A Controller for Optimum Electrical Power Extraction from a Small Grid-Interconnected Wind Turbine

Currently, wind power is the fastest-growing means of electricity generation in the world. To obtain the maximum efficiency from the wind energy conversion system, it is important that the control strategy design is carried out in the best possible way. In fact, besides regulating the frequency and output voltage of the electrical signal, these strategies should also extract energy from wind power at the maximum level of efficiency. With advances in micro-controllers and electronic components, the design and implementation of efficient controllers are steadily improving. This paper presents a maximum power point tracking controller scheme for a small wind energy conversion system with a variable speed permanent magnet synchronous generator. With the controller, the system extracts optimum possible power from the wind speed reaching the wind turbine and feeds it to the grid at constant voltage and frequency based on the AC–DC–AC conversion system. A MATLAB/SimPowerSystems environment was used to carry out the simulations of the system. Simulation results were analyzed under variable wind speed and load conditions, exhibiting the performance of the proposed controller. It was observed that the controllers can extract maximum power and regulate the voltage and frequency under such variable conditions. Extensive results are included in the paper.


Introduction
Nowadays, most countries are promoting the massive integration of renewable energy sources (RES) to replace conventional power plants based on nuclear and fossil fuels [1,2]. Among the different reasons for this transition, the most important include the environmental worry (climate change due to greenhouse gas emissions) and also to reduce the energy dependence on fuels imported from third countries [3,4]. However, RES have a stochastic and uncertain behavior due to their dependence on weather conditions [5]. Indeed, this is considered as an important drawback for their massive integration, as they impose stress on the power systems' operation [6,7]. Among the different RES available, wind energy is widely considered as the most economic, qualified and inexhaustible resource [8,9]. In fact, the cumulative installed wind electrical power extraction proposed in the paper is described in Section 3; Section 4 analyzes the results; finally, Section 5 gives the conclusions of the study.

Wind Turbine Generalities: Small Wind and PMSG
The turbine blades catch the wind and convert it into mechanical energy. As the hub of the rotor is connected to the electrical generator though the shaft, that rotational mechanical energy is converted into electricity. The relationship between the wind speed (s w ) and the aerodynamic available wind power (P w ) can be expressed by Equation (1): where ρ is the air density and A is the swept area by the blades. The mechanical power (P mech ) extracted by the wind turbine is only a fraction of the available power. Indeed, the power coefficient (C p ) measures the efficiency of the first conversation from wind speed to mechanical power. This coefficient depends on the wind speed and the rotor speed, with a maximum value of 59.3% according to the Betz limit [37]. The extracted mechanical power is then given by Equation (2): Thus, the power coefficient can be understood as the aerodynamic efficiency of the rotor. It depends on the blade pitch angle (β) and the tip speed ratio (λ). The tip speed ratio (λ) is defined as the ratio between the peripheral speed of the blades (Ω · R and the wind speed, following Equation (3): where Ω is the rotor speed of the turbine and R is the rotor radius. In the particular case of small wind turbines, they do not usually include a gearbox. Consequently, the rotor speed and the generator speed are the same (Ω = ω). Moreover, the pitch-angle is normally considered as fixed, as already mentioned in Section 1. Hence, for small wind, the power coefficient only depends on λ, as depicted in Figure 1. The maximum power P MPP is extracted from the wind speed when the wind turbine operates at the maximum power coefficient C p,max . For a typical wind turbine with a power coefficient characteristic like the one shown in Figure 1, the extracted power versus the tip speed ratio is depicted in Figure 2. It can be seen that the aerodynamic efficiency of a wind turbine is maximal for a specific value of tip speed ratio. Hence, by keeping the tip speed ratio at its optimum value (λ opt ) through the rotor speed, the maximum power at available wind speed P MPP can be extracted. Consequently, if the wind speed changes, the rotor speed should be adjusted to follow said variation.

