三相同步发电机的电压向量图原文

Voltage Diagrams of the Three-Phase SynchronousGenerator on Balanced LoadThe voltage diagram is of very great importance for analyzing working conditions in a synchronous machine. It is possible to obtain from the voltage diagram the per cent variation of the synchronous generator voltage, the voltage increase with a drop in load and drop voltage for the transition from operation on no-load to operation on-load. The solution of these problems is of great importance: (1) for initial machine design when the necessary excitation current values are to be determined under various operating conditions and (2) when testing a finished machine to decide whether the machine conforms to given technical specifications. By using a voltage diagram, it is also possible to determine the operating conditions of a machine without actually applying the load, something which becomes especially difficult when the machine is of large rating.The voltage diagrams make it possible to obtain the fundamental performance characteristics of a machine by means of calculation. Finally, the voltage diagram allows to determine the power angle θ between the e. m. f. produced by the excitation field and the voltage across the terminals. Angle θplays a very important role in the analysis of the torque and power developed by a machine both in the steady-state and transient conditions.The vector difference between the e. m. f. E0due to the excitation flux and the terminal voltage V of a synchronous machine depends on the effect of the armature reaction and on the voltage drop in the active resistance and leakage inductive reactance of the armature winding.Since armature reaction depends to a very great extent on the type of the machine ( salient-pole or non-salient-pole ) , kind of load ( inductive, active or capacitive ) and on the degree of load symmetry ( balanced or unbalanced ) , all these factors must be duly considered when plotting a voltage diagram.It is necessary to bear in mind that all the e. m. f. s and voltages that participate as components in the voltage diagram should correspond to its fundamental frequency; therefore, all the e. m. f. s and voltages must preliminarily be resolved into harmonics and from each of them the fundamental wave must be taken separately. In the chapter where the armature reaction is considered an analysis was carried out which allowed to obtain the fundamental voltage wave produced by the armature field components revolving in step with the machine rotor.When a new machine is being commissioned, a vector diagram is plotted from the test data obtained from the experimental no-load and short-circuitcharacteristics.The voltage across the terminals is the result of the action of the following factors : (a) the fundamental pole m. m. f. creating fluxФ0 which induces the fundamental e. m. f. E0; (b) the direct-axis armature reaction m. m. f.F ad proportional to the load-current component I d , reactive in respect to the e. m. f. E0 ; (c) the quadrature-axis armature reaction m. m. f. F aq proportional to the current I q component , active in respect to the e. m. f. ; (d) the leakage e. m. f. Eσa=xσa I , proportional to the load current I ; (e) the active voltage drop in stator winding Ir a . Since when I=I n the voltage drop Ir a is less than 1% of the rated voltage, in most cases it may be neglected.The diagram may be constructed by two different methods. In the first method of construction of the vector diagram it is assumed that each m. m. f. exists separately and produces its own magnetic flux, the latter creating its own e. m. f. Thus, four separate fluxes and, accordingly, four e. m. f. s created by them appear in the machine, viz: (a) the excitation fluxФ0’and the fundamental e. m. f. E0’; (b) the flux and the e. m. f. of the direct-axis armature-reactionФad’and E ad’; (c) the flux and e. m. f. of the quadrature-axis armature-reactionФaq’ and E aq’; and (d) the fluxФσa’ and the e. m. f. Eσa’ of armature-winding leakage. If we also take into account the active voltage drop, which, when taken with opposite sign, may be considered as an e. m. f. E r’=-Ir a’, the vector sum of the e. m. f. s. listed above gives as a result the magnitude and phase of the terminal voltage vector V’.Since the vector summation of fluxes and the corresponding e. m. f. s. induced by them by the superposition method is legitimate only when the reluctances are constant in all sections of the magnetic circuit of the machine, this method is directly applicable to the unsaturated magnetic circuit of a synchronous machine. When using this method for machines with a saturated circuit, it is necessary to take into account the actual reluctances of the parts of the magnetic circuit at the given operating conditions and assume that the reluctances are constant so far as the given operating conditions are concerned. The results obtained will be correct, nevertheless it is difficult to determine the real magnetic conditions of the machine.Since by this method a vector summation of synchronous machine e. m. f. s is carried out, the voltage vector diagram obtained in this case may be called the e. m. f. diagram.From the theoretical point of view, this diagram is of very great methodological importance, since it allows to assess with the necessary completeness, the entire combination of factors determining, in the end, the voltage across the synchronous generator terminals, notwithstanding the fact that, for purposes of calculation and test, the diagram is somewhatcomplicated. Therefore, for a series of practical purposes the e. m. f. diagram is given a number of modifications to bring it into a more simple and convenient form.The method that is of greatest