liding Mode contolle fo elf-excited Induction Geneato L. Louze, A. L. Nemmou, A. Khezza and M. Bouchema Laboatoie d Electotechnique de Constantine LEC Mentoui Univesity, Constantine 5000, Algeia E-mail: louze_lami@yahoo.f Abstact. This pape pesents a simple contol stuctue based on the sliding mode algoithm fo an isolated-loaded induction geneato (IG. The machine delives an active powe to a -load via a convete connected to a single capacito on the side. ince the convete/capacito model is nonlinea, the sliding mode technique constitutes a poweful tool to ensue the -bus voltage egulation. The compute simulations ae povided to veify the validity of the poposed contol algoithm. Key wods Induction geneato, liding mode contol, DC voltage contol.. Intoduction The use of induction geneatos is becoming moe and moe popula fo enewable enegy souces, especially fo wind electic systems, both in gid connected and stand alone mode. It is well known that the induction geneato can opeate in self-excited mode using only the input mechanical powe fom the otating pime move and a souce of eactive powe. The eactive powe can be supplied by a vaiety of methods, fom simple capacitos to complex powe convesion systems. Owing to its many advantages, the self excited induction geneato has emeged fom among the well known geneatos as a suitable candidate to be diven by wind tubine. ome of its advantages ae small size and weight, obust constuction, absence of sepaate souce fo excitation and educed maintenance cost. When the induction geneato is connected to an infinite powe net, the analysis becomes simple, since the voltage and fequency ae detemined by the diving netwok. Howeve, an autonomous induction machine is able to geneate electic powe only if self excitation occus [- ], and it can be sustained. The main dawback of such geneatos howeve is its inheently poo voltage egulation, and it becomes necessay to have an appopiate voltage egulating scheme. To ovecome poo voltage egulation of the EIG, a numbe of schemes have been poposed. The scheme based on switched capacitos, this scheme finds limited application because it egulates the teminal voltage in discete steps [-5]. A satuable eacto scheme of voltage egulation involves potentially lage size and weight due to the necessity of a lage satuating inducto [6-7]. In the shot shunt and long shunt configuation, the seies capacito used causes the poblem of esonance while supplying powe to an inductive load [8-9]. The poblems associated with schemes discussed above can be solved by applying nonlinea contol to an invete/ectifie system with a single DC capacito on the DC link. In this pape, a eview of sliding mode contol associated to the flux oiented contol technique is applied to a selfexcited induction geneato. The vecto contol stategy is employed in ode to educe EIG mathematical model complexity. The induction geneato oto flux is contolled by the d-axis stato cuent and the q-axis stato cuent contols the deliveing active stato powe.. Induction Geneato Model The state space model of induction geneato in the synchonously otating efeence fame d and q axes ae [0,]: di = αi + si + α ϕd + mα ϕ q α dt di = si αi mα ϕ d + α ϕq α dt dϕ d M = i + ( ϕd s m ϕq dt τ τ dϕ q M = i ϕq ( s m ϕd dt τ τ Whee: α α σ = +, στ s στ = σl. s σ α = Mστ, Ls L With: τ s = and τ =. s ( σ α =, and Mσ
And the model of the PWM convete is: d C dt = = = d q ( i + i d q Whee d and q ae the Pak's tansfomation of the switching functions a, b and c fo the PWM technique and thei state is defined by the following function: +, k = k = fo k=a,b,c, k = + When the induction geneato is opeated unde the vecto contol conditions, the oto flux estimato can be expessed as ( ϕ = ϕ and ϕ = 0 : d q ( ( dϕ M = i ϕ ( dt τ τ And the synchonous fame velocity is given by: M i s = + (5 τ ϕ The vaiables to be contolled ae the oto flux φ and the DC voltage in the DC side.. Cascade liding Mode Contol A. Geneal concept The vaiable stuctue system and thei associated sliding egimes ae chaacteized by a discontinuous natue of the contol action with which a desied dynamic of the system is obtained by choosing appopiate sliding sufaces. The contol actions povide the switching between subsystems which give a desied behavio of the closed loop system [0], [-6]. The geneal fom of sliding suface which guaantees the convegence of the state x to its efeence x is given as follows: d ( x = + ( x x dt λ (6 Whee is the degee of the sliding suface and λ is a stictly positive constant. It is the fist