supplying energy to microgrid clusters, such as residential and industrial areas. The study emphasized the significance of hydrogen in meeting long-term energy storage needs, thereby ensuring a reliable power supply during periods when solar or wind energy resources are unavailable.

In⁷, Abdelsalam et al. proposed an energy management system for a hybrid AC/DC microgrid consisting of PV, wind, diesel, and hydrogen storage systems. The study included a sensitivity analysis to optimize the installed capacity of each renewable resource, aiming to minimize the levelized cost of electricity and carbon emissions. Their findings showed that hydrogen storage and a balanced mix of renewable sources could reduce reliance on diesel by approximately 72.44%, enhancing environmental sustainability. Wang⁸ analyzed the impact of different inverter control strategies-grid-following (GFL) and grid-forming (GFM)-on microgrid stability. The study demonstrated that mixed use of synchronous generators with GFL and GFM inverters could achieve better transient and steady-state stability, paving the way for reliable 100% renewable systems. Harasis⁹ also investigated DG connected through GFM and GFL inverters in islanded inverter-based microgrids. The author proposed a dynamic droop control to flexibly shape the transient power of microgrid’s DGs. A small-signal verification model of a microgrid under the proposed control has also been performed. Harasis et al.¹⁰ demonstrated the tradeoff between the operating cost and the reliability in microgrid operation. Although the authors deployed flexible control algorithms to optimize the power flow between different energy sources using the particle swarm algorithm, the results showed that the presence of dispatchable sources fueled by fossil fuels is a standard solution to avoid oversizing renewable and energy storage plants. Such a sizing approach decreases initial investments in generation and storage, impacting reliability indices, but it is not aligned with zero-carbon policies.

Daneshvar et al.¹¹ proposed a transactive energy solution for managing 100% renewable multi-microgrids integrated with gas grids. Using stochastic optimization, the authors introduced a fair and risk-averse model that minimized economic risks while ensuring energy reliability. Their results showed that such integrated systems could effectively manage the uncertainties associated with renewable energy production. In¹², Li et al. developed an optimal method for planning and operating a dual net-zero emissions islanded microgrid. Their results indicate that the proposed method reduces planning costs by 25% compared to other methods. Shen et al.¹³ propose a technical solution for planning a net-zero microgrid based on hydrogen storage in renewable-rich remote areas. Their main finding is the viable pathway to decarbonize microgrids using hydrogen storage technology. Wang et al.¹⁴ have presented an economic sizing of a renewable off-grid system using hydrogen storage, wind, solar, and bio-waste sources. Stochastic optimization is employed to represent the uncertainties associated with load, renewable resources, and electric vehicle recharge, and the Red Panda Optimization approach is employed to obtain a reliable optimal solution. The findings demonstrate the acceptable performance of the strategy in boosting the economic status of the island system. Naghibi et al.¹⁵ have developed an approach to allocating and sizing a renewable integrated energy system that incorporates power-to-hydrogen (P2H) and hydrogen-to-power (H2P) technologies within an active distribution network, considering wind, solar, and bio-waste resources, as well as hydrogen storage. The results show an improvement in network operation, reducing voltage drops, and increasing the maximum load capacity.

Shahzad et al.¹⁶ conduct a techno-economic analysis of green hydrogen integration in smart grids, evaluating the impacts of the efficiency and costs of electrolysis technologies, including PEM and alkaline systems. The results show that although green hydrogen reduces carbon emissions and enhances grid flexibility, the infrastructure and cost challenges remain, demanding policy support through incentives to make its adoption viable.

Recent literature highlights a growing effort to move towards power systems that are less dependent on fossil fuels and progressively closer to net-zero emissions. In this context, microgrids emerge not merely as a conceptual trend, but as practical testbeds and scalable solutions for decarbonization. By enabling the coordinated use of diverse renewable sources, storage technologies, and local control strategies, microgrids contribute to reshaping the energy mix, increasing system resilience, and reducing greenhouse gas emissions in a measurable way.

Research gaps

Table 1 summarizes the main highlights of the literature reviewed in this work. The diversity of the studies analyzed reflects a significant research interest in grid decarbonization, with microgrids playing a central role in this process. Renewable energy sources (RES) such as photovoltaic (PV), wind, and waste-to-energy systems are commonly considered, as are storage technologies like batteries and hydrogen. However, there is a noticeable lack of specific studies that include ocean-based renewable sources, such as tidal energy, and that examine how different types of intermittency affect the formation of hybrid renewable generation clusters. Furthermore, there is a shortage of in-depth discussions and analyses regarding the cost of achieving 100% renewable generation and its implications under varying scales of intermittency of primary energy sources.

Table 1.

Bibliographic review summary.

Reference	No. of RES types	Islanded operation	100% renewable	Battery storage	H2V storage	Comments
2	2	Yes	Yes	Yes	No	This paper evaluates the islanded operation of a microgrid comprised of wind, solar, and battery power. The analysis is conducted over a 24-hour horizon.
3	2	No	Yes	Yes	No	The objective is to assess the main challenges for 100% emissions-free microgrids. The article does not propose new methods for sizing or analyzing microgrid operations.
4	1	Yes	No	Yes	No	The objective is to evaluate the feasibility of an isolated microgrid being 100% served by PV and BESS sources, minimizing the use of a diesel generator.
5	1	No	Yes	Yes	Yes	The study considers one type of generation source. The focus is on meeting 100% of demand, and does not include a sensitivity analysis regarding the cost of reliability.
6	1	No	Yes	Yes	Yes	The objective is to build a zero carbon microgrid using multi-objective optimization to minimize total cost, exchanged energy and maximize installed renewable energy.
7	2	No	No	No	Yes	The study proposes a sizing method based on sensitivity analysis involving LCOE, discount rate and fuel price increase rate, however, it does not present a sensitivity analysis between costs and pre-defined reliability criteria.
8	1	No	Yes	Yes	No	This paper proposes an analysis of a microgrid with different renewable generation penetration rates, focusing on the stability and control strategies of electronic converters. Economic and load-supply reliability analyses are beyond the scope of this work.
9	1	Yes	Yes	No	No	This paper proposes a control strategy for a microgrid with multiple distributed sources. The focus is on transient analysis in microgrids consisting of GFM and GFL inverters. A planning (sizing) study focusing on economic and reliability assessment is beyond the scope of this paper.
10	1	Yes	No	Yes	No	The objective is to optimize a set of operational parameters, considering the tradeoff between operating costs and microgrid reliability. The methodology does not include the analysis of multiple sources or hybrid storage systems, nor does it include sensitivity analysis between the total costs and different predefined levels of reliability.
11	–	No	Yes	Yes	Yes	The objective is to optimize power flow between microgrid components and propose a dynamic operating scheme for the storage system. It uses a numerical index to quantify microgrid reliability. However, the focus does not include assessing the cost of reliability in serving the load.
12	3	Yes	Yes	No	Yes	The objective is to optimize the operation of an isolated microgrid with multiple sources and hydrogen. The approach includes a technical and economic analysis of the microgrid’s operation. The work consists of an economic feasibility analysis based on the prices of the microgrid components. However, it does not include an assessment of economic feasibility based on the reliability of meeting demand.
13	2	Yes	Yes	Yes	Yes	This paper proposes a technical-economic analysis of a microgrid with two renewable sources and a hybrid storage system. It also proposes an economic sensitivity analysis based on the expected cost reductions of the main microgrid components, without considering different load-supply reliability criteria.
14	3	Yes	Yes	No	Yes	It proposes the use of stochastic optimization to design an off-grid microgrid with multiple sources, hydrogen, and electric vehicles. The methodology does not include a cost analysis of load-servicing reliability.
15	3	No	Yes	No	Yes	This paper proposes a strategy for planning a system with multiple renewable generation sources and hydrogen storage. The objective is to reduce the installation and maintenance costs of the integrated system. Economic analyses of the cost of reliability are beyond the scope of this work.
16	2	No	No	No	Yes	The objective of the study is to evaluate the integration of green hydrogen into smart grids. The work does not address integration with other storage technologies, such as BESS, or the integration of these resources into isolated zero-carbon microgrids.

