Design optimization of hydraulic energy storage and conversion system for wave energy converters
© The Author(s) 2018
Received: 28 September 2017
Accepted: 31 January 2018
Published: 12 March 2018
Wave energy collected by the power take-off system of a Wave Energy Converter (WEC) is highly fluctuating due to the wave characteristics. Therefore, an energy storage system is generally needed to absorb the energy fluctuation to provide a smooth electrical energy generation. This paper focuses on the design optimization of a Hydraulic Energy Storage and Conversion (HESC) system for WECs. The structure of the HESC system and the mathematical models of its key components are presented. A case study and design example of a HESC system with appropriate control strategy is provided. The determination of the ratings of the HESC system is also investigated in order to achieve optimal system energy efficiency.
As a kind of renewable energy, wave energy and its utilization have obtained increasing interests in the past decade [1–4]. Wave Energy Converter (WEC) is normally used to harvest the wave energy and transform it to electrical energy. Many different WEC systems have been studied and reported [1–8], and they can be categorized into two main types as turbine-type and buoy-type . The turbine-type WECs, including Oscillating Water Column (OWC) WEC  and overtopping WEC [5, 6], use turbines as the main energy conversion device. While the buoy-type WECs, which are also known as Point Absorber (PA) WECs, utilize fully submerged (below surface) absorber (e.g. the Archimedes Wave Swing (AWS) based ) or floating (on the surface) absorber [8–10] to capture the wave energy. The PA-WECs are considered to be more environmental friendly  and have obtained interests from both academic researches [7–10] and industrial prototypes [11, 12].
The Power Take-Off (PTO) systems of the PA-WECs can be categorized into two main types as electric-type and hydraulic-type . The electric PTOs, including linear generator [7, 10] and rotary generator with gearbox , directly convert the captured wave energy to electricity. While the hydraulic PTOs transfer the wave energy to hydraulic energy, which is used to drive either a turbine  or a hydraulic motor  that is connected to an electric generator.
The situation of waves with large force at low speed can be well suited by the hydraulic PTOs since they can provide much larger force density than the electric PTOs, especially at high system pressure . Thus, hydraulic PTOs should be more compact in size and weight, economically competitive, and relatively easy to install and maintain [2, 14]. Furthermore, since the wave energy is highly fluctuating, from both the wave-to-wave and wave states time scales, the required peak power capacity of the PTOs greatly exceeds the time-averaged power delivered to the grid. Energy storage system is thus generally required to smoothen the final electrical power output to avoid the impairment of power quality from the grid point of view [3, 14]. In order to reduce the power ratings of the key components of the PTO for achieving a compact and energy efficient design, the energy storage device is expected to be located directly after the wave energy absorbers. The gas accumulator, which stores the hydraulic energy and fluid by compressing the gas, is currently the most common choice [2, 3, 14].
In this paper, the design optimization of the Hydraulic Energy Storage and Conversion (HESC) system used in the hydraulic PTO system for PA-WECs is presented. The ratings of the HESC system are investigated in order to optimize the system energy efficiency. This paper is organized in the following manner. Section 2 illustrates the structure of the HESC system for PA-WECs and the mathematical models of all the key components are presented. In Section 3, the integration of the HESC system in the WEC is discussed and its performance is illustrated. Design optimization of the HESC system regarding energy efficiency is carried out and system design guidelines are provided in Section 4. Finally, Section 5 draws conclusion.
2 HESC system modelling
2.1 Gas accumulator
The connection interface between the accumulator and the hydraulic system can be described by two variables: the actual flow rate of the fluid entering the accumulator Q a and the fluid pressure at the accumulator inlet p a .
Obtaining υ from (1), the gas temperature can be calculated by (6). Then, gas absolute pressure p g can be obtained by (2).
2.2 Hydraulic motor/pump
Hydraulic motor/pump is an energy conversion device. It converts hydraulic energy to mechanical energy when operating in motor mode, and mechanical energy to hydraulic energy while operating in pump mode. Thus, it has two interfaces: (a) from the hydraulic side where actual flow rate entering the hydraulic motor/pump Q m and pressure difference between the inlet and outlet Δp are required; (b) from the mechanical side where actual torque T m and angular velocity ω are needed.
Swivel angle α0 can be either positive or negative as the hydraulic motor/pump has two operation modes. It is defined in this analysis that the flow rate is positive in motor mode, which corresponds to positive swivel angle.
