Harnessing Ocean Wave Energy to Assess Oscillating Water Column Efficiency in Indonesian Waters

Energy is a fundamental necessity that supports a wide range of human activities across the globe. As the population grows and economic activities become more complex in the modern era, the demand for energy continues to rise steadily [1]. Population growth and national economic development are key drivers of rising energy consumption in Indonesia [2]. Most homes and facilities used daily require electrical equipment.

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As a result, electricity use in Indonesia is increasing in line with population growth and advances in information and technology. Figure 1 is a pie chart of the wave type variable. Data from the Ministry of Energy and Mineral Resources (ESDM) shows that electricity consumption in 2023 rose to 1,337 kWh per capita, marking a 13.s98% increase from 2022’s figure of 1,173 kWh per capita [3]. Energy sources for electricity generation consists of new renewable energy sources 1.8% (Ministry of Energy and Mineral Resources).

Indonesia’s energy consumption remains heavily reliant on non-renewable sources, particularly fossil fuels, which still surpass renewable energy usage [4, 5]. This is a severe concern for the sustainability of energy supply in the future. 

The ocean is renewable energy source, and innovations in current ocean [6-8] energy technology offer the potential to reduce carbon dioxide emissions from electricity generation. This makes it a viable option for long-term, sustainable energy solutions [6, 9].

Indonesia, an archipelago nation with over 17,000 islands and about 65% ocean coverage, has more ocean than land. This provides a substantial opportunity to harness wave energy as tidal energy [10].

A notable advantage of Indonesia's unique geographical characteristics is its extensive coastline of approximately 81,000 km, consistent wave height patterns, and locations with gently sloping seabed topographies, which make it an ideal case for Oscillating Water Column (OWC) technology. A key strength of the region lies in the untapped wave energy potential, which could be efficiently extracted in areas such as East Nusa Tenggara, Central Sulawesi, and other coastal zones, using advanced technologies like OWC. It is now well established that Indonesia's position within the Pacific Ring of Fire and monsoonal wind patterns contributes to a predictable and renewable source of ocean wave energy, offering a sustainable energy solution.

The abundance of ocean area underscores the critical role of wind-driven wave data, which is essential for supporting maritime operations such as determining shipping routes, forecasting ocean hazards, and conducting scientific studies on ocean mixing and air-sea interactions. Additionally, wave energy from Indonesia’s oceans holds promising potential as a renewable energy source for the nation [11].

In economic perspective, the utilization of OWC technology can reduce dependence on fossil fuels, decrease carbon emissions, and provide cost-effective solutions for energy generation in remote and underdeveloped regions, where grid connectivity is limited but wave energy is abundant.

Ocean energy in Indonesia is seen as a promising form of renewable energy [6, 12-15] with the potential to significantly contribute to the global energy mix [6, 16].

Currently, various technologies have been developed for ocean wave power plants, including buoy systems, overtopping devices, and OWC technology [10, 17-22]. OWC technology is well-suited for coastal areas with gently sloping seabed topography and consistent wave height [23]. The suitability of OWC technology for Indonesian waters has been proven through studies in areas such as East Nusa Tenggara, Central Sulawesi, Pantai Baron in Yogyakarta, and Binongko Island in Wakatobi, Southeast Sulawesi. These studies show that OWC technology can efficiently harness wave energy in a variety of environmental conditions.

Previous research conducted in regions such as East Nusa Tenggara [23], Central Sulawesi, Pantai Baron, Gunung Kidul DI Yogyakarya [24], and Binongko Island, Wakatobi, Southeast Sulawesi [25], the OWC technology has been utilized to analyze ocean wave energy potential, leading us to select this technology for analyzing Indonesian waters.

There is a growing body of literature that recognizes the importance of identifying the specific factors influencing the potential power of ocean waves in Indonesia. However, a comprehensive statistical framework is still needed to accurately model this potential and understand the relationship between wave power potential and its determining factors.

