ISSN 1062-7391, Journal of Mining Science, 2016, Vol. 52, No. 2, pp. 313–324. © Pleiades Publishing, Ltd., 2016. Original Russian Text © B.F. Simonov, S.A. Kharitonov, S.V. Brovanov, E.Ya. Bukina, D.V. Makarov, 2016, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2016, No. 2, pp. 88–101.
_______________________________ SCIENCE OF MINING ____________________________ MACHINES
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Voltage Stabilization System for Power Installations in Mines B. F. Simonova*, S. A. Kharitonovb,c**, S. V. Brovanovc***, E. Ya. Bukinab, and D. V. Makarovc a
Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Krasnyi pr. 54, Novosibirsk, 630091 Russia *e-mail:
[email protected] b Novosibirsk State Technical University, pr. K. Marksa 20, Novosibirsk, 630073 Russia **e-mail:
[email protected] c National Research Tomsk Polytechnic University, pr. Lenina 30, Tomsk, 634050 Russia ***e-mail:
[email protected] Received October 15, 2015
Abstract—The authors analyze feasibility of voltage stabilization for permanent magnet synchronous generators in independent variable-frequency power networks. The method of voltage stabilization is based on series connection of the generator and a semiconductor converter generating wattless power. Basic energy characteristics of the semiconductor converter and synchronous generator are analytically defined, frequency constraints of the proposed method are found, and rational frequency range and overall power of the system are determined. Keywords: Synchronous generator, permanent magnets, variable frequency, voltage stabilization, semiconductor converter. DOI: 10.1134/S1062739116020465
INTRODUCTION
For power-consuming industries such as mineral mining and processing, this is a law that energy demand grows faster than gain in productivity. For instance, in USA electricity cost, by estimates, makes more than 15% of the total cost of production [1]. Mining companies pay increasingly more attention to energy saving using power electronics facilities and cost-beneficial methods of power generation, including smart grid concept based on integration of numerous sources of electric energy into an adaptable power pool system. Many companies are attempting to develop projects on diversification of renewable sources of energy such as wind power engineering and photovoltaics. Efforts are made to improve energy efficiency of conventional independent systems of power supply, in particular, diesel-generators with variable frequency electric generators, which considerably reduces fuel cost and makes the system more ecology-friendly [2, 3]. Innovation-inspired mining companies introduce power electronics devices in controlled-velocity electric drives of traction engines, which ensures optimized velocity range of diesel drives. Particular attention is given to gearless controlled electric drives. Energy-saving electric drives are used in USA, China, Canada and Australia, and Siemens VAI has designed low-velocity electric drives for disk mills and multibucket excavators, and is working on electric drives for pumps, conveyors and fridges. Much advertisement is given to replacement of power-operated throttles by semiconductor frequency converters [1]. The use of frequency converters allows considerable energy saving in machines that 313
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transport heavy loads and often enter braking mode. In this case, maintained regeneration regime greatly enhances energy efficiency. Electric companies state that with every electric drive brought to the newest process standards, the global annual energy saving will make round 130 billion kW/h. Introducing energy-efficient technologies of production and power generation, mining companies turn into power supplies and undertake local area electrification. With independent utility power using renewable sources of energy, e.g., wind-driven power plants or ecofriendly diesel-generators, it is required to convert mechanical energy of variable frequency shafts to electric energy [2–4]. This problem is handled with the help of different high-capacity electric generators, as a rule, synchronous generators, which requires sustainable supply of assigned quality electric energy and overall performance reliability [5–12]. Earlier it was necessary to ensure stable line frequency in such systems [13, 14]; this problem has lost urgency recently [15] as considerable portion of generated electric energy is converted using power electronic facilities. Moreover, many loads are uncritical relative to frequency (illumination, heating, etc.), while voltage stability is a stringent requirement as before. Variable frequency option is set by a number of standards in self-contained power supply systems. Efficiency of permanent magnet synchronous generators in such systems is known [7–12]. This article is aimed to study electromagnetic processes in a self-sustained variable–frequency three-phase AC generator with voltage stabilization by means of series actuation of semiconductor frequency converter in generation channel. Unlike the variant with parallel connection of semiconductor converter (SC) [5–12, 16], in this case, SC is designed for current to be not higher than load current and the output voltage of SC can be higher than the output voltage of the generation system. This solution reduces cost of SC in case that parameters of chosen triode transistors remain within the same class of voltage. In order to eliminate current overload of SC under short-circuit conditions, electrical bridging of outlet terminals of the converter are provided. Advantages of this variant is the absence of additional choking equipment for high-frequency SC current pulsation for their part is entrusted to reactances of synchronous generator (SG). The system is adaptable to a transformer (autoconnected transformer) in-between SC and SG, which allows wider range of the converter parameters. Figure 1 shows the structure chart of the described system where SC is a semiconductor frequency converter with the output voltage uVS of variable frequency, phase and value; SG is a magneto–electric synchronous generator with the output voltage uG of frequency varied with the change in the shaft speed n and load current i. Load is a consumer of electric energy, the terminal voltage is governed by the relation uL = uVS + uG , and the rms voltage u L is maintained by means of the conforming variation in the voltage uVS . The function of SC is executed using various conversion diagrams, though it is preferred to involve voltage invertors with high-frequency pulse–duration modulation (PDM). The quality of the generated voltage is high enough in this case, both under static and dynamic modes.