2.2.1 The volumetric efficiency
2.2.2 The torque efficiency
2.5 Electrical generator
2.6 System integration
To integrate the above main components and form the hydraulic system illustrated in Fig. 1, the following rules should be complied with.
2.6.1 The continuity equation
2.6.2 Pressure balance
2.6.3 The equation of motion
3 System implementation
3.1 Control strategy
It is seen from Fig. 4 that the harvested wave energy has a period around 3 s, which is much longer than the electrical time constant of a generator. Therefore, it is justifiable to state that the hydraulic motor and the electrical generator can be controlled to operate at a constant speed, e.g. the synchronous speed of the generator.
Due to the facts that the system input flow rate varies as the input wave energy fluctuates (31) and the storage capability of the accumulator is limited, the flow rate used to drive the hydraulic motor should be well adjusted to ensure smooth power output. Variable-displacement control of the hydraulic motor, which is achieved by varying the fraction of maximum unit capacity x defined in (10), can be adopted for constant speed drive.
when V reaches its maximum allowable volume Vmax, no more fluid is allowed to flow out of the accumulator and x is set to zero;
when V is below a pre-set value V pre (e.g. 80% of Vmax), x is set to one to enable maximum output;
when V is between V pre and Vmax, x is given by
However, the above control strategy of x may result in overloading of the generator. Therefore, power control should be taken into account as well. A simple proportional-integral (PI) regulator is used to adjust the maximum allowable x, where the rated torque of the generator (or the rated phase current amplitude) is set as the reference. The minimum value of x obtained from storage capacity control and torque/current control is chosen when driving the hydraulic motor.
3.2 System configuration
Gas accumulator parameters 
Mass of Gas
Max. Gas Volume
Mass of Foam
Foam Specific Heat
Thermal Time Const.
Hydraulic motor parameters 
Max. Swivel Angle
Laminar Leakage Coef.
Turbulent Leakage Coef.
Hydrodynamic Loss Coef.
PM Flux Linkage
Rated Power Factor
No. of Phases
Hysteresis Loss Coef.
No. of Poles
Eddy Current Loss Coef.
Viscous friction Coef.
Eight gas accumulators are connected in the HESC system to provide enough storage capability. The mass of gas in the reservoir is 2 kg with a pressure of 0.394 MPa. The total effective pipe length and the equivalent pipe internal diameter are estimated to be 12 m and 0.015 m, respectively. The fluid in the system is oil with the density and kinematic viscosity of 869 kg/m3 and 60×10−6 m2/s, respectively.
3.3 System operation performance
4 Design optimization
The efficiency of the example system shown in Fig. 5 is not very satisfactory. Thus, investigation into the design of the system ratings is carried out in this section to optimize the system energy efficiency.
Figure 6c shows the whole system efficiency at sea state 2, where medium wave condition presents and less energy can be extracted. It can be seen that the optimal D value to achieve best whole system efficiency is reduced to around 60 cm3/rev. This is reasonable since the average wave power is reduced, and a system with power ratings close to the wave power level could provide higher energy efficiency.
Moreover, rather than the HESC system efficiency shown in Fig. 6a, the whole system energy efficiency is dependent on the accumulator storage capacity Vmax. Large Vmax will certainly help to increase the system efficiency as shown in Fig. 6b and c. Furthermore, the generator power rating, which can be considered as the system power rating, will also influence the system efficiency. However, the influence is small as can be seen in Fig. 6a though higher power rating is likely to give slightly higher system efficiency when the system is properly designed.
4.1 Influence of system pressure
Compared with the system efficiency at 21 MPa, the energy efficiency increases from 59.8% to 74.0% for sea state 3, from 71.1% to 82.3% for sea state 2. Furthermore, it can be observed that the system storage capacity has its saturation value of around 300 l at sea state 2; while the system efficiency can still be improved by increasing the storage capacity at sea state 2 when 21 MPa system pressure is applied. Thus, increasing the system pressure will help to increase the system efficiency and reduce the system storage capacity required.
Further increase to the system pressure could be considered to achieve slightly higher energy efficiency, e.g. 76.9% and 83.2% for sea state 2 and 3 respectively at 63 MPa. However, the cost of high-pressure devices increases as the pressure rises. Detailed evaluation is needed to find the optimal system pressure, so that the most economical system solution can be obtained.
