# Design optimization of hydraulic energy storage and conversion system for wave energy converters

- Dong Wang
^{1}Email authorView ORCID ID profile and - Kaiyuan Lu
^{1}

**3**:7

https://doi.org/10.1186/s41601-018-0080-6

© The Author(s) 2018

**Received: **28 September 2017

**Accepted: **31 January 2018

**Published: **12 March 2018

## Abstract

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.

## Keywords

## 1 Introduction

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 [1]. The turbine-type WECs, including Oscillating Water Column (OWC) WEC [4] 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 [7]) or floating (on the surface) absorber [8–10] to capture the wave energy. The PA-WECs are considered to be more environmental friendly [1] 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 [3]. The electric PTOs, including linear generator [7, 10] and rotary generator with gearbox [9], 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 [13] or a hydraulic motor [8] 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 [2]. 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
}.

*Q*

_{ a }is equal to the compression rate of the gas in the accumulator

*t*is the time,

*m*

_{ g }is the gas mass, and

*υ*is the gas specific volume. The gas specific volume can be calculated by integrating both sides of (1) if the initial gas specific volume

*υ*

_{0}is known.

*p*

_{ a }is determined by the gas absolute pressure

*p*

_{ g }and the pressure difference between them. The gas absolute pressure

*p*

_{ g }can be calculated according to the Benedict-Webb-Rubin (BWR) equation of state as

*A*

_{0},

*B*

_{0},

*C*

_{0},

*a*,

*b*,

*c*,

*α*, and

*γ*are constants in BWR equation, and

*T*is the gas temperature. In this analysis, nitrogen is considered.

*T*varies during the compression and expansion process and it will cause irreversible heat transfer, i.e. from gas to accumulator wall and eventually to the outside environment. Elastomeric foam with appropriate properties is inserted to perform as “heat sink” and the thermal loss can be reduced significantly. Since the foam has large contacting surface with gas and very small wall thickness, it is appropriate to assume that the foam and gas are at the same temperature

*T*all the time [15]. Thus, the gas energy equation can be written based on the energy balance principle as

*u*is the gas internal energy per unit mass,

*V*is the gas volume,

*m*

_{ f }is the foam mass,

*c*

_{ f }is the specific heat of foam,

*h*is the heat transfer coefficient,

*A*

_{ w }is the effective heat convection area of the accumulator, and

*T*

_{ w }is the accumulator wall temperature. For a real gas,

*u*can be described as

*c*

_{ υ }is the constant-volume specific heat of gas. It should be noted that

*c*

_{ υ }is gas temperature

*T*and specific volume

*υ*dependent

*C*

_{0},

*c*, and

*γ*are constants in BWR equation, and \( {c}_{\upsilon}^0 \) is the constant-volume specific heat for ideal gas. Generally, \( {c}_{\upsilon}^0 \) also varies with the gas temperature

*T*. However, for nitrogen used in this analysis, the change is so small during the normal working temperature range and constant \( {c}_{\upsilon}^0 \) can be used.

Obtaining *υ* from (1), the gas temperature can be calculated by (6). Then, gas absolute pressure *p*_{
g
} can be obtained by (2).

*p*

_{ a }and

*p*

_{ g }is the pressure loss caused by the friction, e.g. flow entrance effects, viscous shear, etc. Detailed modelling of friction loss is possible but its magnitude does not justify the complexity it brings into the analysis. To simplify the model, the pressure loss (as percentage of the fluid pressure

*p*

_{ a }at accumulator inlet) is assumed to be half of the friction loss (as percentage of input

*L*

_{ f }/

*E*), as

*L*

_{ f }is the accumulator friction loss in one cycle,

*E*is the energy input to the accumulator in one cycle, and

*k*is a factor introduced to avoid pressure jump when flow direction changes. A simple linear variation of

*k*when flow direction changes is illustrated in Fig. 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 Δ*p* are required; (b) from the mechanical side where actual torque *T*_{
m
} and angular velocity *ω* are needed.

*D*is the maximum motor/pump displacement per radian,

*ω*is the angular velocity, and

*x*is the fraction of maximum unit capacity. It is known that

*x*is related to the swivel angle

*α*

_{0}of the hydraulic motor/pump as [http://www.insanehydraulics.com/library/files/Hydraulic-Trainings-for-Axial-Piston-Units.pdf].

Swivel angle *α*_{0} 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

*Q*

_{ m }in motor mode, due to leakage, cavitation, and fluid compressibility. By neglecting the cavitation loss, which is small for modern hydraulic motor, the volumetric efficiency can be calculated as [15].

*C*

_{ s }and

*C*

_{ st }are the laminar and turbulent leakage coefficients respectively, and

*β*is the fluid bulk modulus of elasticity (1660 MPa for most hydraulic fluid).

*S*and

*σ*are given as.

*μ*is the fluid viscosity, and

*ρ*is the fluid density.

#### 2.2.2 The torque efficiency

*C*

_{ υ },

*C*

_{ f }and

*C*

_{ h }are the viscous, frictional, and hydrodynamic loss coefficients, respectively. Then, the actual torque

*T*

_{ m }provided by the hydraulic motor can be found, which is used to drive the electric generator.

### 2.3 Reservoir

*p*

_{ r }and

*V*

_{ r }are the gas pressure and volume in the reservoir respectively, and

*n*is heat capacity ratio. For a diatomic gas, such as nitrogen,

*n*= 1.4 [16].

### 2.4 Pipeline

*p*

_{ p }can be estimated by summing the “equivalent pipe length” of all elements

*f*is the friction coefficient,

*L*

_{ p }is the total effective pipe length,

*D*

_{ p }and

*A*

_{ p }are the equivalent pipe internal diameter and cross-sectional area respectively, and

*Q*

_{ p }is the flow through the pipelines.

