Wind Turbine Power Coefficient Analysis of a New Maximum Power Point Tracking Technique

1122 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 3, MARCH 2013

Wind Turbine Power Coefficient Analysis of a NewMaximum Power Point Tracking Technique

Yuanye Xia, Khaled H. Ahmed, Senior Member, IEEE, and Barry W. Williams

Abstract—A small-scale wind energy conversion system cantrack the maximum power point (MPP) based on a linear rela-tionship between V 2

dc and Idc. Unlike conventional MPP tracking(MPPT) methods using a lookup table, an advanced technique isproposed based on this relationship as a variant of the perturband observe (P&O) method. It not only has the advantages of theconventional P&O method but also has a faster tracking speedand better performance. This paper theoretically analyzes thepossible power coefficient drop when using a linear relationshipfor MPPT and establishes that the turbine design can ensure thatthe possible power coefficient drop is small. The simulation resultsshow that the analysis is precise. The validity and performance ofthe proposed MPPT method are confirmed by both simulation andexperimentation.

Index Terms—Maximum power point (MPP) tracking (MPPT),microgrids, perturb and observe (P&O), power coefficient, windenergy.

I. INTRODUCTION

DUE TO environmental reasons and technical improve-ments, large portions of electrical energy demand increase

will be met by smaller generation sources which may bedispersed over a wide area. This concept is known as distributedgeneration (DG) [1], [2]. Clusters of DG units can be connectedto local electric power networks, which are known as micro-grids, to serve local and distributed loads [3], [4]. They canoperate in grid-connected [5]–[7] and islanded modes [8]–[10].Microgrids offer the following advantages. The generation unitsare close to the consumers/load, so the transmission distancesare reduced, thus reducing transmission losses and preventingnetwork congestion. Furthermore, because some microgrids areable to work in an island mode, the chance of a blackout isdiminished [11]. Moreover, as microgrids consist of many smallunits, reliability is also enhanced [12].

DG units, including both renewable and nonrenewablesources, such as wind turbines, photovoltaic generators, fuelcells, and combined heat and power applications, are beingdeveloped [13]–[16]. Wind energy conversion systems are animportant renewable energy source and currently have thelargest utilization. Wind energy generation is interfaced to the

Manuscript received September 15, 2011; revised January 8, 2012 andMarch 30, 2012; accepted June 9, 2012. Date of publication July 6, 2012; dateof current version October 16, 2012.

Y. Xia and B. W. Williams are with the Department of Electronic andElectrical Engineering, University of Strathclyde, G11XW Glasgow, U.K.(e-mail: [email protected]; [email protected]).

K. H. Ahmed is with the Department of Electrical Engineering, Facultyof Engineering, Alexandria University, Alexandria 21544, Egypt (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2012.2206332

grid via power electronic converters. As the microgrids canoperate in both grid-connected and island operation modes,the dc/ac inverter should be able to operate, and seamlesslytransfer between, both modes [8]. The ac/dc converter controlsthe generator to capture maximum wind energy.

At a specific wind speed, the captured wind power is a func-tion of rotor speed. Only when the turbine rotates at optimumspeed can maximum power be extracted from the wind [17].Therefore, the maximum power point (MPP) tracking (MPPT)technique is important for wind energy conversion systems.For DG, the wind energy conversion system is usually smallor medium size. There are two main MPPT methods for smallsystems. The first is perturb and observe (P&O) control, whichis also known as hill-climbing searching control [18]–[23].The turbine speed is adjusted toward the MPP by regulatingthe dc-side voltage or current, according to the results ofcomparison between successive wind turbine generator outputpower measurements [18]–[20]. Such methods suffer from twomain problems: slow response and inefficiency under rapidlyfluctuating wind speed [21]. Methods to address the problemsare mostly associated with MPPT in photovoltaic systems [22],[23]. Due to the large inertia of a wind turbine system, leadingto a long settling time, photovoltaic system methods cannotbe readily extended to a wind energy conversion system. Theauthors of [21] proposed a novel P&O method to solve theproblems, using previously obtained MPP information as anindicator. However, the technique depends on a wind changedetecting scheme.