convegence condition which pemits dynamic system to convege to wads the sliding sufaces. It is a question of fomulating a positive scala function (x > 0 fo the system states vaiables which ae defined by the following Lyapunov function: = (7 ( x ( x To cause the Lyapunov function deceases, it is necessay to ensue that its deivative is negative. This is checked if: ( x ( x < 0 & (8 Now, to define the contol algoithm fo the induction geneato, it contains two tems, fist fo the exact lineaization, the second discontinuous one fo the system stability. U = U + U (9 c eq n - U eq is calculated stating fom the expession ( x = 0 - U n is given to guaantee the attactivity of the vaiable to be contolled towads the commutation suface. To find the contol expession U c, let us conside a class of nonlinea system descibed by the following equation: ( x gu c x & = f + (0 Whee: x state vecto, U c contol inputs, f, g smooth vecto fields, Theefoe: x & ( x = = ( t t We substitute (9 and (0 into (, we get: ( + gu eq + gu n & ( x = f ( x ( When the sliding mode is eached the suface is cancelled and consequently its deivative also & = 0 Theefoe the equivalent contol U eq can be witten as: U eq = g f ( x By eplacing U eq in (, we obtain: & ( & ( x = gu n ( And the attactivity condition expessed by (8 becomes: ( x gu n (5
C IG m dq abc θ s oto Flux, s, and θ s Estimation Equ. 8+ i i Equ. Equ. i i Equ. ϕ ϕ m _ min. ϕ m _ max Fig.. Contol stuctue poposed In ode to satisfy this condition, the sign of U n must be opposed to the one of ( x g. The simplest equation is the fom of elay: U n =ksign( (6 B. Application to the EIG contol In this study, the sliding mode theoy is applied to the oto field oiented induction geneato model, in such a way as to obtain simple sufaces. The poposed elf- Excited Induction Geneato EIG contol scheme is shown in Fig.. It consists of an EIG, a thee phase convete connected to the IG teminals, a DC link voltage and finally a DC load in the DC side convete. Fo the IG sliding mode contolles design, fou switching sufaces ae chosen as: ( ϕ ( i ( ( i = ϕ ϕ = i = = i i i (7 In ode that 0 in finite time, the contol law is designed such that: & & & & ( ( ( ksign k sign = k ( sign k sign (8 We have: & = & & (9 ϕ ϕ Eqs. and 9 yield: M i τ ϕ = ksign τ ( The diect stato cuent set value is deduced as: i τ ksign M ( + ϕ τ = (0 ( With the same manne, the diect stato cuent suface deivative is: & = i& i& ( o: α i + i + α ϕ α i& = k sign ( ( s d Taking into account the Eqs. and 0, we obtain: α ( k sign( α i + i + α i& = ϕ s ( The best way to calculate the aea is to put it into the following fom: P Theefoe: d dt = I = C = P d C dt + (5 (6
The suface of DC voltage is given by: & = & & (7 Eqs 8. and 6 give: P = Cksign( (8 When losses ae not taken into account, the electomagnetic toque will be given by: ince: Then: P T em = (9 Ω T em M = p ϕ i (0 L L P = ( M ϕ i Finally, the suface of i is given by:. imulation esults The poposed contol has been simulated fo an induction machine with the following paametes (.5 kw, cosφ=0.8, poles, 0 (ms, whose pe-phase equivalent cicuit constants ae: L s =L =0.7H, M=0.58H, s =.85 Ω and =.805 Ω. The DC voltage egulation is obtained using the poposed algoithm contolle in spite of the pesence of distubances such as step changing of the esistive load and the mechanical speed (when the EIG is diven by a wind tubine fo example. Fig.. shows a no-load opeation flowed-up by a step changing of the esistive load (50Ω intoduced at t=0.6s when the DC-bus voltage is set to 600. A apid esponse is obtained and the intoduced petubation is immediately ejected by the contol system. We also showed in Fig.. the vaiation in d-axis, q-axis stato cuents and electomagnetic toque in the otating efeence fame. Fig. 5. shows the stato cuent and the build up of geneated voltage at the teminals of the induction geneato. & = & & ( i i Taking into account the Eqs., 8 and, the quadatue stato volatge component efeence value is computed as: α ( k sign( i α i α i& = ϕ s m ( The efeence oto flux linkage equied at any speed is calculated based on this maximum flux linkage, which coesponds to the minimum oto speed. Hence at any oto speed the efeence oto flux linkage is given by equation ( and gaphically its vaiation with oto speed is shown in Fig..[7]: minϕ max ϕ = ( φ φ max φ min min max Fig.. elationship between oto speed and oto flux linkage. Fig.. DC voltage and oto flux vaiation with speed and load vaiation
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