Contributions

In this paper, the authors address the sizing problem of an isolated zero-emission microgrid supplied by renewable sources such as photovoltaic, wind, and tidal power. The temporal mismatch in generation caused by the distinct intermittency patterns of the three renewable sources is investigated. The proposed microgrid includes a hydrogen facility to evaluate the potential for mitigating the temporal mismatch between the installed renewable sources and to analyze its impact on consistent performance in meeting the full annual load demand. This article considers isolated operation as it represents the most severe operational case for a microgrid. The motivation is to illustrate, through a small-scale model, the relevant challenges and viable solutions for the energy transition, with conclusions that can be generalized to any future renewable-based system. The problem is formulated as a multi-objective optimization, in which sensitivity analyses of its components are performed to identify their impacts and contributions to autonomous microgrid operation.

By evaluating critical aspects of zero-carbon microgrids, simulating their operation to draw relevant conclusions about their sizing, temporal variability in generating renewable sources, energy balance, and cost projections, it is possible to address the challenges of managing a microgrid with intermittent and distributed energy sources, highlighting the need for innovation in energy storage technologies and forecasting methods to improve energy generation and distribution.

The focus of this paper is on exploring the interaction among renewable sources with diverse intermittency patterns, which collectively contribute to an integrated energy resource capable of fully meeting demand with the support of multiple storage technologies, as illustrated in Fig. 1.

Fig. 1.

Graphical abstract: Key concepts in designing and operating zero-carbon isolated microgrids.

To address the gaps identified in Section “Research gaps”, this work introduces a sizing framework that distinguishes itself from previous studies in three key aspects: (1) it incorporates not only sources with well-known synergy (wind and solar) but also a less common, highly predictable source (tidal energy); (2) rather than targeting a predefined reliability level (typically 100%) as most studies do, this work identifies and evaluates the practical implications of the trade-off between cost and reliability; (3) it co-optimizes both short-term (BESS) and long-term seasonal (GH2) storage systems to balance this specific mix of generation sources.

The contributions of this article are as follows: a) It has been demonstrated that the autonomous operation of microgrids solely with renewable sources is feasible; b) The critical role of both short- and long-term storage in enabling autonomous microgrid operation has been established; c) The results demonstrated that uninterrupted zero-carbon operation is costly and requires a high rate of curtailed energy; consequently, small load sheddings can significantly decrease both spilled energy and the required size of generation assets; d) The mix of renewable sources has a beneficial impact on microgrid sizing and storage requirements. The article also illustrates the concept of zero-carbon microgrids as building blocks for the energy transition, enabling the development of scalable multi-microgrid compositions for the grids of the future.

The article is organized as follows. In Section “Zero-carbon microgrid”, the concept of a zero-carbon microgrid is introduced and thoroughly explained. Section “Problem formulation” formulates the microgrid sizing problem. Subsequently, the key components of the microgrid, including renewable energy sources and storage systems, are modeled in detail. In Section “Microgrid components”, the cost expressions associated with the microgrid’s operation and infrastructure are elaborated. Finally, the last three sections present a case study, followed by simulations that validate the approach. The discussion section interprets the results, highlighting key insights and implications, while the final section draws conclusions.

Zero-carbon microgrid

Typically, microgrids incorporate a high penetration of renewable energy sources, positioning them as a key component in the decarbonization of the electricity sector. However, the use of dispatchable sources, such as diesel generators, remains a common strategy to compensate for the inherent variability of renewable sources. Although this configuration is a well-established paradigm, it results in carbon emissions during the microgrid’s operation. In this context, a new paradigm is emerging: the zero-carbon microgrid (NZM), a system designed to operate with zero or near-zero carbon emissions. Figure 2 illustrates the concept of an NZM.

Fig. 2.

Zero-carbon microgrid. Source Elaborated by the authors.

According to¹⁷, the main characteristic of an NZM is the limitation of carbon-emitting sources. To meet this condition, advanced control strategies over generation sources are required, in addition to greater dependence on energy storage systems. Furthermore, an NZM can be designed to achieve a net-zero emission balance by offsetting any emissions produced during its operation through the use of its renewable resources.

An isolated NZM, also referred to as a dual-zero microgrid (DZM), is an off-grid microgrid whose operation results in zero carbon emissions and does not exchange electrical power with an external conventional grid¹⁸. In this context, planning and operating a DZM become more challenging. To meet a predefined reliability target, the absence of an external grid and fossil-fuel-based sources necessitates a greater dependence on existing renewable sources and storage systems.

According to¹⁹, current developments for NZMs follow three trends: 1 – high penetration of renewable sources, where the large-scale integration of renewable sources compensates the displacement of fossil fuel-based sources; 2 – extensive deployment of storage systems to compensate for the high variability of renewable sources; 3 – higher number of power electronic devices, since both renewable sources and storage systems typically use electronic converters, this directly affects the stability and control of the microgrid.

In this context, different approaches have been proposed to support the implementation of an NZM, such as storage systems²⁰, carbon capture¹⁸, optimization of the integration between renewable sources and the control strategy²¹, and demand response²².

These approaches demonstrate the technical and economic feasibility of NZMs; however, the relationship between total costs and reliability still requires further investigation. More specifically, the potential for drastically reducing total costs by introducing controlled flexibility in reliability and allowing a predefined small level of load shedding is an aspect that requires further investigation. Therefore, this article presents a sizing methodology to quantify the relationship between these costs and the system reliability, quantified by the Probability of Loss of Supply (LPSP), in a DZM formed of solar, wind, and tidal sources, as well as hybrid battery and hydrogen storage.

