Advances in the Design of Renewable Energy Power Supply for Rural Health Clinics, Case Studies, and Future Directions

Abstract

Globally, effective and efficient healthcare is critical to the wellbeing and standard of living of any society. Unfortunately, several distant communities far from the national grid do not have access to reliable power supply, owing to economic, environmental, and technical challenges. Furthermore, unreliable, unavailable, and uneconomical power supply to these communities contributes significantly to the delivery of substandard or absence of qualitative healthcare services, resulting in higher mortality rates and associated difficulty in attracting qualified healthcare workers to the affected communities. Given these circumstances, this paper aims to conduct a comprehensive review of the status of renewable energy available to rural healthcare clinics around the globe, emphasizing its potential, analysis, procedures, modeling techniques, and case studies. In this light, several renewable energy modeling techniques were reviewed to examine the optimum power supply to the referenced healthcare centers in remote communities. To this end, analytical techniques and standard indices for reliable power supply to the isolated healthcare centers are suggested. Specifically, different battery storage systems that are suitable for rural healthcare systems are examined, and the most economical and realistic procedure for the maintenance of microgrid power systems for sustainable healthcare delivery is defined. Finally, this paper will serve as a valuable resource for policymakers, researchers, and experts in rural power supply to remote healthcare centers globally.

1. Introduction

Healthcare centers need readily available, reliable, sustainable, and accessible power supplies for effective operation. Unfortunately, in Africa and some other parts of the world, the majority of the people living in rural areas do not have access to basic amenities, including a reliable power supply. Moreover, the people living in such communities are classified as poor due to the high poverty index, poor infrastructure, and difficulty in accessing the remote terrain. In addition, another constraint for such people and communities is the lack of access to finances for businesses and markets. Furthermore, due to their locations and characteristics, an extension of power transmission lines to those remote places is usually very expensive and technically impossible in some cases. This unavailable power supply makes it difficult to have adequate healthcare centers available in those places. Unfortunately, those communities with available health facilities depend on fossil fuels, and their supply is becoming more difficult as a result of many regulatory and government policies [1]. In addition, power generation using fossil fuel resources is not clean and poses huge health issues [2,3,4].

Similarly, the world population is increasing, and hence the need for more penetration of healthcare facilities has globally increased. This increase in population will translate into a need for more energy. By extension, there are more healthcare clinics in rural areas, where a greater percentage of the world population resides. Unfortunately, recent predictions by the International Energy Agency (IAE) have shown that energy demand will increase threefold by 2050. These predictions by the IAE have catalyzed energy markets in many parts of the world [5,6,7]. Furthermore, one of the approaches to resolving the global energy need is to use renewable energy sources that are inexhaustible, available, and reliable compared to their fossil counterparts. Hence, there is a need to double the global installed energy capacity. This could help developing countries meet their healthcare energy demand, especially for rural health facilities. Due to this need, many countries across the globe have many targets for increasing the share of renewable energy.

It is clear that during and after the COVID-19 pandemic, the concept of healthcare access based on face-to-face contact between healthcare practitioners and patients is becoming absolute [8]. Furthermore, the world is focusing on the development of other alternative healthcare solutions for rural and underserved populations in the form of e-health, telemedicine, and virtual and mobile clinics to deliver healthcare. These systems have many advantages, such as better healthcare delivery, improvements in quality of service, effective and timely diagnosis, remote patient monitoring, remote assessments of medical conditions, two-way communication between patients, decreased patient appointment time, and healthcare providers, to mention just a few [9,10]. These services are possible with the help of the internet and available modern communication networks. These could resolve the problem of the unavailability of health care services for reasonable populations in both developing and underdeveloped nations. One of the solutions to some of the power shortages in healthcare facilities in remote places is the use of microgrids. Microgrid can be DC, AC, or a combination of both (hybrid mode), depending on the application. It can be single- or three-phase and sometimes be connected to low- or medium-voltage distribution networks [11]. In some cases, it can be operated in standalone mode. In each case, the system requirements differ in control, stability, reliability analysis approaches, etc. Microgrids are usually designed on a small scale with either solar, wind, or a combination of two or more sources.

Many research papers have designed microgrids for healthcare delivery in remote places. However, these papers did not establish an extensive overview and review, taxonomy, and technical design considerations for economical, technical, and reliable power supply to healthcare hospitals in developing countries. Furthermore, the existing reviews were not comprehensive and realistic ways of analyzing the renewable energy potential of the site under consideration. In addition, for the economical and realistic reliability of the power supply of healthcare systems, reliability analysis of each design is of critical importance. Unfortunately, the existing papers ignored this critical factor in the success of reliable power supply to healthcare systems in rural communities. Additionally, this paper proposes indices for the reliability study of renewable energy microgrids to ensure a reliable power supply. These factors, when considered in the design of future energy power supply to health facilities, will guide future research and stakeholders in remote health care service delivery globally. Given these, this paper’s key contributions include the following:

• A comprehensive overview and taxonomy of renewable energy microgrids.
• Detailed procedure on the feasibility analyses of renewable energy resources for electrical power generation.
• Extensive review and taxonomy on the design of electrical power for health care systems.
• A proposed system procedure for reliability studies of renewable energy microgrids suitable for health care services.

The rest of the paper consists of the following sections: Renewable energy resources available for health care applications are defined in Section 2. Section 3 is on battery storage for healthcare applications. A microgrid design procedure is presented in Section 4. Optimization approaches for sizing microgrid systems for healthcare clinics are presented in Section 5. The procedure for assessing the reliability of power supply for rural healthcare clinics is provided in Section 6. Section 7 is on the taxonomy of global health care systems. Modeling environment requirements suitable for healthcare microgrid systems are provided in Section 8. Future directions and lessons learned are presented in Section 9, and the conclusion to the paper is presented in Section 10.

2. Renewable Sources and Availability for Rural Healthcare

It is clear that once the system demand is known for the rural health care system, the next step is to determine the availability of renewable energy resources in the area under consideration. Rural healthcare systems located in developing and developed nations are connected to the national grid. On the other hand, standalone microgrids consisting of solar, wind, and small hydro for the supply of electricity to rural health facilities are usually found in the global south [11]. In this part of the world, the rural health care clinics are located where there is no national grid, too far from the grid, and the extension of the national grid could be economically or technically impossible. Therefore, a standalone microgrid is the best option for rural electricity supply. However, in some cases, even those clinics connected to the grid experienced acute shortages of electricity due to unavailable, unreliable electricity. Other reasons for non-availability could be conflicts and natural disasters, to mention just a few. Hence, the standalone/grid-connected microgrid could help rural health facilities function optimally, efficiently, and economically. Eventually, standalone power systems have the potential to run the healthcare systems during the peak period of electricity demand, in some cases when the national grid is not available or unable to satisfy the system’s electricity demand.

In addition, globally, it has been established that countries on the African continent are blessed with renewable energy resources. Therefore, when these potentials are used optimally, there is a high probability that the energy requirements of health clinics in rural areas of these countries can be met. This could assist in solving the energy needed to supply the heat facilities in these countries, thereby increasing accessibility to healthcare and meeting some of the sustainable development goals of 2030. The renewable energy available in abundance in this part of the world includes sunlight [12,13], biomass [14], water [15,16], and wind [17]. Unfortunately, due to some reasons, this part of the world could harness these resources optimally. Given this, the authors in [11] outline some of the issues to be used in comparing these sources of energy for the electricity supply of rural health care clinics, as outlined in Table 1.

Table 1. Renewable options for rural healthcare in the global south.

S/No	Index	Solar	Wind	Water
1	Safety	Y	Y	Y
2	Effectiveness	Y	Y	Y
3	Durability	Y	Y	Y
4	Resilience	Y	Y	Y
5	Accessibility	Y	Y	P
6	Adaptability	Y	Y	Y
7	Marketability	Y	P	P
8	Affordability	N	P	P
9	Sustainability	P	P	Y
10	Environmental Ability	Y	Y	Y
11	Recycling Ability	P	P	P

Legend: Y = yes; N = no; P = partial; and NA = not available.

