Energy Storage Systems

Transcription

1 Energy Storage Systems Dong Wang, Kaiyuan Lu Department of Energy Technology, Aalborg University Deliverable D3.1

2 Report on Energy Storage systems by Dong Wang, Kaiyuan Lu Department of Energy Technology, Aalborg University August 213 Aalborg University

3 1. Introduction The research project Structural Design of Wave Energy Devices (SDWED) focuses on the development of design tools and a common design basis for wave energy devices. It aims at develop a complete wave-to-wire model, which may effectively lead to: improve the design of wave energy devices, analyse the interaction between different Wave Energy Converter (WEC) components, optimize the performance of individual components as well as the system performance, and eventually, reduce the cost and increase the reliability of wave energy devices, to make it more competitive, securing commercialization prospective. In the work package (WP) 3, the generator and energy storage systems for WECs are investigated. The scope of WP 3 is not to develop new components and simulation technologies for the application in WECs but rather to identify and compare the existing systems. This report covers energy storage systems for wave energy applications. Like the wind, wave generates oscillating energy which is captured by the WEC. For a grid-connected WEC, large power fluctuation brings significant challenges in the area of determination of rated operating power levels for different WEC components, system efficiency optimization and power quality improvement. An energy storage system may transfer and store peak energy waves into a separate device and often in another energy form. This energy will be recovered when the energy production of a WEC is low. As a result, the power to be delivered to the grid will be smoothed with the aid of an energy storage system, and eventually, it may help to achieve a more reasonably sized WEC with improved efficiency and power quality. The main goal of this report is to clarify important aspects when applying energy storage devices in WEC. Different topologies for how an energy storage system may be integrated into WEC will be introduced, followed by an introduction to different energy storage technologies that are available today. A case study and design example of an energy storage system for application in WEC will be given. 1

4 2. Overview of various energy storage techniques 2.1 Introduction to energy storage system for WEC An energy storage system stores the energy generated by waves that exceeds the output demand at specific moments. The stored energy is able to be recovered in opposite situations, to smooth the energy that is delivered to the grid/load. The energy storage is meant to satisfy short-term storage requirements, and the energy to be stored may be converted to different, e.g., chemical, electrical or mechanical energy forms. The wave energy captured by WEC fluctuates continuously at a period of e.g. 2 ~ 1 seconds. Normally, the wave climates for a given site are represented by different sea states, which are characterized by the significant wave height H s and its corresponding peak period T p [21]. Example sea states are given in Fig. 1(a). The power delivered to the grid will fluctuate in corresponding to the wave fluctuation and more severely, the magnitudes of the instantaneous peak power and the average power generated may be significantly different. For example, a power profile at seat state 3 for the WaveStar WEC is shown in Fig. 1(b). [1]. (a) (b) Fig. 1. Example sea states (a) [21], and power profile for a particular seat state 3 for the WaveStar WEC (b) [1]. Fluctuation in the power may harm the stability of the grid. Besides this, power fluctuation brings great challenges in the determination of reasonable power ratings for different WEC components and may also result in low system efficiency. For example, when selecting the generator and power converter ratings for the power profile shown in Fig. 1, it is easy to find that if the generator and power converter are rated near the peak power operating points, there will be a huge economic waste using a 5 kw generator system to deliver 45 kw average power only. But if the power ratings are chosen to be close to the average power, it will require large overloading capacity for the generator and the power converter, which might be very difficult to achieve. This is explained in detail below. For generators, the overloading capacity is limited by the excessive losses, the corresponding temperature rise, and saturation effects. Increased machine current for producing the extra power when overloaded will increase the machine losses, and cause the machine temperature to rise. An electrical machine normally has a thermal time constant of the order of minutes [2]. Therefore overloading the machine for a short period will not bring significant temperature change and this may be tolerated. But it should also be aware of that, the torque increase due to increased machine current is limited by saturation. When the machine iron is deeply saturated, further increase in the 2

5 current will bring negligible torque increase only. Therefore, in order to utilize the overloading capacity in a large range, the machine needs to be designed with more iron and the rated electromagnetic operating point should be kept far below the saturation point. This increases the machine size and cost. Compared to generators, power electronics converters have very limited overloading capacity. It has much shorter time constant compared to electrical machines, of the order of hundreds of milliseconds [2]. On the other hand, to secure the reliability of power electronics converters, they should be operated under constant temperature environment, i.e. to avoid frequent thermal cycling. All these features would require the power converters to be rated at its maximum working point. Besides the challenges in rating the WEC components, fluctuation in wave power will also tend to reduce the system efficiency. Modern electrical machines are often coupled with variable speed drives, which allow maximizing the performance (e.g. efficiency) at different operating speeds and output power levels. However, working below the rated power will always tend to decrease the machine efficiency. The efficiency of the power converter will also be reduced at light load operation conditions. As an example, the electrical and electronics (generator + power converters) units will exhibit a typical efficiency vs. loading percentage curve as shown in Fig. 2 [3]. It could be observed that, the power transfer could achieve good efficiency at rated operating point (1% load). But when the load is less than 5% of the rated load, the power transfer efficiency decreases rapidly, resulting in very low efficiency at light load. As discussed above, the power converter is desired to be rated at its maximum power operating point. For fluctuation power profiles with large difference between the peak power and the average power, the inverter will work mostly at light load situations, and result in very low efficiency. Fig. 2. Efficiency of electrical power transfer vs. loading percentage curve [3]. Based on all the challenges brought by fluctuation power generation of the wave, it is highly recommended to add an energy storage device to the WEC system. With the aid of an energy storage device, peak power may be temporarily stored, instead of being transferred directly to the grid. When the power generated is low, the stored energy may then be recovered, with an attempt to keep the output power to follow the average power and reduce the power fluctuation. This will help the determination of the rated operation points of the generator and the power converters, and will increase the system efficiency by e.g. avoiding working in light load situations especially for the power converters. 2.2 Connecting an energy storage system to the WEC Various energy storage techniques are available today. They are e.g. typically hydraulic energy storage system, battery, flywheel, and supercapacitor, etc. But to choose which energy storage device to use not only depends on the energy storage method itself, but also highly depends on how the chosen energy storage device may be integrated into the existing WEC system. In general, there are two possible ways to introduce an energy storage device to a WEC system. The first approach is to add an energy storage system before the generator, as illustrated principally in Fig. 3. Such a topology has already been adopted in the existing Pelamis WEC [4]-[6]. 3

