Two-way Load Flow Analysis using Newton-Raphson and Neural Network Methods

INTERNATIONAL RESEARCH JOURNAL OF ENGINEERING AND TECHNOLOGY (IRJET) E-ISSN: 2395-0056
VOLUME: 09 ISSUE: 03 | MAR 2022 WWW.IRJET.NET P-ISSN: 2395-0072
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Two-way Load Flow Analysis using Newton-Raphson and Neural Network
Methods
Aya Al Shaltouni1 and Abdulla Ismail2
1MS of Electrical Engineering Student, Department of Electrical Engineering, Rochester Institute of Technology,
Dubai, United Arab Emirates
2Professor, Department of Electrical Engineering, Rochester Institute of Technology, Dubai, United Arab Emirates
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Abstract - This research presents a study of the optimal
power flow for networked microgrids with multiple
renewable energy sources (PV panels and wind turbines),
storage systems, generators, and load. The OPF problem is
performed using a conventional method and an Artificial
Intelligence method. In this research, we investigated the
performance of MGs system with renewable energy
integration with focus on power flow studies. The
calculation of the power flow is based on the well-known
Newton-Raphson method and Neural Network method. The
power flow calculation aims to evaluate the grid
performance parameters such as voltage bus magnitude,
angle, real and reactive power flow in the system
transmission lines under given load conditions. The standard
test system used was a benchmark test system for
Networked MGs with four MGs and 40 buses. The data for
the entire system has been chosen as per the IEEE Standard
1547-2018. The results showed minimum losses and higher
efficiency when performing OPF using NN than the Newton-
Raphson method. The efficiency of the power system for the
networked MG is 99.3% using Neural Network and 97%
using the Newton-Raphson method. The Neural Network
method, which mimics how the human brain works based on
AI technologies, gave the best results and better efficiency in
both cases (Battery as Load/Battery as Source) than the
conventional method.
Keywords: Optimal Power Flow, Microgrid, Newton-
Raphson, Neural Network.
1. Introduction
The electric energy network is a complex and
interconnected system commonly known as the grid.
Growing electricity demand requires more sustainable and
renewable energy sources. Nowadays, a massive
transformation of the current electric energy system is
observed. For instance, the energy flow becomes
bidirectional due to the Distributed Generations (DG)
plants where the energy is transferred between several
nodes of the power grid/Microgrid, according to the
changing demands [1].
A microgrid is a more intelligent and efficient mini-version
of the electric grid. The electric grid is made up of
interconnected sub-systems, namely generation,
transmission, and distribution. On the other hand, the
microgrid is a decentralized group of electricity sources
and loads that are synchronized with the electrical grid but
can be disconnected and operate autonomously in “Island
Mode.” It can serve a small localized area to keep the
power flowing when the electrical grid is down, protect the
microgrid from power outages by relying only on their
own, serve the larger grid, and provide clean and green
energy since they are fueled mainly by renewable energy
sources (RES) [2].
Such a new scenario requires new systems that can allow
the power grid to be smart by managing the bi-directional
energy flow. Figure 1.1 shows the current plan where
different distributed generation plants supply the energy
to customers and the surplus power is injected back to the
grid [1]. In addition, the improvements in storage
technologies allow more flexible operation and reliable
management of energy. Therefore, RES associated with
storage units is considered as actively distributed
generators, which is one of the essential elements of the
“Smart Grid” concept [3].
Bulk power generators are complicatedly connected to the
transmission system, whereas the simple design of
distribution networks allow many customers to easily
connect to them and be the prosumers. The Generating
Companies (GenCos) seek to maximize the utilization of
the existing generation resources by using the appropriate
load distribution. However, the Transmission Companies
(TransCo) tend to keep standard operating conditions in
terms of low transmission line congestion, high value of
minimum bus voltage, and low level of transmission loss
[4]. Loss reduction can be achieved through the
appropriate control of Distributed Generation (DG)
resources in the distribution systems, or more generally,
through the management of dispatchable resources (DG,
load, storage), which can be effectively assessed using
Optimal Power Flow problem.

1.1. Objective and Methodology
The employment of the OPF in smart grids is regarded as a
new development in power system studies. Therefore, this
work aims to study the optimal power flow problem in
microgrid by determining the best way to optimize the
flow of power using the Newton-Raphson approach and
the Neural-Network approach. The optimization of the
power flow using the Newton Raphson method and
Neural-Network method will be performed using
simulation. In addition, the impacts of the distributed
generations, renewable energy sources, storage systems,
and EV Charging stations are investigated.
1.2. Work Organization
Section II gives an overview of previous publications
covering OPF. Section III gives an overview of the Optimal
Power Flow. Section IV highlights the study of OPF using
Newton-Raphson method. In Section V, the OPF Study
using the Neural-Network is analyzed. Discussions and
conclusions are drawn in Section VI and VII respectively.
Fig - 1.1 Current Scenario of the power grid.
2. Literature Review
Lin and shen [5] showed that utilizing renewable
energy sources to reduce carbon emission and minimizing
the fuel cost for energy saving in the OPF problem will
reduce the global warming effect from the power
generation sector. In this paper, a DPOPF (distributed and
parallel OPF) algorithm for the smart grid transmission
system with renewable energy sources was proposed to
account for the fast variation of the power generated by
renewable energy sources. The proposed DPOPF algorithm
combines the recursive quadratic programming method,
and the Lagrange projected gradient method. The
proposed algorithm can achieve the complete
decomposition and be implemented in the smart grid
transmission system to make distributed and parallel
computation possible. results confirm that the computing
speed of the proposed DPOPF algorithm is fast enough to
cope with the fast variations of the power generated by
renewable energy sources. A PSO (Particle Swarm
Optimization) was presented in [6] to find the most
optimal locations and sizes of DGs, with the objective
function to minimize the system's total cost, real power
loss, and the number of the installed DGs. Firstly, a radial
distribution power flow (PF) algorithm is executed to find
the global optimal solution. Then, with respect to voltage
profile, THD and loss reduction and by using the sensitivity
analysis, PSO is used to calculate the objective function and
to verify bus voltage limits. To include the presence of
harmonics, PSO was integrated with a harmonic power
flow algorithm (HPF). The proposed (PSO-HPF) based
approach was tested on an IEEE 15-bus radial distribution
system. According to the authors, these scenarios yield
efficiency in improvement of voltage profile and reduction
of THD and power losses; it also permits an increase in
power transfer capacity and maximum loading. According
to Pazheri et al. [7], an economic/environmental
dispatching (EED) problem formulation was presented for
a hybrid system that comprises thermal units, the solar,
wind, and storage unit. The study was simulated using
MATLAB/Simulink. A consistent optimum EED was
obtained by extracting maximum renewable energy during
their availability and using them for both available and
unavailable periods with the aid of their storages. In [8],
Atwa et al. proposed a probabilistic planning technique to
allocate various DG types (wind, solar, biomass) in the
distribution system with an Objective Function to
minimize the energy loss. The results reveal that
regardless of the combination of the renewable resources
used to calculate the optimal fuel mix, there is a significant
reduction in the annual energy loss. An optimal control
model of a heat pump water heater (HPWH) supplied by a
wind-generator-PV-grid system was presented in [9] with
an OF is to minimize the overall energy cost. This problem
was solved using a mixed integer linear program. The
results show a 70.7% cost reduction upon implementation
of this intervention. Sanseverino et al. [10] showed an
execution monitoring and re-planning approach to solve
the optimal generation dispatch problem in smart grids
with OF to minimize the carbon emissions, production
costs and improve the quality. The replanning module is
based on a heuristic multi-objective optimizer able to
efficiently incorporate constraints. The obtained results
were encouraging and suggest to incorporate into the
Microgrids software technology approaches for managing
uncertainties. A smart energy management system (SEMS)
was presented in [11] to optimally organize the power
production of DG sources and energy storage systems and
minimize the microgrid operational costs. The results
show that the forecasting model is able to predict hourly