2.1. Solar Energy Availability

Due to the availability of solar energy globally, it can be called a promising technology for rural healthcare, especially in countries with an abundance of solar energy. Technology can be divided into two categories. The two categories are those that convert sunlight into thermal energy and electricity directly in the form of direct current (DC). Both options are excellent opportunities for rural healthcare systems because the thermal systems of the healthcare clinics can be satisfied directly. On the other hand, the electricity requirement can be fed directly from the second option. This source of power is an excellent option for satisfying rural healthcare facilities, especially in the global south. In the African and Middle Continents, PV systems have been the best option for rural healthcare systems. Due to its inherent advantages on the continent. Furthermore, due to the high initial cost, rural health centers are still finding it difficult to install on many African continents. In the same way, oil-producing nations still supply rural healthcare facilities with fuel-based power systems. However, some countries have tried to use solar energy for their power supply. It is sad to note that some countries have higher solar energy potential than the solar energy giants of the world. A typical example is a World Bank report that has shown that Zambia has average horizontal solar irradiances between 5.5 Wh/m²/day and 6.3 Wh/m²/day compared to Germany (2.7–3.3 kWh/m²/day). Tanzania’s solar resources are between 4.5 Wh/m²/day and 6.21 Wh/m²/day. Rwanda experienced an average of 4.5 Wh/m²/day; in the same way, Haiti has a GHI of 5 to 8 Wh/m²/day. The availability of these resources is a clear indication that the rural healthcare facilities of global south countries can be satisfied if the solar energy resources of these countries are used optimally [18,19].

In addition, solar irradiance is the power per unit area received from the sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Irradiance may be measured in space or at the Earth’s surface after atmospheric absorption and scattering. It is measured perpendicular to the incoming sunlight. This solar irradiance hits the surface of the earth in two forms, i.e., beam (Gb) and diffuse (Gd). The beam component comes directly as irradiance from the sun, while the diffuse component reaches the earth indirectly and is scattered or reflected from the atmosphere or cloud cover. The total irradiance on a surface is as follows:

G = Gb + Gd (beam and diffuse)

(1)

• For the Dual Axis:

Practical data on solar irradiance for a dual-axis sun tracker were collected. The data contain the solar irradiance value of a particular place from sunset to sunrise, which hourly averaged, and is denoted by I₀. Incidental solar radiation is determined by the method of finding the slope from this hour-by-hour average data.

• For the Single Axis:

The solar irradiance value for a single-axis sun tracker is denoted by the following:

Solar Irradiance (I₁) = cos (δ) ∗ I₀

(2)

where δ = declination angle.

• For the Fixed Panel:

The solar irradiance value for a fixed panel is denoted by I₂. The equation for calculating solar irradiance for a fixed panel is as follows:

Solar Irradiance (I₂) = I₀ ∗ cos (δ) ∗ sin (θ)

(3)

where θ = hour angle and δ = declination angle.

A mathematical model of the output power of the photovoltaic system (PV) is presented in this section. Many models are presented in the literature, depending on the available parameters. A model that uses many input variables is used in the analysis, such as temperature, number of series, and parallel connected cells. In the same manner, standard test conditions, light intensity, and the ambient temperature are assumed. The short-circuit current of the PV module is defined as follows:

$$I_{sc}\left(t\right)=I_{sco}\left(\frac{E_e\left(t\right)}{E_o}\right)[1+\alpha I_{sc}\left(T_c\left(t\right)-T_o\right)]$$

(4)

Maximum-point current, open-circuit voltage, and maximum-point voltage are defined in (5)–(7).

$$V_{oc}\left(t\right)=V_{oc}{+N_s\delta T_c\left(t\right)\mathrm{l}\mathrm{n}(E}_e\left(t\right))+{\beta }_{Voco}{E}_e(t)\left(T_c\left(t\right)-T_o\right)$$

(5)

$$I_{mp}\left(t\right)=I_{mpo}(C_o{E}_e\left(t\right)+C_1{E}_e{\left(t\right)}^2)(1+\alpha I_{mp})\left(T_c\left(t\right)-T_o\right)$$

(6)

$$V_{mp}(t)=V_{mp}{+{C_{2}N}_s\delta T_c\left(t\right)\mathrm{l}\mathrm{n}(E}_e(t))+{{C_{3}N}_s\delta T_c\left(t\right)\mathrm{l}\mathrm{n}E}_e{\left(t\right)}^2+{\beta }_{Vmpo}{E}_e(t)\left(T_c\left(t\right)-T_o\right)$$

(7)

where

• $PSEC$: PV output power;
• $G_{STC}$: solar radiation at standard test conditions;
• $G_c:$ solar radiation from the operating point;
• $P_{STC}$: output power under standard test conditions;
• $T_c\left(t\right)$: PV cell temperature;
• $T_a\left(t\right)$: ambient temperature;
• $T_o$: reference temperature of the model;
• $NCOT$: nominal cell operating temperature;
• $k$: Boltzmann’s constant;
• $n$: empirically determined diode factor for each cell;
• $\alpha I_{sc}$: normalized temperature for $I_{sc}$;
• ${\beta }_{Vmpo}$: temperature coefficient for $V_{mp}$;
• ${\beta }_{Voco}$: temperature coefficient for $V_{oc}$;
• $C_0{C}_1$: empirically determined coefficient relating $I_{mp}$;
• $C_2{C}_3$: empirically determined coefficient relating $V_{mp}$.

Equation (8) defines effective isolation as follows:

$$E_e\left(t\right)=\frac{I_{sc}\left(t\right)}{I_{sco}(1+\alpha I_{sc}\left(T_c\left(t\right)-T_o\right))}$$

(8)

The thermal voltage per cell ($\delta T_c\left(t\right))$ is given by the following expression:

$$T_c\left(t\right)=\frac{nk(T_c\left(t\right)+275.15)}{q}$$

(9)

Also, the temperature inside each cell ($T_c\left(t\right))$ is also defined as follows:

$$T_c\left(t\right)=T_a\left(t\right)+\frac{NCOT-20}{800} E(t)$$

(10)

The output power of the solar energy conversion system is obtained in Equation (11).

$$Pout \left(t\right)=I_{mp}\left(t\right)\times V_{mp}\left(t\right)\times N_{PV}$$

(11)

Cumulative energy over a given period can be determined using the expression defined as follows:

$$\mathrm{Cumulative} \mathrm{Energy}={\int }_{tstart}^{tend}Pout$$

(12)

2.2. Wind Resource Availability

The process of converting electricity from wind speed is performed with the help of a wind turbine. Electricity from the wind energy conversion system is dependent on the geography of the study area and resource availability [20]. Furthermore, the wind turbines used for this conversion are categorized according to their power ratings. Normally, for small communities, homes, and loads such as healthcare, wind turbines of rated power between 1 kW and 100 kW are used. On the other hand, higher-capacity wind turbines can be employed for both grid-connected and standalone microgrids. In the case of rural healthcare facilities, usually smaller wind turbines are used. Other issues surrounding applications of higher-rated power wind turbines are environmental concerns. Some countries with lower wind speeds cannot use wind energy conversion systems for electrical power production. Therefore, it is recommended that countries with wind speeds between 5 and 7 m/s at 50 m height are suitable candidates for standalone electricity generation, including health centers, as shown in Figure 1.

Figure 1. Wind speed and wind power potentials.

The power output of a wind energy-generating system is a function of the three wind speeds, resulting in different design alternatives. The wind speeds include the cut-in speed ($V_{ci}),$the cut-out speed $(V_{co}$) and the rate speed of the wind turbine ($V$). The wind speed and output power are linearly approximated in the range $V_{ci}<V<V_v$ as shown in Figure 2.

Figure 2. Linearized curve of a wind turbine.

After the random distribution is obtained, the power output of the wind energy conversion system is expressed as a function of wind speed.

$$P\left(v\right)=\propto .P_r$$

(13)

$$\propto =\left\{\begin{array}{cc}\frac{V_i-V_{ci}}{V_r-V_{ci}}& V_{ci}<V<V_r\\ 1.0& V_r\le V<V_{co}\\ 0& V\le V_{ci} or V\ge V_{co}\end{array}\right.$$

(14)

${\propto }_{i,k}$ is a constant. The output power can be determined as a piecewise linear relationship of the rated capacity. Therefore, the rated capacity of the wind energy conversion system can be used as a decision variable. Finally, the model decides on the capacity for each design.

3. Battery Storage Systems for Healthcare Power Systems

Battery storage systems perform many functions in power systems. Some of the functions include storing excess energy when the output power from renewable energy sources is greater than the clinical demand. Another application is peak shaving, which also provides energy during outages for grid-connected and standalone microgrids. Therefore, battery storage systems can be used to increase power system reliability, especially for grid-connected microgrids. The battery storage options used for healthcare applications are highlighted briefly in Table 2. The attributes of these battery storage systems are shown in the same table. Some of them are mature for storing electrical energy, while others are still under experimentation and therefore not suitable for commercialization. The major batteries used for healthcare systems in the global south are lithium, lead-acid, nickel, and sodium battery storage systems. However, to achieve the system requirements of higher power and energy densities, it is clear that a compromise has to be reached to meet rural healthcare clinics’ requirements of high reliability and availability [20].