6 Wave Energy storage G Grid Fig. 3. Adding the energy storage device in series to the WEC system. In such a configuration, all the wave energy converted to the electrical energy will be provided by the energy storage unit. Smooth energy will be available at the input shaft of the generator. Therefore, greatly reduced power fluctuation is achieved, which makes the determination of the power ratings for the generator and power converters a lot easier and the electrical system could be designed more efficiently. But the disadvantage of such a system is also obvious the energy storage device needs to be designed to its full scale. The previous mentioned problems caused by fluctuating power to the generator and power converters are now imposed on the energy storage device, which need to be carefully treated with. Another possibility is to connect the energy storage device in parallel to the WEC system, as illustrated in Fig. 4, e.g. through the DC-link capacitor. Wave G Grid Energy storage Fig. 4. Adding the energy storage device in parallel to the WEC system. The generator has normally good overloading capacity. Besides this, power saturation control may be adopted to reduce the power rating and input power fluctuation at the generator side. This is because the input peak wave power is much larger than the average wave power. By limiting the peak power to be captured by the PTO system (i.e. saturating the instantaneous peak power), the available average power will only be slightly reduced [3]. But this helps effectively to lower the ratings for the generator and especially, for the power converters. Limiting the instantaneous power may be realized by e.g. conveniently reducing the PTO applied force [3]. When the energy storage unit is connected in parallel to the WEC system, through e.g. the DC-link capacitor as shown in Fig. 4, it can effectively smooth the power to be transferred to the gird. When the generated power is higher than the average power, the excessive power may be stored in the energy storage device through the parallel path connected to the DC-link capacitor. When the generated power is lower than the average power, the energy storage device may then return the stored energy back to the grid. In such a way, the power rating for the grid-side converter could be greatly reduced and the power transferred to the grid is smoothed with the aid of the energy storage device. The parallel connected energy storage system handles part of the total power only. This reduces the size and cost for the energy storage system compared to the full-scale energy storage system as principally illustrated in Fig. 3. 4

7 2.3 Various energy storage systems a brief introduction To store the energy, the original energy form may need to be converted into another form. An energy storage system must contain an energy conversion unit, to convert / recover the energy, and an energy storage device, for storing the energy for a desired period. For example, when using batteries, the energy is stored in batteries in a chemical form, and this energy may be converted from or recovered to electrical energy by using DC/DC converters. When considering adding an energy storage system before the generator as shown in Fig. 3, a good candidate system could be the hydraulic energy storage system. The hydraulic energy storage system converts the input mechanical energy into the pressure of hydraulic fluid and is contained in accumulators. When the energy needs to be restored, the pressure is then released, driving e.g. a hydraulic motor and the energy is recovered in a mechanical form. Hydraulic energy storage system is a widely used energy storage system today. In section 3, design and application of hydraulic energy storage systems in wave applications are given in detail. The interface to a hydraulic energy storage system is often mechanical. But if, considering the topology shown in Fig. 4, when using the DC-link capacitor to connect the external energy storage system, many other different energy storage systems could be conveniently adopted. The DC-link capacitor behaviours like a nearly constant voltage source, which may be used to drive an electrical machine to convert the energy to e.g. kinetic energy stored in a rotating mass, as illustrated in Fig. 5. This is the well-known flywheel energy storage system [7]. The reported largest flywheel energy storage system has already reached 1.6 MVA, weighing about 1 Kg in real applications [8]. For achieving high energy density, the flywheel often needs to rotate at very high speed. This requirement increases the structure design complexity (need to use e.g. magnetic bearings, etc.) and the system cost. Similar to the flywheel system topology, the compressed air energy storage system is another possibility. The energy taken from the DC-link capacitor may be used to drive an air motor to compress the air and store the energy, as shown in Fig. 6 [9]. Storing the energy by compressing the air has some similarities to the hydraulic energy storage method. But in this case, there is no need to use a non-compressible hydraulic fluid. The air can be simply taken from or released to the surroundings, and there is no need to employ a reservoir to contain pressure-released air. However, a significant drawback of compressed air energy storage system is the low efficiency of the air motor. The peak efficiency could be lower than 2% as reported in [9]. Therefore, use of another energy storage device (e.g. supercapacitor) to optimize the overall energy storage system efficiency might be necessary [9]. Fig. 5 A flywheel energy storage system [7]. Fig. 6 An example compressed air energy storage system [9]. 5

