DEVELOPMENT OF A WEB APP
FOR THE OPTIMAL DISPATCH OF ENERGY
FROM RENEWABLE SOURCES
By
Jaime Andre Burgos
November 2023
Belize City, Belize
ABSTRACT
The electricity sector in Belize is undergoing a transformative shift, characterized by the rapid
integration of innovative technologies such as rooftop solar and electric vehicles into the traditional
power distribution framework. As the imperative to decarbonize the electricity sector gains
prominence, there emerges a compelling need for the electric utility to play a pivotal role in
balancing the variable power generation from these devices with demand. This role, executed at a
granular level, holds the potential to enhance energy resiliency, minimize delivery losses, and
effectively communicate price signals to consumers. Presently, this function relies heavily on
manual economic dispatch mechanisms, an inaccurate process, which becomes increasingly
challenging given Belize's imminent multitude of variable renewable and small-scale consumers
with diverse preferences.
This thesis draws on inspiration from diverse research papers seeking to introduce an innovative
paradigm, termed "Decentralized Locational Marginal Pricing" (DLMP), as well as more traditional
optimization algorithms like Particle Swarm Optimization (PSO) and Locational Marginal Pricing
(LMP). By combining PSO or LMP with DLMP, a price signal at each injection node can be passed
to both consumers and utility scale battery management systems to intelligently charge or discharge.
Results from the study, indicate that residential BESS will become competitive in the Belizean
Market around 2026 with current trends.
This thesis explores the potential of Belize's evolving energy landscape, underpinned by
decentralized economic dispatch, to navigate the complexities of integrating renewables, optimizing
energy dispatch, and fostering a resilient and sustainable power grid. By harnessing innovative
technologies and computational methodologies, Belize can effectively transition to a dynamic
energy ecosystem that accommodates both traditional and emerging energy sources, echoing the
global imperative for a sustainable and decarbonized electricity sector.
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Table of Contents
ABSTRACT .......................................................................................................................... 2
LIST OF FIGURES ............................................................................................................... 9
LIST OF TABLES ................................................................................................................. 9
ABBREVIATIONS ............................................................................................................ 10
GLOSSARY ....................................................................................................................... 10
1.0
INTRODUCTION .................................................................................................. 11
1.1
General ........................................................................................................................ 11
1.2
Objectives .................................................................................................................... 12
1.3
Results of Analysis ............................................. Ошибка! Закладка не определена.
1.4
Recommendations........................................................................................................ 13
2.0
LITERATURE REVIEW........................................................................................ 14
2.1
Computer Language Comparison Python vs. C# ........................................................ 14
2.2
Web Framework Comparison: Django vs. ASP.NET Core ......................................... 15
2.3
Deep Neural Network Models ..................................................................................... 16
2.4
Particle Swarm Optimization ....................................................................................... 18
2.5
Locational Marginal Pricing ........................................................................................ 19
2.6
Decentralized Locational Marginal Pricing .................................................................. 22
2.7
Limitation of Study ..................................................................................................... 24
3.0
METHODOLOGY ................................................................................................. 24
3.1
Framework Selection .................................................................................................. 24
3.2
Weather Data Sources ................................................................................................. 24
3.3
Historical Load Data Sources....................................................................................... 26
3.4
Network Data Source .................................................................................................. 26
3.5
Prediction Model ......................................................................................................... 28
3.6
Generator Costs ........................................................................................................... 30
3.7
Price Forecast .............................................................................................................. 31
3.8
Fuel Management ........................................................................................................ 31
3.9
Batteries in the Mix...................................................................................................... 32
4.0
RESULTS AND DISCUSSION ............................................................................. 34
4.1
Load Forecast .............................................................................................................. 34
4.2
Problem Constraints ........................................... Ошибка! Закладка не определена.
vii
4.3
PSO ............................................................................................................................. 36
4.4
LMP.................................................................... Ошибка! Закладка не определена.
4.5
DLMP ................................................................. Ошибка! Закладка не определена.
5.0
CONCLUSIONS AND RECOMMENDATIONS .................................................. 39
5.1
Conclusions ................................................................................................................. 39
5.2
Recommendations .............................................. Ошибка! Закладка не определена.
5.3
Areas for Further Study................................................................................................ 40
REFERENCES ................................................................................................................... 41
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LIST OF FIGURES
Figure 1: Geographical Map of Belize showing Transmission Network and Substations ................ 11
Figure 2: Representation of perceptrons in Deep Neural Network ................................................... 17
Figure 3: Graph of particles on the search domain converging on the global minimum ................... 19
Figure 4: Temperature forecast and historical (nms) for Belmopan Weather Station Location ........ 25
Figure 5: Temperature forecast and historical (nms) for Tower Hill Weather Station ...................... 25
Figure 6: Detailed BEL Networks ..................................................................................................... 27
Figure 7: Minimized BEL Networks ................................................................................................. 27
Figure 8: Real Power Demand for a 1 week span for all 44 Feeders ................................................ 29
Figure 9: Normalized Real Power, P, and Temperature for 6 Feeders in Belize City (Temperature in
Squares) ............................................................................................................................................. 29
Figure 10: Normalized Real Power Demand and Humidity for 6 Belize City Feeders ..................... 29
Figure 11: Fuel Consumption of Gas Turbine for Various Operating Points .................................... 30
Figure 12: Water Shed of the three dams where rainfall prediction drive fuel management. ........... 32
Figure 13: 2019$ installed cost per kW predictions .......................................................................... 33
Figure 14: Real Load forecasts compared to Actual Real Loads ........................................................ 34
Figure 15: Reactive Load forecasts compared to Actual Reactive Loads .......................................... 35
Figure 16: Forecasted P & Q vs Actual Loads .................................................................................... 35
Figure 17: Global Best of 15 Particles ................................................................................................ 36
LIST OF TABLES
Table 1: Comparison of Web Frameworks ........................................................................................ 16
Table 2: RMSD for weather parameters from three evaluated sources. ............................................ 25
Table 3: PSO Results for Selected Time Span .................................................................................... 37
9
ABBREVIATIONS
ACE: Area Control Error
UC: Unit Commitment
LF: Load Forecasting
ED: Economic Dispatch
PSO: Particle Swarm Optimization
LMP: Locational marginal Pricing
DLMP: Decentralized Locational Marginal Pricing
BESS: Battery Energy Storage System
GLOSSARY
Ancillary services: are the variety of operations on the electricity networks that are required to
balance supply and demand over all time scales, while maintaining voltage and frequency within
safe limits and preventing overload of grid infrastructure.
Distributed generation: Term applied to a variety of small power supplies (eg. solar) located near
the point where the power is used and tied to Distribution Networks (low voltage). Opposite of
central power.
Prosumer: A prosumer is an individual who both consumes and produces.
Utility-scale facility: one which generates solar power and feeds it into the grid, supplying a utility
with energy typically above 1 MW and usually feeder to the transmission grid. Utility-scale solar
facility typically has a power purchase Agreement (PPA) with a utility, guaranteeing a market for its
energy for a fixed term of time.
Residential-scale facility: one which produces energy mostly for self-consumption but may export
to the grid. It is usually connected to the distribution grid and remuneration is handled by an
aggregator who negotiates with the utility or by a commercial agreement with the utility.
Transmission Grid: the part of the network that wheels wholesale power from IPPs to distribution
nodes (distribution substations) at high voltages 115kV, 69kV or 34.5kV.
Distribution Grid: the part of the network that wheels energy from the distribution substation to
residential and commercial customer at a lower voltage 22kV, 11kV, 6.6kV.
10
1.0
INTRODUCTION
1.1 General
Belize, nestled in the heart of the Caribbean, boasts a reputation as one of the
region's leading producers of renewable energy. Yet, amidst the natural splendor of
this nation, a significant portion of Belize's electricity mix relies on imported power
and fossil fuels, predominantly diesel-fired turbines. Despite the strides made in the
past years, Belize finds itself at a crossroads, grappling with a dual challenge:
economic sustainability and environmental responsibility.
Between 2017 and 2021, an impressive 44% of Belize's power output came from
green sources, notably hydro and biomass (bagasse) [1]. Yet, 47% of the electricity
was imported, mainly from Mexico's Comisión Federal de Electricidad (CFE), with
an additional 9% produced by in-country diesel-powered turbines. The Peninsular
Region of the Mexican SIN grid, which supplies Belize, draws merely 12% of its
energy from renewables, with the majority dependent on fossil fuels [2]. Depending
on these external supplies has significant economic implications, costing Belize
around 3.7% of its GDP in foreign exchange for electricity payments. This
considerable outflow emphasizes the urgent need for Belize to pursue a more
independent and sustainable energy trajectory [1].