Problem formulation

The problem aims to determine the optimal sizing of wind and tidal turbines, photovoltaic (PV) panels, as well as the capacity of the BESS (short-term storage) and the hydrogen generation plant (medium/long-term storage), including the fuel cell and converter for the deferred return of this energy as electricity. The formulation consists of a multi-objective nonlinear optimization problem with constraints, as described below.

Objective function

Equation (1) defines the multi-objective function, which aims to minimize both the total cost and the total spilled energy:

1

Where the terms and are described in detail in the following sections, while denotes the vector of decision variables, as defined in Table 2.

Table 2.

Control variables.

Parameter	Description
	Number of PV Panels (units)
	Number of Wind Turbines (units)
	Number of Tidal Turbines (units)
	BESS Capacity (kWh)
	GH2 Plant Capacity (kWh)

Source: Elaborated by the authors

The total cost of the standalone zero-carbon microgrid is given by Eq. (2). The total cost consists of the installation, replacement, operation, and maintenance costs of all microgrid equipment.

2

Where, : Total cost of the system ($); : Total installation cost ($); : Total O&M cost ($) and : Total replacement cost ($).

The total spilled energy (kWh) is given by Eq. (3):

3

4

Where: : Total spilled energy (kWh); : Spilled power at instant (kW); : Time interval; : Total simulation time and : Operation time instant.

Control variables

The control variables of the problem are described in Table 2. These include parameters related to the number of photovoltaic panels (PV), wind turbines, and tidal turbines, as well as the capacities of the BESS and the GH2 plant.

The capacities in kW of each unit are specified in the case study. This approach avoids dependence, in the problem formulation, on the unit sizes currently offered by the market for each generation technology.

Problem constraints

The optimization problem is subject to the following constraints, detailed below:

Power balance

The power balance must be satisfied at every operational instant of the microgrid. Equation (5) represents the power balance equation at time :

5

Where: : Power demand from the load (kW); : Power used to charge the BESS (kW); : Power consumed by the GH2 electrolyzer (kW); : Total power generated by renewable sources (kW); : Power discharged from the BESS (kW); : Power supplied by the GH2 fuel cell (kW); : Power loss due to load shedding (kW).

Renewable generation system constraints

The constraints related to the capacities of PV panels (), wind turbines (), and tidal turbines () are expressed by Eqs. (6), (7), and (8), respectively:

6

7

8

The maximum limits for these renewable sources are defined by the nominal capacity of each source to meet the total load demand alone. The minimum limits are determined based on the minimum operational capacity, corresponding to installing at least one equipment unit for each renewable source.

BESS model and constraints

The BESS is an energy storage system composed of batteries. In this study, lithium-ion batteries are used. It is important to note that a lithium battery has an average lifespan of approximately 8 to 15 years, depending on the depth of charge used²³. The nominal storage capacity of the BESS can be calculated using Eq. (9):

9

Where: : Nominal storage capacity of the BESS (kWh); : Nominal capacity of a single battery (Ah); : Nominal voltage of the battery (V); : Number of batteries connected in series (units) and : Number of batteries connected in parallel (units).

The power of the BESS at time is given by Eq. (10).

10

Where: : Power of the BESS at time (kW); : Input power to the BESS, charging (kW); : Charging efficiency of the BESS (); : Output power from the BESS, discharging (kW) and : Discharging efficiency of the BESS ().

The C-rate is the charge and discharge rate of a battery. For lithium-ion batteries, a 1C C-rate is commonly used, meaning the full charge or discharge is performed within 1 hour at maximum current. The maximum instantaneous charge and discharge power of the BESS are represented by Eqs. (11) and (12), respectively.

11

12

Where: : Charging rate of the BESS and : Discharging rate of the BESS.

The SOC represents the state of charge of the BESS, and it is calculated using Eq. (13).

13

Where: : SOC (); : Initial state of charge of the battery (); : Amount of charge supplied to or withdrawn from the battery during its operation () and : Maximum charge the battery can store ().

Equation (14) represents the , which is the ratio between the current SOC and the maximum SOC of the BESS.

14

The SOC update equation is given by:

15

The maximum capacity and (maximum state of charge) are not necessarily the same. The maximum capacity of a BESS refers to the total amount of energy the system can store, as specified by the manufacturer (nameplate data). On the other hand, SOC is a metric that indicates the current charge level of the battery as a percentage of its total maximum capacity. The maximum SOC may differ from the maximum capacity due to operational restrictions, safety measures, or even battery aging. For our case, for simplicity, we will consider that the sized capacity of the BESS coincides with the maximum , that is:

16

Thus, in the operation of the microgrid, the SOC must satisfy the following constraint.

17

The power limit of the BESS is represented in Eq. (18).

18

Equations (19) and (20) represent the maximum charge and discharge power of the BESS, respectively.

19

20

Where: : BESS charge C-rate, and : BESS discharge C-rate.

Equations (21) and (22) express the maximum and minimum limits of the BESS’s charging and discharging power.

21

22

The nominal capacity of the BESS is defined according to Eq. (23).

23

GH2 model and constraints

Energy storage in the form of GH2 involves three main components: the electrolyzer, responsible for converting surplus energy into green hydrogen; the GH2 storage tank; and the fuel cell, responsible for converting the stored green hydrogen back into electrical energy. Considering this complete cycle, the system can be viewed as a large battery and, therefore, has associated parameters.

Equation (24) represents the instantaneous net power of the GH2 system. It accounts for the power consumption of the electrolyzer and the power injected back by the fuel cell, including their respective efficiency values.

24

Where, : Power of the GH2 system (); : Input power to the electrolyzer (); : Efficiency of the electrolyzer (); : Output power of the fuel cell (); and : Efficiency of the fuel cell ().

Similar to the BESS, we can also define the state of charge (SOC) for the GH2 system. Equation (25) represents the :

25

The SOC update equation for the GH2 system is given by Eq. (26).

26

Where, : SOC of the GH2 system at time () and : SOC of the GH2 system at the previous time step ().

The storage capacity of GH2 is determined by the optimization process, which establishes a balance between the expected curtailment of renewable energy sources and the plant size. In the absence of operational or safety constraints, the value of can reach the maximum capacity , as follows.

27

In the operation of the microgrid, the constraint must be taken into account:

28

In terms of power, the constraint is as follows:

29

The electrolyzer is designed for maximum efficiency, sized to match the maximum load demand, as shown in Eq. (30). This means that even if the microgrid’s consumption is zero at any given time, the electrolyzer can efficiently redirect the unused energy to generate GH2 accordingly. The power limits of the electrolyzer during operational simulation are defined by Eq. (31), ensuring its efficient operation.

30

31

The nominal power of the fuel cell can be determined in a manner similar to the previous case, that is, requiring that the maximum peak of the load demand can be met solely by it, as stated in Eq. (32).