Table 2. Battery storage options for rural healthcare facilities.

S/No	Index	Sodium-Based Batteries	Lithium-Based Batteries	Flywheels	Nickel-Based Batteries
1	Effectiveness	Y	N	Y	Y
2	Performance	Y	Y	Y	Y
3	Durability and robustness	N	Y	Y	N
4	Resilience (local environment)	Y	Y	Y	Y
5	Safety	N	N	NA	Y
6	Operation
7	maintenance	Y	Y	N	N
8	Marketability		N	N	N
9	Affordability	N	N	N	N
10	Environmentally friendly/recycling	Y	N/P	Y	N

Legend: Y = yes; N = no; P = partial; and NA = not available.

4. Design of a Renewable Energy Microgrid for Health Centers

To design a microgrid for power generation in rural health systems, there are basic steps involved in the design. These include renewable energy potential analyses of the site, sizing of the system components, and analysis of the system demand. In this section, approaches used in the analysis are presented. In order to achieve site potential, analyses of the renewable energy resources and some of the probability distribution functions are normally used, as presented here. Eventually, the next step is the selection of the best among them that accurately represents the renewable energy potential of the site. This is normally achieved with the help of error analysis and some goodness-of-fit tests presented in this section. The second stage is the development of an optimization model for the microgrid under consideration. After the development of the model, various optimization functions are used for the determination of the component sizes, as presented in the section below. However, the majority of the design of the microgrid stops after optimization without due regard to the reliability analyses of the designed microgrid. This procedure is well-detailed in the section below. When all these are combined in the design of the healthcare microgrid, it is clear that the designed system will be optimal.

4.1. Energy Demand of Rural Health Care Clinics

According to the definition of rural health clinics by the United States Agency for International Development (USAID), rural health clinics can be defined as category A. According to the agency, category A is a health clinic for rural areas that is characterized by some limitations in staffing and limited medical services. Therefore, these types of health centers needed electricity for lighting and simpler medical surgical procedures, refrigerators for storing vaccines, and other medical essentials. This means that the basic electricity requirement is for powering the hematology mixer, centrifuge, and microscopes. The power rating of this class is usually between 5 and 10 kWh/day. Furthermore, category B’s power rating is between 10 and 20 kWh/day. Finally, category C usually has some more complicated power-consuming equipment that needs more power. In this regard, the power requirements of these rural health centers are usually between 20 and 30 kWh.

4.2. Probability Distributions

Renewable-energy resource assessment is usually carried out using probability distribution functions. Unfortunately, the commonly used models are Weibull, gamma, and Rayleigh distributions. Other probability distribution functions that can be used more for these analyses include lognormal, gamma, beta, and logistics distributions. More details on each of these distributions are explained in Section 4.2.1, Section 4.2.2, Section 4.2.3, Section 4.2.4, Section 4.2.5 and Section 4.2.6.

4.2.1. Weibull Distribution Function

Several works in the literature have confirmed that this model is the most widely used mathematical model. Presently, the Weibull distribution is one of the most widely used probability distributions in renewable energy analyses. Many papers have defined this distribution function, and the mathematical model can be expressed in Equations (15) and (16) [21].

$$f_w=\left(\frac{k}{c}\right){\left(\frac{v}{c}\right)}^{k-1}{e}^{{\left(-\frac{v}{c}\right)}^k}$$

(15)

Also, the cumulative distribution (DF) function is expressed as follows:

$$F_W=1-e^{{(-\frac{v}{c})}^k}$$

(16)

where $c$ = scale parameter and $k$ = shape parameter.

Due to the dependence of this distribution function on c and k parameters, it is well established that accurate modeling using this function is a function of these variables. Given this, there are many methods used to determine these parameters; one such method is the standard deviation method, as presented in Equations (3) and (4).

Once probability density functions are determined, the next stage is the determination of the c and k parameters. It is important to note that the accuracy of fitting Weibull functions to the renewable energy resource data is a function of the c and k parameters. These parameters can be obtained using many available techniques in the literature. One of the methods is called the method of moments [21]. If these parameters are to be determined using this method, Equations (17) and (18) can be used as follows:

$$k=({\frac{\sigma }{V_m})}^{-1.086}$$

(17)

$$c=\frac{V_m}{\mathsf{\Gamma }(1+\frac{1}{k})}$$

(18)

where $\sigma$ is the standard deviation and $V_m$ is the mean element of the sites.

The next step is the determination of the site power density as a function of the c and k parameters. Hence, the next step is the presentation of Weibull average power as a function of these parameters. In this case, power can be presented in Equation (19).

$${\mathrm{W}\mathrm{P}\mathrm{D}}_{\mathrm{w}}=\frac{1}{2}\times \rho \times c^3\mathsf{\Gamma }\left(1+\frac{3}{k}\right)$$

(19)

where $\mathsf{\Gamma }$ is called the gamma function.

The same presentation can be extended for the average site parameters as a function of the c and k parameters. This expression is shown in Equation (20).

$$V_m=c\mathsf{\Gamma }\left(1+\frac{1}{k}\right)$$

(20)

4.2.2. Rayleigh Distribution

Another model of interest to renewable energy system designers is called the Rayleigh distribution model, and the corresponding mathematical expression is shown in Equation (21) [22].

$$f\left(v\right)=\left(\frac{\pi V}{2V_m}\right)\times \mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{\pi }{4}\right)\times {\left(\frac{V}{V_m}\right)}^2$$

(21)

where m is called the average of the parameter.

In a similar way, the Rayleigh cumulative density function can be defined by the following expression:

$$F\left(v\right)=1-\mathrm{e}\mathrm{x}\mathrm{p}(-\frac{\pi }{4}{\left(\frac{V}{V_m}\right)}^2)$$

(22)

Equation (23) defines the variance of the Rayleigh distribution as follows:

$${\sigma }^2=\left(\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$\pi $}\right.-1\right)\times {V_m}^2$$

(23)

Therefore, the average power can be expressed through Equation (24).

$$\mathrm{W}\mathrm{D}\mathrm{P}=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$\pi $}\right.\times \rho \times {V_m}^3$$

(24)

Note that when k = 2, the Weibull distribution becomes the Raleigh distribution. In this regard, the mean of this model is as follows:

$$V_m=c\sqrt{\frac{\pi }{4}}$$

(25)

Also, it can be shown that the wind power density can be defined as follows:

$${\mathrm{W}\mathrm{P}\mathrm{D}}_R=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$\pi $}\right.\times \rho \times {\left(c\sqrt{\frac{\pi }{4}}\right)}^3$$

(26)

4.2.3. Gamma Distribution

In this model, shape α and scale β parameters are the elements that define the gamma density function as follows:

$$f\left(x;\alpha ,\beta \right)=\frac{x^{\alpha -1}}{{\beta }^{\alpha }\mathsf{\Gamma }\left(\alpha \right)}\exp \left[-\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$\beta $}\right.\right],x>0,\beta >0$$

(27)

The cumulative distribution function can be defined as follows:

$$F\left(x\right)=\frac{\mathsf{\Gamma }\left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$\beta $}\right.\right)\alpha }{\mathsf{\Gamma }\left(\mathsf{\alpha }\right)}$$

(28)

where $\mathsf{\Gamma }\left(x\right)$ = gamma function.