Figure 1: Geographical Map of Belize showing Transmission Network and Substations
As highlighted in BEL's 2021 Annual Report, the power cost is a major and
unpredictable component of the country's total expenditures. The imperative to
tackle this issue is magnified by the aim to stabilize price oscillations and reduce
Belize's fossil fuel reliance. Belize understands that strength comes from boosting
domestic energy production, particularly through deliberate solar energy
investments.
Importantly, Belize's top authorities recognize that an over-dependence on fossil
fuel power magnifies the area's environmental impact, contributing to the broader
issue of global climate change. To address this, the leaders of all 15 CARICOM
nations, Belize included, united to endorse the CARICOM Energy Policy in 2013.
11
This pivotal pact obligated the region to systematically elevate its green energy
capacities. The set milestones were demanding: reach 20% renewable capacity by
2017, 28% by 2022, and a striking 47% by 2027. Remarkably, Belize surpassed
expectations, touching the 47% mark as early as 2022.
Taking further initiative, Belize fervently advocates for rooftop solar projects and
has proclaimed an even bolder national objective: deriving a minimum of 75% of
its energy from green sources by 2030. This vision is consistent with the pledges
voiced at the global COP26 summit in Glasgow.
Industry specialist evaluations validate the attainability of this goal, pointing to a
balanced blend of hydro, solar, and biomass as the way forward. While hydro
presents potential, its scalability has bounds. It's evident that as Belize advances,
fulfilling its rising electricity needs and meeting these green energy targets demands
a mix of utility and solar Distributed Generation (DG).
Considering these hurdles and prospects, the emergence of a refined technical
solution shines brightly. Such an innovation not only matches Belize Electricity
Limited's aims but also plays a pivotal role in carving a greener, more resilient
energy pathway for Belize. This technological venture is set to transform Belize's
energy horizon, harmonizing economic growth with ecological conservation.
1.2
Objectives
In the dynamic landscape of the Belizean energy sector, Belize Electricity Limited
(BEL) stands as a central pillar, entrusted with the crucial responsibility of
procuring, producing, and delivering electrical energy to the nation. In pursuit of its
core mission, BEL has meticulously outlined a set of strategic objectives aimed at
optimizing its operations, ensuring energy affordability, and fostering the
sustainable development of Belize. This introduction provides a comprehensive
overview of BEL's key objectives and underscores the pivotal role of a novel web
application, designed to empower BEL in achieving its multifaceted goals.
Least Cost / Least Risk: Foremost among BEL's objectives is the commitment to
delivering energy services to Belizeans at the least cost, characterized by minimal
price fluctuations. This commitment extends to supporting the quality of life,
bolstering the productivity of enterprises, and contributing to national development.
Energy Security is paramount, aiming to avert over-dependence on single energy
sources, such as wind or solar, while mitigating exposure to spot market dynamics
and reducing fuel dependency.
Sustainability: In harmony with the global call for environmental stewardship,
BEL's second core objective revolves around sustainable energy production and
procurement. It emphasizes the imperative of generating and procuring energy in an
environmentally responsible manner, devoid of actions that degrade the natural
environment. A crucial metric for sustainability is the percentage of energy
requirements covered by renewable sources, with a minimum target of 75% by
2030. Additionally, BEL aims to minimize its carbon footprint, with the ultimate
aspiration of Belize achieving carbon neutrality by 2050.
Reliability, Quality of Service, and Resiliency: Ensuring a reliable and resilient
energy supply is central to BEL's mission. This objective assesses the system's
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capacity to efficiently produce, procure, and deliver energy to customers while
minimizing interruptions. It seeks to enhance the quality of life, productivity, and
the management of high-impact, low-probability events. Metrics for evaluation
include system reliability, service quality, and preparedness to withstand and
recover from disruptive events.
As BEL embarks on this transformative journey, these objectives collectively form
the bedrock of its vision for a sustainable, reliable, and cost-effective energy future
for Belize. The development of a sophisticated web application aligns seamlessly
with BEL's aspirations, as it equips the company with the tools necessary to
navigate the complex energy landscape, optimize its operations, and contribute
meaningfully to the well-being and prosperity of Belize and its people.
1.3
Results of Analysis
The most suitable algorithm for optimization is Particle Swarm Optimization
(PSO). PSO provided a robust solution to the complex optimization problems
inherent in power systems management. The analysis revealed that by carefully
balancing the population of particles and the number of iterations, PSO can
converge on feasible solutions that respect the intricate constraints of the system.
In the context of BEL's operations, PSO was instrumental in optimizing the
dispatch of generators while adhering to their capability curves, ensuring that
operational constraints were not violated. The capability curves are critical as they
ensure generators operate within safe and efficient parameters, thus upholding the
reliability and quality of service objectives of BEL.
Furthermore, the analysis underscored the significance of PSO hyperparameters,
which directly impact the speed of convergence and the quality of the solution. By
fine-tuning these hyperparameters, the convergence process can be expedited,
leading to quicker decision-making and more efficient operations.
The application of PSO in the analysis has demonstrated the potential for
significant improvements in operational efficiency, cost reduction, and enhanced
system reliability. These outcomes are pivotal in advancing BEL towards its goal of
a sustainable, reliable, and cost-effective energy future for Belize.
1.4
Recommendations
Based on this analysis, Belize Electricity Limited (BEL) should implement the
Particle Swarm Optimization (PSO) algorithm on a dedicated server that receives
live data from the SCADA master. This setup will enable real-time optimization of
the power distribution network, taking into account the current load and generation
data. For future development, integrating the results of the optimal cost problem
with prosumer’s energy management system is advised. This integration will allow
for the consideration of real-time pricing and demand-side management, enhancing
the capability to balance load and generation in an economically efficient manner.
By doing so, BEL can ensure a more dynamic, responsive, and cost-effective
energy management process that aligns with its strategic goals of sustainability,
reliability, and affordability.
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2.0
LITERATURE REVIEW
2.1 Computer Language Comparison Python vs. C#
In the realm of web application development, the choice of programming language
plays a pivotal role in shaping the project's trajectory. For this research project, a
critical analysis of two prominent languages, Python and C#, was conducted to
discern their strengths, weaknesses, and overall suitability in the context of a web
application tailored to the specific needs of Belize Electricity Limited (BEL).
Python is a versatile and dynamically typed language known for its readability and
ease of use. It offers a plethora of web frameworks, with Django and Flask being
notable examples. Python's simplicity accelerates development, making it a
preferred choice for rapid prototyping and iterative development. Its expansive
standard library simplifies common tasks and facilitates seamless integration of
various components.
C#, on the other hand, is a statically typed language developed by Microsoft. It is
widely used for building Windows applications, but its capabilities extend well into
web development with the ASP.NET framework. C# excels in performance and
type safety, making it an ideal choice for projects where speed and reliability are
paramount.
To compare Python and C# effectively, this project delved into various aspects,
including:
Development Speed: Python's concise syntax and wide array of libraries often
result in quicker development cycles. C#, while more verbose, compensates with
robust development tools and a strong ecosystem.
Performance: C# is known for its superior performance, making it suitable for
resource-intensive applications. Python, while not as performant, boasts extensive
optimization tools and can be potent for most web applications.
Ecosystem and Libraries: Python's extensive library support includes Django for
full-stack web development and Flask for lightweight applications. C# leverages
the ASP.NET ecosystem, which is particularly well-suited for enterprise-level
applications.
Community and Support: Python enjoys a massive, global community, fostering
vibrant discussions and ample resources. C# benefits from strong Microsoft support
and is favored in enterprise environments.
Scalability: Python's scalability depends on the chosen framework and architecture.
C#, with its focus on enterprise development, excels in building highly scalable
applications.
The research uncovered that Python shines in scenarios requiring rapid
development, ease of use, and a wealth of third-party packages. C#, conversely,
emerges as a powerhouse for performance-demanding applications, especially in
enterprise settings.
In the context of BEL's web application development, the choice between Python
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and C# hinges on specific project requirements. Python's agility may be
advantageous for swiftly prototyping and iterating on solutions, while C#'s
robustness and performance could be indispensable for mission-critical
applications. This comparative analysis serves as a foundational decision-making
tool to ensure that the selected language aligns seamlessly with BEL's objectives
and project goals.
2.2
Web Framework Comparison: Django vs. ASP.NET Core
The selection of a web framework is a pivotal decision in the development of web
applications, and it greatly influences the project's trajectory. In the context of
Belize Electricity Limited (BEL), a comprehensive analysis was undertaken to
discern the most suitable framework between Django and ASP.NET Core for the
development of a web application tailored to BEL's specific needs.
Django:

Overview: Django is a high-level Python web framework celebrated for its
rapid development capabilities and its "batteries-included" philosophy. It
follows the Model-View-Controller (MVC) architectural pattern,
emphasizing code reusability and scalability.

