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New Overall Power Control Strategy for Variable-Speed Fixed-Pitch Wind Turbines Within the Wh
ole Wind Velocity Range
Jiawei Chen, Student Member, IEEE, Jie Chen, Member, IEEE, and Chunying Gong, Member, IEEE
Abstract—Variable-speed ?xed-pitch (VSFP) wind turbines have good prospects in small-to-medium-scale wind power markets due to their simple structure, low cost, and high reliability. One dif?culty with VSFP concept wind turbines is to prevent overspeeding and overloading problems at excessive wind velocities, which has rarely been reported in literatures until now. This paper ?rst proposes a sensorless overall power control strategy for a commonly used permanent-magnet-synchronous-generator-based VSFP concept wind power system, with which maximum power point tracking operation, constant speed stalling operation, and constant power soft-stalling operation are all realized. The proposed control scheme has a special advantage of simple structure, i.e., only two regulators are used to realize the three operational modes and also the natural transition between them. An aerodynamic power observer is adopted in the proposed scheme to fasten the MPPT speed. In addition, to enhance system robustness to parameter variations and optimize dynamic and static speedcontrol performance, an adaptive PI-like fuzzy logic controller is proposed and used as speed regulator in the overall power control scheme. The proposed strategy is veri?ed by simulation and experimental results performed by a 1.2-kW VSFP concept wind turbine prototype. Index Terms—Adaptive fuzzy logic controller (AFLC), constant power stalling, dynamic power observer, maximum power point tracking, sensorless control, wind power generation.
ρ ω, ωobs ΩN Udc , Udcopt Udcobs Udcmax U0 kU kopt Pr , Pr max Pr_obs Tr_obs Pe Te Δi? 0 i? 0 eU ΔeU eth Ke , Kec Kμ μ
N OMENCLATURE v Vmin VΩN VN Vmax Cp , Cp max λ, λopt J R Wind velocity (in meters per second). Cut-in wind velocity (in meters per second). Wind velocity at rated rotor speed (in meters per second). Rated wind velocity (in meters per second). Cut-out wind velocity (in meters per second). Wind turbine power coef?cient and its maximum value. Tip speed ratio of wind turbine and its optimal value. Moment of inertia of the blade (in kilogram– square meter). Radius of the turbine (in meters).
Air density (in kilograms per cubic meter). Rotor speed and its observed value (in revolutions per minute). Rated rotor speed (in revolutions per minute). Generator recti?cation voltage and its optimal value (in volts). Observed generator recti?cation voltage (in volts). Rated generator recti?cation voltage (in volts). Terminal voltage of the battery bank (in volts). Generator recti?cation voltage constant. Optimal power constant. Aerodynamic power and its rated value (in watts). Observed aerodynamic power (in watts). Observed rotor torque (in newton–meter). Electrical power (in watts). Electromagnetic torque (in newton–meter). Output of fuzzy decision (in amperes). Output of the PI-like adaptive fuzzy logic controller (AFLC) (in amperes). Generator recti?cation voltage error (in volts). Change of generator recti?cation voltage error (in volts). Error threshold (in volts). Quantization factors of generator recti?cation voltage error and change of error. Output scaling factor of AFLC. Membership grade. I. I NTRODUCTION
Manuscript received October 16, 2011; revised February 8, 2012; accepted April 17, 2012. Date of publication April 30, 2012; Date of current version February 28, 2013. The authors are with the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China (e-mail: cw198520@ yahoo.com.cn; nuaachenjie@163.com; zjnjgcy@nuaa.edu.cn). Color versions of one or more of the ?gures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identi?er 10.1109/TIE.2012.2196901
HE development in the use of renewable energy is becoming the key solution to the serious energy crisis and environment pollution now. Among various kinds of renewable energy, wind energy is by far the fastest growing energy for its free availability, environmental friendliness, policy fostering, and the maturity of turbine techniques, and it has become a research focus and priority all over the world [1]–[3]. According to the market reports of the British Wind Energy Association and the American Wind Energy Association, smallto-medium-scale (1–100 kW) wind turbines, which can meet the easy electricity requirements of the users in urban and remote areas, are becoming popular [4], [5]. In the U.S., small-tomedium-scale wind turbines with unity capacity below 100 kW contribute 100 MW of generated power; in the year 2010, a 20%
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0278-0046/$31.00 ? 2012 IEEE
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Fig. 1.
