Dynamic modelling of a large-scale horizontal-axis wind turbine coupled to a hydraulic pump

Abstract

The recent increase in demand for wind turbines has given rise to concerns about the availability of materials used in their construction. The combination of a wind turbine coupled to a hydraulic pump, instead of an electrical generator, offers an alternative application for this renewable energy technology. This article analyses the dynamic response of a wind/hydraulic system consisting of a wind turbine driving a swash-plate pump. This is done by means of mathematical models utilising MATLAB^® and Simulink^®. The operational aspects of the proposed wind/hydraulic pumping system are validated against the standard baseline 5-MW wind turbine model of the National Renewable Energy Laboratory. Control issues encountered in wind turbines and hydraulic systems are analysed, with the wind turbine control systems used to run electrical generators being adopted to control the pressure-controlled swash-plate pump. The pump lends itself to such applications as it can be controlled by varying the swash-plate angle, thus controlling the pump’s output power and torque. Methods for the generation of artificial wind data are also included, and a simple wind speed time series is developed. This time series is used to test the wind turbine hydraulic system under varying wind conditions using the concept of ‘control regions’. The models developed show the standard steady-state response of the wind turbine together with the dynamic behaviour of the wind turbine. Once the control parameters are established, the system also presents a wind turbine controller and analyses the behaviour of the system under typical and extreme wind conditions. This study concludes that such a system has significant potential to be technically achievable.

Keywords

Wind turbine-driven pump control region swash-plate pump proportional–integral–derivative controller bumpless transfer

Introduction

The use of wind energy technology for the pumping of fluids at high pressure results in efficient energy transfer. It also has the advantage of not using costly materials used in electric generators (Diepeveen, 2009; Diepeveen and Michailidis, 2011; Laguna, 2010), such as copper and other rare metals. Recent research in the field, conducted independently by Delft University of Technology (Laguna, 2010) and the University of Malta (Buhagiar, 2012; Buhagiar and Sant, 2012, 2013), analysed the use of wind energy to drive a positive displacement hydraulic pump that generates a pressurised source of sea water. This concept facilitates the integration of wind power with hydro energy storage systems and reverse osmosis desalination plants (Buhagiar and Sant, 2012, 2013). The concept of hydraulic wind turbines is demonstrated in Figure 1 where a conventional system driving an electrical generator has been included for comparative purposes. Large-scale wind turbines which drive positive-displacement hydraulic pumps are already being developed (Buhagiar and Sant, 2013), among which are those of Mitsubishi Power Systems, Europe (Mitsubishi Power Systems Europe, Ltd., n.d.), and the Delft Offshore Turbine being developed by the Delft University of Technology (Diepeveen, 2009; Diepeveen and Michailidis, 2011; Laguna, 2010).

Figure 1.

Comparison of a conventional wind turbine driving an electrical generator and one driving a hydraulic system.

This article presents a new dynamic model for performance simulation of a horizontal-axis wind turbine (HAWT) directly coupled to a swash-plate hydraulic pump. The model was built using the Simulink^® package and integrates existing engineering models covering swash-plate pumps (Bahr Khali et al., n.d.; Dean and Fales, 2007; Manring, 2005), wind flow and HAWT power performance simulation (Burton et al., 2011; Manwell et al., 2009), wind turbine control (Astrom, 2002; Burton et al., 2011; Lindeberg et al., 2012; Linders and Thiringer, 1993; Novak et al., 1995) and hydraulic systems (Bahr Khali et al., n.d.; Dean and Fales, 2007; Manring, 2005). The model consisted of a simplified blade-pitch controller as well as feedback mechanisms between the swash-plate pump and the wind turbine to limit the rotor torque (Linders and Thiringer, 1993; Novak et al., 1995). The model was applied to a 5-MW hypothetical wind turbine with an optimised pump design and an analysis of the various results is presented in this article.

Methodology

The different power control strategies that were implemented included the following:

Variable speed operation with torque control, which allowed the wind turbine to perform at maximum efficiency for wind speeds between U_cut-in (the cut-in wind speed) and U_rated (the rated wind speed).

Blade pitch control was used to limit the power output between the rated wind speed and U_cut-off (the cut-off wind speed).

Control strategies for wind turbines are listed in Table 1 (Manwell et al., 2009).

Table 1.

Control strategies for wind turbine operation.

	Variable speed	Fixed speed
	U_cut-in <U ⩽ U_rated	U_rated <U ⩽ U_cut-out
Pitch control	Fixed pitch	Control for rated revolutions per minute
Torque control	Control for C_P-Max	Control for smooth power

In view of the lack of methods that control wind turbines coupled to a hydraulic pump, an existing control mechanism (Novak et al., 1995) was modified and used to build a representative mathematical model (as shown in Figure 2), which shows how the various components of the model interact with each other.

Figure 2.

Control mechanism used to control a wind turbine.

