Frequency splitting approach using wavelet for energy management strategies in fuel cell ultra-capacitor hybrid system

2.1. Description of the strategy

Hybrid power system is designed based on the power and energy requirement, their EMS leads mainly to maximize fuel economy, minimize emissions, minimize system cost and achieve good driving performance

For this purpose, and to coordinate between the energy sources and offer the power flow control for the mechanical and electrical path, an appropriate EMS is proposed to consider the specific characteristics of system components (fuel cell ($FC$) dynamics, ultra-capacitor ($UC$) state of charge ($SOC$), efficiency improvement, transient performance, recovering mode …).

Wavelet frequency decomposition is highly perfect method for frequency splitting for achieve to perfect EMS, its main principle is based on the use of the $UC$ (the fastest energy source) for supplying the high band of the load power frequency spectrum ($HF$), thus, avoiding the fuel starvation problem and permitting to propose a downsized design. Conversely, low frequencies ($LF$) are provided by the fuel cell, which contributes to the long-term autonomy and also maintain the $UC$state of charge ($SOC$).

The configuration of hybrid vehicle topology need to control unit of the vehicle for that we use an efficient adaptable control scheme based on a cascaded control loop, as depicted in Fig. 1.

Our hybrid vehicle system is composed on two different sources fuel cell ($FC$) and ultra-capacitors ($UC$), each source is connected by a $DC/DC$converter, for this we have exploited a strong strategy based on wavelet transform to ensure the sharing of power demand and energy between these sources, therefore identify the current trajectory for each source ($iF{C}_{ref}$ and $iU{C}_{ref}$).

This strategy calls for local control of converters current with closed loop for our $FC/UC$ system. Thus, to monitor the current trajectory of each source, we have designed a classic proportional integrator $PI$ controller for each closed current loop.

Fig. 1General chart view of proposed energy management strategy

This control strategy estimates future power demand using the $DC$ bus voltage fluctuations, hence a second Proportional Integrator ($PI$) controller was exploited for allows to generate the load current estimated which represents the power demand trajectory since $V_{BUS}\left(t\right)$ is constant (Fig. 1).

Once the power demand is estimated, the proposed EMS remains to be integrated using wavelet approach.

2.2. Driving cycles

Driving cycle generally represents a set of vehicle speed points as a function of time. It is used to assess a vehicle’s fuel consumption and pollutant emissions in a standardized way, so that different vehicles can be compared with each other.

Many driving cycles are regulated in the European Union, in the United States and in Japan and are called standard driving cycles.

In Europe, the most used are UDC (urban drive cycle) or called ECE-15, EUDC (Extra-Urban Driving Cycle), and NEDC (New European Driving Cycle). The last one is the official cycle to standardize pollutant emissions and vehicle autonomy in Europe; it is made up of an urban part called (ECE), which is repeated four times, and an extra-urban part (EUDC).

In our paper, two driving cycles was tested for comparison: UDC and real driving cycle based on NEDC with taking into account a real world driving schedule, experimentally measured, the following figures show the power load profile of each cycle.

Fig. 2Power profile for UDC driving cycle

Fig. 3Power profile for REAL driving cycle

2.3. Wavelet approach

Nowadays time-frequency representations becomes necessary approach in condition monitoring and signal processing to afford both time and frequency information of the analysis signals, most related approach is wavelet transform as powerful approach for extracting features from the transient signal.

Whenever we want talk about wavelet transform, we have to do small degression toward short-time Fourier transform (STFT).

STFT introduced by Denis Gabor in 1946 and as usually sine and cosine functions are used as base signals for the analysis, their time-span from $-\infty$ to $+\infty$ making them undesirable for transient analysis and also with a fixed window size, in opposite wavelet transform uses a large library of wavelet functions characterized mainly by limited time span and various wave shapes that are appropriate for transient analysis and moreover with a variable size window length allows to give finest time and frequency resolution compared to STFT [28-31].

Consequently, the wavelets transform count as powerful approach in signal processing, in our work we use discrete wavelet transform for frequency decompositions of original signal into two signals one is called signal Approximation with low frequencies and second is called signal detail with high frequencies, the next paragraph reveals theoretical detail about discrete wavelet transform DWT.

2.4. Discrete wavelet transform

Discrete wavelet transform (DWT) use a scale factor and a discretized translation. We call dyadic discrete wavelet transform any wavelet basis working with a scale factor $u=2i$.

Discrete wavelet transform decomposes the sampled input signal, into $n$ Approximation signals at a specific level, and $n$ Detail signals, as show in Fig. 4.

Fig. 4Standard discrete wavelet decomposition

The signal is decomposed as follow:

1) Approximation signal $A_j$ gotten by passing the original signal into high pass filters to analyze the high frequencies ($HF$).