Ideal power curve versus wind velocity.
growth was seen. In the U.K., the total installation capacity of small-to-medium-scale wind turbines has achieved 28.7 MW with a 59% growth compared with the previous year, while a 25% growth on average has been achieved worldwide. The preferred structure of small-to-medium-scale wind turbines is permanent-magnet-synchronous-generator (PMSG)based direct-drive ?xed-pitch concept ones to form a simple structure with high reliability and high ef?ciency. In addition, variable-speed operation is usually adopted to realize MPPT operation [6]–[8]. However, unlike a large horizontal-axis wind turbine, usually variable-pitch variable-speed concept wind turbines which usually use electrical control to realize MPPT operation below rated wind velocity and use aerodynamic control to limit the turbine power at high wind velocities, only electrical control can be used to regulate the rotor speed and power. This adds complexity to the overall power control for variable-speed ?xed-pitch (VSFP) concept wind turbines, particularly speed and power limitation at high wind velocities. Thus, proposing a high reliability but simple overall power control strategy for the VSFP wind turbines is becoming imperative. For a VSFP concept wind turbine, its power is usually controlled to follow an ideal power curve with the variation of wind velocities [9], as shown in Fig. 1. It can be observed that the ideal power curve exhibits three different regions: the MPPT operational region (region I) when wind velocities vary between Vmin and VΩN , constant power operational region (region III) between wind velocities VN and Vmax , and constant speed operational region (region II) between these two regions. According to the recent published literatures which had mentioned the control of the VSFP wind turbines [6]–[15], we can notice that most of the researchers concentrated merely on the power control in the MPPT operational region (region I). Their research interests are proposing some new algorithms to accelerate the MPPT speed. However, it is easy to ?nd out the fact that most of the MPPT algorithms are based on the electrical power (or torque) feedback. For example, in [8], the optimal electrical torque is calculated according to the sensed rotor speed and then used as the reference signal that the generator is supposed to be supplied to realize the MPPT control. However, for reasons that will become clear in this paper, the authors claim that if the aerodynamic power, which can be observed by an aerodynamic power observer, is used as the feedback signal in the MPPT loop, the MPPT speed can become much faster than that of electric power feedback schemes.
Aside from the MPPT control in region I, the power control of VSFP concept wind turbines at high wind velocities (in regions II and III) is particularly hard. However, only a small part of the literatures mentioned the corresponding control methods. In [13] and [14], the constant speed soft-stalling is proposed to regulate the rotor speed and power at high wind velocities. This control not only realizes the limitation of rotor speed but also stalls the turbine and reduces the power captured. A problem with this is that the power output is still greater than the rated value, although lower than what would have been if the MPPT control had continued to be used rather than the constant speed stall algorithm at the increased wind velocity. The generator and power electronics must be rated accordingly. In [15], constant electrical power soft-stalling control method is proposed for vertical-axis wind turbine to regulate its electrical power at excessive wind velocities. The main drawback of this control is that the authors claim to increase the electrical power at high wind velocities to stall the turbine, but at the same time, the electrical power is expected to remain unchanged by the control, which leads to extremely poor system stability. A lowpass ?lter with large time constant (larger than the moment of inertia of the blade) is further used to compensate the system, but this not only lows down the MPPT speed but also increases the electrical power overshooting during transient process at high wind velocities. The intended contribution of this paper is to demonstrate that the dif?culty of the overall power control for VSFP concept wind turbines within the whole wind velocity range can be solved by the proposed control strategy. An encoderless scheme, in which the rotor speed is measured via the dcside voltage of the generator recti?er, is developed to reduce the cost. Furthermore, from the analyses of the operational principle of the proposed control strategy, it can become clear that the power control in all three regions is realized by regulating the rotor speed (or the dc-side voltage of the generator recti?er). To enhance system robustness to parameter variations and optimize static and dynamic speed-control performance, an adaptive PI-like fuzzy