The work also defined a wind turbine controller that adjusted the operational state of the turbine, hence keeping it on its performance curves. The algorithm modelling the turbine controller was capable of determining the operating state of the wind turbine and of uploading the control parameters into the various sub-systems. The model used is a two-mass shaft model. A more elaborate model would have comprised a five-mass model, which would have included the three turbine blades as part of the model (Lindeberg et al., 2012). In this case, the effect of the wind turbine rotor blades is taken into account, by means of a simple model which contributes to the generation of aerodynamic torque.

Artificial wind data can be generated by applying Monte Carlo simulation techniques. This enables system testing under different specific wind speed time series (Klee and Allen, 2011). Wind data sequences of 10-min duration were generated for the various wind turbine control regions (International Standard, 2005–2008). Moreover, in the normal turbulence model (NTM), the representative value of the turbulence standard deviation is given by the 90% quantile for the given hub height wind speed. The probability density function that best describes the behaviour for turbulence is the Gaussian distribution (Manwell et al., 2009). Values for the turbulence standard deviation are shown in Figure 1(a) of standard IEC 61400-1 (International Standard, 2005–2008).

The time series was therefore generated utilising a white noise generator, which utilised a Ziggurat Algorithm (Gavriluta et al., 2012; Marsaglia and Tsang, 2000). Kaimal filters were also used to model local effects such as the type of terrain (Gavriluta et al., 2012; Ray et al., 2006). The model was used to generate wind sequences with an average wind speed and a standard deviation with the values derived from IEC 61400-1. These wind sequences were then used to test the wind turbine.

The National Renewable Energy Laboratory (NREL) 5-MW Reference Wind Turbine (Jonkman et al., 2009) was used as a reference wind turbine, while the C_p–λ curve and its relationship with the pitch angle β (Abbas and Abdulsada, 2010) were used to determine values of the pitch angle β at various wind speeds.

The algorithm governing the wind turbine controller was based on the creation of control regions that were designated as 2.0, 2.5, 3.0 and 3.5 as described in Table 2. The use of control regions also allowed the definition of the control parameters for the wind turbine, which could be downloaded into the model by the turbine controller as the wind conditions changed.

Table 2.

Definition of the wind turbine control regions.

Control region	Minimum wind speed (m s⁻¹) for the control region	Wind speed (m s⁻¹) at the mid-point of the control region	Maximum wind speed (m s⁻¹) for the control region
2.0	4	6.00	8.0
2.5	8	10.00	12.0
3.0	12	15.25	18.5
3.5	18.5	21.75	25.0

The controller was capable of selecting the appropriate control region by calculating the weighted moving average of the wind speed. A low-pass filter enabled the turbine controller to determine the set point of the angular velocity of the wind turbine and that of the pitch angle. The controller also used the instantaneous value of the wind speed to determine the bumpless transfer parameters and the required torque feedback, which is used in control regions 2 and 2.5. Bumpless transfer with tracking (Astrom, 2002; Lindeberg et al., 2012) was used to avoid switching transients. A block diagram of the controller is shown in Figure 3.

Figure 3.

The wind turbine controller.

Developing and testing the models

The flow chart shown in Figure 4 describes the methodology used. The definition of the control regions divided the range of operation of the wind turbine into manageable zones and allowed the derivation of wind data sequences, which were used to test the wind turbine, the hydraulic system and the turbine controller. The values of the wind turbine and the hydraulic system parameters were defined so as to provide a response which equalled the steady-state response of the standard NREL 5-MW Reference Wind Turbine.

Figure 4.

Flow chart showing the methodology.

The control parameters of the three controllers were derived by analysing the system response to various values of proportional, integral and derivative (PID) gain constants. The required response time of the system components for each of the control regions was first determined. The system response times, rise times and percentage overshoot were then analysed for various values of P, I, D and N, until the required response was obtained. The system was also checked for stability. This was done by utilising the MATLAB Control Toolbox^®. Following the definition of the PID parameters, the system was tested under the varying wind conditions by applying the artificial wind sequences derived at the average wind speeds of the various control regions.

Following this, the turbine controller was tested in various wind conditions. This allowed the definition of the torque control feedback level, the bumpless transfer set points for the various controller states and the generation of the steady-state response of the model. This response was also compared with the steady-state response of the NREL 5-MW Reference Wind Turbine (Jonkman et al., 2009). Once all the parameters and feedback levels were defined, the dynamic models were run again to obtain the final results.

