NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Conference Paper

NREL/CP-5000-76016

September 2020

Investigating the Impact of Power-TakeOff System Parameters and Control 

Law on a Rotational Wave Energy 

Converter's Peak-To-Average Power

Ratio Reduction

Preprint

H. Bora Karayaka,1 Yi-Hsiang Yu,2 Nathan Tom,2 and

Eduard Muljadi3

1 Western Carolina University

2 National Renewable Energy Laboratory

3 Auburn University

Presented at the ASME 2020 39th International Conference on Ocean, 

Offshore and Arctic Engineering 

August 3–7, 2020
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Conference Paper

NREL/CP-5000-76016 

September 2020

Investigating the Impact of Power-TakeOff System Parameters and Control 

Law on a Rotational Wave Energy 

Converter's Peak-To-Average Power 

Ratio Reduction 

Preprint

H. Bora Karayaka,1 Yi-Hsiang Yu,2 Nathan Tom,2 and 

Eduard Muljadi3 

1 Western Carolina University

2 National Renewable Energy Laboratory

3 Auburn University

Suggested Citation

Karayaka, H. Bora, Yi-Hsiang Yu, Nathan Tom, and Eduard Muljadi. 2020. Investigating 

the Impact of Power-Take-Off System Parameters and Control Law on a Rotational Wave 

Energy Converter's Peak-To-Average Power Ratio Reduction: Preprint. Golden, CO: 

National Renewable Energy Laboratory. NREL/CP-5000-76016.

https://www.nrel.gov/docs/fy20osti/76016.pdf. 
NOTICE

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NREL 46526.

NREL prints on paper that contains recycled content. 
1 

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INVESTIGATING THE IMPACT OF POWER-TAKE-OFF SYSTEM PARAMETERS AND 

CONTROL LAW ON A ROTATIONAL WAVE ENERGY CONVERTER'S PEAK-TO-AVERAGE 

POWER RATIO REDUCTION

H. Bora Karayaka1

Western Carolina University

Cullowhee, NC, USA

Yi-Hsiang Yu, Nathan Tom

National Renewable Energy Laboratory

Golden, CO, USA

Eduard Muljadi 

Auburn University

Auburn, AL, USA

ABSTRACT

Due to the irregular nature of real waves, the power 

captured in a wave energy converter (WEC) system is highly 

variable. This is an important barrier to the effective use of 

WECs. To address this challenge, this study focuses on a 

rotational WEC power-take-off system in which high-speed and 

high-efficiency generators along with a torque/power 

smoothing inertia element can be effectively utilized. In the first 

phase of this study, the U.S. Department of Energy’s reference 

model 3 (WEC-Sim RM3; two-body point absorber), along with 

a slider-crank WEC, were integrated for linear to rotational 

conversion. Relative motion between the float and spar in RM3 

was the driving force for this slider-crank WEC, which is 

connected to a motor/generator set through a gearbox. RM3 

geometry was scaled down by 25 times to work within the limits 

of the physical motor/generator set used in the experimentation. 

Once the integration in a hardware-in-the-loop simulation 

environment was successfully completed, data on the peak-toaverage power ratio was collected for various wave conditions 

including regular and irregular waves. The control algorithm 

designed to keep the system in resonance with waves was able 

to maintain relatively high speed depending on the specific gear 

ratio and wave period. Initial results with hardware-in-theloop simulations reveal that gear ratio and crank radius have a 

strong impact on the peak-to-average power ratio. In addition, 

it was found that output power from the generator was 

maximized at a larger gear ratio, as the crank radius was 

increased. 

Keywords: Wave energy converter; linear to rotary PTO; 

peak-to-average-power ratio; one-way continuous rotation

INTRODUCTION

A viable renewable energy alternative that has been 

identified in a recent White House report to meet the goals 

established for 2030 is marine and hydrokinetic energy [1]. 

Deep-water wave power resources are abundant, between 1 TW 

and 10 TW [2]. Water also has a high-power density that is 832 

times greater than the air power density. The high-power

density of water implies that large amounts of energy can be 

obtained from relatively small devices in the ocean. For 

example, it would require a wind turbine three times the size of 

a regular-sized underwater turbine to generate the same amount 

1 Contact author: hbkarayaka@email.wcu.edu

of power from wind than what can be generated from water [3]. 