The second conventional MPPT technique is optimum-relationship-based (ORB) control. The control reference isgiven by a lookup table or a preknown relationship to trackthe MPP [24]–[34]. It is also known as power signal feedbackcontrol [24]. Such a technique is faster and more efficient thanP&O control. ORB control relies on preknowledge of a system,which varies from one system to another. Thus, individual testsare required to obtain data for precise and fast MPPT. Thereare several different relationships that are suitable for MPPT. In[25] and [26], a power versus rotor speed relationship is used,and in [27]–[29] and [34], an electromagnetic torque versus ro-tor speed relationship is employed. The systems using these tworelationships for MPPT usually have a voltage source converterat the generator side to fully control the generator torque or ro-tor speed. Mechanical sensors are required, increasing cost. Forsystems using a diode rectifier, power versus rectified dc voltage[30] and dc voltage versus dc current [31] are both suitablerelationships for MPPT. In these cases, no mechanical sensorsare required; only voltage and current sensors are needed. Bothmethods are based on a lookup table, so field tests are required

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XIA et al.: WIND TURBINE POWER COEFFICIENT ANALYSIS OF NEW MPPT TECHNIQUE 1123

to obtain a complete lookup table. In [32], a dc voltage versusdc current relationship is used for MPPT. The advantage is that,instead of a complete lookup table, an equation is obtained tocalculate the reference current for MPPT. The equation canbe expressed as a function of the dc voltage, and there aretwo coefficients in the equation which should be obtained first.Individual tests are still required, and a couple of data setsare needed to calculate the coefficients in the equation. Theauthors of [33] further simplify this equation; there is only oneunknown coefficient in the equation. However, in this paper,the effect of the wind turbine designs is not considered, and thepossible power coefficient drop is not investigated. Moreover,the details of how to obtain such a relationship for MPPT is notprovided, which lowers the practicality of this paper for powerapplications.

In this paper, a relationship for MPPT is derived and strictlyproved, and a new MPPT technique based on this relationshipis proposed. The effectiveness of the relationship for MPPT istheoretically analyzed. Simulation results verify the accuracyof the theoretical analysis. The validity and performance ofthe proposed new MPPT techniques are confirmed by bothsimulation and practical results.

II. WIND ENERGY CONVERSION SYSTEM

A. Wind Turbine Principles

The mechanical power derived from wind is

P =1

2ρCpAv

3w (1)

whereP captured power;ρ air density;CP power coefficient;A wind turbine swept area;vw wind speed.CP is a nonlinear function of tip speed ratio and turbine pitch

angle and can be expressed as [35]

CP = c1

(c2λi

− c3β − c4

)e

−c5λi + c6λ (2)

1

λi=

1

λ+ 0.08β− 0.035

β3 + 1(3)

whereλ tip speed ratio;r turbine radius;Ω turbine angular velocity;β blade pitch angle.

The coefficients c1–c6 are as follows: c1 = 0.5176, c2 =116, c3 = 0.4, c4 = 5, c5 = 21, and c6 = 0.0068. The CP

curve is shown in Fig. 1. The tip speed ratio λ is defined as

λ =rΩ

vw. (4)

Assuming a fixed-pitch-angle wind turbine, at a specific windspeed vw, the parameters ρ, A, r, and λ are constants. From

Fig. 1. Typical power coefficient curve.

Fig. 1, there is an optimum λ at which the power coefficientCP is maximum. CP−max and λopt are fixed for a given windturbine design. From (1) and (4), at different wind speeds

Pmax = k′Ω3opt (5)

where Pmax is the maximum output power at different windspeeds, Ωopt is the optimum rotor speed, and k′ is a constant.

