Keywords

1 Introduction

When designing ship’s unified electric power systems (EPS) with an 50 (60) Hz AC voltage power frequency grid as autonomous power sources on large-tonnage vessels with an atomic power plant turbo-generators (TG) with a rotational speed of 314 rad-1 (3,000 rpm) are usually used [1, 2]. Considering that steam turbines, the operating speed of which is within the range of 628-942 rad-1 (6,000–9,000 rpm), are used as primary engines for turbo-generators, an intermediate reduction gearbox is usually installed on the output shaft of the turbine [2].

2 Block Diagram of Turbogenerator

In order to exclude the intermediate reduction gearbox, it is proposed to use TG with increased rotational speed and special converting devices for power supply of the 50 (60) Hz industrial frequency of ship’s general services in [3].

This article deals with the operation principle and the technical results of the investigation of a mechatronic system (MTS) consisting of a turbo-generator of two different frequencies, rotating directly from the turbine shaft at a frequency of 6,000 rpm c/w an invertible matrix frequency converter (MFC) in circuit with a three-phase TG Rotor winding.

The turbo-generator M1 of two different frequencies - an increased frequency of 200 Hz and an industrial frequency of 50 Hz - contains a stator M1.1 with a cylindrical bore and an implicitly rotor located inside the stator boring and consisting of two parts: the main M1.2 and the additional M1.4 (Fig. 1).

Fig. 1.
figure 1

Flow chart of the mechatronic system in the turbo-generator with three-phase currents of two different frequencies c/w a reversible MFC: U1… U3 - cabinets A, B, C – phases of the power section; U1.1, U1.2 - cascades of three-phase bridges (matrices) of a single phase A; U1.3, U1.4 - blocks of optical converters of a fiber-optic communication line; U4 - microprocessor control system cabinet (MPCS); TV1… TV3 - power transformers; U5, U6 - voltage sensors; U7 - phase current sensors; KM1, KM2 - vacuum contactors; M1 - turbo-generator with brushless excitation device M1.3 and with three-phase winding of the rotor M1.4.

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The internal surface of the stator bore includes two combined three-phase windings located in the grooves - the main and additional windings - with the number of pairs of poles p1 and p2, respectively.

The outer surface of the main part M1.2 of the rotor includes a distributed DC excitation winding with the number of pole pairs p1 placed in the slots, connected to the output of the brushless excitation device M1.3.

The outer surface of the additional part M1.4 of the rotor includes a three-phase alternating current winding with a number of pairs of poles p2 placed in the slots, connected through contact rings and electric brushes to the three-phase output of reversible MFC [4].

In order to avoid mutual influence on the main harmonics of the magnetic field of both windings located both on the stator and on the rotor, their pairs of poles must correspond to the condition \( {\text{p}}_{1} \,{ > }\,{\text{p}}_{2} \) [5, 6].

The TG under consideration functions as follows.

Preliminary the TG shaft (Fig. 1) is rotated by means of turbine T with rotation frequency \( \omega_{1} = \frac{{60\varvec{ f}_{{1\varvec{ }}} }}{{\varvec{p}_{1} }} = \) 628 rad/s (6,000 rpm), where p 1 is the number of pole pairs of the DC excitation winding.

As a result of the interaction of the magnetic field of the rotating DC excitation winding with the main winding of the stator, there is a three-phase voltage of high frequency f 1 = ω 1 p 1/60 = 200 Hz (at p 1 = 2), which via matching transformers TV1… TV3 and vacuum switches KM1; KM2 comes on the input of the reversible MFC.

The variable three-phase voltage of high frequency f 1 is converted in MFC into a three-phase voltage of frequency f 2 . Then this voltage with a smooth increase in its amplitude and frequency from zero to the nominal value f 2n comes through electric brushes and contact rings onto the three-phase winding of the rotor. The angular frequency of rotation ω 2  = 2πf 2 /p 2 of the main magnetizing force (m.f.) of the winding should be directed into the opposite direction of the rotational angular frequency of the rotor ω 1 = 2πf 1 /p 1 [4].

Main wave of m.f. of the three-phase winding of the M1.3 rotor provides the generation of a three-phase voltage with a negative slip frequency equal to the industrial frequency f s \( = \frac{{\omega_{2} - \omega_{1} }}{2\pi } \) = −50 Hz in the additional winding of the stator M1.1. This mode occurs when the TG is started at the moment of exceeding the amplitude (E1) of the electromotive force (e.m.f.) in the three-phase winding of the rotor relative to the amplitude of the voltage coming through the electric brushes and contact rings from the MFC.

Under the effect of the said e.m.f. the electric power of three-phase currents through contact rings and electric brushes comes on the output terminals A, B, C of reversible MFC (Fig. 1). After the reverse conversion to a three-phase current with a frequency f 1 = 200 Hz, through the switches KM1, KM2 and the converting transformers TV1… TV3, the indicated electric power enters the external high frequency network f 1 = 200 Hz.