This means that harvesting structures for open-ocean waves 

would be of a smaller size and be less invasive while producing 

more power than currently implemented wind turbines. 

However, at present, ocean wave energy is the most expensive 

type of water power. Forecasting and calculating the ocean 

energy that can be harvested is not easy because of a lack of 

available models of wave energy converters (WECs) [4]. In 

addition, ideal sinusoidal wave conditions rarely exist in real 

oceans and real wave conditions are highly irregular, which in 

turn pose significant challenges of control and design for 

harvesting a substantial portion of this energy. Therefore, 

developing new WEC models that can efficiently harness wave 

energy is critical for the future of the utilization of ocean wave 

energy in our renewable generation mix. 

A research study conducted in 2011 showed that the ratio 

between peak power and average power absorbed by a WEC 

can be as high as 58 when applying well-known complex 

conjugate control techniques with irregular waves [5]. The 

study also showcased a control method with power saturation 

provisions to reduce this ratio as well as the rating, and the cost

of power electronics equipment. Even in the case presented, it 

required a 110-kW saturation rating to be able to extract 16.4 

kW of average wave power. In another recent study [6], a 

specific type of WEC (oscillating water column) with a highspeed valve is utilized with a nonlinear latching control 

technique to limit the peak-to-average power (PTAP) ratio. 

Both of these research studies employed very specialized power 

saturation or limiting methods, which are only applicable to 

specific WEC-power-take-off (PTO) systems. Although it is 

qualitatively discussed in [6], these research efforts did not 

really quantify the impact of system parameters, such as an 

inertia or gear ratio to the PTAP ratio. In addition to the power 

variability concern, WECs commonly use linear generators and 

often face various challenges that are encountered even at 

relatively low power levels around 10 kW [7].

Motivated by these challenges, the aim of the study 

presented in this paper is to conduct research and development 

(R&D) activities to advance the models for cost-effective wave 

energy conversion to support some of the educational initiatives 

of the U.S. government [8, 9]. These WEC platformindependent models integrated with an inertia element and 
2 

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control law will be specifically addressing the challenge of a 

large PTAP ratio, which is inherent to most WEC systems [6].

The open-source wave energy converter simulation tool 

(WEC-Sim) was originally developed by the collaboration of 

the National Renewable Energy Laboratory and Sandia 

National Laboratories in 2014 [10]. WEC-Sim is developed in 

MATLAB/Simulink and has the ability to model devices that 

comprise rigid bodies, PTO systems, and mooring systems. 

Many additional features have been added since then. The 

present work with its real-time hardware-in-the-loop (HIL) 

environment focus designs and tests a numerical model 

integrated to WEC-Sim that gives an indication on how system 

parameters along with an advanced control algorithm can 

potentially affect a rotational WEC’s PTAP ratio.

1.1 Hypothesis and Research Objectives

A prominent aspect that makes commonly used horizontalaxis wind turbines cost-competitive and efficient is their ability 

to maintain continuous rotation at a relatively fixed speed and 

torque. This is primarily because of the large inertia associated 

with the turbine and advanced control techniques applied to 

power electronic converters [11]. Inspired by this fact, the 

hypothesis of this research is that a rotational WEC-PTO that 

maintains continuous rotation with a large enough inertia can 

achieve a reasonably low PTAP ratio. The objectives for this 

study are to 1) develop an advanced control algorithm that can 

maintain continuous rotation for at least one rotational WEC 

design, and 2) properly couple the system with an inertia 

element and collect and analyze PTAP ratio data depending on 

various wave conditions.

In rotational WEC applications, it is often difficult to 

achieve continuous one-way rotation in an economic, efficient, 

and robust manner. For example, a group of researchers 

successfully designed a mechanical motion rectifier that can be 

used in various energy harvesting schemes [12]. However, this 

mechanism would require additional cost and complexity for a 

WEC system in which the cost of producing electricity is 

already not competitive in comparison to wind or solar energy. 

