5.1. Results
After elaborating on the proposed models using the techniques presented, study cases are performed to verify their performance. In this section, the obtained results are provided below.
The obtained results through the HMM application for GU 2 are outlined in
Table 4 and provide a comprehensive representation of the probabilities associated with specific hidden states. These hidden states correspond to varying levels of obstruction caused by the accumulation of sediments. The likelihood of the GU being in distinct hidden states can be ascertained by analyzing the data within each observed hourly interval.
Whenever the GU is in state S4, which means it has the highest level of obstruction, the transition probability towards a less obstructed state becomes evident only after the time interval H3. This outcome aligns with the plant’s operational practice when they usually keep the unit offline for extended periods when the obstruction level reaches a higher degree.
Alternatively, if the same GU currently has the obstruction level S2 and the GU remains inactive for the time interval H3, there is a significantly higher probability (18.7%) of it remaining in that state. The GU transition to a state cleaner than S2 demands a more extended downtime due to the characteristics of the sedimentation process, in which denser materials take more time to settle.
At the S1 obstruction level, the unit can remain in the same state, or, sometimes, the evolution is identified to a higher obstruction level, changing to S2. This event may occur due to the operation of neighboring GUs, which contributes to the movement of sediments, migrating material to the stopped GU.
In an ideal scenario for the HPP operation, a GU at the highest obstruction level should remain stopped until it is at the lowest dirt level, when it can return to activity. A study case was performed to obtain the probability of the GU migrating from the initial state S4 to S1 as its final state. The result is presented in
Table 5.
It is possible to notice that the provided scenario is more likely to occur only after the H3, with a probability of 24.99%, and it is most probably, with 30.20%, at H4. As expected, it is not common to reach S1 starting from S4 after the H1 or H2 periods, corresponding to 1 to 4 h or 4 to 8 h intervals.
To analyze the differences in downtime between the different GUs,
Table 6 presents information relating to the level of obstruction and the downtime for GUs 1 and 3, respectively.
The following considerations can be conducted through data analysis and using the same study case performed on GU 2 to obtain the probability of the GU migrating from the initial state S4 to S1 as its final state:
The probability of remaining in state S4 shows a balanced dispersion over time for GU 1. This pattern indicates situations where the GU transitions to a cleaner state even within the H1 interval. Conversely, there are cases where a significant time lapse, such as H4, is required for the transition. This variance can be attributed to GU 1’s proximity to the dam’s ravine, potentially contributing to sediment accumulation in specific circumstances.
Concerning GU 3, the likelihood of persisting in state S4 during the H1 and H2 intervals is higher, registering values of 31.1% and 28.1%, respectively. The prevailing trend is for GU 3 to transition to a cleaner state only after the H3 interval.
The dissimilar behaviors observed between GUs 2 and 3 can be attributed to the following factors: GU 1 absorbs sediment from the riverbank and can consequently transfer sediment to GU 2, explaining why GU 2 shifts to a cleaner state only after a more extended downtime. Conversely, GU 3 is unaffected by the same issue due to its greater distance from GU 1, illustrating the impact of neighboring GUs on the sediment decantation process.
Probability outcomes for GUs 31 and 32 are shown in
Table 7.
The behaviors of GUs 31 and 32 differ from those presented for GUs 1 to 3. This difference can be attributed to these GUs being on different margins, separated by kilometers, and to the curvature of the river displayed on the left margin where these GUs are installed. It is possible to observe a certain similarity between the probabilities for GUs 31 and 32, with slight variations in the required time to change between states. Generally, there is migration between states only after the H3 interval, which can be associated with the type of material accumulated in the trash racks.
When the generation units (GUs) exhibit a notably high degree of obstruction, a prevalent trend emerges: substantial clearance of the trash racks occurs only after prolonged GUs downtime. Specifically, if the GU experiences a brief stop time upon resumption of operational activity, a considerable amount of material is expected to obstruct the trash racks persistently.
Observations reveal that units positioned near the riverbank experience a notably higher sediment accumulation, leading to a more pronounced obstruction of the trash racks. Adjacent GUs also experience a residual effect from this sediment accumulation, albeit with a lesser impact.
It is essential to highlight that the HMM technique cannot consider whether neighboring GUs are in operation, nor does it account for the GUs operating power or the time it was generating.
For this reason, BNs are used to consider the factors that directly affect the operation and consequently alter the sediment flow during the GU stop time. Separated BNs are created for each GU to reflect the specificities of each one.
Below are presented the obtained results for different types of BNs queries. For example,
Table 8 shows the CPDs for GU 2.
Utilizing models derived from BN offers a significant advantage due to their inherent query capabilities. Queries involving any model attributes mapped within the network can be completed, thereby facilitating the prediction of posterior values. Specifically, these models empower the prediction of the obstruction level for each distinct downtime interval.
This predictive capacity enhances the ability to forecast and anticipate the progression of obstruction levels during various operational downtimes. In essence, BNs allow for a comprehensive exploration of the network’s attributes, enabling the generation of valuable insights into the system’s expected behavior over time.
Using the BN network shown in
Figure 7, it is possible to estimate the resulting obstruction level using a given scenario to verify which parameters influence the decantation process the most.
Below are the values entered for the BN parameters.
A = [K_Previous: S4]
B = [K_Previous: S4, Right: T3]
C = [K_Previous: S4, Right: T3, Left: T1]
D = [K_Previous: S4, Both: T4]
Data referring to UG 2 were used. In all scenarios, it is considered that the UG is at the highest level of obstruction, S4.
Scenario A is parameterized only with this S4 obstruction information.
Scenario B is configured with the additional ‘Right’ information, whose defined value is T3, which comprises the value ranging from 50% to 75% of the time.