Using a similar transformation, the power can be shown as a function of the c and k parameters, as presented in Equation (29).

$${\mathrm{W}\mathrm{D}\mathrm{P}}_{Gam}=\frac{1}{2}\rho \times c^3\left[k\left(k+1\right)\left(k+2\right)\right]$$

(29)

4.2.4. Lognormal Probability Distribution

In the case of the lognormal distribution function, a random number is defined such that the logarithm is normally distributed with a mean and corresponding standard deviation, defined as $\mu$ and $\sigma$, respectively. The lognormal distribution can be applied once the natural log transformation results in a normal distribution. Mathematically, the corresponding density function of $X$ is defined in Equation (30) [22].

$$f\left(X,\sigma ,\mu \right)=\left\{\begin{array}{c}\frac{1}{\sigma \mathrm{x}\sqrt{2\pi }}EXP-\frac{1}{2{\sigma }^2}{\left[in\left(X\right)-\mu \right]}^2\\ 0, \mathrm{elsewhere}, X<0\end{array}\right.$$

(30)

where $\mu$ and $\sigma$ are the mean and variance of the distribution defined in Equations (31) and (32), respectively [23].

$$\mu =e^{\mu +\frac{{\sigma }^2}{2}}$$

(31)

$${\sigma }^2=e^{2\mu +{\sigma }^2}\left(e^{{\sigma }^2}-1\right)$$

(32)

4.2.5. Beta Distribution

The beta distribution function is usually used to model the uncertainty of some event with parameters $\mathsf{\alpha }>0 \mathrm{a}\mathrm{n}\mathrm{d} \beta >0$. The corresponding density function is defined in Equation (33) [24,25].

$$f\left(x\right)=\frac{\mathsf{\Gamma }\left(\alpha +\beta \right)}{\mathsf{\Gamma }\left(\alpha \right)\mathsf{\Gamma }\left(\beta \right)}{x}^{\alpha -1}{\left(1-x\right)}^{\beta -1} \mathrm{f}\mathrm{o}\mathrm{r} 0\le x\le 1$$

(33)

The mean of this distribution is given by the following expression:

$$\mu =\frac{\alpha }{\alpha +\beta }$$

(34)

The variance is defined in Equation (35).

$$\sigma =\sqrt{\frac{\alpha \beta }{{\left(\alpha +\beta \right)}^2(\alpha +\beta +1)}}$$

(35)

The mathematical models for the determination of $\alpha$ and $\beta$ are given in Equations (36) and (37), respectively.

$$\alpha =\mathrm{A}{x}_m$$

(36)

$$\beta =\mathrm{A}\left(1-x_m\right)$$

(37)

Also,

$$\mathrm{A}=\left\{\frac{x_m\left(1-x_m\right)}{{{\sigma }_m}^2}\right\}-1$$

(38)

where $x_m$ is the mean.

4.2.6. Logistic Distribution

A logistic distribution has a curve that is symmetrical about the mean of the data and is defined mathematically as follows [26]:

$$g\left(x\right)=\frac{\mathrm{e}\mathrm{x}\mathrm{p}[-\raisebox{1ex}{$(x-\overline{x})$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.]}{{\alpha \{1+\mathrm{e}\mathrm{x}\mathrm{p}\left[\raisebox{1ex}{$(x-\overline{x})$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.\right]\}}^2}$$

(39)

where $\overline{x}$ is the mean and $\alpha$ is the scale parameter of the distribution calculated using Equation (40).

$$\alpha =\frac{\sqrt{3\sigma }}{\pi }$$

(40)

4.3. Goodness of Fit

When a forecast is carried out, there is a need to compare the theoretical and forecasted results. Given this, there are standard models developed for this purpose. Some of the models are a coefficient of determination and root mean square method, as presented in Equations (41) and (42) [27,28,29].

4.3.1. Root Mean Square Error (RMSE)

$$\mathrm{M}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{h}\mathrm{l}\mathrm{y} \mathrm{E}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\left(\mathrm{\%}\right)=\frac{P_x-P_A}{P_A}\times 100\mathrm{\%}$$

(41)

Annually, the average error can be defined as follows:

$$\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{E}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\left(\mathrm{\%}\right)=\frac{1}{12}\sum _{i=1}^{12}\frac{P_x-P_A}{P_A}\times 100\mathrm{\%}$$

(42)

where $P_x$ = power density from the assumed probability density function and $P_A$ = actual site power density.

To compare the actual and predicted power densities, Equations (41) and (42) can be used. The closer the error is to zero, the better its fitness for predicting the power of the site.

4.3.2. Kolmogorov–Smirnov Test

Mathematically, it is assumed that the sample consists of $x_1, x_2, \dots x_n$ from the same distribution of the cumulative distribution function $F\left(X\right)$. This test is to check the weather and decide on the continuity of the distribution. The Empirical Cumulative Distribution Function (ECDF) is defined as follows:

$$F_{n }\left(x\right)=\frac{1}{n}\left[\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}\le \left(x\right)\right]$$

(43)

This test uses the largest vertical difference between the density function and the theoretical value. Mathematically, this is defined as follows [27,28,29]:

$$D=\underset{1\le i\le n}{\max }[(F\left(x_i\right)-\frac{i-1}{n},\frac{i}{n}-F\left(x_i\right)]$$

(44)

4.3.3. Anderson–Darling Test

The Anderson–Darling test ($A^2$) can be defined as a procedure that compares the cumulative distribution and the expected cumulative density function of the same distribution, as defined in [27,28,29]. The test tends to give more weight to the tail in comparison with the Kolmogorov–Smirnov test as expressed in Equation (45).

$$A^2=-n-\frac{1}{n}\sum _i^n\left(2i-1\right)\times [inF\left(x_i\right)+in(1-F\left(x_{n-i+1}\right)]$$

(45)

4.3.4. Chi-Square Test

The chi-square test is defined as the test that is carried out to confirm that a particular sample comes from a particular probability function [24]. This test is written as follows:

$$X^2=\sum _{i=1}^k\frac{{(O_i-E_i)}^2}{E_i}$$

(46)

where $O_i$ is the observed frequency, while $E_i$ is the expected frequency that is defined in Equation (47).

$$E_i=F\left(x_2\right)-F\left(x_1\right)$$

(47)

where $F$ = distribution function and the upper and lower limits of the bin are defined as $x_1$ and $x_2$, respectively.

5. Optimization Approaches for Sizing Microgrid Systems for Healthcare Clinics

It has been established that, till today, a significant number of communities are not connected to the national grid. This neglect is making healthcare in such communities a serious setback in achieving healthcare for all. Therefore, to achieve the sustainable development goal of the United Nations, there is a need to take the issue of rural electrification very seriously. In this paper, it’s clear that one of the best approaches to resolving healthcare electricity access is through the use of renewable energy resources onsite. Therefore, this section presents a comprehensive design approach and reliability studies of such systems. The need for understanding is because if such systems are not designed properly, there is a probability that healthcare accessibility in rural areas will not see the light of day in the near future. Furthermore, the need to optimally size the resources is critical for cost, reliability, and environmental concerns [30,31,32,33,34]. Also, the comprehensive advantages and disadvantages of each of the techniques from a sizing point of view are shown in Table 3.

Table 3. Advantages and disadvantages of the sizing techniques.

S/No.	Method	Advantage(s)	Disadvantage(s)
1	Conventional Approaches	Simple	Reliability of power supply is not guaranteed Cost of components might not be realistic
2	Ampere Hourly Method	Simple	Inability to take weather variations into consideration Component sizing could be undersized or oversized
3	Trade-off	Decision-makers and system designers can participate in the final decision	Inability to meet the nonlinearity requirements of the system Time consuming and complex
4	Classical	Complexity of the model could be a serious concern	Time consuming
5	Biological	Capable of solving complex optimization problems Predictability of future states of the system designed Ability to handle noisy data sets	Reliability Measurable Too much focus on nature Theories are developed according to disorders and eventually apply to everyone

5.1. Conventional Approaches

In most cases, the system designers use trial and error. Therefore, the design approach here is usually based on experience. In this case, after the components are assembled, issues arise, such as cost, battery degradation, and the unavailability of the power supply. This could be a serious issue in developing countries where health facilities are located in remote locations [19,35].

5.2. Ampere Hourly Method

In this method, usually an Excel sheet is used to determine the system component sizes. The method is simple, and therefore all component-rated power ratings are multiplied by the hours needed to be in operation per day. Other factors used in the calculations in some cases are losses and battery cycling. System designers also determine storage capacity by considering autonomous days, usually between 3 and 7 days, arbitrarily. An example of sizing renewable energy systems can be seen in [36,37,38]. Unfortunately, this method can lead to oversizing or undersizing of components. This method of design has many drawbacks, such as the inability to consider weather variations and environmental issues in the design [39].

5.3. Trade-Off Technique

This method is proposed to design a renewable energy system by developing a simple database such that all possible combinations are defined. In this case, the system can be simulated under different conditions of operations that could happen in the future. The simulations allow system designers and decision-makers to decide on the final design option. Unfortunately, the current power requirements of rural electrical loads and inclusive health centers are more advanced. Therefore, the system requirements are nonlinear, and optimal solution determination is time-consuming, complex, and cumbersome. Therefore, classical techniques might not be suitable [40,41,42].

5.4. Classical Techniques

Classical techniques depend on calculus and the applications of calculus to determine the optimum sizes of components. These methods are used for the hybridization of renewable energy systems. Examples of the method include linear programming, nonlinear programming, and dynamic programming. In all of them, linear programming is the base; others could be driven from it. Therefore, it has the following format, consisting of objective functions and constraints [43,44].

$$\underset{x}{\min }\left(f^{T}x\right)$$

(48)

$$\left\{\begin{array}{c}A·x\le b\\ A_{eq}·x=b_{eq} \\ lb\le x\le ub\end{array}\right.$$

(49)

where, $f$, $x$, $b,$ $b_{eq}$, $lb$, and $ub$ are vectors, and $A$ and $A_{eq}$ are matrices.

Mixed-integer programming is used when all or some of the decision variables can be integer values. The problem formulation can be presented in the following format, consisting of the objective function and constraints in the following format [45].

$$\mathrm{Maximize} p\left(x\right)={\displaystyle \sum _{j=1}^n{{\displaystyle c}}_j}{{\displaystyle x}}_i$$

(50)

$$\sum _{i=1}^n(\sum _{i=1}^n{a}_{ij}{x}_j\le b_i)$$

(51)

where $x_j\ge 0\forall j\in \left\{1,\left.n\right\}\right.$ and $x_j$ is an integer $\forall i\in \left\{1,\left.I\right\}\right.$.

In addition, when the objective function or one of the constraints is nonlinear, the optimization problem can be formulated as a nonlinear problem with the general structure presented below. This optimization problem is based on Newtonian or Lagrangian techniques [46].

$$\mathrm{M}\mathrm{i}\mathrm{n}f\left(x\right)$$

(52)

Moreover, it is then subjected to the following:

$$g_i\left(x\right)\le b_i\forall i\in \left\{\mathrm{1,2},\dots ,N\}\right.$$

(53)

where some terms in the constraints $g_i \left(x\right)$ or $f\left(x\right)$ are non-linear.

5.5. Biological Techniques of Sizing Microgrid

This classification can be classified into three major techniques, including swarm intelligence, artificial neural networks, and evolutionary techniques.

5.5.1. Particle Swarm Optimization

In 1995, Kennedy and Eberhart developed a technique that is capable of solving complex optimization problems based on the social interaction concept. The technique has been successful in solving complicated mathematical problems; as a result, many problems, such as the size of renewable energy systems, are resolved using this method. The key element of this method is that each particle is represented using velocity and position. In this regard, the velocity and position of each particle can be defined as follows:

$${v_{i,j}}^{k+1}={v_{i,j}}^k+c_1{r}_1\left(x{{best}_{i,j}}^k-{x_{i,j}}^k\right)+c_2{r}_2\left(x{{gbest}_j}^k-{x_{i,j}}^k\right)$$

(54)

$${x_{i,j}}^{k+1}={x_{i,j}}^k+{v_{i,j}}^{k+1}$$

(55)

where

• ${x_{i,j}}^k$ and ${v_{i,j}}^k$ are the jth components of the ith particle’s position and velocity vector, respectively;
• $c_1$ and $c_1$ are the acceleration coefficients;
• $r_1$ and $r_{2 }$ are uniformly distributed random numbers between 0 and 1;
• xbest(i) is the best position of particle i until iteration k;
• gbest is the best position of the group;
• k is the constriction factor.

5.5.2. Genetic Algorithm

A genetic algorithm is a process capable of optimizing a system through the use of natural selection. It was developed by John Holland. The basic steps involved in achieving the solution are inheritance, selection, crossover, and mutation. The process has major building blocks, namely random number generation, fitness, reproduction, crossover, and mutation processes, as shown in Figure 3 [47,48].

Figure 3. Genetic algorithm.

5.5.3. Artificial Neural Network

It has been established that one of the characteristics of a smart microgrid is the ability to forecast the future of the system conditions. Therefore, the sizing of renewable energy microgrids needs an optimization model that can make future predictions, and therefore, ANN is a good candidate for such a situation. Future predictability is critical for power system planners and operators to make necessary changes that could prevent unreliable power supply or unavailability. Therefore, ANN can predict the situation in the hours or days ahead [49]. Also, it can handle noisy and incomplete data with suitable training to perform other tasks such as identification, forecasting, modeling, and control of power flow in the system. The general architecture of the ANN is shown in Figure 4. Furthermore, the general classification of the optimization techniques is shown in Figure 5. Some examples of sizing microgrids are presented in Table 4.

Figure 4. Artificial neural networks.

Figure 5. General classification of optimization techniques.

Table 4. Microgrid sizing with emphasis on objective function and mathematical models.

S/No.	Ref.	Details of the Microgrid, Including Objective Function	Mathematical Model
1	[50]	Characteristics of lead-acid battery storage connected to a hybrid microgrid have been modeled	The model considered the cost, fuel, environment, and operational cost of the system. NSGA II was used to minimize battery life loss
2	[51]	PV-wind-diesel-battery microgrid optimal system component sizes were determined	Dividing the rectangle with DIRECT algorism was used to minimize the total system cost
3	[52]	A PV-wind generator was designed, and system component sizes were obtained considering uncertainties in load and solar radiation at different times.	Modified PSO has been applied to determine the objective function of minimizing cost and determining system reliability
4	[53]	A wind-solar-battery microgrid has been developed, and component sizes have been obtained	PSO determined system cost and reliability for a period of 20 years
5	[54]	Relationship between operational and environmental costs has been modeled and optimized	Integrated approach combining Simulated annealing, ant colony optimization, PSO, and GA have been used to determine the role of diesel generators in microgrids
6	[55]	The objective is to maximize system reliability while minimizing system cost for a PV-wind microgrid	constrained mixed-integer multi objective particle swamp optimization (CMIMOPSO) algorithm
7	[56]	Authors were able to model the effect of location on the optimum design of a microgrid for power supply	Time-matching algorithm has been applied
8	[57]	Model for the optimum design of microgrid has been developed, and it minimizes system cost while minimizing the cost-to-reliability ratio	Linear programming
9	[58]	Total cost and dumped power were considered objective functions; additionally, geographical factors were modeled as system constraints	Grey Wolf Algorithm (GWO) was used to determine the optimum sizes of components. The model has been able to provide better convergence and robustness.
10	[59]	Costs of production, emissions, and customer outages were minimized	Multi-objective optimization has been applied

6. Reliability of Power Supply for Rural Healthcare Clinics

Rural healthcare electricity grid reliability is expected to be high at all times, which presents a critical part of the system design and is paramount to system designers and practitioners. This can be achieved if the stakeholders consider it at the design stage. However, this can be possible if a better definition is proposed and the correct metrics are used in the design. Therefore, there is a need to define the most sensible element guiding the reliability study of this part of the network. In this paper, the reliability of rural health clinics can be defined as the possibility of supplying electricity to the clinics over a period designed under defined system operating conditions without failure. Therefore, for a health clinic microgrid power system to be reliable, it is expected to be adequate and secure from the power system point of view. The essence of the reliability study is to establish the performance of the system against some standard and to determine the ability of the system to provide the minimum required power to the health center. Given this, certain indices are used. However, it is important to note that most of the papers in the literature do not classify the studies at different stages of the system. Therefore, it is also important for the system designers to separate reliability indices at different levels of the network. This could allow for critical understanding and maintenance strategy development of the microgrid system [60,61]. This would significantly improve the reliability of the system. In this paper, the indices are defined as the loss of power supply probability [62].

$$\mathrm{L}\mathrm{P}\mathrm{S}\mathrm{P}=\frac{\sum _{t=1}^{N}LPS\left(t\right)}{\sum _{t=1}^{N}D\left(t\right)}$$

(56)

$$\mathrm{L}\mathrm{P}\mathrm{S}\left(t\right)=D\left(t\right)-E_T\left(t\right)$$

(57)

where E_T (t) is the total energy generated by the source.

$$\mathrm{L}\mathrm{L}\mathrm{P}=\sum _{j}p\left[C_A=C_j\right]·p\left[L>C_j\right]=\sum _j\frac{p_j·t_j}{100}$$

(58)

where

• L: the expected load;
• C_A: available system generation capacity;
• C_j: remaining system generation capacity;
• P_j: probability of a system capacity outage;
• P: probability;
• t_j: % time when the system demand exceeds C_j.

6.1. System-Level Reliability Indices of Microgrids

There is also the need to define indices at the system level of the microgrid. Understanding them can be a source of energy problems for healthcare microgrid power systems. The indices can be defined in Equations (59)–(67). Also, the flow chart shown in Figure 6 can be used for the analysis of these indices as defined in DigSilent [63].

Figure 6. Procedure used in the reliability assessment of a microgrid.

