Description:FIELD OF INVENTION
This invention concerns a statistical machine learning model crafted to efficiently generate and integrate renewable energy into distribution networks. Utilizing sophisticated statistical methodologies, the model optimizes both the generation and distribution processes of renewable energy, ultimately improving the efficiency and reliability of grid infrastructure.
BACKGROUND OF INVENTION
Amidst increasing demands for sustainable energy and the imperative to integrate renewable sources into current power grids, this invention introduces a pioneering statistical machine learning (ML) model crafted explicitly for generating and seamlessly incorporating renewable energy within distribution networks. Conventional energy grids confront formidable obstacles in adapting to the variability and intermittency inherent in renewables like solar and wind power. This ML model confronts these hurdles by employing advanced statistical methodologies to optimize the entire renewable energy process within distribution networks, spanning from generation to distribution. Harnessing historical data on energy production, consumption patterns, alongside meteorological and geographical insights, the model accurately predicts renewable energy generation levels. This predictive ability empowers proactive grid management, allowing utilities to adeptly balance supply and demand, preempt potential disruptions. Moreover, the ML model dynamically adapts energy distribution strategies in real-time, maximizing renewable energy utilization while ensuring grid stability and reliability. Through continual learning and adjustment, the model bolsters overall grid efficiency and resilience, heralding a more sustainable and eco-friendly energy landscape. In essence, this innovative methodology marks a substantial advancement in integrating renewable energy into distribution networks, furnishing a dependable and scalable solution to navigate the challenges of transitioning towards a cleaner energy paradigm.
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SUMMARY
The Statistical Machine Learning (ML) Model for Renewable Energy Generation and Integration in Distribution Networks provides an innovative answer to the urgent need for sustainable energy incorporation into current power systems. Conventional grids struggle with the erratic behavior of renewable sources such as solar and wind energy. This ML model transforms the energy sector by harnessing advanced statistical methodologies to optimize the entire process of renewable energy production and integration within distribution networks.
Through analysis of historical energy data, meteorological factors, and geographical parameters, the model accurately predicts levels of renewable energy generation. This predictive capability enables proactive grid management, ensuring improved balance between energy supply and demand and minimizing potential disruptions. Furthermore, the model dynamically adjusts energy distribution strategies in real-time, maximizing the utilization of renewable energy while maintaining grid stability and reliability.
Continual learning and adaptation further enhance the model's ability to improve overall grid efficiency and resilience. This innovative approach represents a significant stride towards achieving a sustainable and environmentally friendly energy infrastructure. By providing a dependable and scalable solution, the model addresses the complexities of transitioning towards a cleaner energy future, thus laying the foundation for a more sustainable global ecosystem.

DETAILED DESCRIPTION OF INVENTION
In the realm of smart grids and eco-friendly energy, the widespread integration of intermittent renewable distributed generation (DG) has introduced a level of unpredictability into distribution network planning. The focus on hydrogen production from renewable sources has gained traction in the realm of new energy applications due to its minimal energy consumption. This unpredictability significantly impacts the optimization of distribution network operations, necessitating careful planning and design. Consequently, stochastic optimal planning has emerged as a critical consideration in the advancement of smart grid technology. The effects of various uncertain processes on the outcomes of distribution network planning are encapsulated within a complex, nonlinear mixed-integer programming challenge.
Conventional planning approaches typically rely on deterministic scenarios, often overlooking the influence of uncertain elements. Robust programming and stochastic programming serve as primary methods for incorporating uncertain programming into power systems. Robust power system planning combines worst-case scenario analysis with interval optimization theory. Stochastic programming commonly employs probability distributions in modeling uncertain programming. However, the reliability of DG uncertainty probability distributions in stochastic programming models may be constrained by the availability of historical data, potentially introducing biases to the empirical distribution. Additionally, nonlinear stochastic programming methods frequently encounter challenges in achieving efficient solutions. Hence, the establishment of an effective planning model is essential, motivating the research direction of this paper.
Scholars have delved into stochastic planning and inquiry, focusing on decision variables related to DG levels, reactive power devices, PEV charging stations, and more. Probabilistic digital data plays a critical role in uncertainty analyses of power systems, with numerous studies utilizing probabilistic power flow calculations to assess uncertainty's implications. This paper introduces a novel approach to stochastic power grid planning, employing central moments instead of mean and variance in stochastic programming models. The innovation lies in the utilization of PPF in uncertain programming, the dual application of the principle of maximum entropy (POME), and the introduction of a novel uncertain planning model with practical significance.
Stochastic programming holds a central position within uncertain programming, where random variables are treated as ambiguous parameters. By incorporating probability theory, stochastic programming facilitates the planning of new energy systems. Initially, we outline the stochastic programming problem, followed by an introduction to the specific stochastic programming model employed in this study.
Figure 1 underscores the critical importance of considering the uncertain elements within new energy distribution networks. While PV and WP energy sources are natural, their inherent unpredictability presents notable challenges. As additional renewable energy capacity is integrated into the grid, uncertainty within the distribution network amplifies, leading to increasingly complex operational scenarios. Consequently, this heightened complexity poses obstacles to efficiently planning and leveraging new energy resources. In stochastic programming, decision variables are confined to specific values, thereby constraining the potential operating scenarios.

