Bayesian belief network modelling of the challenges associated with hybrid solar-diesel electricity from the end users’ perspective in Bugala Island in Uganda

doi:10.21203/rs.3.rs-3131576/v1

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Bayesian belief network modelling of the challenges associated with hybrid solar-diesel electricity from the end users’ perspective in Bugala Island in Uganda

https://doi.org/10.21203/rs.3.rs-3131576/v1

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Background

A hybrid solar-diesel energy system (HSDES) was installed on Bugala Island located on Lake Victioria in Uganda to increase access to clean, affordable, reliable, and sustainable energy, which is essential for protecting the environment while improving living conditions, human health, and local economic development. However, the challenges associated with HSDES generated electricity from the end-users’ perspective are still unknown. Since these challenges are complex, stochastic, nonlinear, and multidimensional, this study aimed at utilizing a Bayesian belief network (BBN) modelling approach to identify, and rank the challenges experienced by energy consumers on the Island in an intergrated format.

Methods

A cross-sectional research design was employed where a total of 237 randomly selected respondents were involved in this study. Quantitative data were gathered using semi-structured questionnaires. The BBN model was developed basing on well established guidelines and modelling protocols. Using the K-fold partitioning approach (K = 2), the casefile (n = 237) was randomly partitioned into a training portion (70%, n = 165) used to populate the model, and test dataset (30%, n = 72), with which accuracy was assessed. Model accuracy was evaluated using metrics of sensitivity, and predication performance.

Results

The developed model was 81.7% accurate in predicting the challenges correctly. The model's spherical payoff was 0.87 with the logarithmic and quadratic losses of 0.33 and 0.23, respectively indicating a strong predictive power and the model’s classification power. The probability of households to experience significant challenges associated with HSDES generated electricity was 30.6%. The rate of damage of electric appliances increased by 15.6 percentage points. Cases of faulty electric meters increased by 25.8 percentage points. The unit cost of electricity, and the cost of power connection also increased by 1.9 and5.5 percentage points respectively. Cases of electrocution increased by 2.4 percentage points while load shedding increased by 4.7 percentage points.

Conclusion

This study provides the key top ranked challenges that should be given priority in an effort to expand hybrid energy on Bugala Island. We conclude that BBN modelling approach is a promising tool in the field of hybrid renewable energy systems on Islands with potential applications due to its versatility.

Bayesian belief network

Bugala Island

Challenges

Hybrid energy systems

Hybrid solar- diesel systems

Renewable energy

Uganda

Access to clean energy is a fundamental element in achieving the Sustainable Development Goals (SDGs), and it is among the major focus of several global, regional and national initiatives for socio-economic development [1]. However, the proportion of the rural population with access to electricity in Africa and Sub Saharan Africa is still considerably low, at only 37% and 29%, respectively [2]. In Uganda, about 70% of the population lack access to electricity and consequently, the country has to rely heavily on biomass and kerosene as main sources of energy for cooking and lighting [3, 4]. The island communities of Uganda are also notably facing numerous energy challenges since there are far away from the mainland energy grid system [5]. Moreover, the disconnection of islands in Uganda makes it uneconomical and impractical to extend the utility grid to these geographically isolated and disadvantaged areas with dispersed populations [6]. Therefore, considering the particularity of isolated islands in Uganda, innovative approaches are required to deliver SDG 7 of ensuring access to affordable, reliable, sustainable and modern energy for all.

Electrification of isolated areas in both rural and remote island communities using renewable energy (i.e. small scale hydropower, solar and wind energy) has become an effective and suitable instrument for improving living conditions as well as promoting sustainable development of such regions in both developing and developed countries [1, 7]. Moreover, since renewable energy sources are inexhaustible, dependable and environmentally beneficial, there are key in reducing the impact of global warming [8]. To ensure a 24-hour constant power supply and reliability in islands, hybrid power systems have emerged and applied to overcome the intermittent and fluctuating nature of renewables [9, 10]. Hybrid power systems comprise of distributed generator resources (renewables like solar, wind, small-scale hydroelectric power and geothermal or conventional i.e. diesel/petrol generators), energy storage facilities (batteries, loads, and energy control), bus bars, and distribution networks [11]. These combinations can reduce environmental pollution, lower the costs, and optimize the size of the system components, thereby reducing operation costs and ensuring access to affordable, reliable, and sustainable forms of energy [9, 12]. Given their potential, the number of hybrid energy systems has grown significantly from an estimated 0.2 million to 1.4 million across Africa and from approximately 3 million to 8.8 million across Asia between 2008 and 2016 [9].

Despite the existence of several renewable energy sources, most developing countries have prioritized solar energy within their hybrid systems because of its worldwide availability [9]. The major hybrid solar diesel energy systems (HSDES) installed in developing countries include; a) 100 kWp HSDES in Sandwip Island (Bangladesh), b)1 MW HSDES in Bamiyan (Afghanistan), c) 216 kWp HSDES in Ouélessébougou (Mali), d) 10 kW HSDES in Tanzania, e) 202 kW and 20 kW HSDES in Tsumkwe and Gobabeb respectively (Namibia) and f) 1.6 MW HSDES on Bugala Island in Uganda [9]. Although, there are varieties of hybrid solar energy systems with renewable or conventional source combinations [10], this study focused on HSDES which consists of Photovoltaic (PV) panels, diesel generator/s, inverters, battery bank, alternating current (AC) and direct current (DC) buses, and smart control system to ensure that the amount of hybrid energy matches the demand [13].

Of late, HSDES have attracted significant attention from various scholars due to their potential in providing electricity in rural and remote island communities. One study analysed the techno-economic potential of renewable energy hybrid systems on various global small islands [14]. Another study has been conducted on the islands of Lake Victoria, Uganda focusing on the utilization of hybrid solar systems to meet irrigation energy requirement [6]. Besides, a review study by Come Zebra and colleagues also indicates that several studies have been conducted relating to energy management structure, techno-economic performance, adequate utilization of resources, and the size optimization of hybrid systems [9]. Despite the rising interest in HSDES on islands, there are still key challenges for their successful implementation as shown in various studies. For instance, a study conducted on Malaysian islands revealed that the highly fluctuating diesel price made HSDES uneconomical especially in isolated rural poor areas [15]. While on Maldives islands, studies have shown that scaling up hybrid solar energy systems is still challenged by their high initial costs, insufficient financial resources, limited technical capacity, and a lack of understanding of the economic feasibility of the deployment of a renewable system [16, 17]. Review studies on hybrid renewable energy systems by [9, 18] also provide a comprehensive analysis of the most critical barriers to effective implementation of hybrid systems on various islands including inappropriateness of technology, unavailability of skilled manpower for maintenance, unavailability of spare parts, high cost, and unfair energy pricing among others. Moreover, the Pacific Small Independent Developing States also experience similar challenges identified by [18] on top of limited availability of land, remoteness, costly infrastructure, socio-cultural impediments and the frequent cyclones which further restrict the use of HSDES [19–21].

It is evident from the reviewed literature that a good number of studies have covered various policy, economic, social, technical and environmental barriers hindering the installation, power generation, operation and scaling up of HSDES. However, a careful assessment of these prior studies reveals several knowledge gaps. First, these studies focus on single island countries or islands of different countries with varying socio-economic backgrounds, with no explicit comprehensive optimal analysis of HSDES on Bugala Island. Second, these studies do not offer clear evidence of the extent to which HSDES have successfully been integrated into different communities [9], including Bugala Island. Third, to the best of our knowledge, no study addresses the existing challenges associated with using electricity generated from HSDES based on the end-users perspective on Bugala Island. Figuring out the end-users’ perceived challenges associated with electricity generated from HSDES is an important aspect to consider, because community acceptance, scaling up, and the sustainability of HSDES depend on users’ satisfaction [9, 22]. Although not all challenges given by the end-users of electricity on Bugala Island are necessarily equally relevant, all their arguments regarding the HSDES should be taken seriously. However, the challenge is on how to combine multiple views from various individuals with certainty.

In this study, we proposed a sequential Bayesian Belief Network (BBN) approach, which is efficient when modelling uncertain and complex issues associated with community involvement [23]. A BBN is a directed acyclic graph made of the ‘parent’ and ‘children’ nodes connected by edges with a direction associated with them with no feedback loops [24]. The BBN nodes contain mutually exclusive states (i.e. categorical, boolean, continuous or discrete) and are linked by probabilities (i.e. priori or unconditional, conditional and posterior probabilities) to describe a network of complex interactions [24, 25]. BBN models have several advantages over traditional statistical models. BBNs are (1) highly transparent, (2) flexible in modelling causal relationships, (3) capable of integrating information from various sources (i.e. experimental data, historical data, and expert opinion); (4) have the potential to explicitly handle uncertainties and missing data. Because of their versatility, BBNs have been successfully been used in various renewable energy research including modelling onshore, and offshore wind energy sectors [26] and forecasting renewable energy potentials [27]. A detailed review on BBN modelling in renewable energy systems also indicates that various studies have utilised the BBN models to evaluate renewable energy resources, fault detention, maintenance, operation, planning, sizing, renewable energy market assessments, and risk management in energy systems [28]. However, BBN models have not been used to understand the challenges associated with HSDES on Bugala Island and other islands elsewhere.

