Optimal Control Strategies for Small–Scale Wind Energy Conversion Systems

1. Optimal Control Strategies for Small–Scale Wind Energy Conversion Systems by Mahinsasa Narayana Supervision team Dr Ghanim Putrus (Principal Supervisor) Dr Milutin Jovanovic Dr Pak Sing Leung

2. Outline • Introduction • Project Aim • Wind turbine operating principles • MPPT controller • Wind speed forecasting • Case study • Yaw behaviour • Case study • Discussion • Future work

3. Introduction • Stand alone systems • Rural electrification • Home or community type systems When a small-scale wind energy conversion system is operated in a stand-alone mode, it is required to have an energy storage device or an other source of power or both.

4. Grid connected systems With increased interest in renewable energy, grid-connected small-scale wind energy conversion systems are becoming popular in urban areas

5. Grid connected small wind turbines …… Vertical axis Grid-Connect wind turbine 1.5kW Grid-Connect small Wind Turbine installed in Northumbria University Grid connected small wind turbines are becoming popular in urban areas Building-mounted 1kW Grid-Connect Wind Turbine

6. Small wind turbines in urban areas • Small-scale wind turbines are usually installed at congested places with turbulent wind conditions. • Wind speed and direction vary frequently • For optimal operation: • Maximum power tracking • Need to match characteristics of wind rotor and generator • Wind rotor characteristics • Generator characteristics • Wind speed • Rotational speed • Understand yaw behaviour • Yaw error • Yaw rate

7. Project Aim Investigate optimal control strategies of small-scale wind energy conversion systems operating in turbulent wind conditions Develop a generic controller to maximise wind energy harnessing

8. Rotor DC bus Main grid or Local grid PMG AC-DC DC-DC DC-AC Battery  = = =  = Currant Input signals for controller Voltage Duty cycle Wind turbines operating principles Schematic of small wind power system

9. Generator Tail vane Wind rotor DC/AC inverter Tower Load or grid AC output from the generator Battery bank Rectifier unit & control system Main Components • Wind rotor • Controls • Yaw mechanism • Wind vanes (Tail vane and side vane) • Generator • Power control • Inverter/ Battery bank • Tower

10. Wind energy is converted to electrical energy Wind rotor Cm = Torque coefficient Cp= Power coefficient J=9.77kg.m2 D=2.21m Cpmax =0.4

11. Generator Mechanical energy is converted to electrical energy • Asynchronous (Induction) generators • Doubly Fed Induction Generators (DFIG) • Synchronise generators • Permanent magnet generators (PMG) Modern large wind turbines Small wind turbines

12. Rotor Ta. =Te. Maximum aerodynamic power points of the wind rotor Restoring power curve of the generator PMG Power V4 V3 V2 Wind speeds V1 Rotational speed (rev/min) Operating points • Wind energy conversion systems should operate at the points where the wind rotor curve and the electrical generator curve coincide. These points may not be optimal condition of the system. Wind rotor curves

13. Restoring power curve of the generator Power Wind rotor curves V4 V3 V2 V1 Rotational speed (rev/min) Restoring power curve of the generator V4 V3 V2 V1 Restoring power curve of the generator Common control strategy for small wind turbines V4 V3 V2 V1 Power control strategies • Fixed pitch - constant speed • Stall control • Variable pitch - variable speed • Pitch control • Fixed pitch - variable speed • Stall control Power Rotational speed (rev/min) Power Rotational speed (rev/min)

14. Maximum power points • In order to operate at maximum power output of a wind energy conversion system, it is necessary to drive the wind turbine at an optimal rotor speed for a particular wind speed (tip-speed ratio). To find out maximum operating power points: • Wind speed • Rotor speed • Rotor characteristics • Generator characteristics

15. Mechanical input power curve of the generator according to the load curve (2) Mechanical input power curve of the generator according to the load curve (1) Electrical load curve (1) Electrical load curve (2) (2) (1) Optimum operating point First Operating point New electrical load on the generator Function of maximum power point tracker Rotor curves Rotational speed Maximum power point tracker

16. Why is the MPPT Controller not perfect??? • For optimum operation of wind turbine, rotational speed of the wind rotor should be changed according to variation of wind speeds • Rate of change of rotational speed is limited • Wind turbine output power is interlaced with the turbine mechanical (aerodynamic) power and the rate of change of stored energy

