Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 8 Núm. (15) 2025. ISSN: 2737-6249

Optimal location of regulating transformer taps to minimize losses in the electrical system.

DOI: https://doi.org/10.46296/ig.v8i15.0232

OPTIMAL LOCATION OF REGULATING TRANSFORMER TAPS TO

MINIMIZE LOSSES IN THE ELECTRICAL SYSTEM

UBICACIÓN ÓPTIMA DE LAS TOMAS DE REGULACIÓN DEL

TRANSFORMADOR PARA MINIMIZAR PÉRDIDAS EN EL SISTEMA

ELÉCTRICO

1

2

3

Topa-Caseres Walter Fabián ; Quinatoa Carlos ; Ortiz Josué

1

Technical University of Cotopaxi. Latacunga, Ecuador. Correo: walter.topa9134@utc.edu.ec.

2

Technical University of Cotopaxi. Latacunga, Ecuador.

Correo: carlos.quinatoa7864@utc.edu.ec.

3

Japan University Institute. Quito, Ecuador. Correo: jortiz@itsjapon.edu.ec.

Abstract

The electric power system have lines, reactor, regulator voltage, transformer regulator and other

elements. These are necessary to carry the energy towards demand electric. The system operate

with dispatch economic (DE) where it has the objective function and constrains. However, they

DE do not necessary include the minimization power losses that are very import because reduce

operation cost. Therefore, in this paper it is realize an optimal location of regulating transformer

taps to minimize losses in the electrical system using convex optimization in power flow equations.

For this suppose, it take account the bus injection model where it obtain all equations necessary.

Then, the model propose are implemented with IEEE 14 bust system test as validation between

Digsilent Power Factory and the model implement is of the system electric of Quito city in Ecuador.

The result of minimizing lose in optimization process is 0.11 MW.

Palabras clave: Optimization, nonlinear, power flow, loss electric, transformer, regulator.

Resumen

El sistema eléctrico de potencia cuenta con líneas, reactancia, regulador de voltaje,

transformador regulador y otros elementos. Estos son necesarios para llevar la energía hacia la

demanda eléctrica. El sistema opera con despacho económico (DE) donde tiene la función

objetivo y restricciones. Sin embargo, los DE no necesariamente incluyen la minimización de

pérdidas de potencia que son muy importantes porque reducen el costo de operación. Por lo

tanto, en este documento se realiza una ubicación óptima de las tomas de regulación del

transformador para minimizar las pérdidas en el sistema eléctrico utilizando la optimización

convexa en las ecuaciones de flujo de potencia. Para este supuesto, se toma en cuenta el modelo

de inyección de bus donde se obtienen todas las ecuaciones necesarias. Luego, el modelo

propuesto se implementa con la prueba del sistema de bus IEEE 14 como validación entre

Digsilent Power Factory y el modelo implementado es del sistema eléctrico de la ciudad de Quito

en Ecuador. El resultado de minimizar la pérdida en el proceso de optimización es de 0,11 MW.

Keywords: Optimización, no lineal, flujo de potencia, pérdida eléctrica, transformador, regulador.

Información del manuscrito:

Fecha de recepción: 03 de octubre de 2024.

Fecha de aceptación: 19 de diciembre de 2024.

Fecha de publicación: 10 de enero de 2025.

4

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Topa-Caseres et al. (2025)

1

. Introduction

complementing it with Monte Carlo

simulations that validate the

The strategic positioning of taps

within transformers is critical to

maintain voltage regulation and

improve system stability in power

distribution networks. A multitude of

academic papers propose various

methodologies to identify the most

suitable plug configuration for

transformers [1]. One approach

involves using a genetic algorithm to

inte- grate variable transformer

inputs into reactive power pric- ing

models, which reduces the overall

costs associated with reactive power

while increasing system reliability.

effectiveness of the proposed

algorithm in real power distribution

networks [4].

It is essential to establish the ideal

position of taps in regulating

transformers to reduce energy

losses. It is necessary to incorporate

state-of-the-art technologies and

techniques

such

as

genetic

algorithms, reinforced learning and

simulations to increase the eﬀiciency

and stability of the power system.

The location of taps in regulating

transformers causes considerable

energy losses in electrical systems. It

is essential to improve their position

in order to reduce operational costs

and enhance energy eﬀiciency,

taking into account seasonal

variations and distributed resources.

