Localization of Partial Discharges in Hydrogenerators by Ozone Emission

Abstract

We suggest a new method of localization of partial discharges in high-power electrical systems. Ozone in a hydrogenerator is produced by chemical reactions induced by partial discharges in the stator region. The transport of ozone in an operating hydrogenerator is analyzed using a computational fluid dynamics model. The main aim of this work is to evaluate the ozone distribution in the generator radiators. Ozone sources are introduced into the stator model in different positions to analyze their effect on the measured values at the sensing points of radiators. Our results demonstrate a possibility of localization of partial discharges in hydrogenerator stator bars by ozone emission.

1. Introduction

Power outages caused by hydrogenerator failures are costly and disruptive. Predictive maintenance based on online partial discharge (PD) testing has emerged as a powerful tool to avoid failures. Researchers focused on PD levels as an indicator of insulation weakness in hydrogenerators. PDs occur when high voltage stresses create tiny sparks within the insulation, indicating potential problems. PDs are provoked by various issues: poor impregnation, faulty coatings, inadequate coil spacing, loose windings, overheating, contamination, and even foreign objects like screws [1].

Monitoring PDs has become a common method for assessing generator health. When assessing insulation conditions in the equipment, like stator windings, technical staff often use offline PD measurements during testing [2]. The International Electrotechnical Commission (IEC) recommends using low frequencies (below 3 MHz) for the electrical tests due to the electrical properties of the windings, since they act like capacitors and inductors [3]. However, high-frequency components of the PD signal can weaken depending on where the sensor is placed relative to the PD source. This means that using a wider range of frequencies for detection leads to a more accurate identification of PD activity, as confirmed by several studies [4,5].

Online PD testing offers several advantages since real-time data can be acquired continuously during normal operation [6]. It allows analysis and diagnostics during operation to identify issues early and plan corrective actions to minimize downtime [7]. Proactive maintenance also prevents unexpected failures, reducing the risk of unscheduled outages.

However, it is important to mention that PD tests are not immune to errors and imprecision. Their primary role is to alert operators about potential problems, identify the cause, and isolate the issue [8].

Partial discharges within hydrogenerators manifest through various phenomena, including electromagnetic (EM) and acoustic emissions, along with chemical reactions like ozone formation. However, for practical measurement, electrical methods dominate the field. In the most common and straightforward approach, capacitive couplers [9] are used, but alternative solutions are directional couplers [10,11,12] and antennas [13].

Accurately pinpointing the location of PDs within a hydrogenerator from their electromagnetic emissions presents a significant challenge. This difficulty exists in an individual bar and aggravates in groups of bars. The complexity stems from the excitation of high-frequency EM waves by PD events, which propagate within the bar’s insulation and diffract in conductive parts and bar ends. Furthermore, EM waves radiate from the bar into the surrounding air and reflect from neighboring structures, creating numerous electromagnetic couplings [13]. As a consequence, sensors register intricate transient electromagnetic signals (voltages and currents) that necessitate sophisticated analysis for PD localization.

The presence of ozone within air-cooled generators and motors serves as a strong indicator of partial discharge activity [14]. Studies suggest that deterioration of semiconductive coatings is the primary culprit for ozone generation. However, the rate of ozone formation is influenced by numerous variables and may not always offer a reliable assessment of the state’s health. While the direct correlation with total PDs might not exist, ozone concentrations can provide valuable insights into specific types of surface PDs, including slot discharges, corona at coating junctions, and PDs between coils or connections. Therefore, monitoring ozone becomes a valuable tool for predictive maintenance.

A significant challenge in using ozone for PD localization lies in ventilation. Airflow significantly impacts concentrations, as demonstrated by a laboratory experiment where ozone levels dropped dramatically with increased airflow [15]. This imposes some limitations on the absolute ozone level measurements.

