# Selecting and optimal sizing of hybridized energy storage systems for tidal energy integration into power grid

Seifeddine Ben Elghali, Rachid Outbib, Mohamed Benbouzid

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Seifeddine Ben Elghali, Rachid Outbib, Mohamed Benbouzid. Selecting and optimal sizing of hybridized energy storage systems for tidal energy integration into power grid. Journal of Modern Power Systems and Clean Energy, 2019, 7 (1), pp.113-122. 10.1007/s40565-018-0442-0. hal-02390235

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Submitted on 20 May 2020

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# Selecting and optimal sizing of hybridized energy storage systems for tidal energy integration into power grid

Seifeddine BEN ELGHALI<fnref n="1" />, Rachid OUTBIB<fnref n="1" />, Mohamed BENBOUZID<fnref n="2" />,<fnref n="3" /> ID

<figure><img src="image_2.png" /></figure>

**Abstract** The high penetration of renewable energy systems with fluctuating power generation into the electric grids affects considerably the electric power quality and supply reliability. Therefore, energy storage resources are used to deal with the challenges imposed by power variability and demand-supply balance. The main focus of this paper is to investigate the appropriate storage technologies and the capacity needed for a successful tidal power integration. Therefore, a simplified sizing method, integrating an energy management strategy, is proposed. This method allows the selection of the adequate storage technologies and determines the required least-cost storage capacity by considering their technological limits associated with different power dynamics. The optimal solutions given by the multi-objective evolutionary algorithm are presented and analyzed.

**Keywords** Tidal energy, Energy storage system, Optimal sizing, Selection

## 1 Introduction

The integration of renewable energies into the electrical grid is one of the most challenging tasks. In fact, the quality of the power delivered to the grid becomes very crucial when the penetration level of renewable energies is very high [1, 2]. Therefore, the use of energy storage systems (ESSs) can alleviate potential problems. ESS can provide a variety of application solutions along the entire electricity system value chain, from generation support to transmission and distribution support to end-customer uses [3]. Consequently, different ESS applications have been defined and analyzed according to their uses and value of benefits.

For renewable applications, it is common to use ESS for energy time-shift and capacity firming. The energy time shift increases the value of energy and so profits are increased. Indeed, most renewable energy resources produce a significant portion of electric energy at off-peak periods which has a low financial value. As a result, ESS can be charged and used when demand is high and supply is tight [4, 5]. By contrast, capacity firming allows the use of intermittent electric supply as a nearly constant source. Such use may reduce power-related charges and/or offset the need for equipment. Likewise, for effective renewable integration, some requirements are identified and classified in two categories. The first one is the short duration applications including the reduction of power volatility and the improvement of power quality. The second one concerns the long duration applications embracing the reduction of output variability, the transmission congestion

CrossCheck date: 21 June 2018

Received: 30 July 2017 / Accepted: 21 June 2018 / Published online: 3 September 2018

© The Author(s) 2018

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Mohamed BENBOUZID
Mohamed.Benbouzid@univ-brest.fr

Seifeddine BEN ELGHALI
Seifeddine.Benelghali@lis-lab.fr

Rachid OUTBIB
Rachid.Outbib@lis-lab.fr

<footnote n="1">1. LIS-UMR CNRS 7020, University of Aix-Marseille, Marseille, France</footnote>

<footnote n="2">2. UMR CNRS 6027 IRDL, University of Brest, Brest, France</footnote>

<footnote n="3">3. Shanghai Maritime University, Shanghai, China</footnote>
relief, the back-up for unexpected power generation shortfalls and the minimization of load violations.

Satisfying all the earlier announced requirements makes the sizing task very complicated and depending on many parameters (e.g., resource variability, load fluctuation, technologies limitations, life time, costs, etc.). In this context, too many papers in literature deal with the optimal sizing of energy storage systems especially for renewable energy applications [6–10]. The ESS sizing problem was mainly studied either in the time domain [11–13] or in the frequency domain [14–16]. Moreover, it can be noticed that the common practice was the use of one or two pres- elected ESS and then try to find its optimal sizes according to some defined objectives [17–19].