This study uses data that is secondary data obtained from the official website of the Indonesian Maritime Meteorology, Climatology, and Geophysics Agency (BMKG) in 2024. Then in this study using the Generalized Linear Model, this is because based on the results of the Cullen and Frey graph, it can be concluded that greenhouse gas emissions are not normally-distributed but are exponentially distributed, tending to the gamma or beta distribution. If the data is not normally distributed, one of the capitals that are robust against data that is not normally distributed is the Generalized Linear Model, besides that the GLM is also robust to estimate parameters with a relatively very small number of samples [26].

The secondary data from the Indonesian Maritime Meteorology, Climatology, and Geophysics Agency (BMKG), which includes wave type, average wind speed, and weather is incorporated as key predictors in the GLM. This data is analyzed to understand its impact on the ocean wave power potential, especially considering its exponential distribution nature, as indicated by the Cullen and Frey graph. The GLM was selected because it effectively handles non-normally distributed data, such as the gamma distribution, making it a robust approach for analyzing energy potential in datasets with small sample sizes or skewed distributions. By using this model, the study identifies significant factors influencing ocean wave power potential and evaluates their predictive power through maximum likelihood estimation and RMSE-based validation. Figure 2 is the weather variable.

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Figure 2. Cullen and Frey plot

The objectives of this research are to determine whether ocean wave power potential in Indonesian waters can be effectively analyzed using statistical modeling techniques, to identify and quantify the factors influencing wave energy potential through regression analysis, and to evaluate the suitability of OWC technology in the context of Indonesia's diverse marine topography and wave characteristics. This study seeks to obtain data which will help to address these research gaps and enhance understanding of the untapped potential of ocean wave energy as a renewable energy source for Indonesia.

This article presents a novel approach by focusing on the impact of wave types on the potential power generation in Indonesia's unique maritime conditions. Unlike previous studies that broadly assess wave energy potential, this study employs a Gamma Regression model to capture the non-linear relationship between wave types and power potential. Additionally, the analysis incorporates detailed local data on wave types and weather conditions, providing a more tailored model for coastal areas in Indonesia. This research not only contributes to theoretical advancements in wave energy modeling but also offers practical recommendations for optimizing OWC systems in regions with diverse wave climates.

3.1 Ocean wave power potential

The sea wave power plant (PLTGL) OWC method generates electricity by using seawater wave power. MWPP has a working principle: converting sea wave energy (mechanical energy) into electrical energy. The collected sea wave energy rotates the turbine connected to the generator, thus producing electrical energy.

The potential power generated by ocean waves is obtained from mathematical calculations involving several main factors, namely wave height (H), wave period (T), and wavelength (λ). The wave period (T) value can be calculated using the following formula:

$T=3.55 \sqrt{H}$            (1)

Calculations are carried out to find the wavelength value after obtaining the wave period value. The earth’s gravity value is 9.81 m/s² .

$\lambda=\frac{g}{2 \pi} T^2$           (2)

To obtain the total energy value generated by ocean waves, the following formula is used:

$E=\frac{1}{2} \times w \times \rho \times g \times a^2 \times \lambda$            (3)

In this equation, $E$ represent the total energy (in joules), $w$ is the angular frequency of the wave measured in radians per second (rad/s), and $\rho$ denotes the density of seawater, typically in kilograms per cubic meter (kg/m³). The variable $g$ stands for gravitational accelation, approximately, while $a$ represents the wave amplitude, which is the maximum height of the wave from its equilibrium point (in meters). Lastly, $\lambda$ is the wavelength, defined as the distance between two consecutive wave crests.

The total efficiency of the OWC system is the product efficiency of the chamber, the efficiency of the generator system. The efficiency of the chamber is the potential for ocean wave power that can be absorbed by the chamber in the OWC system [24]. Following the prototype used in Pantai Baron, Gunung Kidul, DI Yogyakarta Indonesia [24], the chamber width of the OWC was set at 2.4 meters. With an efficiency of 8%, this dimension was chosen to reflect the optimal conditions expected from the prototype.

With a seawater density of 1,030 Kg/m². After obtaining the total energy value generated, the power can be calculated using the following formula:

$P=\frac{E}{T}$          (4)

The potential power generated by the MWPP OWC method has a unit of Watts. The value of the potential power generated by this MWPP is the response variable in statistical analysis.

