COMPARISON OF THE MOTOR-GENERATOR AND CAPACITOR VERSIONS OF THE POWER SUPPLY SYSTEM FOR THE ELECTROMAGNET OF THE 1.5 GeV TPI SYNCHROTRON

I. P. Chuchalin

(Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)

For a given reactive energy \(Q_{\mathrm{in}} = 880 \cdot 10^3\) J, a pulsed operating mode with a cycle repetition frequency of 1–2 Hz and a current-pulse duration in the electromagnet windings \(\tau = 0.084\) sec, practically the most suitable are two methods of pulsed power supply for the electromagnet of the 1.5 GeV TPI synchrotron:

1) from a capacitor bank (electrical storage of energy);
2) from a rotating generator with a large rotor moment of inertia or an additional flywheel (mechanical storage of energy).

Let us briefly consider and compare each of the indicated methods of pulsed power supply for the electromagnet. In comparing the cost of the electromagnet power supply systems, we shall assume that, in the case of supply from a capacitor bank, the cost of the power supply system will be determined mainly by the cost of the capacitors; in the case of machine supply, by the cost of the generator. The cost of the switching apparatus in all cases will be approximately the same, and therefore will not be taken into account in the comparison.

1. Power supply of the electromagnet from capacitor banks

Usually a capacitor bank is charged from a rectifier and, at specified instants of time, is discharged through switching devices into the electromagnet windings, producing a current pulse in them. The number of capacitors in the bank is determined by the reactive energy stored in them,

\[ Q = \frac{C U_m^2}{2}, \]

where \(C\) is the capacitance of the capacitor bank;
\(U_m\) is the maximum value of the voltage on the capacitors.

With pulsed power supply of the electromagnet, the dimensions of capacitor banks can be significantly reduced in comparison with the dimensions of capacitor banks under continuous power supply. Table 1 gives the data for several capacitors manufactured by our industry [1]. The specific energy serves as an indicator of the dimensions of a capacitor bank intended for storing one and the same amount of reactive energy for different types of capacitors. It is evident from Table 1 that the specific energies of capacitors of the IM 3-100 and IM5-140 types,

Table 1

Note: * — wholesale price per kvar;
** — wholesale price per piece.

which can be used in pulsed power-supply circuits, are respectively 29 and 48 J/dm\(^3\), while the specific energies of KM-type capacitors, which are usually used in continuous power-supply circuits, are 0.8–2.5 J/dm\(^3\). From a comparison of these two types of capacitors it is clear that, in pulsed operation, a capacitor bank may have dimensions 12–60 times smaller than with continuous power supply.

When IM 3-100 capacitors are used in the power-supply circuit of the electromagnet of the 1.5 GeV TPI synchrotron, their total number must be

\[ N=\frac{Q_m}{Q_1}=\frac{880\cdot 10^3}{450}=1960\ \text{units}, \]

where \(Q_1=450\) J is the energy stored in one IM 3-100 capacitor. The cost of the capacitor bank in this case will be:

\[ C_{\mathrm{bk}}=C_1N=40\cdot 1960\approx 80\ \text{thousand rubles}. \]

2. Power supply of the electromagnet from a rotating generator

Two types of power supply of the accelerator electromagnet from a rotating generator are possible:

a) connecting the generator directly to the electromagnet;
b) using the generator with a rectifier-inverter. Let us consider these variants separately.

a. Connecting the generator directly to the electromagnet

Before beginning to consider possible variants of supplying the electromagnet from rotating electrical machines, we note that we shall consider the possibility of using standard electrical generators manufactured by industry. For the creation of powerful pulsed magnetic fields, impact generators can be used. But since impact generators are not at present produced in series by industry—they are only being developed and studied in scientific laboratories [2–7, etc.]—there is no possibility for their economic comparison with standard electrical machines.

When the generator is connected directly to the electromagnet, it is more expedient to use an alternating-current generator (usually single-phase) than a direct-current generator, since operation with the latter gives rise to additional difficulties associated with the presence of a commutator [8, 9]. In addition, for the same power, alternating-current generators are cheaper than direct-current generators, have smaller dimensions, and make it easier to switch the current after the accelerating cycle has ended and the magnetic field is falling.

The electromagnet must be switched on as the voltage passes through zero. After the electromagnet is switched on, the energy stored in the rotating masses of the generator flows into the electromagnet, and the rotational speed of the generator decreases. From the moment when the voltage changes sign, the current flows in the same direction; the energy stored in the electromagnet, except for losses, is returned to the generator, and the speed of the latter increases. The electromagnet is disconnected as the current passes through zero.

The power drawn from the generator is used to cover only active energy losses. The power of the drive motor is determined by the active power losses in the accelerator electromagnet and in the generator. The reactive energy entering the electromagnet from the generator is determined as

\[ Q=\frac{1}{2}J\left(\omega_{\max}^{2}-\omega_{\min}^{2}\right), \tag{1} \]

where \(J=\dfrac{1}{4}GD^2\) is the moment of inertia of the rotor,

\(GD^2\) is the flywheel moment;

\(\omega\) is the angular velocity of rotation of the rotor.