Small Wind
Different definitions are found in the specific literature when referring to small wind turbines: for instance, Urtasun et al. considers that small wind turbines refer to those wind turbines of up to 100 kW [38]. A more concise definition is provided in [39], where it is specified that small wind turbines only include wind turbines with a swept area by the rotor A < 200 m 2 , and powers between 1-15 kW for residential purposes or 15-100 kW for light commercial installations. On the other hand, Muhsen et al. refers to small wind turbines as those with rated power of less than 50 kW [40]. In any case, it is generally agreed that small wind installations are convenient for isolated areas, which are difficult to connect to the main grid due to technical and/or economical limitations [41].
Nowadays, electricity is a key element to developing the economy of any region. However, almost 17% of the world's population does not have access to it, and most of them (nearly 90%) live in rural areas of poor tropical regions [42,43]. Small wind installations only require small foundation plots, with a short construction time (a few months). Moreover, if electricity is generated and consumed in neighborhood areas, these small installations substantially reduce the investment needed to generate and distribute electricity from centralized power plants, also minimizing the losses due to long distance transmissions. Consequently, small wind systems can play an important and practical role in generating reliable and affordable electricity for poor rural areas, reducing their poverty [44].
Together with this, there are also different applications for small wind turbines, such as lifting water to tanks located high, or pumping it from underground [45]; integrating small wind turbines into buildings, or installing them on the rooftops, especially on high-rise buildings [46]; and even providing electricity to on-grid consumers which will supply its excess to the power system (which are usually referred to as prosumers) [47,48].
As small wind installations are commonly located where the electricity is required, these areas can have poor wind conditions [49]. In fact, when they operate in urban zones, they are exposed to severe wind gusts, with fast fluctuations and turbulent winds, which can affect the performance of the wind turbine [50]. These characteristics are due to the following three reasons: (i) the interaction between the wind and the building structures; (ii) the high surface roughness; and (iii) the atmospheric instabilities due to local heat sources [51]. Consequently, due to the influence of wind speed changes on the wind turbine performance, direct driven PMSG are considered as the best alternative for small wind applications, as the permanent magnets produce the magnetic flux without needing any additional element for excitation [52].

Permanent Magnet Synchronous Generator
From the 650 GW of wind power installed worldwide, 35% corresponds to VSWTs equipped with a full-scale converter and PMSG [53]. To model a synchronous machine of a PMSG, projection of phase quantities in a rotating dq-axis greatly simplifies the model, as time varying parameters are simplified to a time independent parameters [54,55]. In the rotating reference frame, the dynamic equations representing the behavior of a PMSG are expressed in Equations (4) and (5) [56]: where V d and V q are the d-axis and q-axis components of the voltage, R s is stator winding resistance, L d and L q are d-axis and q-axis inductances, ω is the generator speed, I d and I q are the d-axis and q-axis components of the current and φ m is PMSG magnetic flux. The electromagnetic torque of the rotor can be expressed as Equation (6), p being the number of poles: The PMSG type is considered as a surface mounted magnet; therefore, L d and L q are almost equal (L d ≈ L q ) [56]. Consequently, the electromagnetic torque in the rotor simplifies to Equation (7): Moreover, the wind turbine torque and electromagnetic torque are related through the so-called swing-equation (8): where the inertia J and damping friction coefficient D are combined for both turbine and generator.