Figure 1: Navigating Uncertainty in New Energy Distribution Networks
Introducing a PPF-Driven Stochastic Programming Model for New Energy Integration in Distribution Networks:

The objective function, represented by f_obj(•), embodies the overarching goal of the planning scheme. Here, p_loss signifies the total active power loss in the distribution network, which can be substituted with alternative economic indicators depending on specific decision-making requirements. E(•) denotes the mean function. YPV and YWP serve as decision variables, symbolizing the rated capacities of PV power and WP, respectively. YPV_max and YWP_max denote the upper limits of the planning capacities for PV and WP. num denotes the count of buses linked to the new energy grid, while num_sys represents the total number of distribution network buses. Vi stands for the voltage amplitude at the ith bus, with V_min indicating the permissible lower limit of Vi. Pr(•) represents a probability function, and α signifies the confidence probability level. While the provided formula delineates the key variables and parameters, it doesn't explicitly clarify the relationship between decision variables and the objective and constraint functions. Therefore, we will elucidate these connections through subsequent formulations.

PPF(•) represents the Probabilistic Power Flow estimation method, specifically a Point Estimation Method (PEM) utilized in this paper. Additionally, pPV denotes the active power generated by PV panels, while pWP signifies the active power generated by wind turbines.
The power generated by new energy sources must be contingent on the planned capacity, as depicted below:

Here, fPV denotes the PV derating factor, G represents the current solar radiation amount, and STC is a subscript indicating standard test conditions. αp stands for the temperature coefficient, TC denotes the PV cell temperature, and NOCT is a subscript representing the nominal operating cell temperature. Ta signifies the ambient temperature, ηmp indicates the maximum power efficiency, τ denotes the solar transmittance of a PV cell, and αab represents the solar absorptance of a PV cell.
Additionally, v represents the current wind speed, vr denotes the nominal wind speed, vci stands for the cut-in wind speed, and vco represents the cut-out wind speed.
By substituting Equations 8–10 into Eq. 7 and treating the capacities and locations of new energy sources as decision variables, we can derive:

The uncertainty calculation method progresses through three primary stages. Firstly, simulated weather data, utilized as inputs for Eqs 8–10, are introduced. Subsequently, the Probabilistic Power Flow (PPF) method is utilized, generating origin moments as outcomes. Finally, a technique for solving Eq. 6 is introduced, utilizing central moments and Particle Swarm Optimization (PSO). This proposed methodology is succinctly illustrated in Figure 2.

Figure 2: Illustrative Representation of the Proposed Methodology
Simulation of Weather Uncertainty
The weather simulation process integrates a copula function, marginal probability distributions, and logical operations, as illustrated in Figure 3. Initially, marginal probability distributions are introduced to represent various weather types. Subsequently, the copula function is elucidated.

Figure 3: Flowchart of Weather Uncertainty Simulation
The expression for the marginal probability distribution of G is given by:

The marginal probability distribution of 𝑣v can be expressed as:
f(v)=σ2π1exp(−2σ2(v−μ)2)
where 𝜇 is the mean wind speed, 𝜎 is the standard deviation of wind speed, and exp denotes the exponential function.

The marginal probability distribution of 𝑇𝑎Ta can be expressed using the Principle of Maximum Entropy (POME) as:

The estimation of 𝜆𝑘in Eq. 18 can be accomplished using the program in:

A Gaussian copula function is employed to model the correlation among 𝐺, 𝑣, and 𝑇𝑎. We estimate 𝜌 for the matrix of linear correlation parameters using real weather data.

The Monte Carlo (MC) method is utilized to generate random weather simulation samples from the Gaussian copula with ρ. Here, 𝜌 is a coefficient estimated for a matrix of linear correlation parameters based on a Gaussian copula, copulafit(•) is a fitting function, and cdf(•) is a cumulative distribution function (CDF).