In this paper, a HESC system for WECs is introduced and modelled in details. Control strategy is proposed to ensure that all the components are operating properly within their maximum limits. A case study of the HESC system is provided to evaluate the proposed control strategy and the system efficiency by taking the power profile of the WaveStar project as an example. Design investigation of the HESC system is then carried out to optimize the system energy efficiency. It is found that increasing the system pressure will help to increase the system efficiency and reduce the required optimal system storage capacity although the cost of high-pressure components will also increase. The balance between the system cost and payback of extra energy harvest should be carefully evaluated. The analysis carried out in this paper can be used to achieve the optimal system design of the HESC system.
DW carried out the design of the study, developed the system model, performed the system design investigation and optimization, analyzed the data, and drafted the manuscript. KL initialized the problem, coordinated the resources, participated in the design and data analysis, and helped to draft the manuscript. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Muetze, A., & Vining, J. G. (2006). Ocean wave energy conversion - a survey. Industry Applications Conference - 41st IAS Annual Meeting, 3, 1410–1417.Google Scholar
- Drew, B., Plummer, A. R., & Sahinkaya, M. N. (2009). A review of wave energy converter technology. Proc of The Institution of Mechanical Engineers, Part A-journal of Power and Energy, 223(8), 887–902.View ArticleGoogle Scholar
- Falcao, A. F. de O. (2010). Wave energy utilization: A review of the technologies. Renew Sust Energ Rev, 14(3), 899–918.Google Scholar
- Dorrell, D. G., Halliday, J. R., Miller, P., & Findlater, M. (Sep. 2004). “Review of wave energy resource and oscillating water column modelling,” 39th international universities power Eng Conf (Vol. 1, pp. 649–653).Google Scholar
- Kofoed, J. P., Frigaard, P., Friis-Madsen, E., & Sorensen, H. C. (2006). Prototype testing of the wave energy converter wave dragon. Renew Energy, 31, 181–189.View ArticleGoogle Scholar
- Vicinanza, D., Margheritini, L., Kofoed, J. P., & Buccino, M. (2012). The SSG wave energy converter: Performance, status and recent developments. Energies, 5(2), 193–226.View ArticleGoogle Scholar
- Polinder, H., Damen, M., & Gardner, F. (Sept. 2004). Linear PM generator system for wave energy conversion in the AWS. IEEE Transactions on Energy Conversion, 19(3), 583–589.View ArticleGoogle Scholar
- Hansen, R. H., Andersen, T. O., & Pedersen, H. C. (2011). Model based Design of Efficient Power Take-off Systems for wave energy converters. The Twelfth Scandinavian International Conference on Fluid Power, 2, 35–49.Google Scholar
- Tedeschi, E., Carraro, M., Molinas, M., & Mattavelli, P. (2011). Effect of control strategies and power take-off efficiency on the power capture from sea waves. IEEE Transactions on Energy Conversion, 26(4), 1088–1098.View ArticleGoogle Scholar
- Holm, R. K., Berg, N. I., Walkusch, M., Rasmussen, P. O., & Hansen, R. H. (2013). Design of a magnetic lead screw for wave energy conversion. IEEE Transactions on Industry Applications, 49(6), 2699–2708.Google Scholar
- Wave Star A/S. http://www.wavestarenergy.com.
- AWS Ocean Energy Ltd. http://www.awsocean.com.
- Weinstein, A., Fredrikson, G., Parks, M. J., & Nielsen, K. (2004). AquaBuOY - the offshore wave energy converter numerical modeling and optimization. Proceedings of MTTS/IEEE Techno-Ocean’04, 4, 1854–1859.Google Scholar
- Sabzehgar, R., & Moallem, M. (2009). A review of ocean wave energy conversion systems. Proceedings IEEE Electrical Power Energy Conference (EPEC),1, pp. 1–6.Google Scholar
- Pourmovahed, A., Beachley, N. H., & Fronczak, F. J. (Mar. 1992). Modeling of a hydraulic energy regeneration system – Part I: Analytical treatment. J Dyn Syst Meas Control, 114, 155–159.View ArticleMATHGoogle Scholar
- White, F. M. (2009). Fluid Mechanics (7th ed.p. 827). New York: McGraw Hill.Google Scholar
- Pourmovahed, A., Beachley, N. H., & Fronczak, F. J. (Mar. 1992). Modeling of a hydraulic energy regeneration system – Part II: Experimental program. J Dyn Syst Meas Control, 114, 160–165.View ArticleMATHGoogle Scholar