32

The power limits of the fuel cell for the simulation of the operation are defined by Eq. (33).

33

The nominal capacity of the BESS is defined according to Eq. (34).

34

Loss of power supply probability (LPSP)

This is a key reliability metric used in the energy and power sectors to evaluate the likelihood that electricity demand will surpass supply capacity at a given time. In this context, LPSP is employed to assess the impact of supply shortages on loads over short time intervals throughout the year.

Considering that the unmet energy (Loss of Power Supply - LPS) at the time [] is given by Eq. (35), the value of can be calculated using Eq. (36). Equation (37) expresses the limit of the load loss restriction. The limit values adopted in this study are: 0%, 2.5%, 5%, 7.5%, and 10%.

35

36

37

Where: : total energy not supplied (kWh); : Percentual energy not supplied (); : Maximum allowed energy not supplied (); : Loss of power at the instant t (kW) and : Load demand at the instant t (kW);

Multi-objective optimization algorithm

In this study, the multi-objective optimization problem formulated in the previous section was solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). For complex multi-objective problems, the NSGA-II is specifically designed to identify a set of non-dominated solutions that constitute the Pareto front, effectively mapping the trade-off between conflicting objectives. The algorithm’s ability to recombine and modify solutions through selection, crossover, and mutation operators ensures robust and efficient convergence. Consequently, the NSGA-II is notably recognized as a powerful tool for solving microgrid sizing and operation problems, as seen in^24–26.

The algorithm was implemented in the MATLAB environment using the gamultiobj function from the Global Optimization Toolbox. The simulations were configured with a population size of 100 individuals, 500 generations, and rates for crossover, mutation, and elitism of 10%, 5%, and 5%, respectively.

Microgrid components

Photovoltaic system

The power generated by the PV system at time is given by Eq. (38)²⁷. In this study, the CS6W-550MS photovoltaic module manufactured by Canadian Solar was used. This model has a nominal power of 550 W and an efficiency of 21.3%²⁸.

38

Where, : Number of photovoltaic panels (); : Nominal power of each photovoltaic panel (); : Reduction factor for photovoltaic generation (); : Irradiation value incident on the panels at time (); : Temperature coefficient of the panel (−0.45%); : Temperature of the PV panels (); : Nominal operating temperature of the PV panels ().

Wind generation model

In this study, the Excel 7.5 kW Wind Generator turbine from Bergey, shown in Fig. 3, was used²⁹. Table 3 shows the specifications of the wind turbine.

Fig. 3.

Bergey Excel 7.5 kW Turbine. Source:²⁹.

Table 3.

Wind turbine specifications.

Parameter	Specification	Value
	Nominal power	7.5 kW
	Cut-in wind speed	3 m/s
	Cut-out wind speed	15.6 m/s
	Nominal wind speed	13 m/s

Source: ²⁹

The wind turbine power curve provided by the manufacturer is modeled by a 9th-degree polynomial function of wind speed, represented as in Eq. (39). The turbine power curve indicates the turbine’s power output as a function of the available wind speed. Figure 4 compares the polynomial function with the power curve provided by the manufacturer.

39

Where, : Polynomial function of wind speed; through : Coefficients of the polynomial.

Fig. 4.

Wind turbine power curve. Source: Elaborated by the authors.

Wind turbine generation power is modeled by Eq. (40).

40

Where, : Modeled power of a wind turbine (kW); : Wind speed (m/s); : Cut-in wind speed (m/s); : Cut-out wind speed (m/s); : Nominal wind speed (m/s); : Nominal power of the wind turbine (kW).

The modeled power will be multiplied by the number of turbines installed, as expressed in Eq. (41).

41

Where, : Number of wind turbines (units); : Modeled power of a wind turbine (kW).

Tidal generation model

The tidal turbine model SmartMonofloat with a nominal power of 5 kW, shown in Figure 5, was considered. Table 4 presents its technical specifications.

Fig. 5.

Smart Monofloat turbine. Source:³⁰.

Table 4.

Specifications of the tidal turbine.

Parameter	Specification	Value
	Nominal power	5 kW
	Cut-in speed	0.5 m/s
	Cut-out speed	2.8 m/s
	Nominal speed	2.8 m/s

Source: ³⁰

The power curve as a function of tidal current speed, provided by the turbine manufacturer, was modeled using a 5th-degree polynomial function given by Eq. (42). Figure 6 compares the polynomial function with the power curve provided by the manufacturer.

42

Where, : Polynomial function of tidal current speed.

Fig. 6.

Tidal turbine power curve. Source: Elaborated by the authors.

The power generation of tidal turbines is modeled by Eq. (43).

43

Where, : Modeled power of a tidal turbine (kW); : Tidal current speed (m/s); : Cut-in speed of the tidal turbine (m/s); : Cut-out speed of the tidal turbine (m/s); : Nominal speed of the tidal turbine (m/s); : Polynomial function of the tidal power curve; : Nominal power of the tidal turbine (kW).

The modeled power will be multiplied by the number of installed turbines, as expressed in Eq. (44). In this tidal model, the effects of turbulence between turbines are not considered.

44

Where, : Number of tidal turbines (units); : Modeled power of a tidal turbine (kW).

Costs

The total cost of acquisition and installation of microgrid components is expressed by Eq. (45).

45

Where, : Total installation cost ($); : Number of PV panels (units); : Number of wind turbines (units); : Number of tidal turbines (units); : Capacity of the BESS (kWh); : Capacity of the GH2 system (kWh); : Acquisition and installation cost of PV panels ($/unit); : Acquisition and installation cost of wind turbines($/unit); : Acquisition and installation cost of tidal turbines ($/unit); : Acquisition and installation cost of the BESS ($/kWh); and : Acquisition and installation cost of the GH2 system (electrolyzer and fuel cell) ($/kWh).

The annual operation and maintenance (O&M) costs are expressed by Eq. (46), adjusted by the interest rate over the system’s lifetime.

46

Where, : Total O&M cost ($); : O&M cost of PV panels ($); : O&M cost of wind turbines ($); : O&M cost of tidal turbines ($); : O&M cost of the BESS ($); : O&M cost of the GH2 system (electrolyzer and fuel cell) ($); : Annual O&M interest rate (); : Project year (); and : Project lifetime ().

The replacement cost is given by Eq. (47), where each component type has a different lifetime. The replacement value is adjusted according to the simulation time. Replacement costs for the GH2 system include the electrolyzer and the fuel cell.

47

Where, : Total replacement cost ($); : Replacement cost of PV panels ($/unit); : Replacement cost of wind turbines ($/unit); : Replacement cost of tidal turbines ($/unit); : Replacement cost of the BESS ($/kWh); : Replacement cost of the GH2 system (electrolyzer and fuel cell) ($/kWh) : Annual replacement interest rate (); : Project year (); and : System lifetime ().

The total cost of the microgrid is defined by Eq. (2).