logic controller (FLC) is proposed to replace the conventional PID controller in the speed regulator. The rest of this paper is organized as follows: The novel, and simple, overall power control strategy is proposed, and its operational principle, particularly the comparative study between the conventional electric power feedback MPPT algorithm and the new aerodynamic power feedback MPPT algorithm, is analyzed in detail in Section II. In Section III, the adaptivefuzzy-logic-based speed regulator is carefully designed to improve the control performance. Before conclusion, a fourth part gives out the simulation and experimental results performed by both a simulation model based on Matlab/Simulink and a 1.2-kW laboratory prototype; the correctness and effectiveness of the proposed strategy are veri?ed by the simulation and experimental results. II. N EW OVERALL P OWER C ONTROL S TRATEGY The system con?guration studied in this paper is shown in Fig. 2. It is constructed by a PMSG-based direct-drive ?xedpitch wind turbine with a Cp ?λ curve shown in Fig. 3. Through
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and power of the turbine at high wind velocities. To achieve this, the output power (or current) is controlled in accordance with the operational regions of the turbine. The control block diagram of the proposed strategy is also shown in Fig. 2, and the detailed operational principle will be expanded on later. A. Detailed Analyses of the Proposed Algorithm 1) MPPT Operation: According to the Aerodynamics, the aerodynamic power of the wind turbine can be expressed as Pr = 1 ρπR2 Cp (λ)v 3 . 2 (1)
When the rotor speed is adjusted to maintain its optimal value, the maximum power can be gained as
Fig. 2. Block diagram–system con?guration with new overall power control.
Pr max = kopt ω 3 where kopt is decided by kopt = ρπR5 Cp max . 2λ3 opt
(2)
(3)
Take into account that the generator recti?cation voltage (Udc ) is proportional to the rotor speed (ω ) for the PMSG, i.e., Udc = kU · ω. (4)
Fig. 3. Cp ?λ curve. TABLE I PARAMETERS OF W IND T URBINE AND PMSG
a diode recti?er, the output power of PMSG is transferred to an output-current-controlled dc/dc converter, which is used to control the output power of the system. Considering the rather stiff bus voltage (because a battery bank is connected to the output terminal), the output power can be simply regulated by regulating the output current. The detailed parameters of this system are shown in Table I. The overall power control strategy proposed in this paper is expected to control the generated power of the wind turbine following the ideal power curve. This process includes tracking the wind varieties at low wind velocities and limiting the speed
Here, discussion is made to (4): According to [16], one can use a more accurate equation to approximate the rotor speed of the PMSG using the recti?cation voltage. However, the relationship between them is not a straight line. Thus, although the equation used in [16] is a more accurate approximation than (4), it makes the implementation of the sensorless control much more complicated. In order to implement as simple a control strategy as possible, it is desirable to implement a straightline relationship. In this case, one can choose a straight-line approximation, which approximates the higher wind velocities more closely, to the whole rotor speed–recti?cation voltage relationship. In such a way, although the chosen straight-line approximation will not provide maximum power capture at low wind velocities, the relatively low power of the system at low wind velocities makes the rough approximation acceptable. Thus, the controller can not only provide optimum system performance but also can simplify the sensorless control. kU is then chosen based on the earlier analysis, as listed in Table I. Substituting (4) into (2), we have Pr max = kopt 3 3 · Udc . kU (5)
The power curve determined by (5) is the so-called optimal power curve (versus Udc ), based on which the MPPT operation can be achieved. The optimal power can be calculated by detecting the generator recti?cation voltage real-time. If the power of the wind turbine is controlled to follow the optimal power very well, the MPPT operation is then achieved naturally [8], [10].
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Fig. 4.
MPPT operational mode simpli?ed control block diagram.
Fig. 6. Constant speed operational mode simpli?ed control block diagram.
suddenly increases to v1 , the aerodynamic power will step up to Pr1 . However, since the electric power Pe cannot suddenly change with the wind velocity due to the large moment of inertia of the blade, the optimal generator recti?cation voltage calculated from Pe will remain Udcopt0 at this very moment. Consequently, the turbine will accelerate due to the torque difference acting on the turbine shaft, which has a value determined by the following equation: ΔTEPSF = kU · ( Pr 1 ? Pr 0 ) . Udcopt0 (7)
Fig. 5.