With a focus on HSDES on Bugala Island, the objectives of the study were to: 1) develop a novel, and effective knowledge based BBN model to examine the challenges associated with using electricity generated from HSDES based on the perspective of end-users; and 2) predict and rank the challenges experienced by users of hybrid electricity on Bugala Island. Our contribution to the literature on hybrid energy systems is three-fold. First, this is the first study to provide a probabilistic approach to combine human perceptions, and reasoning as well as quantifying the uncertainties from a diverse set of respondents regarding the challenges associated with electricity generated from the HSDES. The presented approach turns conceptual value-thinking of electricity end-users into a quantitative format. The graphical representation of the developed BBN model makes it easy to visualize and communicate the results. Second, since human reasoning, and perceptions about the challenges associated with electricity from HSDES are complex, the developed BBN model is able to handle uncertainties caused by imperfect understanding of the challenges, contradictory knowledge among the energy users and incomplete knowledge. Third, this study is also the first to use a BBN model to predict, and rank the challenges experienced by users of hybrid electricity on Bugala Island. Ranking, and prioritising challenges is crucial because it helps to allocate resources for targeted interventions within the constraint of limited funding.

Study area

The study was conducted on Bugala Island in Kalangala district (Fig. 1), an Island district located on Lake Victoria with an estimated population of 54,293 people [29]. The district is situated in South western Uganda between longitudes 32^o01' East and 32^o52' East and latitudes 0^o10 South and 1^o00' South [6]. The district is made up of 84 islands widely scattered in Lake Victoria over a total area of 9,066.8 sq. km, of which 432.1 sq. km (4.8%) is land and the rest is water mass. Bugala Island being the biggest Island in the district, was chosen for this study. Within Bugala Island, Kalangala Town Council and Mugoye sub-county were purposively selected for this study because; Mugoye is where the HSDES plant is located, while Kalangala Town Council has the highest number of electricity users on the Island. The HSDES managed Kalangala Infrastructure Services (KIS) has a generation capacity of 1.6Mw arising from 2832 solar panels and 3 generators. There are two alternative transport routes to access the district; 1) through Bukakata (i.e. an inland port in Masaka district) to Luku (i.e. an inland port in Kalangala district) using the Bukakata- Luku Ferry and 2) via the Northern route i.e. from Entebbe (Nakiwogo Landing site), where steamer/ferry services operated by MV Kalangala dock at Lutoboka Landing site. Other private services can be accessed at Kasenyi and Kitubulu landing sites, in Wakiso district and these provide major gateways into the district using private means of water transport.

Application of the BBN modelling approach to the study problem

This study followed well established the guidelines and protocols for developing BBN models [30, 31]. In this study a comprehensive survey of relevant literature on the challenges associated with hybrid renewable energy was conducted. The search for publications followed well established criteria by Wondimagegn Mengist, and colleagues [32], and the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines [33]. First, the searching strings, and terms were determined [i.e. “Renewble energy” AND “Islands”, “Hybrid solar energy” AND “Islands”, “Hybrid solar energy” AND “Challenges”, etc.] to obtain publications relevant to the study. The search was done in four internationally recognised databases most relevant for the study: MEDLINE (Pubmed®), EMBASE®, Scopus®, and Web of Science®. Google scholar, and Mendeley search engines were also used to obtain more relevant literature not covered in the databases. Second, the publications extracted for review, were only those, which met the following criteria. Papers:

published in scientific peer-reviewed journals
written in the English language
with predefined keywords existing as a whole or atleast in the titles, keywords or abstract section of the papers.
with relevancy to the African and Ugandan islands
accessible
not duplicated within the searched publications.

After the rigorous screening, 14 publications [1, 8, 11, 12, 17, 18, 20, 21, 34–39] met the above criteria, downloaded, and later imported in Mendeley referencing software for review. Based on the reconnaissance study done on Bugala Island in February 2022, and a review key studies, we selected 12 key challenges (i.e., variables) relevant to the Bugala Island, and these were we organized into an influence diagram (Fig. 2) based on our previous BBN modelling experience [40–42].

