Research on the HHT-Based Analysis Method of Tidal Power Generation Power Distribution Law ^†

Abstract

Tidal power generation technology has advanced quickly in recent years. In this study, the Hilbert-Huang transform (HHT) was used to examine the electrical energy distribution law of tidal power generation according to the time periods of days, months, and years based on observed data for tidal power generation. Our analysis summarized the tidal power generation law as follows: in the span of one day, the motor ran for 14 h before shutting off for 10 h. The frequency was 28 Hz, and the maximum voltage was 259 V. The tidal power generation swung twice a month, reaching its peak in the middle of the month and its trough at the beginning. The tidal power output fluctuated twice a year, reaching its peak in August, September, and October and its trough in February, March, and April. In the investigation of tidal power generation patterns, the HHT transformation’s precision and potency were confirmed.

1. Introduction

The widespread use of coal, oil, and natural gas in recent years has resulted in numerous issues, including the greenhouse effect, environmental degradation, and ecological devastation, which have presented severe dangers to the existence and advancement of humans worldwide [1,2]. The aforementioned environmental issues can be resolved by substituting renewable energy for fossil energy. Ocean energy, wind energy, and solar energy are currently the three main new energy sources accessible to humans. Wave energy, tidal power, salinity gradient energy, and offshore wind energy are some of them. Ocean energy is currently the focus of new energy research.

Tidal power generation has always been a popular area of research both domestically and internationally as a type of innovative marine energy generation. We can only more effectively direct the development and usage of tidal power generation by explaining the electric energy distribution legislation of its generation. The analysis approach of the tidal power electric energy distribution law is investigated with a focus on the unique electric-energy-generation features of the tidal power generation system. By concentrating on the periodic features of tidal power generation, it is possible to more accurately forecast and analyze the tidal quality and give correct data references to direct the application of tidal power generation equipment testing.

In the contemporary study and analysis of electrical energy laws, the Fourier transform, the Wavelet transform, and the Stockwell transform (ST) are frequently utilized. When analyzing steady signals, the Fourier transform is typically used, and both its fast Fourier transform and extended discrete Fourier transform create phase-detection errors [3,4]. The window function of the ST cannot be a root function. It is adjusted to the actual needs of specific projects, lacking generality. Additionally, it is computationally intensive [5,6]. Although the Wavelet transform is suitable for the analysis of nonstationary signals, the selection of wavelet bases is complicated [7]. The Hilbert-Huang transform (HHT), a novel nonlinear non-smooth signal analysis technique, is adaptive, and its basic function does not need to be predetermined, which provides good data-processing flexibility and circumvents the drawback of the Wavelet transform’s preset basis function [8].

HHT has been extensively used in numerous fields as a mature analysis algorithm. In preliminary research, researchers in [9] investigated the application of a novel automatic segmented HHT (SHHT) method for evaluating the SEC of the voltage sag caused by different types of symmetrical and unsymmetrical faults in both transmission and distribution networks. Reference [10] proposes the application of the HHT method for the decomposition of the PQ data into their individual frequency components to separate the nonstationary voltage sag waveform containing the fundamental frequency component. In reference [11], the feasibility of HHT for fault detection in VSC-based high-voltage direct current systems is analyzed. Reference [12] proposes the use of HHT and CNN for the classification of PS alterations. The HHT is used to obtain the time-frequency spectrum of the PSs that are signals characterized by a time-varying trend. Reference [13] proposes a fault-diagnosis method based on the combination of the Hilbert-Huang transform and convolutional neural network for the fault identification of transmission lines in distribution networks containing distributed power sources. It was discovered that HHT is very suitable for the nonlinear and non-smooth stochastic characteristics of the output electric energy of tidal power generation, even though both domestic and foreign scholars have largely ignored its use in the analysis of the electric energy law of tidal power generation.

In this article, we introduce a novel concept for employing HHT to study the distribution law of tidal power generation. Based on the measured tidal power data, the analysis first examines the start-stop, sharp acceleration, and sharp deceleration of the tidal generation system over the course of one day and then summarizes the transformation law of tidal generation over the course of 24 h. To determine the monthly and yearly distribution rules, the Hilbert spectra of the tidal power generation after 30 days and 12 months are then calculated using HHT. The Hilbert spectra shows the trend of the tidal power generating system over one month and one year. Finally, to confirm the precision and efficiency of HHT analysis in the investigation of tidal power generation patterns, the monthly and annual distribution curves are compared with the observed data.

2. Materials and Methods

Tidal power is the kinetic energy created by the seawater’s regular flow due to the Sun and Moon’s changing gravitational pull on the water. As seen in Figure 1a, when the Sun, Moon, and Earth are in a straight line, the gravitational pulls of the Moon and Sun are overlaid, causing greater tides known as spring tides. A neap tide is generated when the Sun, Moon, and Earth are at an angle, canceling out the gravitational forces that would otherwise result in higher tides Figure 1b. On days with spring tides, the tidal current velocity is higher, and the captured and output power of the system generating tidal power are greater; on days with neap tides, the tidal current velocity is lower, and the system’s captured and output power are consequently lower [14].

The tidal power generation platform “Zhongke Hydropower No. 1” built by the Institute of Electrical Engineering of the Chinese Academy of Sciences in Zhoushan, Zhejiang Province, is shown in Figure 2. A maximum of 20 kW of electricity can be generated by the platform, which uses two tidal power generation devices to harness the tidal power of nearby seas in real-time. The platform for generating tidal power is also outfitted with a full tidal current detection system, which can track and record characteristics, including tidal current speed, flow direction, output voltage, current, and power in real-time.

The platform, which costs roughly 200,000 RMB, underwent a yearlong test in the water off Zhoushan, Zhejiang Province, China, between 2016 and 2017. The generated electricity was cleaned and delivered to the islands’ electrically dependent machinery. According to estimates, power costs roughly RMB 2 per unit on average.

On spring tide days, the platform records the more typical daily tidal energy generation data obtained, as shown in Figure 3.

It is clear in Figure 3 that over the 24 h of a high-tide day, the output power of tidal power encounters four peak power-generation processes: high tide, low tide, high tide, and low tide. Different seawater flow rate circumstances also cause proportional changes in the motor’s output voltage and power. Seawater moves through the tidal power plant at roughly 0.4 m/s. When the seawater velocity reaches its first peak, the motor’s highest output voltage is roughly 250 V; when it falls below a particular point, the motor shuts off. After that, the direction of the seawater flow shifts, the tidal velocity steadily increases, and the tidal power generator set also resumes operating from a halt.

In conclusion, the output power of tidal power generation systems similarly exhibits regular periodic fluctuations along with the periodic changes in the seawater flow rate. The efficiency of tidal power generation at the load side or the grid connection are both directly impacted by this transition, which occurs with some regularity. Studying the power distribution law of tidal power generation is crucial for this reason.

3. Hilbert-Huang Transform

On nonlinear and nonstationary data, Hilbert-Huang transform (HHT) is used to perform analysis and processing more effectively [15]. To obtain the intrinsic mode function (IMF) and the Hilbert spectrum and time-frequency energy spectrum of the signal for signal analysis, HHT first applies empirical mode decomposition (EMD) to the signal to generate the IMF.

3.1. Empirical Mode Decomposition (EMD)

Empirical mode decomposition adaptively decomposes any complex signal into a series of intrinsic mode functions (IMF) based on the signal characteristics. It satisfies the following two conditions:

• The number of extreme value points of the signal is equal to zero points or differs by one;
• The local mean of the upper envelope defined by the extreme value and the lower envelope defined by the extreme minima of the signal is zero.

The EMD process is as follows:

• For the input signal x(t), find the maximum value point x(t_i) and the minimum value point x(t_j);
• Construct the upper and lower envelopes of the signal by interpolating the third spline function for the maximum and minimum points, and calculate the mean value function xl(t) for the upper and lower envelopes;
• Examine whether xl(t) satisfies the IMF condition, if it does, go to the next step, otherwise perform the first two steps on xl until the kth step satisfies the IMF condition, and obtain the first IMF component, noted as c₁;
• Get the first residual r₁ = x − c₁, operate on r₁ as in the above three steps to get c₂, and so on;
• Until r_n is a monotonic signal or there is only one pole.

Eventually, the original signal [16] is expressed as:

$$x={\displaystyle {{\displaystyle \sum }}_{i=1}^n}{c}_i+r_n$$

(1)

3.2. Hilbert Spectrum Analysis

Suppose x(t) is an arbitrary signal and the Hilbert transform of x(t) is:

$$y\left(t\right)=\frac{1}{\pi }{{\displaystyle \int }}_{-\infty }^{+\infty }\frac{x\left(\tau \right)}{t-\tau }d\tau$$

(2)

Its Hilbert inverse transform is:

$$x\left(t\right)=\frac{1}{\pi }{{\displaystyle \int }}_{-\infty }^{+\infty }\frac{y\left(\tau \right)}{\tau -t}d\tau$$

(3)

Obtain the resolved signal:

$$z\left(t\right)=x\left(t\right)+iy\left(t\right)=a\left(t\right)e^{j\varnothing \left(t\right)}$$

(4)

where: a(t) is the instantaneous amplitude and ∅(t) is the phase.

$$a\left(t\right)=\sqrt{x^2\left(t\right)+y^2\left(t\right)}$$

(5)

$$\varnothing \left(t\right)=\mathit{arctan}\frac{y\left(t\right)}{x\left(t\right)}$$

(6)

The instantaneous frequency is:

$$f\left(t\right)=\frac{1}{2\pi }\frac{d\varnothing \left(t\right)}{dt}$$

(7)

Equations (5) and (7) are expressions for instantaneous amplitude and instantaneous frequency, which are obtained from a simple modulation and demodulation process.

The voltage and frequency of the power generation fluctuate from moment to moment due to the energy source’s waveform nature. The HHT’s measurements of instantaneous voltage and frequency clearly show the variable features.

4. Analysis of Tidal Power Generation Data

4.1. Analysis of Daily Distribution Pattern of Electricity Generated by Tidal Power

The output power data of the tidal energy generator set throughout the day are shown in Figure 3. The output voltage of the motor changes throughout the day in Figure 3. Voltage surges and drops occur throughout the generator operation, and voltage interruptions occur during motor stalls. Next, the EMD decomposition of the signal in Figure 3 is shown. The first three IMFs were taken for analysis, as shown in Figure 4. It can be seen in Figure 4 that the signal’s symmetry causes the signal’s primary modes to be concentrated in IMF1. A residual function that is monotonically decreasing is the outcome of the EMD decomposition.

The Hilbert spectrum of the all-day tidal energy generation data is shown in Figure 5.

In the Hilbert spectrum, it can be seen that:

• There is no curve from 0:00–4:30, indicating that the voltage and frequency are zero. The motor is at a standstill, with a standstill time of 4.5 h;
• From 4:30 to 5:00, the curve appears in dark blue color. Compared with the color bar on the right side, the amplitude is small. The curve of the spectrogram is wider, and the middle value is taken as its frequency, which is lower at this time. After that, the curve in the spectrogram of the signal shows an upward trend, indicating that the frequency increases. The color changes from dark blue to light blue, compared with the right color bar, indicating that the amplitude increases;
• From 7:00 to 7:30, the amplitude and frequency reach the first peak of 248.9 V and 26.6 Hz, after which the curve in the spectrum begins to decrease, which indicates a decrease in frequency. The color began to deepen from light blue to dark blue, suggesting a decrease in amplitude;
• From 9:30–10:30, the curve disappears, and the voltage decreases to zero at 9:30, and the motor stops for 1 h;
• From 10:30 to 11:30, the curve reappears and the motor starts again and runs for an hour;
• From 11:30–15:30, the curve disappears, and the voltage decreases to zero at 11:30. Moreover, the motor stops for 4 h;
• From 15:30, the curve appears again in dark blue, with a smaller amplitude and lower frequency. After, the curve height rises rapidly and the color changes from dark blue to light blue again, suggesting that the signal amplitude and frequency increase. The motor speed speeds up, and the output voltage increases;
• From 18:00 to 18:30, the amplitude and frequency reach the second peak with an amplitude of 258.7 V and a frequency of 27.7 Hz. After, the curve in the spectrum is maintained at a high level for a while and then begins to decline, with the color gradually changing from light blue to dark blue and the output voltage gradually decreasing until 22:00, when the voltage reduces to zero and the motor stops;
• From 22:00–22:30, the motor stops for half an hour, and the spectrum curve reappears at 22:30, indicating that the motor starts;
• From 22:30 to 24:00, the curve rises and falls, and the color changes from dark to light, then light to dark. The voltage and frequency rise and then fall.

In conclusion, the motor ran for 14 h and then idled for 10 h. The highest voltage was 259 V, and the frequency was 28 Hz, as can be seen in the Hilbert spectrum, which shows that the duration of the motor operating for a day, the duration of halting, and the duration of the maximum voltage appearing are consistent with Figure 3.

4.2. Analysis of Monthly Tidal Power Generation Electricity-Distribution Pattern

The distribution of electrical energy measured by the tidal energy generation system in September 2016 is shown in Figure 6.

The maximum power-generating point occurred on 16 September, the big tidal day, when the daily power generation was above 2 kW·h for more than half the month. Power generation increased over a five-day span from 16 September to 20 September, and it also increased at the start and end of the month. Power generation decreased from 8 September to 10 September and on 24–25 September, respectively.

With the results in Figure 6, we generated the graph of the monthly variation of tidal power generation electricity by calculating the daily average voltage of tidal power generation, as shown in Figure 7.

The EMD decomposition waveform of the tidal power monthly generation waveform is shown in Figure 8. The first three IMF signals are taken for analysis. Due to the symmetry of the signal, most of its modes are in IMF1, and the decomposition of the signal’s abrupt moments is also mirrored in IMF2 and IMF3.