Operational principle of the power feedback method.
Another equivalent means to realize MPPT operation reported in literatures is to use the identical deformation formula of (5), as shown in the following equation: Udcopt = kU ·
3
Pr kopt
(6)
i.e., the operational power is detected and used to calculate the optimal generator recti?cation voltage Udcopt . MPPT is realized by controlling the generator recti?cation voltage to track this signal [6]. The MPPT methods mentioned earlier are commonly de?ned as the power signal feedback (PSF) method. However, we can easily notice the fact that most of the reported PSF strategies use electrical power, which is generated by the generator and has a value equal to the aerodynamic power of the blade at steady state, as the feedback power signal to generate the optimal generator recti?cation voltage reference (further de?ned as EPSF method). That means, in (6), the aerodynamic power Pr is replaced by the electrical power Pe to calculate Udcopt ; moreover, in (5), it is the electrical power Pe that is controlled to follow the optimal aerodynamic power. The study of this paper shows that the MPPT speed can be greatly increased if we use the aerodynamic power Pr to calculate the optimal generator recti?cation voltage Udcopt , de?ned as the APSF method in this paper, for the reason referring to the MPPT process discussed as follows. According to the proposed control scheme in Fig. 2, power regulator PID is reverse saturation under MPPT operational mode. The control block diagram of this mode can be then simpli?ed in Fig. 4. To the EPSF method, Pe is used to replace Pr . Suppose that the wind turbine is operating at the maximum point (Q0 ) of a certain wind velocity v0 , the optimal generator recti?cation voltage and aerodynamic power of the turbine are Udcopt0 and Pr0 , as shown in Fig. 5. If the wind velocity
The optimal generator recti?cation voltage reference signal Udcopt will increase slowly with the increase of Pe along with the optimal power line (shown in Fig. 5). The MPPT process will not stop until the turbine reaches new steady state, point Q1 . To the APSF method, the optimal generator recti?cation voltage reference will immediately change from Udcopt0 to Udcopt according to (6) because the aerodynamic power is used. However, considering the blade’s large moment of inertia, the generator recti?cation voltage Udc cannot change as fast as the wind velocity. Thus, there exists a large negative voltage error in the input of the speed-loop regulator where an AFLC is proposed to optimize the system performance. According to its operational principle which will be analyzed in detail in the next section, a large negative voltage error will cause the AFLC to be reverse saturation very quickly and output a zero current reference. The electrical power Pe will reach zero because the output current of the dc/dc converter is controlled to track this zero current reference quickly. The turbine will accelerate very fast due to the large torque difference acting on the turbine shaft ΔTAPSF = kU · Pr 1 . Udcopt0 (8)
Obviously, ΔTAPSF is much greater than ΔTEPSF , which is the main acceleration mechanism of the APSF method. Thus, the APSF MPPT method is employed in the proposed control scheme through an aerodynamic power observer. 2) Constant Speed Operation: The generator recti?cation voltage Udc will increase with the increasing of wind velocity when it is below VΩN under MPPT operational mode. As soon as the wind velocity exceeds VΩN , the optimal generator recti?cation voltage reference determined by (6) will reach the upper limit, which is set at its rated value Udcmax . Even if the output power of the wind turbine would still increase with the increasing of the wind velocity, the generator recti?cation voltage will remain constant. Under this operational mode, the aerodynamic power is still smaller than the rated power; the power regulator PID continues to be reverse saturation. The simpli?ed control block diagram of this mode is shown in Fig. 6.
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Fig. 7. Constant power operational mode simpli?ed control block diagram.