Household survey

A household survey was conducted between March and July 2022. The survey utilized a cross-sectional research design to obtain an in-depth, multi-faceted understanding of socially constructed multiple realities about the challenges associated with HSDES from the perspective of electricity end-users on Bugala Island. As per the KIS records, the total number of electricity users on Bugala Island was 4715, of these, 2109 consumers were located in Mugoye and 2606 located in Kalangala Town Council. These consumers were put into Microsoft excel to randomly sample households that used electricity. Random sampling technique was used to obtain unbiased and representative sample. A sample size of 237 households (i.e. 124 households from Kalangala Town Council, and 113 households from Mugoye Subcounty) was determined based on Krejcie and Morgan equation [43] as shown below

s = X² NP(1- P) ÷ d² (N – 1) + X² P(1 - P)

Where:

s = required sample size

X² = table value of Chi-square for 1 degree of freedom at the desired Confidence level (3.841).

N = population size

P = the population proportion (assumed to be 0.5 since this would provide the maximum sample size).

d = the degree of accuracy expressed as a proportion (0.05)

Data was collected using a questionnaire to capture all the identified variables shown in Fig. 2. Questions for each variable (i.e. challenge) were designed to solicit discrete responses (i.e. ‘high or ‘low’ or ‘yes’ or ‘no’) from the respondents. The questionnaire was designed in the Kobo Toolbox, an Open Data Kit (ODK) application used for data collection. The choice for automated data collection exercise was justified by its cost-effectiveness, reduced survey and data processing time, elimination of data entry errors, incorporation of completeness and consistency checks as well as its ability to capture photos and geo-locations. Before the Kobo designed questionnaire was used, it was first tested for its reliability and validity using the Cronbach’s Alpha Coefficient and Kaiser-Meyer-Olkin (KMO) and Bartlett tests respectively. The reliability test results (i.e. Alpha = 0.828) and validity test results (KMO = 0.841) were greater than 0.7 cut-off, which is deemed acceptable for further analysis.

Model development and parameterization

The influence diagram (Fig. 2) was turned into a BBN model. Data collected from household survey was used to structure and parameterize the BBN model using Netica software 6.09 (Norsys Software Corp. Vancouver, Canada). Variables in each node of the BBN model were parameterized into categorical states (beliefs) (i.e. ‘high’ and ‘low’ or ‘yes’ and ‘no’) to accommodate values. In the structured BBN model, “parent” nodes fed into “child” nodes, and following through the network, some “child” nodes became “parents” of others. The states were limited to two levels to have manageable conditional probability tables (CPT) [44] while obtaining the desired precision and prediction of estimates that captured the corresponding range of input values [25].

Model calibration

A household survey data file containing a total number of households (n = 237) was turned into a casefile in a Microsoft Excel format recognized by Netica software. A train and test approach was used to quantitatively evaluate the developed BBN model. Using the K-fold partitioning approach (K = 2), the casefile (n = 237) was randomly partitioned into a training portion (70%, n = 165) used to populate the model and test dataset (30%, n = 72), with which accuracy was assessed [45, 46]. A 70/30 data split is among the standard partition ranges recommended for model calibration, and testing [47]. The portions were generated using JMP 13 software (JMP Statistical Discovery LLC, North Carolina, USA). The vertical lookup (V-lookup) function in Excel was used to extract the randomly partitioned portions from the main casefile (n = 237). The K 2-fold partition was used to simplify the calibration exercise and to avoid a large correlation associated with numerous training sets when the actual sample was small. The training dataset was entered into the BBN model as findings. Learning the conditional probability tables (CPTs) was based on expectation maximization (EM) learning algorithm, a robust technique which automatically updates initial parameter estimates by fitting the casefile data to the final model [44].

Model validation and evaluation

The accuracy of the BBN model was evaluated using metrics of sensitivity and predication performance [25]. In the sensitivity analysis, variables that had the most influence on ‘level of challenge’ and the causal relationships of importance were identified using the mutual information (entropy reduction) values. Mutual information represents the symmetric between two nodes, and is a measure of magnitude with which a finding at one node (findings or explanatory node) is expected to alter the beliefs (measured as entropy reduction) at another node (the query node) [25]. The function of ‘sensitivity to findings’ in Netica software was invoked on the output node (i.e. level of challenge) to calculate the entropy reduction for other variables in the network and the results were expressed as a percentage of the total entropy of the query output node.