Case study

The case study focuses on the São Marcos Bay region, specifically the Boqueirão Channel, formed by Medo Island and São Luís Island (the capital of the State of Maranhão, Brazil). Figure 7 shows an aerial image of the study area, located approximately at 2.5288S, 44.3596W. The hypothetical microgrid of this case study has a demand profile representative of the various oceanic islands in the study area. Figures 8 and 9 illustrate, respectively, the typical demand profile of communities in the region, both annually and weekly. The average demand is approximately 42 kW, with a maximum peak of 77 kW. The total annual energy demand is 365.73 MWh. These data were processed to obtain a semi-synthetic curve representing a period of 1 year with a sampling interval of 1 min, as described in³¹.

Fig. 7.

Aerial view of the study area. Source: Aerial photograph taken by the authors.

Fig. 8.

Annual load demand. Source: Elaborated by the authors.

Fig. 9.

Weekly load demand. Source: Elaborated by the authors.

Considering that a key objective of this work is to analyze how different generation source profiles impact system efficiency (measured by spilled energy) and cost, using a case study based on real data provides greater practical validity to the technical and economic conclusions. Furthermore, this approach enables a more realistic assessment of the complementarity between sources, particularly tidal power. An analysis of this nature would be unfeasible if conducted with the generic or non-existent data provided by standard benchmark systems.

Energy characterization of the area

Measurements of tidal current velocity were conducted through moorings in the Boqueirão Channel, located within São Marcos Bay. Wind speed and solar irradiance data were obtained from the measurement stations of the Alcântara Launch Center (CLA). The favorable wind regime in the Baía de São Marcos is strongly influenced by the trade winds, with both synoptic regimes and the sea breeze tending to align perpendicular to the coast³².

Figures 10, 11, and 12 respectively show the measurement data for solar irradiance, wind speed, and tidal current velocity. The measurement data, collected over a period of 1 year with an initial sampling interval of 10 minutes, were interpolated to 1-minute intervals, resulting in a total of 525,600 data points.

Fig. 10.

Solar irradiance. Source: Elaborated by the authors.

Fig. 11.

Wind speed. Source: Elaborated by the authors.

Fig. 12.

Tidal current velocity. Source: Elaborated by the authors.

Based on the measurement data and using Eqs. (38), (40), and (43), it is possible to calculate the power generated by the solar, wind, and tidal energy sources, respectively. The specifications of the wind and tidal turbines used are detailed in Tables 3 and 4, respectively.

Figures 13, 14, and 15 illustrate the daily energy generation by a single unit of each source.

Fig. 13.

Daily photovoltaic generation. Source: Elaborated by the authors.

Fig. 14.

Daily wind generation. Source: Elaborated by the authors.

Fig. 15.

Daily tidal generation. Source: Elaborated by the authors.

The capacity factors of the renewable generation components of the microgrid are shown in Table 5.

Table 5.

Capacity factors.

Equipment	CF (%)
Photovoltaic panel	15.09%
Wind turbine	32.15%
Tidal turbine	17.04%

Source: Elaborated by the authors

Equipment costs

The costs were estimated based on^33–37. The values presented in Table 6 are estimates that encompass purchase, installation, transportation, loading, mounting, electrical cabling, and other items. The O&M cost was estimated at 10% of the installation cost.

Table 6.

Equipment costs.

Equipment	Installation cost	Reference	Nominal capacity
PV	USD 1,000.00	USD/unit	550 W
Wind	USD 30,000.00	USD/unit	7.5 kW
Tidal	USD 25,000.00	USD/unit	5 kW
BESS	USD 458.00	USD/kWh	1 kWh
GH2	USD 600.00	USD/kWh	1 kWh

Source: Elaborated by the authors

Storage specifications

The maximum capacity limit of the BESS, as a short-term storage system, was assumed to be up to eight times the maximum load demand peak (576 kWh). The maximum capacity limit of the green hydrogen (GH2) storage system, considering its function as long-term storage, was assumed to be up to one hundred times the maximum load demand peak (7500 kWh). These limits can also be interpreted as a reflection of investment constraints in the project. From the perspective of the optimization metaheuristic, they establish an upper bound to aid in a more efficient search process.

Table 7 summarizes the specifications of the storage devices (BESS and GH2) established for this investigation. The simulations considered the following priority order of source dispatch: tidal, wind, and photovoltaic.

Table 7.

Technical specifications for BESS and GH2.

Parameter	Values used
initial	100%
	30%
	70%
	1C
	1C
	95%
	95%
initial	0%
	100%
	0%
	100%
	127 kW
	70%
	127 kW
	70%

Source: Elaborated by the authors

General and optimization parameters

Table 8 summarizes the key parameters, control variable limits, and objective functions that define the optimization framework and simulation scenario.

Table 8.

Summary of general and optimization parameters.

Category	Parameter (description)	Symbol (unity)	Value	Used in Eq(s).
General simulation parameters
	Simulation horizon	(min)	525,600	(3), (35), (36)
	Time step	(min)	1	(3), (15), (26), (35), (36)
	Load Shedding Scenarios	(%)	0 to 10	(37)
Cost model parameters
	O&M Cost (% of each installation cost)	(%)	10	(46)
	Project lifetime	(years)	25	(46), (47)
	Annual O&M interest rate	(%)	5	(46)
	Annual replacement interest rate		5	(47)
	PV panels lifetime	(years)	20	(47)
	Wind turbines lifetime	(years)	20	(47)
	Tidal turbines lifetime	(years)	20	(47)
	GH2 system lifetime	(years)	15	(47)
Control variables (Limits)
	Limits for PV panels		[1, 400]	(6)
	Limits for wind turbines		[1, 40]	(7)
	Limits for tidal turbines		[1, 40]	(8)
	Limits for BESS capacity	(kWh)	[288, 576]	(23)
	Limits for GH2 capacity	(kWh)	[0, 7500]	(34)
Objective functions (Optimization Outputs)
	Total system cost	($)	To be minimized	(1), (2)
	Total spilled energy	(kWh)	To be minimized	(1), (3)

Results

The case study was conducted using the configuration of the isolated microgrid shown in Fig. 1, with real data obtained from on-site measurements in the São Marcos Bay region. Sizing studies were carried out considering: i) meeting the load 24 hours a day throughout the year; ii) sensitivity analysis assuming increasing load shedding from 0 to 10%; and iii) the impact of source intermittency characteristics on the sizing process.

Case 1: Operation of a zero-carbon microgrid with three renewable sources to meet 100% of load demand

The zero-carbon microgrid consists of three distinct renewable energy sources: wind, tidal, and photovoltaic energy. It is designed to meet 100% of the energy demand. To support this, a hybrid energy storage system combines battery energy storage systems (BESS) and green hydrogen (GH2). The maximum storage capacity of the BESS is set at 576 kWh, which is approximately eight times the maximum peak load demand.