Electricity generated by both stator windings M1.1 (primary and secondary) in the form of three-phase currents of two different frequencies f1; fs after their synchronization is transmitted through the switches KM3, KM4 to the external power supply with the corresponding frequency.

The reversible cascaded MFC (Fig. 1) includes a three-phase power part U1… U3 with parallel connected cascades and a microprocessor control system (MPCS) U4.

Figure 2 shows the electrical circuit of a single MPCS cascade, built on fully controllable IGBT-modules with two-way conductivity, which are connected in the form of a matrix according to the scheme of a three-phase bridge.

Fig. 2.
figure 2

The scheme of a three-phase bridge of one cascade (matrix) MFC. U sa , U sb , Usc - voltage of the phases of the power source (network); TV1 - power transformer; e 2ta , e 2tb , e 2tc – e.m.f. of the secondary winding of the transformer; L ta , L tb , L tc , R ta , R tb , R tc - the parameters of the transformer; U ta , U tb , U tc , i 2ta , i 2tb ,i 2tc - the voltages and currents of the secondary winding of the transformer; VM1… VM6 - keys of IGBT-modules with two-way conductivity; A1… A6 – IGBT- modules drivers; C1… C6 - snubber capacitors; U dm , i dm - voltage and current at the output of a three-phase bridge; e dm , L d , R d - load parameters.

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3 Time Diagram of Control Signals of Sinusoidal PWM

The program of the MPCS, implementing a predetermined algorithm of control signals for switching the keys in three-phase bridges of each cascade, alternately implements the frequency of the pulse width modulation (PWM) modes of either active rectification or inverting. The control angle α at the power frequency of 200 Hz is α = 0, and the interval of the allowed open state of the keys in the bridge arms is equal to (120° + γ) electric, where γ is the angle of the joint open state of two adjacent bridge arms [7].

In the program form both modes are implemented by the PWM enable functions J i , where i = 1, 2, … 6 are the serial numbers of the bridge arms, the switching points of which are synchronized in phase with the e.m.f. (e 2ta , e 2tb , e 2tc ) (Fig. 2) of the secondary windings of the transformer TV1.

When the sinusoidal PWM signals K i and Ǩ i  ± 3 coincide with the PWM J i resolution functions, control signals are generated for switching the keys in the arms of the three-phase bridges of each cascade, thereby generating positive and negative half-waves of voltages on their outputs (Fig. 3).

Fig. 3.
figure 3

Time diagrams of sinusoidal PWM control signals and calculated curves of phase currents (i dA , i dB , i dC ) and voltages (U dA , U dB , U dC ) at the outputs of each bridge in each phase of MFC at a frequency of 60 Hz.

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According to the time diagrams (Fig. 3), the currents at the output of each stage are summed, providing the necessary values of the three-phase currents at the output terminals of the MFC.

4 Calculation of Power of MFC and Harmonic Components

The positive technical result of the MTS under consideration consists in reducing the total power of the reversible MFC, which is determined by calculating the total power (P 2 ) of the three-phase winding of the TG rotor.

The calculated total power P 2 of the three-phase winding of the rotor in the generator operating mode of the TG with the negative slip frequency f s  = −50 Hz at the angular rotational speed of the rotor of ω 1  = 628 rad −1 (6,000 rpm) and the total power of the reversible MFC, equal to it, are determined by the Formula [8]:

The discrete signals of sinusoidal PWM with adjustable curvature K i и Ǩ i  ± 3 = 1− K i (straight and inverse), where i = 1, 2, … 6 - the ordinal numbers of the bridge arms correspond to the work of each three-phase bridge in the regime of active rectification, or inverting.

$$ P_{2} = sP_{add} \cong - 0.5P_{add} 100\% \cong - 50\% P_{add} $$
(1)

Where: P add is the calculated total power of the additional winding of the stator TG for power supply of the 50 Hz industrial power frequency; \( s = \frac{{\omega_{2} - \omega_{1} }}{{\omega_{1} }} \) = −0.5 - motor slip in relative units (the minus sign denotes the generator mode of the stator winding TG).