3) Constant Power Operation: When the wind velocity exceeds the rated value VN , the aerodynamic power Pr of the wind turbine is supposed to be well constrained to the rated power for safety consideration. In order to realize the constant power operation, this paper claims to force the turbine into low-speed stall region. To do this, power regulator PID is employed and starts to regulate once Pr exceeds its rated value Pr max . It outputs a compensated value Udccom , which is added to the output of the MPPT loop (Udcmax at this time), to temporarily decrease the optimal generator recti?cation voltage reference Udcopt , thereby increasing the electrical power to force the turbine to stall by controlling the dc/dc converter. Consequently, the generator recti?cation voltage, controlled to track Udcopt , decreases, and the wind turbine enters into the stall operational region. The power coef?cient Cp decreases to keep the aerodynamic power of the turbine constant. The equivalent control block diagram is shown in Fig. 7. Known from the operational principle of the proposed strategy discussed earlier, the transition among the three operational regions is just the natural saturation or limiting of power regulator PID and the optimal generator recti?cation voltage reference generating unit, written as Udcopt = f (Pr ) in Fig. 2. The proposed strategy gets rid of the direct-cut operation strategy proposed in [17], in which three different control loops are set separately for different regions and a judgment mechanism is employed to pick up a proper control loop according to the operational region of the wind turbine. Therefore, soft transition is achieved, and the transient load acting on the wind turbine can be decreased. Moreover, while achieving the overall power control, only two regulators are used in the proposed control strategy, which makes the control structure very simple. B. Aerodynamic Power Observer From the earlier analyses, the aerodynamic power Pr , which is a quantity impossible to be measured directly, is a key parameter to achieve the proposed strategy. Fortunately, it can be observed by an aerodynamic power observer proposed here. The aerodynamic torque Tr can be calculated from the generator torque Te and generator recti?cation voltage Udc if the rotor inertia J is known. The relation is Tr = Te + J dUdc . · kU dt (9)
Fig. 8.
Aerodynamic power observer.
is equal to the product of the aerodynamic torque multiplied by the rotational speed, we have the aerodynamic power observer as shown in Fig. 8. To know the aerodynamic observer better, more explanations are made here. As shown in Fig. 8, the generator torque Te is subtracted from the (observed value of the) rotor torque Tr_obs . After division by the rotor inertia J , this value is integrated and leads to an estimation of rotor speed and, then, the generator recti?cation voltage Udcobs . The difference between the real value Udc and the estimated value Udcobs is fed into a PI controller, which tries to adjust the observed rotor torque Tr_obs so that the estimated generator recti?cation voltage becomes equal to the measured value. If this relation would always hold, the observed aerodynamic power Pr_obs would be exactly the aerodynamic power Pr captured by the rotor blades. To achieve this, the PI regulator is set to be very fast in this paper to eliminate the difference between the rotor speed and its estimated value in only a very short delay. The integration time constant of the PI regulator is chosen to be 5 ms in this paper. III. A DAPTIVE F UZZY L OGIC S PEED C ONTROLLER The PID regulator, which has the advantage of simple structure, is the most commonly used regulator in industry applications. However, the design of the PID regulator must be based on the model of the control object. Unfortunately, due to the randomness characteristic of the wind, the operating point of wind energy conversion system (WECS) is changing from time to time, which shows a property of high degree of time varying and nonlinearity. To get the accurate model of WECS is most likely to fail, particularly when the diode recti?er is used in the system. Nowadays, FLC, in which the design of controller is based on human experience through a set of empirically determined design rules, is widely employed in the WECS to enhance system robustness to parameter variations and optimize the system performance [18]–[21]. However, we can easily notice that most of the FLC reported in these literatures are based on a ?xed fuzzy membership function and a static rule base, for example, conventional FLC. In addition, whereas conventional FLC provides an excellent speed control performance, it results in additional current harmonics, which add extra stress to the turbine shaft [21]. Although these can be reduced by optimizing one of the FLC parameters, for example, by using nonlinearly distributed fuzzy sets in the membership function of the control variable, this causes the speed control performance to deteriorate [22]. Thus, an adaptive PI-like FLC strategy, which can result in a good speed-control performance, improved system robustness, and also low current harmonics,
While this relation is simple, differentiation always introduces an ampli?cation of noise as well as the risk of instability in the system. Thus, in this paper, we replace the differentiation by an unproblematic integration and use a controller to adjust the input of the integrator so that the outcome of the integrator becomes the same as the value which is to be differentiated; the output of the controller is then taken as the derivative of the output of the integrator. Considering that the aerodynamic power
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are used during the inference. Finally, the center of gravity defuzzi?cation method is used to the AFLC, and an incremental change of the control signal Δi? 0 (k ) is gained [the membership function of the output fuzzy set used for defuzzi?cation is shown in Fig. 10(b)]. The control signal i? 0 , i.e., the output of the ? ? ? AFLC, is then obtained as i? 0 = i0 (k ) = i0 (k ? 1) + Δi0 (k ) after using a digital approximation for integration. The basic fuzzy logic control details can be referred to [17]–[23].