Fig. 1. Structure chart of a variable frequency generator. JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
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Fig. 2. Function chart of a power generation system.
Under consideration is a variant of stabilizing the output voltage u L by means of SC generation of the voltage uVS with its first harmonic to be orthogonal to the load current. This means that the converter generates variable value and sign wattless power. Voltages, currents and total powers of the generation system elements are estimated, and special index points in the system operation under the variation in the shaft speed are detected. Preferable working ranges are defined and evaluated, physical limits of voltage stabilization are determined, and shortcomings and benefits of this method of the synchronous generator voltage stabilization are discussed. A version of the function chart of such system is shown in Fig. 2. Here, VI is a voltage inverter with high-frequency PDM; TS is a thyristor switchboard for bridging of VI under short-circuit conditions in the load and under abnormal modes of VI; Cf are capacitor filters; CRD is a charging-and-rectifying device of low capacity to charge capacitors C and compensate resistive loss in VI; it is possible to reject CRD under relevant choice of parameters and modes of operation. 1. VOLTAGE STABILIZATION PRINCIPLES AND OPERATION MODES
The principle of voltage stabilization in the system with the series SC and variable frequency can be explained with a vector diagram of the first harmonics of current and voltages. For such generators are as a rule explicit-pole generators, the vector diagram appears as the arrow plot in Fig. 3 [9]. It is plotted under assumption that the resistive loss in SG is zero and PDM frequency is much higher than SG output voltage frequency. Here, X , in accordance with the electrotechnics notations, is a vector in the Cartesian coordinates d, q, varying under the harmonic law of a value x, with the length equal to the current value of x; I is a current value of the first harmonic of load current; r are active resistances of phase winding of the generator stator; Ld = Lσ + Lad , Lq = Lσ + Laq , I d , I q are inductances of the generator and the longitudinal and transverse projections of the current I; Lσ is a leakage inductance, Lad , Laq are principal inductances of the generator in lines of d and q; Ψ0 is a flux linkage created by permanent magnets; U VS , U L are current values of the first harmonics of SC and SG voltages. It follows from Fig. 3 that stabilization of the output voltage U L under the change in the current I or SG frequency is possible through the change in the value and sign of SC voltage always maintained orthogonal to the current. This stabilization technique is physically equivalent to the increase or decrease in the voltage drop on the leakage inductive reactance of SG. The next section is devoted to the change in the voltage of the system elements under the variation in the SG frequency, and the load current value and behavior given the load voltage is maintained equal to the nominal voltage U Lnom . JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
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Fig. 3. Vector diagram of (a) voltage and (b) current in the generation system.