3.2 Types of waves

Waves are the movement of the rise and fall of seawater in a direction perpendicular to the sea surface that forms a sinusoidal movement. According to the Meteorology, Climatology, and Geophysics Agency, there are seven categories of waves, namely calm waves with a height of 0.01m – 0.5m; low waves with a height of 0.5m – 1.25m; medium waves with a height of 1.25m – 2.5m; high waves with a height of 2.5m – 4m; very high waves with a height of 4m – 6m; and extreme waves with a height of 6m – 9m [35]. Two main types of waves are generated by seismic activity: pressure waves traveling at five km/s, and shear waves traveling at one km/s [36].

3.3 Wind speed

Wind speed is a unit that measures the pressure of air flow speed from high pressure to low pressure. It is measured using an anemometer or can be classified using the Beaufort scale based on observations of the specific effects of certain wind speeds. Wind speed is critical for generating energy from wind turbines, both onshore and offshore. Since differences in wind speed affect the efficiency of energy production, it is crucial to monitor and predict wind speed to run wind turbines in the best possible way [37]. Wind speed is critical to support renewable energy, especially in hybrid energy systems that combine wind and solar power. This study shows that the wind speed of traffic flow on a highway increases the energy potential by 22% compared to natural wind, generating a total power of 552.11 watts. This potential shows that wind speeds from both natural and artificial sources can help improve the efficiency of renewable energy production [38]. Wind speed is often used in wind power generation to generate sustainable energy, as the wind moves from an area of high pressure to an area of low pressure. It is affected by differences in air pressure and temperature in different places [39].

3.4 Weather

Weather is the current condition of the atmosphere in a relatively short time in a narrow area. The Meteorology, Climatology, and Geophysics Agency state in its weather forecasts that there are ten types of weather in Indonesia, namely, sunny, partly cloudy, cloudy, light rain, moderate rain, heavy rain, thunder rain, heavy cloudy, local rain, and fog. Weather patterns consist of various atmospheric conditions, such as temperature, humidity, wind speed, and air pressure; the interaction between these conditions causes phenomena such as storms, droughts, and seasonal climate change. Natural processes and, significantly more, human activities alter atmospheric composition and temperature [40].

3.5 Generalized Linear Model (GLM)

The Generalized Linear Model is a development of linear regression models in which the distribution of the response variable belongs to the exponential distribution family [41]. In GLM the distribution form of the response variable is not required to be in the form of a symmetrical bell curve or normally distributed, but distributions that belong to the exponential family distribution, including the Poisson, gamma, binomial, inverse Gaussian, normal, and binomial negative distributions [42]. The assumption that the response has an exponential family distribution is used in this linear model [43].

GLM chosen for the flexibility in handling mixed predictor variables, including category variables coded as dummies. In this study, ability to handle both continuous and categorical predictors, including dummy variables allows GLM to capture the influence of specific categories in the model, which cannot be handled directly by ordinary linear regression

Data variables such as wave type, average wind speed, and weather derived from BMKG are incorporated into the model as predictors. This integration allows the exploration of their relationship with ocean wave power potential while addressing the challenges of data skewness and limited sample size through the gamma regression approach.

3.6 Gamma regression model

Testing the distribution of the data using Cullen and Frey plots, the ocean wave potential energy variable follows a Gamma distribution. Gamma regression is a component of the Generalized Linear Model. This ensures that the model can accurately identify complex relationship in the data. The gamma distribution is a continuous distribution introduced by Stacy in 1962, applicable to positive random variables with variable values (Y_i) in the range $(0, \infty)$.  It is widely used in various medical fields [14, 44]. When the random variable (y) follows a two-parameter gamma distribution [44].