8 The above mentioned two energy storage systems require an electrical machine to be connected to the DC-link capacitor, in order to be able to convert the energy from the DC-link to the energy storage device. A simpler structure could be to connect a DC/DC converter (instead of an electrical machine) to the DC-link capacitor and store the energy in devices that are controlled by dc voltages directly like the battery and supercapacitor. The connection is illustrated in Fig. 6 (the rightbottom corner). Such a system could be the simplest in structure among many different energy storage systems. Compared to the battery, the supercapacitor has many advantages with respect to power density, charging / discharging cycles and efficiency. It has become extensively studied in recent years for many applications that require energy storage devices [1]-[12]. A more detailed discussion about the performances of battery and supercapacitor may be found in the first symposium report [13] for this project. As an interesting candidate, using supercapacitor and DC/DC converters for energy storage might be worth to study. 6

9 3. Hydraulic energy storage system 3.1 Mathematical modelling of hydraulic energy storage system This section starts with an introduction of the system topology, components functions and their mathematical descriptions. Based on these, a complete mathematical model is then established. A hydraulic energy storage system typically consists of hydraulic accumulator, hydraulic pump/motor, reservoir, connecting lines and controller. The schematic diagram of such a system may be illustrated in Fig. 7. [14]. In most hydraulic systems, the hydraulic fluid used is oil. Therefore, oil is used to represent hydraulic fluid hereafter. Accumulator Gas Shaft Connecting line Control signal Oil Hydraulic input / output Controller Pump/ Motor Mechanical input / output Reservoir Hydraulic energy storage system Fig. 7 Schematic diagram of the hydraulic energy storage system. The hydraulic energy storage system shown in Fig. 7 is a very good example to start with. In this topology, the hydraulic input is used to pre-charge the accumulator to a certain level of system pressure only and the mechanical input/output is connected to a flywheel, which is a mechanical energy storage device. In such a way, flywheel can consume and generate energy from/to the hydraulic energy storage system, simulating energy cycles that will occur in real applications of energy storage systems. Due to the losses, the speed of the flywheel will decrease with respect to the time. In such a way, the performance of the energy storage system at different working points may be studied. Experimental results of such a hydraulic energy storage/regeneration system were presented in [15], which gives a solid base for validating the model developed in this project. Mathematical descriptions of the system main units in [14] are taken as the main reference to construct the system model, system data and test results in [15] are used afterwards to verify the model established in Simulink. 7

10 3.1.1 Accumulator A hydraulic accumulator can store hydraulic energy through compression of the gas in the accumulator. In a hydraulic system, accumulator can absorb surplus hydraulic fluid (oil). Oil level in the accumulator rises and gas in the accumulator is therefore compressed. The system pressure keeps increasing until it reaches the pre-determined maximum pressure. Then the relief valve is triggered to prevent surplus hydraulic fluid from entering the accumulator. The stored oil may be consumed later when the source input is reduced. To integrate the accumulator into the hydraulic system, two parameters are needed, which are the actual flow rate of oil entering the accumulator ( Q a ) and oil pressure at the accumulator inlet ( p ). Inlet oil pressure p can be calculated by knowing the accumulator data, its initial conditions and actual flow rate Q a. The mathematical model is described below. When there is oil flowing in/out, the gas in the accumulator will be compressed/expanded. The actual flow rate of oil entering the accumulator Q a is equal to the rate of compression of the accumulator gas, d Qa mg (1) dt where t is time, m g is gas mass, and is gas specific volume. Equation (1) can be integrated to predict the gas specific volume when knowing the initial gas specific volume and actual flow rate Q a. Gas temperature 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. Such thermal loss can be as high as 4 percent of the input energy. But it can be substantially reduced by inserting elastomeric foam with appropriate characters [14]. As the foam has large contact surface with gas and very small wall thickness, it is appropriate to assume foam and gas have the same temperature all the time. Thus the gas energy equation can be written as following based on the energy balance principle: du dv dt mg pg m f c f haw T Tw (2) dt dt dt where t is the time, mg is the gas mass, pg is the gas absolute pressure, 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, T is the absolute gas or foam temperature, h is the heat transfer coefficient, Aw is the effective area of the accumulator for heat convection, and Tw is the accumulator wall temperature. The left side of (2) represents the change of gas internal energy. On the right side of (2), the first item represents gas expansion work; the second item represents heat absorption of foam, and the third item represents heat transfer to the accumulator wall. The internal energy per unit mass u for real gas, is given by: 8