Under the predication performance, the randomly generated test dataset (30%, n = 72), was used to evaluate model accuracy using the ‘test with cases’ function of Netica software. Three standard test metrics were used to evaluate model performance [25]. First, a confusion matrix was used to test the model’s ability to predict both high, and low challenges associated with HSDES correctly. Finally, the error rate, and scoring rules of logarithmic loss, quadratic loss, and spherical payoff were used to determine the classification and prediction ability of the model. For logarithmic loss (0-infinity) and quadratic loss (0–2) ranges, scores close to zero are considered to be better, while 1, indicates the best model performance for spherical payoff (0–1) [25, 48].

Bayesian belief network model

The developed knowledge based BBN model is shown in Fig. 3 and is based on the data which was collected from the hybrid electricity users on Bugala Island.

The model demonstrates a joint probability distribution of variables that are shown as nodes and linked with arrow. The output node (i.e. level of challenges) shows a collective effect of all variables expressed as posterior conditional probabilities. The model has an error rate of 18.31% implying that it has an overall accuracy of 81.69% to predict the level of challenges correctly. (i.e. high and low). Other model performance are presented in Table 1.

Table 1

A confusion matrix showing the model performance results.
	Actual High	Scores	Actual Low	Scores	Total
Predicted High	TH	13(18.3%)	FH	6(8.5%)	19(26.8%)
Predicted Low	FL	7(9.9%)	TL	45(63.4%)	52(73.2%)
Total (Test dataset)		20(28.2%)		51(71.8%)	71(100%)
Performance	Sensitivity TH/TH + FL	0.65(65%)	Specificity TL/TL + FH	0.88(88%)
Scoring Rule Results
	Logarithmic loss	0.3313
	Quadratic loss	0.228
	Spherical payoff	0.8688
Model Error rate		18.31%

TH: True ‘Highs’, FL: False ‘Lows’, FH: False ‘Highs’ and TL: True ‘Lows’

The scoring rule results illustrate the model's strong predictive power with both the logarithmic loss (0.3313) and quadratic loss (0.228) scores close to zero. The spherical payoff score of 0.8688 indicates an excellent model performance. According to our model output results (Fig. 3), the probability of electricity users on Bugala Island to experience no high challenges is 30.6% while electricity users with low challenges stand at 69.4%. Although BBNs have been used extensively in analyzing renewable energy systems [28], they have not been used to examine the challenges associated with the HSDES generated electricity from the consumers' perspective. This study represents one of the first efforts to fill this critical void. In this proposed framework, the graphical BBN model is used to summarize the results in a visually attractive and easy-to-analyse format. The challenges presented here can help the HSDES managers to create comprehensive energy management plans when multiple challenges overlap. Although knowledge about public perceptions and reasoning about the challenges associated with HSDES does not guarantee acceptance or adoption, its absence is likely to result in failure [36]. The graphical tool can also help the electricity users on Bugala Island to learn about each other's challenges. This can help the community to familiarise with the challenges and this can eventually improve on the uptake of specific energy technologies to solve a given a challenge [36].

Ranking and predicting the challenges associated with HSDES generated electricity on Bugala Island

To identify the contribution of each challenge on the model output, sensitivity analysis was performed. Sensitivity analysis is a useful technique that shows which variable gives the most accurate information about the existence of the target outcome node [25]. By calculating the effect of small changes in conditional probabilities of variables on the output variable (i.e., posterior probabilities), sensitivity analysis could identify and rank the critical factors having the most significant effects on the target nodes in BBN. With level of challenge as the target node in the BBN model (Fig. 3), the sensitivity resul ts were ranked as shown in Table 2. The results mutual information and entropy reductions expressed as percentages.

Table 2

Sensitivity analysis results ranked in decreasing order of influence on the outcome node based on mutual information and entropy reduction
Nodes	Mutual Information	Entropy reduction (%)	Variance of beliefs
Cost of maintaining appliances	0.01811	2.04	0.0051744
Rate of damage of electric appliances	0.01367	1.54	0.0043798
Cases of faulty electric meters	0.00961	1.08	0.0029985
Cost of power connection	0.00851	0.96	0.0024791
Unit cost of electricity	0.00668	0.75	0.0020804
Cases of electrocution	0.00441	0.49	0.0013988
Load shedding levels	0.00316	0.36	0.0009438
Service fee	0.00229	0.26	0.0006949
Inadequate access to energy saving equipment	0.00113	0.13	0.0003409
Voltage level	0.00033	0.04	0.0000980
Inadequate electricians	0.00028	0.03	0.0000819
Incidences of illegal connections	0.00012	0.01	0.0000343