Other one-way rotation mechanisms usually need a one-way 

clutch to keep the generator’s shaft rotating in one direction and 

latching techniques in case of extreme waves, which adds to the 

complexity of their structures [13]. This study makes use of an 

advanced control methodology that ensures one-way 

continuous rotation at relatively high speed and efficiency. This 

method does not rely on the wave motion (small, large, fast, or 

slow) to achieve continuous rotation. To do that, the electric 

machine operates in the generator and the motor modes for 

every half cycle of a wave [13]. This way the WEC-PTO 

resonates with the waves. This control methodology can be 

applied to any oscillating WEC-PTO system that comprises a 

linear-to-rotary linkage. In the study presented in this paper, 

WEC-Sim reference model 3 (RM3) and slider-crank linear to 

rotary linkage is utilized to fulfill the research objectives. The 

integration scheme is shown in Fig. 1. The slider on the right is 

assumed to be attached to the float section of WEC-Sim RM3 

and will be housed and move freely within the spar section of 

WEC-Sim RM3. The slider crankshaft, as well as gearbox and 

the electrical generator, are assumed to be fixed to the spar 

section. The orientation of the slider crank’s upstroke is in the 

same direction with the float’s upward motion with waves.

FIGURE 1: INTEGRATION OF WEC-SIM (RM3) AND THE 

SLIDER-CRANK WEC TO FORM A ROTATIONAL WEC-PTO.

1.2 Methodology

The basic scientific approach behind PTAP ratio reduction 

can be explained through an armature-controlled (constant 

field) DC machine block diagram, as shown in Fig. 1. This 

principle can also be generalized to vector-controlled 

asynchronous or synchronous AC machines in which torque 

and flux producing current components are decoupled to 

provide similar control advantages as in DC machines. 

FIGURE 2: ARMATURE-CONTROLLED DC GENERATOR 

BLOCK DIAGRAM. 

In the control framework, mechanical torque developed by 

WEC-PTO Tm is treated as a torque input to the DC machine. 

Shaft speed, ω, is the machine’s output. Te is an 

electromechanical torque developed by the machine. The other 

symbols in Fig. 1 are Vb, back electromotive force; Va, armature 

voltage; Kb, voltage constant; Km, torque constant; Ra and La, 

armature resistance and inductance, respectively; and B and J, 

rotational viscous damping and inertia, respectively. Equations 

(1) – (6) show that the electrical power output from this system 

has a time constant that is directly proportional to the system 

inertia, J. 

Assuming much smaller electrical stage time constant 

defined by La/Ra than mechanical stage time constant J/B, Ge(s) 

can be reduced to Km/Ra. Then, the transfer function that relates 

ω to Tm in the time domain is: 

GG1(ss) = ωω(ss)

TTmm(ss) = GGmm(ss)

1 + KKbbGGee(ss)GGmm(ss) = ττ/JJ

1 + ττ (1)

where s is the Laplace variable and the system time constant 

is: 
3 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

ττ = RRaaJJ

(RRaaBB + KKbbKKmm)

 (2)

The transfer function that relates ω to Va can be found 

similarly:

GG2(ss) = ωω(ss)

VVaa(ss) = GGee(ss)GGmm(ss)

1 + KKbbGGee(ss)GGmm(ss) = ττKKmm/(JJRRaa)

1 + ττ (3)

Finally, ω output can be represented based on Va and Tm inputs 

using the principle of superposition:

ωω(ss) = GG1(ss)TTmm(ss) + GG2(ss)VVaa(ss) (4)

The electrical power supplied by the machine is then: 

PPee(ss) = VVbb(ss)IIaa(ss) = KKbb

KKmm

ωω(ss)(TTmm(ss) − ωω(ss)GGmm(ss)) (5)

where Ia(s) is the armature current. If ω(s) from (4) is 

substituted in (5) and “(s)” terms are omitted for the sake of 

simplicity:

 PPee = KKbb

KKmm

{(GG1 − GG1

2/GGmm)TTmm

2 + (GG2 − 2GG1GG2/GGmm)VVaaTTmm

− GG2VVaa

2

/GGmm} (6)

It can be shown that the transfer functions in (6) that 

multiply TTmm

2 , VVaaTTmm, and VVaa2 terms have some low pass filter 

functionality characterized by the time constant, ττ. In this 

study’s PTAP ratio reduction approach, electromechanical 

torque, Te (controlled by Va), tracks WEC-PTO torque, Tm, to 

achieve continuous unidirectional rotation. When the 

machine’s torque limit is exceeded, additional torque is 

smoothed by the time constant, ττ, which is a function of inertia 

and viscous damping coefficients, J and B, respectively. 