Optimum Electrical Power Extraction
For a VSWT with a PMSG and a back-to-back full-scale converter, it is possible to control both the rotor speed and generated electromagnetic torque. This way, the tip speed ratio can be maintained at the optimum value so that the aerodynamic efficiency is at its maximum (C p,max ), which means that the energy conversion is maximized.
The basic control philosophy comes from Equations (7) and (8) of Section 2. As already described, the extracted mechanical power does not only depend on the wind speed, but also on the rotor speed (refer to Equation (2) in Section 2). By correlating the PMSG electromagnetic torque with the rotor speed using Equation (8), and taking the Laplace transform, Equation (9) is gotten: Similarly, Equation (7) can be expressed as: where K is a constant obtained as: Equations (9) and (10) can be represented in a mathematical block diagram, as shown in Figure 3. This diagram is the speed control block diagram of a PMSG. In order to control the rotor speed to a specified (reference) value, the required reference current I q,re f can be obtained as indicated in the diagram. According to Equation (8), and as was presented in Sections 1 and 2, small wind turbines with PMSG do not usually include a gearbox. Consequently, the speeds of the PMSG (ω) and of the blades (Ω) are the same, and a one-mass mechanical model (mathematically expressed in terms of Equation (8)) is enough to determine such a rotational speed. Following this, and with the block diagram of Figure 3, only ω re f , PI values, K, J, D and T m are needed to obtain the rotational speed: • ω re f is estimated from the wind speed s w and considering Equation (3). As the aim is to obtain the optimum value of λ (λ opt ), and according to the specific literature, its optimum value is between 6.5 and 7.5 [57], the reference value of ω = Ω is obtained by choosing a λ value within that range.
• PI values are presented in Table 1.
• K is determined following Equation (11), where p and φ m are given in Table 1.
• J and D are given in Table 1.
• T m is determined from T m = P mech /Ω, using the mechanical power (Equation (2)) and the rotational speed Ω = ω. Since the electromagnetic torque is directly proportional only to the q-axis current I q , for the same electromagnetic torque, the generator voltage drop and power losses can be minimized by setting the d-axis current to zero, I d = 0. The two reference currents (I q,re f obtained above and I d,re f set to zero) can then be used to determine the reference dq-axis voltages for the generator using Equations (4) and (5) from Section 2. This is depicted in the mathematical block diagram representation in Figure 4.
The tuning of the PI controllers for the speed controller in Figure 3 depends on the combined inertia and damping friction coefficients of turbine and PMSG rotor, whereas the tuning of the PI current controllers of Figure 4 depends on the stator winding resistance and inductance of PMSG. Hence, these controllers' parameters are independent of the wind speed. In operating conditions, signals I d , I q and ω are feedback signals from the generator. The V d and V q references obtained from the block diagram of Figure 4 are then used to generate the gate signal sequences for the six IGBTs of the generator side converter after converting these to the phase quantities and normalizing them with the DC output voltage of the converter.

Results
The wind turbine model is based on the Anelion SW 3.5 GT wind turbine [58]. The power curve of the wind turbine under consideration is presented in Figure 5: the black line is the power curve according to IEC 61400-12, whereas orange and gray lines depict the maximum and minimum operation range, respectively. The generator rectifier is responsible for the rotor speed control [59]. This controller optimizes the power extraction from the wind at variable wind speed. This is achieved by a control system that generates the appropriate sequences of gate signals for the converter IGBTs. The grid-side inverter is simply a current source inverter feeding the extracted electrical power instantly to the grid at constant voltage and frequency. Figure 6 represents the small wind turbine system connected to a grid. This includes the wind turbine and PMSG, the generator side and grid-side converters, an electrical line and the AC grid. The wind energy conversion system depicted in Figure 6 was implemented in detail using the MATLAB/SimPowerSystems environment, in line with several published papers [60][61][62][63]. SimPowerSystems is a MATLAB tool to model and simulate electric power systems in the Simulink environment, allowing users to perform different studies (such as power flow analysis, frequency analysis and transient analysis) [64]. In this case, authors analyzed the performance of the proposed optimum electrical power extraction model under wind speed variations and load variations. The generator and turbine parameters considered for this study are presented in Table 1.   Figure 7 presents the main results from the simulation with variable wind speed. The initial wind speed was fixed at 10 m/s; then, at 1.1 s, the speed dropped to 8 m/s, and at 1.6 s, the speed raised to 9 m/s (Figure 7a). In this way, it is possible to analyze the behavior of the small wind turbine, both when wind speed decreases and when it increases. As can be seen from the power coefficient C p depicted in Figure 7b, it only suffers from small transients in the time-moment when the wind speed changes (at t = 1.1 s and t = 1.6 s). For the rest of the time under analysis, it is maintained as constant at nearly its maximum value, ensuring that the controller is able to maintain a constant top speed ratio under the varying wind speed. The rotor speed simultaneously and proportionally changes with the wind speed, both the reference (black line) and the actual (pink line) rotor speeds. Moreover, the actual rotor speed faithfully follows the reference one for optimum system operation under increasing and decreasing wind speed variations. Due to the mathematical relationship between power, torque and speed (P = T · Ω), the extracted power from the turbine of Figure 7d is in line with the rotor speed of Figure 7c and the turbine torque of Figure 7f (pink line). In fact, as can be seen from Figure 7f, turbine torque only suffers from small transients in the time-moment when the wind speed changes, which last less than 0.01 s. Moreover, and comparing the results with the power curve of the wind turbine considered, it can be seen that the extracted turbine power shown in Figure 7d represents the maximum power (refer to Figure 5).