The information ‘Right’, ‘Left’ or ‘Both’ refers to the percentage of time that the adjacent unit operated when the GU was stopped for decantation. In this case of scenario B, the analyzed GU is the 2, and the ‘Right‘ neighbor GU is the 3.
Scenario C is configured with the same value for the ‘Right’ parameter: T3. Additionally, the ‘Left’ information is set to T1, which comprises the value up to 25% of the time.
Scenario D is configured with the value for the ‘Both’ parameter equal to T4, which means that both the ‘Right’ and ‘Left’ GUs, in this case, 3 and 4, respectively, operated for the time interval comprising the 75% to 100% of time in which the GU 2 was stopped for decantation.
The results are presented in
Table 9.
In scenario A, the probabilities that GU 2, stopped at the worst obstruction level, will resume operation at levels S2 and S3 are approximately 38.8% and 32.9%, respectively. In scenario B, these values are close, 32.3% and 30.7%, respectively. The operation of the neighboring GU, in this case, GU 3, did not significantly impact the obstruction level of GU 2.
In scenario C, the most favorable cleaning results were obtained, with a 40% probability that the UG would return at the cleanest level of obstruction: S1. The probable explanation for such behavior may be that the operation of the left GU, in this case, GU 1, has pulled the sediment from GU 2, migrating the GU more quickly to a lower level of obstruction.
Finally, in scenario D, both neighbors were in operation for the entire time GU 2 was stopped. The results demonstrate a more uniformly distributed probability between levels S1, S2 and S3, with values of 48.4%, 35.2% and 42.1%, respectively.
The results show that the decantation process when the GU is stopped is significantly influenced by the neighboring GUs. This relationship changes depending on the time the neighboring GUs were operating and the level of dirt when the GU stopped.
The BN was parameterized to present modeling outputs for each final obstruction level when resuming GU operation for all available downtimes to enable a more comprehensive view of data, including more complete probability results. The obtained results are shown in
Table 10.
Given that the GU was stopped at the higher obstruction level S4, the following behavior can be observed in the table for many scenarios: after stopping time H1, the highest probability is that the GU resumes operation still at level S4. For time H3, the restart must occur at level S2, and, finally, the stop for time H4 increases the probability of resuming at level S1.
Only on the H2 stop time interval does this pattern not hold. Instead of resuming at level S3, the GU remains at level S4, demonstrating that stopping the GU for short intervals does not influence the level of obstruction so strongly.
5.2. Discussions
The main feature of HMMs is their suitability for use with sequential data, where the order of observations is essential. In this work, the HMMs captured temporal dependencies and transitions between different states, which evidenced the relation between the obstruction level and elapsed time when GUs are stopped for decanting. The flexibility of HMMs enabled usage with time-series input data, while levels of obstruction are mapped as states in the model.
The two main advantages of HMMs are related to the probabilistic modeling and the incorporation of hidden states. The first feature captures the uncertainties, which fits the objectives of this work: map the ratio of accumulated sediment and the required downtime to settle this material. The second maps the unobserved obstruction levels underlying processes as hidden states, enabling the estimation of the sediment settlement according to the elapsed time.
On the other hand, the limitations of HMMs in this model are, once the transition probabilities are influenced by the neighboring GU, the Markov property is directly affected and may not hold. The Markov property can also struggle to capture long-range dependencies effectively.
Another limitation is related to the fixed state space: the number of hidden states was determined in advance and may not represent the best possible scenario. Choosing the appropriate number of states was challenging since it could affect model performance. A significant effort was required to ensure that the selected state space reflects the best option.
The results showed that the expressiveness of the HMM technique alone is limited since the models might not effectively capture complex relationships between variables. The training complexity represents a time bottleneck since a new training cycle must be performed with each new parameter and state mapping variation.
The Bayesian networks’ advantages rely on the fact that BNs provided a natural and intuitive way to model uncertainties and dependencies in data obtained from the real HPP operation. As the BN is a probabilistic framework, it was possible to infer even when some variables appear unrelated.
The causal inference of BNs allowed for understanding how the neighboring GU usage affected other variables. That feature was valuable for decision making about using the GUs while the next ones are stopped for sediment settling. With the help of problem domain experts of the Jirau HPP, it was possible to validate prior beliefs and causal relationships obtained by the resulting modeling.
BNs allowed exploratory analysis and efficient inference related to sediment behavior, which helped to uncover hidden patterns that were not immediately apparent from the raw data and compute probabilities of different scenarios, providing query evidence. As the real operational data from the HPP were available, it was possible to use the BN to learn the conditional probabilities parameters from these data, which makes the model consistent with the plant reality.
Bayesian networks present some limitations, such as the heavy dependence on the graph structure. It was challenging to correct specifying the design, which required domain expertise since the model might not effectively capture the true relationships without expert input.
The needed training time was a bottleneck to realize parameter variations during the modeling because the high number of GUs represents a computational complexity problem. Finally, the correlation and causation relationships represented a challenge because assuming causation based on correlation could sometimes be dangerous.
A strength of the presented work is the union of the HMM with the BN, which made it possible to take advantage of the main characteristics of each of the techniques. The model’s robustness allows probability information extraction. It brings to light details related to the behavior of the obstruction in the trash racks, including the neighboring GU impact in the sediment settling behavior.
Because it is a pioneering work, which addresses the problem of obstruction of trash racks with consequent impact on the operation of hydroelectric plants, studies still need to be conducted for contextual reference and comparison. This sediment issue is specific to HPPs located within the Amazon basin. In the case of the Jirau plant, the challenge of high sediment transport rates arises only during particular periods of the year. For this reason, only data referring to flood seasons are used.