However, this may not be satisfactory in some cases where the 

difference between these two torques is significant. Therefore, 

WEC-PTO torque, Tm, is modified up and down by adjusting 

the gear ratio and slider-crank radius based on the formulation 

of Tm discussed at length in [13]. This way, fluctuations in the 

output power and PTAP radio can be further minimized.

1.3 Experimental Setup and Design

The experimental setup was designed using the WEC-Sim 

RM3 [13] and applying this model to a physical experiment. 

WEC-Sim RM3 outputs the hydrodynamic forces, which are

the input into a Simulink system where an HIL simulation takes 

place. Fig. 3. gives a detailed visualization of the project’s 

scope and experimental setup. 

FIGURE 3: OVERVIEW OF PROJECT SCOPE VIA 

HARDWARE-IN-THE-LOOP SIMULATION AND 

EXPERIMENTAL SETUP

In Fig. 3, IPTO* is the WEC-PTO torque reference for the 

motor controller, Ia(m1) is the measured armature current for the 

motor, and Ia(m2) is the measured armature current for the 

generator. The experiment consists of two DC machines

coupled together, one acting as the motor or PTO torque 

emulator and the other acting as the generator. The control of 

two separate machines is achieved using the dSPACE 1104 

digital signal processor (DSP) board, which allows the full 

control of an electric machine drives board. The DSP control 

board takes measurements and sends the data to the dSPACE 

Control Desk software, a GUI application that displays the data 

and records the measurements. The slider-crank WEC-PTO 

model that represents the “Rotational WEC-PTO model” block 

was used in this project [13]. 

The torque developed by slider-crank WEC is divided by 

the motor torque constant to convert to the current reference. 

This reference is applied to the motor controller that controls 

the current into the motor, which acts like the PTO torque 

emulator in the system. The speed sensed from the encoder 

attached to the motor/generator shaft is integrated to calculate 

the shaft position/angle. Both shaft speed and position 

information are used by the slider-crank WEC-PTO model for 

torque calculation. The generator control algorithm takes the 

position information and processes through its multiple-stage 

control blocks. Eventually, the algorithm generates pulse-width 

modulated (PWM) signals for armature voltage control to make 

sure the generator synchronizes with the excitation force acting 

on WEC-Sim RM3 (a reactive control method in which the 

wave excitation force and WEC-PTO velocity are kept inphase). The entire simulation model (upper left half of Fig. 3) 

is eventually uploaded and runs from the DSP hardware board 

(attached to the desktop computer in the far-left side of the 

experimental setup).

In WEC-Sim RM3 (a two-body system), both 

hydrodynamic bodies (float and spar) were restricted to move 

in the heave direction only. This way, the excitation force that 

actuates the PTO can be preprocessed for the sake of simplicity. 
4 

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This excitation force is calculated by subtracting the excitation 

force for the float from the excitation force for the spar.

The Simulink system designed for the integration of WECSim RM3 and slider-crank models in a closed-loop HIL 

simulation environment is shown in Fig. 4. The WEC-Sim 

block represents the mechanical subsystem in Fig. 4. The 

electrical subsystem details are provided in Fig. 5. This system 

includes a PTO torque emulator, which is the violet frame in 

the lower-left corner. The emulator processes the PTO force 

input from the mechanical subsystem. This force goes through 

the slider-crank torque function, which produces the crankshaft 

torque. This torque is then divided by the DC motor’s torque 

constant to issue the reference armature current for the PTO 

torque emulator, which produces PWM signals to control the 

DC motor through the electric machines drive board. The DC

motor’s shaft is directly coupled to the generator’s shaft, which 

is controlled by the green frame in the upper right corner in Fig. 