Wind Speed Variation
The current control characteristic (Figure 7e) clearly indicates that the q-axis current I q (black line) is changing in line with the wind speed. Since the electromagnetic torque generated by the PMSG (black line of Figure 7f) changes proportionally with this q-axis current, this results in an optimum extraction of the wind turbine power, as depicted in Figure 7d. In fact, the d-axis PMSG current I d (pink line of Figure 7e) is maintained to a zero value except for some small transients when the wind speed changes. In this way, the generator voltage drop and power losses are minimized, as already justified in Section 3.
The inverter outputs are shown in Figure 7g-i in terms of AC output voltage, AC output current and 3-phase power. These are the AC grid-side characteristics of the system. As can be seen, the voltage remained constant during the whole simulated time-period, equal to 1 p.u. In contrast, the three phase inverter AC current changes with the wind speed variations, firstly reducing from 2.5 A to 1.95 A, and then increasing to 2.1 A. Due to the relationship between active power, voltage and current (P = V · I), the output power of the small wind turbine system changes due to the dependence of current and wind speed; subsequently, the output power also changes in line with the wind speed.  Figure 8 presents the main results from the simulation with variable load. Initially, a load of 2 kW was connected immediately after the inverter (in between the inverter and the grid), as marked in Figure 6. Two more loads, each one of them of 2 kW, were then added at 0.6 s and 1 s, respectively. In this case, the wind speed was kept constant at 11 m/s, as shown in Figure 8a With regard to the inverter output of Figure 8g-i, voltage was again maintained at 1 pu. However, some transients were found for the current and power output values when the load increased. Consequently, this means that in steady state, there is no effect even in the inverter output for local load variation. In fact, it is interesting that even though the new added loads had the same power (2 kW each), the transient of the first load at t = 0.6 s was bigger and longer than the one at t = 1 s. This is because before the first load was added (t < 0.6 s), the power was flowing from system to the initial load and the grid. Then, when the first load was added at t = 0.6 s, the power flow changed its direction (from grid towards the new loads) to fulfill the new consumed power. Consequently, at t = 0.6 s, there was a sudden transition of the power flow to/from the grid. However, when the second load was included at t = 1 s, the direction of the power flow from the grid remained unchanged even with the change in local demand.

Conclusions
This paper has presented a maximum power point tracking controller scheme for a grid-interconnected variable speed small wind turbine with a PMSG. The controllers generated the appropriate gate signal sequence for PWM generator side converter to control the rotor speed and torque with PI controllers. It has been observed that with the controller, the rotor speed simultaneously and proportionally changes with the wind speed. The power coefficient was maintained constant nearly to its maximum value except small transients at the instant of wind speed change. This ensures the optimum possible power extraction from the wind turbine with varying wind speed. Only short-time transients were obtained when the wind speed changed, thereby implying less stress from the wind turbine point of view. It was also witnessed that the system was operating tat its optimum with no disturbances on the generator side performance of the system with variation in load. However, if the change of load caused the reversal of power flow direction to and from the grid, some major transients were observed in the inverter output currents and power. The tuning of the PI controllers only depends on the inertia and damping friction coefficients of the turbine generator rotor and stator winding resistance, and the inductance of the generator, without any dependency on the wind speed. Funding: This work was partially supported by the Spanish Ministry of Education, Culture and Sports-reference FPU16/04282.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: