Artículo Académico / Academic Paper

Recibido: 12-11-2024, Aprobado tras revisión: 09-01-2025

Forma sugerida de citación: Zhañay, K.; Leiva, C.; Pilataxi, E.; Quitiaquez, W. (2025) “Modelo de Correlación desgaste –

cantidad de Sedimentos para la Programación de Mantenimiento Preventivo de una Central Hidroeléctrica. Revista Técnica

“energía”. No. 21, Issue II, Pp. 39-47

ISSN On-line: 2602-8492 - ISSN Impreso: 1390-5074

Doi: https://doi.org/10.37116/revistaenergia.v21.n2.2025.691

Esta publicación está bajo una licencia internacional Creative Commons Reconocimiento –

No Comercial 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)

Wear - Sediment Quantity Correlation Model for Preventive Maintenance

Scheduling of a Hydroelectric Power Plant

Modelo de Correlación Desgaste - Cantidad de Sedimentos para la

Programación de Mantenimiento Preventivo de una central Hidroeléctrica

K. Zhañay1

0009-0002-4413-3748

C. Leiva1

0000-0002-8255-1337

E. Pilataxi1

0009-0009-2633-0407

W. Quitiaquez1

0000-0001-9430-2082

1Universidad Politécnica Salesiana, Quito, Ecuador

E-mail: kzhanay@est.ups.edu.ec; cleiva@ups.edu.ec; epilataxi@ups.edu.ec; wquitiaquez@ups.edu.ec

Abstract

The present research is carried out for the improvement

of the availability of a hydroelectric power plant

through a wear-sediment quantity correlation model for

the scheduling of its preventive maintenance, the data is

based on the measurement of blade thicknesses, as well

as visual inspection to identify discontinuities in the

water equipment, once the data has been collected, data

analysis techniques can be used to evaluate the

condition of the Francis turbine and determine the need

for preventive maintenance under working condition.

The data analysis detailed is the least squares method

where the independent variables considered are power

and suspended particles with their nephelometric unit of

measurement of turbidity in parts per million (PPM). By

means of the aforementioned analysis, it is possible to

complete the results with the projection of the wear to

years after the data obtained from the inspection point,

and it also allows taking preventive measures before a

failure occurs, which helps to reduce downtime and

maintenance costs. Thus, the hydroelectric power plant

under study has an annual average availability of 97.21

%, reduced by the suspension of power generation due

to reservoir flushing and scheduled maintenance

shutdowns. While the annual average reliability is 99.89

%, it is reduced by unscheduled failures. The result of

the correlation statistical model determined the

preventive maintenance for improvement conditions of

98 % of the availability in the hydroelectric power plant

and is reflected in the reduction of days of no electricity

generation.

Resumen

La presente investigación se realiza para la mejora de la

disponibilidad de una Central Hidroeléctrica a través de

un modelo de correlación desgaste-cantidad de

sedimentos para la programación de su mantenimiento

preventivo, los datos se basan en la medición de

espesores de los alabes, así como la inspección visual

para identificar discontinuadas en los equipos hídricos,

una vez que se han recopilado los datos, se pueden

utilizar técnicas de análisis de datos para evaluar el

estado de la turbina Francis y determinar la necesidad

de mantenimiento preventivo bajo condición de trabajo.

El análisis de datos que se detalla es el método de

mínimos cuadrados donde las variables independientes

que se consideran son potencia y partículas de

suspensión con su unidad de medida nefelométricas de

turbidez en partes por millón (PPM). Mediante el

análisis mencionado se logra culminar los resultados

con la proyección del desgaste a años posteriores a los

datos obtenidos del punto de inspección, además que

permite tomar medidas preventivas antes de que se

produzca una falla, lo que ayuda a reducir el tiempo de

inactividad y los costos de mantenimiento. Es así como

la Central Hidroeléctrica en estudio tiene un promedio

anual del 97.21 % de disponibilidad, se reduce por la

suspensión de la generación eléctrica, debido al lavado

del embalse y las paradas por mantenimiento

programado. Mientras que, la confiabilidad promedio

anual es el 99.89 %, se reduce por fallas no

programadas. El resultado del modelo estadístico de

correlación determino el mantenimiento preventivo por

condiciones de mejora del 98 % de la disponibilidad en

la Central Hidroeléctrica y se refleja en la disminución

de días de no generación eléctrica.