$f(y ; \theta, \tau)=\frac{\theta^\tau}{\Gamma_\tau} y^{\tau-1} \exp \exp (-\theta y) I_{0, \infty} y \quad \tau, \theta>0$             (5)

In other terms, Eq. (1) can be rewritten as follows [44]:

$f(y ; \theta, \tau)=\frac{\theta}{\Gamma_\tau}(\theta y)^{\tau-1} \exp \exp (-\theta y) I_{0, \infty} y$           (6)

where, $\tau$ represents the shape parameter, and $\Gamma($.$)$ denotes the gamma function. With $E\left(Y_i\right)=\frac{\tau}{\theta}$ and $V\left(Y_i\right)=\frac{\tau}{\theta^2}=\mu^2\left(\frac{1}{\tau}\right)=$ $\sigma^2\left(E\left(Y_i\right)\right)^2$. The cumulative distribution function (CDF) is expressed as:

$F(y)=\frac{1}{\Gamma_\tau} \int_0^y u^{\tau-1} e^{-u} d u$              (7)

When the shape parameter $\tau$ is not fixed and instead includes a linear component, it can be modeled accordingly. This allows the gamma regression model to jointly account for both the mean and shape parameters of the gamma-distributed variable. Specifically, let $Y_i \sim G\left(\mu_i, \tau_i\right)$ for $i=1,2, \ldots, n$ [44].

Here, the linear predictor for the mean is defined as $\eta_{1 i}=$ $g\left(\mu_i\right)=x_i \beta$, and for the shape as $\eta_{2 i}=h\left(\alpha_i\right)=z_i \gamma$. The parameters $\beta=\left(\beta_0, \beta_1, \ldots, \beta_p\right)$ and $\gamma=\left(\gamma_0, \gamma_1, \ldots, \gamma_k\right)$ correspond to the regression coefficients for the means and shape, respectively. The function $g(\mu)$ serves as the link function for the mean (typically the natural link function), and $h(\alpha)$ is the link function for the shape (commonly logarithmic). The linear predictors are $\eta_{1 i}$ and $\eta_{2 i}$, with $x_i=$ $\left(x_{i 1}, \ldots, x_{i p}\right)$ as the vector of independent variables for the mean and $z_i=\left(z_{i 1}, \ldots, z_{i k}\right)$ as the vector shape.

3.7 Parameter estimation of gamma regression model

The parameters of the gamma regression model are $\theta$ and $\tau$. The parameter estimation can be done using the Maximum Likelihood Estimation (MLE) method. The MLE method can obtain consistent estimates and smaller variances that are easier to understand.

The likelihood function of the gamma regression model in equation is as follows [44].

$\begin{gathered}L=\prod_{i=1}^n f(y ; \theta, \tau) \\ L=\prod_{i=1}^n \frac{1}{\Gamma_{\tau_i}}\left(\frac{\tau_i}{\mu_i}\right)^{\tau_i} y_i^{\tau_i-1} \exp \left(-\frac{\tau_i}{\mu_i} y_i\right) \\ \log \log (L)=\sum_{i=1}^n\left\{-\log \log \left(+\tau_i \log \log \left(\frac{\tau_i y_i}{\mu_i}\right)\right.\right. \\ \left.\quad-\log \log \left(y_i\right)-\left(\frac{\tau_i}{\mu_i}\right) y_i\right\}\end{gathered}$               (8)

where, $\mu_i=x^{\prime} \beta$ and $\tau_i=\exp \left(z^{\prime} \gamma\right)$.

$\begin{gathered}\frac{\partial L}{\partial \beta_j}=\sum_{i=1}^n-\frac{\tau_i}{\mu_i}\left(1-\frac{y_i}{\mu_i}\right) x_{i j}; j=1, \ldots, p \\ \frac{\partial L}{\partial \gamma_k}=\sum_{i=1}^n-\tau_i\left[\frac{d}{d \tau_i} \log \log \Gamma_{\tau_{\mathrm{i}}}-\log \log \left(\frac{\tau_i y_i}{\mu_i}\right)-1\right. \left.+\frac{y_i}{\mu_i}\right] z_{i k} ; \\k=1, \ldots, r \quad, j \geq k, p \geq r\end{gathered}$            (9)

Through the Hessian Matrix, which is a matrix of second-order partial derivatives for a multivariable function, all possible second-degree partial derivatives of the function are represented [44].