5. The reference speed for the generator’s controller is issued

by the control algorithm (the gray frame in the upper left corner)

to keep the PTO velocity in resonance with the wave excitation 

forces. Measured speed on the shaft (small gray block in the 

middle) is integrated to calculate the displacement and velocity 

for the slider crank, which are issued as outputs to the 

mechanical subsystem (WEC-Sim RM3). There is a total of 

three proportional-integral (PI) controllers employed in the 

electrical subsystem. One PI controller is designed to control 

the armature current for the PTO torque emulator and the other 

two PI controllers that operate in a nested loop topology are 

designed to control the armature current and shaft speed for the 

generator. On the other hand, the resonance control algorithm 

(represented by the gray frame) is a rule-based phase-lock 

control mechanism discussed in detail in [13]. In short, this 

control process detects zero crossings and half-periods through 

pre-processed data arrays and “Period Calc1” block in Fig. 5 

under the assumption of perfect knowledge of the wave 

excitation force. After that, the angular variation for the future 

half cycle is predicted by a linear interpolation method in 

“Angle Reference Gen” block in Fig. 5. This is the reference

FIGURE 4: MAIN SIMULINK SYSTEM DESIGNED FOR CLOSED-LOOP REAL-TIME CONTROL

PTO Force

Buoy position

Buoy velocity

Trigger()

Electrical 

Subsystem

Pos

Vel

Force

WEC-Sim

RTI Data

ENCODER

MASTER SETUP

DS1104ENC_SETUP1

Rate Transition

Rate Transition1

Rate Transition2

DS1104 Board

Timer B interrupt

Timer Interrupt

Host Service #1

Main

Data Capture

Lowpass

Lowpass Filter2
5 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

FIGURE 5: SIMULINK ELECTRICAL SUBSYSTEM DETAILS

angle that is compared against the measured shaft angle to 

evaluate the control error. To maintain phase-lock/resonance 

condition, the angle error is later processed by a control 

algorithm to generate a speed reference for the generator’s

controller. The reference needs to be issued before the next half 

cycle begins for proper angle tracking. This reference is finally 

low-pass filtered to avoid sharp transients in the generator 

dynamics. In the simulation system, a gearbox model was placed 

between the slider crank and the motor/generator shafts.

In this study, perfect knowledge of future half-period 

knowledge of the wave excitation force was assumed. An 

adaptive autoregressive filter prediction algorithm for the 

excitation force was developed and analyzed for regular and 

irregular wave conditions in [14]. The prediction performance of 

this filter was also analyzed in a slider crank WEC simulation

scheme in [15]. The results with irregular wave peak periods of 

6 through 10 s showed that captured wave power was reduced 

approximately 4% in comparison to the perfect knowledge of 

wave excitation force case. Testing with regular wave periods 

resulted in negligible reduction in captured power. 

In terms of real-time simulation software design, the 

following challenges had to be overcome: 

- The sampling time for the electrical subsystem (anything 

other than the WEC-Sim block in Fig. 4) has to be at least 

0.5 ms to ensure appropriate current and torque control. 

However, WEC-Sim uses a continuous-time simulation 

solver that picks up the fastest sampling time in the Simulink 

framework. If that happens, every subsystem was supposed 

to run at a 0.5-ms sampling time, which caused task overrun 

errors during the real-time build and upload cycles. To 

overcome this challenge, the electrical subsystem was 

discretized and packaged to be triggered by the digital signal 

processor board’s hardware-timer interrupt at 0.5-ms 

intervals. This way, the electrical subsystem was scheduled 

as a higher priority task than the mechanical subsystem, 

which is not necessarily run at fast sampling speeds.

- WEC-Sim RM3 PTO was normally supposed to be actuated 

by motion, which is the position information for the slidercrank WEC. This actuation method required position, 

velocity, and acceleration and was extremely sensitive to 

any noise because of the derivation process. The actuation 

method was changed to a much more stable force input

framework, which was driven by a proportional-integralderivative (PID) controller for a specific position setpoint. 

Tuning of this controller was done manually (P parameter 

first for a minimal error, then D parameter to avoid jitter, 

and finally I parameter for eliminating the steady-state 

error).