2) Detail signal $D_j$ gotten by passing the original signal through a series of low pass filters to analyze the low frequencies ($LF$).

The Eq. (1) and Eq. (2) express that decomposition:

where $A_{j-1}$ is the approximation of the level immediately above level $j$, $k=\mathrm{1,2},....K$ where $K$ is the length of the filter vector [28-30].

Three steps are necessary in our wavelet decomposition for reach to efficient management strategy:

1) First is Mother wavelet choice for decomposition is Haar, Haar characterized by great characteristic that is the only symmetric wavelet with a compact support can easily decomposes signals into low-pass and high pass components sub-sampled by 2

2) Second: number of level decomposition is three levels using Haar wavelet transform [31].

3) Third is final signal was obtained through reconstruction based on summation of decomposition signals (details and approximation), the particular characteristic of Haar basis is capable to synthesized with perfect reconstruction filters having a linear phase.

Using Haar wavelet can appropriately reach to a perfect EMS, with easy structure and architecture; however, attain our main aim of control.

3.1. Result under UDC driving cycle (wavelet Vs FFT)

All figures of last variables already mentioned are depicted in Fig. 5-9, for UDC driving cycle. and Fig. 10-14 for Real driving cycle, it is important to say that the value of $UC$, voltage reference is $V_{UCref}=$ 150 V and $DC$ bus voltage reference is $V_{BUSref}=$ 410 V.

Fig. 5Hybrid system response under UDC driving cycle (wavelet vs FFT)

Fig. 6Hybrid system response under UDC driving cycle (wavelet vs FFT)

Fig. 7Hybrid system response under UDC driving cycle (wavelet vs FFT)

Fig. 8Hybrid system response under UDC driving cycle (wavelet vs FFT)

Fig. 9Hybrid system response under UDC driving cycle (wavelet vs FFT)

3.2. Result under real driving cycle (wavelet vs FFT)

Figs. 5-14 shows clearly the difference through its waveform responses between two EMSs based one on wavelet approach (left side) and second based on Fourier approach (right side).

Fig. 10Hybrid system response under real driving cycle (wavelet vs FFT)

By comparing wavelet analysis (left side) vs Fourier analysis (right side), power responses show (Fig. 5 and Fig. 10) that the EMS imposes to each source respecting its own characteristics.

Fig. 11Hybrid system response under real driving cycle (wavelet vs FFT)

Back to Fig. 1 and in order to protect the converters as well as the sources (UCs and FC) against over currents, the installation of internal current loops which allow the current of each source to be conducted is a necessity

FFT analysis of $FC$ current $iFC$, exhibits more oscillations compare to $iF{C}_{ref}$ as given away in right side of Fig. 6 and Fig. 11.

Although in our study, we opted for the Proportional-Integral ($PI$) control structure to ensure robustness to load variations, we can spot proper the wavelet method implemented for frequency splitting has perfect advantages over simulation results:

First: for $FC$ current behaviour ($iFC$) as a low band pass filter shown in left side of Fig. 6 and Fig. 11.

Second: for $UC$ current behaviour ($iUC$) as a high-band pass filter shown in left side of Fig. 7 and Fig. 12.

Fig. 12Hybrid system response under real driving cycle (wavelet vs FFT)

Fig. 13Hybrid system response under real driving cycle (wavelet vs FFT)

Fig. 14Hybrid system response under real driving cycle (wavelet vs FFT)

As shown in (Fig. 8 and Fig. 13), power load affect the $DC$ link voltage $V_{BUS}$ transiently with a slight deviation because of wavelet approach characteristic, overshoot less than 1 %, the reference $V_{BUSref}=$ 410 V is followed perfectly).

In opposite side and in both driving cycle using FFT analysis, $V_{BUS}$ follows $V_{BUSref}=$ 410 V with small steady state error.

Ultra-capacitors can react quickly to sudden transients in the current of the load; these $iUC$ transients are induced by bus voltage regulation and allow insurance of the major part of the transient component of the demanded power. Energy transfer from $UCs$ to the $DC$ bus therefore operates correctly and compensates for the energy that is not supplied by the Fuel cell. This allows the battery to react without abrupt variations in its current to the load requests.

Then, as the current of the $FC$ increases, the discharge of the $UCs$ characterized by the decrease in its tension attenuates until it is cancelled. A rebalancing regime is then established (called compensation), characterized here by recharging the bank of $UCs$to its reference value ($V_{UCref}$) fixed at 150 V (Fig. 9 and Fig. 14). In addition, the system control reacts perfectly by following the trajectory currents (Fig. 6 and Fig. 11) and (Fig. 7 and Fig. 12).

In addition, Wavelet analysis provides hydrogen consumption saving (13 % under UDC driving cycle and 16 % under real driving cycle) which makes it relevant regarding fuel economy.