$\begin{gathered}\frac{\partial_L^2}{\partial \beta_k \beta_j}=\sum_{i=1}^n \frac{\tau_i}{\mu_i^2}\left(1-\frac{2 y_i}{\mu_i}\right) x_{i j} x_{i k} ; j, k=1, \ldots p \\ \frac{\partial_L^2}{\partial \gamma_k \beta_j}=\sum_{i=1}^n \frac{\tau_i}{\mu_i}\left(1-\frac{y_i}{\mu_i}\right) x_{i j} z_{i k} ; k=1, \ldots r, j=1, \ldots, p \\ \frac{\partial_L^2}{\partial \gamma_k \gamma_j}=\sum_{i=1}^n-\tau_i\left[\frac{d}{d \tau_i} \log \log \Gamma\left(\tau_i\right)-\log \log \left(\frac{\tau_i y_i}{\mu_i}\right)-1\right. \left.+\frac{y_i}{\mu_i}\right] z_{i j} z_{i k} \\ -\sum_{i=1}^n \tau_i\left[\frac{\tau_i d^2}{d \tau_i^2} \log \log \Gamma\left(\tau_{\mathbf{i}}\right) -1\right] z_{i j} z_{i k} ; j, k=1, \ldots, r\end{gathered}$                 (10)

The Fisher Information Matrix was used to compute the contrast matrix corresponding to the maximum likelihood estimates of my agencies [44].

$\begin{gathered}I(\beta)=\left[-E\left(\frac{\partial_L^2}{\partial \beta_k \beta_j}\right)-E\left(\frac{\partial_L^2}{\partial \gamma_k \beta_j}\right)-E\left(\frac{\partial_L^2}{\partial \gamma_k \beta_j}\right)\right. \left.-E\left(\frac{\partial_L^2}{\partial \gamma_k \gamma_j}\right)\right] \\ -E\left(\frac{\partial_L^2}{\partial \beta_k \beta_j}\right)=\sum_{i=1}^n \frac{\tau_i}{\mu_i^2} x_{i j} x_{i k} \\ -E\left(\frac{\partial_L^2}{\partial \gamma_k \beta_j}\right)=0, k=1, \ldots, r ; j=1, \ldots, p \\ -E\left(\frac{\partial_L^2}{\partial \gamma_k \gamma_j}\right)=\sum_{i=1}^n \tau_i^2\left[\frac{d^2}{d_{\tau_i}^2} \log \log \Gamma\left(\tau_i\right)-\frac{1}{\tau_i}\right] z_{i j} z_{i k} ; j, k=1, \ldots, r \\ I(\beta)=\left[\sum_{i=1}^n \frac{\tau_i}{\mu_i^2} x_{i j} x_{i k} 0 \sum_{i=1}^n \tau_i^2\left[\frac{d^2}{d_{\tau_i}^2} \log \log \Gamma\left(\tau_i\right)\right.\right. \left.\left.-\frac{1}{\tau_i}\right] z_{i j} z_{i k}\right]\end{gathered}$              (11)

The Fisher Information Matrix is noted to be a diagonal matrix, with one block associated with the medium regression parameters and another with the shape regression parameter. This structure implies that the maximum likelihood estimators for $\beta$ and $\gamma$ are independent of each other. Consequently, the parameters of the Gamma Regression Model (GRM) cannot be estimated using conventional methods. Instead, we apply the Fisher scoring method, a repetitive algorithm similar to the Newton-Raphson method or iterative weighted least squares, using the expected value of the second derivatives matrix. This algorithm yields estimates for the parameters and $\hat{\beta}$ and $\hat{\gamma}$ [43].

$\hat{\beta}^{k+1}=\left(X W_1^k X\right)^{-1} X W_1^k Y$                  (12)

A diagonal matrix with elements along the main diagonal, denoted as $W_1^k$, contains these values.