To mitigate energy losses in power

Another

methodology

tap position

conceptualizes

adjustment as a Markov decision

process, which leverages

reinforcement learning algorithms to

reduce voltage discrepancies within

the system [2], proving effective in

numerical simulations related to

power supply distribution testing.

Furthermore, it is advisable to refine

the evolutionary strategy aimed at

systems,

several

transformer

technologies can be implemented.

Amorphous core transformers use an

amorphous metal alloy core, which

significantly reduces energy losses

due to their minimal core losses and

high magnetic perme- ability, making

them exceptionally eﬀicient [5].

determining

the

optimal plug

arrangement for off-line distribution

transformers [3], taking into account

seasonal variations and the impact of

distributed energy resources on

Similarly, nanocrystalline core

transformers take advantage of a

voltage

constraints,

by

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 8 Núm. (15) 2025. ISSN: 2737-6249

Optimal location of regulating transformer taps to minimize losses in the electrical system.

nanocrystalline structure to reduce

core losses and improve eﬀiciency,

which further contributes to reducing

losses in power systems [6]. High

temperature superconductors (HTS)

also present a very promising

alternative as they exhibit zero

electrical resistance at elevated

arrangement through a linear power

flow model to calculate the voltage

in- tensity. This method reduces

voltage variation in power distribution

systems, and its effectiveness has

been proven through numerical

simulations on IEEE test feeders

[11]. In addition, an evolution

strategy is used to establish the ideal

configuration of the taps as a function

of the average load. Monte Carlo

simulations analyze the possibility of

violating voltage constraints after

optimization, ensuring that the

configuration adheres to voltage

regulations [12]. The ideal taps

temperatures,

which

minimizes

power losses when incorporated into

transformers [7], [8]. In addition,

ferrite

core

transformers

are

recognized for their low core losses

and high magnetic permeability,

making them a predominant choice

for en- ergy eﬀicient systems. Finally,

transformers equipped with power

configuration

transformers

for

distribution

practically

factor

correction

(PFC)

are

was

specifically designed to improve

power factor and decrease power

losses, thus increasing overall

system eﬀiciency [9].

established, achieving acceptable

results in tests with real feeders [13].

Optimal placement of transformer

regulating tap chang- ers is crucial

for reducing energy losses in power

systems. By strategically deploying

transformer tap changers, utili- ties

can significantly reduce energy

waste while maintain- ing eﬀicient

power transfer [14]. The operational

The

optimization

of

variable

transformer taps using the genetic

algorithm in the pricing method

decreases the reactive power cost by

employing transformer taps as a

control variable. In addition, the

improvement of trans- former inputs

increases system protection and

decreases end-user costs [10]. In

contrast, a batch reinforcement

learning algorithm improves the tap

capability

changers

of

transformer

tap

enables

real-time

adjustment of voltage levels, which

improves system eﬀiciency [15]. In

addition,

the

architecture

of

4

2

Topa-Caseres et al. (2025)

regulating transformers incorporating

integrated tap changers streamlines

these adjustments and makes them

vital for minimizing energy losses

understand because it this can be

modeling the power flow and

optimization problem equations. In

the Fig. 1, it can see all elements that

connected this bus.

[

15]. Performing power flow analysis

helps identify regions where

Fig. 1. Bus Injection Model

significant power losses occur,

allowing utili- ties to optimize their

systems

effectively

[16]

Implementing these methodologies,

along with other loss reduction

strategies such as optimizing

transformer design and using

advanced materials, can significantly

reduce operating costs and impact

the environment [17]. Therefore, the

optimal placement of transformer

regulating tap changers is a critical

element in achieving an eﬀicient

electrical sys- tem [17]. Establish the

ideal position of taps in regulating

transformers to reduce energy losses

in electrical systems, through the

implementation of sophisticated

techniques and novel technologies,

optimizing energy eﬀiciency and

distribution system stability.

B. Transformer

The transformer is element important

for transmission of energy from

generation to load, it changing of

voltage level. In the sub-transmission

and transmission system these

transformers have OLTC in of

primary and sec- ondary winding.

•

t

p

.-In the primary winding for

each tap step the

increases or decreases 2.5

n

i

%.