17. Generated aerodynamic torque by wind rotor Restoring torque of generator (controllable) Response time of MPPT mechanism Where; J – Momentum of inertia of all the rotating parts - Mechanical torque generated by wind rotor -Restoring torque of generator (controllable variable) - Torque due to the friction losses (Generator & gear box); function of rotational speed () Therefore, the ideal response time of MPPT controller;

18. Wind Speed Forecasting • The linear prediction methods • Wind speed-time series data typically exhibit autocorrelation, which can be defined as the degree of dependence on preceding values. • Autocorrelated time series models are commonly used for the wind speed prediction. • Time series prediction takes an existing series of data and forecasts the future values. • Neural networks for wind speed prediction • It is called a neural network because it is a network of interconnected elements. • These element were inspired from studies of biological nervous systems. • Neural networks can train to learn sequential or time-varying pattern.

19. Autoregressive (AR) model • The wind speeds in the autoregressive (AR) model can be generally expressed as a function of past wind speed values.

20. To find the coefficients…. • The coefficients of a linear prediction model can be estimated by using the least square error method. To find the coefficients 1, 2, 3,… p, a set of equations as follows; • Element in the matrix, , are the coefficients which can be found by least squares error method.

21. Case study AR(10) predicted and measured wind data at Ekala, Sri Lanka (136 data with 10s period logging time)

22. Vt-1 Vt-2 Vt-3 Vt-4 Vt-5 Vt-6 Vt-7 Vt-8 Vt-9 Vt-10 Hidden layer Output layer Input layer Neural networks for wind speed prediction A neural network incorporated with a tapped delay line with delay from 1 to 10 and five neurons in hidden layer is used for wind speed prediction. This is a dynamic network, which consist of a feedforward network trained by backpropergation with tapped delay line at an input. This is called the focused time-delay neural network (FTDNN). • Number of Input Delays: 10 • Number of hidden layer: 1 • Number of neurons in hidden layer: 5 • Number of output neurons: 1 • Number of iterations for training: 600 Vt

23. NN predicted and measured wind data at Ekala, Sri Lanka (136 data with 10s period logging time)

24. Comparison of AR (10) model and Neural network prediction In order to measure the performance of different methods, root mean square error (RMSE) can be used. Root mean square error (RMSE) = According to this results, Focused Time-Delay Neural Network method is more accurate than AR (10) model.

25. NN & AR predicted and measured wind data at Kalpitiya, Sri Lanka (175 data with 1hr period logging time) NN : RMSE=0.3491 AR: RMSE=0.7302

26. NN predicted and measured wind data at Belfast, (400 data with 10min period logging time) RMSE=0.5636

27. How can time series predictions be used to improve MPPT mechanism ?? • Response time and Control algorithm • can be controlled to extract more energy if future wind speed value is known. • is adjusted to achieve predicted optimum value while synchronizing with optimum actual value • Tracking performance • Wind speed, Rotor speed, Rotor characteristics, Generator characteristics are required to track the MPP. • In sensorless strategy, predicted values can be used to improve the MPP tracking performance.

28. Wind speed Wind speed Restoring torque of electrical generator Turbine speed reference (Lookup table) Wind Energy Conversion System Controller + - Wind turbine speed MPPT controller with wind speed sensor Lookup table:

29. Wind speed Wind turbine speed Turbine speed reference (Lookup table) Wind speed - Restoring torque of electrical generator + Controller (Control algorithm) Wind Energy Conversion System Turbine speed reference (Lookup table) + - Wind turbine speed predicted wind speed value MPPT controller with wind speed sensor and wind prediction methods

30. With time series prediction Without time series prediction t t+1 actual t opt actual pre opt and MPPT control • Control algorithm • is adjusted to achieve predicted optimum value while synchronizing with optimum actual value is adjusted to synchronise with measured optimum value

31. Restoring torque of electrical generator Control limitations of • Maximum acceleration • Maximum deceleration

32. Simulation with MPPT • Wind speeds • Wind speed prediction by NNs • Wind rotor characteristics Energy extraction by the wind rotor • With wind speed prediction • Without wind speed prediction Wind rotor Radius of wind rotor : 1.105m Blade profile : NACA4415 Number of blades : : 2 Moment of inertia (I) : 9.77kg.m2