power generation according to the weather forecasting
inputs.
Similarly, an optimal energy management system of
storage devices in grid-connected microgrids was
presented in [12], where the stored energy is controlled to
balance the loads and renewable sources and minimize the
total cost of energy at the PCC (Point of Common
Coupling). Bracale et al. [13] presented an optimal control
approach for a DC microgrid that included dispatchable
(micro-turbine) and non-dispatchable (PV generator)
units, storage system, and controllable/non-controllable
loads. It was designed to achieve a minimum daily total
energy cost and it shows that the power provided by the
dispatchable unit and the storage system allowed the
minimization of the daily costs of energy. A novel OPF
algorithm for islanded microgrid was presented in [14],
where it provides minimum losses and a stable operating
point with relevant droop parameters used to regulate the
primary voltage and frequency. Shen et al. [15] presented
an energy management scheme containing battery storage,
diesel generators, PV, and wind. As a result, the proposed
energy management system is effective in engineering
practice and beneficial for both the microgrid and the
customers. Hassanzadehfard et al. [16] employed battery
banks as long-term storage and ultra-capacitors as short-
term storage to control the frequency in a microgrid. The
simulation results showed that considering interruptible
loads for the microgrid results in cost reduction for the
microgrid.
The development of EVs technology has a significant
impact on microgrid operations. Yu et al. in [17] analyzed a
model to find the effect of EV technology on-demand
response mobility. Numerical results show that EVs
mobility of symmetrical EV fleet is able to achieve
synchronous stability of network and balance the power
demand among different districts. Moreover, Laureri et al.
[18] presented an optimization technique to integrate the
EVs into the smart grids. The results prove that the
integration of electric vehicles in the smart grids can help
in sustaining the grid processes when parked and so
playing in costs minimization. Paterakis et al. [19]
developed an optimization technique to minimize the
energy procurement costs of a smart household.
Coordination strategy was proposed in order to satisfy the
transformer capacity limits while promoting its
economically fair usage by the households. Lin et al. [20]
utilized an active power limitation strategy to reduce PV
power injection during peak solar irradiation to avoid
deviations in voltage. The results show that the control for
PV power rejection increases the installation capacity of a
PV system to make full use of solar energy resources and
to maximize the net present value of a PV system
investment. Moreover, a study was conducted in [21] to
find the optimal design of a PV/Battery hybrid system
regarding PV modules' numbers, the PV module's tilt,
batteries numbers, and capacities. Results show that the
choice of installation place and of the system type can
significantly affect the optimization results significantly. In
particular, the optimum PV module tilt angle value changes
according to electrical energy demand of the domestic
utility. In [22], an optimization of the power flow of the PV
system connected to the grid was presented. It was
performed by calculating the root of the active and
reactive power equation using Newton's Raphson method.
Simulation results have shown the maximum value of the
active power system at 1000 W/m2 irradiation was 408
W, as the reactive power is needed only 11.82 Var. In [23],
an application for optimization of the energy flows in
smart power systems consisting of electric vehicles (EV),
distributed energy sources (DER), flexible loads, and
bidirectional storage is proposed, as well as an
optimization model for energy distribution between
electric vehicles, electric storage devices, and photovoltaic
generators. A nonlinear optimization problem with linear
constraints for optimizing the power flows in the system is
defined and solved. A multi-objective problem is
determined to satisfy PV production criteria and maximize
the power flow to the EVs. An algorithm for finding the
optimal solution to the multi-objective optimization
problem is also proposed. The approach is beneficial for
energy flow control and analysis of DER behavior. The
algorithm proposed for solving the multi-objective
problem is applicable when storage and PV generation
units are used in the DER system.
Rigo-Mariani et al. [3] investigated different procedures
for the optimal power dispatching of a grid-connected
prosumer with energy storage consisting of a high-speed
flywheel. According to the paper, optimal off-line
scheduling for the day ahead aims to minimize the cost
with regard to the daily energy rates and consider the
forecasts for both consumption and production. That
dispatching is performed using global optimization
procedures based on a trust-region method or a niching
genetic algorithm. Another approach developed by the
authors in [3] is using step-by-step optimization and
exploiting an original self-adaptive dynamic programming
strategy. Kim and Lavrova [24] used an advanced
optimization method to present optimal power flow and
energy-sharing among smart buildings. The authors
claimed that this method could improve the smart grid's
optimal power flow and energy-sharing stability among
smart buildings and enhance energy dissipation balance to
reach stability among many smart buildings in the smart

grid.
Ke et al. [25] presented a new probabilistic OPF (POPF)
model with chance constraints that reflect the
uncertainties of wind power generation (WPG). The
results show the satisfactory accuracy of the PLF
(Probabilistic Load Flow) method, and the effectiveness of
the proposed P-OPF model. In [26], a probabilistic AC OPF
(POPF) was presented, considering the load variation,
stochastic wind behavior, and variable line's thermal
rating. It was observed that a reduction on the mean cost
and also on the probability of reaching higher generation
costs was obtained when dynamic limits where used. An
optimization system to calculate the optimal operation of a
system comprising electric vehicles and offshore wind
farms connected to the grid through an HVDC link was
presented in [27]. It has been shown that the uncertainty
associated with availability of power from wind farm and
PEVs affects the overall cost of operation of system. Lin
and Lin [28] proposed a risk-limiting optimal power flow
(RLOPF) problem for systems with high wind power
penetration; the aim was to address the issue of possibly
violating the security constraints in power systems due to
the instability of wind power generations.
3. Optimal Power Flow
3.1. OPF of Conventional Power Grid
Load flow, also known as a power flow, is a network
solution that displays currents, voltages, and real and
reactive power flows at each bus and lines in the power
system. The calculation of power flow necessitates the
solution of non-linear equations. It can calculate the
transmission system's electrical response to a specific set
of loads and generator power outputs. Carpentier
presented Optimal Power Flow in 1962 [4]. The OPF is
typically a non-linear and non-convex problem with
Objective Function that must be optimized (maximized or
minimized), a set of equality and inequality constraints
that must be satisfied, and a problem-solving method.
Specifically, OPF optimizes a given Objective Function
controlling power flow throughout an electrical system
without violating power flow constraints or operational
limits [4]. In other words, each power plant's actual and
reactive power should be scheduled so that the total
operating cost is kept to a minimum. Thus, it can help grid
operators address various challenges in grid planning,
operation, and control. OPF can also be used to determine
prices on the day-ahead market [29]. Some of the extended
OPF versions are illustrated below [4]:
 SCOPF: It selects the optimal control settings for
the base system to minimize the objective function
while ensuring that no violations occur.
 DC OPF: The reactive power and transmission
losses are not taken into account.
 AC OPF: It has to do with the AC grid and is based
on the system's natural PF characteristics. As a
result, the outputs of this type of OPF are more
precise.
 Mixed AC/DC OPF: it is related to the OPF in both
AC and DC grids.
OPF has been solved using a variety of conventional
optimization methods such as Linear Programming
method, Non-linear Programming method, Quadratic
Programming method, Newton’s method, and Interior
Point method [30]. However, all of these methods have
their own set of benefits and drawbacks which will be
discussed further.
3.2. OPF Problem Formulation
 The following is a description of a general
minimization problem:
 Minimize: f(x,u) (the objective function) where
f(x,u) is the objective function.
 Subject to: hi(x,u) = 0, i = 1,2,3,…. m (equality
constraints) where hi(x,u) is set of equality
constraints.
 gi(x,u) ≤ 0, j =1,2,3, …. n (inequality
constraints) where gi(x,u) is set of inequality
constraints, u represents a set of controllable and
x represents dependent variables.
3.3. Objective function
These objective functions vary from fuel cost generation,
active and reactive power transmission loss, reactive
power reserve margin, security margin index, and
emission environmental index [31].
3.3.1. Minimization of Generation Fuel Cost
The key objective of the OPF solution is to reduce the
system's total operating costs. When there is a light load,
the cheapest generators are always chosen to run first.
More expensive generators will be brought in as the load
increases. As a result, the operational cost plays a critical

part in the OPF solution. The amount of fuel or input to a
generator is usually measured in British thermal units per
hour (Btu/hr) and the output in megawatts (MW) [30].
In all practical cases, the cost of generator i can be shown
as a function of real power generation,
Ci = [ai + (bi Pi) + (ci Pi2)] * fuel cost (3.1)
which is expressed in expressed in $/hr
Where Pi is the real power output of generator i, and ai, bi,
ci are the cost coefficients.
The incremental cost can be obtained from the derivative
of Ci with respect to Pi,
dCi/dPi = (bi +2ci Pi)* fuel cost (3.2)
which is expressed in $/MWhr.
3.3.2. Minimization of Active Power
Transmission Loss
The OPF problem goal is to minimize the power loss.
The formulation of the real power loss can be represented
by [31]:
Minimizing PLoss = ΣPi = ΣPgi – ΣPdi, i = 1, ……., Nb (3.3)
where PLoss is the total I2R loss in the transmission lines
and transformers of the network.
3.3.3. Minimization of Reactive Power
Transmission Loss
The total VAR loss is minimized as per the following
equation [31]:
Minimizing QLoss = ΣQgi – ΣQdi, i = 1, …., Nb (3.4)
3.4. Control and Dependent Variables
There are two relevant variables in an optimization
problem: independent/control variables and
dependent/state ones. Firstly, the optimal value must be
determined for control variables to help minimize the
objective function, and then, based on it, state variables
should be calculated [4].
In the OPF problem, control variables may include active
power generation of all generator buses except slack bus,
the voltage of all generator buses, transformers tap ratio,
reactive power injection of shunt capacitor banks, etc.
Moreover, dependent variables may also include an active
power output of the slack bus, voltage angles of all buses
excluding the slack bus, load bus voltages, reactive power
generation of generators. It should be noted that the
number of control variables determines the solution space.
In fact, a problem with n-control variables results in an n-
dimensional solution space [4]. The classification of power
system buses is shown in Table 3.1 [31].
Table – 3.1: Classification of Power System Buses.
Classifications Knowns Unknowns
Load Bus P, Q V, δ
Generator Bus P, V Q, δ
Slack (Swing) bus V, δ P, Q
3.5. Equality constraints
Both the physicality of the power system and the
required voltage set points are reflected in the OPF's
equality constraints. The power system physics is enforced
by power flow equations that require that actual and
reactive power injection for each bus amount to zero [30].
This can be attained by the following analysis:
Pi = PLoad + PLoss (3.5)
Qi = QLoad + QLoss (3.6)
where Pi and Qi are the active and reactive power outputs
respectively.
PLoad and QLoad are the active and reactive load
power respectively.
PLoss and QLoss are the active and reactive power loss
respectively.
The power flow equations of the network can be given as:
G(V,δ) = 0 (3.7)
where
G(V,δ) = Pi(V,δ) - Pi
net, Qi(V,δ) – Qi
net, Pm(V,δ) - Pm
net (3.8)
where Pi and Qi are the calculated real and reactive power
at PQ bus respectively
Pi
net and Qi
net are the specified real and reactive
power for PQ bus respectively
V and δ are the magnitude and phase angle of voltage
at different buses respectively

3.6. Inequality constraints
Components and equipment in the power system have
operational limitations created to ensure system security
and minimize the required objective function [30].
Inequality constraints:
Pgi
min ≤ Pgi ≤ Pgi
max (3.9)
Qgi
min ≤ Qgi ≤ Qgi
max (3.10)
ΣPgi – PD – PLoss = 0 (3.11)
where Pgi is the amount of generation in MW at generator i.
Qgi is the amount of generation in MVAR at generator
i.
The inequality constraints on voltage magnitude V of each
PQ bus
Vi
min ≤ Vi ≤ Vi
max (3.12)
where Vi
min and Vi
max are the minimum and maximum
values of voltages at bus i.
The inequality constraints on phase angle δ of voltages at
all buses i
δi
min ≤ δi ≤ δi
max (3.13)
where δi
min and δi
max are the minimum and maximum
values of phase angle at bus i.
For a typical Microgrid system, the basic components are
given in Table 3.2 [12]:
Table - 3.1 Typical Microgrid components.
Where the PCC corresponds to the “slack” bus. It is always
indexed as bus 1.
3.7. Conventional Vs Recent Optimization Methods
for OPF
The Conventional methods are based on linear Objective
Functions that apply sensitivity analysis and gradient-
based optimization algorithms. The conventional
optimization methods are illustrated below [32]:
3.7.1. Linear Programming method
LP method is one of the fully developed methods now in
common use. It easily handles inequality constraints. Non-
linear objective functions and constraints are handled by
linearization [33]. LP method is used for linearizing the
problems of non-linear system optimization; it is reliable.
It has a good convergence feature, but the main
shortcoming is that errors may occur due to digital
computer rounding, especially under constraints.
3.7.2. Non-Linear Programming method
NLP is a process of solving an optimization problem where
the constraints and the OF are non-linear. It helps to find
the best solution to a problem using constraints that are
not linear. The non-linear method (NLP) is more precise

than the linear method, where non-linear objective
functions and constraints can be applied. The NLP
techniques use the Lagrange multiplier to use the reduced
gradient method. The significance of this method is that it
can be applied in a large-scale system, whereas the
disadvantages are that some system components are not
taken into consideration [32].
3.7.3. Quadratic Programming method
A particular nonlinear programming approach can be seen
in quadratic programming (QP), where the objective
function is quadratic, and the constraints are linear. The
determination of gradient steps is not necessary for this
method. The solution that has been obtained using the QP
Method is more accurate compared to the previous
methods. In addition, it has fast convergence
characteristics [32].
3.7.4. Newton’s method
The Newton Method is commonly used in power flow
problems by applying second-order partial derivatives to
create the Lagrangian. It is a high-speed convergence
method, but it may give problems with inequality
constraints. It was proved that Newton-Raphson
converged in many cases. Moreover, most Newton-
Raphson power flow problems converge in less than ten
iterations. The disadvantages are that the Newton-
Raphson method requires high computer storage and
computation time, and it is very much sensitive to the
selection of initial conditions [33].
3.7.5. Interior Point method
IP method is one of the fully developed and widely used
methods for OPF. The IP method is generally used for large
problems to solve the optimal power problem [32].
However, the results achieved by IP results are better and
require fewer iterations than LP. It easily handles
inequality constraints [33].
The conventional methods are not always appropriate for
optimizing the power flow since the optimal power flow is
a non-linear (non-convex) problem. Therefore, new
optimization methods are introduced to solve the OPF. The
advantages of these recent methods are the following [32]:
1. They can be applied in small and large scale
systems
2. It has a high reliability
3. They converge rapidly compared to the
conventional methods.
The recent optimization methods can be classified as
follows [32]:
 Swarm and Bio-inspired Optimization Techniques
The natural and bio-inspired algorithm is an emerging
approach based on the inspiration of the moving and
looking behavior of animals or birds for food sources.
 Human-Inspired Optimization Techniques
Various techniques of optimization simulate human
behavior, particularly when it comes to thinking or making
decisions.
 Physics-Inspired Optimization Techniques
Algorithms based on physics are conceptualized in space
through physics laws or natural phenomena.
 Evolutionary-Inspired Optimization Techniques
Evolutionary optimization algorithms come from natural
selection mechanics and genetics or living bodies or
animals.
 Hybrid Optimization Techniques
Several algorithms have been proposed for hybrid
optimization to gain advantages of multiple techniques
and obtain better results than single techniques.
 Artificial Neural Network (ANN) and Fuzzy Logic
Approach
Artificial neural networks (ANNs) are computational
methods that emulate the operation of biological neural
networks. At the same time, the fuzzy set theory is a
natural and appropriate tool for inaccurate relations.
4. Networked Microgrid Test System
A Microgrid can connect with the main grid by a
DG control entity to serve local loads. The balance between
the generation and load must be kept under all operating
conditions to keep the frequency and voltage of MGs
within operating limits. These DGs may be dispatchable or
non-dispatchable. For example, the power generation from
PV panels and wind turbines is usually non-dispatchable.
In contrast, the power output from the microturbines, fuel
cells, combined heat and power (CHP), and diesel
generators are fully dispatchable. The grid, which serves as

the MG's slack bus, handles this balance in grid-connected
mode. While in an islanded mode, dispatchable DG must
have sufficient capacity to balance load and generation and
avoid load shedding.
Figure 4.1 shows the electrical single-line diagram of the
test system with comprehensive buses, loads, and
generation. A three-digit number is used to identify each
bus in the system. All lines, including the tie lines, are
underground cables. Table 4.1 shows more details on the
four microgrids [34].
The first bus of each microgrid (101, 201, 301, and 401)
serves as the slack bus of that microgrid, and its equipped
with two or three units of conventional Synchronous
Generators to allow the microgrid to function effectively in
isolated mode, with load balancing and reactive power
supported. While in grid-connected mode, the slack bus of
microgrid 1 (101) is the slack bus on the complete system
[34]. Load and generation balance is performed through
this bus.
As shown in Table 4.1, microgrid 1 consists of 6 buses, 11
underground cables, and three standby Synchronous
Generators, each of 5000 kVA connected to bus 101.
Moreover, 3 PV panels are installed at buses 102, 103, and
104. microgrid 2 consists of 9 buses, eight underground
cables, and three standby Synchronous Generators at bus
201. Additionally, 3 PV panels (at buses 202, 203, and 204)
and 2 Wind Turbines (at buses 206 and 209) are always
available to generate power to the network. microgrid 3
has 18 buses and 17 underground cables. Bus 301 has
three standby Synchronous Generators and 6 PV panels (at
buses 303, 304, 305, 306, 307, and 315) and 2 Wind
Turbines (at buses 314 and 317). Finally, microgrid 4 has
seven buses and eight underground cables, 3 PV panels at
(at buses 405, 406, and 407), and two standby
Synchronous Generators installed at bus 401. All these
standby SGs are of equal capacity and have self-starting
capability [34].
The networked microgrid system is designed to operate on
11 kV three-phase underground cables. The utility feeder
is a 33 kV three-phase single circuit overhead line. In
addition, there are three 20 MVA parallel step-down
transformers to maintain the voltage of 11 kV at bus 101.
Fig - 4.1 Single-line diagram of the Networked MGs test
system.
As shown in Figure 4.1, microgrid 1 can share power with
microgrid 2 through PCC1 and microgrid 3 through PCC2.
While microgrid 2 can share power with microgrid 3
through PCC4 and microgrid 4 with PCC3. microgrid 3 and
microgrid 4 can exchange power through PCC5. If a failure
occurs in microgrid 1, microgrid 2 and 3 can be connected
to the utility grid directly to ensure the continuity of
supply.
Table - 4.1 Details of Microgrids of the test system.
Components MG 1 MG 2 MG 3 MG 4
Buses 6 9 18 7
Lines 11 8 17 8
SGs 3 3 3 2
PV Systems 3 3 6 3
WT Systems 0 2 2 0
Slack Bus 101 201 301 401
MG Type Meshed Radial Radial Meshed
The line and bus data are necessary to perform out an
optimal power flow analysis. The data from the networked
microgrid system lines such as resistance, reactance, and
cable length is presented in Table 4.2 [34]. Moreover,
Table 4.3 shows the tie-cable data between the microgrids
[34].

Table - 4.2 Line Data of the Networked MG System.
S.
No.
From
Bus
To
Bus
Length
(km)
Resistance
(P.U)
Reactance
(P.U)
1 101 102 3 0.7661 1.18
2 101 103 2.4 0.7715 0.991
3 101 104 3 0.7661 1.18
4 101 105 1.6 0.514 0.6604
5 101 106 1.6 0.514 0.6604
6 102 103 2 0.6429 0.825
7 102 105 1.5 0.4822 0.619
8 103 104 2 0.6429 0.825
9 103 105 1.2 0.3857 0.495
10 103 106 1.2 0.3857 0.495
11 104 106 1.5 0.4822 0.619
12 201 202 1.4 0.4500 0.577
13 202 203 1.6 0.5143 0.660
14 202 206 1.5 1.9710 1.338
15 203 204 2.2 0.7072 0.908
16 203 207 1.4 1.8396 1.249
17 204 205 1.8 0.5786 0.743
18 204 208 1.2 0.3857 0.495
19 208 209 0.8 1.0512 0.714
20 301 302 1.2 0.3857 0.495
21 302 303 1.8 0.5786 0.743
22 302 309 1.5 0.4822 0.619
23 302 311 1.4 1.8396 1.249
24 303 304 1.2 0.3857 0.495
25 303 313 1.5 1.9710 1.338
26 304 305 1.4 0.4500 0.577
27 304 314 1.4 1.8396 1.249
28 305 306 1.6 0.5143 0.660
29 305 315 1.4 1.8396 1.249
30 306 307 1.5 0.4822 0.619
31 306 317 1.4 1.8396 1.249
32 307 308 1.5 1.9710 1.338
33 307 318 1.7 0.5465 0.701
34 309 310 1.5 0.4822 0.619
35 311 312 1.2 1.5768 1.071
36 315 316 1.2 1.5768 1.071
37 401 402 0.6 0.3148 0.260
38 401 405 1 0.5247 0.433
39 401 406 1.8 0.9446 0.780
40 402 403 2 1.0495 0.867
41 403 404 0.6 0.3148 0.260
42 404 407 1 0.5247 0.433
43 405 406 1.5 0.7871 0.650
44 406 407 1.5 0.7871 0.650
Table - 4.3 PCC/Tie-cables Data.
S.
No.
From
bus
To
Bus
Length
(km)
Resistance
(P.U)
Reactance
(P.U)
T1 102 201 1 0.2553 0.394
T2 104 301 1.5 0.3830 0.591
T3 208 401 2 0.6429 0.825
T4 205 310 2.5 0.8037 1.032

T5 318 404 1 0.3214 0.412
A one-year dataset has been provided in this system. Table
4.4 provides the load data for the Networked Microgrids
[34]. Table 4.4 indicates that the overall system loads are
30.802 MW and 6.374 MW, including critical loads of 6.16
MW and 1.27 MVAR. In addition, the table lists three types
of buses: 1) Type 1 bus: Slack bus; 2) Type 2 bus:
Generator bus; 3) Type 3 bus: Load bus (PQ bus).
Table - 4.4 Load Data of the Networked MG System.
Bus
ID
Bus
Type
Total Bus Load Critical Load Bus
Load %
of
System
Load
kW kVAR kW kVAR
101 1 0 0 0 0 0
102 2 2125 336 450 68 6.9
103 2 3329 1023 650 124 10.81
104 2 2050 555 200 50 6.66
105 3 1257 310 200 35 4.08
106 3 1056 240 200 35 3.43
201 2 600 100 0 0 1.95
202 2 1250 487 500 80 4.06
203 2 1203 410 500 80 3.91
204 2 1366 443 650 138 4.43
205 3 764 36 0 0 2.48
206 2 503 21 0 0 1.63
207 3 345 11 0 0 1.12
208 3 629 8 0 0 2.04
209 2 642 12 100 25 2.08
301 2 580 150 0 0 1.88
302 3 650 85 250 50 2.11
303 2 673 96 0 0 2.18
304 2 439 135 0 0 1.43
305 2 600 128 250 50 1.95
306 2 560 112 0 0 1.82
307 2 851 145 385 50 2.76
308 3 420 25 0 0 1.36
309 3 500 45 0 0 1.62
310 3 637 33 0 0 2.07
311 3 788 95 350 83 2.56
312 3 125 50 0 0 0.41
313 3 169 20 0 0 0.55
314 2 200 43 0 0 0.65
315 2 250 32 125 25 0.81
316 3 213 12 0 0 0.69
317 2 133 25 0 0 0.43
318 3 200 38 0 0 0.65
401 2 426 80 0 0 1.38
402 3 318 78 125 20 1.03
403 3 356 81 125 20 1.16
404 3 459 88 0 0 1.49
405 2 820 91 0 0 2.66
406 2 2500 635 850 150 8.12
407 2 816 60 250 44 2.65
Total
Load
30802 6374 6160 1127 100
Base voltage: 11 kV; Specified voltage at all buses: 1 p.u.
Table 4.5 presents details of DERs installed at different MG
locations. Excess power is saved in energy storage systems
installed with each PV system to use the stored energy
when the PV solar is unavailable. Also, the details of the
Synchronous Generators are presented in Table 4.6 [34].
Table - 4.5 Installed Capacity of PV and WT in MGs.
Bus
ID
DG
Type
PG
(kW)
QGmin
(kVAR)
QGmax
(kVAR)
Network
Area
102 PV 2000 0 400 MG1
103 PV 2400 0 480 MG1
104 PV 2000 0 400 MG1
202 PV 1600 0 320 MG2
203 PV 1600 0 320 MG2
204 PV 2400 0 480 MG2
206 WT 800 -250 250 MG2
209 WT 500 -200 200 MG2
303 PV 2000 0 500 MG3
304 PV 400 0 100 MG3
305 PV 800 0 160 MG3
306 PV 800 0 160 MG3
307 PV 800 0 160 MG3
314 WT 500 -250 250 MG3
315 PV 800 0 160 MG3
317 WT 1200 -600 600 MG3
405 PV 1600 0 320 MG4
406 PV 2400 0 500 MG4
407 PV 1600 0 320 MG4
Table - 4.6 Standby Synchronous Generators Data in MGs
Bus
ID
Unit
Capacity
(kVA)
Number
of Units
QGmin
(kVAR)
QGmax
(kVAR)
Network
area
101 5000 3 -3000 5000 MG1
201 2000 3 -1500 2000 MG2
301 2000 3 -1500 2000 MG3
401 2000 2 -1000 2000 MG4
The Energy Storage Systems are installed at different
buses, which are Lithium-ion batteries. With 80% of DOD.

The SoC of batteries is assumed to be 20% of their total
capacity. The details of the ESS are shown in Table 4.7
[34].
Table - 4.7 Energy Storage Capacity.
Location
(Bua ID)
Battery
Storage
Capacity
(kWh)
Peak Power
Supply
(Kw)
Network
Area
102 3000 2000 MG1
103 4000 2400 MG1
104 3000 2000 MG1
202 4000 1600 MG2
203 4000 1600 MG2
204 4000 2400 MG2
303 3600 2000 MG3
304 800 400 MG3
305 2000 800 MG3
306 2000 800 MG3
307 2000 800 MG3
315 2000 800 MG3
405 3000 1600 MG4
406 6000 2400 MG4
407 3000 1600 MG4
5. OPF in Microgrids using Newton-Raphson
method
For the networked microgrids illustrated in the previous
chapter, an Optimal Power Flow study will be performed
using Newton-Raphson method.
5.1. Principle of Newton-Raphson method
A nonlinear equation in a single variable can be expressed
as:
f (x) = 0 (5.10)
For solving this equation, select an initial value x0. The
difference between the initial value and the final solution
is Δx. Then x1 = x0 +Δx is the solution of nonlinear
equation (5.10). That is [35]:
f (x0 +Δx) = 0 (5.11)
Expanding the above equation with the Taylor series yields
[35]:
f (x0 +Δx) = f (x0) + f ′(x0) Δx + (f ′′(x0)(Δx)2)/2! + · · · + (f
(n) (x0)(Δx)n)/ n! + · · · = 0 (5.12)
where f ′(x0), … , f (n) (x0) are the derivatives of the
function f (x).
If the difference Δx is very small (meaning that the initial
value x0 is close to the solution of the function), the terms
of the second and higher derivatives can be neglected.
Thus equation (5.12) becomes a linear equation as below
[35]:
f (x0 +Δx) = f (x0) + f ′(x0) Δx = 0 (5.13)
Then:
Δx = − f (x0)/f ′(x0) (5.14)
The new solution will be:
x1 = x0 +Δx = x0 − f (x0)/f ′(x0) (5.15)
Since equation (5.13) is an approximate equation, the
value of Δx is also an approximation.
Thus the solution x is not a real solution. Further iterations
are needed. The iteration equation is [35]:
xk+1 = xk +Δxk = xk − f (xk)/f ′(xk) (5.16)
The iteration can be stopped if one of the following
conditions is met:
|Δxk|< 𝜀1 or |f (xk)|< 𝜀2 (5.17)
where 𝜀1, 𝜀2, which are the permitted convergence
precisions, are small positive numbers.
The Newton method can also be expanded to a nonlinear
equation with n variables.
f1(x1, x2, … , xn)= 0
f2(x1, x2, … , xn) = 0
· · ·
fn(x1, x2, … , xn) = 0
For a given set of initial values x1, x2, … , xn, we have the
corrected values Δx1,Δx2, … ,Δxn. Then:
f1(x1 +Δx1, x2 +Δx2, … , xn +Δxn)= 0
f2(x1 +Δx1, x2 +Δx2, … , xn +Δxn) = 0
· · ·
fn(x1 +Δx1, x2 +Δx2, … , xn +Δxn) = 0

Similarly, expanding the above equations and neglecting
the terms of second and higher derivatives, a matrix can be
formed to find the solution at kth iteration [35]:
xk+1i = xki +Δxki i = 1, 2, … , n (5.18)
The above two equations can be expressed as
F(Xk) = −JkΔXk (5.19)
X k+1 = Xk +ΔXk (5.20)
where J is an n × n matrix called a Jacobian matrix.
5.2. Power Flow Solution
The complex voltage, real and reactive powers of each bus:
(5.21)
(5.22)
(5.23)
where 𝜃ij = 𝜃i − 𝜃j, which is the angle difference between
buses i and j.
For each PV or PQ bus, we have the following real power
mismatch equation:
(5.24)
For each PQ bus, we also have the following reactive
power equation:
(5.25)
where Pis, Qis are the calculated bus real and reactive
power injections, respectively.
According to the Newton method, the power flow
equations (5.24) and (5.25) can be expanded into Taylor
series and the following first-order approximation can be
obtained [35]:
where
The steps for calculation of the Newton-power flow
solution are shown in the following flowchart:
(5.26)
(5.27)

Fig - 5.1 FlowChart of Newton-Raphson method.
5.3. Power Flow Results using Newton-Raphson
method
After applying the Newton-Raphson method to the
networked microgrids, the results are shown in the
following sections:
5.3.1. Using Storage as a load:
Using the line and bus data provided in the
previous chapter for the networked microgrids, the power
flow solution is obtained using the Newton-Raphson
method with MATLAB computations. This yields the
results shown in Table 5.1. Note that for more accessible
dealing with numbers, the three-digit numbers for buses
from 101 to 407 are described as 1 to 40 buses.
Table - 5.1 Power Flow Results using Newton-Raphson –
Storage as Load.
In the first case where the storage systems are considered
as loads, the ESS, which is installed next to each PV system,
will absorb the generated power and store it in the
batteries—assuming that from 6 A.M to 6 P.M, the energy
from the sunlight is absorbed by the PV cells in the panel
to produce electricity. Wind Turbine, the PV system, and
the synchronous generators units are operating, the
batteries are charged from the PV system. The calculations
through MATLAB Software has convincing results:

 A constant voltage for nodes such as 1 and 7, and a
particular variation limit for others.
 The balance of the system is ensured as the loads
should be equal to the generated power from the
sources. As shown in Table 5.1, the load is
designed to be 54.002 MW, while the generation is
56.062 MW.
 The losses are calculated to be 2.065 MW/ 2.582
MVAR due to cable length, resistance, and
reactance.
 The execution time is 1.263629 seconds.
 The number of iterations is 11.
 Maximum Power Mismatch = 1.15132e-05.
5.3.2. Using Storage as a source:
In the second case, from 6 P.M to 6 A.M, the ESS is
considered to be a source that can generate power to
maintain system balance and reliability when the PV
system is not operating while wind turbines and
synchronous generators units are operating. The batteries
are discharging with a DOD of 80%. Table 5.2 illustrates
the power flow results when the batteries are discharging.
The following are observed from the power flow output:
A constant voltage for multiple nodes and a certain
variation limit for others.
As shown in Table 5.2, the load is designed to be 30.802
MW, while the generation is 31.697 MW.
The losses are calculated to be 0.896 MW/1.149 MVAR due
to the cable length, cable resistance, and reactance
The execution time is 1.032611 seconds.
The number of iterations till convergence is 10.
Maximum Power Mismatch = 1.98777e-06.
Table - 5.2 Power flow Results using Newton-Raphson -
Storage as Source.
6. OPF in Microgrids using Neural-Network
method
After applying the Neural-Network method to the
networked microgrids, the results are shown in the
following sections:
6.1. Principle of Neural Network method
The evolutionary computing of Artificial Intelligence is
solely entering the world and spreading the idea that it is
easier and more intelligent than the conventional methods
in performing complex tasks. The Neural Network displays
spatial capacities based on human logic.
Neural networks are a subset of machine learning and are
the heart of deep learning algorithms, also known as

artificial neural networks(ANNs) or simulated neural
networks (SNNs). Their name and structure are inspired
by the human brain, imitating the working strategy of the
brain using mathematical methods to match the biological
neuron [36].
Neurons are the simplest processing element of an ANN.
ANNs consist of node layers, including an input layer, one
or more hidden layers, and an output layer, as shown in
Figure 6.1 [36]. Each node is linked to another and has
several elements such as weight, activation function, and
threshold. The nodes represent computational units and
need inputs that should be processed in neurons to
present the output. Weights are multiplied with inputs and
then added in the summing function, then the sum is
processed in the activation function. The output is then
passed via an activation function to determine the output.
If the output exceeds a threshold, the node is activated,
and the data is passed into the next network layer. This
results in the output of one node, which becomes the input
of the next node. This data transmission procedure from
one level to the next characterizes this neural network as a
feedback network. The output is generated as shown in
Figure 6.2 and the equations (6.10) and (6.11) [37].
Depending on the nature of the NN's system, the hidden
network layers can be set in numerous ways. When
weights are generally calibrated on the branched hidden
layers, a relatively sophisticated approach called
backpropagation was considered.
Fig - 6.1 Neural Network Architecture.
Fig - 6.2 Neuron Mathematical Function.
yj = x1·w1 + x2·w2 + x3·w3 + xn·wn (6.10)
yj = ∑ (6.11)
There are a few different forms of learning/training based
on operation or system in which the neural network, the
most generally used and known learning approach, is
applied [37].
 Supervised Learning: the NN is fed with labeled
datasets to find the correct decision at the test
stage; the more this training/learning process, the
more the accuracy [37].
 Unsupervised Learning: the NN is fed with
unlabeled datasets (containing only the input
data). The ANN will be able to categorize the data
by clustering the data according to the distances
and finding the patterns [37].
 Reinforcement Learning: it is a kind of Learning
that involves the surrounding environment,
starting by getting a state, taking action to change
the state, and sending that action to either get a
penalty or reward, to learn from its experience
and reach the goal [37].
The steps of how the Neural Network works is shown in
the following flowchart in Figure 6.3.

Fig - 6.3 FlowChart of Neural Network method.
6.2. Neural Network Training Algorithms
6.2.1. Feed-Forward Propagation
The input data is forwarded throughout the network in the
feed-forward network. Every hidden layer accepts,
processes, and passes the input data in accordance with
the activation function. In other words, the information
moves only in one direction – forward- from the input
nodes, through the hidden nodes and to the output nodes,
there are no cycles or loops in the network. The feed-
forward network helps in forward propagation.
The processing takes place in two steps at each neuron in
the hidden or output layer:
a. Preactivation: it is a weighted sum of inputs.
Based on this aggregated sum and activation
function, the neuron decides whether to pass this
information or not.
b. Activation: the calculated weighted sum of inputs
passed to the activation function. The activation
function is a mathematical function which adds
non-linearity to the network. There are four
commonly used and popular activation functions –
sigmoid, hyperbolic tangent (tanh), ReLU, and
Softmax.
6.2.2. Backpropagation
The backpropagation is an efficient algorithm for training
feedforward neural networks; it computes the gradient of
the loss function concerning each weight by the chain rule,
one layer at a time. Then, it iterates backward from that
last layer and adjusts the weights between the input and
the neuron to reduce the cost function and minimize the
loss, as shown in Figure 6.4 [38].
Fig - 6.4 Backpropagation.
6.2.3. Gradient Descent
The Gradient Descent is an algorithm for finding a local
minimum of a differentiable function. It is used in machine
learning to find the values of a function’s
parameters/coefficients that minimize a cost function. The
idea of this algorithm is to take repeated steps in the
opposite direction of the gradient of a function at the
current point (direction of the steepest descent). While if
the steps were taken proportional to the positive of the
gradient, the local maximum of a function would be
approached, this is so-called Gradient Ascent as shown in
Figure 6.5 [39].
Fig - 6.5 Gradient Descent.
To perform the training phase in MATLAB for the optimal
power flow problem, the learning algorithm used was the