•

t

s

.- In the secondary

winding for each tap step

2

. Formulation of the problem

n

j

increases or decreases 0.625

A. Bus injection model

%.

The bus injection model is

fundamental

and

necessary

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 8 Núm. (15) 2025. ISSN: 2737-6249

Optimal location of regulating transformer taps to minimize losses in the electrical system.

In generally the auto-transformer

substation in the primary winding tp

has five step tap ± 5% and the

secondary winding has thirty-three

step tap ± 10%. The Fig.2 show the

tap.

Fig. 2. Auto Transformer

The tap help system to regulation

The equation (1) is the objective

voltage and it is variable integer into

the optimization problem.

function that represent the minimum

loses of the network and it is

nonlinear, the equations (2) and (3)

are power balance constraints and it

represent bus injection model, the

equations (4) and (5) are the power

flow active and reactive from i to j and

it is nonlinear, the equations (6) and

C. Models and their equivalence

The power flow are necessary to

observe the state system in the

system and it diagnose that operate

correctly. Therefore, it is important

include the on-load tap chargers

(7) are the power flow active and

(OLTC) in the power transformer whit

reactive from j to i and it is nonlinear.

The equation (8) is number of turns

of the primary winding transformer,

the equation (9) is number of turns of

the secondary winding transformer.

it objective of voltage regulation for it

minimizing the loses through optimal

location Taps and into of power flow

equations. Accordingly, we present

the following nonlinear model, which

is defined as:

4

Topa-Caseres et al. (2025)

The equation (10) is the constraint of

angle of nodes of system.

ineffective. These techniques, such

as genetic algorithms, simulated

annealing and parti- cle swarming,

are especially useful in problems with

large, nonlinear search spaces.

Metaheuristics work by exploring and

The equation (11) is the constraint of

voltage of nodes of system. The

equation (12) and (13) are the

constraints of active and reactive

power generation the nodes of

system. The variables tp and ts are

integers that they represent steps of

primary an secondary transformer

exploiting

the

solution

space

intelligently, seeking a balance

between global exploration and local

exploitation.

Their main advantage is the ability to

find good quality solutions in a

reasonable time, being applicable in

fields such as engineering. The main

problem with metaheuristics is their

dependence on specific parameters

and the lack of global optimality

guarantee.

D. Problem

The model optimization presented

previous is hard to solve, because it

is nonlinear mixed integer problem.

The function objectives is nonlinear.

The term cos and they variables vi,

vj, θi, θj, ni and nj increase the

complexity

of

problem.

The

Convex optimization is a sub-

equations (4) - (7) are balance active

and reactive power are nonlinear and

finally the equation (8) and (9) are

lineal integer for the variable tp and

ts.

discipline

of

mathematical

focuses on

optimization

that

problems where the objective

function and constraints are convex.

In these problems, any linear

combination of points within the

domain also belongs to the domain,

and any local minimum is also a

In the literature, there are two form

for solve this problem:

•

Meta-heuristic

global

minimum.

Convex

Convex optimization

optimization is fundamental because

many real-world problems, such as

Metaheuristics is an optimization

methodology that seeks to find

approximate solutions to complex

problems where exact methods are

cost

minimization,

profit

maximization, and system design,

can be modeled in this way.

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 8 Núm. (15) 2025. ISSN: 2737-6249

Optimal location of regulating transformer taps to minimize losses in the electrical system.

Furthermore, eﬀicient algorithms

exist for solving convex problems,

which guarantees optimal and robust

For the transmission line i to j the

equation is following:

solutions in

economics,

fields

such

as

engineering

and

we define the following variable:

machine learning.

3

. Model Solution

with the previous equation. We can

write the following:

For to address

the

model

optimization nonlineal mixed integer

and special the previous problem. In

this paper take of account convex

optimization due they have several

advantage with respect meta-

heuristic. Into the problem relation

are: Hyperbolic cone, semidefinite

programming, second order cone

programming, linear programming,

quadratic programming and others.

In this case only use the second

order order cone programming. If we

define the new variables using

trigonometric function such as:

If we take the equations 17 to 20 and

it change the variable in equations a

to 7. We have the following:

The voltage magnitude constraints

1

1 can be changed accordingly then

with the new introduced variables.

equations (14) and (15) are

represented in Cartesian form as

follows:

The power constraints can be

modified:

4

6

Topa-Caseres et al. (2025)

4

. Validation

The validation of model propose it

take account the following

assumptions:

Besides, the new variables 14 to 15

and 17 to 19 have the following

relations:

•

The primary Tap’s can controller

the voltage or power active and

reactive.