Systems Average Interruption Frequency Index (SAIFI):

$$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}=\frac{\sum {\mathrm{A}\mathrm{C}\mathrm{I}\mathrm{F}}_i{·C}_i}{\sum C_i}$$

(59)

Customer Average Interruption Frequency (CAIFI):

$$\mathrm{C}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}=\frac{\sum {\mathrm{A}\mathrm{C}\mathrm{I}\mathrm{T}}_i{·C}_i}{\sum A_i}$$

(60)

Average System Interruption Frequency Index (ASIFI):

$$\mathrm{A}\mathrm{S}\mathrm{I}\mathrm{F}\mathrm{I}=\frac{\sum L_m}{L_T}$$

(61)

The average duration a customer experienced interruptions for one year is called SAIDI.

$$\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}=\frac{\sum {\mathrm{A}\mathrm{C}\mathrm{I}\mathrm{T}}_i{·C}_i}{\sum C_i}$$

(62)

Customer Average Interruption Duration Index (CAIDI):

$$\mathrm{C}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}=\frac{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{D}\mathrm{I}}{\mathrm{S}\mathrm{A}\mathrm{I}\mathrm{F}\mathrm{I}}$$

(63)

Average System Interruption Duration Index (ASIDI):

$$\mathrm{A}\mathrm{S}\mathrm{I}\mathrm{D}\mathrm{I}=\frac{\sum (r_m-L_m)}{L_T}$$

(64)

Average Service Availability Index (ASUI):

$$\mathrm{A}\mathrm{S}\mathrm{U}\mathrm{I}=\frac{\sum {\mathrm{A}\mathrm{C}\mathrm{I}\mathrm{T}}_i{·C}_i}{8760·\sum C_i}$$

(65)

Average Services Availability Index (ASAI):

$$\mathrm{A}\mathrm{S}\mathrm{A}\mathrm{I}=1-\mathrm{A}\mathrm{S}\mathrm{U}\mathrm{I}$$

(66)

Average Customer Curtailment Index (ACCI):

$$\mathrm{A}\mathrm{C}\mathrm{C}\mathrm{I}=\frac{\mathrm{E}\mathrm{N}\mathrm{S}}{\sum A_i}$$

(67)

6.2. Maintenance and Reliability Indices

At the maintenance level of the system, four indices should be used in the analysis for a realistic design of the microgrids. Unfortunately, none of the research papers have explored the reliability studies of healthcare microgrids at system levels. However, the systems could not be reliable and were sometimes unavailable due to approximations in the reliability studies at system levels. Given these, these papers propose indices to be taken into consideration while designing microgrids. These indices include Barbiums, criticality, network reliability achievement, and network reliability reduction [64,65,66,67,68,69,70]. These indices are defined in Equations (68)–(71).

The Barbiums index is a measure for measuring component importance to system reliability failures as defined in Equation (68).

$$I_i^B\left(t\right)=\frac{\partial R_s\left(t\right)}{\partial R_i\left(t\right)}$$

(68)

Criticality index is a measure that can help system designers understand the contributions of particular components or blocks to the reliability improvement of the entire microgrid, given mathematically as follows:

$$I_i^{CI}\left(t\right)=I_i^B\left(t\right)·\frac{F_i\left(t\right)}{F_s\left(t\right)}$$

(69)

The reliability achievement model is for the establishment of the component responsible for the entire system failure at time t, as presented in Equation (69).

$${\mathrm{N}\mathrm{R}\mathrm{A}\mathrm{W}}_i=\frac{R_s\left(t;R_i\left(t\right)=1\right)}{R_s\left(t\right)}$$

(70)

Network reliability reduction is important to determine the increment in system reliability due to a particular component or subsystem of the microgrid structure, as defined in the following equation:

$${\mathrm{N}\mathrm{R}\mathrm{R}\mathrm{W}}_i=\frac{R_s\left(t\right)}{R_s\left(t;R_i\left(t\right)=0\right)}$$

(71)

7. Taxonomy of Proposed Energy Sources for Healthcare Facilities

The taxonomy in Table 5 shows that several works have proposed a hybrid version of power supply for healthcare facilities, which is mostly comprised of solar, wind, diesel generators, and battery storage, and only a few works suggest the use of solar-standalone power sources. The majority of the work is conducted in rural areas of many countries, where the energy supply can be inconsistent and healthcare access is a critical concern. Additionally, it can be seen that most of the works utilized Hybrid Optimization of Multiple Energy Resources (HOMER) to conduct simulation and analysis of their proposed system design and implementation.

Table 5. Related literature on the sizing of healthcare microgrids.

