3.3 Methodical instructions

3.3.1 It should be mentioned, that zone of intermittent currents exists at relatively small values of rectified current and from the fact that induction in the loading net of the convertor is the finite quantity, and as the result loading current is smoothed non-ideal [7]. Thus between continuous and intermittent current exists initially-continuous current mode, i.e. limiting mode. It is characterized by the fact that valves covering is absent, but there is no zero current intervals yet, as shown in the figure 3.5 а), as well as current at the beginning of each interval (at the moment of opening of next valve) is equal to zero. Thus voltage of converter exactly correspond to its e.m.f.

а) b)

Figure 3.5 – Diagram of e.m.f. and currents of thyristor converter in limiting a) and intermittent b) modes.

E.m.f. and currents of converter and also motor velocity for the intermitting current mode at the variable α and λ, might be calculated by the formulas:

; (3.1)

, (3.2)

. (3.3)

In expressions (3.1)-(3.3) the following designations are used:

E_d is e.m.f. of convertor;

E_2λmax is the amplitude value of liner e.m.f. of transformer, ;

α is the angle of valve opening;

λ is the angular duration of impulse;

m is phase phenomena of convertor;

I_d is the rectified current of convertor (current of the motor armature);

ω₀ is angular frequency of the source;

L_Σ is the inductance of armature circuit, which consists of two phases of transformer and inductance of the motor armature;

ω_Д is the angular velocity of the motor;

С_Д is the e.m.f. coefficient of the motor.

; (3.4)

; (3.5)

, (3.6)

where ;

Х_а is reactance of the transformer phase:

; (3.7)

U_K is short-circuit voltage of the transformer, U_K=6%;

І_ф.тр.=І_нд; ω_н is the nominal velocity of the motor, ;

p= 2 is the number of pole pairs of the motor;

; (3.8)

,

is active resistance of the armature circuit during intermittent current.

Obtained dependence values of intermittent current and velocities (3.2), (3.3) from the value of valve opening angle and the angular current pulse duration is graphically presented by ellipse (Fig. 3.2), which must be drawn into e.m.f. graphs of convertor:

.

3.3.2 During loading of the motor, which correspond to continuous current, electromechanical characteristics and mechanical characteristics can be considered as linear and are calculated by the formulas

; (3.10)

, (3.11)

where Е_dmax is maximal value of rectified e.m.f. of the convertor at α=0.

During С_еФ = С_мФ = С_д the equations (3.10), (3.11) will look like:

; (3.12)

. (3.13)

At m = 6, α = 0 and λ = π/m from (3.1) we obtain:

, (3.14)

where .

.

Total active resistance of the armature circuit: . In the expression (3.11) the active resistance consists of motor resistance R_д, commutation resistance R_к and the resistance of transformer phases, which because of its small value can be neglected. Commutation resistance: .

Calculation and construction of electromechanical  characteristic we calculate by (3.12) for the continuous current mode we need to define for values I_dгpmax, I_dн, 0.5I_dн. The value of І_dгpmax is determined by substitution into (3.2) m=6, α=π/2, λ=2π/m:

.

Since: , where ,

then

I_dгpmax= 276,6 (1 - 0,524·1,732)/314L_Σ = 8,2·10^-2 /L_Σ.

For characteristic (3.13) its also necessary to take into account three moment values M_гpmax, 0.5M_н, M_н, where М_гpmax=С_д·І_dгpmax, and M_н=С_д·І_н.

3.3.3 Speed regulation upward from basis is realized by decreasing of excitation flow. Mechanical characteristics for this mode are necessary to built only in engine mode. They are determined by the expression (3.13) at α = const, which corresponds to the nominal mode of the motor. New values of constructive motor constant should be taken into account

, (3.15)

And so-called angular coefficients of mechanical characteristic tgγ, which are determined in the item 3.3.4. Speed regulation in that range provides the continuity of capacity on the motor shaft, that’s why individual points, that limit the zone of admissible continuous moments (Fig. 3.4) is determined from the expression М = Р_H/ω.

Zone of intermittent currents is now defined by two straight lines: ordinate axis and line, which is parallel to it and passing through the point of limit current on the main motor characteristic.

3.3.4 New value of С_д' in the relevant characteristic is determined with:

.

Solving this equation relatively to the С_д':

.

And taking into account, that М∙ω_д = Р_н, we obtain:

.

Because the engine runs in the  system ТП-Д, then instead of U=U_н its necessary to substitute into the equation e.m.f. of convertor E_dн, which provides a nominal mode of motor:

,

where Е_н is the e.m.f. of the motor at nominal mode, V;

I_dн is the nominal current of the armature, А.

Thus at known Е_dн, R_Σ, Р_н some constant К is calculated, for the chosen variant of the task and according to it dependence .

Taking into account, that , we obtain the anguler coeficient

,

where m_M, m_ω are scales of the moment and velocity.

All calculation results are shown in the table 3.2.

Table 3.2 – Calculation results.

ωд,с-1	М=Рн/ωд, Нм	Cд’=К/ωд	Cд’2	RΣ/ Cд’2	tgγ
1,2ωн
1,Зωн
1,4ωн
1,5 ωн
1,6ωн

3.3.5 E.m.f., current and velocities for intermittent current modes should be calculated, and take individual values of variables α and λ, shown in (Table 3.3).

Table 3.3 – Calculation result of e.m.f., current and velocity for intermittent current modes.

Value	α, rad	λ,rad
		π/12	π/6	π/4	π/З
Еd, V Іd, А ω, с-1	π /12
	π /6
	π /4
	π /З
	5 π /12
	π /2
	7 π /12
	2 π /3
	З π /4
	5 π /6
	11 π /12
	π

In explanatory note there must be three individual tables. Calculation results of moment М_гр = С_дI_dгр for intermittent current zone its enough to show for the next values of α and λ, given in the (Table 3.4).

Table 3.4 Calculation results of moment for intermittent current zone.

Value	α, rad	λ,rad
		π/12	π/6	π/4	π/З
М, Nm	π /12
	π /6
	π /4
	π /З
	5 π /12
	π /2

3.3.6 Calculation results of velocity and moment in intermittent current zone for construction of electromechanical and mechanical characteristics are shown in the Table 3.5, 3.6.

3.3.6 Results and computing speed moment in the continuous current for the construction of electromechanical and mechanical characteristics cited in the table. 3.5, 3.6. Table 3.5 - Results of calculations of electromechanical characteristics.

Table 3.5 Calculation results of electromechanical characteristic.

Value	α, rad	Id, А
		Іdгp	0,5Idн	Idн
ωд, с-1	π/12
	π/6
	π/4
	π/З
	5π/12
	π/2	Idгрмах
	7π/12
	2π/3
	3π/4
	5π/6
	11π/12
	π

Table 3.6 Calculation results of mechanical characteristic.

Value	α, rad	М, Nm
		Мгр	0,5Мн	Мн
ωд, с-1	π/12
	π/6
	π/4
	π/3
	5 π/12
	π/2	Мгрмах