From Table 2, the cost of maintaining appliances is the most significant factor causing the largest entropy reduction (2.04%) on the level of challenges associated with electricity from HSDES. Rate of damage of electric appliances and cases of faulty electric meters also show a strong conclusive influence on the level of challenges with more than 1% entropy reduction values each. These are followed by other challenges in their decreasing order of importance as shown in Table 2. This study represents one of the first efforts to rank the critically localized challenges associated with using HSDES generated electricity on Bugala Island using a BBN modeling approach. Studies have shown that public perceptions and responses can serve as a check on new energy technologies with potentially risky outcomes [36]. The sensitivity analysis results show the key challenges that should be prioritized and where resources should be allocated to achieve optimum coverage of hybrid electricity on Bugala Island. Since renewable energy managers usually have limited resources at their disposal [28], prioritizing and optimizing resource allocation can greatly help in achieving the objectives of supplying hybrid electricity on Bugala Island.

To estimate the contribution of each challenge to the outcome node, we performed a scenario analysis using the develop BBN model in Fig. 3. In the scenario analysis, we focused on the outcome node where it is ‘High’ state belief was tagged to 100% to reveal the estimated changes as shown in Table 3. Further in Table 3, changes in beliefs were used to calculate percentage point differences for each independent variable to express the predicted challenges associated with the HSDES generated electricity. A positive percentage point difference meant that households were more likely to experience a “High” challenge associated with HSDES generated electricity. A negative percentage point difference meant households were less likely to experience a “High” challenge associated with the HSDES generated electricity.

Table 3

Predicted changes in belief of states when a “High” state finding in the outcome node (i.e. level of challenges) was made 100%.
Nodes and states	Initial state-beliefs^a	New state-beliefs^b	Changes in beliefs^c	Percentage point change
Level of challenges
High	0.30588	100
Low	0.69412	0
Cost of maintaining appliances
High	0.38542	0.27096	-0.114	-11.4
Low	0.61458	0.72904	0.114	11.4
Rate of damage of electric appliances
High	0.072829	0.22905	0.156	15.6*
Low	0.92717	0.77095	-0.156	-15.6
Cases of faulty electric meters
High	0.12064	0.37895	0.258	25.8*
Low	0.87936	0.62105	-0.258	-25.8
Cost of power connection
High	0.44931	0.46835	0.019	1.9*
Low	0.55069	0.53165	-0.019	-1.9
Unit cost of electricity
High	0.89781	0.95264	0.055	5.5*
Low	0.10219	0.04736	-0.055	-5.5
Cases of electrocution
High	0.041881	0.06637	0.024	2.4*
Low	0.95812	0.93363	-0.024	-2.4
Load shedding levels
High	0.3143	0.36092	0.047	4.7*
Low	0.6857	0.63908	-0.047	-4.7
Service fee
High	0.87868	0.85055	-0.028	-2.8
Low	0.12132	0.14945	0.028	2.8
Inadequate access to energy saving equipment
Yes	0.09119	0.10857	0.017	1.7*
No	0.90881	0.89143	-0.017	-1.7
Fluctuating voltage level
High	0.81157	0.20109	-0.610	-61.0
Low	0.18843	0.79891	0.610	61.0
Inadequate electricians
Yes	0.07278	0.06596	-0.007	-0.7
Low	0.92722	0.93495	0.008	0.8
Incidences of illegal connections
High	0.075711	0.08078	0.005	0.5*
Low	0.92429	0.91922	-0.005	-0.5

^a Represents the initial state belief probabilities for each challange in the BBN model

^b Reflects new state belief probabilities for the challenges when a positive state belief finding in the output node of the BBN model was made 100%.

^c Indicates the predicted relative changes in probabilities from the initial to new state-beliefs.

* Represents the actual challenges

Table 3 provides the first attempt to estimate the contribution of each variable to the level of the challenges associated with the HSDES generated electricty. The changes in beliefs reveal that the cost of maintaining appliances, service fee, voltage level and inadequate electricians decreased the level of challenges associated with the electricity generated from the HSDES as depicted by the negative percentage points (Table 3). However, the rate of damage of electric appliances increased the level of challenges associated with the HSDES generated electricity by 15.6 percentage points (from 7.3–22.9%). This challenge may persist on Bugala Island given that most technicians are located on the mainland, especially in urban areas [34]. During the field work study, it was observed that whenever appliances got damaged on the Island, they were abandoned because the people did not know the right people to consult. This finding is in-line with other studies. For example, a study conducted on the Islands of Bangladesh reveal that whenever households got a technical challenge on their solar systems, they immediately replaced them with new ones, because the Islands lacked technically skilled persons to repair them [49]. In such situations, households unable to buy new ones may end-up sticking to their conventional energy sources while missing out on the potential benefits and opportunities offered by solar energy [34].