In this context, the superscript 𝑠 denotes that a variable is simulated, and copularnd(•) represents the generation of random vectors using a Monte Carlo (MC) approach. By utilizing the simulated Cumulative Distribution Functions (CDFs), we can obtain the simulated weather samples.
Remark 2: We integrate weather variables into the model to ensure the applicability of the research outcomes to power grid planning under various weather conditions. Classical probability functions are employed for solar radiation and wind speed. Regarding temperature simulation, the Principle of Maximum Entropy (POME) is utilized to estimate the unknown probability distribution.
The Probabilistic Power Flow (PPF) Calculation
The Point Estimation Method (PEM) utilizes samples to obtain estimates. We can determine the statistical moments of the population using PEM. The statistical moments of power flow solutions are obtained from weighted samples at various positions. For deterministic power flow (DPF) calculations, MATPOWER as described is employed. A two-point estimation (2PEM) approach is applied, determining two values on both sides of the mean value of each uncertain variable.

We introduce the following data into the Deterministic Power Flow (DPF) calculation using MATPOWER:
𝑥𝑖 represents the 𝑖th uncertain variable (i.e., 𝑝𝑃𝑉 or 𝑝𝑊𝑃), where 𝑖=1,2,…,𝑚 and 𝑚 is the number of uncertain variables.
𝑋mean, is the mean of 𝑥𝑖.
𝑋standard, i is the standard deviation of x.
𝑘 takes values of 1 or 2 (where 2 reflects the values on both sides of 𝑋mean,𝑖).
skewness𝑖 is the sample skewness of 𝑥.
spik is a location-specific measurement.

where dpf(•) represents the Deterministic Power Flow calculated using MATPOWER, and 𝑢is the obtained voltage, power flow, or other variable.
Next, we provide the formula for the origin moment of 𝑢:

where 𝑀origin(•) is the function for the origin moment of order 𝑗, and 𝑤𝑖𝑘 represents the weights for a given location set.
From Eq. 25, we can derive the following equations:

where 𝑝loss is one type of 𝑢, 𝑉 is the PQ node voltage set related to 𝑢, and 𝑉om,𝑗 is the origin moment of order 𝑗.
At this stage, we have derived the objective function formula, i.e., Eq. (28), using the Probabilistic Power Flow (PPF) calculation based on the two-point estimation method (2PEM). The next challenge is to transform PPF results into constrained probabilities. For this probability transformation, the quadratic fourth-order moment (QFM) estimation method is introduced by converting Eq. (29) into Eq. (6). However, the inputs of QFM are central moments. Therefore, we need to convert the origin moments to central moments. It is well-known that:

where 𝜇𝑗(•) is the function for a central moment of order j.
This equation can be utilized to obtain:

Uncertainty Constraint
Here, we present a method for solving Eq. (6) utilizing the Quadratic Risk Model (QRM) and central moments. The QRM serves as a theory for estimating failure probability. We determine the qualified voltage probability based on the principle that the sum of failure probability and qualified probability equals one.

where 𝑃𝑓 is the failure probability, an unqualified concept.
The limit state function for the voltage amplitude is expressed as:

Expanding 𝑔(𝑉𝑖) to a Taylor series at 𝑉𝑖∗, we obtain the following equation:



We convert the moments of the voltage amplitude into moments of voltage amplitude constraints via equations (38)-(41).
The subsequent formulas do not restrict the number of buses, and a portion of 𝑍Z is eliminated. We then transform moments into other digital characteristics.

where 𝑐sz is the skewness coefficient and 𝑐ks is the kurtosis coefficient.
We transform 𝑍 to a standard normal vector 𝑌, and the moments of 𝑌 are calculated with:




The voltage probability information is converted into voltage constraints via the Quadratic Fourth-order Moment (QFM) approach, representing a novel method to utilize Probabilistic Power Flows (PPFs) for obtaining constraint solutions in stochastic programming.

DETAILED DESCRIPTION OF DIAGRAM
Figure 1: Navigating Uncertainty in New Energy Distribution Networks
Figure 2: Illustrative Representation of the Proposed Methodology
Figure 3: Flowchart of Weather Uncertainty Simulation , Claims:1. Statistical ML Model for Generation and Integration of Renewable Energy Using Distribution Networks claims that renewable energy integration into distribution networks presents challenges due to uncertainty.
2. Probabilistic Power Flows (PPFs) offer effective tools for analyzing distribution networks under uncertainty.
3. A Statistical Machine Learning (ML) model optimizes renewable energy generation and integration.
4. Stochastic programming models aid in planning new energy systems.
5. Weather simulation incorporates copula functions and marginal probability distributions.
6. PPFs provide estimates for uncertain parameters in power flow calculations.
7. Conversion from origin moments to central moments facilitates probability transformation.
8. Quadratic Risk Model (QRM) is used to estimate failure probability for voltage constraints.
9. Transformation of voltage probability information into constraints is achieved via the QFM approach.
10. This innovative approach enhances the reliability and efficiency of distribution networks amidst renewable energy integration.