$\begin{gathered}W_1^k=\frac{\left(\mu_i^2\right)^k}{\tau_i^k} \\ \hat{\gamma}^{k+1}=\left(Z W_2^k Z\right)^{-1} X W_2^k Y\end{gathered}$                  (13)

where, $W_2^k=\frac{1}{\tau_i^k}$.

3.8 Multicollinearity

Multicollinearity is when the predictor variables have a linear relationship or high correlation. The amount that can be used to detect the presence or absence of multicollinearity is the Variance Inflation Factor (VIF).

$V I F_j=\frac{1}{1-R_j^2}, j=1,2, \ldots, k$               (14)

with $R_j^2$ is the coefficient of determination between $X_j$ other predictor variables. The value $R_j^2$ can be calculated using the following formula,

$R_j^2=\frac{\sum_{j=1}^k\left(\widehat{X}_j-\bar{X}\right)^2}{\sum_{j=1}^k\left(X_j-\bar{X}\right)^2}$               (15)

The criteria used to detect the presence or absence of multicollinearity are $V I F>10$ if the value of $V I F>10$ it is said to be multicollinear in the data.

To detect multicollinearity, a VIF threshold of 10 was used, consistent with established guidelines. Predictor variables with a VIF exceeding this threshold were considered to exhibit significant multicollinearity. If detected, such variables were either removed from the model or combined with other related variables to reduce redundancy and improve model stability.

3.9 Model significance test

The model significance test is carried out to determine whether the predictor variables can simultaneously influence the response variable. The Likelihood Test (LRT) is used to test the significance of the model in gamma regression with the following hypothesis,

H₀: There is no significant fit difference between the simple and more complex models.

H₁: There is a significant difference in fit between simple and more complex models, with more complex models better explaining the data.

Test Statistics

$G^2=2 \sum_{i j} f_{i j} \ln \left(\frac{f_{i j}}{e_{i j}}\right)$                (16)

with

$e_{i j}=\frac{f_{i .} \times f_{. j}}{f_{. .}}$               (17)

$f_{i j}$: cell frequency of i-th row and j-th column

$e_{i j}$: expected frequency of cells of i-th row and j-th column

Test Criteria

Reject H₀ if the value $G^2<\chi_{(\alpha, 1)}^2$ with a free degree of 1 and a significance level of $\alpha$. In this study used a value $\alpha$ of 10%.

3.10 Parameter significance test

A parameter significance test is conducted to determine whether the parameters used have a significant effect on the model or not. The Wald test is used to test the significance of parameters with hypotheses,

H₀: $\beta_j=0$, with $j=1,2, \ldots, m$ (There is no effect of the jth predictor variable on the response variable)

H₁: $\beta_j \neq 0$, with $j=1,2, \ldots, m$ (There is an effect of the jth predictor variable on the response variable)

Test Statistics

$W=\frac{\widehat{\beta}_J}{S E\left(\widehat{\beta}_I\right)}$                (18)

with

$W$: Wald test statistic

$\widehat{\beta}_J$: Estimator of $\beta_j$

$S E\left(\widehat{\beta}_J\right)$: Standard error of $\beta_j$

Test Criteria

Reject $H_0$ if value $|W|>\left|Z_{\frac{\alpha}{2}}\right|$ or when the p -value $<\alpha$, accept in all other cases.

3.11 Root Mean Square Error (RMSE)

RMSE is the square root of the mean squared error (MSE) [45]. RMSE is a method of summing the square of the error or difference between the real and predicted values. In this case, RMSE is the prediction of potential ocean wave power compared to the actual observed potential ocean wave power value, calculated by squaring the error, divided by the average amount of data, and then rooted [46].

$RMSE =\sqrt{\frac{1}{N} \sum_{k=1}^N\left(\hat{y}_k-x_k\right)^2}$              (19)

with

N: number of data

$x_k$: true value

$\hat{y}_k$: predicted value

3.12 Data

The data used in this study were obtained from official and reputable sources, including the Indonesian Maritime Meteorology, Climatology, and Geophysics Agency (BMKG). To ensure accuracy, we cross-referenced the data with other publicly available reports and performed consistency checks to detect and correct anomalies. These steps included verifying wave height categories, wind speed ranges, and weather classifications against historical records and BMKG’s standardized measurement guidelines (Table 1).