Additionally

Pmax = ΩoptTopt (6)

where Topt is the optimum torque value.From (5) and (6)

Topt = k′Ω2opt. (7)

If the control unit controls the system based on (7), MPPTcan be achieved at different wind speeds. This Ω2 versus Trelationship can be used for MPPT [27]–[29].

B. System Configuration

A conventional small-scale wind energy conversion system,where the MPPT technique is investigated, is shown in Fig. 2.A three-blade horizontal-axis wind turbine is directly cou-pled to a permanent magnet synchronous generator (PMSG).An ac–dc–ac power converter converts the variable-frequencyvariable-amplitude ac power to meet the requirement for micro-grid connection [36]. A diode bridge rectifier is used rather thana controlled rectifier, due to its lower cost and high reliability.The rectified dc voltage is regulated by a boost converter, notonly to track the MPP but also to step up the dc voltage formicrogrid connection. The voltage source inverter (VSI) shownin Fig. 2 stabilizes the dc link voltage and converts the dcvoltage to ac. When required, the VSI can also supply reactivepower to the microgrid for voltage support. As a PMSG with ahigh number of pole pairs is adopted, this configuration doesnot require a gear box or external excitation current. It alsooffers full controllability of the system for MPPT. Therefore,it is favored for small-scale wind energy conversion systemsfor DG.


Fig. 2. Normal wind energy conversion system.

III. RELATIONSHIP-BASED MPPT

For a PMSG with a constant flux, the rms value of the phaseback electromotive force E is a linear function of the generatorrotational speed

E =1√2ΩpΦ (8)

wherep number of pole pairs;Φ generator flux;Ω generator rotational speed.

An approximation of the rectified dc voltage can be obtainedusing standard equations for a three-phase full-bridge dioderectifier with line inductance [37]

Vdc =3√6

πE − 3

πΩpLsIdc (9)

whereVdc average rectified voltage;Idc average dc-side current;Ls generator phase inductance.

From (8) and (9), an approximate relationship can be derived

Vdc ∝ Ω. (10)

If the dc-side current is controlled to be ripple-free dc current,then the generator-side phase a current can be expressed as [38]

ia =

∞∑k=1,5,7,...

(A0k cos kθ +B0k sin kθ) (11)

where

A0k =

√3Idc(−1)l+1

π

{2 sin ku

k+

1

1− cos u

×[−2 sin ku

k+

sin(k + 1)u

k + 1

+sin(k − 1)u

k − 1

]}(12)

B0k =

√3Idc(−1)l

π

{2 cos ku

k+

1

1− cos u

×[2(1− cos ku)

k− 1− cos(k + 1)u

k + 1

− 1− cos(k − 1)u)

k − 1

]}(13)

u = cos−1

(1− 2XaIdc√

6E

)

k =6l ± 1(l = 0, 1, 2, . . . , k > 0)

whereu overlap angle;Xa phase impedance.

Since the ac circuit is assumed balanced, phase b and ccurrents are known as they have 2π/3 and 4π/3 phase shiftsrelative to phase a current, respectively. Then, using a dq0transformation

iq = −2

3

(ia sin θ + ib sin

(θ − 2

3π

)+ ic sin

(θ +

2

3π

)).

(14)Substituting (11) into (14)

iq = −∞∑

k=1,5,7,...

(A0k sin(θ − kθ) +B0k cos(θ − kθ)) .

(15)From (15), the average iq can be expressed as

ıq =1

2π

2π∫0

iqdθ = −B01 (16)

where

B01 =

√3Idcπ

(2 + 2 cosu− 1− cos 2u

2(1− cosu)

). (17)

The average electromagnetic torque can be written as

T̄e =3

2pφı̄q. (18)

From (16)–(18)

Idc ∝ Te. (19)

Based on (7), (10), and (19), for a given design, at the MPP,there is an approximate relationship

Idc-opt = kV 2dc-opt (20)

where Idc-opt and Vdc-opt are the optimum dc-side current andvoltage when the system is at the MPP, respectively, and k is aconstant.