The technical result of improving the quality of electric power in the 50 Hz power grid consists in reducing the total factor of the harmonic components k gs , which can be determined from the results of the calculation of the amplitudes Eν of the harmonic components of the phase e.m.f. of the additional winding of the stator TG according to the formulas [8]:

$$ k_{gs} = \frac{{\sqrt {\sum\nolimits_{5}^{\nu } {E_{\nu }^{2} } } }}{{E_{1} }}; \to \,\,E{}_{\nu } = 4.44\;f_{\nu } w_{1} k_{1wind.\nu } k_{c\nu } \phi_{\nu } $$
(2)

Where: \( \phi_{v} \) is a magnetic flux of the v th space harmonic in the air gap of one phase of the three-phase winding of the rotor;

w 1 - the total number of turns in the phase of the stator winding;

k 1 wind.ν - Winding coefficient of the v th stator winding e.m.f. harmonic;

k c.ν  = \( \frac{{2sinv\frac{{\pi \cdot b_{z} }}{2\tau }}}{{\pi \cdot v\frac{{b_{z} }}{\tau }}} \) - the coefficient of the bevel of the grooves; b z - width of the stator slot.

Magnetic flux \( \varPhi_{v} \), due to the magnetizing force (m.f.) \( F_{\phi v} \) from the currents in the three-phase winding of the rotor, is determined by the formulas [8]:

$$ \left. {\begin{array}{*{20}c} {\phi_{\nu } = \frac{{2\mu_{0} F_{\phi \nu } \tau l_{\delta } }}{{\pi \delta k_{\delta } k_{\mu } }}} \\ {F_{\phi \nu } = \frac{{2\sqrt 2 w_{2} }}{{\pi \nu p_{1} }}k_{2wind.\nu } I{}_{a}} \\ \end{array} } \right\} $$
(3)

Where: τ - the pole division; l δ - the active length of the rotor package;

k 2 wind.ν - Winding coefficient of the v th harmonic of the m.f. of rotor winding;

w 2 – the total number of turns in one phase of the rotor winding;

δ - Air gap; k δ is the air gap coefficient;

k μ - Coefficient, taking into account the saturation of the magnetic circuit of the rotor;

ν is the order of the spectrum (1, 5, 7, etc.) of spatial harmonics from the m.f.;

I a is the amplitude of the phase current in the rotor winding.

The winding coefficients k 1 wind.ν , k 2 wind.ν, respectively, for the additional three-phase winding of the stator and for the three-phase winding on the additional part of the rotor are determined by the multiplication of the two components [8]:

$$ \left. {\begin{array}{*{20}c} {k_{1wind.\nu } = k_{y.\nu } k_{p.\nu } } \\ {k_{2wind.\nu } = k_{y.\nu } k_{p.\nu } } \\ \end{array} } \right\} $$
(4)

Where: k y.ν  = \( sinv\beta \frac{\pi }{2} \) is the coefficient of shortening of the y step at the winding of the rotor (stator);

k p.ν  = \( \frac{{sin\frac{\pi }{2m}}}{{q \cdot sinv\frac{\pi }{2mq}}} \) - the distribution coefficient of the winding in the grooves;

q = z/2p 1 ·m is the number of z slots per pole and phase;

m is the number of phases of the winding;

y - Winding step (coil turns, coil group) in the slots;

β = y/τ - the relative step of the rotor (stator) winding.

It is commonly known that [8] the amplitudes of the odd harmonic components of the phase e.m.f. E ν can be significantly reduced by either distributing the coil winding groups by the slots at q > 1, or by shortening the winding pitch, for example, by 1/6 or 1/12 of the step.

According to (2) and (3), the amplitudes of the odd harmonic components of the phase e.m.f. of stator windings are determined under otherwise equal condition by a multiplication of winding coefficients k 1wind.ν· k 2wind.ν of stator and rotor windings.

Table 1 shows the results of calculations of distribution and shortening parameters of the step of three-phase stator and rotor windings and winding coefficients for odd harmonic components of the phase e.m.f. at q = 4 and shortening of the step in the stator winding by 1/6 (β 1  = 5/6) and at q = 3 and shortening of the step in the rotor winding by 1/12 (β 2  = 11/12).

Table 1 Table 1.
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Taking into account (2)–(4) and the data of Table 1, the total coefficient of harmonic components of the curve phase e.m.f. of the additional stator winding is:

$$ k_{U} = \frac{{\sqrt {\sum\nolimits_{5}^{\nu } {k_{wind.\nu }^{2} } } }}{{k_{1wind.1} .k_{2wind.1} }} = \frac{{\sqrt {2.83585} }}{0.88}10^{ - 2} = \frac{1.4624}{0.88} \cong 1.7\% $$
(5)

5 Conclusion

The proposed technical solution of the mechatronic system with a turbo-generator (TG) of electric power with two different frequencies at a rotor speed of 628 rad −1 (6,000 rpm) equal to the turbine rotation frequency, complete with a matrix frequency converter (MFC) included into the three-phase winding of an additional part of the TG rotor, provides the following technical results:

  • Exclusion of the intermediate reduction gear in the turbine;

  • Significant reduction (~by 50%) of the estimated total capacity of the necessary transforming devices (reversible MFC);

  • Improvement of the electric power quality (total harmonic component factor k gs  <3%) in the electric power network with the industrial frequency of 50 Hz.