Index Terms— Hydroelectric power plant, sediments,

turbine, maintenance

Palabras clave— Central Hidroeléctrica, sedimentos,

turbina, mantenimiento

Edición No. 21, Issue II, Enero 2025

1. INTRODUCCIÓN

The generation of electric energy in several Latin

American countries has been linked to the use of fossil

fuels in their energy matrix, causing a problem of

environmental pollution, which has led to the search for

other less invasive, more efficient, and environmentally

friendly energy sources. The development of the

electricity sector takes shape when focusing on

improving the energy matrix with renewable energy

such as hydroelectric power plants. By adopting an

improved energy matrix, Ecuador not only benefits the

electric distribution field but also avoids contamination

and danger to the country's fauna and flora. Pinargote et

al. [1] 39 MW, of which 5243.37 MW correspond to

renewable energy sources, representing 64.9 %. Of the

renewable sources, 5082.35 MW corresponds to the

participation of the hydraulic source, representing

96.9 %. Only 3.1 % correspond to wind, solar, and

biomass energy together [2].

Rojas et al. [3] detail that in the last seven years

hydroelectric power plants within the energy matrix will

represent 93% of the effective generation power,

however, the development and maintenance of such

infrastructure must be considered. Fonseca et al. [4]

propose a proportional distribution to the average water

flow contributed by each municipality within the

catchment area of the hydroelectric power plant and the

size of the area flooded by its reservoir through an

analysis of the balance between precipitation and

evapotranspiration for all municipalities in Brazil,

yielding only a 3 % difference concerning the observed

water flow. As a result of the proposed methodology,

the number of municipalities benefited increased from

41 to 167 drainage areas, providing financial resources

to the municipalities and allowing them to invest in

conservation techniques to ensure the maintenance of

water resources [5].

Liu et al. [6] describe an analysis focused on the

concentration of sediment and silt in the turbined water,

the Kaplan, Pelton, and Francis turbines which are the

most used in hydroelectric plants are the focus of the

study considering as parameters of analysis of the silt

density, sediment size, velocity and direction. Using

three concentrations of sand 25, 50, and 85 kg/m3 with

different sizes 0.531, 0.253, and 0.063 mm, where the

increase of quantity and size causes damage by

cavitation for which they propose to cover the surfaces

that suffer when losing their efficiency and in a direct

way the reduction of the generation time. Chavarro [7]

details a Kaplan turbine a CFD modeling under various

functional parameters that determine its wear, these

parameters are pure water, cavitation erosion, erosion

by silt, and combined erosion, like the Francis and

Pelton turbine the operation of the Kaplan turbine under

sediment erosion, generates efficiency drop of 2.47%

with the increase in the diameter of the sediment to

100 μm and the concentration of sediment

10000 ppm [8], [9].

Sangal et al. [10] state that due to the sedimentation

of the turbine water, the turbine components wear,

especially the guide vanes, when performing a fluid

dynamic analysis and simulation of the guide vane of

the Francis model turbines with different thicknesses of

17 and 21 mm, through a geometric study of both vanes

it was found that, by increasing the blade thickness, the

line of attack (chord) of the current blade

(21 millimeters thick), has a small linear deviation of

0.13 millimeters concerning the original blade

(17 millimeters thick), causing an increase in the flow

angle [11].

Rai et al. [12] studied the erosion caused by

sedimentation on different materials under the same

erosive and hydraulic conditions where they conducted

experiments simultaneously with varying ranges of

velocity, exposure duration, sediment size, and

concentration on 1:8 scale reduced Pelton cubes of a

hydroelectric plant in India, for application on Pelton

turbines made of 6 materials such as 3 types of steel,

2 types of coatings and bronze for heights up to 200 m

the scale. Sun et al. [13] mention the study of sediment

abrasion, cavitation erosion, and synergistic erosion in a

rotating disk test rig. They also compared the anti-

abrasion properties of HVOF high-speed oxy-fuel

sprayed stainless steel and HVOF sprayed martensitic

WC-CO-Cr stainless steel. They found that the latter is

more suitable for the sediment-laden flow environment.

Cruzatty et al. [14] analyzed by CFD the runner

blades of a Francis turbine where they presented a

higher erosion rate on the suction side near the trailing

edge. The presence of higher sediment erosion is the

trailing edge of the suction side, the result of the

numerical analysis reflects that the erosion damage

increases significantly for higher flow rates when the

guide vane opening exceeds 85 % opening considering

the closed position as a reference. Noon and Kim [15]

describe a CFD analysis where the leakage flow

generates a step vortex, which moves away from the

wall as it moves downstream, decreasing the intensity,

and demonstrating the minimization of the coalescing

impact of secondary flow and sediment erosion. Several

studies show that the efficiency of the Francis turbine

varies between 3 and 6 % depending on changes in

sediment concentration and secondary flow phenomena.

However, a loss of between 2 and 3.5 mm of channel

thickness is observed.