The Idc versus V 2dc characteristics of a typical kilowatt

power rating wind turbine at different wind speeds vw1, vw2,and vw3 are shown in Fig. 3(a), which are plotted based on


Fig. 3 Wind energy conversion system electrical characteristics: (a) Curves ofIdc versus V 2

dc at different wind speeds and the linear equation and (b) powerversus dc voltage curves for different wind speeds.

numerical data from simulations including turbine and powerelectronic converter models. The dotted nonlinear line is theactual optimum relationship between Idc and V 2

dc of a givendesign, for MPPT. The intersections (V 2

dc1, Idc1), (V2dc2, Idc2),

and (V 2dc3, Idc3) are the optimum operating points at wind

speeds vw1, vw2, and vw3, respectively. The output power ofthese operating points, which are the maximum output powersP1, P2, and P3 are shown in Fig. 3(b). The three solid linesshown in Fig. 3(a), which are (20) with different k values,approximate the nonlinear relationship of Idc versus V 2

dc. The kvalues are expressed as

k1 =Idc1V 2dc1

k2 =Idc2V 2dc2

k3 =Idc3V 2dc3

. (21)

Correspondingly, the power versus Vdc curves, when apply-ing the linear lines for MPPT, are also shown in Fig. 3(b). Theyshow that the power curves, when applying (20) for MPPT, areclose to the actual maximum power curve at different windspeeds. The power difference is small. Therefore, it can beconcluded that (20) is valid for MPPT. This is because theturbine design assures that the Cp curve is flat topped as shownin Fig. 1. Thus, there is a relatively large margin for errorin MPPT accuracy, where the power transfer efficiency of the

system will not be greatly affected [19]. Detail analysis is givenin Section V.

IV. ADVANCED MPPT TECHNIQUE

Fig. 3 shows that the V 2dc versus Idc relationship is effective

for MPPT. If k in (20) is known by the control system, thenby sensing the dc-side voltage, the dc-side current referencecan be obtained for MPPT. This is similar to the MPPT controltechniques based on a lookup table or an optimum relationship.It has a fast tracking speed and good response. However, k in(20) varies from one system to another. Simulation and fieldtests are required to get precise k values for an individualsystem. Moreover, the value of k may change due to possibleparameter shift for the turbine or generator.

The P&O method is an effective MPPT technique to solvethe aforementioned problems. Preknowledge of a system isnot required, and turbine or generator parameter shift cannotaffect tracking. Conventional P&O methods use rotor speed,dc-side voltage, or boost duty ratio as the control parameter forperturbing. It leads to a disadvantage of P&O control: These pa-rameters vary when the wind speed changes; therefore, it takesa long time to track the MPP again. A comparison betweensuccessive output power measurements cannot be made untilthe system is at steady state. Therefore, the response is slowwhen the turbine has a large inertia.

The proposed MPPT technique uses k in (20) as the controlparameter for perturbing. Instead of looking for the exactoperating points for different wind speeds, it finds an optimumrelationship for MPPT. It is established in Section V that thevariation in k is small for different winds. Moreover, the kobtained at a specific wind speed is valid for a full range ofwind speeds. Therefore, a significant advantage of using k asdisturbance quantity is that the tracking speed and response arebetter than with the conventional P&O control.

Equation (20) can be written as

Idc-opt = (a tan θ)V 2dc-opt. (22)

As the values of V 2dc and Idc are of different magnitude

orders, a in (22) is used to scale their values. θ in (22) isused as the control parameter for perturbing rather than k in(20). Fig. 4 shows the concept of the proposed method. WhenLine A enters into the gray area, by perturbing θ, MPPT canbe achieved. Of course, there will be an optimum θ for aspecific wind speed. However, the range of θ for different windspeeds is within the gray area, and Section V shows that, withinthis gray area, the power coefficient is almost a maximum fordifferent wind speeds. Note that, once Line A enters the grayarea, it will always oscillating inside this area as the windspeed change does not affect the location of the gray area. Thisis a significant advantage compared to the conventional P&Ocontrol.