*f*is related to the fluid velocity through the pipelines. When the fluid velocity is high enough, the flow in the pipelines becomes turbulent flow instead of laminar flow. Reynolds number is used to judge the flow type

*v*is the fluid kinematic viscosity. For laminar flow

### 2.5 Electrical generator

*T*

_{ e }is the machine electromagnetic torque,

*n*

_{ ph }is the number of phases,

*p*is the number of pole-pairs,

*λ*

_{ pm }is the flux linkage from the permanent magnets,

*I*

_{ s }is the machine current amplitude, and

*φ*

_{ i }is the internal power factor angle (angle between current and internal voltage).

*φ*

_{ i }

*=*1. Thus,

*I*

_{ s }can be obtained according to (22) for certain

*T*

_{ e }. Then, the machine copper loss can be calculated as

*R*

_{ s }is the machine phase resistance.

*n*

_{ r }, the corresponding machine electrical frequency

*f*

_{ s }can be calculated as

*f*

_{ s }and \( {f}_s^2 \), respectively. Then, the generator energy efficiency can be calculated as

*B*

_{ m }is the machine viscous friction coefficient,

*C*

_{ hys }and

*C*

_{ edy }are the hysteresis and eddy current loss coefficients, respectively.

### 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

*Q*

_{ e }is equal to the sum of the actual flow rates entering the accumulator

*Q*

_{ a }and the hydraulic motor

*Q*

_{ m }

*Q*

_{ e }is equal to the system input flow rate

*Q*

_{ in }when relief valve is not activating

#### 2.6.2 Pressure balance

#### 2.6.3 The equation of motion

*J*is the total moment of inertia of the rotary parts of the hydraulic motor and electrical generator.

## 3 System implementation

*P*

_{ in }, the system input flow rate can be calculated as

*p*

_{ a }is the accumulator inlet pressure.

### 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.

*V*. The control strategy of

*x*could be:

- (a)
when

*V*reaches its maximum allowable volume*V*_{max}, no more fluid is allowed to flow out of the accumulator and*x*is set to zero; - (b)
when

*V*is below a pre-set value*V*_{ pre }(e.g. 80% of*V*_{max}),*x*is set to one to enable maximum output; - (c)
when

*V*is between*V*_{ pre }and*V*_{max},*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 [17]

Mass of Gas | 1.213 kg | Max. Gas Volume | 15.271×10 |

Mass of Foam | 1.496 kg | Foam Specific Heat | 2300 J/kg·K |

Friction Loss | 4% | Gas Constant | 8.31446 J/K/mol |

Max. Pressure | 21 MPa | Thermal Time Const. | 300 s |

Hydraulic motor parameters [17]

Displacement | 107 cm | Max. Swivel Angle | 25 deg |

Friction Coef. | 0.0048 | Laminar Leakage Coef. | 1.042×10 |

Viscous Coef. | 153,407 | Turbulent Leakage Coef. | 1.20×10 |

– | – | Hydrodynamic Loss Coef. | 0 |

Generator parameters

Rated Power | 35 kW | Phase Resistance | 0.1625 Ω |

Rated Voltage | 380 V | PM Flux Linkage | 1.035 Wb·t |

Rated Current | 54.26 A | Rated Efficiency | 93.5% |

Rated speed | 1500 rpm | Rated Power Factor | 0.98 |

No. of Phases | 3 | Hysteresis Loss Coef. | 9.4893 |

No. of Poles | 4 | Eddy Current Loss Coef. | 0.1898 |

Rotor Inertia | 0.0885 kg·m | Viscous friction Coef. | 0.0020 |

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/m^{3} and 60×10^{−6} m^{2}/s, respectively.

### 3.3 System operation performance

*x*of the hydraulic motor is one to maximize its output. Due to the surge input, the output power of the hydraulic motor increases as the system pressure increases. Thus,

*x*is adjusted by the controller to limit the hydraulic motor shaft output, so that the generator will not exceed its rated value. It can be seen that the energy efficiency of the HESC system itself is around 61.7%. While for the whole system, where the overflow is considered as loss, the energy efficiency is about 53.2%.

## 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.

*D*decreases in a wide range (40 to 120 cm

^{3}/rev). However, the maximum accumulator gas volume

*V*

_{max}(storage capacity) has limited influence on the HESC system efficiency. This is because that the energy overflow is not considered as losses of the HESC system, since it could be handled by another HESC system as shown in Fig. 3b. However, such assumption will result in unreasonable small system capacity, since small

*D*means small torque (13). Thus, the whole system efficiency should be taken into account when performing design optimization. It can be seen in Fig. 6b that there is an optimal

*D*value (around 100 cm

^{3}/rev), which can provide higher whole system 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 cm^{3}/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 *V*_{max}. Large *V*_{max} 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

*D*can help to increase the HESC system efficiency. However, small

*D*will reduce the system power rating (13), and the whole system efficiency is decreased due to large amount of energy overflow. A straightforward way is to increase the system pressure. According to (13),

*D*can be halved when Δ

*p*is doubled. Fig. 7 shows the whole system energy efficiency when the system pressure is 42 MPa. It can be seen that the whole system efficiency for both sea state 2 and 3 can be balanced when

*D*is around 50 cm

^{3}/rev, which is about half of the original

*D*in Table 2.

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.

## 5 Conclusion

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.

## Declarations

### Authors’ contributions

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.

### Competing interests

The authors declare that they have no competing interests.

**Open Access**This 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.

## Authors’ Affiliations

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