Table 3 provides further evidence that cases of faulty electric meters resulted in a 25.8 percentage points increase (from 12.1–37.9%) in the level of changes. Results of both faulty meters and damage of electric appliances are not surprising, since there are inadequate enforcement mechanisms to monitor the quality of electric appliances including solar PV systems’ components and kits on the Ugandan market [5]. This problem coupled with rampant corruption, lack of suitable trained professionals, and the necessary equipment to assess the quality electric appliances, has resulted in an influx of dealers who import, smuggle and sell poor quality electric appliances to various parts of the Uganda including islands. The problem of poor quality products especially solar lights and controllers, has also been reported in the study conducted on the Islands of Bangladesh [49]. To make matters worse, most of the electric appliance users in Uganda are unable to distinguish between the counterfeit and good quality products found on the market [34]. Even though these poor quality products may initially be cheap, they tend to become more expensive over time through additional repairs and replacement which could negatively affect the consumers' attitude towards their use. If the challenge of poor electric appliances on the Ugandan market is not holistically addressed, this will negatively influence the adoption of solar energy systems in Uganda including Islands. Elsewhere, it has been observed that the rising counterfeits and pirated solar related products, represent a major obstacle to the widespread use of solar energy in Ghana, Kenya and South Africa and the rest of African countries [37].

Additionally, the changes in beliefs further reveal that the unit cost of electricity and the cost of power connection also increased the level of challenges associated with use of HSDES generated electricity by 1.9 percentage points (from 44.9–46.8%) and 5.5 percentage points (from 89.8–95.3%) respectively. The unit cost of electricity (i.e. 0.221 U.S. Dollar per kWh for households and 0.246 U.S. Dollar per kWh for businesses or commercial use)¹ on the Island was expensive because of the high costs of diesel (1.384 U.S dollars per litre) which was used in the hybrid solar energy system to generate power. Additionally, such high tariffs could be attributed to a small market size on the Island and lack of competition given that KIS is a sole manager of the Island's electricity from generation, transmission, distribution, and selling. Such monopolistic situations tend to cause a rise in prices of products. Moreover, the unit cost of electricity on the Island appeared to be more expensive than that of hydroelectric power (i.e. 0.164 U.S. Dollar per kWh for households and 0.119 U.S. Dollar per kWh for businesses) used on the mainland. The inability to afford payment has been singled out to limit the widespread use of solar energy among various African countries [37]. Incidences of faulty meters made it difficult for most households to pay electricity bills as many lost the trust in their billing capability.

The high connection costs could have been attributed to two factors. First, all Uganda’s electricity projects are highly capital-intensive investments and require huge initial financial resources which have been catered for by external debt/loans [38] and such loans are supposed to be paid back with interest. Besides, the HSDES on the Island has high operations and maintenance expenditures relating to metering, network faults, network expansions, new customer connections, and environmental impact mitigation interventions. Thus, both the cost recovery needs and the direct costs associated with the loans which was used to establish the HSDES plant on the Island, have a bearing on the cost of connections. Similar observations have been made in rural Kenya, where high transaction costs have been linked to managing a large network of small-scale solar energy installations within a highly dispersed customer base [37]. Second, the unfavorable tax regimes levied on various solar components (i.e. solar modules, solar chargers, control units, inverters, solar PV cables, and batteries among others) might also have prompted KIS to raise the connection costs. These taxes include import duty (25%), withholding tax (6%), value added tax (18%) and infrastructural levy (1.5%) [5]. Suppose such high taxes are not reduced or exempted, they will continue to act as additional and discouraging costs on solar energy investment and installation not only on Bugala Island but Uganda in general.

Cases of electrocution increased the level of challenges associated with the use of hybrid electricity by 2.4 percentage points (from 4.2–6.6%). This challenge could have been attributed to lack of information and public awareness [5] about the dangers of electricity. Meanwhile, load shedding also increased the level of challenges by 4.7 percentage points (from 31.4–36.1%). Although load shedding was a concern among electricity users, on the side of KIS management, it was a deliberate disconnection of electrical power and was used as a preventive measure to maintain system balance when supply was expected to be short of the amount needed to serve the entire Bugala Island. During load shedding, small amounts of electricity were rationed to some segments of consumers while allowing bigger electricity loads to continue to be served to essential services like health centres and hotels. Although load shedding was undesirable among consumers, the anticipated, controlled and limited use of this extreme measure should be seen as an instrument to maintain security of energy supply. However, load shedding should not be frequent because higher rates of load shedding over a given period signifies non-resilient and unreliable electricity supply system which is not cable to satisfy peak load and electricity demands [38].