- Motor faults in the electronic controller boards were causing 

continuous disruption during testing. The solution was later 

Control Algorithm

Generator Controller

PTO Torque Motor Controller

f()

Trigger

f(u)

Crankshaft Torque

-KCurrent Reference

Generation

Ia_Reference

Ia_Measured

Vc_i

Motor_I_Controller

ADC

DS1104ADC_C5

20

Ia_Measured

Vc_i Duty_Ratios

Motor_Duty_Cycle

0

dC1

m

Duty cycle a

Duty cycle b

Duty cycle c

DS1104SL_DSP_PWM3

Wm_Measured

Speed_Measurement1

-KConvert to wave 

frequency

f(u)

Buoy displacement

y u

DC Gen. Angular position

K Ts (z+1

2(z-1)

Discrete-Time

Integrator

1

PTO Force

1

Buoy position

Host Service #2

Electrical

Data Capture

f(u)

Buoy velocity function

2

Buoy velocity

t

T_s

T1_s

pn_flag

T

T1

Period Calc1

u

yterrt1ki

Angle Reference Gen

-CConstant

T_s

Constant1

T1_s

Constant2

-Cpn_flag

ADC

DS1104ADC_C6

20

Ia_Measured1

Vc_i Duty_Ratios

Generator_Duty_Cycle

Wm_Reference

Wm_Measured

Ia_Reference

Generator_Speed_Controller

Ia_Reference_Generator

Ia_Measured_Generator

Vc_i

Generator_I_Controller

PWM Channel 1

PWM Channel 2

PWM Channel 3

PWM Channel 4

DS1104SL_DSP_PWM1 0

dC2

m

-KGain

0.001998z -1

1-0.998z -1

Discrete 1st Order Filter 

0.25s time constant

12:34

Digital Clock

Saturation

GeneratorP

MotorP

Terminator

Terminator1 40

Constant3

-40

Constant4

 Ts (z+

2(z-1)

ConEner

K Ts (z+1

2(z-1)

GenEner

dA1
6 

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discovered through a data sheet (for metal oxide 

semiconductor field effect transistor (MOSFET) gate drive 

circuitry IR2133) provided by the manufacturer. 

Accordingly, the potentiometers for the motor and the 

generator drive circuitry were adjusted to meet expected 

current limits based on the specifications. 

Once these challenges were overcome, the following testing 

methods and constraints were applied to collect the real-time 

data from the hardware-in-the-loop simulation environment: 

- WEC-Sim RM3 was scaled down for testing by Froude 

scaling law [16] to comply with the hardware components 

ratings. The original geometry was decided to be scaled 

down by 25 times (Fr = 25) after some initial analysis. 

Accordingly, the hydrodynamic forces are reduced by Fr3 = 

15625, wave heights are reduced by Fr = 25, and wave 

periods as well as simulation time are reduced by √Fr = 5. 

- Regular waves to be tested were i) height (H) = 2 m for 

periods (T) = 5, 10 and 15 s, ii) height (H) = 1 m, periods (T) 

= 5, 10 and 15 s.

- Irregular waves to be tested (using the Brettschneider

spectrum) were significant wave height (Hs) = 1.5 m, and

peak period (Tp) = 10 and 15 s. These irregular waves were 

formed by the composition of 70 regular waves. 

- The test duration was 80 s (original test duration of 400 was 

divided by the time scaling factor explained earlier) for 

regular waves. The test duration was 320 s for irregular 

waves to cover a broad range of operations. 

- The gear ratio was varied between 20 to 80, with 10 steps, 

and data were collected, as long as the motor overcurrent 

fault did not occur. 

- The slider-crank radius to connecting arm length ratio (l/r in 

reference to Fig. 1) was fixed at 0.5 throughout the testing.

Slider-crank radius (full scale) values of 1.25 m, 2 m, and 

2.5 m were used during testing.

- WEC-Sim RM3 bodies (float and spar) were restricted to 

move in heave direction only.

- The power electronic converters that feed the motor or the 

generator are capable of operating these machines in four 

quadrants. Each converter consists of six MOSFETs, of 

which only four were utilized for DC-DC bidirectional 

power transfer mode. The main DC bus is configured for 40

V through an external DC power supply.

1.4 Experimental Results

The WEC-PTO design with HIL simulations successfully 

resulted in unidirectional continuous rotation, as shown in Fig. 6

for both regular and irregular waves. It is important to note that 

the time scale is approximately four times larger in the case of 

the irregular wave, so the ramp rates in speed are more benign 

than what is perceived. In addition, output voltage fluctuation of 

± 1% within the rated value of 40 V (DC Bus) was achieved. The 

maximum fluctuation observed, which corresponded to peak 

power durations, was about 30 mV.