Figure 16 illustrates the Pareto Front for two objective functions: minimizing total cost and minimizing spilled energy. A total of thirty-five solutions were identified, each representing a trade-off between these functions. As illustrated in Fig. 16, the solution called Solution 1 offers the lowest total cost but results in the highest spilled energy, while the solution called Solution 35 presents the highest total cost but with the lowest spilled energy. The Pareto Front shows an inversely proportional relationship between the two objective functions: as solutions are adopted to minimize spilled energy, the total cost tends to increase. In contrast, a higher spilled energy implies a lower total cost. These results suggest that the objective functions are not aligned and are in conflict with one another.

Fig. 16.

Pareto Frontier for Case 1. Source: Elaborated by the authors.

Details of the Pareto Front results shown in Fig. 16 are presented in Fig. 17. The control variables listed in Table ?? and the constraints in Table 7 were considered. For each solution, the following parameters are detailed: installed generation capacity (kW), reflecting the composition of renewable sources; installed storage capacity (kWh), representing the composition of energy storage systems; total cost (US$); and finally, spilled energy (kWh).

Fig. 17.

Result compositions for Case 1. Source: Elaborated by the authors.

The Pareto Front solutions presented in Fig. 17 show that the lower the spilled energy, the higher the total cost, influenced by increased installed storage capacity. It is also observed that as storage capacity grows, installed generation capacity tends to decrease.

In Fig. 14, the daily wind energy generation throughout the year is displayed, highlighting lower generation between March and June and generation peaks between August and September. Due to this variation, wind power plant must be oversized to meet load demand during periods of low generation, which consequently leads to a significant increase in spilled energy during months of higher wind generation. On the other hand, tidal generation exhibits lower variability and is more predictable, contributing as a more stable energy source.

Among the solutions presented in the Pareto Front (Fig. 16), the extremes are solution 35 (higher cost with lower spilled energy) and solution 1 (lower cost with higher spilled energy). The latter is less expensive because, although it involves installing larger generation units with smaller storage capacity, the cost of storage is significantly higher and dominates the objective function. This most economical case is described in detail below.

Table 9 presents a summary of the sizing of Solution 1. This solution prioritizes the lowest total cost and presents a more modest storage system sizing. In this case, the installed generation capacity is 331.65 kW, and the storage capacity is 1476 kWh.

Table 9.

Sizing Summary for Case 1 - Solution 1.

Description	Sizing	Installed capacity
FV	153 units	84.15 kW
Wind	21 units	157.5 kW
Tidal	18 units	90 kW
BESS	576 kWh	576 kWh
GH2	900 kWh	900 kWh

Source: Elaborated by the authors

Figures 18 and 19 show the monthly and daily energy balances, respectively. The amount of spilled energy, primarily from PV and tidal sources, is particularly significant from September to December. One reason for this increase in spilled energy is the limited investment in storage solutions, which results in insufficient capacity to store all the available energy generated. There are notable monthly fluctuations in energy generation, with wind energy being the dominant source.

Fig. 18.

Monthly energy balance for Case 1 - Solution 1. Source: Elaborated by the authors.

Fig. 19.

Daily energy balance for Case 1 - Solution 1. Source: Elaborated by the authors.

The figures indicate that energy demand remains relatively constant throughout the year; however, the limited storage capacity means some available energy goes unused. This insufficient storage results in a greater reliance on current energy sources and contributes to increased energy spillage during periods of high generation.

Figures 20 and 21 show the monthly and daily composition of the spilled energy, respectively. Spilled energy is significant year-round, especially from June onward, with wind power contributing the most. The limited storage system prevents the microgrid from utilizing all available energy, particularly during increased wind and solar availability.

Fig. 20.

Monthly composition of spilled energy for Case 1 - Solution 1. Source: Elaborated by the authors.

Fig. 21.

Daily composition of spilled energy for Case 1 - Solution 1. Source: Elaborated by the authors.

Figure 22 shows the variation of the SOC of BESS and GH2 over the evaluated period. The SOC of the BESS varies more frequently, indicating that this storage system is used extensively to balance demand. In contrast, the SOC of the GH2 remains more stable, suggesting that hydrogen serves primarily as a long-term reserve, with a smaller capacity of 900 kWh.

Fig. 22.

SOC BESS and SOC GH2 for Case 1 - Solution 1. Source: Elaborated by the authors.

Table 10 presents the energy summary of Solution 1 (lower cost) compared to Solution 35 (lower spilled energy). The total renewable generation reached , with wind contributing , tidal , and PV . The total spilled energy amounted to , equivalent to of the load demand. Wind energy accounted for of this spilled energy, highlighting the lack of storage capacity. Notably, the spilled energy nearly equaled the total load demand.

Table 10.

Energy summary for Case 1 - Solution 1 and 35.

Description	Solution 35 (less spilled energy)	Solution 01 (less costly)
Supplied energy (MWh)
PV	126.08	36.79
Wind	20.09	203.78
Tidal	249.45	132.85
Total	395.63	373.43
Energy consumption (MWh)
Load	365.72	365.72
Renewable sources details
Spilled energy (MWh)
PV	15.70	74.44
Wind	1.03	239.75
Tidal	4.35	1.51
Total	21.08	315.72
Additional Details
Total cost (USD)	5,457,221.29	3,485,795.30

Source: Elaborated by the authors

These two extreme Pareto solutions are particularly illustrative, as they emphasize the considerable impact of storage investments relative to the cost of generation equipment. The less efficient solution, characterized by a high level of spilled energy, proves more economically feasible for ensuring continuous load supply. Conversely, minimizing spilled energy through greater storage investments increases the total cost from $2.4 million to $5.4 million. Encouragingly, the cost per MWh of storage is decreasing, which could significantly change this scenario³⁸.

Figure 23 shows the composition of the total cost for this solution. Note that renewable sources represent the largest part of the total cost, corresponding to 77% of the total value. GH2 and BESS are evaluated with 13% and 10%, respectively. Since the strategy in this solution aims to minimize total cost, there is a lower investment in storage. However, this reduction in storage investment leads to increased spilled energy.

Fig. 23.

Composition of the total cost for Case 1 - Solution 1. Source: Elaborated by the authors.

Case 2: Microgrid operation considering load shedding scenarios

In this section, the authors conduct a sensitivity analysis of the microgrid operation, examining the implications of not fully meeting demand and its effect on total costs. A gradual reduction, ranging from 0% to 10% of the annual load, was applied to evaluate the behavior of the microgrid and its components, as well as the impact on the investment cost.

Figure 24 presents the Pareto Front for different levels of load shedding: 0%, 2.5%, 5%, 7.5%, and 10%, and shows the relationship between the total cost and the spilled energy for each allowed load shedding scenario. Allowing for a more significant load shedding reduces total costs, though this reduction is not linear. In scenarios with 0% load shedding, the total cost is higher due to the need for robust infrastructure sizing. As the acceptance of load shedding increases, the solutions shift to more economical configurations, resulting in a reduction in spilled energy; however, this relationship presents a saturation point, where the gains in cost reduction become less pronounced.