interest is the Blondel two-reaction theory, according to which all fluxes due to the load current I, including leakage flux Фσa‘, are resolved along the direct and quadrature-axes. In connection with this, we introduce the concept of synchronous machine direct and quadrature-axes reactances x d and x q, and their components, which represent some of the fundamental parameters of a synchronous machine and serve for assessment of its performance characteristics.By the second method we may determine first the resultant m. m. f. of the generator, obtained as the result of interaction of the excitation m. m. f. with a armature-reaction m. m. f. , and, having found from it the resultant flux in the air gapФδ,then determine the e. m. f. Eδactually induced in the machine. By subtracting vectorially from e. m. f. Eδ’ the inductive voltage drop in the leakage reactance j Ixσa’and the active voltage drop Ir a’, we may find the resultant voltage across the generator terminals.The diagram of m. m. f. s and e. m. f. s obtained in this case is called the Potier regulation, or e. m. f. diagram.For balanced load conditions, assuming that the parameters of all phases are equal, we may restrict the construction to a diagram for one phase only.It should be noted that the vector diagrams constructed for a synchronous generator operating as a generator may be readily extended to its operation as a synchronous motor and a synchronous condenser.The most simple voltage diagram is obtained for balanced load of a synchronous non-salient-pole generator with an unsaturated magnetic system. We shall therefore begin the discussion with the latter generator.Let us construct the e. m. f. diagram of a synchronous non-salient-pole generator first for the case of inductive load, when 0<φ<90o. Align the vector of the generator voltage across the generator terminals with the positive direction of the ordinate axis and draw the current vector I’ lagging behind the voltage vector V’ by an angle φ. Then draw the vector of the e. m. f. E0’ produced by the magnetic excitation fluxФ0’, as leading the current vector I’ by an angle φ. According to the general rule, fluxФ0’ leads the e. m. f. vector E0’ by 90o.The fundamental wave of the armature-reaction m. m. f. F a’of a synchronous generator rotates in step with its rotor. In a non-salient-pole type machine the difference between permeances along the direct axis andquadrature axes mat be neglected, and if may be assumed that m. m. f. F a’creates only a sine wave of reaction fluxФa’. This flux coincides in phase with the current I’ and induces in the stator winding an e. m. f. F a’lagging in phase behind I’by 90o.If x a is the inductive reactance of armature reaction for a non-salient-pole machine, then E a’=-j I’x a.By vector addition of the flux vectorsФ0’ and Фa’ and, respectively, the e. m.f. vectors E0’ and E a’ we obtain : (1) the vector of the resultant flux Фδ’ which actually exists in the generator air gap and determines the saturation of its magnetic circuit, and (2) the vector of the resultant e. m. f. Eδ’ in the stator winding, proportional to flux Фδ’ and lagging behind it by 90o.Existing together with the armature-reaction flux is a stator winding leakage flux Фδa’ , the vector of which, like that of flux Фa’, coincides in phase with current I’and creates in the stator winding a leakage of fundamental frequency Eσa’ =-j I’xσa lagging in phase behind current by 90o. Here xσa is the leakage reactance of the stator winding. Besides, it is necessary to take into account the e. m. f. E r’ =-I’r a which is opposite in phase to current I’; here r a is the active resistance of the stator winding.By vector addition of the e. m. f. vectors E0’ , E a’ , Eσa’ and E r’ , or, what is the same, the e. m. f. s E a’,Eσa’ and E r’ , we obtain the vector V’ of the voltage across the generator terminals. The angle φ by which current I’lags behind voltage V’is determined by the parameters of the external power circuit to which the generator is connected and feeds into. The vector V c’of the line voltage is in opposition to generator voltage vector V’.When constructing the vector diagrams of a synchronous machine, it is not e. m. f. s E a’,Eσa’ and E r’ that are represented, but their inverse values, which are the reactive and active voltage drops in the given sections of the circuit, i. e.-E a’=j I’x a, - Eσa’= j I’xσa, -E r’=I’r aIn this case the voltage diagram gives, obviously, the resolution of the e. m.f. E0’ due to the excitation flux into components representing the voltage drops j I’x a, j I’xσa and j I’r a and the generator terminal voltage V’. On the other hand, the voltage diagram show not the fluxesФ0’,Фa’ and Фδ’, but the m. m. f. s F0’, F a’and Fδ’ which produce them ; this makes it legitimate to call it the e. m. m. f. diagram.The voltage drop vectors j I’x a and j I’xσa may be substituted for by a common voltage drop vectorj I’x a + j I’xσa = j I’x swhere the reactancex s = x a+ xσais termed the synchronous reactance of the salient-pole machine.It is interesting to represent the relative arrangement in space of the main parts of machine , the stator and the rotor ,and the windings on them , together with the m. m. f. s they create . Angle φ indicates the space displacement of the conductors carrying maximum current I relatives to the conductors which have maximum e. m. f. E0and are opposite the pole axis .By this same angle φcurrent I’ lags behind e. m. f. E0’ in time phase . If we add the m. m. f. vector F a’to the excitation winding m. m. f. vector F0’ , we shall obtain the resultant m. m.f. vector Fδ’ which lags in space from F0’ by the same angleθ’ ,by which the e. m.f. Fδ’ lags behind e. m. f. E0’ in time phase .。