Advantages:
o Rapid Development: Django's robust set of built-in features, such as
an ORM (Object-Relational Mapping) system, admin interface, and
authentication, accelerate the development process.
o Scalability: Django's architecture is designed to handle growth,
making it suitable for projects of various sizes.
o Community and Ecosystem: Django boasts a large, active
community and a vast library of third-party packages, enabling
developers to extend its functionality easily.
o Security: Django incorporates security best practices, such as
protection against common vulnerabilities like SQL injection and
cross-site scripting (XSS).
ASP.NET Core:


Overview: ASP.NET Core is a versatile, open-source web framework
developed by Microsoft. It operates on the .NET Core runtime, providing
cross-platform compatibility.
Advantages:
o Performance: ASP.NET Core is renowned for its exceptional
performance, particularly in scenarios requiring high concurrency
and resource efficiency.
o Versatility: ASP.NET Core supports a wide range of deployment
options, including Windows, Linux, and containerized
environments.
o Integration with Microsoft Stack: For organizations that rely on
Microsoft technologies, ASP.NET Core seamlessly integrates with
other Microsoft products and services.
o Security: ASP.NET Core incorporates robust security features and is
15
regularly updated to address emerging threats.
Characteristic
Django
ASP.NET
Best for Server Side Processing
Best for developing REST API
Scalability
Ease of Developing Prototype
Windows Environment Integration
Maturity and Plugins
Speed of Development
Table 1: Comparison of Web Frameworks
The research revealed that Django excels in scenarios where rapid development and
code simplicity are paramount. Its comprehensive feature set and extensive
community support make it a top choice for web applications that require agility.
ASP.NET Core, on the other hand, shines in performance-critical environments and
within organizations heavily invested in the Microsoft ecosystem. Its scalability,
cross-platform compatibility, and integration with Microsoft technologies make it a
formidable choice for enterprise-level projects.
The choice between Django and ASP.NET Core for BEL's web application
development depends on specific project requirements and organizational
preferences. Django offers speed and ease of use, while ASP.NET Core delivers
unparalleled performance and Microsoft integration. This comparative analysis
serves as a valuable guide to ensure that the selected framework aligns seamlessly
with BEL's objectives and project goals.
2.3
Deep Neural Network Models
TensorFlow is an open-source machine learning framework developed by the
Google Brain Team. It was designed with the aim of providing a flexible, scalable,
and production-ready platform for developing a wide range of machine learning
models, from simple linear regressions to complex deep neural networks (DNNs).
One of the most compelling features of TensorFlow is its computational graph
abstraction. Instead of running operations step-by-step, TensorFlow defines a
computational graph where nodes represent mathematical operations, and the edges
represent multidimensional arrays (tensors) passed between them. This allows for
efficient and optimized parallel computations, especially on GPU hardware.
TensorFlow's adaptability stems from its modular design. Its high-level APIs, like
Keras, simplify the process of model design, making it accessible even to those
new to machine learning. For more intricate designs or research purposes,
TensorFlow provides low-level APIs to offer granular control over model
architectures and training loops.
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Deep Neural Networks (DNNs) are a class of machine learning models that have
gained significant attention in recent years due to their unprecedented successes in
tasks like image recognition, natural language processing, and predictive analytics.
DNNs consist of multiple layers of interconnected nodes (neurons) that transform
the input data into a desired output. The 'deep' in DNNs refers to the depth of these
layers, which can number from tens to hundreds in advanced architectures.
Figure 2: Representation of perceptrons in Deep Neural Network
A DNN learns by adjusting the weights of its connections based on the error
between its predicted output and the actual output during training. This process is
often guided by backpropagation, a technique that calculates the gradient of the
error with respect to the model's weights. The weights are then updated using
optimization algorithms like Stochastic Gradient Descent (SGD) or its variants.
Several factors contribute to the effectiveness of DNNs. With a sufficient number
of neurons and layers, DNNs can approximate any continuous function, given the
right set of weights. In tasks like image recognition, initial layers might capture
simple patterns (e.g., edges or textures), while deeper layers combine these to
detect complex structures (e.g., shapes or objects).
In the context of the project, a feedforward neural network was employed to predict
the P and Q load values based on a set of features derived from combined feeder
and weather station data. The neural network architecture consists of two hidden
layers with 64 and 32 neurons, respectively, and an output layer designed to predict
both P and Q values.
The chosen model was compiled with the Adam optimizer, which is an adaptive
learning rate optimization algorithm designed to handle sparse gradients on noisy
problems. The mean squared error was used as the loss function, which is
appropriate for regression tasks where the goal is to minimize the difference
between predicted and actual values.
Training a neural network model involves iteratively updating its weights using the
provided training data until the model's predictions closely match the observed
outcomes. In this project, the model was trained over 100 epochs with a batch size
of 32. After training, the model was serialized and stored for later use, allowing the
web app to make predictions on new data quickly and efficiently.
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In conclusion, TensorFlow and deep neural networks provide a robust and flexible
framework for developing predictive models for diverse applications. Their ability
to learn intricate patterns from large datasets makes them especially suited for tasks
like load forecasting and generation forecasting.
2.4
Particle Swarm Optimization
Particle Swarm Optimization (PSO) is a metaheuristic optimization technique
inspired by the social behaviors exhibited by flocking birds or schooling fish. The
algorithm represents potential solutions as individual particles within a swarm, and
these particles move through the solution space based on their own experience and
the experience of their neighbors. According to Barnika Saha and Suraj Rath, the
algorithm leads to reliable and stable convergence for a 30-bus electric network [3].
In PSO, each particle has a position in the search space, representing a potential
solution to the problem at hand. Along with its position, each particle has a velocity
determining its direction and distance of movement in the next iteration. As the
particles "fly" through the solution space, they remember their best position (𝑝𝑏𝑒𝑠𝑡 )
and also have knowledge of the best position among all particles (𝑔𝑏𝑒𝑠𝑡 ). The
movement of each particle towards the 𝑝𝑏𝑒𝑠𝑡 and 𝑔𝑏𝑒𝑠𝑡 positions in the search space
is influenced by random factors, which ensures exploration and exploitation of the
search space.
The update equations for the position and velocity of each particle are as follows:
(𝑡+1)
𝑣𝑖
(𝑡)
= w × 𝑣𝑖
(𝑡)
+ c1 × 𝑟and × (𝑝𝑏𝑒𝑠𝑡,𝑖 − 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑖 ) + c2 × 𝑟and
(𝑡)
× (𝑔𝑏𝑒𝑠𝑡 − 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑖 )
(𝑡+1)
positio𝑛𝑖
(𝑡)
(𝑡+1)
= positio𝑛𝑖 + 𝑣𝑖
Where:
(𝑡)
𝑣𝑖 = velocity of particle i at time t
(𝑡)
positio𝑛𝑖 = position of particle i at time t
𝑝𝑏𝑒𝑠𝑡,𝑖 = best known position of particle i
𝑔𝑏𝑒𝑠𝑡 = best known position among all particles
w = inertia weight
c1, c2 = acceleration coefficients
rand = random number between 0 and 1
The challenge in optimizing power generation across various nodes lies in the
multidimensional nature of the problem. Each node has different power generation
capabilities, constraints, and requirements. By utilizing PSO, we can efficiently
navigate this vast solution space to identify optimal power outputs for each node.
In the context of this project:
1. Each particle represents a specific configuration of power generation across the
nodes.
2. The fitness or objective function is to minimize the cost of overall power
generation plus valorized transmission losses while ensuring individual node
18
constraints are met.
3. Based on the fitness values, the 𝑝𝑏𝑒𝑠𝑡 and best valuess are updated. Particles
then adjust their velocities and positions according to the PSO equations, moving
towards the more optimal areas of the solution space.
4. The algorithm continues until a stopping criterion is met, such as a maximum
number of iterations or when the solution quality reaches an acceptable threshold.
Figure 3: Graph of particles on the search domain converging on the global minimum
By applying Particle Swarm Optimization to the problem of power generation
optimization at nodes, we can explore a wide variety of power distribution
configurations efficiently. This ensures that we find a solution that maximizes
power generation and distribution while adhering to the constraints and
requirements of each node. PSO's ability to balance between exploration and
exploitation makes it an ideal choice for such complex, multi-dimensional
problems.
2.5
Locational Marginal Pricing
In their paper, Authors Haifeng Liu, Leigh Tesfatsion, and A. A. Chowdhury, who
are associated with IEEE, discuss the basics of Locational Marginal Pricing (LMP)
in the context of restructured wholesale power markets. It delves into the concepts,
definitions, calculations, and related constraints associated with LMP. Although,
LMP is primarily utilized in a deregulated power market with variable pricing and
Belize currently has a fixed price scheme, the LMP provides invaluable pricing
data that is necessary to optimize the battery charge and discharge cycles of both
utility and residential BESS.
Locational Marginal Pricing (LMP) signifies the cost associated with delivering an
incremental unit of electricity to a specific point in the electricity grid. In the
context of this study, LMP ensures that the dispatch of electricity is performed in
the most economically efficient manner.