FIGURE 6: MOTOR/GENERATOR SHAFT SPEED FOR A 

REGULAR WAVE (LEFT) AND AN IRREGULAR WAVE (RIGHT) 

CASE

Generated electrical power’s PTAP ratio results for regular 

and irregular waves are summarized in Table 1 for a slider-crank 

radius of r = 2.5 m. Mean values of generated electrical power 

for regular and irregular waves are summarized in Table 2 for a 

slider-crank radius of r = 2.5 m. The drive torque for a slider 

crank linkage is directly proportional to the crank radius under 

the assumption of fixed l/r ratio. Therefore, the shaft power for 

a given speed would increase proportionally with increasing 

radius. This was also observed during the tests. For a given gear 

ratio, larger radius yielded larger power and smaller PTAP ratio.

The results for the gear ratio of 50 are listed in Table 3. 

In terms of the PTAP ratio, the gear ratio of 50 and r = 2.5

m was the overall best. In terms of average extracted power, the 

gear ratio of 60 and r = 2.5 m was the overall best. The gear ratio 

of 60 should be selected because the PTAP ratio difference 

between 50 and 60 was negligible. 

The rationale for some of the data labeled by “NA” can be 

explained as follows. In the case of T=5 s with regular waves, 

testing with a gear ratio of 70 or above resulted in overcurrent 

faults. Therefore, the results were not collected for the ratio of 

70 or for the ratio of 80, as shown in Tables 1 and 2. In addition, 

the gear ratio of 70 or above would not result in appreciable 

values of PTAP ratio and output power because the PTAP ratio 

was increasing and average power was decreasing by increased 

values of gear ratio. In the case of irregular waves, the system 

was unable to extract positive power at Hs=1.5 m and Tp=10 s, 

because incoming mechanical power through the torque 

emulator was not high enough to overcome losses in the energy 

conversion chain. Therefore, the PTAP ratio was not calculated 

for this data set. However, the system was able to extract positive 

power at Hs=1.5 m and Tp=15 s, as shown in Table 2. Similar 

cases of not being able to extract power did occur with regular 

waves as well. For example, the crank radius of 1.25 m, 

regardless of the gear ratio, did not result in any positive power 

at H=1 m and T=5 s or T=10 s as shown by “NA” in Table 3. 

An observation of the PTAP ratio was also conducted on the 

motor side (torque emulator). The motor’s incoming power 

needs to be larger than the generator’s output power by a certain 

offset to ensure positive efficiencies. In the case of regular waves 

(r=2.5 m), the incoming slider-crank power draw was varying 

generally between 40 and 80 W. The PTAP ratio for this power 

was always smaller than the electrical power output and varying 

generally between 2 and 4. In the case of irregular waves (again 

r=2.5 m), the incoming slider-crank power was varying 
7 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

generally between 30 and 50 W. The PTAP ratio for this power 

was varying generally between 3 and 10. These results support 

the electrical power vs. PTAP ratio trends in Tables 1 and 2 (i.e., 

the higher the electrical power (absorbed or generated), the lower 

the PTAP ratio). This fact can be explained by a sine wave biased 

with a certain fixed positive value. As this value increases, the 

PTAP ratio would decrease. The relationship between the 

characteristics of power through the torque emulator and the 

generator are shown in Figs. 7 and 8 for a specific case of a 

regular wave, gear ratio, and crank radius.

One final observation in terms of PTAP ratio reduction was 

in the control law. If the voltage ramp rates to the torque 

emulator motor were kept in a certain range, then the PTAP ratio 

reduces. However, this method has a limit. Beyond a certain 

limit, the controller has a disadvantage of not catching up with 

the fast torque/current transients in a timely manner. Eventually, 

this may result in overcurrent faults on the drives board.

TABLE 1. PTAP RATIO FOR THE GENERATOR AND SLIDERCRANK RADIUS OF 2.5 M

Gear 

Ratio

Regular Waves H=1 m Regular Waves H=2 m Irregular Wave 

Hs=1.5 m 

T=5 s T=10 s T=15 s T=5 s T=10 s T=15 s Tp=10 s Tp=15 s

40 10.6 57.0 2.31 8.63 15.8 2.34 NA 407

50 15.3 25.4 2.38 11.5 8.71 2.34 NA 35.4

60 32.8 17.5 2.48 13.4 7.88 2.42 NA 25.2

70 NA 20.5 2.66 NA 7.82 2.61 NA 23.6

80 NA 45.4 3.15 NA 9.87 2.90 NA 21.8

TABLE 2. EXTRACTED AVERAGE ELECTRICAL POWER 

(WATTS) FROM THE GENERATOR FOR SLIDER-CRANK 

RADIUS OF 2.5 M

Gear 

Ratio

Regular Waves H=1 m Regular Waves H=2 m Irregular Wave 

Hs=1.5 m 

T=5 s T=10 s T=15 s T=5 s T=10 s T=15 s Tp=10 s Tp=15 s 

40 14.9 2.25 13.4 18.8 7.52 14.2 -14.0 0.41

50 14.7 5.02 19.3 17.0 12.9 20.1 -10.7 5.57

60 5.68 7.10 23.7 13.6 14.3 24.6 -9.60 8.77

70 NA 6.23 26.3 NA 15.2 27.3 -10.3 10.6

80 NA 2.92 27.5 NA 13.6 29.2 -13.2 12.1

TABLE 3. PTAP RATIO AS A FUNCTION OF CRANK RADIUS

FOR THE GENERATOR AND GEAR RATIO OF 50

Crank 

Radius 

(m)

Regular Waves H=1 m Regular Waves H=2 m Irregular Wave 

Hs=1.5 m

T=5 s T=10 s T=15 s T=5 s T=10 s T=15 s Tp=10 s Tp=15 s

1.25 NA NA 19.0 NA 123 24.3 NA NA

2 NA 52.0 3.12 37.4 8.71 3.06 25.0 NA

2.5 15.3 25.4 2.38 11.5 7.73 2.34 20.4 35.4

FIGURE 7: PTAP RATIO FOR THE GENERATOR (BLUE) AND 

THE TORQUE EMULATOR (ORANGE) 

FIGURE 8: AVERAGE POWER FOR THE GENERATOR (BLUE) 

AND THE TORQUE EMULATOR (ORANGE)

CONCLUSIONS

The hypothesis was justified, and unidirectional continuous 

rotation was achieved for a wide range of regular and irregular 

waves (although inertia was kept constant at its default value). 

As the crank radius was increased, the maximum average power 

was achieved at a larger gear ratio. The best overall results for 

both the PTAP ratio and average power were achieved with a 

crank radius of 2.5 m. As the wave period reduced, maximum 

power was achieved at a smaller gear ratio. The best overall 

results for both the PTAP ratio and average power were achieved 

with a gear ratio of 60. The electrical output power extracted at 

the generator was smaller than incoming power at the torque 

emulator, with efficiencies varying between 40 and 60% per 

machine. The PTAP ratio can be further reduced for specific gear 

ratios and crank radius settings. Incoming mechanical power 

should be increased to avoid the offsets because of the standby 
8 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

power used to maintain speed and overcome losses. A minimum 

of ~40 W at the torque emulator is required to ensure positive 

electrical power at the generator. 

The important future steps in this study can be listed as 

follows. Because the default inertia of the coupled 

motor/generator system was assumed throughout the project, 

inertia testing should be conducted thoroughly for multiple 

different configurations to investigate the impact on the PTAP 

ratio. Scaling the original RM3 geometry by Froude’s law needs 

to be reevaluated to improve full-scale electrical power and 

PTAP ratio projections. Another rotational WEC-PTO instead of 

RM3 or slider crank should be evaluated for performance. In 

addition, the impact of phase-lock condition (between generator 

and wave forces) on PTAP ratio and power output should be 

investigated. Finally, wave excitation forces for the 3 degreesof-freedom WEC-Sim RM3 should be evaluated during runtime 

for more realistic simulations.

ACKNOWLEDGEMENTS

This work was supported [in part] by the U.S. Department 

of Energy, Office of Science, Office of Workforce Development 

for Teachers and Scientists under the Visiting Faculty Program. 

Task Number Visiting Faculty Program ERPG. 10213.04.01.01. 

The views expressed in the article do not necessarily represent 

the views of the DOE or the U.S. Government. The U.S. 

Government retains and the publisher, by accepting the article 

for publication, acknowledges that the U.S. Government retains

a nonexclusive, paid-up, irrevocable, worldwide license to 

publish or reproduce the published form of this work or allow 

others to do so, for U.S. Government purposes.

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