Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 9 Núm. (17) 2026. ISSN: 2697-3693

Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

DOI: https://doi.org/10.46296/ig.v9i17.0339

ANALYSIS OF LOCAL MARGINAL PRICES IN TRANSMISSION SYSTEMS

DOMINATED BY HYDROELECTRIC GENERATION

ANÁLISIS DE PRECIOS MARGINALES LOCALES EN SISTEMAS DE

TRANSMISIÓN DOMINADOS POR GENERACIÓN HIDROELÉCTRICA

1

2

Sánchez-Masaquiza Manuel ; Quinatoa-Caiza Carlos

1

Universidad Técnica de Cotopaxi. Latacunga, Ecuador.

Correo: manuel.sanchez4580@utc.edu.ec. ORCID ID: https://orcid.org/0009-0007-7072-8119.

2

Universidad Técnica de Cotopaxi. Latacunga, Ecuador. Universidad de Jaén. España.

Correo: carlos.quinatoa7864@utc.edu.ec. ORCID ID: https://orcid.org/0000-0001-6369-7480.

Resumen

En los mercados eléctricos competitivos, las señales de precio son fundamentales para guiar las

decisiones de inversión en expansión y repotenciación de la red, especialmente cuando se

identifican congestiones en generadores, transformadores y líneas de transmisión, por lo que

este artículo propone una metodología para analizar dichas congestiones en el Sistema Nacional

Interconectado (SNI) Ecuatoriano mediante un modelo de optimización con flujo DC que

incorpora pérdidas eléctricas, determinando los Precios Marginales Locales en cada nodo bajo

tres escenarios clave: red sin límites de transmisión, red con capacidad real de los elementos y

red real incluyendo pérdidas, cuya comparación permite identificar y cuantificar las congestiones

y su impacto económico, obteniendo así índices cuantitativos que asisten al planificador en la

toma de decisiones óptimas de inversión, con resultados preliminares que revelan puntos críticos

de congestión en líneas y generadores específicos cuya repotenciación minimiza los costos

globales de operación del sistema.

Palabras clave: Planificación energética, Precios marginales, Incertidumbre, Costo marginal,

Precios nodales, Congestión en las líneas, Pérdidas en las líneas.

Abstract

In competitive electricity markets, price signals are essential for guiding investment decisions on

grid expansion and repowering, especially when congestion is identified in generators,

transformers, and transmission lines. This article therefore, proposes a methodology for analysing

such congestion in the Ecuadorian National Interconnected System (SNI) using an optimization

model with DC flow that incorporates electrical losses, determining the Local Marginal Prices at

each node under three key scenarios: a network without transmission limits, a network with the

actual capacity of the elements, and a real network including losses. Comparing these scenarios

allows for the identification and quantification of congestion and its economic impact, thus

obtaining quantitative indices that assist planners in making optimal investment decisions.

Preliminary results reveal critical points of congestion in specific lines and generators whose

repowering minimizes the overall operating costs of the system.

Keywords: Energy Planning, Marginal prices, Uncertainty, Marginal cost, Nodal prices, Line

congestion, Line losses.

Información del manuscrito:

Fecha de recepción: 09 de enero de 2026.

Fecha de aceptación: 20 de marzo de 2026.

Fecha de publicación: 20 de abril de 2026.

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Sánchez-Masaquiza et al. (2026)

1

. Introduction

operators of the electrical market

include in the offer prizes of the lines

transmission restriction trough which

energy is sold. Whence the problems

such as trapped charge or

generations required to maintain the

operation of the power system within

safe ranges become conditions that

agents use to influence nodal prices

or to achieve higher margins in the

market, due to their strategic position

in the transmission system.

Currently, in Ecuador as well as in

different countries, the electric

systems face new challenges related

with

the

electric

demand

increasement, the introduction of

variable

sources

renewable

and the

generation

uncertainty

produced by these technologies [1],

the study of nodal prices or LMP

(Location Marginal Prices), is a topic

of analysis and great importance,

due to it is precise to stablish

adequate rates that provide efficient

and optimal economic signals [2].

In many electricity markets, the

busbar price is determined without

considering congestion, and losses

are approximated to calculate the

market cost [6]. For example, the

authors in [5] utilize a DC flow

methodology to estimate losses. The

current methodology does not

account for reactive power or

uncertainty in renewable energy

sources. However, other authors,

such as [7] and [8], present linearized

flow equations that assist in

determining losses by finding a

global optimum [9]. Additionally,

some authors, like [10], develop

methods to account for the

uncertainty in local nodal prices.

The analysis of congestion as an

indicator of the application of models

for planning the expansion in

generation and transmission must

consider various factors, such as the

incorporation of new electrical

infrastructure, the construction of

generating plants, substations and

power transmission lines [3], [4].

Generally, the electricity prize for

each period is determined by the

variable cost of the last required

generation unit to meet the demand

[

5]. That one that has available

generation capacity, which is why

said unit is called Marginal. It is

important to point out that the

Nonetheless,

their

optimization

models rely on a DC flow model and

do not incorporate electrical energy

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Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

losses. In [11], the issue of how

strategic generators interact in

deregulated electricity markets is

addressed using machine learning to

maximize profits, including the

integration of distributed generation

and grid faults. Meanwhile, in [12],

the authors examined settlement,

electricity supply and demand.

Previous literature review linearizes

the marginal price level (LMP) using

DC flow. However, they do not

consider actual AC losses, which

could lead to price signal deviations.

Based on the above, we suggest

developing an optimization model

implemented in Python using Pyomo

and the GLPK solver. This model

aims to determine nodal prices in the

National Interconnected System

congestion,

instruments within the electricity

market. However, the LMP

and

financial

decomposition depends on the

energy reference bar used in the

OPF model, and the simulation is

carried out in a simplified system.

(SIN) under three scenarios. The first

scenario assumes unlimited

transmission line capacity, allowing

analysis of system behavior without

network constraints. The second

Because of restrictions on the

transmission network and on the

operation of electric generators,

energy flows are redistributed and

more expensive units are used [13].

As a result, nodal price separation

occurs, and marginal power lines

scenario

incorporates

actual

transmission line capacities, without

considering electrical losses. The

third scenario includes both real line

capacities and network losses,

resulting in a nonlinear optimization

problem. Because of this complexity,

the last case is solved using the

IPOPT solver. The database feeding

the model is obtained from

(MPL) increase. Therefore, the MPL

reflect not only the marginal cost of

energy, but also the cost of

maintaining system reliability and

stability.

simulations

performed

in

the

Local marginal process must account

for losses and congestion in

DIgSILENT PowerFactory software.

The data is automatically extracted

using a Python script developed

transmission

lines,

generators,

transformers, and other components.

This is necessary to determine the

true cost of the transition between

within

the

PowerFactory

enabling efficient

environment,

386

Sánchez-Masaquiza et al. (2026)

integration of simulation results with

the optimization model.

2.1.1.3. Transmission system

losses

Transmission

system

losses

2

. Methodology

increase generation requirements

and depend on the technology,

usage, and length on the lines. The

price generated by these losses is

justified by the relative location effect

between generation and demand:

when a load is electrically distant

from the marginal generator, this

price component increases at its

node; conversely, it decreases when

the load is closer.

2.1.1. LMP composition

2.1.1.1. Energy price

The Price is determined by

disregarding both losses and

network constraints, that is, by

performing an ideal energy dispatch.

In this stance the LMP (Lower

Maximum Permissible Limit) is equal

to the single-node price with infinite

transmission line capacity.

This price formation mechanism is

applied in both developing and

2.1.1.2. Network restrictions

developed

electricity

markets

This component is associated with

the operational constraints of the

equipment that makes up the

electrical power system. Such as

thermal, voltage, and stability limits.

The cost of constraints arises when

these limitations prevent the dispatch

of lower-cost generators, forcing the

use of more expensive units located

closer to load centers to meet

demand. This price component is

zero when the grid has no active

constraints or when the system

operates well beyond its operational

limits.

because it improves efficiency and

maintains transparency in the

system, generating economic signals

for new investments in generation or

transmission.

The calculation of nodal prices is

based on optimization models, such

as DCOPF and ACOPF; in practice,

DCOPF is used because its

simplicity and speed, while ACOPF is

used for offline studies because of its

greater accuracy [14].

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 9 Núm. (17) 2026. ISSN: 2697-3693

Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

2

.1.2. Optimal power flow

solving the optimization problem

provides the inputs for calculating the

maximum permissible limits (MPL).

Optimal power flow

involves

determining the state variables of a

power system by optimizing an

The DC model is an approximation of

the AC model, which can be solved

more quickly and generally yields a

global optimum [15]. Therefore, the

equation used to solve case studies

1 and 2 corresponds to the DC

optimization model.

objective

function

while

simultaneously adhering to a set of

physical operational constraints. In

this study, the objective function is to

minimize generation costs subject to

network equality and inequality

operational constraints. Therefore,

(

1)

2)

min 푧 = ∑ 퐶푖 ∗ 푝푔푖

ꢀ

∈푁

푠. 푎

∑

푓푖, 푗 − ∑ 푓푗, 푖 + 푝푔푖 = 푑푖 ∀푖 ∈ ꢂ

ꢀ

,ꢁ∈퐿

ꢁ.ꢀ∈퐿

(

3)

4)

푓푖, 푗 = 푣푖 푣푗(휃푖 − 휃푗) / 푥푖, 푗 ∀푖, 푗 ∈ ꢃ

푓푖, 푗| ≤ 푓_ꢀ^푚_,_ꢁ^ꢄ^ꢅ, ∀푖, 푗 ∈ ꢃ

|

(

5)

6)

푚ꢀ푛

퐺

푚ꢄꢅ

≤ 푃 ≤ 푃

ꢆꢀ

푃

∀푖 ∈ ꢂ

ꢆꢀ

ꢀ

휃_ꢀ^푚^ꢀ^푛≤ 휃푖 ≤ 휃_ꢀ^푚^ꢄ^ꢅ∀푖 ∈ ꢂ

the transmission lines. Equation (4)

imposes the corresponding upper

limit on the line power flows.

Equation (1) formulates the objective

functions aimed at minimizing the

total generation cost. This equation is

subject to constraints. Equation (2)

Equation

(5)

determines

the

maximum generation capacity of

each unit, and finally, equation (6)

restricts the voltage angle to the

permissible range.

imposes

the

nodal

balance,

considering the incoming and

outgoing power flows in the nodal

power balance (fj.i denotes the

power flow entering node i from node

j), simply th opposite of the outgoing

flow fi,j. Subsequently, equation (3)

represents the power flow through

To implement case 3, in which

system losses are implemented, the

DC model with losses is applied.

388

Sánchez-Masaquiza et al. (2026)

(

7)

min 푧 = ∑ 퐶푖 ∗ 푝푔푖

ꢀ

∈푁

푠. 푎

(

8)

9)

∑

ꢃ퐹푔푖 ∗ 푝푔푖 − ∑ ꢃ퐹푑푖 ∗ 푑푖 = 푃ꢃ + 푂푓푓푠푒푡

ꢀ

∈푁

ꢀ∈푁

∑

푓푖, 푗 − ∑ 푓푗, 푖 + 푝푔푖 = 푑푖 + 푃ꢃ ∀푖 ∈ ꢂ

ꢀ

,ꢁ∈퐿

ꢁ,ꢀ∈퐿

(

10)

11)

푓푖, 푗 = 푣푖 푣푗(휃푖 − 휃푗) / 푥푖, 푗 ∀푖, 푗 ∈ ꢃ

|

푓푖, 푗| ≤ 푓_ꢀ^푚_,_ꢁ^ꢄ^ꢅ, ∀푖, 푗 ∈ ꢃ

(

12)

13)

푚ꢀ푛

퐺

푚ꢄꢅ

≤ 푃 ≤ 푃

ꢆꢀ

푃

∀푖 ∈ ꢂ

ꢆꢀ

ꢀ

휃_ꢀ^푚^ꢀ^푛≤ 휃푖 ≤ 휃_ꢀ^푚^ꢄ^ꢅ∀푖 ∈ ꢂ

requiring that at each node the sum

of line flows and local generation

equals demand, assigning the

absorption of total system losses to

the reference node.

Equation (8) represents overall

system balance, in which total

generation and demand are adjusted

using loss factors, so that their

difference is equivalent to the system

losses (LP) plus a compensation

term. In this formulation, Pl

represents the total transmission

losses and incorporates their effect

on the overall power balance.

Because the lost factors are obtained

3

. Procedure for obtaining nodal

prices in python software

using PYOMO and the GLPK

solver

3

.1. Electrical Power System

through

linear

approximations,

arise between

discrepancies

The electrical system under study is

the National Interconnected System

generation, demand, and estimated

losses. Therefore, the OFFSET

parameter is applied to correct these

discrepancies, thus ensuring the

exact closure of the power balance

constraint in the DC model with

losses. Finally, equation (9) ensures

power balance and the nodal level,

(SIN). The system is modeled using

the Power Factory DIgSILENT

simulation software. This data is

crucial, as it provides the necessary

input for the optimization model,

which is then used to calculate nodal

prices. The analysis is based on the

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Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

Figure 1: Implementation of the Script for

2

025 case study, considering a peak

Data Extraction in Python Format.

demand scenario. This scenario

includes 181 transmission lines and

191 busbars.

3.2. Data Extraction by Python

application.

Given the nature of this electrical

system, which models the National

Interconnected System, manually

extracting the necessary data for the

database is complex. Therefore,

Python programming software is

used. Specifically, a Python script, as

shown in Figure 1, must be created

within the case study’s libraries to

automatically extract data using

Excel paths. This data will then be

chronologically organized in a .dat

file. It is important to note that the

data should be extracted from the

SNI Zone. Extracting data from the

entire case study, including the

Santo Domingo Zone, Quito Zone,

Cuenca Zone, and others, will result

in data discrepancies due to the lack

of connections between lines and

busbars.

3

.3. Convert the entire system to

per unit and perform the base

changes

Once the system data is obtained, it

is advisable to normalize all systems

parameters to a common basis using

the per-unit (p.u.) system. For input

into the Python software, this

process must be performed correctly,

respecting the electrical system data.

Due to the amount of data, the

process can be carried out in Python

or using Excel, simplifying data

management. The conversion is

performed using equation (15), which

must adhere to the power system

basis.

푅푒푎푙 푉푎푙푢푒

퐵푎푠푒 푉푎푙푢푒

(14)

푉푎푙푢푒 in 푝. 푢. =

For this purpose, a base power must

be established for the entire system,

in this case which is Sbase = 100

MVA, because it is the default value

390

Sánchez-Masaquiza et al. (2026)

used in the DIgSILENT software,

however, the base voltage is

determined by the nominal voltages

of the lines and transformers.

to the selected system base, in this

case 100 MVA. This adjustment aims

to ensure that the parameters are

consistent. The base change is

performed using equation (18)

Therefore, the 풁_풃_풂_풔_풆is determined

푆_푏_ꢄ_ꢇ_ꢈ_,_푛_ꢋ_ꢈ_ꢌ_ꢄ

(18)

푍_ꢊ_._ꢋ_푛_ꢋ_ꢈ_ꢌ_ꢄ= 푍_ꢊ_._ꢋ_ꢄ_푛_ꢍ_ꢀ_ꢆ_ꢋ_ꢄ∗ (

)

according

to

equation

(15),

푆푏ꢄꢇꢈ,ꢄ푛ꢍꢀꢆꢋꢄ

necessary to convert the values of

the lines to p.u.

3.4. Generator costs

One of the main inputs for obtaining

the LMPs is the cost of generators,

since, based on these costs and line

and generator limits, dispatch and

the determination of nodal prices will

be carried out.

Equation (16) shows the value

obtained for 풁_풃_풂_풔_풆for a 500 kV

voltage level, which is operated by

the line L_INGA_SRAFA_3_1.

Equation (17) shows the value

obtained for 풁_풃_풂_풔_풆for a voltaje level

of 230 kV, which is operated by the

line L_PIMA_POMA_2_1.

The

costs

of

thermal

and

hydroelectric power generators in

Ecuador are obtained from two

databases, in CVS and TXT formats

respectively. These prices serve as

(

15)

2

^푉푏ꢄꢇꢈ

푍_푏_ꢄ_ꢇ_ꢈ

=

푆_푏_ꢄ_ꢇ_ꢈ

(

16)

17)

₀₀_푘_푉2

an

Internationally

recognized

5

푍_푏_ꢄ_ꢇ_ꢈ

=

= ꢉ500

= 5ꢉ9

1

00푀푉퐴

benchmark.

ꢉ30푘푉²

푍_푏_ꢄ_ꢇ_ꢈ

1

00푀푉퐴

To determine the prices at the

busbars, an analysis of the

generators connected to the busbar

must be carried out, determining the

respective value, which is why Table

Once the 풁_풃_풂_풔_풆value is obtained for

each voltaje level, it is easy to find the

p.u.values of the lines by dividing the

actual value in Ω by the base value.

1

presents 3 costs of the 191 existing

busbars.

The transformers exhibit X1 values in

p.u., which are specified in their

machine nominal bases. Therefore, it

is necessary to readjust these values

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Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

Table 1: Costs in the SNI busbars, 5

the busbars. The second column

values.

contains the line’s reactance, and

finally, the third column contains the

line’s maximum flux. Table 3 shows

an example of the five lines of the

electrical system and how their

parameters are defined.

Busbar

Cost

65

118.076

205.155

B_Manta_13.8_ATM

B_Alluriquin_U1_13.8

B_Baba_69

3

.5. Building the database (.dat)

to feed the model)

First, in the .txt file, the slack bus

must be defined as a parameter.

Regarding the bus parameters, the

data is divided into five columns: the

first defines the bus number, the

second defines the demand at that

bus, the third defines the maximum

power (in this case, generation), the

fourth defines the coast at the bus,

and finally, the maximum angle. This

must be done for each bus in the

power system, ensuring the data is

correctly organized. Table 2 shows

an example of the first five buses in

the electrical system and how their

parameters are defined.

Table 3: Definition of the parameters

corresponding to the transmission lines.

nl

reac

0.00215

0.1243512

0.112278

0.185567

0.104143

fmax:

0.541

0.478

0.23

0.276

0.416

1

2

2 3

6

4

6

5

6

7

3.6. Building the Python model

using Pyomo and the GLPK solver

The problem is formulated as an

optimal DC power flow (DC-OPF)

using the Pyomo library, which

allows representing the behavior of

Ecuador’s National Interconnected

System (SNI) under a generation

cost

minimization

approach,

network

considering

constraints.

physical

Table 2: Definition of the parameters

corresponding to the busbars.

nb

1

2

3

4

dem

0

0.0116

pmax

0.139

0

0.039

0.03

0.35

cost

anmax:

3.34

1.77

1.04

The model is defined as an

AbstractModel, which allows the

mathematical formulation to be

separated from the system data,

which are subsequently loaded form

a .dat file.

65

118.076

0

6.95

0

5

3.08

Finally, to define the lines, there are

three columns. The first column

contains two pieces of data: the

starting point of the line and the

ending point in terms of connection to

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Sánchez-Masaquiza et al. (2026)

3

.6.1.

Implemented Model

extraction of data from the

DIgSILENT software, continuing with

the construction of the optimization

model, and finally obtaining the nodal

prices.

Process

Figure 2 shows the process followed

by the method, starting with the

Figure 2: Flowchart of the implemented model.

4

. Result analysis

.1. Case 1.

across the system. This is attributed

to the presence of very low-cost local

generators or zero-cost generation

constraints that lead to local

dispatch. Therefore, it does not imply

congestion, but rather a natural

consequence of economic dispatch

with multiple marginal bids.

4

In case 1, Ecuador’s National

Interconnected System (SIN) was

modelled

assuming

infinite

transmission capacity on all lines of

the network. Therefore, any type of

congestion is eliminated, reducing

the problem to a purely economic

dispatch, where generation is

allocated based on the marginal

costs of the generators. The problem

was solved using a linear DC-OPF

solution with the GLPK solver,

yielding an optimal feasible solution.

Due to the absence of congestion,

the market price depends on the

marginal cost of the dominant

generator, that is, the one that is not

saturated and can offer a margin.

Based on the results obtained, the

market

price

Pmarket=35.7

USD/MWh, is observed; this value

corresponds to the shadow price

obtained from the dual of the

optimization model.

Although the lines are considered

infinite, the results show that nodal

prices are not completely uniform

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Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

The resulting price data shows low

values associated with hydroelectric

USD/MWh corresponding to zones

with expensive or isolated

generation

~

6

USD/MWh,

generation. This behavior results in a

multimodal distribution, which is

expected in large-scale systems

such as the National Interconnected

System.

intermediate values of 30 to 45

USD/MWh corresponding to the

dominant zone of the system, and

high

values

exceeding

100

Figure 3: Diagram corresponding to the prices obtained for each node of the SNI in case 1.

Figure 4: Diagram corresponding to the prices obtained for each node of the SNI in case 1.

394

Sánchez-Masaquiza et al. (2026)

moderate coefficient of variation,

indicating controlled price dispersion

even under unlimited transmission

conditions. Furthermore, Figure 5

shows the histogram and normal

distribution for case 1.

Figures (3) and (4) show the different

nodal prices obtained for case 1,

which assumes infinite line capacity.

This confirms that the system

exhibits significant concentration

around the average price, with a

Figure 5: Histogram and Normal Distribution of Case 1.

direct impact of transmission

congestion on system nodal prices.

4.2. Case 2.

In case 2, Ecuador’s (SNI) was

modelled considering the actual

transmission capacities of the lines,

as defined in the system model in

DIgSILENT Power Factory. Electrical

losses are not considered; therefore,

the analysis corresponds to a

lossless DC-OPF with capacity

constraints on the lines. This

scenario allows for determining the

The results show a high dispersion of

nodal prices, with values reaching a

maximum of 235.3 USD/MWh and

multiple

intermediate

levels

associated with different areas of the

system. This variability is a clear sign

of congestion in the transmission

network, which prevents lower-cost

generation from supplying the entire

system uniformly. The increases in

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Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

nodal prices, in contrast to case 1,

are presented in Table 4. It can be

observed how the nodal process

rose, thus determining the correct

implementation of case 2. Therefore,

the values tend to increase in the

different nodes of the system, as

observed in case study 2.

suggesting an adequate local

generation availability. However, due

to line limitations, energy cannot be

transmitted to other parts of the

system without violating maximum

power flow restrictions on the

transmission lines.

Figures (6) and (7) show the different

nodal prices obtained for case 2,

which considers the actual line

Table 4: Nodal prices contrasts in case 1

and case 2

Node

Case 1

Case 2

1

2

5

8

2

3

4

0

6

9

36.6237

39.6237

35.7000

40.0639

102.0850

47.8000

135.4000

102.0850

capacities.

Therefore,

when

comparing with figures (3) and (4), a

significant increase in the prices of

some nodes is evident. This is

attributed to compliance with the

maximum flow rates that must occur

on the transmission lines.

Nodes with low prices between 6 and

USD/MWh are mainly located in

8

areas near hydroelectric plants or

low marginal cost generators,

Figure 6: Diagram belonged to prices obtained for each node SIN in case 2.

396

Sánchez-Masaquiza et al. (2026)

Figure 7: Diagram belonged to prices obtained for each node SIN in case 2.

distribution, with a pronounced right

tail, characteristic of congested

electrical systems.

Furthermore, Figure 8 shows the

histogram and normal distribution for

case 2. It shows an asymmetrical

Figure 8: Histogram and Normal Distribution from case 2.

losses. This case study is more

complex to implement because

different parameters must be

included, and the solver must be

4

.3. Case 3.

In case 3 of this study, the nodal

prices are obtained considering the

real flows of the system and including

397

Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 9 Núm. (17) 2026. ISSN: 2697-3693

Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

changed to achieve optimization,

thus minimizing costs for the buses

Then by applying equation (21), the

LF loss factors can be obtained.

(

21)

푑ꢃꢎ

The new parameter to be considered

in the present case study is the

resistance in per unit, which must be

correctly extracted from the DIgSilent

software for each of the system lines.

=

ꢉ ꢑ∑ 푅ꢎ 푓ꢎ 퐻푖, ꢎꢒ

푑푝푔푖

푚휖휄

Loss factors make it easy to

determine the offset, which which

considers the actual AC losses of the

base case, which correspond to 38.1

MW. The code calculates the

difference between the generated

and demand power, multiplies it by

the loss factor obtained for each bus.

Finally, it subtracts the product of the

power and the LF (Lower Line

Factor) at each bus from the system

loss factor, thus obtaining and offset

of 36.73MW.

The implemented procedure is found

in the study; this process begins with

obtaining the line-node incidence

matrix, which will be used to obtain

the distribution factor.

To determine both the line-node

incidence matrix and the Y-transfer

matrix, a Python code was applied,

which extracts the data from an Excel

file containing the information

necessary for the study. The code

then generates the incidence matrix

Finally, it is necessary to stablish

new conditions in the code for

obtaining nodal prices, which are

determined by equations (22) and

considering

the

line-node

connections, defining 1 as the bus to

which the flow originates. -1 as the

bus to which the power flow arrives,

and 0 if there is no connection.

Furthermore, the Y-transfer matrix is

(

23).

(

22)

23)

∑ ꢃ퐹푔푖 ∗ 푝푔푖 − ∑ ꢃ퐹푑푖 ∗ 푑푖 = 푃ꢃ + 푂푓푓푠푒푡

ꢀ

∈푁

ꢀ∈푁

∑

푓푖, 푗 − ∑ 푓푗, 푖 + 푝푔푖 = 푑푖 + 푃ꢃ ∀푖 ∈ ꢂ

ꢀ

,ꢁ∈퐿

ꢁ,ꢀ∈퐿

generated

by

extracting

the

In the third case study, after

implementing the loss factors and the

OFFSET implementation, values are

obtained that are accordance with

the real prices of the SNI bars; these

reactance of lines i-j, which form the

diagonal. Once both matrices are

obtained, equation (20) is used to

calculate the distribution factors.

푇

ꢏꢐ

퐻푖, ꢎ = 훾 ∗ 퐴 ∗ (퐴 ∗ 훾 ∗ 퐴)

(20)

398

Sánchez-Masaquiza et al. (2026)

values are presented in figures (9)

and (10)

Figure 9: Diagram belonged to the prices obtained for each node of the SNI in case 3

Figure 10: Diagram corresponding to the prices obtained for each node of the SNI in case 3.

USD/MWh. Figure 10 shows that,

Based on the results obtained, it can

although there is a dominant average

be observed that nodal prices have

value. There are no single prices,

an approximate range between 15

which confirms the influence of the

and 43 USD/MWh, with a majority of

concentration

around

34-36

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Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 9 Núm. (17) 2026. ISSN: 2697-3693

Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

transmission systems and losses on

price transformation.

While the busbars with the lowest

nodal prices generally correspond to

areas near large power plants and

sectors with a lower marginal impact

from losses. At these busbars, the

marginal cost of supplying additional

demand is lower, resulting in reduced

nodal prices.

It was determined that the busbars

with highest nodal prices are

primarily associated with areas far

from major hydroelectric generation

centers, and sectors where energy

must travel long distances through

the transmission line. Within the

Figure 11 shows the nodal Price

context

of

the

National

histogram,

which

shows

an

Interconnected System (SNI), these

prices reflect the higher cost of

supplying an additional unit power,

since meeting the increased demand

at these nodes implies growth in both

generation and system losses.

approximately normal distribution,

with a maximum frequency around

the system average price, moderate

dispersion, and extreme values

representing nodes with particular

congestions conditions or high

losses

Figure 11: Histogram and Normal Distribution of case 3.

400

Sánchez-Masaquiza et al. (2026)

4

.4. Statistical

Indicators

evaluation the progressive impact of

actual line flows and losses.

Analysis.

Table 5: Statistical Indicators for the study

In case 2, the actual transmission

cases

capacities

of

the

SNI

are

Indicator

Mean

Case 1

45.48

Case 2

70.27

Case 3

34.06

incorporated, the statistical results

show an increase in the average

values, with a mean of 70.27

USD/MWh and a median of 47.80

USD/MWh, as well as a standard

deviation of 55.55 and a coefficient of

variation of 0.7905. These values

indicate a high price dispersion,

associated with the appearance of

congestions in the transmission

network.

USD/MWh

Median

USD/MWh

Standard

Deviation

Coefficient

of variation

35.70

45.57

1.002

47.80

55.55

35.38

4.43

0.13

0.7905

To evaluate the impact of the

transmission network and losses on

the formation of nodal prices of the

National Interconnected System of

Ecuador,

three

progressive

scenarios were analyzed, for which

the nodal prices obtained in the 191

bars of the system were evaluated,

calculating statistical indicators such

as the mean, median and standard

deviation.

Finally, case 3 represents the most

realistic scenario, as it considers

both the actual flows on the lines and

system losses. In this case, the

statistical indicators show a different

behavior, with a mean of 34.06

USD/MWh, a median of 35.38

USD/MWh, a standard deviation of

Case 1, which assumes infinite

capacity in the transmission lines,

shows a mean of 45.48 USD/MWh

and a median of 35.70 USD/MWh,

accomplished by a high standard

deviation of 45.57 and a coefficient of

variation close to 1.002. Due to this

behavior, a high relative dispersion of

prices is determined. This case does

not fully represent the reality of the

National Interconnected System

4

.43, and a coefficient of variation of

.13. These values exhibit greater

0

consistency. It is determined that the

inclusion of losses smooths out the

extreme differences observed in the

previously study cases, reflecting a

more balanced representation of the

actual behavior of the National

(SNI), but it serves as a basis for

Interconnected (SNI).

System

Therefore, it is determined that the

401

Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 9 Núm. (17) 2026. ISSN: 2697-3693

Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

model with losses adequately

captures the real behavior of the

national interconnected system,

obtaining consistent and accurate

nodal prices in accordance with

actual values.

demonstrating network congestion.

Therefore, high nodal prices indicate

areas where demand cannot be met

with more economical generation

due to network limitations, forcing the

system to use more expensive local

generators, thereby increasing the

marginal cost. Based on the above, it

is concluded that transmission plays

a key role in nodal price formation, as

it not only guarantees the operational

security of the system but also

provides economic signals for the

local of new generation.

5. Conclusions

When considering transmission lines

with a infinite capacity, the electric

power system behaves as a perfectly

integrated market with no energy

transport

restriction.

Therefore,

prices tend to homogenize across

most busbars; in this case, the

predominant process across most

busbars was 35.7 USD/MWh. This

presents a theoretical ideal scenario

in which the cheapest generators can

supply existing demands at the

busbars, regardless of the flows

through the lines, but without

exceeding their generation capacity.

This scenario is far removed from the

actual operation of Ecuador’s

National Interconnected System, as

it ignores the physical limitations of

the network.

The determination of nodal prices in

Ecuador’s National Interconnected

System, considering the actual line

capacity, real power flows and

system losses, yielded values

consistent with the system’s actual

physical. However, the results also

demonstrate the inclusion of losses,

disrupting price uniformity and

generating differences in nodal

values due to the higher marginal

cost of meeting demand and nodes

far from major generation centres or

with a greater marginal loss. In

conclusion, case 3 demonstrates that

the transmission system and the

losses play a significant role in nodal

price formation. Furthermore, it was

The

incorporation

of

actual

transmission line capacities revealed

significant differences, raising nodal

prices at most busbars and thus

determined

that

implementing

402

Sánchez-Masaquiza et al. (2026)

mathematical optimization models

using the open – source Python

software, with solvers such as GLPK

and IPOPT, yields consistent values

that align with real-world nodal

prices. Therefore, the results provide

a solid technical foundation for future

[4]

Q. Wang, G. Zhang, J. D.

McCalley, T. Zheng, and E.

Litvinov,

Locational Marginal Pricing

and Congestion

“Risk-Based

Management,” IEEE Trans.

Power Syst., vol. 29, no. 5, pp.

2518–2528, Sep. 2014, doi:

10.1109/TPWRS.2014.23053

03.

research,

given

the

models'

effectiveness.

[

5]

F. Li, “Continuous Locational

Marginal Pricing (CLMP),”

IEEE Trans. Power Syst., vol.

Bibliographic

22, no. 4, pp. 1638–1646,

Nov. 2007, doi:

[

1]

A. Zakariazadeh, R. Ahshan,

R. Al Abri, and M. Al-Abri,

10.1109/TPWRS.2007.90752

.

1

“Renewable

energy

integration in sustainable

water systems: A review,”

Clean. Eng. Technol., vol. 18,

p. 100722, Feb. 2024, doi:

[6]

F. Li and R. Bo, “DCOPF-

Based LMP Simulation:

Algorithm, Comparison With

ACOPF, and Sensitivity,”

IEEE Trans. Power Syst., vol.

10.1016/j.clet.2024.100722.

22, no. 4, pp. 1475–1485,

[

2]

H. Yang, L. Wang, Y. Zhang,

H.-M. Tai, Y. Ma, and M.

Zhou, “Reliability Evaluation

of Power System Considering

Time of Use Electricity

Pricing,” IEEE Trans. Power

Syst., vol. 34, no. 3, pp. 1991–

Nov. 2007, doi:

1

4

0.1109/TPWRS.2007.90792

.

[7]

H. Yuan, F. Li, Y. Wei, and J.

Zhu, “Novel Linearized Power

Flow and Linearized OPF

Models for Active Distribution

Networks With Application in

2

1

5

002,

May

2019,

doi:

0.1109/TPWRS.2018.28799

3.

Distribution IEEE

Trans. Smart Grid, vol. 9, no.

, pp. 438–448, Jan. 2018,

doi:

LMP,”

[

3]

B. Tamimi and S. Vaez-

Zadeh, “An Optimal Pricing

Scheme in Electricity Markets

Considering Voltage Security

Cost,” IEEE Trans. Power

Syst., vol. 23, no. 2, pp. 451–

1

10.1109/TSG.2016.2594814.

[8]

Z. Yang et al., “LMP Revisited:

A Linear Model for the Loss-

Embedded LMP,” IEEE Trans.

Power Syst., vol. 32, no. 5, pp.

4080–4090, Sep. 2017, doi:

4

1

0

59,

May

2008,

doi:

0.1109/TPWRS.2008.92018

.

403

Revista Científica ‘‘INGENIAR”: Ingeniería, Tecnología e Investigación. Vol. 9 Núm. (17) 2026. ISSN: 2697-3693

Analysis of local marginal prices in transmission systems dominated by hydroelectric generation.

1

0.1109/TPWRS.2017.26488

6.

“Asignación

unidades de generación en

regiones múltiples aplicando

eficiente

de

[

9]

Z. Yang, H. Zhong, A. Bose, T.

Zheng, Q. Xia, and C. Kang,

optimización

Rev. Científica, vol. 7, 2024.

multiobjetivo,”

“A Linearized OPF Model With

Reactive Power and Voltage

Magnitude: A Pathway to

Improve the MW-Only DC

OPF,” IEEE Trans. Power

Syst., vol. 33, no. 2, pp. 1734–

[14] J. S. Ortiz, C. I. Quinatoa, and

J. H. Acurio, “A New Model

Optimization Convex Using

Wirtinger

Calculus

for

Economic Dispatch,” in 2024

8th International Conference

on Power Energy Systems

and Applications (ICoPESA),

Hong Kong, Hong Kong:

IEEE, Jun. 2024, pp. 557–

1

5

745,

Mar.

2018,

doi:

0.1109/TPWRS.2017.27185

1.

[

10] Rui Bo and Fangxing Li,

Probabilistic LMP

“

5

1

4

66.

doi:

Forecasting Considering Load

Uncertainty,” IEEE Trans.

Power Syst., vol. 24, no. 3, pp.

0.1109/ICOPESA61191.202

.10743906.

1279–1289, Aug. 2009, doi:

10.1109/TPWRS.2009.20232

68.

[15] C. Quinatoa, A. Chasi, V.

Puetate, A. Casilimas, L.

Camacho, and J. Ortiz,

“

Optimization

Model for

Multistage

[

11] F. Aydin and C. Karatekin,

Strategic Integration of

Coordinated

“

Planning of the Generation-

Transmission System with

Demand Forecasting Using

Distributed Generation in a

Deregulated Power Market:

An Agent-Based Approach,”

IEEE Access, pp. 1–1, 2024,

doi:

Neural

Networks,”

in

Proceedings of the 4th

International Conference on

Electronic Engineering and

1

7

0.1109/ACCESS.2024.3512

81.

Renewable

Energy

Systems—Volume 1, B. Hajji,

A. Gagliano, A. Mellit, A.

Rabhi, and M. Calì, Eds.,

Singapore: Springer Nature

Singapore, 2025, pp. 573–

[

12] F. O. S. Saraiva and V. L.

Paucar, “Locational Marginal

Price Decomposition Using a

Fully Distributed Slack Bus

Model,” IEEE Access, vol. 10,

pp. 84913–84933, 2022, doi:

581.

1

2

0.1109/ACCESS.2022.3197

23.

[

13] T.-P. D. Gabriela, Q.-C. C.

Iván, and C.-C. L. Hernán,

404