33. MPPT Control performances with and without NN predictions

34. Energy extraction within 1350 Sec Cpmax =0.4

35. Yaw behaviour • Many horizontal axis small-scale wind energy conversion systems use tail vane to keep the wind turbine into the wind direction • Small-scale wind energy conversion systems are usually installed at congested places with turbulent wind conditions • Yaw behaviour is important for maximum energy extraction • With fluctuating wind direction, wind energy extraction is reduced due to relative slow dynamics of the system • To improve the system dynamics, prediction of the turbine yaw behaviour in response to actual wind condition is needed

36. Development of a model to investigate the yaw behaviour of small horizontal axis wind turbines • Dynamic loads- D' Alembert's principle (Therefore effects such as gyroscopic and centrifugal/centripetal are not separately considered) • Aerodynamic forces on the rotor - modified Blade Element Method combined with Momentum theory • Aerodynamic forces on the tail vane- unsteady slender body theory

37. By using D’Alembert’s principle a dynamic system can be converted into a static system. The system can be analysed by using static equilibrium conditions. For each and every point forces of magnitude mi.fiare applied in the opposite direction to its acceleration. mi is mass at the point i and fi is acceleration at the point Moments of D’Alembert forces on the rotor, generator and turn table about “O”; Momentum of D’Alembert forces on the rotor

38. The blade element theory is used to determine the forces and moments by assuming the blade as composed of a number of aerodynamically independent cross sections f Skewed wake axis Expansion angle at r r - - W Var Wind velocity r Vrr Overall flow pattern through the rotor

39. Axial thrust Side thrust Rotor moment  Wind velocity Aerodynamic forces on the wind rotor • The blade element theory is used to calculate the elementary aerodynamic forces

40.  U1 U1   V1 (Wind velocity) Dynamic response of wind vane The unsteady slender body theory is used here to derive the moment due to a single tail vane Where  is the angle between the wind velocity and the vane,  is the wind direction, U1 is the effected wind velocity to the tail vane and b1, b2, b3, k1, k2, k3 and k4 are constant. It can be shown that the wind force is proportional to the angle from the instantaneous horizontal wind velocity component to the moving tail vane

41. Where, and I1= Moment of inertia of tail vane about the axis Dynamic behaviour of the wind turbine The equation of angular motion of the system is, Where, Mk is the D’Alembert moment of rotor about the k axis, MRk is the aerodynamic moment of rotor about the k axis.

42. Case study • Wind rotor Radius of wind rotor : 1.105m Blade profile : NACA4415 Number of blades : 2 Moment of inertia (I) : 9.77kg.m2 • Tail vane Vane area : 0.08m2 Distance to the centre of mass of the tail vane from axis (lv) : 1.2m Moment of inertia around axis (I1) : 7 kg.m2 m=25kg, AV=0.08m2, Cds=0.2 and As=0.2m2

43. Validation:- Simulation study • Simulation by applying 5 degrees step ramp of yaw error. • To process simulation for 125 seconds time period, 5000 iterations were executed with 0.025 second time intervals. • Parameters of the tail vane such as area (Av) and momentum of inertia were varied and simulated for different wind speeds and rotational speeds. • To evaluate gyroscopic effect of wind rotor due to yaw motion, simulated the model by yaw angle variations with wind direction changing rate of 8deg/sec.

48. Variations of Mj and yaw angle with change of wind direction

49. Yaw angle and yaw rate • Rotational speed of the rotor and wind speed are affected to dynamic characteristics of the system • The system is more stable at high rotational speeds and high wind speeds. • High yaw rates occur at low rotational speeds of the rotor. • These results comply with the field tests [1] References 1.Wright A., K. and Wood, D. H., 'Yaw rate, rotor speed and gyroscopic loads on a small horizontal axis wind turbine,' Wind Engineering, 2007, vol. 31, pp. 197-209

50. Discussion • Neural networks can be used for more accurate wind speed predictions • Perfect MPPT control is not possible due to limitation of rate of change of rotational speed of wind rotor • Wind turbine output power is interlaced with the turbine mechanical (aerodynamic) power and the rate of change of stored energy • Wind speed predictions can be used to improve MPPT mechanism in turbulent wind conditions • Wind speed and direction changes are caused for yaw error and yaw rate of turbine • Rotational speed of rotor and wind speeds are affected to yaw behaviour of horizontal axis small wind turbines