In contrast, this paper proposes a new approach allowing the selection of the adequate storage technology and determines the required least-cost storage capacity by considering its technological limits associated to different power dynamics. Therefore, a simplified sizing method, integrating an energy management strategy, is proposed. To highlight its effectiveness, the proposed strategy is applied to a tidal energy system, but it can be employed with any other renewable energy such as photovoltaic (PV), wind turbine, etc. This paper is organized as follows. First, Section 2 recalls the particularities of the tidal energy and describes the power fluctuation dynamics. Subse- quently, Section 3 announces the adopted energy man- agement strategy. The approach to the selection of the appropriate ESS is defined in Section 4. Section 5 presents the sizing optimization algorithm. Lastly, Section 6 con- cludes the paper and provides directions for future research.

## 2 Power fluctuation dynamics

In order to model the whole system, multi-physics approach was adopted including the resource, the marine turbine, and the ESS. This simulator can evaluate marine current turbine performances and dynamic loads over dif- ferent operating conditions. Throughout the paper, we will use $\mathcal{P} = (T_0, T_p)$, with $0 \le T_0 < T_p$, to denote the period of analysis.

The kinetic power harnessed by a marine current turbine (MCT) can be calculated as:

$$P_{MCT}(t) = \frac{1}{2} \rho C_p A V_{tide}^3(t) \quad t \in \mathcal{P} \qquad (1)$$

where $V_{tide}$ is the current speed in the turbine cross section; $\rho$ is the sea water density; $C_p$ is the power coef- ficient; A represents the swept rotor area.

Equation (1) expresses that the power produced by the MCT is proportional to the cube of the current speed in the

turbine cross section. For more accuracy, the swell effect, which is considered as the most disturbing one for the considered resource model, is added based on Stokes model. This model is a very classical first-order model used to predict the swell influence in the sea water column. For a given swell amplitude $H$, a period $T$, a swell length $L$ and ground sea depth $d$, the speed potential $\phi$ can be calculated for each depth $z$. The water speed created by the swell effect can be deduced by a spatial derivation of this potential [20].

$$\left\{ \begin{array}{l} V_{swell} = \operatorname{grad}\phi \\ \phi = -\frac{HL}{T} \frac{\cosh2\pi\left(\frac{z+d}{L}\right)}{\sinh2\pi\left(\frac{d}{L}\right)} \sin2\pi\left(\frac{t}{T} - \frac{x}{L}\right) \end{array} \right. \qquad (2)$$

This speed disturbance, calculated for typical intense swell specifications, can be added to the predicted tidal current speed to estimate how the swell can disturb the tidal current values in the turbine disk.

Thus, the $P_{MCT}$ is highly dependent on the fluctuations in the marine current speed [21–23]. Two main kinds of power fluctuations can be identified: on a large time scale the generated power fluctuates over a period of 6 or 12 hours which is related to tidal astronomical phenomena; on a small time scale it can fluctuate with a period of a few seconds to several minutes shown in Fig. 1. Consequently, these fluctuations affect the power storage system which can be evaluated by:

$$P_{ss}(t) = P_{MCT}(t) - P_{grid}(t) \quad t \in \mathcal{P} \qquad (3)$$

where $P_{grid}$ is the targeted power to be delivered to the grid. More precisely, $P_{grid}$ can be any continuous function in time and having values in $\mathbb{P} = (P_{grid}^{\min}, P_{grid}^{\max})$. This function can be chosen to answer to some specific uses. However, in this work, and for sake of simplicity, this function is assumed to be constant on $\mathcal{P}$.

From (3), $P_{ss}$ is defined positive during the charging period and negative during the discharge period. In order to highlight the different dynamics of the storage power flow, a fast fourier transform (FFT) is established. Figure 2 shows three scales of dynamics which obviously need different types of storage system.

## 3 Energy management strategy based on a frequency approach

According to the FFT, a hybridization of three types of storage systems corresponding to the different dynamics of power flow seems to be the best solution to deliver smooth power to the grid. In order to determine the part of each
<figure><img src="image_4.png" /><figcaption>Fig. 1 Harnessed tidal power during one year</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2 FFT of power storage system</figcaption></figure>

ESS, an energy management based on frequency approach is tested [24, 25]. Two low pass filters, defined in (4), are used to share out the power flow $P_{ss}$ between the 3 ESSs

<figure><img src="image_6.png" /><figcaption>Fig. 3 Energy management procedure</figcaption></figure>

shown in Fig. 3. $ESS_l$, $ESS_m$, $ESS_h$ are devoted to storage low, medium and high dynamics, respectively.

$$ 
\left\{ 
\begin{aligned}
P_{ESS_l}(s) &= \eta_l \left( \frac{2\pi f_1}{2\pi f_1 + s} \right) P_{ss}(s) \\
P_{ESS_m}(s) &= \eta_m \left( \frac{2\pi f_2}{2\pi f_2 + s} \right) (P_{ss}(s) - P_{ESS_l}(s)) \\
P_{ESS_h}(s) &= \eta_h (P_{ss}(s) - P_{ESS_l}(s) - P_{ESS_m}(s))
\end{aligned}
\right. 
\quad (4) 
$$

with $\eta$ is the ESS efficiency defined by:

$$ \eta_k = \begin{cases} \frac{1}{\eta_{ESS}} & P_{ESS} \ge 0 \\ \eta_{ESS} & P_{ESS} < 0 \end{cases} \quad k \in \{l, m, h\} \quad (5) $$

In this paper, the ESS efficiency is considered equal during the charge and discharge operations shown in Table 1.

This approach ensures the compatibility between the frequency components of the power flow and the intrinsic characteristics of the different sources.

## 4 Selection of ESSs

Storage system performance characteristics for any power applications can be described in terms of two parameters, i.e., specific power and specific energy. Figure 4 shows different types of ESSs in the energy-power plane called “Ragone chart” and includes information about the suitable application time period for each element [26].

As it can be noticed, batteries are more suitable for applications with long term variations on the scale of minutes to several hours, while superconducting magnetic energy storage systems and ultra-capacitors are more adapted for applications on the time scale of several seconds.

Accordingly, the two key criteria to consider when selecting an energy storage system are the system power and the energy ratings. Based on the energy management
<table><caption>**Table 1** Technical and economical characteristics of electrical energy storage technologies</caption><thead><tr><th>Technologies</th><th>Energy density (J/L)</th><th>Power density (W/L)</th><th>Power capital cost ($/kW)</th><th>Energy capital cost ($/kWh)</th><th>Charge/discharge efficiency (%)</th></tr></thead><tbody><tr><td>PHS</td><td>210<sup>3</sup>–5.510<sup>3</sup></td><td>0.5–1.5</td><td>2500–4300</td><td>5–100</td><td>87</td></tr><tr><td>CAES</td><td>210<sup>3</sup>–710<sup>3</sup></td><td>3–6</td><td>400–1000</td><td>2–120</td><td>70–79</td></tr><tr><td>Flywheel</td><td>3.610<sup>6</sup>–1810<sup>6</sup></td><td>20–80</td><td>250–350</td><td>1000–5000</td><td>90–93</td></tr><tr><td>Lead{–}acid</td><td>3610<sup>3</sup>–144010<sup>3</sup></td><td>50–80</td><td>300–600</td><td>200–400</td><td>85</td></tr><tr><td>Li{–}ion</td><td>5.410<sup>6</sup>–3610<sup>6</sup></td><td>200–500</td><td>1200–4000</td><td>600–2500</td><td>85</td></tr><tr><td>NaS</td><td>50010<sup>3</sup>–65010<sup>3</sup></td><td>150–300</td><td>1000–3000</td><td>300–500</td><td>85</td></tr><tr><td>NiCd</td><td>29010<sup>3</sup>–210<sup>6</sup></td><td>15–150</td><td>500–1500</td><td>800–1500</td><td>85</td></tr><tr><td>VRFB</td><td>210<sup>3</sup>–710<sup>3</sup></td><td>16–33</td><td>600–1500</td><td>150–1000</td><td>75–82</td></tr><tr><td>ZnBr</td><td>3.610<sup>3</sup>–9010<sup>3</sup></td><td>30–60</td><td>700–2500</td><td>150–1000</td><td>60–70</td></tr><tr><td>Capacitor</td><td>36010<sup>6</sup>+</td><td>2–10</td><td>200–400</td><td>500–1000</td><td>75–90</td></tr><tr><td>Double-layer capacitor</td><td>36010<sup>6</sup>+</td><td>10–30</td><td>100–300</td><td>300–2000</td><td>95–98</td></tr><tr><td>SMES</td><td>3.610<sup>6</sup>–1410<sup>6</sup></td><td>0.2–6.1</td><td>200–300</td><td>1000–10000</td><td>95</td></tr><tr><td>Hydrogen fuel cell</td><td>210<sup>6</sup>–3.610<sup>6</sup></td><td>500–3000</td><td>300–1500</td><td>2–15</td><td>59</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>**Fig. 4** Ragone chart</figcaption></figure>