Air velocity, temperature, and voltage are all likely to play a role, with the specific impact depending on the specific operating conditions of the hydrogenerator. In [16], a developed ozone prediction model based on the mechanism of ozone generation in a corona discharge region shows that ozone concentration decays as the air velocity increases. This occurs because the gas velocity becomes the main factor in governing the ozone transport characteristics. At even higher air velocities, the gas with diluted ozone will experience increased turbulence. This turbulence can enhance the mixing of the ozone with the surrounding air, leading to faster diffusion and a wider distribution of the ozone. For example, large-scale climate patterns like El Niño Southern Oscillation (ENSO) can significantly impact the ozone in the atmosphere. El Niño events are linked to a decrease in ozone concentration specifically within the lower-middle stratosphere [17].

Higher temperatures generally increase the kinetic energy of gas molecules, including ozone. This increased energy leads to more frequent collisions between molecules, promoting faster diffusion [18,19]. An hydrogenerator operating at a higher voltage may lead to the production of more partial discharges and ozone molecules. However, the impact on diffusion is less straightforward. The increased energy imparted to the gas and the local increase of temperature [20] during the discharge process could promote diffusion.

Combining ozone data with PD levels, machine load, voltage, and temperature leads to a more comprehensive diagnostic panorama. For instance, rising PD levels with stable ozone concentrations could suggest internal insulation PD. Furthermore, ozone measurements can complement traditional PD tests, particularly in high humidity conditions where surface PDs through capacitive couplers become less detectable [21].

Typical ozone concentrations in generators range from dozens to hundreds of ppb (parts per billion). Therefore, initial measurements should utilize equipment with high precision in this range. The measurement range of various ozone sensors using different techniques for measurement was reported in [22]. Portable devices often rely on optical sensors with wide dynamic ranges. However, if electrochemical sensors are chosen, establishing a baseline measurement beforehand is crucial to selecting the sensor with the most appropriate range.

While the importance of ozone monitoring in hydrogenerators for detecting partial discharges is well-established, the definition of the sensor positions remains open. This lack of guidance poses challenges for accurate and reliable diagnostics, potentially hindering effective maintenance and insulation condition assessment. Therefore, investigation of the influence of the sensor position on ozone concentration measurements and PD detection accuracy is a relevant subject of scientific research. Using computational fluid dynamic (CFD) modeling of a hydrogenerator in operation, this work aims to analyze the influence of the positions of the internal sources of ozone produced by PDs on the detection of ozone concentrations at the radiator outlets. This allows one to associate distinct insulation defects in the generator with ozone concentration measurements.

2. Materials and Methods

Figure 1a is a photo of a typical hydrogenerator. Our structure model for the following analysis is presented in Figure 1b. The structure was created by the COMSOL Multiphysics 5.5 software using as a base a generating unit from the Brazilian Campos Novos hydroelectric plant.

The hydrogenerator stator winding is made up of 378 coil-type bars with an interior made of copper and an external surface with a semiconductor coating layer. The bars have dimensions of 672.7 mm × 3.961 m, and their details are shown in Figure 2. The material of the floor and walls of the generator were modeled using concrete. The floor has an octagonal shape with edges measuring 5.385 m, and the walls are 4.20 m high. The radiators have dimensions of 1.72 m × 4.20 m. They are made of copper, and their grid structure was approximated by a surface as defined in [24].

The air directors guide the air flow from the rotor to the radiators. These elements are made of stainless steel and have a wedge-like shape with side dimensions of 1.615 m, an external side at a radius of 5.468 m, and a height of 4.20 m. The stator core is made up of 47.2 mm thick sections of stainless steel sheets with a spacing between the sections for ventilation of 15 mm. Its total height is 2.658 m, and it has an external radius of 4.180 m and an internal radius of 3.820 m. To accommodate the stator bars, the structure has grooves measuring 128 mm × 33.3 mm and teeth measuring 128 mm × 30.2 mm. Finally, the rotor was modeled by a cylinder with a radius of 3.8075 m, a height of 3.3418 m, and an external surface with epoxy resin coating.