•

The secondary Tap’s can

controller the voltage or power

active and reactive.

and, finally the equations 30 to 32,

we introduce the second order cone

programming relaxations he to make

•

The bus voltage can variate +-

1

0% of 1 per unit (0.90 a 1.10)

these

be

convex

inequality

The numbers of primary and

constraints. We transform the

equality sign into inequality sign and

present them into a 2-norm format to

ensure the convexity.

secondary Tap’s is the same Fig.

2

.

If the primary Tap’s are controller the

voltage the secondary Tap’s must

not controller voltage, the same in

the other case. This conditions is

typical operation real life in the power

system. The IEEE 14 bus system is

reference for it validation of model,

the data it found here [18]. The active

power loses in normal conditional is

Therefore,

the

load

flow

optimizations problem can be

summarized as:

1

3.38 MW.

The methodology previous is

implement in Gams using knitro

solver and it also Digsilent 2021 the

active power loses is 13.31 MW.

Subject to:

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 8 Núm. (15) 2025. ISSN: 2737-6249

Optimal location of regulating transformer taps to minimize losses in the electrical system.

Nevertheless, the reduction is 0.07

MW. The TAP’s position are the

following:

46 kV, 23 kV, 13.8 kV, 13.2 kV. The

total loses of the system take

account the TAP´s in the 0 positions

is 8.86 MW. Also, the system have

auto-transformers and two winding

transformers.

Table 1. Validation de TAP’s and GAMS y

DIGSILENT

The assumptions are te following:

•

The auto-transformers have five

TAP´S in the primary and the

thirty two TAP´s in the

secondary. The step are 2.5%

and 0.625% respectively.

The voltage magnitude in the

process optimization is the following:

Fig. 3. Voltage magnitude

•

The two winding transformers

has eight step with 2.5% in the

primary and the secondary

winding do not has TAP´s.

•

The limit voltage up and low is

1

.05 and 0.95 by bus.

The angle voltage is −π/2 and

π/2

The bus voltage the fig 3 meet into

constrains of optimization model.

Whit the propose model validation

with it digsilent, we model is well

definite.

The limit voltages and angles help

meet the stability of voltage in all

system. The optimal location TAP´s

of auto- transformer, we can observe

the following table:

5

. Results

The electric system to obtain the

result is all circuit electric Quito, the

data for modeling all the system are

obtain National Electricity Operator

(CENACE). These have 146 buses,

the voltages 138 kV, 110 kV, 69 kV,

4

8

Topa-Caseres et al. (2025)

Table 2. Optimal location auto-transformer

Table 4. Statistical summary in Vpu

TAP´s

The optimal location TAP´s of two

The whisker box is present per unit

voltages of all buses, the majority of

data are around 1 per unit. Theses

voltages are very import for stability

voltage.

winding

transformer

are

the

following:

Table 3. Optimal location two winding

transformer TAP´s

Fig. 4. Per Unit Voltage

The bus voltages we can observe the

majority are close 1 per unit

The system have 96 two winding

transformer and the table show the

transformers with TAP´s are different

of zero.

Fig. 5. Per Unit Voltage

The per unit voltages (Vpu) all buses

are describe in the following table,

the Min and Max value are 0.93 and

1

.06 that occurs in two buses of low

voltages:

Finally, the objective is 8.75 MW and

the location optimal TAP’s are

previous. Therefore, the difference is

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 8 Núm. (15) 2025. ISSN: 2737-6249

Optimal location of regulating transformer taps to minimize losses in the electrical system.

0

.11 MW of reduction in the system.

and meets the constraint that helps

to maintain voltage stability, while the

optimizer meets the optimal TAP’s

location.

6

. Conclusions

The proposed methodology is very

important because it helps to

convexify the power flows that are

non-linear and hard to solve, for this

we used conic approximation of

second degree. Therefore, the

problem is linear integer for the

integer variables of the transformer

TAP’s. These convex equations help

to find the global optimum and

uniqueness of the solutions to

operate in real time.

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