Selecting and optimal sizing of hybridized energy storage systems for tidal energy integration into power grid
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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 Selection1 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 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, 7, 8, 9, 10]. The ESS sizing problem was mainly studied either in the time domain [11, 12, 13] or in the frequency domain [14, 15, 16]. Moreover, it can be noticed that the common practice was the use of one or two preselected ESS and then try to find its optimal sizes according to some defined objectives [17, 18, 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. Subsequently, Section 3 announces the adopted energy management 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 concludes 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 different 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.
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
Technical and economical characteristics of electrical energy storage technologies
Technologies | Energy density (J/L) | Power density (W/L) | Power capital cost ($/kW) | Energy capital cost ($/kWh) | Charge/discharge efficiency (%) |
---|---|---|---|---|---|
PHS | \(2 10^3{-}5.5 10^3\) | \(0.5{-}1.5\) | \(2500{-}4300\) | \(5{-}100\) | 87 |
CAES | \(2 10^3{-}7 10^3\) | \(3{-}6\) | \(400{-}1000\) | \(2{-}120\) | \(70{-}79\) |
Flywheel | \(3.6 10^6{-}18 10^6\) | \(20{-}80\) | \(250{-}350\) | \(1000{-}5000\) | \(90{-}93\) |
Lead{-}acid | \(36 10^3{-} 1440 10^3\) | \(50{-}80\) | \(300{-}600\) | \(200{-}400\) | 85 |
Li{-}ion | \(5.4 10^6{-} 36 10^6\) | \(200{-}500\) | \(1200{-}4000\) | \(600{-}2500\) | 85 |
NaS | \(500 10^3{-}650 10^3\) | \(150{-}300\) | \(1000{-}3000\) | \(300{-}500\) | 85 |
NiCd | \(290 10^3{-}2 10^6\) | \(15{-}150\) | \(500{-}1500\) | \(800{-}1500\) | 85 |
VRFB | \(2 10^3{-}7 10^3\) | \(16{-}33\) | \(600{-}1500\) | \(150{-}1000\) | \(75{-}82\) |
ZnBr | \(3.6 10^3{-}90 10^3\) | \(30{-}60\) | \(700{-}2500\) | \(150{-}1000\) | \(60{-}70\) |
Capacitor | \(360 10^6+\) | \(2{-}10\) | \(200{-}400\) | \(500{-}1000\) | \(75{-}90\) |
Double-layer capacitor | \(360 10^6+\) | \(10{-}30\) | \(100{-}300\) | \(300{-}2000\) | \(95{-}98\) |
SMES | \(3.6 10^6{-}14 10^6\) | \(0.2{-}6.1\) | \(200{-}300\) | \(1000{-}10000\) | 95 |
Hydrogen fuel cell | \(2 10^6{-}3.6 10^6\) | \(500{-}3000\) | \(300{-}1500\) | \(2{-}15\) | 59 |
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.
5 Sizing optimization
5.1 Problem formulation
In this study, the sizing variables considered are the power grid \(P_{grid}\) and the two cut-off frequencies \(f_1\in \mathcal{F}_1\) 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.
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
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 \(f_{ESS_{l}}^{i}\!,f_{ESS_{m}}^{i}\!,f_{ESS_{h}}^{i}\,\) /*Use (4), (6) and (10) */ |
6: Check_Constraint(2) /*The constraint is given in (21) */ |
7: Calculate \(OF_{E},OF_{\mathrm{\Delta} P},OF_{C}\, /*{\text Use}\) (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 ≤ N_iterations Then Goto 4 |
Else Return(P) |
EndIf |
5.3 Results and discussion
Numerical values used for analysis and simulation
Constant | Value |
---|---|
\(C_p\) | 0.4 |
\(P_{MCT}\) | 1500 kW |
N_individuals | 50 |
N_iterations | 100 |
\(\rho\) | 1000 \(\mathrm {kg/m}^3\) |
\(f_1^{\mathrm {min}}\) | \(5 \times 10^{-6}\) Hz |
\(f_2^{\mathrm {min}}\) | \(5 \times 10^{-5}\) Hz |
\(f_1^{\mathrm {max}}\) | \(5 \times 10^{-5}\) Hz |
\(f_2^{\mathrm {max}}\) | \(5 \times 10^{-2}\) Hz |
\(P_{grid}^{\mathrm {min}}\) | 100 kW |
\(P_{grid}^{\mathrm {max}}\) | 1 MW |
\((P_{grid}^{real})_{\mathrm {avg}}\) | 210 kW |
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 turbulence, it is easier to integrate successfully the produced energy in the grid.
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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