strategy, $P_{ESS}^{max}$ the power upper limit that an ESS cannot exceed when supplying energy and $E_{ESS}^{A}$ the active energy required to efficiently smooth the delivered power are estimated for each ESS. The evolution of the ESS energy is given by:

$$E_{ESS}(t) = \int_{T_0}^{t} P_{ESS}(\tau) d\tau \quad t \in \mathcal{P} \qquad (6)$$

Thus, the stored active energy $E_{ESS}^{A}$ can be expressed by:

$$E_{ESS}^{A} = \max_{t \in \mathcal{P}}(E_{ESS}(t)) - \min_{t \in \mathcal{P}}(E_{ESS}(t)) \qquad (7)$$

The maximum power of the ESS is defined as:

$$P_{ESS}^{max} = \max_{t \in \mathcal{P}}(|P_{ESS}(t)|) \qquad (8)$$

Figures 5, 6, 7 and 8 show an example of power and energy variations within 24 hours for $ESS_m$ within 15 minutes for $ESS_m$ obtained through the energy management strategy. In

<figure><img src="image_8.png" /><figcaption>**Fig. 5** $ESS_m$ power fluctuation over 24 hours</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 6** $ESS_m$ energy fluctuation over 24 hours</figcaption></figure>

order to create a relation between the power flow dynamics and the different storage system technologies, the notion of specific frequency [27] is introduced and defined as the ratio between the power density $\rho_{ESS}^P$ and the energy density $\rho_{ESS}^E$:

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>
<figure><img src="image_12.png" /><figcaption>Fig. 7 ESSh power fluctuation over 15 minutes</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 8 ESSh energy fluctuation over 15 minutes</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 9 Power Ragone chart in frequency plane</figcaption></figure>

$$f[\text{Hz}] = \frac{\rho_{ESS}^{P}[\text{W/L}]}{\rho_{ESS}^{E}[\text{J/L}]} \qquad (9)$$

Therefore, the different elements of the Ragone chart can be reported on frequency plane using (9) as shown in Fig. 9. The storage system specifications, summarized in Table 1, are based on data collected from [28]. Similarly, the specific frequency of the installed ESS can be defined as:

$$f_{ESS} = \frac{P_{ESS}^{\max}}{E_{ESS}^{A}} \qquad (10)$$

# 5 Sizing optimization

## 5.1 Problem formulation

In this work, the objective of the sizing optimization consists in maximizing the energy delivered to the grid

during a period $P$ with a minimum of power fluctuations and using the least cost solution. It is assumed that over the period $P$, $P_{MCT}$ is known by using prediction model based on the predictability of tidal coefficients. In our study, $P_{MCT}$ is calculated over one year using a turbulent resource [29]. Let $P_{grid}^{real}$ be the real power delivered to the grid expressed by:

$$P_{grid}^{real}(t) = P_{MCT}(t) + \sum_{k \in \mathcal{D}} \alpha_k P_{ESS_k}(t) \quad t \in \mathcal{P} \qquad (11)$$

where $\mathcal{D} = \{l, m, h\}$; $\alpha_k(k \in \mathcal{D})$ is set equal to one when $ESS_k$ is selected and equal to zero elsewhere. Let also $E_{grid}^{real}$ denote the real energy delivered to the grid expressed by:

$$E_{grid}^{real}(t) = \int_{T_0}^{t} P_{grid}^{real}(\tau) d\tau \quad t \in \mathcal{P} \qquad (12)$$

Let also $\Delta P_{grid}^{real}$ be the power variation expressed by:

$$\Delta P_{grid}^{real} = \max_{t \in \mathcal{P}} P_{grid}^{real}(t) - \min_{t \in \mathcal{P}} P_{grid}^{real}(t) \qquad (13)$$

For now on, we use $C_{ESS_k}(k \in \mathcal{D})$ to design the cost of $ESS_k$. We assume that $C_{ESS_k} \in S_{ESS_k}(k \in \mathcal{D})$ where $S_{ESS_k}$ is the set of costs of the selected solutions for each dynamic (low, medium and high). In order to estimate the cost of each storage system, the volume needed for a given $ESS_k(k \in \mathcal{D})$ is expressed by:

$$V_k = \max \left( \frac{E_{ESS_k}^{Tot}}{\rho_{ESS_k}^{E}}, \frac{P_{ESS_k}^{max}}{\rho_{ESS_k}^{P}} \right) \qquad (14)$$

with

$$E_{ESS_k}^{Tot} = \frac{E_{ESS_k}^{A}}{DOD_{ESS_k}}$$

where $DOD_{ESS_k}$ is the depth of discharge. If the volume is obtained from the energy ratio, the system cost will be calculated as:

$$C_{ESS_k} = C_{ESS_k}^{Ec} E_{ESS_k}^{Tot} \quad k \in \mathcal{D} \qquad (15)$$

where $C_{ESS_k}^{Ec}$ is the energy capital cost ($/kWh). In the case where the volume is sized by the power ratio, the cost will be given by:

$$C_{ESS_k} = C_{ESS_k}^{Pc} P_{ESS_k}^{max} \qquad (16)$$

where $C_{ESS_k}^{Pc}$ denotes the power capital cost ($/kW). For reasons of simplification, only average values of capital costs, calculated from Table 1, are considered. In order to be more realistic, it should be noted that operating and maintenance costs must be considered.

In this study, the sizing variables considered are the power grid $P_{grid}$ and the two cut-off frequencies $f_1 \in \mathcal{F}_1$
<figure><img src="image_15.png" /><figcaption>Fig. 10 Problem of sizing optimization</figcaption></figure>

and $f_2 \in \mathcal{F}_2$ shown in Fig. 10 where $\mathcal{F}_1$ and $\mathcal{F}_2$ denote the sets of all admissible frequencies.

Now, we are in position to state the problem formulation. By using the notations introduced above, the problem of sizing optimization aims to solve simultaneously three sub-problems that are:

$$OF_E = \max_{P_{\text{grid}} \in \mathbb{P}} E_{\text{grid}}^{\text{real}}(P_{\text{grid}}) \quad (\text{SP1})$$

$$\begin{aligned} OF_{\Delta P} = & \min_{f_1 \in \mathcal{F}_1} \Delta P_{\text{grid}}^{\text{real}}(f_1, f_2, P_{\text{grid}}) \quad (\text{SP2}) \\ & f_2 \in \mathcal{F}_2 \\ & P_{\text{grid}} \in \mathbb{P} \end{aligned}$$

and

$$\begin{aligned} OF_C = & \min_{\substack{f_1 \in \mathcal{F}_1 \\ f_2 \in \mathcal{F}_2 \\ P_{\text{grid}} \in \mathbb{P}}} C_{\text{ESS}}(f_1, f_2, P_{\text{grid}}) \quad (\text{SP3}) \\ & P_{\text{grid}} \in \mathbb{P} \end{aligned}$$

with

$$C_{\text{ESS}} = \sum_{k \in \mathcal{D}} \alpha_k C_{\text{ESS}_k}$$

The first objective function is $OF_E$ aims to maximize the annual energy delivered to the grid, the second one $OF_{\Delta P}$ intends to minimize the power fluctuation while the third function $OF_C$ targets the total cost minimization of the selected storage systems. However, and generally speaking, the three sub-problems do not possess necessarily a common

solution. Thus, we rather seek to solve the problem of sizing optimization can be formulated as:

$$\begin{aligned} OF_G = & \min_{\substack{f_1 \in \mathcal{F}_1 \\ f_2 \in \mathcal{F}_2 \\ P_{\text{grid}} \in \mathbb{P}}} F(E_{\text{grid}}^{\text{real}}, \Delta P_{\text{grid}}^{\text{real}}, C_{\text{ESS}}) \\ & \quad (17) \end{aligned}$$

where $F$ is a suitable function expressing a global objective.

Besides, the problem (17) must be solved by respecting the following constraints:

$$P_{\text{grid}}^{\text{real}}(t) \in (P_{\text{grid,min}}^{\text{real}}(t), P_{\text{grid,max}}^{\text{real}}(t)) \quad t \in \mathcal{P} \quad (18)$$

where

$$\left\{ \begin{array}{l} P_{\text{grid,min}}^{\text{real}}(t) = P_{\text{MCT}}(t) - P_{\text{ss}}(t) - \Delta P_{\text{grid}}^{\text{real}} \\ P_{\text{grid,max}}^{\text{real}}(t) = P_{\text{MCT}}(t) - P_{\text{ss}}(t) + \Delta P_{\text{grid}}^{\text{real}} \end{array} \right. \quad (19)$$

with, and by using the third equality of (3):

$$P_{\text{ss}}(t) = \sum_{k \in \mathcal{D}} P_{\text{ESS}_k}(t)$$

It should be noted that the optimization problem stated by (17) is complex and in our knowledge it can not be solved explicitly. Besides, the number of possibility, depending on desired sampling accuracy and the technology types, can become very large. Hence, one must seek for a suitable strategy that solve the problem by respecting a balance between the accuracy and the computation time.

## 5.2 Strategy for solving problem

In this work, the problem is solved by using the multi-objective optimization based on the non-dominated sorting

<figure><img src="image_16.png" /><figcaption>Fig. 11 Optimization process</figcaption></figure>
genetic algorithm-II (NSGA-II). Indeed, NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to Pareto-archived evolution strategy and strength-Pareto evolutionary algorithm [30]. The optimization strategy is described by Fig. 11 and is given by Algorithm 1.

**Algorithm 1 NSGA-II**

/* It is assumed that technical and economical characteristics of electrical energy storage technologies are predefined*/

1: Get $V_{tide}$

2: Calculate $P_{MCT}$ /* Use (1)*/

3: For i:=1 To $N$_individuals

Generate ($P_{grid}^i, f_1^i, f_2^i$)

EndFor

4: Check_Constraint(1) /*The constraints are defined by (20) */

5: Calculate $f_{ESS}^i, f_{ESS_m}^i, f_{ESS_h}^i$ /*Use (4), (6) and (10) */

6: Check_Constraint(2) /*The constraint is given in (21) */

7: Calculate $OF_E, OF_{ΔP}, OF_C$ /* Use (17) */

8: $P_1$= Crossover($P$) /*Use a predefined crossover function [30]*/

9: $P_2$= Mutate($P$) /*Use a predefined mutate function [30]*/

10: $P$= New Generation($P, P_1, P_2$) /*Evaluate, group and sort ($P, P_1, P_2$) by dominance and crowding and select $N$ individuals by elitism [30] */

11: If $j \le N$_iterations Then Goto 4

Else Return($P$)

EndIf

The pre-simulation constraints considered in this study are:

$$ \begin{cases} f_1 \in \mathcal{F}_1 = (f_1^{\min}, f_1^{\max}) \\ f_2 \in \mathcal{F}_2 = (f_2^{\min}, f_2^{\max}) \\ P_{grid} \in \mathbb{P} \end{cases} \quad (20) $$

with

$$ 0 \le P_{grid}^{\min} < P_{grid}^{\max} \le P_{MCT}^{\max} $$

The post-simulation constraints are:

$$ f_{ESS} \in (f_{ESS}^{\min}, f_{ESS}^{\max}) \quad (21) $$

## 5.3 Results and discussion

The non-dominated sorting genetic algorithm NSGA-II is applied to the optimization process [30]. The numerical values used for the analysis are given in Table 2.

The best trade-offs are projected in the 3D plane ($OF_E, OF_{ΔP}, OF_C$) shown in Fig. 12. The best optimal solution is given for the individual minimizing the three

<table><caption>**Table 2** Numerical values used for analysis and simulation</caption><thead><tr><th>Constant</th><th>Value</th></tr></thead><tbody><tr><td>$C_p$</td><td>0.4</td></tr><tr><td>$P_{MCT}$</td><td>1500 kW</td></tr><tr><td>$N$_individuals</td><td>50</td></tr><tr><td>$N$_iterations</td><td>100</td></tr><tr><td>$\rho$</td><td>1000 kg/m<sup>3</sup></td></tr><tr><td>$f_1^{\min}$</td><td>5 &times; 10<sup>-6</sup> Hz</td></tr><tr><td>$f_2^{\min}$</td><td>5 &times; 10<sup>-5</sup> Hz</td></tr><tr><td>$f_1^{\max}$</td><td>5 &times; 10<sup>-5</sup> Hz</td></tr><tr><td>$f_2^{\max}$</td><td>5 &times; 10<sup>-2</sup> Hz</td></tr><tr><td>$P_{grid}^{\min}$</td><td>100 kW</td></tr><tr><td>$P_{grid}^{\max}$</td><td>1 MW</td></tr><tr><td>$(P_{grid}^{real})_{avg}$</td><td>210 kW</td></tr></tbody></table>

<figure><img src="image_17.png" /><figcaption>**Fig. 12** Projection of the Optimal Pareto front onto ($OF_E, OF_{ΔP}, OF_C$) plane</figcaption></figure>

objective functions. However, as it can be noticed, there is no absolute minimum solution. Therefore, a compromised solution can be obtained by giving more importance to two of the three criteria. In our case, we focused on the total cost and the power fluctuation shown in Fig. 13. This choice is justified by the fact that the annual energy does not change too much according to the $OF_E$ axis.

Figure 14 shows the energy storage system selected for the two points shown in Fig. 12. The first solution is obtained with the hybridization of double layer capacitor (DLC) and hydrogen fuel cell systems with a total cost of 81 k$ and only 13% of power variation. While the second solution is based on the combination of the SMES and hydrogen fuel cell systems with a total cost of 31 k$ and only 26% of power variation. In both cases, the low dynamic presented by the frequency $f_{ESS_1}$ does not correspond to any storage system, therefore only two storage
<figure><img src="image_18.png" /><figcaption>**Fig. 13** Projection of the Optimal Pareto front onto (OF<sub>ΔP</sub>, OF<sub>C</sub>) plane</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>**Fig. 14** Example of solution based on hydrogen fuel cell and SMES</figcaption></figure>

systems are selected. Thus, the real power delivered to the grid will be smoothed according to high and medium dynamics and will present a low dynamic fluctuation shown in Fig. 15. For better smoothing performances, other types of storage systems may be used but it will leads to very expensive solutions. Indeed, a more smoothed power $P_{\text{grid}}^{\text{real}}$ was expected since we were using a constant $P_{\text{grid}}$ value as input for the NSGA-II algorithm. Therefore, we investigated other solutions from second and third Pareto-front rank. Figure 16 shows an hybridized solution where three types of ESS are selected (VRFB, PHS and SMES). In this particular case, the ESS cost is ten times higher than the DLC and hydrogen system with practically no power variation shown in Fig. 17). Thus, despite of its good performances according to the second objective function OF<sub>ΔP</sub>, the solution is sorted at the second Pareto-front due to its very high cost.

The obtained results highlights the fact that only the medium and high dynamic must be considered for the ESS sizing problem in tidal energy applications. Indeed, the astronomic nature of the tidal energy resource makes it predictable for low dynamics. Therefore by filtering the power generated by the daily moon cycle, swell effect and

<figure><img src="image_20.png" /><figcaption>**Fig. 15** Example of filtered power grid from the first set solutions</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Fig. 16** Example of Selected ESS from the second Pareto-Front solutions</figcaption></figure>

turbulence, it is easier to integrate successfully the produced energy in the grid.

<figure><img src="image_22.png" /></figure>
<figure><img src="image_23.png" /><figcaption>**Fig. 17** Example of filtered power grid from the second Pareto-Front solutions</figcaption></figure>

## 6 Conclusion

In this paper, an optimal sizing strategy for hybridized energy storage systems were presented. This approach is based on a simplified frequency energy management method. Optimal solutions are obtained using a multi-objective genetic algorithm. However, the procedure is highly time consuming, especially when using annual tidal speed data with one second as sampling time. Therefore, some simplifications were used to reduce computational time by excluding the estimation of the life span and considering a limited database of storage systems with average values of power and energy density related to average values of power capital and energy capital costs of the ESS. Nevertheless, the obtained results are very interesting and give a good idea about the optimal solutions to be considered according to their cost and performances.

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**Seifeddine BEN ELGHALI** received the B.Sc. degree in Electrical Engineering in 2005 from ENIT, Tunis, Tunisia, the M.Sc. degree in Automatic Control in 2006 from the University of Poitiers, and the Ph.D. degree in Electrical Engineering in 2009 from the University of Brest. Since 2010, he is an Associate Professor of Electrical Engineering in the University of Aix-Marseille, France. His research interests include modeling and control of renewable energy applications.

**Rachid OUTBIB** received his Ph.D. degree in applied mathematics in 1994 and his Habilitation à Diriger des Recherches degree in automatics control in 1998, respectively from the University of Metz and the University of Amiens (France). He was Full Professor at the University of Technology at Belfort (France), from 2003 to 2006. Since 2007, he is Full Professor at the University of Aix-Marseille. He is head of the ESCODI a team of the LSIS_lab. His research interests include nonlinear systems methods with applications to fluid power, automotive and energetic systems.

**Mohamed BENBOUZID** received the B.Sc. degree in Electrical Engineering from the University of Batna, Batna, Algeria, in 1990, the M.Sc. and Ph.D. degrees in Electrical and Computer Engineering from the National Polytechnic Institute of Grenoble, Grenoble, France, in 1991 and 1994, respectively, and the Habilitation à Diriger des Recherches degree from the University of Picardie "Jules Verne," Amiens, France, in 2000. After receiving the Ph.D. degree, he joined the Professional Institute of Amiens, University of Picardie "Jules Verne," where he was an Associate Professor of electrical and computer engineering. Since September 2004, he has been with the Institut Universitaire de Technologie de Brest, University of Brest, Brest, France, where he is a Professor of electrical engineering. He is also a Distinguished Professor at the Shanghai Maritime University, Shanghai, China. His research interests include analysis, design, and control of electric machines, variable-speed drives for traction, propulsion, and renewable energy applications, and fault diagnosis of electric machines. He is an IEEE Senior Member. He is the Editor-in-Chief of the International Journal on Energy Conversion (IRECON). He is also an Associate Editor of the IEEE Transactions on Energy Conversion, the IEEE Transactions on Industrial Electronics, the IEEE Transactions on Sustainable Energy, the IEEE Transactions on Vehicular Technology. He is a Subject Editor for the IET Renewable Power Generation.

<figure><img src="image_24.png" /></figure>