Fig. 9. Block diagram of the proposed AFLC.
A. Self-Tuned Output Scaling Factor Clearly, the output of the FLC Δi? 0 should be large during transient operation so that the output current reference i? 0 can integrate to a low or high value very quickly to accelerate the electrical power response and further accelerate the dynamic response of the system. In addition, Δi? 0 should be reduced during a steady-state operation so that the output current can be controlled with little ripple. Therefore, it is desirable to dynamically adjust the output of AFLC such that, under a transient operating condition, Δi? 0 is increased, and conversely for a steady-state condition. This can be achieved by adjusting the output scaling factor Kμ dynamically by comparing the measured generator recti?cation voltage error eU to a preset error threshold eth . A detailed implementation method is given as follows: When the detected generator recti?cation voltage error eU is larger than eth , which means that the system is in transient process, the scaling factor Kμ should be increased. On the contrary, Kμ should be decreased to optimize the steadystate performance. This process can be simply expressed as ? ? k1_in Kμ (k ? 1), |eU | > eth , k1_in > 1 Kμ (k ) = k1_de Kμ (k ? 1), |eU | < eth , k1_de < 1 ? other condition Kμ (k ? 1), (10) where, in the aforementioned equation, Kμ (k ) and Kμ (k ? 1) stand for the present and the previous scaling factor, respectively, and constants k1_in and k1_de are the adjusting coef?cients, which can be optimally chosen by means of simulation and experiments. In this paper, k1_in and k1_de are chosen to be 1.05 and 0.95, respectively.
Fig. 10. Membership functions of input and output fuzzy sets. (a) Fuzzy sets of input variables eU (k) and ΔeU (k). (b) Fuzzy sets of output variable Δ i? 0 (k ). TABLE II RULE BASE OF AFLC
is proposed in this paper. The adaptation being achieved simply by adjusting the output scaling factor of FLC according to the difference between the measured generator recti?cation voltage error and an error threshold, which can either be ?xed or selftuned, is called AFLC in this paper. Fig. 9 shows the block diagram of the proposed AFLC. The inputs are the error eU and the change of error ΔeU . The error signal eU is sampled with a sample period Ts ; the change of error is computed as ΔeU (k ) = eU (k ) ? eU (k ? 1), where k is the sample number; and Z ?1 represents the unit time delay. The error eU (k ) and the change of error ΔeU (k ) are fed into the AFLC for fuzzi?cation after adjusting by the quantization factor Ke and Kec . The membership functions of the input fuzzy sets used for fuzzi?cation are shown in Fig. 10(a), with (Positive Big) PB, (Positive Medium) PM, (Positive Small) PS, (Zero) ZO, (Negative Small) NS, (Negative Medium) NM, and (Negative Big) NB being the linguistic labels and μ being the membership grade. After fuzzi?cation, the well-known Mamdani inference mechanism is adopted for fuzzy reasoning. The fuzzy rules shown in Table II, which are deduced from the system control experience,
B. Self-Tuned Error Threshold The value of error threshold eth is also found to have great impact on the system control performances. On the one hand, in order to get rid of the vibration caused by the generator recti?cation voltage ripple at error threshold eth , it cannot be set too small; on the other hand, if eth is set too large, the dynamic performance will be compromised because the system will enter into the static operation ahead of time because of the improper prejudgment. Thus, the error threshold is also selftuned similar to that of the scaling factor, shown as ? ? k2_in eth (k ), |eU | > eth (k ), k2_in > 1 eth (k + 1) = k2_de eth (k ), |eU | < eth (k ), k2_de < 1 ? other condition. eth , (11)
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Fig. 12.
Real and observed aerodynamic powers (Pr and Pr_obs ).