The Hilbert spectrum of the monthly generation waveform of tidal energy is shown in Figure 9.

After normalizing it, it can be seen that:

• From 1 September to 10 September, the curve gradually moves from light green to yellow to red as it oscillates downward, showing a decline in energy and a subsequent decline in daily power generation;
• From 10 September to 16 September, the color gradually shifts from red to yellow to light green as the curve climbs quickly, signifying an increase in energy and a quickening of daily power generation;
• On 16 September, the energy of the curve reaches its highest point. With a daily power generation of 5.69 kW·h, the 16th is the month’s highest power-generating day;
• From 16 September to 24 September, the color gradually shifts from light green to yellow and then from yellow to red as the curve steadily declines, showing a gradual decline in energy before a sudden decline in daily power generation;
• From 24 September to 30 September, the curve rises rapidly, with the color gradually changing from red to yellow and then from yellow to light green, indicating a rise in energy and a rapid increase in power generation.

In summary, the HHT transformation’s distribution pattern of tidal power generation is compatible with the observed data shown in Figure 6.

4.3. Analysis of the Annual Distribution Pattern of Tidal Power Generation Electricity

The yearly distribution pattern of the system is shown in Figure 10 based on the measured power generation data of the tidal power generating system in 2016–2017, where the horizontal coordinate corresponds to the current month, and the vertical coordinate represents the system’s monthly power generation.

According to Figure 10, the power generated by tidal current energy generators is higher in September, October, and November, with monthly power generation of over 70 kW·h; it is lower in April, May, and June, with monthly power generation of less than 50 kW·h; and it is essentially between 35 kW·h and 50 kW·h in the remaining months.

The Hilbert-Huang transform and EMD decomposition were then applied to the signal in Figure 11 to generate the corresponding results shown in Figure 12 and Figure 13. The average voltage of tidal power generation was used as the input for this HHT process to obtain its annual voltage distribution pattern (as shown in Figure 11).

According to Figure 13:

• From July 2016 to September 2016, the curve oscillates upward and gradually changes color from dark blue to light blue, indicating a sharp increase in energy and a sharp increase in power generation. The curve reaches its highest point in September, indicating the maximum energy and the most power generation in that month;
• From September 2016 to December 2016, the curve decreases slowly and then rapidly, and the color changes from light blue to dark blue, indicating that the energy decreases slowly and then rapidly;
• From January 2017 to March 2017, the curve increases slowly with a dark blue color and gradually becomes lighter, demonstrating an increase in energy and a gradual increase in power generation;
• From March 2017 to June 2017, the curve decreases with a dark blue and gradually deepening color, indicating a decrease in energy and a gradual decrease in power generation.

In conclusion, the distribution law of tidal power generation discovered by the HHT is also compatible with the observed data shown in Figure 10, demonstrating the viability and efficiency of the HHT for studying the distribution law of tidal power generation.

5. Conclusions

This paper proposes a concept for analyzing the electric energy distribution law of tidal power generation by using HHT transformation to process and analyze the measured data of tidal power generation. This study eventually obtained the electric energy distribution law of tidal power generation in 24 h, 30 days, and 12 months as follows:

1.

Within 24 h, the tidal power generation started and stopped more rapidly, and the voltage varied greatly within a short period of time. The tidal power generation time was mainly divided into four time periods, corresponding to two high tide and two low tide processes;

2.

There were two fluctuations in tidal energy generation within 30 days, with the peak position located in the middle of the month and the trough position at the beginning of the month;

3.

There were also two fluctuations in tidal power output during the 12-month period, with peaks in August, September and October and troughs in February, March and April.

A full verification of the accuracy and efficacy of the application of HHT analysis in the study of tidal power generation law was provided by the fact that the distribution law of tidal power generation electricity obtained using the HHT in this paper was essentially consistent with the measured tidal power generation data of the offshore platform. In addition, the following issues were considered in this report and require more study in follow-up work:

1.

The spectrum maps obtained in this paper sometimes show curve oscillations. In further studies, the image can be deeply optimized by optimizing data selection by selecting the sampling frequency;

2.

This paper focuses on verifying the accuracy and effectiveness of applying HHT analysis in studying the law of tidal power generation. A future step can be to consider the effectiveness and feasibility of other algorithms, such as wavelet and Fourier applied in this field and compare and analyze the results with those of this paper;

3.

Additionally, further studies also can apply the ideas of this paper to the analysis of the electrical energy law or power quality of other ocean energy power generation systems, such as wave energy, and summarize the characteristics of different forms of ocean energy power generation to guide the application of ocean energy power generation.