Levenberg–Marquardt (LM) backpropagation.
The Levenberg-Marquardt algorithm is designed to work
specifically with loss functions which take the form of a
sum of squared errors. It works without computing the
exact Hessian matrix. Instead, it works with the gradient
vector and the Jacobian matrix.
Levenberg-Marquardt is a combination of two other
methods: The Gradient Descent and Gauss-Newton. Both
methods are iterative algorithms, which means they use a
series of calculations to find a solution. The gradient
descent differs in that at each iteration, the solution
updates by choosing values that make the function value
smaller. In other words, the sum of the squared errors is
reduced by moving toward the direction of steepest
descent. Whereas, the Gauss-Newton is more accurate and
faster than the gradient descent when close to the
minimum error [40].
6.3. Power Flow Results using Neural Network
method
To get the power flow results for the Networked
Microgrids when the storage is either operating as a load
or as a source using Neural Network, the tool which is used
in MATLAB is the ‘nntool’ which opens the Network/Data
manager window, which allows for importing, creating,
using, and exporting Neural Networks and data.
6.3.1. Using Storage as a Load:
The custom neural network when the batteries are
charging during the day is shown in Figure 6.6, Input (P)
which is the input matrix that represents power demands
and generation from the bus data as shown in Table 6.1.
Fig - 6.6 Custom Neural Network – Storage as Load.
Table - 6.1 Input Matrix - Storage as Load.
Target (T) represents the desired output resulted from
Newton-Raphson method shown in Table 5.1.
Using Feed forward backpropagation network, and the
learning was performed according to the Levenberg-
Marquardt algorithm (trainlm).
The simulation gives the following results:
Network Regression

Fig - 6.7 Training, Validation, and Test Regression -
Storage as Load.
The Network Regression figure displays the output of the
network versus the target sets for training, validation and
testing. To have the best results, the regression line should
be fit at 45 degrees where all the outputs are equal to the
targets. As shown in Figure 6.7, the R value equal to
0.96017, so the fit is extremely good as the value is close to
‘1’where it is 100% precise.
Neural Network Training Performance
Fig - 6.8 Training Performance - Storage as Load.
The performance is calculated using the mean squared
error. It minimizes the sum of squared errors between the
network output and the targets according to epochs. The
MSE is measured on the training, validation and testing
sets.
Neural Network Training State
Fig - 6.9 Training State - Storage as Load.
The Training state represents the current progress/status
of the training at a specific time while training is in
progress.
Output (Y)
The output matrix of the neural network method:

Table - 6.2 Power Flow Results using Neural Network –
Storage as Load.
 Number of iterations: 18 iterations
 Execution time: Less than one second
 Total Losses: 1.6508 MW/5.5460 Mvar
6.3.2. Using Storage as a Source:
The custom neural network when the batteries are
discharging during the night is shown in Figure 6.10, Input
(P) which is the input matrix that represents power
demands and generation from the bus data as shown in
Table 6.3.
Fig - 6.10 Custom Neural Network – Storage as Source.
Table - 6.3 Input Matrix - Storage as Source.
Target (T) represents the desired output resulted from
Newton-Raphson method shown in Table 5.2.
Using Feed forward backpropagation network, and the
learning was performed according to the Levenberg-
Marquardt algorithm (trainlm).

The simulation gives the following results:
Network Regression
Fig - 6.11 Training, Validation, and Test Regression -
Storage as Source.
As shown in Figure 6.11, the R value equal to 0.93546, so
the fit is extremely good as the value is close to ‘1’where it
is 100% precise.
Neural Network Training Performance
Fig - 6.12 Training Performance - Storage as Source.
The performance is also calculated using the mean squared
error. It minimizes the sum of squared errors between the
network output and the targets according to epochs. The
MSE is measured on the training, validation and testing
sets.
Neural Network Training State
Fig - 6.13 Training State - Storage as Source.
Output (Y)
The output matrix of the neural network method:

Table - 6.4 Power Flow Results using Neural Network –
Storage as Source.
 Number of iterations: 10 iterations
 Execution time: Less than one second
 Total Losses: 0.214 MW/3.018 Mvar.
7. Discussion and Conclusion
7.1. Discussion
Power flow or load-flow studies are essential for
planning the future expansion of power systems and
determining the best operation of existing systems. The
principal information obtained from the power flow study
is the magnitude and phase angle of the voltage at each bus
and the real and reactive power flowing in each line.
Therefore, it is essential for the reliable and efficient
operation of electrical networks. In this paper, optimal
power flow is obtained for a networked microgrids system
involving loads, decentralized sources of renewable energy
(Solar PV panels and Wind turbines) and batteries as
storage unit, using a conventional method (Newton
Raphson method) and compared to a modern method
(Neural Network method or Artificial Neural Network
(ANN)). According to the results obtained above from
MATLAB optimization and deep learning toolbox. The
efficiency of the two methods is shown in Table 7.1 and
Table 7.2.
In the first case where the batteries are operating as load,
the losses efficiency are described in Table 7.1:
Table - 7.1 Comparison between NR and NN methods -
Storage as Load.
Optimization Method Losses and Efficiency
Newton-Raphson method 2.065 MW – 96%
efficiency
Neural Network method 1.6508 MW – 97%
efficiency
In the second case where the batteries are operating as
source, the losses and efficiency are illustrated in Table
7.2:
Table - 7.2 Comparison between NR and NN methods -
Storage as Source.
Optimization Method Losses and Efficiency
Newton-Raphson method 0.896 MW – 97.1%
efficiency
Neural Network method 0.214 MW – 99.3%
efficiency

It is clearly shown that losses when the Neural Network
was applied are lower and could produce more efficient
results than the Newton-Raphson method. Also, the
execution time is less when the OPF is performed using the
Neural Network method, even though the iterations are
more. For the Newton-Raphson method, the execution
time takes more than one second in both cases. Still,
Neural Network, a rapid convergence method, takes less
than a second to convergence. The regression value is
0.93-0.98, approximately equal to 1, indicating that the
results are good and have high accuracy and precision.
According to the results obtained from both methods, it is
clearly shown that the Neural Network method gave more
accurate results and achieved the balance between load
and generation to minimize the losses as much as possible.
In other words, the generated active power from each bus
was more accurate, and it was sufficient to supply the load
with minimum losses. Furthermore, both methods did
almost the same in producing other values, such as the bus
voltages and angles.
7.2. Conclusions
This research focuses on studying the optimal power flow
using a conventional method (Newton-Raphson) and AI
method (Neural Network) for a networked MG test system.
The load flow analysis considered two cases, when the
storage units are charging from the generation sources
during the day and when the storage units are supplying
power at night to compensate the power when the PV
panels can’t generate power. Both methods were
performed using Optimization and Deep Learning
toolboxes in MATLAB. The Neural Network method based
on AI represents more efficient results with minimum
losses compared to the conventional method.
In future work, there are various technologies to be added
to the microgrids architecture such as multiple energy
storage systems (flywheels, electrolyzer-fuel cell),
different energy rates related to the cost of the grid power
depending on the target load (storage charge or consumer
feeding), integrating the EVs to the microgrids which can
help in global warming concerns and other grid services
such as peak shaving and load shifting to increase the
reliability of the system. The networked MG can also be
used to validate other studies in the extended work,
including reliability and resiliency analysis, economic
dispatch, control and stability studies, and protection
analysis.
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