2. MATHEMATICAL MODEL OF THE GENERATION SYSTEM
The mathematical model assumes that: under analysis is the static mode; the magnetic system of SG is unsaturated and linear; the load is symmetrical; SG has no damping circuits; the generator voltage changes according to the sinusoidal law, with the amplitude and frequency proportional to the rotation speed Ω; the resistive loss in the generator is low and neglectable; SC operates at PDM with the frequency much higher than the frequency of the generated voltage; SC rectifiers are “ideal”; the calculation is performed relative to the first harmonic. Considering the assumptions, the mathematical model of the system in the coordinates that rotate synchronously with SG rotor, given that the d-axis is oriented along the longitudinal axis of SG is given by [14, 17]: d u L = uVS + u G = uVS − − ωΨ , dt (1)
Ψ = Li − ωΨ0 , where Ψ = [Ψd Ψq ] , Ψd , Ψq are the flux linkages of the generator along the longitudinal and t
transverse axes; uVS = [UVSd U VSq ] t , u G = [U Gd U Gq ] t , i = [ I d I q ] t , u L = [U Ld U Lq ] t are the voltage vectors of SC, SG, current and load; Ψ0 = [Ψ0 0] t = const is the flux linkage created by permanent
magnets; L = diag{Ld Lq } ; ω = ⎡0 − ω ⎤ , ω is the circular frequency of the synchronous generator 0 ⎥⎦ ⎢⎣ω voltage. With the chosen variables as SG AC and considering that I d = I sin β , I q = I cos β according to
Fig. 3, Eq. (1) after simple transformations gives in the scalar form for the steady-state mode: π U Ld = ω Lq I cos β + U VS sin ⎛⎜ − β ⎞⎟ , ⎝2 ⎠
(2)
π U Lq = ω Ψ0 − ω Ld I sin β − UVS cos ⎛⎜ − β ⎞⎟ . ⎝2 ⎠ From (2) and Fig. 3a:
E0 = ω Ψ0 = U L cos(β − ϕ ) + UVS sin β + ωLd I sin β , JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
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where U L cos β
cos β =
(U L sin ϕ + ωLq I + U VS ) 2 + (U L cos ϕ ) 2 U L sin ϕ + ωLq I + U VS
sin β =
(U L sin ϕ + ω Lq I + U VS ) 2 + (U L cos ϕ ) 2
, (4) .
The relations (3) and (4) enable determination of the functional dependences U VS = f (ω , I , cos ϕ ) , U G = ξ (ω , I , cos ϕ ) to ensure that U L = U L nom at the pre-assigned Ld , Lq , Ψ0 , and calculation of the installed capacities of SC and SG. For the affinity of the results, we use the relative units denoted by an asterisk. The basic values are the nominal voltage, current and overall load capacity: U b = U L nom , I b = I nom , S b = 3U L nom I nom , and the circular frequency ω b = ω nom , at which U VS = 0 , U G = U L and the operating mode of the generation system is normal: I = I nom . Introduce the denotations: kL =
Lq , Ld
k sc =
I sc , I nom
E 0 nom = ω nom Ψ0 ,
where I sc is the estimated value of the short-circuit current; the coefficients k L and k sc characterize the difference in the magnetic resistances of SG along the longitudinal and transverse axes and the excess of the estimated short-circuit current of the nominal current in SG. The short-circuit current, given the accepted assumptions: Ψ I sc = 0 . Ld This relation helps calculating Ld at the pre-assigned flux linkage Ψ0 : Ψ Ψ0 . Ld = 0 = I sc k sc I nom
(5)
⎛ ω Ψ⎞ With the relative units and the expression (3–(5), we find off-load EMF ⎜⎜ E 0*nom = nom ⎟⎟ from U nom ⎠ ⎝ the transcendental equation:
E 0*nom =
⎛ E* E* 1 + (1 + k L ) 0 nom sin ϕ + k L ⎜⎜ 0 nom k sc ⎝ k sc
1+ 2
⎛E E k L sin ϕ + ⎜⎜ k sc ⎝ k sc * 0 nom
* 0 nom
2
⎞ ⎟⎟ ⎠ . 2 ⎞ k L ⎟⎟ ⎠
(6)
* With the known E 0*nom , from (3)–(6), we derive an equation to find relative value of the voltage U VS such that U = U nom for the pre-assigned load current I * and cos ϕ :
* 1 + (U VS )2 +
ω * E 0*nom =
ω * E 0*nom I * k sc
⎛ ω * E 0*nom I * ⎞ ω * E 0*nom I * * * * + U VS + sinϕ ⎟⎟ + + sin ϕ ) + 2U VS k L ⎜⎜ (U VS sin ϕ k k sc sc ⎠ ⎝ .(7)
⎛ * ⎛ * ω * E 0*nom I * ⎞ ω * E 0*nom I * ⎞ + + 1 + 2 ⎜⎜U VS k L ⎟⎟ sin ϕ + ⎜⎜U VS k L ⎟⎟ k sc k sc ⎝ ⎠ ⎝ ⎠