11 pg du c dt T pg d (3) T where c is the constant-volume specific heat of gas, and is the gas specific volume. The gas pressure p g can be calculated by the Benedict-Webb-Rubin (BWR) equation of state, which takes gas temperature T and specific volume as inputs, p g e T B RT A C T brt a a C RT (4) where A, B, C, a,b, c,, and are constants in BWR equation [16]. In this analysis, nitrogen is injected into the accumulator. Combining (2), (3) and (4), it yields m c f f dt Tw T 1 RT b C c d B RT e mgc dt c T T (5) dt with a thermal time constant of m c g (6) haw Equation (5) is the energy equation for the gas and may be integrated to predict the gas temperature. Then (4) can be used to predict the gas pressure. For a foam-filled accumulator, the thermal time constant is in an order of several minutes [14]. For real gas, constant-volume specific heat of gas c varies with both gas temperature T and gas specific volume, as 2 6 C c 3c 2 1 c c e (7) T T where C, c, and are constants in BWR equation, and c is the constant-volume specific heat for ideal gas. c varies with gas temperature T as well. But for nitrogen, the change is so small during the normal working temperature range [18] and it may be assumed to be constant. Its value at 2 C and 1 atm may be used, which is.743 kj/kg K. When there is oil flowing in/out, friction loss is created by flow entrance effects, viscous shear, etc. This loss causes the pressure difference between gas pressure p g in the accumulator and oil pressure p at accumulator inlet. 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 percent of oil pressure p at accumulator inlet) is assumed to be half of the friction loss (as percent of energy input E ), as pg p k Lf sgndv (8) p 2 E 9

12 1 oil outflow sgndv (9) 1 oil inflow where V is the gas volume, Lf is the accumulator friction loss in one cycle, E is the energy input to accumulator in one cycle, and k is a factor introduced to avoid pressure jump when flow changes its direction. In this analysis, friction loss of the accumulator is set to be 4 percent of the input energy, and then the pressure drop due to friction is 2 percent of oil pressure at accumulator inlet. Such simplification brings a problem when oil flow changes its direction: the pressure drop changes its sign accordingly, and a pressure jump at accumulator inlet occurs when gas pressure changes continuously. In order to avoid the pressure jump, which doesn t exist in real applications, the factor k is introduced to smooth the pressure drop as shown in Fig. 8. sgn dv 1 sgndv k dv ( Q ) a -1 Fig. 8 Illustration of pressure drop coefficient Hydraulic pump/motor Hydraulic pump/motor is an energy conversion device. It can convert mechanical energy to hydraulic energy when operating in pump mode; and convert hydraulic energy to mechanical energy when operating in motor mode. To integrate the pump/motor into the hydraulic system, both hydraulic and mechanical parameters are required. From the hydraulic side, interface parameters are the actual rate of flow leaving the hydraulic pump/motor Q and pressure differential p ; from the mechanical side, actual torque pm T pm and angular velocity are needed. The mathematical descriptions for modelling variabledisplacement piston, gear, or vane pump are summarized in the followings. The volumetric efficiency of a pump The ideal flow rate of oil through a hydraulic pump/motor can be calculated by, xd (1) Q i where x is the fraction of maximum unit capacity, is the angular velocity, and D is the maximum pump/motor displacement per radian. x is related to the swivel angle [17] by, sin sin x (11),max where, max is the maximum swivel angle of the hydraulic pump/motor. 1

13 Swivel angle of hydraulic pump/motor can be either positive or negative as it has two operation modes. As Q pm is defined to be the actual rate of flow leaving the hydraulic pump/motor swivel angle is defined to be positive in pump mode to obtain a positive Q i. Due to leakage, cavitation, and fluid compressibility, the ideal flow rate is always higher than the actual flow rate in pump mode. Pump volumetric efficiency is defined to be, Qpm (12) Q i By neglecting the cavitation loss, which is small for modern oil pump, pump volumetric efficiency may be calculated by, where Cs and Cs p Cst 1 (13) xs x Cst are the laminar and turbulent leakage coefficients respectively, p is pump/motor pressure differential (always > ), and is the fluid bulk modulus of elasticity (166 MPa for most hydraulic fluid). S and are given by, S p (14) 1 3 D (15) 2 p 1 2 where is the oil viscosity, is the oil density, is the angular velocity, and D is the maximum pump/motor displacement per radian. The torque efficiency of a pump The torque required to drive an ideal pump is, T i x p D (16) A larger torque is needed in the real situation as friction loss and other types of losses always exist. Pump torque efficiency is defined to be the ratio of ideal torque T i and actual torque T pm, T i t (17) Tpm Pump torque efficiency can also be calculated by counting all the losses, where C, C and f 1 t C C S f 1 x x 2 2 C x h C h are the viscous, frictional, and hydrodynamic loss coefficients, respectively. (18) By following the same idea, the equations for motor mode are: 11