Fig. 11. Laboratory test rig.
where eth (k ) and eth (k + 1) are the present and the next error threshold, respectively, and k2_in and k2_de are the error threshold adjusting coef?cients. According to (11), if the absolute value of the measured generator recti?cation voltage error |eU | is continuously larger than the error threshold eth , it signi?es that eth has been set too low and should be increased. Similarly, if |eU | is continuously lower than eth , then it should be decreased. In this paper, the error threshold adjusting factors are optimally chosen as k2_in = 1.02 and k2_de = 0.98 depending on the simulation and experiments.
Fig. 13. Simulated dynamic processes of Cp , Tr , Te using APSF and EPSF methods when the wind velocity steps from 7 to 11 m/s and then from 11 to 7 m/s.
IV. S IMULATION AND E XPERIMENTAL V ERIFICATION A 1.2-kW simulation model based on Matlab/Simulink and a laboratory prototype of VSFP concept WECS are designed and established based on which the proposed control scheme is veri?ed in this section. The wind turbine itself is emulated by a permanent-magnet synchronous motor (PMSM) driving a PMSG. The PMSM, which has the same parameters with the PMSG, is driven by an inverter working in the torque control mode, where the torque demand is given by the wind turbine simulator (WTS) based on a TMS320F2812 DSP. The same turbine characteristic, as shown in Fig. 3, is also programmed in the WTS to perfectly simulate the wind turbine’s dynamic and static performance. The correctness and validity of the WTS used in experiments have been veri?ed by the authors, as can be referred to [24]. Fig. 11 shows a picture of the test rig setup. The values of some extra parameters (not shown in the above sections) are listed in the following. 1) Inductor in the dc/dc converter: Lf = 200 μH. 2) Terminal voltage of the battery bank: U0 = 24 V. 3) Gains of power regulator PID: KP = 0.002 and KI = 0.02. 4) Initial value of the error threshold: eth = 3 V. 5) Initial value of the scaling factor: Kμ = 0.004. 6) Quantization factors: Ke = 0.05 and Kec = 7. 7) Optimal tip speed ratio: λopt = 4.1. 8) AFLC sample period: Ts = 1 ms.
Among the parameters given above, the gains of the power regulator, the initial value of error threshold, the initial value of scaling factor, and the value of the quantization factors are all tuned by experiments aiming to optimize the system performance. Fig. 12 shows the aerodynamic power (Pr ) calculated by (1) using a TMS320F2812 DSP and the output of the aerodynamic power observer (Pr_obs ) when the wind velocity steps up from 10 to 14 m/s. Despite a very short time delay during the transient process, it can be seen that the observed aerodynamic power complies with the calculated value (the real operational aerodynamic power of the turbine) very well. Thus, the effectiveness of the aerodynamic power observer is veri?ed. To support the declaration in this paper that the MPPT speed of the proposed APSF algorithm is much faster than that of the EPSF method, simulation and experimental evidences are shown in Figs. 13 and 14. These two ?gures give out the simulated and experimental dynamic processes of power coef?cient Cp , electrical torque Te , and aerodynamic torque Tr during wind velocity stepping from 7 to 11 m/s and then stepping back to 7 m/s. Notice the process that when the wind velocity steps up, according to the theory analyzed in Section II, to the APSF method, the current reference (the output of AFLC) i? 0 will be reverse saturation (the value is set to zero) very quickly. Considering that the output current (or power) is controlled to follow this current reference, the generator electric torque, which can be re?ected by the output current, will get a zero value during the dynamic process, as can be seen in Figs. 13 and
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Fig. 16. Experimental results with a dynamic wind velocity time series.
Fig. 14. Experimental dynamic processes of Cp , Tr , Te using APSF and EPSF methods when the wind velocity steps from 7 to 11 m/s and then from 11 to 7 m/s. (a) Variation of Cp . (b) Variation of Tr and Te .
Fig. 17. Measured electrical power versus generator recti?cation voltage.
Fig. 15. Experimental results with step changes of wind velocity.