Zhañay et al. / Wear-sediment quantity correlation model for preventive maintenance

For the analysis of the loss of thickness in the

turbine blades, a series of inspections must be carried

out, which must be contemplated in the elaboration of

the maintenance plan for Francis turbines, since the

frequency of maintenance is of utmost importance to

establish inspection and repair costs, avoiding energy

production losses as much as possible. Toapanta [16]

states that using non-destructive NDT inspection such

as visual inspection VT, penetrating liquids PT,

magnetic particles MT, conventional ultrasound, and

phased array UTPA, it is possible to identify and

interpret the relevant indications to be evaluated if they

comply with the acceptance criteria of standards or

technical specifications. If damage is left unrepaired or

improperly repaired, it will spread very quickly,

decreasing the performance, efficiency, and lifetime of

the unit. When pitting damage approaches 20 % of the

blade thickness or ½” deep, whichever is less, then

corrective action should be taken

immediately [17], [18].

A Hydroelectric Power Plant is under the study of a

wear correlation model - the amount of sediment and

generation power for the scheduling of its preventive

maintenance. The organization of this manuscript is as

follows. The introduction describes the importance of

hydroelectric power plants for the generation of electric

power as well as details the main factors that cause wear

and damage to water systems, which should be

considered to establish maintenance schedules. In

materials and methods, the inspection techniques, data

obtained, analysis ranges, and software used for

statistical analysis are presented. The results section

details the prediction and optimization considered to

improve the availability of the hydroelectric plant

promptly in the maintenance of the Francis turbine

blades.

2. MATERIALS AND METHODS

The technical characteristics of the equipment used

are presented below. Additionally, the standards used

for experimental development are indicated, as well as

the range of applications and the procedure to be

followed in each of them is described. Fig. 1 shows the

procedure to be followed to carry out the present

investigation.

Figure 1: Flowchart to obtain projections report for preventive

maintenance under condition

Francis’s turbine

The Francis turbine is normally used in medium and

high drop hydroelectric power plants, the turbine

consists of a set of rotating blades mounted on a shaft

that is connected to an electric generator. A correlation

model is proposed between the wear of the equipment

and the sediments found in the water, so it is necessary

to study and identify the sediments present in the water,

to evaluate the wear of the runner, the main element of

the Francis turbine [19], [20].

The section in red in Fig. 2 is where there is wear of

the Francis runner, which causes higher water

consumption, increased vibrations, temperature, and

others.

Figure 2: Wear section in the Francis turbine of the power plant.

Edición No. 21, Issue II, Enero 2025

Table 1: Construction dimensions at inspection points

Description

Dimensions at impeller blade edge

Inner dimensions

Bottom dimensions

Tol. Max.

25,1

21,8

18,4

18,2

33,2

25,5

47,8

43,5

40,7

Nominal

20,8

17,7

14,5

14,3

28,9

22,6

22,1

43,5

41,6

36,8

Tol. Min.

17,4

14,4

11,4

11,2

25,5

18,5

40,1

36,5

33,7

Blade

Control limit

The control limits given by the manufacturer

Mitsubishi establishes a minimum and maximum

tolerance in the thicknesses of the runner blades, table 1

to maintain the maximum efficiency in the electrical

generation the blade thicknesses to be maintained within

the maximum and minimum tolerance being the

optimum dimension the “nominal” in the inspection

points from “a” to “l”.

Fig. 3 shows the positions of the inspection points a,

b, c, d, e, f, g, h, i, j, k, l, which are inspected and

measured on all blades 1 to 17 considerations made by

the manufacturer MITSUBISHI.

Figure 3: Location of inspection points on the impeller blade.

MINITAB STATISTICAL Software

To obtain the data correlation, the values obtained

by measuring thicknesses are used as part of the

statistical analysis, the wear variable is plotted with its

control limits to evaluate the blades with their respective

positions that comply with the recommended tolerances

as shown in Fig. 4, when representing the distribution of

the data of a variable in a box plot, the position of the

median, quartiles and extreme values are shown. If the

data have extreme values, these will appear as points

outside the boundaries of the box plot; therefore, it is

used to visualize the distribution of the values of the

predictor variables of the model and to detect if there

are outliers or extreme values that may affect the

accuracy of the model [21], [22].

Figure 4: Statistical box plot of blades 1 to 17 in “a”.

Once the wear data, there are no outliers that affect

the multiple regression analysis, the statistical

regression model starts to obtain the equations that

project the wear in the following periods for the

scheduling of preventive maintenance under condition.

To obtain the equation we proceed as follows [23], [24]:

• Analysis of the inspection point “a” in the

blades from 1 to 17 that make up the

impeller.

• The multiple regression equation applied is:

Y= b0 + b1X1 + b2X2 + b3X3 + b4X4 +

b5X5 + b6X6.