The value of a can be the ratio of the rated values of V 2dc

and Idc of a given wind energy conversion system, which isexpressed as

a =Idc-ratedV 2dc-rated

. (23)


Fig. 4. Concept of the proposed MPPT control.

Fig. 5. Control block diagram.

The assignment of a is not critical to the MPPT performance.Equation (23) assures that the gray area in Fig. 4 will bearound 45◦.

The proposed MPPT technique control block is shown inFig. 5. The P&O block is similar to the conventional P&Omethod, except that θ is used as the control parameter. Thealgorithm is implemented in the following manner, with thecontrol flow chart shown in detail in Fig. 6. The dc-side voltageand current are sampled at a particular rate, and the dc powerincremental change is computed. If the power incrementalchange is positive, then the sign of Δθ remains the same;otherwise, the sign of Δθ changes.

The advantage of the proposed technique includes those ofthe conventional P&O control, but it has a faster tracking speedand response and is suitable for larger wind turbine inertiasystems.

V. POWER COEFFICIENT ANALYSIS

In this section, it will be established that, when the windspeed changes, the power coefficient drop is small using the kobtained at one specific wind speed. That is, for different windspeeds, the difference between optimum k values is small. Thischaracteristic is the advantage of the proposed MPPT techniquecompared to the conventional P&O control. The analysis isbased on the configuration shown in Fig. 2.

First, k can have different values. It is assumed that k isobtained at a given wind speed v1

k =Idc-v1V 2dc-v1

(24)

where Idc-v1 and Vdc-v1 are the optimum dc current and voltagefor MPPT when the wind speed is v1. The corresponding

Fig. 6. Control flow chart.

optimum rotor speed is Ω1. When the wind speed changes tov2, from (4), the optimum rotor speed is Ω′

2

Ω′2 =

v2v1

Ω1. (25)

When the system is controlled based on (20) for MPPT, therotor speed is Ω2. As Ω′

2 �= Ω2, the error, ΔΩ, causes a powercoefficient drop in the system at wind speed v2.

At wind speed v2, the mechanical torque Tm and rotationalspeed Ω can be expressed as

P = ΩTm. (26)

Substituting (1)–(4) into (26)

Tm=ρAv322Ω

{c1

[c2

( v2rΩ

−0.035)−c4

]e−c5( v2

rΩ−0.035)+c6rΩ

v2

}.

(27)

Equation (27), Tm = f(Ω), represents the turbine mechani-cal characteristic at a specific wind speed.

The electromagnetic torque can be expressed as

Te =3

2pΦiq. (28)

Substituting (16) into (28)

Te = −3√3Idc2π

pΦ

(2− 2XaIdc√

3ΩpΦ

). (29)

From (9) and (20), the rotor speed Ω and dc-side current havethe following relationship when using (20) for MPPT:

Idc =π2

18kΩ2p2L2+

√3Φ

L−

√π4

324k2Ω4p4L4+

√3π2Φ

9kΩ2p2L3.

(30)


TABLE ISYSTEM PARAMETERS

TABLE IIRESULTS

Substituting (30) into (29) gives equation Te = f(Ω).When the system is at steady state, the sum of mechanical

and electromagnetic torques is zero

Tm + Te = 0. (31)

The rotor speed Ω2, when applying (20) for MPPT, can becalculated based on (27)–(31). According to (25), Ω′

2 can beobtained. Then, the power coefficient drop can be assessedfrom (2).

A. Analysis Result

The wind energy conversion system shown in Fig. 2 is usedto evaluate the effectiveness of (20) for MPPT. The systemparameters are summarized in Table I. k is obtained when thewind speed is 8 m/s, where the power coefficient is optimum,and at other wind speeds, it drops.

In order to analyze the power coefficient drop, the rotorspeed, when applying (20) for MPPT, is calculated based on(27)–(31). The simulation results using MATLAB/Simulinkfor the same system are also given to validate the theoreticalanalysis. Both results are given in Table II, where the theoreti-cal analysis matches the simulation results. This validates thetheoretical analysis. Also, the actual optimum rotor speed isgiven. It can be concluded from Table II that, when applying(20) for MPPT, there is a difference between the actual rotorspeed and the optimum rotor speed. This difference, ΔΩ, leadsto the power coefficient drop. The results are plotted in Fig. 7,to make this result clear.

Substituting the results in Table II into (2), the power co-efficient drop due to the ΔΩ can be calculated. The results

Fig. 7. (Dotted line) Optimum rotor speed at different wind speeds, (solidline) actual rotor speed obtained by calculation, and (crosses) actual rotor speedobtained by simulation.

Fig. 8. Power coefficient at different wind speeds.

are plotted in Fig. 8 and show that, for the given wind energyconversion system, the maximum coefficient drop is 0.71%,which is small. This substantiates the effectiveness of using (20)for MPPT and also indirectly proves that the k variation is smallfor different wind speeds.

B. Different Wind Turbine Models

Table II shows that there is a 5% maximum differencebetween the optimum rotor speed and the actual rotor speedwhen applying (20) for MPPT. However, as shown in Fig. 8,the actual power coefficient difference is smaller. Therefore,the validity of (20) is mainly based on the design of the windturbine. There are several different Cp equations proposed in[39]–[41], which are shown as follows:

CP =(1.12λ−2.8)e−0.38λ (32)

Cp=0.22

(116

λi−0.4β−5

)e− 12.5

λi (33)

Cp=(0.44−0.0167β) sinπ(λ−2)

13−0.3β−0.00184(λ−2)β. (34)

Using the same theoretical analysis to analyze the afore-mentioned equations to test the validity of (20) for MPPT,


Fig. 9. Power coefficient drop: (a) Equation (32), (b) (33), and (c) (34).

TABLE IIITHEORETICAL ANALYSIS OF Cp DROP WITH DIFFERENT EQUATIONS

the result shows that the Cp drop is small. In the analysis, kin (20) is obtained when the wind speed is 8 m/s; therefore,when the wind speed changes, Cp drops. Assuming that thewind variation range is from 5 to 11 m/s, the results are shownin Fig. 9. The possible maximum Cp drop is summarized inTable III, showing that, with different Cp equations, (20) andthe proposed MPPT technique remain valid.

VI. SIMULATION RESULT

MATLAB/Simulink simulations are used to verify the per-formance of the proposed MPPT technique. The system config-uration is the same as shown in Fig. 2, except that the dc link iskept constant by a dc voltage source for simplicity. The systemparameters are the same as shown in Table I, except that k isunknown and (22) is used instead of (20). For comparison, the

Fig. 10. Conventional P&O control flow chart.

TABLE IVCONTROLLER PARAMETERS

conventional P&O control is simulated based on the same pro-posed system configuration and parameters. Its control schemeis shown in Fig. 10. For simplicity, the controller uses the boostduty ratio for perturbing. As the dc link voltage is constant, theboost input dc voltage is indirectly used for perturbing. The twocontroller parameters are summarized in Table IV.

To properly validate the proposed technique, a realistic windprofile is employed based on a wind speed model for sim-ulation periods shorter than an hour. It is approximated asthe superposition of a mean wind speed v̄w and N sinusoidalcomponents having amplitude Ai, frequency ωi, and randomphase ϕi [42]

vw(t) = v̄w +

N∑i=0

Ai cos(ωit+ ϕi). (35)

The von Karman power spectrum [43] is used to determinethe amplitudes Ai

Ai(ωi) =2

π

√1

2[Svv(ωi) + Svv(ωi+1)] [ωi+1 − ωi] (36)

Svv(ωi) =0.475σ2

(Lv

v̄w

)(1 +

(ωiLv

v̄w

)2) 5

6

(37)

where σ is the wind turbulence intensity and Lv is the windturbulence length scale [43]. The frequencies ωi are chosen tobe logarithmically spaced.


Fig. 11. Simulation results of the (black curve) proposed P&O techniqueand (gray curve) conventional P&O technique. (a) Wind speed. (b) Powercoefficient. (c) Rotor speed. (d) Power versus speed. (e) Torque versus speed.(f) Output power.

Fig. 11. (Continued). Simulation results of the (black curve) proposed P&Otechnique and (gray curve) conventional P&O technique. (g) Output energy.(h) θ value. (i) Boost duty ratio.

The simulation results are shown in Fig. 11. The windcondition based on equations (35)–(37) is shown in Fig. 11(a).Fig. 11(b) shows the power coefficient of the two approachesand that the proposed P&O technique has a higher overallefficiency than the conventional P&O method with a fastertracking speed. It also indirectly established the theoreticalanalysis in Section V that the power coefficient drop is smallwhen the system tracks the MPP based on a proposed optimumrelationship. The rotor speed of the proposed technique shownin Fig. 11(c) better tracks the wind profile. Fig. 11(d) showsthe power versus rotor speed curve, where the dotted line is theideal power versus speed profile for MPPT, the black line isthe proposed method, and the gray line is for the conventionaltechnique. It can be observed that the proposed method bettertracks the ideal MPPT profile than the conventional technique.Fig. 11(e) shows the torque versus rotor speed curve, whichsuggests the same conclusion. Fig. 11(f) and (g) shows thesystem output power and energy within the simulation period,respectively. The proposed technique has a higher energy out-put, with approximately 28 kJ. Therefore, within the 140-speriod, the output power of the proposed technique is 0.2 kWhigher than that of the conventional method. The averagepower during the period of the conventional method is 5.6 kW.Therefore, the overall power efficiency is 3.6% higher usingthe proposed technique. Fig. 11(h) shows the θ in the proposed


Fig. 12. Wind energy conversion system hardware arrangement.

Fig. 13. Wind energy conversion system test rig.

TABLE VEXPERIMENTAL SYSTEM PARAMETERS

method, while Fig. 11(i) shows the boost duty ratio in theconventional method.

The conventional P&O is significantly affected by turbineinertia because large turbine inertia causes a long settlingtime, leading to a significant time lag between the change ofsystem parameter for perturbing and observed change in power.As the conventional P&O technique searches for a specificoperating point, if this point is not accurate, the power captureefficiency decreases significantly. Therefore, the conventionalP&O method is only suitable for small power rating systemswith low inertia. However, the turbine inertia does not havesuch a significant effect on the proposed P&O technique. Asestablished in the theoretical analysis, the variation in k is smallfor different wind speeds. It is established that the k obtained ata specific wind speed is valid for a full range of wind speeds,resulting in a small Cp drop. Therefore, even if the significanttime lag is caused by large inertia, the power coefficient doesnot decrease significantly using the proposed technique. Hence,the proposed MPPT technique can be implemented in largepower rating systems.

VII. EXPERIMENTAL RESULTS

A prototype MPPT system, as shown in Figs. 12 and 13,was developed based on the proposed MPPT technique. A

Fig. 14. Experimental results of the (black curve) proposed P&O techniqueand (gray curve) conventional P&O technique. (a) Wind speed. (b) Powercoefficient. (c) Rotor speed. (d) Power versus speed. (e) Torque versus speed.(f) Output power.


Fig. 14. (Continued). Experimental results of the (black curve) proposed P&Otechnique and (gray curve) conventional P&O technique. (g) Output energy.(h) θ value. (i) Boost duty ratio.

2.0-kW induction machine (IM) is controlled by a DSP as awind turbine emulator. The wind data, as well as experimentalresults, are stored in the DSP. The rotor speed is measured,and a torque signal is then calculated, according to the windturbine characteristic, to control the IM. The boost converter iscontrolled based on the proposed MPPT technique. The boostoutput voltage is kept constant by a switch to model a constantdc link voltage. The parameters are summarized in Table V.