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Fig. 4. (a) Relative nominal off-load EMF of SG versus k sc and (b) relative voltage of the converter versus the frequency of SG EMF. * of SC and using the vector diagram in Fig. 3a, we calculate Having found the output voltage UVS
the relative value of SG voltage: * sin ϕ ) 2 + (U * cos ϕ ) 2 = 1 + 2U * sin ϕ + (U * ) 2 . U G* = (1 + U VS VS VS VS
(8)
The relative values of the overall capacities of SC, SG and the entire system of power * , S * and S * , respectively, are given by: generation, SVS G ∑ * = I *U * , SVS VS
SG* = I * U G* ,
* + S* . S ∑* = SVS G
(9)
Considering that SC generates and consumes no actual power, the power factor of the synchronous generator is:
χG =
3U L I cos ϕ cos ϕ = . 3U G I U G*
(10)
3. QUANTITATIVE ASSESSMENT OF THE CONVERTER AND GENERATOR VOLTAGES TO MAINTAIN OUTPUT VOLTAGE OF THE POWER GENERATION SYSTEM
When self-sustained power supply is designed, setting of nominal parameters is added with specification of overload conditions characterized by the current I max at which the terminal voltage of the generator is to equal the nominal voltage: I max = (1.5 ÷ 2) I nom . Besides, the short-circuit current I sc is set such that the ratio of the estimated short-circuit current and the nominal current is k sc = I sc / I nom = 2–4. Such an excess of I sc over I nom ensures selective shut-off of improper loads through the assistance of automatic breakers and cutout fuses. Figure 4 shows the curves of the nominal off-load EMF E 0*nom and the ratio k sc (Fig. 4a) and the * versus the relative frequency of SG EMF (Fig. 4b) calculated from (6) and (7) relative SC voltage UVS for two values of cos ϕ * given that U = U nom . * and the ratio k , which is the difference of the magnetic Figure 5 shows the curves of E 0*nom , U VS L resistances of SG along the transverse and longitudinal axes. It is seen that the influence of k L is * * at k = 1 and k ≠ 1 is not higher than the error insignificant, the difference between E 0nom and U VS L L * under the given method of due to accepted assumptions. So, assessment of the values E 0*nom and U VS voltage stabilization can be conducted at k L = 1 . The relations (6) and (7) are greatly simplified:
*Hereinafter, inductive load of the power generation system is assumed. JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
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* 0 nom
=
k sc sin ϕ + k sc2 cos 2 ϕ k sc2 − 1
* U VS = (ω * E 0*nom ) 2 − cos 2ϕ − sin ϕ −
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,
I *ω * E 0*nom . k sc
The latter relation is in principle a scaled law of change in the module of the voltage inverter-based SC pilot signal in the coordinates d, q. This law ensures stabilization of the output voltage of the power generation system under the change in SG frequency and in the value and nature of the load. Considering that E 0*nom = ω nom Ψ0 /U nom , and the relation (5), it follows from Fig. 4a that at the preassigned nominal parameters of load, the function E 0*nom (k sc ) correlates Ψ0 and Ld of the generator. The behavior of k sc – E 0*nom relation (Fig. 4a) is obvious: as it increases, a decrease takes place in the value of the required EMF E 0*nom for external characteristic of the generator becomes more “rigid;” as the inductive nature of the load becomes more intensive, the rotor response grows and it appears necessary to increase E 0*nom . * (ω *) in Fig. 4b are plotted at E * The curves U VS 0 nom = 1.31 for k sc = 3 , cos ϕ = 0.8 , k L = 1 . It is * seen that the maximum converter voltage U VS max depends on the idle pass load at the maximum * . The maximum converter voltage takes place for cos ϕ = 1 , I * = 0 and is working frequency ωmax
given by: 2 * * E* U VS (ω max max = 0 nom ) − 1 .