LMP consists of three primary components. The first is energy cost which
represents the incremental cost of electricity generation. Next is congestion cost
which corresponds to the price implications of transmission bottlenecks, which can
prevent the most economical power sources from supplying electricity to all
19
regions. The last is loss cost which quantifies the costs associated with energy
losses during the transmission process.
The goal is to employ LMP in BEL’s daily operations by using advanced
optimization algorithms. These algorithms factor in technical grid constraints,
variable generation costs and limits, and the intricacies of transmission.
LMP values differ across grid locations due to variations in transmission
constraints and inherent power losses. These values will guide dispatchers in
deciding which generation units should be dispatched and their respective outputs
to most economically meet the demand.
When applied to optimization problems, LMP helps ascertain the most economical
dispatch of generation assets. The decision variables and constraints in this
optimization context are detailed below:
The AC OPF problem aims to minimize the total generation cost while meeting
system demand and ensuring all technical constraints are satisfied. The primary
equations are:
Objective Function (Cost Minimization):
min
∑ 𝑐𝑖 (𝑝𝑖 )
𝑝𝑖 , 𝑞𝑖 , 𝑥
𝑖∈I
Where:
𝑐𝑖 (𝑃𝐺𝑖 ) = cost function of the generator ( i ) as a
function of its real power output ( PGi ).
Power Balance Constraints:
Real Power:
𝑓𝑝𝑘 (𝑥) + ξ𝑘 + 𝐷𝑘 − ∑ 𝑝𝑖 = 0
for 𝑘 = 1, … , 𝑁
𝑖∈I𝑘
Reactive Power:
𝑓𝑞𝑘 (𝑥) + 𝑄load𝑘 − ∑ 𝑞𝑖 = 0
for 𝑘 = 1, … , 𝑁
𝑖∈I𝑘
Where:
𝑥 = [θ1 θ2 ⋯ θ𝑁−1 V1 V2 ⋯ V𝑁−1 ]
𝑓𝑝𝑘 (𝑥) is the real power flowing out of bus k:
𝑁
𝑓𝑝𝑘 (𝑥) = ∑ 𝑉𝑘 𝑉𝑖 [𝐺𝑘𝑖 cos(𝜃𝑘𝑖 ) + 𝐵𝑘𝑖 sin(𝜃𝑘𝑖 )]
𝑖=1
fqk (x) is the reactive power flowing out of bus k:
N
fqk (x) = ∑ Vk Vi [Gki sin(𝜃𝑘𝑖 ) − Bki cos(𝜃𝑘𝑖 )]
i=1
I𝑘 is the set of generators connected to bus 𝑘
𝑝𝑖 is the real power output of generator 𝑖
𝑞𝑖 is the reactive power output of generator 𝑖
𝐷𝑘 is the given real power load at bus 𝑘
𝑄load𝑘 is the given reactive power load at bus 𝑘
20
ξ𝑘 is an auxiliary parameter associated with bus 𝑘 that is set to zero.
Changes in ξ𝑘 will later be used to parameterize the real load increase
at bus k in order to derive the real power LMP at bus 𝑘.
𝑉𝑘 𝑎𝑛𝑑 𝑉𝑖 are the voltage magnitudes at nodes 𝑘 and 𝑖, respectively.
𝜃𝑘𝑖 = θk − θi is the voltage angle difference between nodes 𝑘 and 𝑖
Gki and Bki are the real and imaginary parts of the admittance
between nodes 𝑘 and 𝑖.
Network Constraints:
0 ≤ 𝑆𝑖𝑗 (𝑥) ≤ 𝑆𝑖𝑗𝑚𝑎𝑥
𝑉𝑘𝑚𝑖𝑛 ≤ 𝑉𝑘 ≤ 𝑉𝑘𝑚𝑎𝑥
Where:
𝑆𝑖𝑗 (𝑥) is the magnitude of the complex power flowing from bus 𝑖 to
bus 𝑗
𝑉𝑘𝑚𝑖𝑛 and 𝑉𝑘𝑚𝑎𝑥 are the minimum and maximum Voltage Magnitudes
bus 𝑘
Generator Output Constraints:
𝑝𝑚𝑖𝑛
≤ 𝑝𝑖 ≤ 𝑝𝑚𝑎𝑥
𝑖
𝑖
𝑞𝑚𝑖𝑛
≤ 𝑞𝑖 ≤ 𝑞𝑚𝑎𝑥
𝑖
𝑖
Where:
𝑝𝑚𝑖𝑛
and 𝑝𝑚𝑎𝑥
are the minimum and maximum real power outputs for
𝑖
𝑖
generator 𝑖, respectively.
𝑞𝑚𝑖𝑛
and 𝑞𝑚𝑎𝑥
are the minimum and maximum reactive power
𝑖
𝑖
outputs for generator 𝑖, respectively.
The AC OPF model provides higher accuracy compared to the DC OPF model,
though it often faces convergence issues. Furthermore, the AC OPF can take up to
60 times longer than its DC counterpart [4]. For calculating LMP in power market
operations, the DC OPF model (sometimes referred to as the linearized AC OPF
model) is commonly utilized. LMPs are calculated using the DC Optimal Power
Flow (DC OPF) model. However, there are certain assumptions and simplifications
in the DC OPF model that one must be aware of, especially in the context of LMP
calculations.
The DC OPF model linearizes the power flow equations, making the computational
process simpler and faster. This is particularly useful for real-time and day-ahead
market operations.
While the DC OPF model provides a simplified approach to calculating LMPs, it's
important for power system operators and market participants to be aware of its
limitations. When the aforementioned conditions are not met, the DC OPF may
lead to inaccuracies in LMP values. In such cases, using an AC OPF model or
applying corrective factors might be necessary to get more accurate pricing signals.
The Power Balance Constraints of the AC OPF problem become reduced to:
21
𝑁
∑
[
𝑚=1,𝑚≠𝑘
1
(θ − θ𝑚 )] = ∑ 𝑃𝑖 − 𝐷𝑘 = 𝑃𝑘 − 𝐷𝑘
𝑋𝑘𝑚 𝑘
for 𝑘 = 1 … 𝑁
𝑖∈𝐼𝑘
Where:
𝑋𝑘𝑚 is the Reactance of the line from bus 𝑘 to 𝑚
θ𝑘 𝑎𝑛𝑑 θ𝑚 are the voltage angles at bus 𝑘 and 𝑚
This is only acceptable under these assumptions:
 Voltage Angles Difference are very small and so the sine and cosine
of the angle difference can be approximated as:
cos(θ𝑘 − θ𝑚 ) ≈ 1
sin(θ𝑘 − θ𝑚 ) ≈ θ𝑘 − θ𝑚
 DC OPF assumes a lossless transmission system. This is equivalent to
having very low branch power. This allows us to assume the voltage
profile across the network should be relatively flat. Typically, the bus
voltage is assumed to be 1 per unit.
 Reactive Power is zero.
 The DC OPF model becomes more accurate when the resistance to
reactance ratio (𝑅𝑘𝑚 /𝑋𝑘𝑚 ) of the transmission lines is less than 0.25.
Systems with higher rkm/xkm ratios may exhibit discrepancies
between the DC and AC OPF results.
2.6
Decentralized Locational Marginal Pricing
The DLMP algorithm proposed by Sruthi Davuluri at MIT integrates perfectly with
Belize's radial electric distribution systems [5]. This approach is designed to tackle
the central problem of maintaining system stability in a small grid like Belize’s
network while trying to profitably accommodate the uptake of renewable energy by
catering to prosumers individualized demand functions. Computational feasibility
and adherence to the physical constraints of the system are also addressed in this
approach. Unlike existing methodologies, which often involve numerous iterations
or lack convergence, the algorithm presented here consistently converges to the
same solution as a centralized operator armed with perfect information, and it
achieves this convergence with only two system-wide sweeps [5]. Through a proofof-concept analysis conducted on a 46-bus system, this research demonstrates the
tangible physical and economic advantages of the decentralized algorithm, even
when managing varying levels of distributed energy resources.
DLMP solves the limitations of centralized OPF algorithms like PSO and LMP.
OPF assumes perfect information under static scenarios. It is not feasible for
centralized operators like BEL to account for many distributed resources at the
household level. The increased penetration of Distributed Energy Resources (DER)
exacerbates information asymmetry. Renewable energy resources, which are
intermittent and harder to predict, strain the traditional model. Lastly, current
models do not adequately factor in diverse customer preferences or the varied
elasticity of demand for different products.
The decentralization of optimization calculations overcomes the challenges of
information asymmetry and diverse demand functions. This is achieved by the
implementation of more localized operations, e.g., solving the objection function at
each prosumer node. There are technologies that enable this such as smart meters
22
which host Linux operating systems. Manufacturers provide SDKs for creating
customized apps.
DLMP relies on a recursive distributed algorithm where downstream nodes
communicate with upstream parent nodes. The radial distribution network is
modeled as a graph. Nodes in this graph have relationships (parent-child), which
denote informational or physical connections. Since all distribution feeders in the
BEL network are radial, the algorithm can leverage BEL GIS data to establish
connectivity.
True, real-time optimization can be achieved with a decentralized operation, where
data processing and decision-making are distributed across multiple nodes or
entities as opposed to the traditional centralized approach. With decentralization,
each node or entity might make decisions based on localized information, which
could be more detailed and timelier than information available in a centralized
system.
In order to qualify as an agent, a prosumer must be able to control the energy
exported and imported into the grid such as by utilizing BESS. As each agent will
function as a dispatchable generator, it must determine how much to feed or take
from the grid. This can be achieved by two sweeps across the graph. The forward
sweep starts at nodes at the periphery and ends at the head node which is at the
substation. The head node receives pricing information for energy from the
transmission grid at that node.
The forward sweep optimization function is:
∏ 𝑖, 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 ∶
min
𝐶 (𝑥 ) + ∑ 𝐵𝑐 (𝑦𝑖𝑐 )
𝑥𝑖 , 𝑦𝑖𝑐 𝑖 𝑖
𝑐∈ℂ𝑖
𝑠. 𝑡. ∶ 𝑥𝑖 + 𝑦̂𝑝𝑖 = ∑ 𝑦𝑖𝑐 (𝜆𝑖 )
𝑐∈ℂ𝑖
𝑥𝑖𝑚𝑖𝑛 ≤ 𝑥𝑖 ≤ 𝑥𝑖𝑚𝑎𝑥
𝑚𝑎𝑥
𝐹𝑖𝑐𝑚𝑖𝑛 ≤ 𝑦𝑖 ≤ 𝐹𝑝𝑖
Where:
𝑦̂𝑝𝑖 is the parent branch injection
𝑦𝑖𝑐 is the child branch injection from child 𝑐 to node 𝑖
𝑥𝑖 is the power injected at the node by agent 𝑖
𝐶𝑖 is the cost function of agent 𝑖
𝐵𝑐 is the children bid function
𝑚𝑎𝑥
𝐹𝑖𝑐𝑚𝑖𝑛 and 𝐹𝑝𝑖
are the branch power limits
𝜆𝑖 represents the solution of the Lagrangian for three
different expected injections from the parent nodes (𝜆𝑖 , 𝑦̂𝑝𝑖 ),
(𝜆+
̂𝑝𝑖 ), (𝜆−
̂𝑝𝑖 ) where 𝜖 is chosen to be a small
𝑖 , (1 + 𝜖)𝑦
𝑖 , (1 − 𝜖)𝑦
number such as 0.001
The backward sweep optimization function is:
min
∏ 𝑖, 𝐵𝑎𝑐𝑘𝑤𝑎𝑟𝑑 ∶ 𝑥 , 𝑦 , 𝑦 𝐶𝑖 (𝑥𝑖 ) + ∑ 𝐵𝑐 (𝑦𝑖𝑐 ) + 𝜆𝑝𝑖 𝑦𝑝𝑖
𝑖 𝑝𝑖 𝑖𝑐
𝑥∈ℂ𝑖
23
𝑠. 𝑡. ∶ 𝑥𝑖 + 𝑦𝑝𝑖 − ∑ 𝑦𝑖𝑐 = 0
𝑥∈ℂ𝑖
𝑚𝑖𝑛
𝑚𝑎𝑥
𝑦𝑝𝑖
≤ 𝑦𝑝𝑖 ≤ 𝑦𝑝𝑖
𝑥𝑖𝑚𝑖𝑛 ≤ 𝑥𝑖 ≤ 𝑥𝑖𝑚𝑎𝑥
𝑚𝑖𝑛
𝑚𝑎𝑥
𝐹𝑝𝑖
≤ 𝐷𝐹𝑖𝑖 𝑥𝑖 + 𝐷𝐹𝑖𝑝 𝑥𝑝 ≤ 𝐹𝑝𝑖
Where:
𝑦̂𝑝𝑖 is the parent branch injection
𝑦𝑖𝑐 is the child branch injection from child 𝑐 to node 𝑖
𝑥𝑖 is the power injected at the node by agent 𝑖
𝐷𝐹𝑖𝑗 correspond to the element in 𝑖 𝑡ℎ row and 𝑗 𝑡ℎ column of the
Distribution Factor matrix DF
𝜆𝑝𝑖 is the Lagrangian solution or the nodal price communicated from
the parent node to its children node
𝐵𝑐 is the children bid function
𝑚𝑎𝑥
𝐹𝑖𝑐𝑚𝑖𝑛 and 𝐹𝑝𝑖
are the branch power limits
The results of DLMP and a centralized OPF were established for the island of
Flores in the Azores. DLMP provides a cost similar to OPF for a 46 bus network
[5]. In the context of this study, DLMP ensures convergence to an optimal solution
comparable to the centralized OPF with perfect information.
2.7
Limitations of the Study
The study assumes electrical loads are symmetrical and balanced. This
simplification may not hold true in practical scenarios where loads can be
asymmetrical and unbalanced, leading to different optimization outcomes.
Three-Winding Transformers were modeled as Two-Winding due to the
negligible load on the tertiary winding. If tertiary loads are large, the model
will not hold
3.0
METHODOLOGY
3.1
Framework Selection
In the rapidly changing landscape of web development, companies must make
strategic choices that align with their long-term vision and available resources. For
our company, the decision to choose ASP.NET and C# over Python and Django is
rooted in several crucial considerations. Our company has a significant investment
in Microsoft technologies and infrastructure. Adopting ASP.NET and C# ensures
seamless integration with our existing systems, thereby reducing the complexities
and potential pitfalls of integrating disparate technologies. Django inability to
integrate with Microsoft SQL Server is its death knell.
3.2
Weather Data Sources
Accurate weather data is essential for this application. For our project, we sourced
weather data from several renowned platforms, evaluating them for the best quality
and reliability; namely, meteomatics.com, Tomorrow.io, and Visual Crossing.
24
For obtaining historical weather data, we relied on the Belize National
Meteorological Service. Their data repository, accessible at
https://surface.nms.gov.bz/api/rawdata, provided us with an expansive archive of
historical weather data. To ensure the highest relevance and accuracy, the weather
station closest to each feeder’s centroid was selected as the primary data source.
Temperature at Belmopan
33,00
31,00
29,00
27,00
25,00
23,00
21,00
19,00
17,00
15,00
2023-10-27 03:00:00
2023-10-28 03:00:00
meteomatics
nms
2023-10-29 03:00:00
tomorrow_io
visualcrossing
Figure 4: Temperature forecast and historical (nms) for Belmopan Weather Station Location
Temperature at Tower Hill
35,00
30,00
25,00
20,00
15,00
2023-10-27 03:00:00
meteomatics
2023-10-28 03:00:00
nms
tomorrow_io
2023-10-29 03:00:00
visualcrossing
Figure 5: Temperature forecast and historical (nms) for Tower Hill Weather Station
Error - Root Mean Squared Deviation
Tomorrow.io irradiance was not available in trial.
temperature humidity wind_speed wind_direction irradiance rainfall
Parameter
meteomatics
1.64
14.01
3.42
172.53
99.28
1.93
1
tomorrow.io
1.59
15.64
3.76
177.12
0.00
2.76
visualcrossings
1.88
15.13
4.25
167.09
154.96
2.03
1
Table 2: RMSD for weather parameters from three evaluated sources.
25
For weather forecasting, we evaluated the three major online platforms. After
rigorous testing, both Meteomatics and Tomorrow.io consistently displayed the
smallest root mean deviation squared for weather parameters, emerging as top
contenders for our forecasting needs.
While both platforms displayed remarkable accuracy, the decision to opt for
Tomorrow.io was influenced by its unique feature of supporting polygon shapes in
its API. This capability allowed us to obtain average weather parameters across a
specified area, providing a more holistic and accurate perspective, especially
beneficial for regional analyses.
3.3
Historical Load Data Sources
One of the foundational data sources for our project was the Supervisory Control
and Data Acquisition (SCADA) system from Belize Electricity Limited (BEL). The
SCADA system, serving as BEL's master data repository, played a pivotal role in
offering real-time and historical electrical data essential for our research and
operational needs.
From the SCADA master, we primarily extracted two crucial electrical parameters,
Active Power (P) and Reactive Power (Q). These parameters are fundamental in
understanding and analyzing the power dynamics and the overall performance of
the electrical system. To provide a comprehensive analysis, it was imperative to
correlate the electrical data with weather patterns. The key to achieving this
seamless integration was the use of Coordinated Universal Time (UTC). Both the
electrical data from BEL's SCADA and the weather data were timestamped in
UTC, ensuring uniformity and precision.
By synchronizing the datasets using UTC time, we were able to superimpose
electrical patterns over weather trends, facilitating a holistic understanding of how
weather variations influence power dynamics. This synchronization not only
improved the accuracy of our analyses but also enriched the depth of insights
drawn from the combined data.
3.4
Network Data Source
The foundation of our network analysis and subsequent optimizations was rooted in
the comprehensive data extracted from an existing ETAP (Electrical Transient
Analyzer Program) model. ETAP, being a robust electrical engineering software,
facilitated the precise modeling of our electrical system.
The ETAP model was made available to us in an XML (Extensible Markup
Language) format. XML, being a structured document standard, allowed for
systematic parsing of the myriad of electrical parameters embedded within.
Through a series of parsing algorithms, we were able to successfully extract and
interpret all the essential network constraints.
A salient feature of our system is its configurability. Post extraction, the data was
seamlessly integrated into our software, enabling users to make real-time
modifications. Particularly, users possess the capability to alter the status of
switches, thereby actively reconfiguring the network layout. This flexibility
empowers users to simulate various operational scenarios and deduce optimal
strategies.
The ETAP model was not just limited to basic network layout. It provided in-depth
26
data about generators, including their minimum and maximum active (P) and
reactive (Q) power limits. Furthermore, the model outlined specific constraints like
line current limits and transformer power limits, crucial for ensuring network safety
and efficiency.
Figure 6: Detailed BEL Networks
Figure 7: Minimized BEL Networks
In line with our objective of achieving efficient calculations, our software
incorporates a network minimization feature. This process involves the removal of
unnecessary nodes and edges, simplifying the network without compromising its
integrity. The image on the right showcases the streamlined graph postminimization. This pared-down representation ensures quicker calculations,
enhancing the overall user experience.
Through meticulous parsing and integration of the ETAP XML model, we have
established a dynamic and configurable network system. The inclusion of in-depth
generator data and constraint details, combined with the minimization feature,
ensures that our software achieves its goal of efficiency and precision.
27
An integral part of our network analysis and optimization process is the modeling
of the distribution network. Our approach to modeling the distribution network is
characterized by its simplicity and accuracy in representing real-world scenarios.
Key to our modeling approach is the representation of zones within the distribution
network as point loads. This method involves approximating the load of a zone
based on the average daily kilowatt-hour (kWh) consumption of the customers
within that zone. By doing so, each zone's load is proportional to the feeder it is
connected to, reflecting a realistic and manageable model of the distribution
network's load distribution.
Our model incorporates network switching devices and tie disconnect switches,
essential elements for operational flexibility. These components enable the
reconfiguration of zones within the network. This flexibility is crucial for
simulating various operational scenarios, such as load shifting or emergency
response strategies, allowing for a comprehensive analysis of network behavior
under different conditions.
The inclusion of these elements in our model enhances the ability to simulate realworld network configurations and response strategies. It allows for a more detailed
and accurate analysis of the distribution network, particularly in understanding how
different zones interact and how changes in one part of the network can impact the
overall system. This level of detail is crucial for devising optimal strategies for
network management and contingency planning.
3.5
Prediction Model
The construction of our predictive model started with integrating vital weather
parameters. Weather plays an indispensable role in power demand fluctuations,
especially in Belize where a large portion of load is due to motors in cooling
devices like A/Cs and fridges. These formed the bases of our feature inputs while P
and Q are the outputs to predict.
To enhance the accuracy and reliability of our predictions, a list of additional
elements was integrated into the model. These include:
hour: Recognizing the time of day is vital as power demands vary between peak
and off-peak hours.
Week number: Week of the year can indicate demand patterns, especially in
touristic regions where there is seasonal demand.
P(1hr ago) and Q(1hr ago): Demand data from an hour ago can provide short-term
trend insights.
P(1 day ago) and Q(1 day ago): Daily demand variations can offer a broader view
of the demand curve.
Event number: This caters to specific events that may surge or plummet the power
demand such as holidays.
Pavg(past 3hrs) and Qavg(past 3hrs): Three-hour average values to observe intra-day
demand changes.
Pavg(past 24hrs) and Qavg(past 24hrs): A day's average to track daily patterns.
Outage energy: One of the most innovative aspects of our model is the inclusion of
outage energy, extracted from an outage database. This data represents the
unserved energy during outages and will be instrumental in accounting for planned
28
outages in future predictions.
Figure 8: Real Power Demand for a 1 week span for all 44 Feeders
The first image presents a comprehensive view of feeder demands over a week. It
demonstrates that despite the natural variability, there exists a significant degree of
predictability in demand. Daily rhythms and recurring patterns are evident,
showcasing the viability of our predictive approach.
Figure 9: Normalized Real Power, P, and Temperature for 6 Feeders in Belize City (Temperature in Squares)
Figure 10: Normalized Real Power Demand and Humidity for 6 Belize City Feeders
The second image presents a comparison between normalized temperature values
and power demand (P). The remarkable correlation between these two variables is
evident. As temperature rises or falls, corresponding peaks and troughs in the power
demand can be observed. This strong interdependency reinforces the need to
consider temperature as a crucial predictor in our model. The third image shows the
correlation between P and humidity. Although not as strong as temperature, it is a
factor to be inputted into the model.
Our predictive model's construction, rooted in a synthesis of historical data, realtime inputs, and innovative parameters like outage energy, positions it as a robust
tool for future demand forecasting. The evident correlation between temperature,
humidity and power demand further validates our approach. Such comprehensive
modeling ensures grid stability, efficient resource allocation, and optimal power
29
distribution to meet future challenges.
3.6
Generator Costs
For optimal operation and planning of power systems, understanding the efficiency
curves of generators is paramount. These curves define how much fuel a generator
consumes to produce a given amount of power. As such, they are a critical
component for economic dispatch and optimizing operational costs.
Gallons of Diesel
West Lake Gas Turbine Efficiency Curve
180
160
140
120
100
80
60
40
20
0
y = 0,4514x2 - 14,957x + 202,76
0
2
4
6
8
10
12
14
16
18
20
LM2500 Real Power Output (MW)
Figure 11: Fuel Consumption of Gas Turbine for Various Operating Points
The efficiency curve for the West Lake Gas Turbine, as showcased in the provided
graph, was derived from historical production data. This data comprises records of
the power output of the turbine and the corresponding fuel consumption, measured
in gallons of diesel. The same methodology was employed with BEL’s other
generators where the fuel consumption is passed on to consumers.
The data points on the graph represent individual recorded instances of power
output and fuel consumption. To extract a tangible relationship from these points, a
best-fit curve was employed. The y value is the gallons of diesel consumed and x is
the MW output of the generator.
It's evident from the equation and the graph that the relationship between power
output and fuel consumption is quadratic, typical for many turbine efficiency
curves. The quadratic nature suggests that there are optimal operating points where
the turbine is most efficient and deviations from these points result in increased fuel
consumption per unit of power output.
The derived fuel efficiency curve is instrumental in optimization problems. With
the knowledge of how much fuel is consumed for a given power output, decisionmaking algorithms can make informed choices about how to dispatch the generator.
For instance, if there's a need to minimize fuel costs during operation, the algorithm
can refer to this curve to determine the most fuel-efficient power output level.
Additionally, in a scenario with multiple generators, each with its efficiency curve,
the system can be optimized to dispatch the right combination of generators to meet
demand at the lowest possible fuel cost.
30
3.7
Price Forecast
Electricity importation is very important in BEL’s strategy to ensure reliability,
diversify the energy mix, and capitalize on economical pricing. In the context
discussed here, the importation of electricity from Mexico constitutes a significant
portion, approximately 40%, of the annual consumption.
Mexico operates a deregulated electricity market, which means that the prices of
electricity are determined based on supply and demand dynamics rather than being
set by a centralized authority. Within this market, the concept of Locational
Marginal Pricing (LMP) is utilized. LMP represents the price of electricity at
specific nodes or locations within the grid. It takes into account factors such as
generation costs, transmission constraints, and demand at that specific location.
BEL imports electricity specifically from the BEL-115 node in Mexico. Due to the
deregulated nature of the market, it's crucial for BEL to have an understanding of
the expected price fluctuations at this node to make informed buying decisions.
To aid in decision-making, the Mexican electricity market provides a price forecast
for each node. For the BEL-115 node, this forecast is given per hour and extends
two days into the future. This granular and short-term forecast allows for more
accurate planning, especially when integrating these prices into an optimization
problem.
When optimizing the dispatch of generation units and determining the ideal level of
electricity imports, the LMP values from the BEL-115 node become a key input.
The optimization problem, in this case, is solved as a time series, considering each
hour within the two-day forecast period.
The objective of the optimization is to minimize costs, possibly reduce emissions,
and ensure good operating reserve margins. Given the significant proportion of
electricity that is imported from Mexico, the forecasted LMP values can have a
substantial impact on the resulting optimal solution.
For instance, if the LMP values indicate high prices for certain hours, the
optimization problem might favor increased local generation (if feasible) during
those hours to offset expensive imports. Conversely, during hours when the LMP
values are low, it might be more economical to increase imports and reduce local
generation.
3.8
Fuel Management
Belize's energy sector features a mix of resources, with hydroelectric dams playing
a pivotal role in ensuring a consistent power supply. The Vaca, Mollejon, and
Chalillo watersheds feed the three primary dams that fuel a significant portion of
the country's energy needs. In an environment where diverse energy sources
contribute to the national grid, it's crucial to manage each fuel type effectively. This
includes not only traditional fuels like Heavy Fuel Oil (HFO) and diesel but also
'water fuel' – the inflow to the hydroelectric dams.
31
Figure 12: Water Shed of the three dams where rainfall prediction drive fuel management.
Short-term predictions can be achieved by leveraging meteorological data and river
flow rates. It's possible to anticipate inflows for upcoming days and weeks. These
predictions guide immediate operational decisions, such as reservoir releases and
turbine dispatches.
Long-term predictions are a little trickier. Seasonal weather patterns, historical
data, and advanced hydrological models help forecast inflows over months or even
years. This assists in long-term planning and infrastructure decisions.
Ensuring that the reservoirs maintain optimum water levels is key to providing a
consistent power supply. This requires a delicate balance - holding enough reserve
to handle peak demands, yet also allowing for controlled releases to sustain river
ecosystems downstream.
While hydroelectric power can provide a consistent energy source, other
contributors like biomass are seasonal. During periods when biomass or other
sources are at low generating capacity, the dams need to be primed to take on a
larger share of the load. Predicting and preparing for these shifts ensures that
Belize's energy supply remains stable year-round.
While water is a renewable and sustainable fuel source, Belize's energy grid also
relies on traditional fuels, namely HFO and diesel. Effective management of these
fuels is essential for several reasons. Ensuring a consistent supply of HFO and
diesel requires coordination with suppliers, transportation logistics, and storage
considerations. Global oil prices can be volatile. By maintaining strategic reserves
and employing hedging strategies, it's possible to mitigate the impact of sudden
price hikes. Lastly, traditional fuels have a larger carbon footprint than renewable
sources. Effective management also means optimizing their use to minimize
environmental impacts.
3.9
Batteries in the Mix
Renewable energy sources, such as solar and wind, have transformed the energy
landscape by providing cleaner alternatives to fossil fuels. However, they also
introduce a level of variability and unpredictability due to their reliance on natural
32
phenomena. Solar panels, for example, produce energy only during the day and can
be affected by cloud cover, while wind turbines rely on wind speeds that can be
inconsistent.
Figure 13: 2019$ installed cost per kW predictions
To address this variability, batteries can be employed to act as a buffer, storing
excess energy produced during peak renewable generation times and releasing it
during periods of low generation or high demand. This ensures a consistent and
reliable power supply. Rapid fluctuations in renewable generation can lead to
voltage and frequency instabilities in the power grid. Batteries can quickly absorb
or release energy to stabilize these parameters, ensuring grid reliability. Batteries
can also be discharged during periods of peak demand, reducing the need for
expensive peaker plants and alleviating stress on the grid.
As the energy sector evolves with more distributed energy resources, there's a
growing need for a more granular pricing mechanism – enter nodal pricing. Nodal,
or locational marginal pricing (LMP), reflects the value of electricity at specific
locations, or nodes, within the grid, considering generation costs, demand, and
transmission constraints.
For battery storage systems, nodal pricing plays a crucial role in several ways.
Knowing the LMP at different locations helps determine the most economically
viable sites to place battery storage systems. Areas with frequent congestion or high
price differentials can benefit the most from battery installations. Batteries can be
programmed to charge during periods of low LMP (excess supply or low demand)
and discharge during high LMP periods, maximizing economic returns. Regions
with high LMP variability might signal a higher potential return on investment for
battery storage, attracting more developers and investors to those areas.
33
4.0
RESULTS AND DISCUSSION
4.1 Load Forecast
The forecasting performance of our neural network model, developed using
TensorFlow, was satisfactory. The model's predictions were based on weather
metrics and the 12-day average load values corresponding to each hour of the day.
The neural network’s forecasting accuracy was assessed by comparing the actual
load values with the forecasted values across different hours and nodes within the
network. The nodes, designated as OWK01, OWK02, OWK03, and OWK04,
represent distinct points within the network where telemetry is installed to monitor
load.
Below, the provided graphs depict the performance of a neural network in
predicting the actual active power (P) and reactive power (Q) across various
electrical feeders over a set period. In the first graph, "Actual P vs Forecasted P by
Feeder," we observe the comparison between actual and forecasted P values for
different feeders, labeled OWK01 through OWK04, with their respective forecasts.
The graph demonstrates a reasonable degree of accuracy in the forecasts, yet there
are noticeable discrepancies between the predicted and actual values. To enhance
the accuracy of these predictions, one approach could be to incorporate the
immediate historical values of P and Q just before the forecast period. This
inclusion could enable the model to capture the transient behaviors and recent
trends in power consumption, potentially improving forecast precision.
Actual P vs Forecasted P by Feeder
4
3,5
3
2,5
2
1,5
1
0,5
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
OWK01
OWK01_forecast
OWK02
OWK02_forecast
OWK03
OWK03_forecast
OWK04
OWK04_forecast
Figure 14: Real Load forecasts compared to Actual Real Loads
The second graph, "Actual Q vs Forecasted Q by Feeder," shows similar trends in
the Q forecasts across the same feeders. Again, the disparities between forecasted
and actual Q values suggest that the model may benefit from the inclusion of recent
power trends leading up to the forecast period. This adjustment could be
34
particularly beneficial for capturing short-term fluctuations caused by reactive
loads, which are inherently more volatile due to their dependency on the
operational state of the network's inductive and capacitive components.
Actual Q vs Forecasted Q by Feeder
0,8
0,6
0,4
0,2
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
-0,2
-0,4
OWK01
OWK01_forecast
OWK02
OWK02_forecast
OWK03
OWK03_forecast
OWK04
OWK04_forecast
Figure 15: Reactive Load forecasts compared to Actual Reactive Loads
In both OWK02 and OWK04 feeder, which are both rural feeders located furthest
from the temperature measurement point, the deviations are more pronounced. This
suggests that geographical factors and localized weather conditions significantly
impact the prediction accuracy for this feeder. Improving the model could involve
incorporating weather measurements taken closer to the weighted centroid of the
feeder. Doing so would allow for more localized and thus relevant environmental
input variables, which are likely to reflect the actual conditions experienced by the
consumers served by this feeder.
Power Aggregated by Load Center
10
8
6
4
2
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
OWK_P
OWK_P_forecast
OWK_Q
Figure 16: Forecasted P & Q vs Actual Loads
35
OWK_Q_forecast
Lastly, the third graph, "Power Aggregated by Load Center," aggregates the P and
Q values for the four feeders, presenting a consolidated view of the load center's
total power. The aggregated forecasts follow the actual trends quite closely, which
indicates that while individual feeder predictions may have some inaccuracies, the
overall systemic forecasts can still reliably indicate broader trends. In the network
model, feeder loads are aggregated on a single node for simplicity. Nevertheless,
the strategies suggested for improving individual feeder forecasts could also
enhance the aggregated predictions, ensuring that the system's operators can make
well-informed decisions for load management and dispatch planning.
Quantitative performance metrics such as, Root Mean Squared Error (RMSE) were
utilized to provide a statistical measure of forecast accuracy. This metrics helps in
identifying the extent of deviation from actual load values and in evaluating the
model's precision. Refinements in the training data are necessary to improve the
forecast.
The influence of weather metrics on the load forecasting was analyzed, recognizing
that certain weather conditions have a more pronounced effect on load variations.
The model's reliance on historical averages also played a significant role in shaping
the forecast outcomes.
Overall, the neural network model exhibited a commendable level of forecasting
proficiency, with certain areas identified for enhancement. The comparative
analysis underscores the model's potential in predicting electrical load.
4.2
PSO Output
The implementation of Particle Swarm Optimization (PSO) in the operational
strategy of Belize Electricity Limited (BEL) has yielded insightful results. In the
recent instance, the PSO algorithm ran with a configuration of 15 particles, with the
objective of minimizing the operational cost of electricity production. The
convergence graph illustrates the algorithm's progression over 26 iterations,
highlighting a significant reduction in global best cost.
Global Best Cost out of 15 Particles
$20 000,00
$18 000,00
$16 000,00
$14 000,00
$12 000,00
$10 000,00
$8 000,00
$6 000,00
$4 000,00
$2 000,00
$0,00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
iterations
Figure 17: Global Best of 15 Particles
36
Initially, the PSO algorithm generated a diverse set of particles, each representing a
potential solution to the optimization problem. Each particle's position and velocity
were initialized to explore the solution space, with the aim of satisfying the power
balance constraints. These constraints are vital to ensure that the total generation
equals the total demand plus losses, maintaining the stability and efficiency of the
power network.
Upon generation, the values encapsulated by each particle were evaluated to
determine if they met power balance constraints. Particles meeting these constraints
were then inputted into a PandaPower network model. PandaPower, an open-source
Python library, serves to simulate and analyze power system networks. The model's
role was to validate each particle by checking if a power flow convergence could be
achieved. Convergence in this context means that the model's iterative process
successfully calculated the voltages and power flows throughout the network
without diverging, confirming the feasibility of the particle's solution.
The cost associated with each validated particle was computed, reflecting the
economic expenditure required to operate the network under the conditions
proposed by the particle. As iterations progressed, particles were guided by their
own best-known positions and the best-known positions of their neighbors,
gravitating towards the most cost-effective solutions.
The optimization process demonstrated a sharp decrease in global best cost,
indicating that the PSO was effective in identifying and honing in on lower-cost
operational strategies. After the initial iterations, the rate of cost reduction
plateaued, suggesting that the algorithm was approaching an optimal solution. The
end result was a cost that significantly undercuts the initial estimates, underscoring
the potential of PSO in enhancing the economic efficiency of BEL's energy
distribution.
time
2023-10-27 3:00
2023-10-27 3:00
2023-10-27 4:00
2023-10-27 4:00
2023-10-27 5:00
2023-10-27 5:00
2023-10-27 6:00
2023-10-27 6:00
2023-10-27 7:00
2023-10-27 7:00
2023-10-27 8:00
2023-10-27 8:00
island_name
Main
CCK
Main
CCK
Main
CCK
Main
CCK
Main
CCK
Main
CCK
total_cost price_per_MWh load_P
load_Q
losses
$13779.55
$195.955 69.78485 4.609202 0.76103
$989.5391
$778.0383 1.246455 0.405513 1.995785
$15117.05
$191.0595 78.48334 6.378405 0.807488
$888.1195
$771.6268 1.126041 0.35784 2.165949
$16765.8
$219.2251 75.97591 6.242106 0.655926
$875.1926
$770.8117 1.111465 0.347453 2.109523
$14303.84
$194.9938 72.83234 5.743592 0.712994
$883.0995
$771.4148 1.120225 0.35145 2.144841
$13385.64
$188.8596 70.40274 5.464116 0.667969
$878.1615
$771.3309 1.113933 0.35663 2.158003
$14953.37
$220.4103 67.48759 4.685156 0.524341
$853.223
$769.0061 1.084843 0.354037 2.223557
Table 3: PSO Results for Selected Time Span
The tabulated results post-optimization reveal a remarkable improvement in the
economic operation of BEL's grid. Each entry in the table represents an optimized
state of the network at a specific hour, detailing the total cost of operation, the price
37
per megawatt-hour (MWh), the active power (P) load, the reactive power (Q) load,
and the system losses.
For instance, on 2023-10-27 at 3:00, the total operational cost for the Main Grid
stood at $13,779.55 with a price of $195.955 per MWh, indicating a competitive
market rate. The load P and load Q were recorded at 69.78485 MW and 4.609202
MVAR, respectively, with losses amounting to 0.76103%. In contrast, Caye
Caulker (CCK) island, smaller and with a significantly higher price per MWh of
$778.0383, has a greater challenge in optimizing its operational strategy, due to
high cost diesel generators.
As the hours progressed, there was a consistent pattern where the total cost and
price per MWh fluctuated in response to the changing load demands. This dynamic
nature highlights the PSO's ability to adapt and find cost-effective solutions across
different load conditions and times of the day. It is noteworthy that the losses
remained relatively low, emphasizing the effectiveness of the optimized
configurations in minimizing waste.
The optimized cost for each island was computed, taking into account the specific
constraints and requirements of each area. The PSO's flexibility in handling unique
operational characteristics of each island is evident from the variations in total costs
and prices per MWh.
However, the algorithm did not just optimize for cost; it also maintained the system
within operational constraints. Voltage constraints were continuously monitored,
ensuring that all bus voltages remained within the acceptable range, thus
safeguarding the integrity of the network and the quality of service to the
consumers. Similarly, transformer power constraints and line current constraints
were observed, with any potential violations being promptly addressed. This
comprehensive approach ensured that the solutions were not only economically
feasible but also operationally viable, balancing cost-effectiveness with reliability.
The PSO's application in BEL's operational strategy thus demonstrates its utility as
a tool not only for cost reduction but also for maintaining system integrity. By
factoring in various constraints and losses, the PSO provided a holistic solution that
could potentially be applied to real-world scenarios, contributing to more efficient
and reliable power system operations. The results underscore the PSO's potential to
enhance the operational efficiency of electricity markets, particularly in scenarios
that necessitate consideration of complex and dynamic network conditions.
4.3
LMP Algorithm
Locational Marginal Pricing (LMP) serves as a cornerstone in modern electricity
markets, offering a mechanism to determine electricity prices based on the marginal
cost of supplying the next unit of electricity at a specific location. While
theoretically sound for continuous variables, LMP faces significant challenges
when applied to discrete variables, notably in the case of capacitors used in power
systems for voltage control and reactive power management. It also violates the
PUC mandated fixed price structure.
Capacitors in power systems are inherently discrete in nature. Their operation,
characterized by binary states (on/off), presents a stark contrast to the continuous
38
generation outputs typically modeled in LMP calculations. This discreteness poses
a challenge for the LMP algorithm, which is fundamentally designed for and most
effective with continuous optimization models. The inability of LMP to accurately
account for the binary switching of capacitors leads to an oversimplified
representation of the power system's reactive power capabilities and voltage
regulation mechanisms. Consequently, this limitation can result in operational
inefficiencies, such as suboptimal voltage profiles and reactive power flows,
potentially compromising system reliability and economic efficiency.
The situation becomes more complex when considering the operational philosophy
of Belize Electricity Limited (BEL). BEL's approach to pricing and cost allocation
emphasizes equal cost-sharing among consumers, irrespective of their geographical
location, and maintains a fixed price structure. This philosophy, while equitable in
intent, may not align well with the LMP model, which by design creates locational
price variations to reflect the actual cost of electricity delivery, including
transmission losses and congestion costs. BEL's uniform pricing approach,
juxtaposed with LMP's locational variability, can lead to disparities between the
theoretical LMP-based prices and the practical, uniform rates charged to
consumers.
In conclusion, while LMP provides a robust framework for pricing in electricity
markets, its application to systems with significant discrete components such as
capacitors, especially under pricing philosophies like that of BEL, reveals notable
limitations. These limitations underscore the need for advanced modeling
techniques that can seamlessly integrate discrete decision-making processes into
continuous optimization frameworks. The development of such hybrid models,
capable of capturing the nuanced dynamics of modern power systems, represents a
vital area for future research, promising enhanced operational and economic
efficiency in electricity markets.
5.0
CONCLUSIONS
5.1 Conclusions
In conclusion, the success of the Particle Swarm Optimization (PSO)
implementation hinges critically on the integrity of the data fed into the system.
Each hour that is modeled within the PSO framework must correspond to an
accurate network representation. It is therefore imperative for dispatch operators at
Belize Electricity Limited (BEL) to meticulously update the state of switches in the
model to reflect any changes in the network topology. This ensures that the PSO
algorithm is working with the most current and correct configuration of the
physical network.
Data validation is another cornerstone of the process. It is essential to establish
rigorous protocols to verify that the inputs passed to the PSO algorithm are viable
and that they accurately represent the actual state of the network. Infeasible inputs
can lead to the generation of invalid particles, which would compromise the
optimization process and potentially result in suboptimal dispatch strategies. Thus,
the creation of valid particles, which presuppose the accuracy and reliability of the
underlying data, is critical for the PSO algorithm to function effectively.
39
For BEL, this underscores the need for a robust data management system that can
ensure the veracity of real-time data inputs. The integration of such a system with
the PSO algorithm would not only streamline the optimization process but also
fortify the overall decision-making framework. With a reinforced commitment to
data integrity, BEL can maximize the efficacy of its optimization efforts, thereby
supporting its mission to provide reliable, cost-effective, and sustainable energy to
Belize.
5.2
Areas for Further Study
Based on the comparative analysis, recommendations for model improvement are
proposed. These include the refinement of input data granularity, the integration of
additional predictive indicators, and the adjustment of the model's neural
architecture to better capture the complex relationships within the data.
In order to improve the speed of calculations, GPU integration in the prediction
mode and optimization algorithm can be attempted. Trying different values for the
PSO hyperparameters and determining the optimal number of particles can be
beneficial to operational efficiency.
40
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