3. Fluid Dynamics Theory

3.1. Basic Equations and Boundary Conditions

Viscous incompressible fluids flow as described in the steady-state Navier-Stokes equations [25] of conservation of momentum given by

$$({\overrightarrow{u}}_m·\nabla ){\overrightarrow{u}}_m=-\frac{1}{{\rho }_0}\nabla p+\nu {\nabla }^2{\overrightarrow{u}}_m+\overrightarrow{a},$$

(1)

$$\nabla ·{\overrightarrow{u}}_m=0,$$

(2)

where ∇ is the vetorial operator $\nabla \stackrel{def}{=}(\partial /\partial x,\partial /\partial y,\partial /\partial z)$, ${\overrightarrow{u}}_m=(u,v,w)$ is the flow speed in m/s, and $u,v$, and w are the components of the velocity vector; p is the scalar pressure field in Pa, ${\rho }_0$ is the fluid density in kg/m³, $\nu$ is the kinematic viscosity of the fluid in m²/s, and $\overrightarrow{a}$ is the gravitational acceleration in m/s².

On rigid surfaces, walls are considered impermeable and non-slippery. Therefore, the following boundary conditions can be used:

$$u_n=0,$$

(3)

and

$$u_t=0,$$

(4)

where the subscripts n and t indicate, respectively, the components of ${\overrightarrow{u}}_m$ normal and tangential to a considered solid surface. Equation (3) guarantees impermeability, and (4) ensures that the obstacle is not slippery.

The mass conservation law [25] for a chemical species i in the steady state is given by

$$\nabla ·{\overrightarrow{J}}_i+{\overrightarrow{u}}_m·\nabla c_i=R_i,$$

(5)

and

$${\overrightarrow{J}}_i=-D_i\nabla c_i,$$

(6)

where $c_i$ is the species concentration given in mol/m², ${\overrightarrow{J}}_i$ is the diffusion flux vector given in mol/(m²s), ${\overrightarrow{u}}_m$ is the average mass velocity given in m/s, $R_i$ is the reaction rate for the species given in mol/(m³s), and $D_i$ is the diffusion coefficient given in m²/s.

Equations (1), (2), (5) and (6) are solved numerically by COMSOL Multiphysics software version 5.5 using the finite element method.

3.2. Fluid Dynamics Applied to Ozone

The parameter $R_i$ associated with ozone generation in (5) can be calculated by [26]

$$R_i=\frac{\eta ·P}{m·V_{O_3}},$$

(7)

where $\eta$ is the ozone generation efficiency, P is the power of the partial discharges, m is the molar mass of ozone, whose value is 47.998 g/mol [27], and $V_{O_3}$ is the volume of the region where ozone is generated.

The distribution of ozone in an environment can be calculated with (5); however, part of this ozone ends up being eliminated due to reactions with molecules of the environment and reactions with the surfaces. The flux of ozone deposition on surfaces can be calculated by [28]

$$J_s=-\gamma \frac{<v_B>}{4}C{|}_{y=\frac{2}{3}l},$$

(8)

where $J_s$ is the net flux of species to the surface calculated at a small reference distance y from the reaction surface, as established in [28]. $\gamma$ is the mass accommodation coefficient between ozone and the deposition surface and is defined as the fraction of all ozone molecules colliding with the surface that undergo deposition. C is the ozone concentration, l is the mean molecular free path with a value of 6.5 × 10⁻⁸ m at 293 K and 1 atm, and $<v_B>$ is the Boltzmann velocity for ozone, given by

$$<v_B>=\sqrt{\frac{8kT}{\pi m}},$$

(9)

where k is the Boltzmann constant equals to 1.38 × 10⁻²³ JK⁻¹ and T is the ambient temperature in K. Considering T = 293 K, the Boltzmann velocity for ozone has the value of 3.6 × 10² m/s.

According to [18,28,29], the diffusion coefficient $D_i$ for ozone in (6) is 1.82 × 10⁻⁵ m²/s in the air under atmospheric conditions at sea level and a temperature around 298 K. The parameter $\gamma$ in (8) depends on the surface material; see

Table 1. Parameter $\gamma$ for materials used in the model.