* = 0, and this point characterizes the moment of change in the sign of the SCAt ω * = ω0* , UVS * advances the load current (see Fig. 3a) and when generated wattless power. When ω * > ω0* U VS * . The frequency ω * is calculated from: ω * < ω0* the load current advances the voltage U VS 0
⎛ I* I* + 1 − ⎜⎜ cos ϕ sin ϕ k sc k sc ⎝ ω 0* = ⎡ ⎛ I * ⎞2 ⎤ ⎟⎟ ⎥ E 0*nom ⎢1 − ⎜⎜ ⎢⎣ ⎝ k sc ⎠ ⎥⎦
⎞ ⎟⎟ ⎠
2
.
Fig. 5. Influence of magnetic resistance of the generator along the transverse and longitudinal axes on (a) * at k = 3 . and (b) U VS sc
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Fig. 6. The plot of the frequency ω0* and the load current at k sc = 3 .
In the plot of the frequency ω0* and the load current in Fig. 6, under the off-load ω 0* = 1 / E 0*nom , the frequency ω0* quickly grows with the load current, especially at the low values of the load capacity coefficient, while it asymptotically tends to infinite in the mode of the short-circuit. * , the voltage U * is limited by the ultimate capacity of this When ω * < ω0* , at the certain ω * = ω min VS voltage stabilization method as is illustrated in Fig. 7. At this frequency, the generator EMF phase coincides with the load current phase; under further reduction in the frequency to maintain the equality U = U nom , it is required to increase EMF, which is infeasible. * The frequency ω * = ω min is given by: * = ωmin
cos ϕ , E0*ном
and the related SC voltage: ⎞ ⎛ I* * UVS sin ϕ + cos ϕ ⎟⎟ . min = − ⎜ ⎜ k sc ⎠ ⎝
Fig. 7. Vector diagram for the mode of the minimum possible frequency of SG.
* * * – k sc and (b) UVS Fig. 8. The curves (a) ωmin min – I .
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* * is illustrated in Fig. 8. As k * –k * The behavior of the curves ωmin sc and U VS min – I sc grows, ω min * * = cosϕ . The value of U VS is in the range asymptotically goes nearer ωmin min [0, − (sin ϕ max + cos ϕ max )] and in the range [0, ϕ max ] when the load current changes from zero to the short-circuit current and the angle ϕ . Figure 9a shows the curves of U G* , χ G and ω * calculated from the relations (8) and (10) for different I * and cos ϕ . With the reduction in ω * , the voltage of the generator lowers and this trend goes on until a certain ω * = ω g*0 at which the phase shaft between the load current and the generator
voltage is zero (see Fig. 10). At this point, SG power coefficient equals unit (Fig. 9a). With the further decrease in the frequency, the generator voltage grows as the equivalent load becomes capacitive. We find ω g*0 using the relation (8) and Fig. 10:
ω g*0 =
The change in ω g*0
cos ϕ 2
.
(12)
⎛ I* ⎞ ⎟⎟ E 0*nom 1 − ⎜⎜ ⎝ k sc ⎠ as function of the load current at varied cos ϕ is illustrated in Fig. 11. When
* I * = 0 , ω g*0 = ωmin as follows from the relations (11) and (12); with the higher load current, ω g*0 grows
quickly and tends to infinity under the short-circuit regime. The curves of the relative value of the overall capacities of the semiconductor converter and synchronous generator at different currents and cos ϕ are demonstrated in Fig. 12. The behavior of these curves depends much on the features of the voltage variation and allows judging on the rated capacities of SG and SC based on the maximum values within the working range of the frequencies Δω w* . The range of Δω w* is found as:
Δω w* = ω w* max − ω w* min , where ω w* max , ω w* min are the maximum and minimum frequencies of the power generation system.
Fig. 9. (a) Relative voltage and (b) power coefficient of SG versus frequency ω * at k sc = 3 .
Fig. 10. Vector diagram to conform with the regime of ω * = ω g*0 . JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
Fig. 11. Frequency ω g*0 versus load current at k sc = 3 .
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Fig. 12. Relative overall capacities of (a) SC and (b) SG versus frequency ω * at k sc = 3 .
Fig. 13. Relative overall capacity of the power generation system versus frequency ω * in choosing the working range [ω w* min , ω w* max ] at k sc = 3 .