14 Q i (19) Qpm 1 Cs x S 1 p Cst x (2) Tpm t (21) T C S C t x x x i f Ch (22) x is negative for motor mode. Therefore, absolute value of x is used in (2) and (22). By comparing (13) vs. (2) and (18) vs. (22), the following relationships may be found:, motor 1 2 (23), pump t, motor 1 2 (24) t, pump Reservoir A reservoir works as tank in hydraulic system, which provides a slightly higher pressure than the minimum intake pressure of hydraulic pump/motor. A low-pressure accumulator with a relatively large volume often serves this purpose. Therefore, the relative volume change of the gas (usually nitrogen) is limited to a certain range during the operation, which means the change of gas pressure and temperature are limited. The thermodynamic process can be assumed to be quasi-static and the gas can be treated as ideal without sacrificing accuracy. Actual flow rate of oil leaving the reservoir Q r and oil pressure at the reservoir inlet p are the interface parameters in order to integrate the reservoir into the hydraulic system. As discussed above, the thermodynamic process is quasi-static, then friction loss on pressure can be neglected and oil pressure p res at reservoir inlet is equal to gas pressure p g in the reservoir. Mathematical model of the gas thermodynamic process in reservoir is described by Polytrophic relationship [19], n pg V const. with n 1.4 (25) Connecting lines Connecting lines are used to connect the main units, such as accumulator, pump/motor, and reservoir, to form a whole hydraulic system. 12

15 Connecting lines include pipes, hoses, unions, fitting, bends, valves, etc.. All the connecting elements have similar characteristics regarding pressure loss, which is proportional to the square of actual flow rate through the element. Thus, the total pressure drop in the connecting lines can be estimated by summing the equivalent hose length of all elements. Interface parameters of connecting lines are actual flow rate Q l and pressure drop pl mathematical description is given by,, and the 2 L Ql pl f 2 (26) D 2 A where f is the friction coefficient, is oil density, L is the total effective hose length of connecting lines, D is hose internal diameter, and A is hose internal cross-sectional area. The friction coefficient f is related to the fluid velocity through the hydraulic lines. When the fluid velocity is too high, the flow in the connecting lines becomes turbulent flow instead of laminar flow. Reynolds number is used to judge the flow type, and it is given by, where v is the oil kinematic viscosity. For laminar flow, the friction coefficient is given by, For turbulent flow, the friction coefficient is given by, 4 Q Re l (27) D v f 64 Re, Re 2 (28) 1 4 f.332 Re, 2 Re 1 (29) System integration When the above discussed main units are connected for forming a hydraulic energy storage/regeneration system, the following equations must be satisfied: (a). The continuity equation. There are two aspects to be considered. Firstly, the actual flow rate entering the accumulator is equal to the sum of the actual flow rate from the hydraulic input to accumulator and the actual flow rate from the pump/motor to the accumulator. For the hydraulic energy storage/regeneration system, there is no hydraulic input during the operation process, the relationship is described as: Q a Q Q Q (3) pm l Secondly, the actual flow rate entering the accumulator is equal to the rate of compression of the gas in accumulator as given in (1). The same consideration applies to the reservoir. (b). Pressure balance. Pump/motor pressure differential can be calculated by applying the pressure balance equation to the hydraulic system by, r L p p p res sgn p (31) 13

16 where 1 pump mode sgn (32) 1 motor mode Pump/motor swivel angle is defined to be positive in pump mode as discussed before. The above equations are used to describe the relationships between the main units in the hydraulic energy storage/regeneration system. However, the interfaces among the hydraulic energy storage system and external hydraulic and mechanical systems should also follow the equations described below: (a). The continuity equation. This relationship should be followed by the interface between hydraulic energy storage system and external hydraulic input/output, and has been considered already when building the hydraulic energy storage system. (b). The equation of motion. This relationship describes the interface between hydraulic energy storage system and external mechanical input/output, dn T f Tpm (33) dt 2 I where N is shaft speed, I is total inertia of rotary parts of pump/motor and mechanical input/output, T is torque loss of mechanical input/output which is always negative, and f Tpm is the actual torque of hydraulic pump/motor which is positive in pump mode as defined in (16) System control Controller is used to control the operation of hydraulic pump/motor, including the operation mode (pump or motor) and the swivel angle if variable-displacement pump/motor is applied. As mentioned at the beginning of section 3.1, for system verification purpose, a hydraulic energy regeneration system is built based on the hydraulic energy storage system by pre-charging the accumulator and using flywheel as the mechanical input/output. The potential energy of compressed gas in accumulator is converted to kinetic energy in the flywheel when hydraulic pump/motor operates in motor mode, and flywheel kinetic energy is converted back to the accumulator potential energy by switching the pump/motor to the pump mode. The switching of pump/motor operation mode is controlled by the controller by using the following strategy: (a). Switch to motor mode by setting pump/motor swivel angle to negative value when pump/motor shaft speed is zero. (b). Switch to pump mode by setting pump/motor swivel angle to positive value when gas in accumulator expands to its maximum possible volume. 14