Table 1. Variables in research

Ocean wave power potential refers to how much energy can be generated by ocean waves. It indicates the ability to harness energy from the movement of ocean waves based on wave conditions. This variable is critical to assessing the feasibility of using ocean wave energy as a sustainable renewable energy source.

The average rate at which wind moves through the atmosphere is known as the average wind speed. It is critical to understanding how wind affects the formation and intensity of ocean waves because wind speed contributes to wave formation and height. In a maritime context, wind speed is measured in knots (KTS), a unit commonly used to measure wind speed. Average wind speed is measured as a continuous variable over a given period, rather than in specific categories, and provides useful information on how wind affects the possible use of wave energy.

Wave type refers to the classification of waves based on height, which helps in understanding the different wave conditions that can impact the potential wave energy. According to the Indonesian Meteorology Climatology and Geophysics Agency, seven categories of waves, namely calm waves with a height of 0.01m – 0.5m; low waves with a height of 0.5m – 1.25m; medium waves with a height of 1.25m – 2.5m; high waves with a height of 2.5m – 4m; very high waves with a height of 4m – 6m; and extreme waves with a height of 6m – 9m. These classifications are important in assessing how different wave conditions affect energy generation. This classification is important for assessing how different wave conditions affect energy generation.

Wave behavior and energy potential can be affected by various weather components, such as cloud cover, rainfall, and temperature. Some weather types are classified based on cloud cover and rain intensity. For example, cloudy indicates thin cloud cover; heavy cloudy indicates thick cloud cover; bright sunny indicates a combination of sunshine and clouds; heavy rain indicates heavy rainfall; localized rain indicates localized rain; and light rain indicates light rainfall. These weather types are classified by the extent of cloud cover.

To enhance the chamber efficiency in the OWC system, specific design parameters were implemented. The chamber width was set to 2.4 meters, consistent with the prototype used in Pantai Baron, Yogyakarta, Indonesia, which demonstrated optimal performance under similar wave conditions. Additionally, the airflow outlet was modified to optimize energy conversion during wave oscillations. Numerical simulations were conducted to evaluate the impact of these modifications on energy absorption and conversion efficiency, focusing on the interaction between wave dynamics and air pressure within the chamber.

3.13 Data processing

Data processing using R software with attached syntax. The research framework in this study is shown in Figure 3.

3.png

Figure 3. Research framework

Hypothesis

The alternative hypotheses used are:

H₁: There is an influence between the wave types, average wind speed, and weather to the ocean wave power potential.

Data preprocessing was conducted in R to ensure the quality and reliability of the dataset before analysis. Missing data were identified and addressed using the mice package for multiple imputations, ensuring minimal bias in the dataset. Outliers were detected using boxplots and handled through capping at the 1st and 99th percentiles to reduce the influence of extreme values. Variables were standardized using the scale() function to ensure uniformity in measurement scales, which is particularly critical for regression models. Additionally, categorical variables such as wave type and weather were converted into dummy variables using the model.matrix() function to integrate them into the analysis effectively. The final dataset was verified for consistency, and summary statistics were recalculated to confirm data integrity before proceeding with modeling.

Based on the modelling analysis results, the average potential power generated by ocean waves in Indonesian waters using gamma regression with Maximum Likelihood Estimation (MLE) parameter estimation shows that the wave type factor influences the average potential power generated by ocean waves in Indonesian waters. Meanwhile, the average wind speed and weather factors do not affect the potential power generated by ocean waves in Indonesian waters. The model’s prediction results are accurate because the RMSE value obtained is 2.93e-10, which is close to 0, indicating that the prediction results of the model are very close to the actual values. However, the wave type has minor effect on the potential power generated. When there is one-unit increase in low and medium wave types, the resulting power potential decreases compared to calm waves. However, the decrease that occurs is not too significant. For a low waves, a one-unit increase only reduces the value of the potential power generated by 0.0000083%, and for medium waves, a one-unit increase only reduces the value of the potential power generated by 0.0000113% compared to calm waves.