The values of ω w* max and ω w* min are chosen using the relationships between the overall capacity
S ∑* and ω * of the power generation system plotted in Fig. 13 for different I * and cos ϕ . We choose Δω w* = 2 as the most common working frequency range and assume that the load capacity coefficient is within the most potential range cos ϕ = 0.8 ÷ 1 . In addition it is assumed that the power generation system has three-phase short-circuit current ( k sc = 3 ) and ensures double overload relative to the nominal current ( I * = 2 ) at all possible cos ϕ . For the pre-set conditions, ω w* max = 1.578 , ω w* min = 0.789 . This is feasible given that S ∑* = 3.038 . As a rule, the latter is called the rated capacity of a system. Under the pre-assigned conditions, the rated capacity of the system is higher than the maximum load capacity γ ∑ = S ∑ / S L max = S ∑* / 2 = 1.519 times. Figure 14 shows the relationship between the overall capacities of the system and its elements as against the frequency ω * at two values of the load capacity coefficient: cos ϕ = 0.8 and cos ϕ = 1 , and the found capacities of SG and SC for the minimum and maximum working frequencies. The selection * = 1.271 , from the two maximum possible rated capacities for the two elements of the system yields: SVS
S G* = 2.177 . Accordingly, the rated capacities of SC and SG are related with the maximum load capacity as: S S* S S* γ VS = VS = VS = 0.635 , γ G = G = G = 1.089 . 2 2 S L max S L max The values of γ VS , γ G and γ ∑ are useful in comparing different systems and methods of SG voltage stabilization. Within the chosen range of the working frequencies, the voltages of SC and SG vary as * = 0 ÷ 1.74 , U * = 1 ÷ 2 . follows: U VS G JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
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Fig. 14. Curves of the relative overall capacities of (a) SC and (b) SG and the frequency ω * at k sc = 3 and
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cos ϕ = 1 .
So, the output voltage is stabilized within the frequency range equal to 2. As follows from Figs. 13 and 14, the wider working range may increase the rated capacities of the semiconductor converter and synchronous generator. At the same time, keeping within the same class of voltages and models of semiconductor devices will cause no essential growth in the weight and cost of the system, which is an advantage of this approach to voltage stabilization. A disbenefit is the requirement to bring out the start and end of phase windings of the generator, which makes a connector box and, accordingly, the generator as a whole bigger. CONCLUSIONS
It has been found possible to stabilize the output voltage of the permanent-magnet variedfrequency synchronous generators within self-sustained power supply systems by the series connection of a semiconductor converter to generate wattless power. The defined constraints of the said stabilization method relative to the minimum shaft frequency are conditioned by the physics of the stabilization process by means of adjustment of the wattless power using the semiconductor converter. For example, under conditions of short-circuit current 3 times higher than the nominal current, the minimum possible frequency for the stabilized voltage is not to be less than 0.6 of the nominal frequency. The derived analytical expression for the voltages, current and capacities of the semiconductor converter and synchronous generator enable, by the preset range of the variation in the output voltage, by the value of current in the modes of load and short-circuit and by the load behavior and value, choosing the electric parameters of the synchronous generator and the semiconductor converter, e.g. off-load EMF and inductance along the longitudinal and transverse axes of the generator, maximum output voltage and current of the converter as well as the law of control over the converter current to ensure stabilized output voltage in the system subjected to the variation in the SG shaft rotation and the current behavior and value. For the range of the SG shaft frequencies equal to 2, the ultimate frequencies and minimized rated capacities of the synchronous generator and semiconductor converter are defined. When the load is twice the nominal regime, the ratios of the rated capacities of the semiconductor converter and the synchronous generator to the maximum load capacity will make 0.635 and 1.089, respectively. The research findings are applicable to selecting generators for independent power supply systems in coal and metal mines. ACKNOWLEDGMENTS
The study was supported by the RF Ministry of Education and Science, in the framework of the federal targeted program on R&D in Priority Areas of Advancement in the Russian Science and Technology in 2014–2020, grant agreement no. 14.577.21.0198, ID no. RFMEFI57715X0198. JOURNAL OF MINING SCIENCE Vol. 52 No. 2 2016
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