17 3.1.7 System verification Round-trip efficiency is introduced to evaluate the performance of the hydraulic energy regeneration system. As mentioned above, accumulator potential hydraulic energy is converted to flywheel kinetic energy and back again to the hydraulic energy stored in the accumulator. Such cycles (round trips) keep repeating and due to the system losses, the energy stored in the system dissipates gradually. The cycle efficiency is defined to be ratio of the stored energy of two successful cycles (cycle No. i vs. cycle No. i 1). As all the stored energy may be considered to be the flywheel kinetic energy when flywheel reaches its peak speed, and kinetic energy is proportional to speed square, so the cycle efficiency is given by, where i 1 i 2 N p rt i (34) N p N p is the peak flywheel speed, which decreases a function of the time. The hydraulic energy regeneration system is established in Matlab Simulink as shown in Fig. 9. System data including the data of main units, oil properties, initial conditions, etc., from reference [15] are applied to the model. The simulation results are compared with the experimental results in [15] to verify the model. Hydraulic Energy Regeneration System Acc_v Acc_v Ppm_Qa Leav e Acc Ppm_alpha Acc_p FW_N Scope Ppm_alpha Scope Ppm_Qa Accumulator Control FW_N Scope Acc_p Ppm_alpha Acc_p Ppm_Qa Ppm_Ta FW_N Scope FW_N Ppm_Qa CL_pl CL_pl Ppm_Ta Ef f _rt Res_p Scope Eff_rt Pump/Motor Flywheel Connecting Lines Ppm_Qa Res_p Scope Ppm_Ta Reservoir Fig. 9 Simulink model of hydraulic energy regeneration system. 15

18 Fig. 1 to Fig. 13 compare the simulation results and the results presented in [15], with pre-charged accumulator pressure of 2.79 MPa and pump/motor swivel angle of 2. Each reference result obtained from [15] in Fig 1 to Fig. 12 has two separate curves. One is from measurement, the other one is the simulation result from [15]. 2 P/M Angle = 2 Deg, Cold Oil Flywheel Speed (r/min) Time (s) (a). Simulation result Fig. 1 Flywheel speed. (b). Reference result 2 P/M Angle = 2 Deg, Cold Oil 15 1 P/M Torque (Nm) Time (s) (a). Simulation result Fig. 11 P/M torque. (b). Reference result 2 P/M Angle = 2 Deg, Cold Oil Gas Pressure (MPa) Time (s) (a). Simulation result (b). Reference result Fig. 12 Gas Pressure in accumulator. 16

19 1 P/M Angle = 2 Deg, Cold Oil 8 6 Round-trip Efficiency, % Cycle Number, i (a). Simulation result (b). Reference result Fig. 13 Cycle (round-trip) efficiency. It may be seen that for the first 1 seconds, the simulation results carried out in this project agree very well with the reference results obtained from [15]. For the results after 1 seconds, simulation shows a higher performance than the reference measurement results. This may due to the reason that the mathematical model of the hydraulic pump/motor describes the pump/motor performances better in near rated load working range than that in light load working range. This means the model works better at high speed and high pressure difference than at low speed and low pressure difference. However, this model can still give a good indication of the performance of real systems and is therefore used for further investigations. 3.2 Case study - application of hydraulic energy storage system to WaveStar This section starts with an introduction of how the previously described hydraulic energy storage system may be connected to a real WEC, like the WaveStar, as a case study. The construction of the Simulink model, performance simulation and optimization will be discussed. Fig. 14 illustrates the power take-off system of WaveStar [2]. It may be observed that each float module has its own generator. When absorbed wave power exceeds the power rating of the accompanied generator, excessive energy is merged into a common line and transferred to a system named energy overflow system. The energy overflow system consists of accumulator, hydraulic motor, tank (reservoir) and a generator as shown in Fig. 14 (b). 17

20 (a). Float Module (b). Power take-off system Fig. 14 WaveStar Power take-off system [2]. Compared with the schematic diagram of the hydraulic energy storage system illustrated in Fig. 7, it can be seen that the energy overflow system is actually a hydraulic energy storage system with: (a). excessive hydraulic energy from float modules as input, and (b). mechanical energy transmitted to an electrical generator as output. Therefore, mathematical model described in the previous section can be used to simulate the performance and guide the design of hydraulic energy storage system in WaveStar. In the following analysis and discussion, wave energy from only one float module is studied. However, the model can be extended to simulate system with several float modules easily by simply adding more hydraulic energy input units described below and summing their outputs together as the input to the hydraulic energy storage system System integration and control To adopt the Hydraulic Energy Storage/Regeneration System build in the above section into WaveStar, following changes are needed: (a). introduce a new unit to simulate the hydraulic input, (b). replace the flywheel with a synchronous AC generator, (c). update the control strategy for WaveStar application. Cylinder and check valve hydraulic energy input unit The cylinder and check valve shown in Fig 14 (a) determine the hydraulic energy input to the hydraulic energy storage system. The function of this unit is to pass part of the absorbed wave power that is greater than the rated power of the generator in float module to the hydraulic energy storage system. Provided that knowing the wave power curves, the transmitted hydraulic power P is given by, in (35) P in Pwave PG, float where Pwave is hydraulic power extracted from wave, and P G, float is the power rating of generator in the float module. 18