Mathematical models

The wind turbine model

The power extracted by the wind turbine from the wind is given by equation (1), where C_p is the power coefficient (Burton et al., 2011; Manwell et al., 2009)

P_{w} = \frac{1}{2} ρ A C_{p} (λ, β) U^{3}

(1)

From which the aerodynamic torque, T_a is given by

T_{a} = \frac{1}{2} ρ A r C_{p} (λ, β) U^{2}

(2)

where

C_{p} (λ, β) = λ C_{q} (λ, β)

(3)

The relationship between C_p, the tip speed ratio, λ, and the pitch angle, β, is given by equation (4) (Abbas and Abdulsada, 2010)

C_{p} (λ, β) = (0.44 - 0.167 β) s i n [\frac{π (λ)}{15 - 0.3 β}] - 0.160 (λ) β

(4)

As shown in Figure 2, the model consisted of three modules: the aerodynamic module, the mechanical module and the hydraulic module. The mechanical module included the inertia of the turbine and pump and the properties of the shaft connecting the two rotating systems. The mechanical module consisted of two rotating masses with an interconnecting shaft (Singh and Santoso, 2011). The model included the interaction between the aerodynamic, the mechanical and the hydraulic modules, respectively (Novak et al., 1995). The relationship between the aerodynamic torque, T_a, and the pump torque, T_p, is given by equation (5) (Singh and Santoso, 2011). This relationship was used to integrate the wind turbine with the hydraulic system

T = T_{a} - T_{p} = J_{t} {\overset{•}{ω}}_{t} + R_{s} ω_{t}

(5)

In control engineering, if the signals in a complex non-linear system are small enough, then within a limited operating range, it is mathematically possible to approximate the non-linear system using a linear one (Houpis and Sheldon, 2003; Ogata, 2010). The complex relationship described by the non-linear equations was therefore transformed into a linear relationship. This traditional approach is commonly used when using linear controllers such as PIDs (Ogata, 2010). The mathematical relationship shown in equation (5) was therefore linearised, resulting in the use of three scaling parameters, γ, ε and δ, which transformed angular velocity, wind speed and pitch into torque, as shown in equation (6)

J_{t} {\overset{•}{ω}}_{t} + R_{s} ω_{t} = γ Δ ω_{t} + ε Δ U + δ Δ β

(6)

where (Abbas and Abdulsada, 2010)

\begin{array}{l} γ = J_{t} {\frac{\partial {\overset{•}{ω}}_{t}}{\partial ω_{t}} |}_{o p} = \frac{1}{2} ρ A r^{2} U_{o p} {\frac{\partial C_{q}}{\partial λ} |}_{o p} \\ ε = J_{t} {\frac{\partial {\overset{•}{ω}}_{t}}{\partial U} |}_{o p} = \frac{1}{2} ρ A r U_{o p} [2 {C_{q} |}_{o p} - λ_{o p} {\frac{\partial C_{q}}{\partial λ} |}_{o p}] \\ δ = J_{t} {\frac{\partial {\overset{•}{ω}}_{t}}{\partial β} |}_{o p} = \frac{1}{2} ρ A r U_{o p}^{2} {\frac{\partial C_{q}}{\partial β} |}_{O P} \end{array}

(7)

Basic dynamic equations (Lindeberg et al., 2012; Novak et al., 1995) establish a relationship between the inertia of the wind turbine, J_t, the inertia of the pump, J_p, and the properties of the drive shaft in terms of the angular velocities and the difference between T_a and T_p. The relationship is governed by the following equations

ω_{t} (s) = (T_{a} - T_{p}) • (\frac{1}{s J_{t} + R_{s}})

(8)

From which

ω_{p} (s) = (T_{a} - T_{p}) • (\frac{1}{s J_{t} + R_{s}}) • \frac{(s K_{s 1} - s R_{s} + B_{s 1})}{(s^{2} J_{p} + s K_{s 2} + B_{s 2})}

(9)

The dynamic equation of the pitch actuator is given by equation (10)

\frac{U_{o} (s)}{U_{a} (s)} = \frac{\frac{k_{a}}{s k_{s_{1}}}}{1 + \frac{k_{a}}{s k_{s_{1}}}} = \frac{k_{a}}{k_{s 1} s + k_{a}}

(10)

By combining equations (5) to (10), the mathematical model shown in Figure 5 was obtained. This was then constructed in Simulink®. The model had two look-up tables which include the set points for the angular velocity, ω_ref, of the wind turbine and the pitch angle, β_ref. These set points were determined through the use of a low-pass filter, which filters the value of the wind speed providing stability to the wind turbine.

Figure 5.

The completed wind turbine model as designed in Simulink®.

The model incorporated bumpless transfer with tracking, which was required to smooth out the transients which would be caused by the switching of PID parameters. The method used was that shown in Figure 6 (Astrom, 2002). The external input to the system was held constant until the PID settled down from the switching transient. This time duration was controlled by a step function. After the time elapsed, control was switched back to the PID. Both parameters were set by the controller, according to the value of the wind speed at the time of the switching.

Figure 6.

PID bumpless control transfer with tracking mode for the wind turbine. Values are set by the controller according to wind speed (Astrom, 2002).