Material	$\mathit{\gamma }$
Concrete	$7.90\times {10}^{-5}$ [30]
Stainless steel	$1.80\times {10}^{-7}$ [31]
Semiconductor coating layer	$1.11\times {10}^{-6}$ [32]
Epoxy	$2.00\times {10}^{-6}$ [33,34]

.

4. Numerical Model

4.1. A General Description

The effect of the rotor rotation in the model is described through the air velocity boundary condition. The two velocity components were defined: the first one is the angular velocity of 87.344 m/s, which corresponds to the velocity on the rotor surface for rotation of 200 RPM (revolutions per minute), and the radius of the rotor equals to 3.8075 m.

The second velocity is the radial one. In order to define this velocity on the rotor surface, we have measured the radial velocity at the outlet of a radiator in the working generator unit. It has the value of 3 m/s. However, the air guides confine the flow path, enhancing the velocity. Therefore, the radial velocity at the rotor surface is lower than at the radiator exit, so it was evaluated as 2.2 m/s. For each radiator and its circular section in the hydrogenerator, a specific label from $R_1$ to $R_8$ was assigned, as illustrated in Figure 3.

In order to demonstrate the suggested method of PD localization in the stator winding, ten ozone sources corresponding to PD locations were defined (see Figure 4 and

Table 2. Ozone source locations

Source	$\mathit{\rho }$ Coordinate (mm)	$\mathit{\varphi }$ Coordinate (Degrees)	z Coordinate (mm)
$S_1$	3880	247.5	4020
$S_2$	3880	268	4020
$S_3$	3814	247.5	2100
$S_4$	3871	247.5	2100
$S_5$	3890	247.5	2100
$S_6$	3814	268	2100
$S_7$	3871	268	2100
$S_8$	3890	268	2100
$S_9$	3880	247.5	130
$S_{10}$	3880	268	130

). The exact geometry and positioning of one of the ozone sources are shown in Figure 5. To represent the ozone sources, square cuboids measuring 20.2 × 20.2 × 15 mm were placed and activated individually in each simulation.

Each ozone source has a fixed value of ozone reaction rate, which represents a steady-state regime value. Square sources are used to represent averaged emissions instead of using irregularly shaped sources. By averaging the emission rate over the area of the square source, the model can capture the overall impact of the source without requiring a detailed representation of its geometry. Square sources are relatively straightforward to implement in a CFD model compared to more complex shapes. This kind of approximation can be beneficial when working with structures with complex geometries.

4.2. Numerical Mesh

A finite element mesh for the simulations was generated using a pre-defined calibration method for fluid dynamics models in COMSOL Multiphysics. In this way, the mesh was built with 6,116,483 tetrahedral elements, of which 2,025,344 were triangles, 698,438 edge elements, and 152,484 vertex elements. To refine the mesh in the critical ozone source region, a maximum edge length of 7.5 mm was used. The computational mesh is shown in Figure 6.

The simulations were carried out using two workstations working in parallel, each equipped with an AMD Ryzen 9 5950X 16-Core processor and 128 GB of RAM. The execution time of each simulation varied between 12 and 14 h, and they required approximately 124 GB of RAM.

5. Results and Discussion

In order to validate the numerical results that will be presented below, experiments were carried out to verify the accuracy of the developed CFD model. With the impossibility of carrying out such experiments in a real hydrogenerator, simpler laboratory tests were conducted using a stator bar in an acrylic chamber. The results demonstrating a good accordance of the calculated and measured data are presented in Appendix A.

Calculation of the airflow is important for understanding how ozone is transported from PD sources to the radiator outlets. Figure 7 shows the air velocity field in the horizontal plane z = 2100 mm, in the proximity of radiator $R_1$. The air flow, which is more intense near the rotor, is affected by the stator bars and the air directors.

Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 show the distribution of ozone concentration on the radiators’ output planes measured in ppb (part per billion) when a specific ozone source is activated. When source $S_1$ is activated, the generated ozone is transported and divided between radiators $R_1$ and $R_2$. This occurs due to the high angular component of the velocity in the upper and also in the lower regions of the generator. Therefore, even if the source $S_1$ is located in the central angular region of the radiator $R_1$, the velocity angular component is strong enough to capture and divide ozone between two radiators (Figure 8a,b). When source $S_2$ is activated, the corresponding output ozone distribution is observed mostly in the upper right part of radiator $R_2$; see Figure 9a. In this case, ozone is not present in radiator $R_1$.