Where,

• Y = dependent variable, impeller blade

thickness wear at inspection points 1 to 17

at inspection points “a” through “l”,

estimated by the regression equation.

• b1, b2, b3, b4, b5 and b6= net regression

coefficients (the best weighted set among

the independent variables, in order to

achieve maximum prediction) X1, X2, X3,

X4, X5 and X6 = independent variables

such as: Cumulative PPM, Cumulative

MWh Power, PPM, MWh Power,

Maximum MW Power and Minimum MW

Power.

Zhañay et al. / Wear-sediment quantity correlation model for preventive maintenance

• b0= Constant or Y-intercept.

The construction sequence of the equation for the

inspection point at “a” of blade 1 is 1 = 23.930 - 0.1965

X1, where X1 corresponds to the independent variable

cumulative PPM, and the rest of the positions of “a” are

presented in Fig. 5. The equation construction report

includes several sections, which provide information on

different aspects of the model construction process [25].

Selection of predictor variables: This section describes

how the predictor variables for the model were selected

and what criteria were used to select them. It includes

information on the relative importance of each variable

and how it will be protracted.

Figure 5: The statistical plot of the multiple regression of the

equation construction on vane 1 at point “a”

Exploratory data analysis: This section describes

how the data was explored before building the model,

including graphs and descriptive statistics for each

variable. 1Initial model: This section describes the

initial model that was built and how the quality of fit

was assessed. It may include information on hypothesis

testing for regression coefficients and residual variance.

In the execution of the MINITAB software with the

multiple regression, the results of the linear or nonlinear

equations are presented with their respective correlation

Table 2 in the position of “a” in the vanes from 1 to 17

with the variables considered, type of equation [26].

Table 2: Equations at position “a” on vanes 1 to 17

Blade

Regression equation

Model

Correlation

23,930 - 0,1965 PPM acu.

linear

Negative

25,537 - 0,2150 PPM acu.

linear

Negative

28,131 - 0,3028 PPM acu.

linear

Negative

23,193 - 0,2663 PPM acu.

+ 0,400 PPM

linear

Negative

For the validation of the quality of the correlation

model obtained at inspection point “a” to “l” on blades 1

to 17, the following aspects are considered:

• Residuals vs. fitted values.

• Summary report on the obtained equation.

• Special effects were found in the interaction.

Fig. 6 details the normal likelihood in the residuals

vs. the fitted values are the search for patterns, such as

strong curvature or clusters to indicate problems with

the regression model, differences between the observed

values of the response variable and the values predicted

by the model. It includes plots of the residuals and

statistical tests to assess normality, homogeneity and

independence of the residuals.

Figure 6: Plot of residuals vs. fitted values at vane 1, 4, 10, 15 at

point “a”

If the model is properly fit to the data in a

statistically significant relationship between Y and X

variables can be explained by R-squared in % of the

variation in Y, the model run in multiple regression is

the detailed description of the model, it provides

valuable information about the quality and ability to

predict the values of the response variable.

3. RESULTS

The prediction and optimization report on the

multiple regression model run provides information on

the accuracy of the model predictions and how they can

be optimized. This report is used to evaluate the

performance of the model and determine if

improvements can be made to the accuracy of the

predictions. Therefore, the three-year prediction of the

wear sequence in the parameters of the independent

variables such as PPMx10⁶ cumulative and PPM x 10⁶,

is estimated in Table 3.

Edición No. 21, Issue II, Enero 2025

Table 3: Data projected to 3 years in the independent variables in

the analysis of the wear of the runner of the Francis turbine of the

power plant

Year

PPMx10⁶ acu.

PPMx10⁶

Latest fact.

2020

24,3

0,6

Ranks

24,3

1,39

2023

36,81

1,39

Applying the equations obtained in the multiple

regression for each of the inspection points, project the

wear data in Table 4, estimates given by the regression

equations considered for the next three years from the

last record.

The connection between the variables of the amount

of sediment and turbine wear is demonstrated by means

of a casual correlation applying the multiple regression

method, which shows that the independent variable

PPM affects 38 %. Where the equations presented are

distributed in linear equations in 72 % and non-linear

equations in 28 %. With the results, Fig. 7 shows the

projection of wear in subsequent years to the data

obtained from the inspection point of “a” in the blades

from 1 to 17.

With the analysis performed, a condition

maintenance plan (CMP) is the maintenance strategy

that focuses on monitoring and analyzing the condition

of critical equipment in real-time to identify any signs

of deterioration or failure before they are foreseen. This

approach allows preventive action to be taken before a

failure occurs, which helps reduce downtime and

maintenance costs. With the collection of information,

data analysis techniques can be used to assess the

condition of the turbine and determine the need for

preventive maintenance under conditions. Based on the

results obtained, preventive measures can be taken,