A model for the hydraulic pump

Pumps used for power transmission are of the positive displacement type (Buhagiar and Sant, 2013). These include swash-plate pumps (Buhagiar and Sant, 2013; Douglas et al., 2011; Manring and Johnson, 1996). In a pressure-controlled system, the swash-plate angle, α, is controlled via the output pressure of the pump, and the mathematical relationship between the volumetric displacement, V_d, and α is as shown in equation (11) (Manring, 2005)

V_{d} = \frac{N_{p} A_{p} r_{p} \tan (α)}{π}

(11)

The relationship between the flow and the pressure differential is given by equation (12) (Laguna, 2010)

P_{h y d} = Δ p Q

(12)

where

V_{d} = \frac{Q}{ω_{p}}

(13)

The dynamic equations of the pressure-controlled swash-plate pump are given in equation (14) (Manring, 2005)

\overset{•}{P_{d}} = - \frac{β' K_{p}}{V} (P_{d} - P_{d_{o}}) + \frac{β' G_{p}}{V} (α - α_{o}) and \overset{•}{α} = - \frac{2 K_{q} A_{v}}{A_{c} L_{c} (k_{v} + 2 K_{f_{q}})} (P_{d} - P_{d_{o}})

(14)

Equations (11), (12) and (14) were therefore represented in Simulink® with the model shown in Figure 7, which also included a PID (Hongliu and Manring, 2001; Bahr Khali et al., n.d.) controller, a feedback loop and two look-up tables; one converted ω_p into the nominal discharge pressure of the pump, $P_{d_{o}}$ , while another converted ω_p into the nominal swash-plate angle, α_o.

Figure 7.

Integration of the PID controller, look-up tables, hydraulic load and flow calculation into a pressure-controlled swash-plate pump.

The equations lead to the Simulink® models shown in Figures 5 and 7. These were further integrated into the model as shown in Figure 8, which shows the connections between the various system components. The model also contained an output torque feedback loop, which was established by the relationship shown in equation (5).

Figure 8.

Integrating the wind turbine module, hydraulic system module and the hydraulic load in MATLAB^® and Simulink^®.

The turbine controller

As outlined in Figure 3, the turbine controller controlled the wind turbine, the swash-plate pump and the pitch actuator. Figure 9 shows the transfer of control signals between the turbine controller and the wind turbine, the swash-plate pump and the pitch actuator. The turbine controller performed the following functions:

Analysed the last 60 s of wind speed data and computed the weighted average of the wind speed. This determined in which control region the wind turbine will operate in for the next 60 s and changed the PID parameters and reference values accordingly;

Calculated the torque control gain according to the current wind speed, thereby setting the feedback conditions for the torque controller;

Calculated the linearisation parameters for the wind turbine according to the current wind speed;

Decided the set point for the wind turbine, ω_ref, by filtering the wind speed data stream, by means of a low-pass filter;

Decided the bumpless transfer set points for the PID controllers according to the current wind speed.

Figure 9.

Control signal flow between the wind turbine and the turbine controller.

Steady-state performance curves for the wind turbine

Equation (4) was used to define the values of β for the region U_rated > U > U_cut-out. The results from this equation were compared to those of the NREL 5-MW Reference Wind Turbine (126 m diameter, three blades), as shown in Figure 10(a). The values of β were calculated using an iterative methodology. Equation (10) also gave values of C_p against λ. For β = 0, C_p peaked at λ = 7.5. Figure 10(b) shows the resulting C_p–λ curves. The steady-state response of the wind turbine was initially generated using the conditions shown in Table 3. The results are shown in Figure 11, and these were comparable to the steady-state response of the NREL 5-MW Reference Wind Turbine (Jonkman et al., 2009).

Figure 10.

Wind turbine characteristics: (a) values of pitch β, in degrees, against wind speed compared to NREL base values and (b) C_p–λ curves for the wind turbine.

Table 3.

Operating conditions for steady-state analysis of the wind turbine.

Wind speed (m s⁻¹)	Tip speed ratio, λ	Angular velocity (rad s⁻¹)	Pitch (degrees or radians)
$0 < \bar{U} < 4$	0	0	0
$4 \leq \bar{U} < 12$	Constant at 7.55	$ω_{a} = \frac{\bar{U} λ}{r}$	0
$12 \leq \bar{U} < 25$	$λ = \frac{ω_{a} r}{\bar{U}}$	1.42 (rated angular velocity)	Calculated according to look-up table
$\bar{U} \geq 25$	0	0	90° (1.57 rad)

Figure 11.

Steady-state response of the wind turbine to wind speed: (a) aerodynamic power, (b) wind turbine angular velocity, (c) tip speed ratio, λ, (d) pitch angle, (e) power coefficient, C_p, and (f) aerodynamic torque versus wind speed.

Physical parameters for the hydraulic system

The operating parameters of the swash-plate pump were based on the properties of a Hägglunds MB 2400 (Rexroth (Bosch Group), n.d.) pump and are shown in Tables 4 and 5. The relationships between the parameters were determined using equations (11) to (13) and have been chosen in a manner that makes them as realistic as possible. Due to this, the chosen parameters:

Gave realistic dimensions as regards piston radius, piston stroke, piston diameter and swash-plate angle displacement, which was limited to 30° at the maximum flow rate of the pump;

Provided an operating characteristic which could match that of the wind turbine;

Showed stability over the parametric range of pressure and flow which governed the operating range of the wind turbine.

Table 4.

Physical parameters of the swash-plate-pump.

Parameter	Value
Pump parameters
Maximum displacement	1 m s⁻³
Maximum discharge pressure	35 MPa
Nominal angular velocity, ω_nom	1.67 rad s⁻¹
Pump moment of inertia, J_p	534,116 kg m²
Pump physical parameters
Number of pistons, N_p	5
Piston area, A_p	0.79 m²
Pump radius, r_p	2 m
Controller arm moment, L_c	3 m
Controller actuator valve cross-sectional area, A_c	0.79 m²
Bulk modulus of hydraulic fluid (sea water), β′	2200 MPa
Discharge volume, V	7 m³ s⁻¹
Control valve physical parameters
Control valve flow gain, K_q	5000 m² s⁻¹
Control valve flow force gain, k_fq	5500 N m⁻¹
Control valve spring rate, k_v	550 N m⁻¹
Actuator valve cross-sectional area, A_v	0.78 m²
Critical pump parameters
Damping factor, ζ	0.707

Table 5.

Calculated parameters for the pressure-controlled swash-plate pump.

Calculated parameters
Pump leakage coefficient, K_p	3.63 × 10⁻⁵ m³ Pa⁻¹ s⁻¹
Pump natural frequency, f_n	8992 Hz
Bandwidth of the pressure-controlled swash-plate pump, f_n	2998 Hz
System rise time, t_r	5.89 × 10⁻⁵ s
System settling time, t_set	1 × 10⁻⁴ s
Maximum percent overshoot, M_p	4.32%
Pump gain, G_p	4.175

Figure 12 shows the expected variation of flow, swash-plate angle and pump pressure with wind speed. The values from these graphs were placed in look-up tables, as shown in Figure 7. Table 6 shows the results which were expected when applying the wind sequences with an average value of wind speed, corresponding to the mid-points of the control regions defined in Table 2. Figure 12(a) shows that the system was designed in such a manner so that the flow of sea water in the swash-plate pump was larger for lower wind speeds. This was done by increasing the reference angle for the swash plate at lower wind speeds, as shown in Figure 12(b). The hydraulic system was designed to have a maximum flow at lower wind speeds, as this would be ideal for regions with average wind speeds which are either in control region 2.0 or 2.5. The characteristics of the flow can be changed according to the average wind speed of the region, that is, the maximum flow could also be in control regions 3.0 and 3.5.

Figure 12.

The calculated pump behaviour with wind speed: (a) flow, (b) swash-plate angle and (c) output pressure.

Table 6.

Expected calculated average values for the various control regions with the wind data sequence applied at the operating point shown in column 2.

CR	Average wind speed at the operating point (m s⁻¹)	Average angular velocity (rad s⁻¹)	Average output pressure (Pa)	Average flow (m³ s⁻¹)	Average output torque (N m)	Average output power (MW)
2.0	6	0.710	1.17 × 10⁶	0.617	1 × 10⁶	0.722
2.5	10	1.198	8.747 × 10⁶	0.412	3.00 × 10⁶	3.603
3.0	15.25	1.427	1.695 × 10⁷	0.296	3.48 × 10⁶	5.010
3.5	21.75	1.427	1.695 × 10⁷	0.296	3.48 × 10⁶	5.010

CR: control region.

Analysis and discussion

Generation of the artificial wind data streams

Sequences of artificial wind data were generated, with an average wind speed corresponding to the mid-point of every control region. Table 7 shows the average wind speed of each data sequence, together with the standard deviation of the wind speed distribution. These are according to the NTM described in IEC 61400-1 (International Standard, 2005–2008). These sequences were then used to test the model. The histogram and the wind sequence generated for control region 2.5 are shown in Figure 13. The wind sequences were also analysed utilising a power spectrum density function in MATLAB®, with the results for the control region 2.5, also being shown in Figure 13. The sampling frequency used was 1 Hz. Since only normal turbulence was generated in the wind sequence, the power spectrum density only shows the turbulent part of the wind energy spectrum. Similar sequences were obtained for control regions 2.0, 3.0 and 3.5.

Table 7.

Values of mean and wind speed variance for the artificial wind sequences in the four control regions (International Standard, 2005–2008).

Control region	Average theoretical wind speed (m s⁻¹) for the control region	Average wind speed of the artificial wind data sequence (m s⁻¹)	Turbulence standard deviation for the normal turbulence model(IEC 61400-1) (m s⁻¹)	Turbulence standard deviation obtained from model (m s⁻¹)
2.0	6.00	6.11	1.1	1.12
2.5	10.00	10.11	1.4	1.42
3.0	15.25	15.36	1.8	2.00
3.5	21.75	21.36	2.0	2.25

Figure 13.

Wind values for control region 2.5 (Manwell et al., 2009).

Wind turbine behaviour within different control regions

The behaviour of the model at the mid-points of the various control regions was analysed by applying the generated wind sequences. The results obtained are shown in Figures 14 to 17. These show how the wind speed, the wind turbine angular velocity, the aerodynamic torque and output torque and water pressure and flow varied with time.

Figure 14.

Results obtained for control region 2: (a) wind speed and angular velocity, (b) output torque and aerodynamic torque and (c) output pressure and output flow.

Figure 15.

Results obtained for control region 2.5: (a) wind speed and angular velocity, (b) output torque and aerodynamic torque and (c) output pressure and output flow.

Figure 16.

Results obtained for control region 3.0: (a) wind speed and angular velocity, (b) output torque and aerodynamic torque and (c) output pressure and output flow.

Figure 17.

Results obtained for control region 3.5: (a) wind speed and angular velocity, (b) output torque and aerodynamic torque and (c) output pressure and output flow.

Table 8 shows that the values of angular velocity, average output pressure and average output torque are very close, or equal, to the calculated steady-state values, at the applied average wind speed. The model also showed stability over the operating range with the chosen PID gain parameters.

Table 8.

Model-generated results compared with calculated values.

CR	Pump angular velocity (rad s⁻¹)		Average output pressure (Pa)		Average flow (m³ s⁻¹)		Average output torque (N m)		Average output power (MW)
CR	Calculated	Model	Calculated	Model	Calculated	Model	Calculated	Model	Calculated	Model
2.0	0.71	0.71	1.17 × 10⁶	1.18 × 10⁶	0.617	0.611	1.00 × 10⁶	1.01 × 10⁶	0.722	0.720
2.5	1.08	1.19	8.74 × 10⁶	1.04 × 10⁷	0.412	0.406	3.00 × 10⁶	2.88 × 10⁶	3.603	4.222
3.0	1.42	1.39	1.695 × 10⁷	1.62 × 10⁷	0.296	0.308	3.48 × 10⁶	3.48 × 10⁶	5.010	4.989
3.5	1.42	1.41	1.695 × 10⁷	1.66 × 10⁷	0.296	0.295	3.48 × 10⁶	3.49 × 10⁶	5.010	4.897

CR: control region.

The wind turbine controller characteristics

The model was then tested with the turbine controller under varying wind conditions. The results are shown in Figures 18 and 19. Figure 18 shows the response obtained by subjecting the model to a ramping wind speed sequence which starts at 4 m s⁻¹ and ends at 27 m s⁻¹ over a time period of 600 s. The wind speed was incremented by 1 m s⁻¹ every 25 s. This ensured that the changes in wind speed are within the 60-s monitoring period used by the controller and that wind changes did not occur in unison with the controller timings. The results indicated that the turbine followed the wind input and provided an angular velocity, pressure and flow which were according to the calculated values. In control region 2.5, it was noted that the angular velocity of the wind turbine at times exceeded the required value, but then settled to the required value after a few seconds. In this period, the angular velocity was being controlled by the torque feedback loop.

Figure 18.

Response to rising (ramp-up) wind conditions: (a) wind speed and angular velocity, (b) output torque and aerodynamic torque and (c) output pressure and output flow.

Figure 19.

Response to typically varying wind conditions (Farrugia and Sant, 2011): (a) wind speed and angular velocity, (b) output torque and aerodynamic torque and (c) output pressure and output flow.

The model was also subjected to a typical wind data stream (Farrugia and Sant, 2011), and the model’s behaviour is that shown in Figure 19. Over a period of 600 s, the wind speed range varied from 4 to 21 m s⁻¹, taking the turbine from a stationary condition, with the wind speed being below the cut-in wind speed, U_cut-in, to beyond the rated wind speed, U_rated, but mostly operating in control regions 2, 2.5 and 3.

The response of the wind turbine to wind changes in control regions 2 and 2.5 depended on the amount of feedback from the output torque. The wind turbine model gave a different response to the changes in wind for different levels of torque feedback as can be seen in the following section.

Steady-state response using the dynamic model

The model was also validated against the NREL 5-MW Reference Wind Turbine (Jonkman et al., 2009) by generating its steady-state response. This also determined the level of feedback required to control the aerodynamic torque as described in equation (5) and gave a maximum power output in the control regions 2 and 2.5. Different levels of torque feedback were therefore applied until the correct amount of feedback was established. The steady-state response was generated by applying a wind speed, which was sequentially increased from 4 to 25 m s⁻¹, each time incremented by 0.25 m s⁻¹, allowing the system to settle and then recording the steady-state output from the model. This response curve was obtained with a feedback gain given by $G a i n = - m U + c$ , with the results being shown in Figure 20. The model operated in optimal conditions, that is, stable and with the output following the expected results when m < 0.2. Stability was therefore also a function of the amount of torque control applied to the wind turbine.

Figure 20.

Steady-state response of the wind turbine model with Gain = −0.2U + 1.25 for: (a) aerodynamic and output power, (b) angular velocity and (c) aerodynamic torque and output torque.

The effect of different values of m on the behaviour of the wind turbine was also analysed. The stability results for different values of m are shown in Table 9. The table shows that the system was unstable for larger values of m. Although stability increased with smaller values of m, the power output best matched the aerodynamic output at m = 0.2. The system was stable for values of m < 0.2, but the power output did not follow the ideal aerodynamic power curve. This is shown in Figure 21. In control regions 3.0 and 3.5, the output torque was controlled by changing the pitch angle β and therefore the feedback gain was set to zero.

Table 9.

Stability analysis using the steady-state response of the wind turbine with increasing values of m.

m	Gain equation	System stability
0.725	$G a i n = - 0.725 U + 1.25$	Unstable
0.625	$G a i n = - 0.625 U + 1.25$	Unstable
0.525	$G a i n = - 0.525 U + 1.25$	Unstable
0.225	$G a i n = - 0.225 U + 1.25$	Stable and following ideal curve
0.105	$G a i n = - 0.105 U + 1.25$	Stable but not following ideal curve
0.0625	$G a i n = - 0.063 U + 1.25$	Stable but not following ideal curve
0.0500	$G a i n = - 0.050 U + 1.25$	Stable but not following ideal curve

Figure 21.

Torque curves for: (a) m = 0.725 and (b) m = 0.0625.

Conclusion

The salient points and the key results obtained in the research are summarised below:

Modelling results have shown that it is possible to drive a swash-plate pump using a wind turbine, hence reducing the weight of a tower-mounted nacelle. Due to the slow rotational speed of the pump, which matches that of the wind turbine rotor, a gearbox is not required, as in the case of electric generators. The total weight of a 5-MW induction generator (ABB Group, n.d.) and an equivalent gearbox is approximately 48 tonnes (Wikov, n.d.),while the weight of the pump is 6.5 tonnes (Rexroth (Bosch Group), n.d.). Therefore, a savings of 42 tonnes in nacelle weight is achievable.

The steady-state response of the wind turbine was similar to that of the NREL 5-MW Reference Wind Turbine, while the dynamic model parameters are the same as those for the NREL 5-MW Reference Wind Turbine.

A wind turbine controller was designed to determine in which control region the wind turbine was operating using a moving average calculation. The turbine controller also downloaded bumpless transfer parameters and torque gain parameters according to the current wind conditions. The behaviour of the turbine controller under varying wind conditions was determined. Torque control was analysed where the parameters for a stable system and the best torque feedback mechanism were determined. A stability study carried out for different values of gain determined the best values for the feedback parameters.

Analysis determined the range of system stability and maximisation of power output. Following the determination of the correct level of the torque feedback, the steady-state response of the system was determined using the dynamic model.

As the design is for an offshore wind turbine, the hydraulic system was designed with sea water as the hydraulic fluid. However, any hydraulic fluid can be used. This is done by changing the bulk modulus of the fluid in the system. In the case of an offshore HAWT, the use of sea water has several advantages. Sea water is cheap and readily available in limitless quantities. Moreover, the sea can be used as a hydraulic source and sink so that the environment is protected against hydraulic fluid leakage. As a disadvantage, one also has to consider that the corrosive properties of sea water could be a major issue.

Footnotes

Appendix 1 Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

References

Abbas

FAR

Abdulsada

(2010) Simulation of wind-turbine speed control by MATLAB. International Journal of Computer and Electrical Engineering 2(5): 1793–8163.

ABB Group (n.d.) Technical note: Wind power generators, one platform for all high speed solutions. Available at: http://www05.abb.com/global/scot/scot234.nsf/veritydisplay/9ea1742a317b2389c125784f0038036b/$file/Technical%20Note%20One%20platforms%20LR.pdf (accessed 11 June 2015).

Astrom

(2002) Control System Design (Chapter 6). Department of Mechanical and Environmental Engineering, University of California. Available at: http://www.cds.caltech.edu/~murray/courses/cds101/fa02/caltech/astrom.html///

Bahr Khali

Svoboda

Bhat

(n.d.) Modelling of Swash Plate Axial Piston Pump with Conical Cylinder Blocks. Montréal, QC, Canada: Mechanical and Industrial Engineering Department, Concordia University.

Buhagiar

(2012) Analysis of a Wind Turbine Driven Hydraulic Pump. Final Year Thesis, Department of Mechanical Engineering, University of Malta, Msida.

Buhagiar

Sant

(2012) Performance analysis of a wind turbine driven swash plate pump for large scale offshore applications. Journal of Physics: Conference Series 555: 012016.

Buhagiar

Sant

(2013) Analysis of a stand-alone hydraulic offshore wind turbine coupled to a pumped water storage facility. In: The ISE annual conference, Institute for Sustainable Energy, University of Malta, Msida, 21 March 2013, pp. 40–48.

Burton

Sharpe

Jenkins

. (2011) Wind Energy Handbook (2nd edn). New York: John Wiley & Sons.

Dean

Fales

(2007) Modern control design for a variable displacement hydraulic pump. In: American control conference (ACC ‘07), New York, 9–13 July, pp. 3535–3540. New York: IEEE.

10.

Diepeveen

NFB

(2009) Seawater-based hydraulics for offshore wind turbines. WE@Sea Progress Report, Delft University Wind Research Institute, Delft, August.

11.

Diepeveen

NFB

Michailidis

(2011) Conceptual design of a DOT farm generator station. In: EWEA offshore conference, Amsterdam, 29 November–1 December.

12.

Douglas

Gasiorek

Swaffield

. (2011) Fluid Mechanics (6th edn). Upper Saddle River, NJ: Prentice Hall.

13.

Farrugia

Sant

(2011) Wied Rini II – A five year wind survey at Malta. Wind Engineering 35(4): 419–432.

14.

Gavriluta

Spataru

Mosincat

. (2012) Complete methodology on generating realistic wind profiles based on measurements. In: International conference on renewable energies and power quality, Santiago de Compostela. European Association for the Development of Renewable Energies, Environment and Power Quality. Available at: http://icrepq.com/icrepq'12/828-gavriluta.pdf

15.

Hongliu

Manring

(2001) A single-actuator control design for hydraulic variable displacement pumps. In: Proceedings of the American control conference, Arlington, VA, 25–27 June, vol. 6, pp. 4484–4489. New York: IEEE.

16.

Houpis

Sheldon

(2003) Linear Control System Analysis and Design with MATLAB® (6th edn). Florida: CRC Press, Taylor & Francis Group.

17.

International Standard (2005–2008) IEC 61400-1: Wind Turbines – Part 1: Design Requirements (3rd edn). Geneva, Switzerland: International Electrotechnical Commission.

18.

Jonkman

Butterfield

Musial

. (2009) Definition of a 5-MW Reference Wind Turbine of Offshore System Development. Colorado: National Renewable Energy Laboratory.

19.

Klee

Allen

(2011) Simulation of Dynamic Systems with MATLAB^® and SIMULINK^® (2nd edn). Florida: CRC Press, Taylor & Francis Group.

20.

Laguna

(2010) Steady-state performance of the Delft Offshore Turbine. MSc Thesis, Delft University of Technology, Delft.

21.

Lindeberg

Svendsen

Uhlen

(2012) Smooth transition between controllers for floating wind turbines. In: Energy Procedia, Deep Sea Offshore Wind R&D Conference, vol. 24, Trondheim, Norway, 19–20 January 2012, pp. 83–98. Amsterdam: Elsevier Science Publishers.

22.

Linders

Thiringer

(1993) Control by variable rotor speed of a fixed-pitch wind turbine operating in a wide speed range. IEEE Transactions on Energy Conversion 8(3): 520–526.

23.

Manring

(2005) Hydraulic Control Systems. New York: John Wiley & Sons.

24.

Manring

Johnson

(1996) Modelling and designing a variable-displacement open-loop pump. Journal of Dynamic Systems, Measurement and Control 118: 267–272.

25.

Manwell

McGowan

Rogers

(2009) Wind Energy Explained: Theory, Design and Application (2nd edn). New York: John Wiley & Sons.

26.

Marsaglia

Tsang

(2000) The ziggurat method for generating random variables. Journal of Statistical Software 5(8): 1–7.

27.

Mitsubishi Power Systems Europe, Ltd. (n.d.) Sea Angel: The future of offshore wind. Available at: http://www.artemisip.com/sites/default/files/docs/2011-11%20SeaAngel%20Brochure2_0.pdf (accessed 11 October 2015).

28.

Novak

Ekelund

Jovik

. (1995) Modelling and control of variable speed wind-turbine drive-system dynamics. IEEE Control Systems 15(4): 28–38.

29.

Ogata

(2010) Modern Control Engineering (5th edn). New Jersey: Pearson.

30.

Ray

Rogers

McGowan

(2006) Analysis of Wind Shear Models and Trends in Different Terrains. Colorado: National Renewable Energy Laboratory.

31.

Rexroth (Bosch Group) (n.d.) Hägglunds drive systems. Available at: http://www.boschrexroth-us.com/country_units/america/united_states/en/Documentation_and_Resources/a_downloads/Rexroth-Hagglunds_Drive_Systems.pdf (accessed 11 June 2015).

32.

Singh

Santoso

(2011) Dynamic Models for Wind Turbines and Wind Power Plants. Colorado: National Renewable Energy Laboratories.

33.

Wikov (n.d.) Available at: http://www.wikov.cz/en/mechanical-gearboxes/according-to-application/wind-and-tidal (accessed 11 June 2015).