Fig. 24.

Pareto Front for the Case 2. Source: Elaborated by the authors.

Figure 25 compares the different configurations of installed generation and storage capacities for the microgrid, considering various load shedding percentages: 0%, 2.5%, 5%, 7.5%, and 10%. The figure illustrates how the composition of generation and storage capacity changes along the Pareto Front solutions based on different levels of load shedding.

Fig. 25.

Generation and storage capacities under different load shedding levels for Case 2. Source: Elaborated by the authors.

As load shedding is allowed, the sizing of generation and storage sources is progressively reduced, especially for load losses of 2.5% to 5%. However, the reduction in installed capacity is much less pronounced for higher levels of loss, such as 7.5% and 10%. Similarly, Figure 26 compares total cost and spilled energy along the Pareto Front solutions for different load shedding levels: 0%, 2.5%, 5%, 7.5%, and 10%.

Fig. 26.

Total cost and spilled energy under different load shedding levels for Case 2. Source: Elaborated by the authors.

Table 11 presents the energy summary for Case 2, considering load shedding of 2.5% and 10%. It is important to note that allowing load shedding of 2.5% and 10% results in total costs that correspond to 46% and 35%, respectively, of the total cost of Solution 35 in the Table 10 (0% load shedding and lower energy spill). If 10% of the load is allowed to be cut, the investment decreases to nearly one-third of the initial value.

Table 11.

Energy summary for Case 2 - 2.5% and 10% of load shedding.

Loss load	2.5%	10%
Supplied energy (MWh)
PV	38.20	24.99
Wind	182.48	292.71
Tidal	14.01	14.93
Total Renewable Generation	360.79	332.64
Energy consumption (MWh)
Base load	365.72	365.72
Load Shedding	9.14	36.57
Total	356.59	329.16
Spilled energy (MWh)
PV	63.38	21.53
Wind	203.91	214.19
Tidal	2.54	0.00
Total	269.83	235.72
Costs
Total cost (USD)	2,497,898.37	1,906,821.42
Cost reduction	46%	35%

Source: Elaborated by the authors

From now on, without loss of generality, only the scenario with 10% load shedding is illustrated in more detail. Table 12 summarizes the sizing for this case, with installed generation and storage capacities of 225.2 kW and 576 kWh, respectively. The wind source dominates, with 180 kW, while the photovoltaic (PV) and tidal sources contribute 35.2 kW and 10 kW, respectively. High variability in wind sources contributes to energy losses. In this case, the tolerance for a 10% load shedding was sufficient not to implement GH2 storage.

Table 12.

Sizing Summary for the Case 2 (10% Load Shedding).

Description	Sizinhg	Installed capacity
PV modules	64 units	35.2 kW
Wind turbines	24 units	180 kW
Tidal turbines	2 units	10 kW
BESS Capacity	576 kWh	576 kWh
GH2 Capacity	0 kWh	0 kWh

Source: Elaborated by the authors

Figures 27 and 28 show the monthly and daily energy balance, respectively. Wind energy is predominant throughout the year. Load shedding is more evident between January and July, with peaks in April coinciding with the lowest wind energy generation. Between August and December, load shedding decreased due to the growth in wind energy generation.

Fig. 27.

Monthly energy balance for the case 2 (10% Load Shedding). Source: Elaborated by the authors.

Fig. 28.

Daily Energy Balance for the Case 2 (10% Load Shedding). Source: Elaborated by the authors.

Figures 29 and 30 illustrate the energy spilled on a monthly and daily scale, respectively. A greater amount of spilled energy is observed between August and December, which corresponds to the peak period of wind energy generation. The high volume of spilled energy is attributed to the variability of wind energy and the relatively small size of the storage capacity.

Fig. 29.

Monthly composition of spilled energy for Case 2 (10% Load Shedding). Source: Elaborated by the authors.

Fig. 30.

Daily composition of spilled energy for Case 2 (10% Load Shedding). Source: Elaborated by the authors.

The variation of the SOC (State of Charge) of the BESS throughout the operation of the microgrid is shown in Fig. 31. During the first months of the year, higher cycling is observed due to the increased variability of renewable generation. In the second half of the year, the SOC variability is less pronounced, remaining closer to its maximum value for longer periods.

Fig. 31.

SOC of BESS and GH2. Source: Elaborated by the authors.

Figure 32 presents the cost composition for this case. It is observed that 63% of the costs are attributed to the contribution of the wind source, while the other components have a smaller share in the cost composition.

Fig. 32.

Composition of total cost. Source: Elaborated by the authors.

Impact of renewable energy sources on microgrid sizing and operation

In this section, the authors analyze how the type of renewable energy source and its intermittent characteristics influence the sizing, operation, and efficiency of the system. Two scenarios were considered:

1. Operation with PV and Tidal Energy

2. Operation with PV and Wind Energy

In scenario (a), solar energy generation depends on daily solar radiation, while tidal energy offers a more predictable generation pattern.

In Figure 33, the Pareto Front distribution indicates that, for scenarios with 0% load loss, solutions require higher infrastructure investments to ensure total demand fulfillment, resulting in lower levels of energy spillage. As a higher load loss is allowed, the reduction in total costs becomes more pronounced at initial levels (e.g., from 0 to 2.5% and 5%). This reduction reflects the decreased requirements for generation and storage capacity, enabling the microgrid to operate with less robustness. However, when allowed load loss exceeds 5%, economic gains diminish compared to the increase in energy spillage, highlighting a saturation point in terms of cost-benefit trade-offs.

Fig. 33.

Pareto Frontier for PV and tidal energy sources. Source: Elaborated by the authors.

Figure 34 illustrates that the installed generation and storage capacity tend to decrease as the load loss increases. In scenarios with 0% load loss, the installed capacity of photovoltaic and tidal energy sources is maximized to meet all demand, requiring robust generation systems and storage capacities. As flexibility in demand increases (up to a 10% load loss), a gradual decrease in installed capacity is observed, reflecting an optimization strategy to reduce oversizing, particularly in storage systems such as Battery Energy Storage Systems (BESS) and Green Hydrogen (GH2). This reduction is most evident at intermediate levels of load loss, resulting in lower total costs and reduced capacity sizing requirements.

Fig. 34.

Comparison of load loss for PV and tidal energy sources - Generation and Storage Capacity. Source: Elaborated by the authors.

The case (b) considers only PV (Photovoltaic) and Wind Energy, both characterized by high variability. Figure 35 shows the Pareto Front for different levels of load shedding, similar to the previous case.

Fig. 35.

Pareto Front for PV and Wind Energy Sources. Source: Elaborated by the authors.