Finally, the changes in beliefs reveal that inadequate access to energy saving equipment and incidences of illegal connections also increased the level of challenges by 1.7 percentage points (from 9.1–10.9%) and 0.5 percentage points (from 7.6–8.1%) respectively. The challenge of illegal connections on the Island is not surprising. In Uganda, power thefts is a well-known crime executed by electricity customers with the help of power distribution employees who ‘tap’ electricity by hooking unauthorized wires to electricity distribution cables, and tempering with power billing meters [38]. Continued illegal connections on Bugala Island will affect the Island’s electricity security on two fronts: First, illegal connections will cause low voltage levels as well as interfering with the reliable supply of hybrid electricity to legitimate customers. Second, it will cause economic loss to KIS, power supply disruptions, and adversely affect system reliability in the long run. Thus, more punitive measures are urgently required to reduce illegal connections and increase electricity security on the Island.

In this study, we have applied a BBN modelling approach to combine challenges experienced by the hybrid electricity users on Bugala Island in an integrated format. This is the first attempt to use a probabilistic approach to quantify and visualize the variability in the challenges associated with using HSDES generated electricity. The developed model can to be used as a decision support tool to prioritize and solve the identified challenges. Results of the sensitivity analysis indicated that the cost of maintaining appliances was the most significant factor causing the largest entropy reduction (2.04%) on the level of challenges associated with using HSDES generated electricity. Rate of damage of electric appliances and cases of faulty electric meters also showed a strong conclusive influence on the level of challenges with more than 1% entropy reduction values each. The sensitivity analysis results highlight and rank key priority challenges which require urgent monitoring and strategic interventions. The scenario analysis results also show the estimates of each variable to the level challenges. Some limitation of this study should be noted. Admittedly, a single case within the context of Bugala Island is not enough to cover other Islands’ prevailing situations. Challenges could defer from one place to another due to varying geographical and economic prevailing situations. Nevertheless, this study still provides a new research perspective and methodology, which are of considerable significance to other Island countries experiencing a fast growth in hybrid energy systems. Future research can further explore the demographic and social-economic determinants influencing the use of HSDES generated electricity on Bugala Island. Other studies may focus on combining BBN and geographical information system to model the spatial extent of HSDES generated electricity on Bugala Island.

AC: Alternating current; BBN: Bayesian belief network; DC: Direct current; HSDES: Hybrid solar-diesel energy system; KIS: Kalangala Infrastructure Services; SDGs: Sustainable Development Goals; PV: Photovoltaic.

Ethics approval and consent to participate

This study was conducted in accordance with the ethical principles stated in the Helsinki Declaration. During data collection, the informed consent of eligible respondents was sought before starting the interviews. The datasets used was fully anonymised.

Consent for publication

Not applicable.

Availability of data and materials

Data will be provided on request

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

This work was supported by the NORHED II Project (2021 - 2026): ‘Capacity Building for Socially Just and Sustainable Energy Transitions in East Africa (SET Project)’

Authors' contributions

P.K. contributed to conceptualisation, data collection, formal analysis, preparation, revision and editing of the original draft. H.M.S. participated in conceptualisation, methodology, developing and validating the BBN model, drafting and revising the original draft and supervision. H.W, F.M, P.I.M, helped with the project administration, conceptualisation, revision and editing of the manuscript. All authors approved the final manuscript. All authors read and approved this version of the manuscript.

Acknowledgements

The authors are grateful to the management of Kalangala Infrastructure services, the residents of Kalangala Town Council and Mugoye sub-county, the technical staff, and the political leadership of Kalangala local government who provided the necessary information and support for this study.

Authors' information

¹Department of Geography, Geo-informatics and Climatic Sciences, Makerere University, P.O Box 7062, Kampala, Uganda.

Endnote

¹One US dollar was equivalent to 3,700 Uganda shillings when data collection was conducted in March 2022.

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Bayesian belief network modelling of the challenges associated with hybrid solar-diesel electricity from the end users’ perspective in Bugala Island in Uganda

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Application of the BBN modelling approach to the study problem

Household survey

Model development and parameterization

Model calibration

Model validation and evaluation

Results and discussion

Bayesian belief network model

Ranking and predicting the challenges associated with HSDES generated electricity on Bugala Island

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