The practical results of the proposed and the conventionalmethods are shown in Fig. 14. Fig. 14(a) shows the frequentlyfluctuating wind speed derived based on equations (35)–(37).The comparison of the power coefficient in Fig. 14(b) showsthat the proposed technique has a higher overall efficiency thanthe conventional P&O method. The rotor speed is given inFig. 14(c). Fig. 14(d) and (e). shows the power and torqueversus speed curves, respectively, which establish that the pro-posed technique tracks the ideal MPP profile better than theconventional method. The system output power and energyare shown in Fig. 14(f) and (g). The output energy of theproposed technique is approximately 11.7 kJ higher than thatof the conventional method, within the 180-s period. There-fore, the average output power is 0.065 kW higher using theproposed technique. Considering that the average power of theconventional method is approximately 0.838 kW, the overallpower efficiency is improved by 7.8%. Fig. 14(f) shows theparameter θ of the proposed method, and Fig. 14(g) shows the

boost duty ratio of the conventional method. These perturbationparameters change slower than those in the simulation dueto the larger experimental time constant. Therefore, it takeslonger for the system to settle. The test rig larger time constantalso relates to the performance of the machine driver for windturbine emulation.

VIII. CONCLUSION

A linear relationship between V 2dc and Idc for MPPT has

been established. A modified P&O MPPT technique has beenproposed where the theoretical analysis of this relationshiphas shown its validity and performance for MPPT. The powercoefficient drop when using this relationship is small, whichhas been confirmed by both theoretical analysis and simulation.This characteristic has led to the advantages of the proposedMPPT technique over the conventional P&O control. It has afaster tracking speed and better performance (overall efficiencyhas been improved by 3.6% and 7.8% in simulation and exper-imentation, respectively). Moreover, it is suitable for systemswith high wind turbine inertia. Both simulation and practicalresults have validated the proposed MPPT technique.

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Yuanye Xia received the B.Eng. degree from Zhe-jiang University, Hangzhou, China, in 2008 and thePh.D. degree from the University of Strathclyde,Glasgow, U.K., in 2012.

He is with the Department of Electronic and Elec-trical Engineering, University of Strathclyde. Hisresearch interests are the digital control of powerelectronic systems, wind energy conversion system,and current source converter.

Khaled H. Ahmed (S’08–A’08–M’11–SM’12) re-ceived the B.Sc. (first-class Hons.) and M.Sc. de-grees from the Faculty of Engineering, AlexandriaUniversity, Alexandria, Egypt, in 2002 and 2004,respectively, and the Ph.D. degree in electrical en-gineering from the Department of Electronic andElectrical Engineering, University of Strathclyde,Glasgow, U.K., in 2008.

Since 2009, he has been a Lecturer with Alexan-dria University. He has authored or coauthored morethan 40 technical papers in refereed journals and

conferences. His research interests are the digital control of power electronicsystems, power quality, microgrids, distributed generation, and HVdc.

Dr. Khaled is a reviewer for the IEEE Transactions and several conferences.

Barry W. Williams received the M.Eng.Sc. de-gree from The University of Adelaide, Adelaide,Australia, in 1978, and the Ph.D. degree from theUniversity of Cambridge, Cambridge, U.K., in 1980.

After seven years as a Lecturer with Imperial Col-lege, London, U.K., he was appointed as the Chair ofElectrical Engineering with Heriot-Watt University,Edinburgh, U.K., in 1986. He is currently a Professorwith the University of Strathclyde, Glasgow, U.K.His teaching covers power electronics (in whichhe has a free Internet text) and drive systems. His

research activities include power semiconductor modeling and protection,converter topologies, soft switching techniques, and application of ASICs andmicroprocessors to industrial electronics.

Documents

Wind Turbine Power Coefficient Analysis of a New Maximum Power Point Tracking Technique