When source $S_3$ or $S_4$ or $S_5$ is activated, ozone appears at the center of radiator $R_1$ (see Figure 10b and Figure 11a,b), but this source remains undetectable at radiator $R_2$. In these cases, the $\rho$ coordinate of the sources only impacts the intensity of detected ozone. However, the intensity is also influenced by the power of partial discharges occurring in the source, which is determined by the severity of the insulation problem.

Sources $S_6$, $S_7$, or $S_8$ are located close to the air director nozzle. Figure 13 shows ozone distributions on radiator $R_1$ when sources $S_7$ and $S_8$ are activated. In the case of a DP source with a smaller $\rho$ coordinate (source $S_6$), ozone can be detected on the right edge of radiator $R_1$ as well as on the left edge of radiator $R_2$; see Figure 13a,b. Due to proximity of the source to the rotor, where the air speed is greater, ozone is carried to the neighboring radiator, where it can be detected.

As already mentioned, in the top and bottom regions of the hydrogenerator there are the ends of the ferromagnetic core and the stator bars, so that in these regions the air flow is freer from obstacles, and thus the air velocity vectors have more intense azimuthal and vertical components in the vicinity of radiators. This can also be noted when the sources $S_9$ and $S_{10}$ are activated, as shown in Figure 9a,b. In the case of source $S_{10}$, its effect is perceived mostly on the lower right part of the radiator $R_2$, showing that the azimuthal component of air velocity had a stronger effect transporting ozone also to the radiator of the adjacent sector (Figure 10a).

6. Conclusions

The study utilizes a CFD model to simulate airflow and the ozone distribution in the radiators of high-power hydrogenerators. Validation of the model by laboratory experiments confirms its effectiveness. The location of an ozone source within the hydrogenerator directly affects the distribution of ozone in the radiator. By activating different sources, we observed ozone concentration in distinct areas of the radiator. In some cases, ozone appears in two adjacent radiators simultaneously.

The configuration of stator bars, air directors, and rotation of the rotor have influence on the air velocity, especially near the radiators. A more unobstructed airflow path near the top and bottom of the hydrogenerator leads to stronger azimuthal and vertical air velocity components. This results in an indirect trajectory of ozone transport that can lead to maximum ozone concentration in the radiator of the adjacent sector. Thus, maps of correspondence between positions of sources and maximum ozone concentration in the radiator can be created by numerical modeling.

The location of partial discharges within the stator could be estimated using a database generated from CFD simulations. This database would correlate the detected ozone locations on the radiator plane with their respective source points within the stator. The total power of the partial discharges in a specific source region could then be estimated by referencing the results obtained from a dual barrier discharge chamber experiment. This experimental setup allows for the relationship between the produced ozone concentration and the discharge power to be established. While diffusion can make it difficult to pinpoint the exact location of an ozone source or measure the concentration at a specific point, simulations have shown that the dominant axis of the ozone’s advection trajectory, from the source to the radiator, can still be identified.

When identifying multiple ozone sources operating concurrently, if the sources are in close proximity, it is possible that only a single ozone spot may be detected on the radiator. However, in most cases, it is indeed feasible to identify and distinguish between sources due to the presence of multiple ozone spots on the radiator. In such instances, the location of the faults can be pinpointed. Consequently, the area requiring maintenance, which is the crucial information for practical purposes, can be determined.

In practice, by placing several ozone sensors in different points of the radiators or using scanning of the area of the radiator by a sensor, one can define the position of the PD source in the stator. If there are several sources of PDs in the proximity of a radiator, the distribution of ozone in the radiator will be a superposition of the emission of each individual source. A discrimination of these sources can be determined by some methods of the signal processing.

Finally, the suggested methodology can be applied to the problem of PD localization in other high-voltage electrical equipment.