These results imply that, in comparison to low or medium waves, calm calm waves offer more stable circumstances. Building and running a Marine Wave Power Plant is safer and simpler due to the stability of calm wave conditions, which also lowers the possibility of equipment damage. Moreover, calm waves' consistency and predictability might be helpful for dependable energy generation, even though wave form has little bearing on potential power.

Calm or stable wave condition in Indonesian waters is often observed during dry season, typically from May to September, when the southeastern monsoon wind dominates, resulting in reduced turbulence and consistent sea conditions. These periods provide ideal condition for optimizing the operation of OWC systems, ensuring stable energy generation and minimizing risks associated with equipment stress.

The OWC technology is ideal for areas characterized by flat seabed topography and consistent wave heights, as it requires minimal construction space. In Indonesia, one of the regions that meet these criteria is West Kalimantan, where the coastal waters feature a flat seabed and stable wave conditions. These characteristics make West Kalimantan a promising location for implementing OWC systems. This study aims to provide insights that can assist the West Kalimantan Regional Government in developing policies for establishing Marine Wave Power Plants (PLTGL) in the area.

Considering the model results, the siting and development of Marine Wave Power Plants using OWC should prioritize areas with stable wave conditions, especially during the dry season when the waves tend to be calmer and more predictable. Additionally, based on the model’s findings showing only a minor impact of low and medium waves on potential power, the capacity of OWC systems in areas with low or medium waves can be scaled down to optimize costs without significantly compromising power Bahaefficiency. Maintenance schedules should also be adjusted based on local wave conditions, where systems in areas with more stable waves may require less frequent maintenance, while systems in areas with stronger waves may require more frequent maintenance to ensure optimal operation and prevent damage.

These findings provide the following insights for feature research:

1. Additional Research into Other Factors: Future investigations may look into other factors or combinations of factors that could affect the potential power output, as wave type has a negligible impact.
2. Marine Wave Power Plant Optimization: Since calm wave conditions are preferred in plant design, it is important to optimize MWPPs to function well in these circumstances. Doing so could result in more reliable and economical energy production.
3. Extended Regional Studies: Similar analyses in different regions could help validate whether the observed effects are consistent across various locations and environmental conditions.
4. Long-Term Monitoring: Implementing long-term monitoring could provide insights into how seasonal and temporal variations affect wave power potential and operational efficiency
5. Use of Other Analysis Techniques: Consider using additional analysis techniques, such as principal component analysis (PCA) or clustering, to identify hidden patterns in the data and see how the results of the gamma regression analysis can be strengthened.

This study used gamma regression with Maximum Likelihood Estimation (MLE) parameter estimation to gather and evaluate data on the power potential produced by ocean waves in Indonesian waters. The average power potential generated in this investigation was found to be influenced by the wave type component, with calm waves exhibiting more stable conditions than low or medium waves. The power potential does, however, slightly drop when wave type varies, indicating a negligible impact of wave type on power potential. By applying a gamma regression model, which can produce precise findings that are near to the true value, the limitations of the available data have been addressed. Additional research is recommended by this study in order to examine the data variability in greater detail and to take various places' wave conditions into account. Additional study with data from more places and longer time periods is needed to gather more thorough information. To ensure the technology's sustainable deployment with an aim to reduce dependence on fossil fuels, thereby lowering greenhouse gas emission and mitigating the effects of climate change, by concentrating on wave energy, a lot emission and renewable energy source.

Compared to traditional energy generation techniques, OWC technology has negligible environmental impact as it does not require much land or emit harmful pollutants. The paper also emphasizes how OWC systems can be incorporated into existing marine infrastructure, which will reduce the demand for new development while protecting marine habitats. However, additional factors that must be considered include environmental impact assessments and the creation of novel technologies for ocean wave energy conversion. In order to validate these results and offer a more comprehensive understanding of the potential of ocean wave power throughout Indonesian waters, future research could involve more thorough and in-depth data analysis.