Figure 36 highlights the comparison of installed generation and storage capacity for different levels of load shedding.

Fig. 36.

Comparison of Load Shedding for PV and Wind Energy Sources - Generation and Storage Capacity. Source: Elaborated by the authors.

In Case (a), which combines PV and Tidal Energy, the stability of generation is more pronounced due to the higher predictability of tidal generation. This feature results in a lower storage capacity requirement compared to the other scenarios. The solutions found tend to have lower total costs and less energy spillage, as tidal generation acts as a stabilizing factor, offsetting the variability of PV generation.

On the other hand, Case (b), which combines only PV and Wind Energy, is characterized by the high variability and intermittency of both sources. This configuration has implications for storage requirements and their lifespan³¹. The result is greater energy spillage and higher total costs in many cases, reflecting the challenges of maintaining stability and efficiency with more intensely intermittent sources.

Discussion of results

The simulations were conducted to minimize total cost and spilled energy, as illustrated by the presented Pareto Fronts. Solutions that offer higher energy efficiency tend to require higher initial investments, while more cost-effective solutions lead to higher levels of spilled energy. Therefore, the choice of objective functions directly influences the sizing of generation and storage sources, consequently affecting the microgrid’s behavior under different operational scenarios.

A key finding of this work is that, over the course of a year, the critical periods of renewable source insufficiency are few and relatively short. This fact becomes evident when a load shedding simulation is performed, for instance, with a 2.5% reduction. This results in a significant reduction in the required sizing of the generation plant. For higher load reductions (between 5 and 10%), the investment reduction is not as significant.

This scenario is beneficial, as with minimal effort - and negotiating through an interruption agreement - it is possible to enable not a zero-carbon microgrid, but rather a low-carbon microgrid. The composition of generation sources (photovoltaic, wind, and tidal) and storage systems (BESS and GH2) has a direct impact on system performance. In Case 2, which considers operation with only two renewable sources, greater variability was observed, highlighting the need for increased storage capacity to ensure regularity in supply, particularly in the short term.

A key finding of this work is the non-linear relationship between reliability and total system cost, exemplified by the 46% cost reduction when the Loss of Power Supply Probability (LPSP) is relaxed from 0 to 2.5%. This result reveals a fundamental principle of this type of microgrid: the prohibitive cost of achieving 100% reliability in load supply. To make this perfect reliability scenario possible, heavy investments in energy assets are necessary, even if they are rarely used at their nominal capacity. By allowing for some flexibility in reliability (e.g., an LPSP of 2.5%), the microgrid is released from the obligation to meet even the rarest mismatch between generation and load. This permits a drastic reduction in the sizing of energy assets and can even lead to the complete elimination of some components, as illustrated in the 10% LPSP case (Table 12), which enables the removal of the GH2 system. These findings support the need to adopt demand-side management strategies and contracts that tolerate controlled load curtailment. Such strategies should not be seen as complementary tools but as enabling mechanisms for the economic viability of zero-carbon microgrids.

Conclusion

The operation of isolated microgrids powered 100% by renewable sources faces significant technical and economic challenges, mainly due to the temporal variability between generation and load over time. This imbalance directly influences system sizing, affecting storage needs and generator capacities. Furthermore, a zero-carbon microgrid can be considered the cornerstone of the energy transition.

In this paper, the problem of sizing an isolated 100% renewable microgrid was formulated, considering only clean energy sources to meet the load demand. This approach enables a detailed analysis of the technical and economic implications associated with the design and operation of sustainable microgrids. The following observations and conclusions can be highlighted from this investigation.

• The use of storage technologies, including seasonal storage alternatives, such as hydrogen storage systems, is essential to ensure the reliability of energy supply in zero-carbon microgrids. These systems help mitigate the intermittency of renewable sources, ensuring the ability to meet demand even during periods of low production or high variability.

• It is concluded that a renewable source with a less intermittent profile, in this case, tidal energy, can reduce storage dependence, helping to smooth generation variability. This choice has a positive impact on the sizing of generator units and the storage system. When comparing the PV-Wind and PV-Tidal configurations to supply 100% of the load with minimal spilled energy, the excess energy amounts to 4.9 kWh and 0.8 kWh, respectively, with investment costs of USD 5.3 million and USD 4.9 million. Clearly, the PV-Tidal configuration significantly reduces spilled energy while requiring a lower investment cost.

• The least-cost configuration with three renewable sources supplies 100% of demand but generates excess energy equivalent to 86.33% of the load, predominantly from wind (75.91%), due to limited storage use. Curtailing this surplus requires storage expansion, which raises total costs from USD 2.4 million to USD 5.4 million. A key finding is that if a small load curtailment of 2.5% is accepted, the cost decreases to 46% of this value - practically matching the minimum cost - while eliminating all spilled energy. This result underscores the role of demand reduction or interruption agreements as a viable mechanism to enhance the feasibility of low-carbon energy systems.

• The studied structure for the zero-carbon microgrid in islanded operation can be expanded for application in larger networks, contributing to large-scale energy transition. This expansion may involve the interconnection of multiple microgrids, enabling greater flexibility, resource sharing, improved load demand management, and cost reductions at the regional level.

• Green hydrogen has excellent potential as seasonal and long-term storage, complementing short-term storage with lithium-ion batteries and similar technologies. The results showed that green hydrogen is a viable solution to compensate for the seasonal variability of renewable sources.

• The integration of different renewable sources, such as solar, wind, and tidal energy, was found to contribute to the microgrid with a reasonable degree of complementarity. The use of short-term storage systems (BESS) and long-term storage (GH2) is effective in balancing the different variability scales of sources, reducing spillage. However, combining more intermittent sources, such as solar and wind, may require greater investment in storage, especially short-term storage.

• Although spilled energy is a clear waste, in practice, it can be minimized but is hardly eliminated.

Although the current costs associated with operating zero-carbon microgrids, especially those with storage systems, may be high, they tend to decrease with technological advancements, larger production scales, and economic incentives. The results indicate that technological evolution and incentive policies can make costs more competitive, which favors greater adoption of microgrids. The study was conducted on a small-scale microgrid; however, the analyses and conclusions remain valid for systems of any scale. This claim is grounded in the well-established scientific practice of employing minimal and scale models to capture the essential dynamics of complex phenomena³⁹.

Author contributions

W.M., O.R., P.B. and D.Q. wrote the manuscript text; W.M. prepared the simulation tools and the figures; W.M., O.R., P.B. and D.Q. developed the conceptualization and the problem formulation. All authors reviewed the manuscript.

Funding

This publication has been funded by CAPES under the PDPG Amazonia Legal Project (Grant 88881.510240/2020-01). INEOF has financial support from CNPq and FAPEMA. Partial support for author O. Saavedra was provided by FAPESP under project number 2021/11380-5.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval and consent to participate

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The authors agree with the paper publication, when/if accepted, respecting all publishing policies from Springer.