21 Supposing the accumulator is connected directly after the check valves of float modules, then the oil pressure entering the hydraulic energy storage system is equal to the oil pressure at the accumulator inlet ( p ). Flow rate from float module to hydraulic energy storage system Q in may then be calculated by, Pin Qin (36) p According to the continuity equation, the relationship given below should be satisfied, Q in Q Q (37) a where Qa is the actual flow rate of oil entering the accumulator, and Qm is the actual flow rate of oil entering the hydraulic pump/motor. Besides the cylinder and check valves that work together as system hydraulic energy input, a relief valve is modelled in this unit as well, which is used to limit the system pressure to ensure system safety. As the hydraulic pump/motor only works in motor mode as shown in Fig. 14 (b), oil flow has only one direction, i.e. from float module to hydraulic motor. Maximum system pressure occurs at the flow entering point (the accumulator inlet position as mentioned above), where the relief valve is connected to. When the simulated oil pressure at the flow entering point reaches the pre-set value, which should be a value lower than the system maximum allowable pressure, the relief valve opens and excess flow from hydraulic power supply (float module) is relieved to tank (reservoir) directly. No flow enters the accumulator to increase the system pressure further. Synchronous AC generator mechanical energy output unit Synchronous AC generator is connected to the hydraulic motor output to serve as the load in the model. The interface parameters between hydraulic motor and AC generator are torque and speed. By empoying a synchronous AC generator as the load, the control of the generator may be greatly simplified as the speed is now maintained at a constant value, for example, 15rpm for a 4-pole 5Hz generator. It may be seen from Fig. 1 that the harvested wave energy has a time period of greater than 2 seconds, which is much longer than the electrical time constant of generator. Therefore, the electromagnetic torque of generator can be controlled quickly to maintain the speed constant when the torque from hydraulic motor varies due to the fluctuation of wave energy. In addition to this assumption, detailed model of synchronous AC generator may be saved. Compared to the hydraulic energy storage system, the fast dynamics of the generator may be neglected and the generator is assumed to work in steady state, which is sufficient. Control strategy controller As shown in Fig. 14 (b), the hydraulic pump/motor only works in motor mode in the hydraulic energy storage system. Besides, as the hydraulic motor runs at constant speed but with fluctuating wave energy input, the output mechanical torque will vary accordingly. Therefore, variabledisplacement control of hydraulic motor is required. The swivel angle of hydraulic motor is m 19

22 controlled to obtain different x (the fraction of maximum unit capacity) and thus different torque is achieved according to (16). Two factors are considered when controlling the hydraulic motor swivel angle : maximum allowable volume of the gas in the accumulator and rated torque of the synchronous AC generator: (a). When gas volume in the accumulator reaches its maximum allowable volume, no more oil is allowed to flow out of the accumulator. In order to stop the flow, hydraulic motor swivel angle is set to be zero according to (1). It is noticeable that the minimum allowable volume of the gas in the accumulator is limited by maximum system pressure and is controlled by the relief valve in the hydraulic energy input unit. (b). When the output torque of hydraulic motor exceeds the rated torque of synchronous AC generator, absolute value of hydraulic motor swivel angle should be reduced according to (16). It should be noticed that the reduction of will reduce the amount of flow through hydraulic motor. Then the input flow from float module will enter the accumulator and cause system pressure to increase. The working process can be summarized below: (a). the hydraulic energy input from float module drives the hydraulic motor and thus the synchronous AC generator; (b). if there is too much energy input and exceeds the rating of the synchronous generator, oil flow through hydraulic motor is reduced to maintain the output torque at its rated value; (c). excess flow enters the accumulator and energy is stored there; (d). when there is not enough hydraulic energy input to drive the generator working at rated power, energy stored in the accumulator will help to drive the generator, i.e. oil flow out of accumulator to drive the hydraulic motor; (e). when energy stored in the accumulator runs out, i.e. the gas volume in the accumulator reaches its maximum allowable volume, hydraulic swivel angle is set to zero and there is no energy output to synchronous generator. System is waiting for energy input from the float module. Detailed control strategy is described below: (a). when gas volume in the accumulator is below the pre-set value (8 percent of maximum allowable accumulator gas volume is set in the model), the fraction of maximum unit capacity x is set to be 1; (b). when gas volume in the accumulator exceeds the pre-set value, x is given by, Vmax V x (38) Vmax V pre where V is gas volume in the accumulator, V max is maximum allowable accumulator gas volume, and Vpre is the pre-set gas volume. 2

23 (c). torque is controlled by a PI regulator. Rated torque of the synchronous generator is set as the reference and the actual torque is the feedback. The output of PI regulator is the x value to ensure the actual torque follows the reference. When setting the parameters of PI regulator, 2% or even more overshoot is acceptable depending on the generator data. Fig. 15 illustrates the Simulink model of the torque PI regulator. Fig. 15 Simulink model of torque PI regulator. (d). The minimum value of x from gas volume control and torque control is used to determine the hydraulic motor swivel angle. The Matlab Simulink model of hydraulic energy storage system of WaveStar is shown in Fig. 16. Different sea state can be selected to simulate the system performance. The system efficiency s is calculated by, E out s (39) Ein where Ein is the hydraulic energy input to hydraulic energy storage system, and E out is the energy output from hydraulic energy storage system to the synchronous AC generator. 21