Ref.	Proposed Energy Source	Major Findings	Location
Tool(s)	HOMER
Olatomiwa et al. [71]	Hybrid (solar, wind, diesel, and battery)	Among the site analyses, Sokoto and Jos have the highest wind potentials. Also, all the sites are suitable for small solar power. Finally, PV/diesel/battery is ideal for healthcare.	Nigeria
Ani [72]	Solar energy with battery storage	PV-storage is proposed as the best for primary healthcare. The system could reduce 9371 kg of carbon if implemented and is suitable for the equipment of the center while decreasing the lifecycle and costs by 75% each.	Karshi, Nigeria
Soto et al. [73]	Solar energy	Explore the opportunities and challenges associated with solar energy for rural health centers. The study is on the operational, environmental, and economic viability of green energy solutions.	-
Olatomiwa et al. [74]	Hybrid (solar, diesel, and battery)	Techno-economic studies of different health centers have been presented. The results have shown that wind and solar energy availability in Nigeria could improve healthcare accessibility.	Fatika, Nigeria
Olatomiwa [75]	Hybrid (solar, wind, diesel, and battery)	The optimal design of three grid-unconnected villages has been analyzed [76]. The results have shown that a PV/wind diesel generator storage system is viable and is the best option for Maiduguri and Enugu. However, the Iseyin site is better with the PV/diesel/battery system option.	Maiduguri and Enugu, Nigeria
			Iseyin, Nigeria
	Hybrid (solar, diesel, and battery)
Olatomiwa et al. [77]	Hybrid (solar, diesel, and battery)	Demand-side energy management has been developed for rural health centers. The output of various simulations has shown a decrease in cost energy of 25.8% while the net present value decreased by 70%.	Karu, Nigeria
Oladigbolu et al. [77]	Hybrid (solar, diesel, and battery)	Techno-economic analysis of PV/wind/diesel generator/battery has been carried out, and the results have shown that operating, fuel, and energy costs, as well as fuel consumption are sensitive to system sensitivity parameters of the entire power system.	Kudu, Nigeria
Nwachuku [78]	Micro hydropower plants	The study has suggested the use of micro hydropower as the best technology that could improve electricity access to the health clinics in the study area.	Orumba, South Nigeria
Palanichamy and Naveen [79]	Solar, wind, diesel generator, and battery	Wind-PV-DG-battery microgrid was proposed for all India Institute of Medical Sciences (AIIMS) return on investment, payback period, and levelized cost of energy have shown the possibility of the proposed system.	Madurai, India
Peirow et al. [80]	Solar energy	A rooftop hospital possibility has been investigated in order to improve electricity access in Tehran.	Tehran, Iran
Twizeyimana and Ndisanga [81]	Solar PV with a backup system interconnected with power grid and diesel generator	HOMER.	Kolandoto Hospital, Tanzania
Olatomiwa et al. [82]	Hybrid, PV-wind-diesel generator-battery microgrid	HOMER software.	Geo-political zones of Nigeria
Babatunde et al. [83]	Standalone PV-battery microgrid	A standalone PV system was designed for a health clinic in Northwest Nigeria. The proposed system could avoid 8357–8956 kg/year of CO2 when implemented.	Abadam, Local Govt, Northwest Nigeria
Kowsar et al. [84]	Solar PV grid-connected microgrid	Analysis of the proposed system has shown that a grid-connected system is the best option in the study area. The cost of electricity is significantly lower than the present electricity price in Bangladesh.	Charbhadrashan Upazila, Faridpur District Bangladesh
Nourdine and Saad [85]	Utility+PV+battery microgrid	Moroccan health centers have been investigated for solar energy microgrids. The proposed system has been analyzed for efficiency, cost, and environmental effects.	Souss-Massa region in Morocco
Islam et al. [86]	Utility+PV+battery microgrid	Load analysis of the system has shown that a 32 kW solar grid-connected system is required for the optimum system power supply.	Gangachara Upazila Northwest Bangladesh
Isa et al. [87]	Utility+PV+battery microgrid	A grid-connected solar PV system for the supply of electricity to the health clinics in Malaysia has been analyzed. Parameters analyzed include total net present value, levelized cost of energy, and total net present post.	Temerloh Pahang, East Peninsular Malaysia
Alsagri et al. [88]	PV-battery-fuel cell-electrolyzer-DG	Different excess electricity reduction methods have been investigated. Also, it has been shown that a 30% renewable energy fraction supplies electricity to the health clinic at a rate of 0.105 USD/kWh.	Al Hayyaniyah, Saudi Arabia
Razmjoo et al. [89]	PV/WT/diesel generator/fuel cell/battery	Carbon reduction has been developed. The optimal design has shown a cost of 0.151 $/kWh at a 15.6% rate of return, and also, 2000 kg of carbon emissions have been estimated per household annually.	Iran
Amin et al. [90]	PV/WT/biodiesel generator/diesel generator/Battery	PV-wind/fuel/battery microgrid has been designed, and the design has shown a salvage effect on the short and long term in the range of 3 to 30%. Also, 12.5 and 21.4% of the renewable energy fraction have achieved 0.130 USD/kWh to 0.167 USD/kWh in electricity costs.	Iran
Kobayakawa and Kandpal [91]	Standalone PV/biomass generator/battery	Off-gird PV microgrids have been analyzed, considering operation, maintenance, and cost of energy. HOMER.	India
Singh and Baredar [92]	Standalone, PV/fuel cell/biomass gas	Total power from the system has been found to be 36 kWh/year. Also, the economics of the system have been analyzed, and it is clear that the proposed microgrid is economically and technically viable. HOMER.	India
		HOMER software.
Tool(s)	MATLAB
Assaf and Shabani [93]	PV/fuel cell/solar collector	Solar PV with hydrogen and solar thermal systems have been analyzed. The proposed system has a reliability between 95 and 100%.	Australia
Hohne et al. [94]	Solar and electrical energy storage device	Solver in the OPTI-Toolbox for MATLAB (SCIP).	Bloemfontein, South Africa
Renedo et al. [95]	Gas turbine and diesel generator	Trial-and-error method.	Spain
Miguel et al. [96]	Combined heat, cooling, and power systems	Model development and solving using mixed-integer linear programming.	Zaragoza, Spain
Najafi et al. [97]	PV/battery	PV-battery power system designed for providing peak power demand, and the economic analysis has shown an improvement in COE and NP by 8.1 and 6.7, respectively. Also, the system is economical when the demand is above 10 kWh/d.	Iran
Ogedengbe et al. [98]	PV/WT	A renewable energy calculator was developed to enable system designers to determine energy audits and energy savings for hybrid renewable energy power systems.	Nigeria
Pena-Bello et al. [99]	PV/battery	Open-source software is proposed for the choice of battery storage option in different environments. The proposed method has shown about 66% improvement compared to PV self-consuming systems.	Switzerland, USA
Ayeng’o et al. [100]	PV/battery	A PV model that considered incident solar radiation, temperature, and the number of cells. The model is tested in Tanzania and is proposed to be used in any part of the globe.	Tanzania
Guangqian et al. [101]	PV/battery	A hybrid algorithm for sizing of wind-PV-biodiesel-battery storage has been developed and tested in Iran. The objective function is to minimize the life-cycle cost of the system. Simulated annealing and harmony search algorithms were used in hybrid modes.	Iran
Eteiba et al. [102]	PV/biomass/battery	A techno-economic study of the proposed microgrid has been carried out by minimizing the net present value, loss of power supply probability, and percentage of excess energy. Also, different battery storage options have been analyzed. Among all the algorithms used, the Firefly algorithm has the least execution time and the best performance.	Egypt
Nadjemi et al. [103]	PV/WT/battery	The sizing of microgrids using the Cuckoo search algorithm has been presented, and it was found to be better compared to the particle swarm optimization technique. The model was tested in Algeria; it was analyzed economically, technically, and environmentally.	Algeria
Sanajaoba and Fernandez [104]	PV/WT/battery	In this optimization, the Cuckoo search algorithm is found to outperform GA and PSO for optimizing hybrid renewable energy microgrids. Other parameters used in the optimization include the wind turbine generator and the force outage rate.	India
Lorenzi and Silva [105]	PV/battery	A model has been proposed to reduce electricity costs due to the presence of battery storage. In order to implement the proposed model, linear programming for time-of-use optimization applications for battery storage and demand response has been proposed.	Portugal
Tool (s)	Other tools and techniques
Vaziri et al. [106]	Objective function and constraints developed and solved using integer programming	A grid-connected microgrid energy management model was designed to minimize energy costs and ensure both surgeons and patients pleasures are maximized.	Iran
Vaziri et al. [107]	Grid-connected PV-wind microgrid	IBM ILOG CPLEX Optimizer v12.3.	Iran
Alamoudi et al. [108]	Solar PV grid-connected microgrid	The ANFIS technique was used for the analysis of the PV system at King Abdulaziz University in Saudi Arabia. Using the response surface model, the optimal working condition of the microgrid has been established, while ANFIS was used to determine the performance of the solar panel.	Saudi Arabia
Yoshida et al. [109]	Grid-connected microgrid	Operational strategies and the system structure of a grid-connected microgrid have been proposed. Eventually, the output of the optimization will show that hybrid microgrids will be suitable for the hospital.	Japan
Zubi et al. [110]	PV/battery	IHOGA software was used to design and model a microgrid under different operating conditions for a period of 30 years (2020–2040). Eventually, a PV battery system is selected as the best option for the selected cities.	Sample cities, worldwide
Bingham et al. [111]	PV/WT/biodiesel generator	It has been established that net-zero buildings have a lower life cycle cost compared to standard buildings. Also, thermal insulation could reduce the energy consumption of electrical systems by 30%. NSGA II was used to determine the optimal system configuration.	Bahamas
O’Shaughnessy et al. [112]	PV/battery	It has been established that solar PV microgrids have the potential to improve end-user economic conditions, considering time of use and demand charges, to mention just a few.	United States of America
Rodríguez-Gallegos et al. [113]	PV/diesel generator/battery	Non-dominated sorting algorithm III has been proposed to optimize the microgrid with the objectives of reducing the cost of electricity, carbon emissions, and voltage deviations. Considering weather conditions, the results have shown the advantages of a hybrid system in terms of reduced cost, emissions, and power quality improvements.	Indonesia

Furthermore, it was stated in [114,115] that over the past three decades, coinciding with the rapid expansion of the global economy, there has been a substantial surge in energy demand. Projections indicate that from 2015 to 2040, there will be an estimated 30% increase in global energy consumption. In response to this escalating demand and to mitigate the adverse environmental effects associated with fossil fuels, there has been a noteworthy emphasis on exploring renewable energy sources (RESs) like solar, wind, and hydropower. In the year 2022, many nations implemented policies aimed at fostering the advancement of renewable energy.

At present, approximately one-fourth of the world’s electricity is derived from renewable sources. Notably, hydropower stands as the most prevalent RES on a global scale, closely trailed by wind and solar power, both of which are experiencing rapid expansion. Careful observation in the table above has shown that many of the proposed renewable energy power supply systems were left at the design stages [116]. One such system is the design of a renewable energy system for Chennai, a smart city in India. It has been established that the proposed system can satisfy the proposed system demand. The study recommends a hybrid microgrid consisting of wind, PV, and DG as the best option using HOMER software.

It is worth noting that realistic planning of renewable energy systems, especially in the health care section, requires a technical understanding of battery storage systems, as explained in the previous section. Furthermore, some of the storage systems need further studies and more in-depth analyses to be suitable for healthcare applications. Other areas of concern to the system designers include environmental concern, storage capacity, and size, to mention a few [117].

Authors in [118] have shown that in sub-Saharan Africa, a huge gap has been observed in health care provision. However, if realistic planning is considered and investments in a power supply are holistically carried out, nearly 281 million people could have access to healthcare and reduce travel time. In the same vein, the cost estimate for the provision of about 50,000 health facilities in the region is approximately 484 million euros. The analysis has shown that renewable energy systems could provide a clean, reliable, and economical way of solving the electricity requirements of the region.

It can be discovered from the reviews above that the hybrid system is the most recommended. However, solar cannot be useful on a rainy day, just as wind cannot be useful on a calm day. Fossil generators, too, can be reliable, but they are also expensive. Hence, adding a battery storage system to the health care facility microgrids is recommended for reliable and economical power supply to the systems.

8. Characteristics of Modeling Tools for Realistic Sizing of Healthcare Center Energy Requirements

It is evident in the literature that there are various techniques and modeling tools for sizing renewable energy microgrids for health applications. However, specifically due to the requirements for reliability, availability, and sensitivity of healthcare load systems, a tool suitable for modeling such a type of load needs to meet certain requirements as presented in Section 8.1, Section 8.2, Section 8.3 and Section 8.4.