14(b). However, to the EPSF method, due to the large moment of inertia of the blade, the electric torque cannot be controlled to response the fast variation of wind velocity, as can also be seen in Figs. 13 and 14(b). As a result, it only takes the APSF method 0.5 s to track the variation of wind, while it takes the EPSF method nearly 2 s to accomplish this process, as shown in Figs. 13 and 14(a). During the process when the wind velocity steps down, the same conclusion can be obtained. To demonstrate the overall power control strategy, step changes of wind velocity (from 7 m/s → 10 m/s → 13 m/s → 16 m/s) are applied to the wind turbine system, as shown in Fig. 15. When the wind velocity is varying below the rated value VN (0 s < t < 20 s), the turbine is operating in the MPPT region, the controller tracks the maximum power points very well, and power coef?cient Cp remains at the maximum value. Moreover, in the constant power stalling region (32 s < t < 40 s), the controller stalls the turbine by reducing the generator recti?cation voltage (viz., rotor speed). The electrical power is quickly regulated to be constant at the rated value of 1.2 kW. In addition, between the MPPT region and constant power stalling region, there exists a constant speed stalling
region (20 s < t < 32 s) in which the generator recti?cation voltage is controlled to be constant at the rated value of 150 V. A time series of dynamic wind velocity is applied to the wind turbine system to further demonstrate the effectiveness of the proposed control scheme, as shown in Fig. 16. Focus ?rst on the period between t = 30 s and t = 60 s. The controller works in the MPPT mode because the wind velocity is below the rated value VN . The power coef?cient Cp remains at the maximum value Cp max , and the electrical power Pe is correspondingly less than its rated value (1.2 kW). Then, consider the period from t = 4 s to t = 7 s when the wind velocity varies between VΩN and VN . The controller works in the constant speed mode, and the generator recti?cation voltage is controlled to remain at its rated value of 150 V to get rid of overspeeding problems. Finally, let us focus on the period between t = 7 s and t = 26 s. The controller stalls the wind turbine through reducing the generator recti?cation voltage because the wind velocity exceeds the rated value. The electrical power generated by the generator during this period is controlled constant at the rated value of 1.2 kW, showing that the system is indeed operating in constant power stalling mode. What is more, the time-series experimental results of electrical power and rotor speed are also measured in power versus generator recti?cation voltage plane as shown in Fig. 17. The three operational regions can be more directly observed, which further verify the validity of the proposed overall power control strategy. V. C ONCLUSION A novel overall power control strategy for VSFP wind turbines in the whole wind velocity range has been proposed
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in this paper. The structure and operational principle of the proposed strategy are elaborately analyzed. An aerodynamic power observer is proposed to help the controller handle the aerodynamic power based on which an APSF MPPT method is further proposed. Through simulation and experiments, the MPPT speed is proved to be much faster than the conventional EPSF method. The acceleration mechanism is also analyzed by comparing the MPPT process of these two methods. An AFLC is also proposed to enhance the system robustness to parameter variations and to optimize the dynamic and static control performance. The proposed control strategy is proved to be simple but effective by both simulation and experiments. Advantages of the proposed scheme include simplicity of controller structure, ease of implementation, avoidance for an anemometer or shaft encoder, and robustness to parameter variations. The scheme can potentially reduce the cost of the WECS. R EFERENCES
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Jiawei Chen (S’12) received the B.S. and M.S. degrees from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2008 and 2010, respectively, where he is currently working toward the Ph.D. degree. His research interests include power electronics circuits, renewable-energy generation systems, and digital control.
Jie Chen (M’12) was born in Zhejiang, China, in 1982. He received the B.S. and Ph.D. degrees in electrical engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 2004 and 2011, respectively. Since October 2011, he has been with the College of Automation Engineering, NUAA, as a Lecturer. His research interests include renewable-energy generation systems, microgrids, and electronics circuits in airplanes.
Chunying Gong (M’07) was born in Zhejiang, China, in 1965. She received the B.S., M.S., and Ph.D. degrees in electrical engineering from Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China, in 1984, 1990, and 1993, respectively. From 1984 to 1987, she was an Electrical Assistant Engineer with Chendu Aircraft Design and Research Institute. In 1993, she joined the College of Automation Engineering, NUAA, as a Lecturer, where, in 1996 and 2004, she became an Associate Professor and a Professor, respectively. Her research focuses on static inverters, power electronic systems stability and power quality, renewable energy, and distributed generation.