24 Hydraulic Energy Storage System Ppm_Qa Leave Acc Acc_v Acc_v Ppm_alpha CC_Qa Acc_p Gen_T Scope Ppm_alpha Scope Ppm_Qa Accumulator Control FW_N Ppm_alpha Ppm_Qa Gen_N Scope Gen_N Acc_p Ppm_Ta Gen_T Ppm_Qa CL_pl CL_pl Res_p Ppm_Ta Gen_Pin Scope Gen_T Acc_p Cy l_p Pump/Motor Electric Generator Wave_no Wave Type 1, 2 or 3 Wav_t Res_p CC_Qa CC_P Connecting Lines Scope Ppm_Ta Gen_Pin Whl_Eff Cylinder and Check Valve Ppm_Qa Cyl_P CC_P Sy s_ef f Scope Eff_Sys Res_p Efficiency Calculation CC_Qa Scope CC_Qa Reservoir Fig. 16 Simulink model of hydraulic energy storage system of WaveStar System performance and verification Power profile at sea state 3 shown in Fig. 1(b) is selected for this case study first. Check valve gate value is set to be 6kW, i.e. the wave power greater than 6kW will enter the hydraulic energy storage system. The pre-set relieving pressure of relief valve is set to be 35MPa, the maximum allowable accumulator gas volume V max is set to 3 liters, the maximum hydraulic pump/motor displacement D is set to 65 cm 3 /rev, and generator rated power is 4kW at 15 rpm rated speed. Fig. 17 shows the effect of relief valve. It may be observed in Fig. 17 (a) that during the time interval (2184s to 2185s), power input after relief valve is set to be zero repeatedly. This is due to that the system pressure has reached the pre-set maximum allowable system pressure, and relief valve opens and relieves the excess hydraulic power input directly to the tank as shown in Fig. 17 (b). During this time interval, hydraulic motor is driving the generator running at its full capacity (4kW) as shown in Fig. 17 (c). Fig. 17 (d) shows that the system efficiency is lower if using power input before the relief valve instead of using the power input after the relief valve to calculate the system efficiency. This means there is some energy goes through the relief valve and is wasted. 22

25 Before Relief Valve After Relief Valve Power Input [kw] Time (s) (a). Power input Pressure [MPa] Flow Rate [m 3 /s] Pressure and Flow Rate at Accumulator Inlet x Time (s) (b). Pressure and flow rate at accumulator inlet x Shaft Power [kw] Fraction of Maximum Unit Capacity and Shaft Power Time (s) (c). Fraction and shaft power of hydraulic motor Before Relief Valve After Relief Valve 1.5 System Efficiency, % Time (s) (d). System Efficiency Fig. 17 Effect of relief valve. The effect of torque PI regulator can be observed in Fig. 17 (c). The instantaneous shaft power is greater than the generator rated power (4kW). Therefore, the capability of hydraulic motor is keeping decreasing its absolute value drops from.93 to.78 during time interval 2184s to 2185s, and the shaft power reduces from 48kW to 42kW. Fig. 18 shows the effect of accumulator gas volume control. After the time of 925s, there is no hydraulic power input; hydraulic motor runs at its full capacity with the energy stored in the accumulator. Oil stored in the accumulator is pressed out to drive the hydraulic motor and the gas volume increases. System pressure keeps dropping and shaft power drops as well. At the time of 93s, gas in the accumulator has expanded to its pre-set volume (8 percent of maximum allowable accumulator gas volume). Accumulator gas volume control scheme begins to take effect. Swivel angle begins to decrease and hydraulic motor runs at its partial capacity. When gas volume reaches the maximum allowable accumulator gas volume, swivel angle reduces to zero as well and there is no shaft power. After the time of 953s, there is hydraulic energy input again. Hydraulic motor begins to generate power. There is also oil flow into the accumulator. Gas is compressed and system pressure rises again. 23

26 x Shaft Power [kw] Hydraulic Power [kw] -.5 Fraction of Maximum Unit Capacity Shaft Power and Hydraulic Input Power Time (s) Time (s) (a). Fraction, shaft power and hydraulic input Gas Volume [m 3 ] Flow Rate [m 3 /s] Pressure [MPa] Gas Volume, Flow Rate and Pressure x Time (s) Time (s) (b). Gas volume, flow rate and pressure Fig. 18 Accumulator gas volume control. It may be seen from Fig. 17 and 18 that the hydraulic energy storage system performs as expected. The Simulink model gives acceptable results and is used for further investigation System optimization and discussion The system performance shown in section is not impressive as the system efficiency is not very high less than 7 percent as shown in Fig. 17(d). The reasons could be: (a). The accumulator is not big enough. The accumulator is not able to store all the excess energy, which is the hydraulic energy input minus the energy used to drive the hydraulic motor. Therefore, there is some hydraulic energy relieved through relief valve, which is wasted as shown in Fig 17 (a). (b). Hydraulic motor has a higher rated power than synchronous AC generator. Torque PI regulator adjusts the capacity of hydraulic motor to fit the generator ratings as shown in Fig 17 (c) and the capacity x is less than.8 at generator ratings. Therefore, hydraulic motor always works at partial capacity. The efficiency of hydraulic motor at partial capacity is lower than its efficiency at full capacity, which affects the system efficiency as well. (c). Power ratings of hydraulic motor and synchronous generator are not big enough. They are not able to consume enough hydraulic energy input from float module. Therefore, there will be energy accumulated in the accumulator rapidly and finally relieved through relief valve when system pressure reaches its maximum allowable value. These aspects are considered by varying the corresponding parameters and repeating the simulation. The system efficiency is then calculated at different conditions with different accumulator volume, hydraulic motor full capacity displacement, synchronous generator rated power, and sea state, in order to find a combination that can give the best system efficiency. 24