Characteristics of Salient Pole Generator

Characteristics of salient-pole generators: The air gap between the stator and the rotor is non-uniform. The air gap under the pole shoe is relatively small, while the air gap between the two poles is relatively large. That is to say, the magnetic reluctances of the direct axis and the quadrature axis of the salient-pole synchronous generator are different. Therefore, the armature magnetomotive force will generate different armature fluxes at different positions in the air gap.

As known from the analysis of the armature reaction of synchronous generators, under normal circumstances, the armature current can be decomposed into two hypothetical current components, namely the direct-axis current component Id=Issin⁡ΨI_d = I_s\sin\PsiId=IssinΨ and the quadrature-axis current component Iq=Iscos⁡ΨI_q = I_s\cos\PsiIq=IscosΨ. These two components respectively establish the magnetomotive forces FdF_dFd and FqF_qFq, and these two magnetomotive force components respectively generate the direct-axis armature reaction flux Ψd\varPsi_dΨd, the direct-axis electromotive force EdE_dEd, the quadrature-axis armature reaction flux Ψq\varPsi_qΨq, and the quadrature-axis electromotive force EqE_qEq. The sum of these two electromotive forces gives the total armature reaction electromotive force EsE_sEs. In addition, all other quantities are the same as those of non-salient-pole generators. When ignoring the resistance of the stator winding, the electromotive force balance equation of one-phase stator winding of a salient-pole generator is:

E0+Ed+Eq+EL=UE_0 + E_d+E_q + E_L=UE0+Ed+Eq+EL=U (2 - 38) or E0=U−Ed−Eq−ELE_0 = U - E_d - E_q - E_LE0=U−Ed−Eq−EL (2 - 39)

If the magnetic circuit of the generator is not saturated or the influence of magnetic circuit saturation is not considered, EdE_dEd and EqE_qEq can also be expressed in terms of reactance voltage drops, that is:

where XsdX_{sd}Xsd - direct-axis armature reaction reactance;

XsqX_{sq}Xsq - quadrature-axis armature reaction reactance.

EdE_dEd and EqE_qEq respectively lag behind the corresponding IdI_dId and IqI_qIq by 90∘90^{\circ}90∘. The magnitudes of XsdX_{sd}Xsd and XsqX_{sq}Xsq respectively reflect the strengths of the direct-axis and quadrature-axis armature reactions.

Since the stator leakage flux is also generated by the stator current IsI_sIs, and IsI_sIs is regarded as the phasor sum of EdE_dEd and EqE_qEq, the leakage induced electromotive force is:

EL=−jIsXL=−j(Id+Iq)XL=−jIdXL−jIqXLE_L=-jI_sX_L=-j(I_d + I_q)X_L=-jI_dX_L - jI_qX_LEL=−jIsXL=−j(Id+Iq)XL=−jIdXL−jIqXL (2 - 41)

E0=U+jIdXsd+jIqXsq+jIdXL+jIqXLE_0=U + jI_dX_{sd}+jI_qX_{sq}+jI_dX_L + jI_qX_LE0=U+jIdXsd+jIqXsq+jIdXL+jIqXL

=U+jId(Xsd+XL)+jIq(Xsq+XL)=U + jI_d(X_{sd}+X_L)+jI_q(X_{sq}+X_L)=U+jId(Xsd+XL)+jIq(Xsq+XL)

=U+jIdXd+jIqXq=U + jI_dX_d + jI_qX_q=U+jIdXd+jIqXq (2 - 42)

where XdX_dXd - direct-axis synchronous reactance of the salient-pole synchronous generator; XqX_qXq - quadrature-axis synchronous reactance.

Or rewrite equation (2 - 24) as U=E0−jIdXd−jIqXqU = E_0 - jI_dX_d - jI_qX_qU=E0−jIdXd−jIqXq

This relationship shows that the salient-pole generator, like the DC generator, can be represented by a simple equivalent circuit. In the figure, E0E_0E0 is the no-load electromotive force, and its internal impedance is composed of the parallel combination of XdX_dXd and XqX_qXq.

When the magnitude and nature of the load and the synchronous reactance are known, the phasor diagram of the salient-pole synchronous generator can be drawn.

From the above analysis, XdX_dXd and XqX_qXq are the basic parameters of the salient-pole synchronous generator, which reflect the magnetic field and magnetic circuit conditions of the salient-pole generator. For a salient-pole generator, the magnetic reluctance in the direct-axis direction is greater than that in the quadrature-axis direction. Therefore, under the action of the same armature reaction magnetomotive force, φsd>φsq\varphi_{sd}>\varphi_{sq}φsd>φsq, thus Xsd>XsqX_{sd}>X_{sq}Xsd>Xsq and Xd>XqX_d > X_qXd>Xq. For a non-salient-pole generator, the magnetic reluctances in the direct-axis and quadrature-axis directions are basically equal, so Xsd=Xsq=XsX_{sd}=X_{sq}=X_sXsd=Xsq=Xs and Xd=Xq=XtX_d = X_q = X_tXd=Xq=Xt.

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