8.1. Ability to Represent the Variability

This is important because future energy microgrids are expected to integrate all possible renewable energy resources; therefore, the modeling tool should be able to represent the renewable energy resources in realistic ways, considering a reasonable time scale from seconds to years. Spatial resolutions and statistical representations are also characteristic requirements of such tools.

8.2. Renewable Base Power Generation

Decarbonization of society is one of the sustainable goals, however challenging. One of the simplest is the replacement of the conventional system of power generation with renewable energy. This can be achieved by using a more renewable energy mix to supply other essential loads, such as health systems. Furthermore, this method could allow for more penetration of intelligent power systems, which is a basic requirement of healthcare feeders. This technology could give health facilities and equipment access to clean energy for electricity, heating, and laboratory needs in hospitals for present and future generations.

8.3. General System Benefit

In addition to the electricity supply to the health centers, the proposed utilization of renewable energy systems could assist society in achieving one of the sustainable development goals by 2030. In this regard, renewable energy could be a catalyst for resolving the missing link between many attributes of an ideal society. These attributes include climate, health, quality water supply, and land use, to mention just a few.

8.4. Validation of the Results

It is important to understand the need for the modeling tool/environment to be testable and verifiable. This attribute is critical, such that system designers and stakeholders should be able to test the results and verify all the results obtained as a result of various design options. This is important to ensure the validity and accuracy of the results. Therefore, there is a need for this stage to avoid overestimation or underestimation of the system parameters designed.

9. Future Directions and Lessons Learned

This section presents the lessons learned as a result of the presented overview on the realistic application of the procedure for the achievement of higher penetration of renewable energy resources in the area of health care, especially for rural clinics.

9.1. Inaccurate Load Modeling Techniques

It has been clear from the papers reviewed that many of the research papers estimate load based on power rating and operating hours. However, this technique could lead to oversizing or undersizing of system components. Eventually, the microgrid design might not be optimal due to this shortcoming. To resolve the situation, the system designers need to consider the variation of the system demand because, in health centers, some equipment or parts of the system consume power even while in standby mode. In addition, this approximation led to higher costs for healthcare microgrids.

9.2. Lack of Optimal Sizing

One of the purposes of proposing a renewable energy system in health facilities for power supply is to supply power to critical loads and the entire health center at the lowest cost. Unfortunately, without a realistic sizing approach, this global shortage of electricity supply to these facilities might not see the light of day in the near future. Furthermore, due to the approximations introduced at the design stage, there is a need to design the system most economically; this is possible if all the design variables are considered during the design of the microgrid. One of the factors that need to be considered is weather and load variations in the design of the microgrid. Furthermore, critical loads should be considered in the design of such systems. Hence, it is important to use artificial intelligence techniques in the sizing of renewable energy for healthcare applications to supply electricity at minimum cost.

9.3. The Need for Reliable Power Supply

This paper focused on the health care facilities supplied with reliable power supplies. Unfortunately, developing countries with acute shortages of electricity could not extend the grid to rural areas where health centers are located. This makes it difficult to attract qualified personnel to the local areas. Also, the availability of medical services in those areas is increasing. This research has shown that energy in rural health facilities is one of the critical elements of achieving universal health care globally. Therefore, without reliable electricity in health clinics, it has been established that life-saving health services will be impossible. This universality in universal health accessibility is defined as one of the sustainable development goals. Finally, many of the health centers lack basic power supplies such as lighting, diagnosis, communication, and other complicated medical equipment. Furthermore, laboratory service will be unavailable or inadequate due to the absence of a reliable power supply. Other services that will be unavailable due to the shortage of electricity include surgery, intensive care unit services, and the safekeeping of medics.

9.4. The Need for Realistic Reliability Studies of the Developed Models

It has been established from the literature that the majority of the papers on the design of microgrids designed for health facilities do not consider reliability analyses of the design. Thereby making the design unrealistic and sometimes uneconomical. Therefore, this paper proposes the reliability analysis of healthcare microgrid systems, considering component, system, and load point reliability before a final realistic design is achieved. Also, comprehensive reliability analyses considering the demand and supply of the expected health facilities are important.

9.5. Development of Maintenance Strategies

Strategies need to be developed on how electricity access and availability could be enhanced in rural communities so that access to health care can be improved. This will assist in the delivery of health care and improve access, thereby decreasing the mortality rate, especially in developing countries. Others include health and safety, staff retention and recruitment, logistics, and administration.

9.6. Applications of Artificial Intelligence Techniques for Rural Healthcare Applications

Due to the complexity of the future energy grid, it is becoming unrealistic to perform complex tasks without switching to soft computing techniques. Unfortunately, the design of microgrids for healthcare applications is a complex task. Therefore, it can be established here that for realistic sizing of microgrids suitable for medical microgrids, there is a need to use the new domain of complex optimization techniques. Furthermore, it has been established that most of the complex analysis that requires intelligent work is occurring in the field of soft computing. Also, due to certain automation requirements, a lot of researchers are proposing many solutions to problems related to electricity supply to rural healthcare clinic systems using soft computing techniques. Some of the recent soft computing techniques are neural networks, genetic algorithms, and fuzzy logic techniques. In summary, some soft computing techniques and areas of application in renewable energy conversion systems are presented in Table 5.

Fuzzy logic is applicable in MPPT pitch angle controls and power predictions. ANFIS models have been applied to forecast renewable energy systems’ output power at the regional level. Power factor predictions, power factor optimizations, and pitch angle determinations of wind energy conversion systems can be achieved using genetic algorithms. Another model is ANN, which finds applications in power prediction, online power predictions, short-term renewable energy predictions, and sometimes fault detection in systems. More details about them can be seen in Table 6.

Table 6. Applications of soft computing models to renewable energy conversion systems.

Mathematical Model (Technique)	Application Domain	References	Advantages and Disadvantages
Fuzzy logic model	Wind turbine MPPT control, wind turbine pitch control, wind power prediction, forecasting of wind power, wind turbine parameter determination/prediction, solar energy predictions, design, and analysis.	[119,120,121]	Flexibility Ease of implementation Robustness Interpretability Disadvantages Depends on human expertise, Tuning difficulty Limited accuracy Computational complexity
ANN	Controller design for grid-connected systems, PID control, forecasting of wind energy, wind power forecasting for online applications, wind power forecast for short-term applications, system sizing, fault detection, and determination of flicker.	[122,123]	It has the ability to improve the sizing process Capability to learn the input and output relationship Future forecast of the system’s behavior
GA	Pitch angle control, controller tuning, system modeling, siting of wind turbines, system modeling, optimization of power factor, and the energy of the system, etc.	[124,125]	Understandability Disadvantages Not efficient algorithm Does not guarantee the quality of the solution Computational challenges due to fitness value calculations
Inference-based technique	Power factor prediction	[126,127,128,129,130]	Uncertainty handling capability Ability to model complex systems easily Save time and resources Disadvantages Domain experts are required to develop a model Expensive to compute when a complex system is involved Interpretation difficulty
Fuzzy-based adaptive technique	Forecasting regional power	[131,132,133,134]	Adaptation capabilities, High generation capability, Flexibility Ability to capture the nonlinearity of the process Disadvantages High computational cost, Location of a membership function Curse of dimensionality Accuracy, interpretability, and trade-off

10. Conclusions

Hospitals in rural areas of developing countries are performing below expectations due to unavailability and unreliable power supply, resulting in poor health care and health-related services. In practice, it is difficult to attract qualified personnel due to difficulty in supplying the needed sophisticated equipment, unrealistic diagnoses, and poor equipment handling, leading to higher mortality rates in those communities. All these problems are attributed to an unreliable power supply that needs to be addressed urgently. This paper reviews the current state of power supply to these remote communities and presents realistic and reliable strategies for available power supply to cater to the power supply needs of health centers in remote communities. Specifically, the methods for renewable energy resources are critically analyzed, and the accompanying optimization models are elaborated. In addition, the maintenance strategies for reliable and economical power supply to those health facilities are assessed comprehensively. Key findings from the study reveal that power supply for health centers is based predominately on sizing. Also, the study showed that existing tools used for renewable energy resources for rural health care microgrids are based on trial-and-error methods, resulting in extensive time consumption and prohibitive costs, posing serious challenges to effective power supplies for rural healthcare systems. Another challenge that system designers often ignore in the design of rural healthcare power supplies is the development of systematic reliability analysis models. This paper exposes the gaps in renewable energy power supply for rural health clinics in Africa and beyond. Last, the paper provides a technical and professional guide to researchers, policymakers, and practitioners in the area of power supply, especially for rural healthcare centers.