It is seen from formula (1) that it is advantageous to use a generator with a weighted rotor (with an additional flywheel), and especially with a high speed of its rotation. A very large change in the rotor rotation speed causes large mechanical oscillations of the unit. A reduction of the speed by some fraction, usually no more than 10%, is permissible.

The possibilities of obtaining reactive energy from the electrical machine are determined by the technical possibilities of creating a rotor with a large flywheel moment and a high rotation speed. From the generator, a pulse power can be obtained that exceeds the corresponding rated power of continuous operation by as many times as the pulse current can be increased in comparison with the corresponding rated current of continuous operation.

In ordinary generators the permissible overload is determined by the heating conditions and the mechanical strength of the generator. The commutated power \(P_k=I_mU_m\) is related to the energy by the relations [10]:

\[ P_k=\frac{2\pi}{\tau}Q, \tag{2} \]

for a sinusoidal current pulse,

\[ P_k=\frac{4}{\tau}Q, \tag{3} \]

for a triangular current pulse;

where \(\tau\) is the duration of the current pulse.

When the generator is connected directly to the electromagnet, the greatest pulse duration is obtained with the smallest number of generator poles (two) and depends on the number of revolutions

\[ \tau=\frac{\pi}{\omega}. \]

The desire to increase the duration of the current pulse in order to reduce the commutated power leads to a reduction in the number of generator revolutions. A reduction in the number of revolutions, however, proportionally reduces the power of the generator. Thus, in order to obtain wide current pulses, powerful generators are required. This is the disadvantage of direct connection of the generator to the electromagnet.

Let us calculate what generator is required when it is connected directly to the electromagnet of a 1.5 GeV synchrotron. With a sinusoidal current-pulse shape, the commutated power will be equal to

\[ P_k=\frac{2\pi}{\tau}Q=\frac{2\pi}{0.084}\cdot 880\cdot 10^3=66\ \text{MVA}. \]

From the heating conditions, the rated current of the generator in continuous operation must be equal to the effective current in pulsed operation:

\[ I_n=I_{\mathrm{eff}}, \]

where

\[ I_n=\frac{P_n}{U_n} \]

is the rated current in continuous operation,

\[ I_{\mathrm{eff}}=\frac{I_m}{2}\sqrt{\frac{2\tau}{T}} \]

is the effective current in pulsed operation;

\(T\) is the period between the beginnings of cycles.

When selecting the generator it is necessary to take into account that, in order to obtain a current pulse with the specified duration, the rotor rotation speed must be reduced by

\[ n = 2 f \tau \ \text{times}, \tag{5} \]

where \(f\) is the nominal frequency of the generator voltage.

When the number of revolutions of the rotor is reduced, the generator voltage will correspondingly decrease:

\[ U_{\mathrm{g}} = U_{\mathrm{m}} = \frac{\sqrt{2}\,U_{\mathrm{n}}}{n} = \frac{U_{\mathrm{n}}}{\sqrt{2}\,f\tau}. \tag{6} \]

Solving (2), (4), and (6) simultaneously, we obtain

\[ P_{\mathrm{n}} = P_{\mathrm{k}} f\tau \sqrt{\frac{\tau}{T}} . \tag{7} \]

Substituting the corresponding numerical values, we find the required power of a single-phase generator:

\[ P_{\mathrm{n0}} = 66 \cdot 10^{6} \cdot 50 \cdot 0.084 \sqrt{\frac{0.084}{0.5}} = 110\ \text{MW}. \]

Our industry does not manufacture single-phase synchronous generators of such a power. It is therefore necessary to choose a three-phase synchronous generator. Since only two phases of the three-phase synchronous generator will be used, the generator power must be

\[ P_{\mathrm{nt}} = \sqrt{3}\,P_{\mathrm{n0}} = \sqrt{3}\cdot 110 \cdot 10^{6} = 190\ \text{MW}. \]

The cost of a TVV-200-2 turbogenerator with a power of 200 MW, with a VGT-2700-500 exciter and a gas cooler, is 518 thousand rubles [11], i.e., 6.5 times the cost of the capacitor bank.

6. Powering the Electromagnet from a Rotating Generator with a Rectifier-Inverter

In this version of the electromagnet power-supply circuit, alternating-current generators are usually used; at a certain instant of time, through ionic converters, they are connected into the circuit of the magnetizing winding. Here a large number of generator half-waves is used, and not just one, as in direct connection of the generator to the magnet. The switching devices on the leading edge of the current pulse are unlocked only during positive half-waves of the voltage, and on the falling edge of the current pulse, during negative half-waves of the voltage.

In the rectifier mode (the leading edge of the current pulse), energy is supplied from the generator to the electromagnet, and the generator speed decreases. In the inverter mode (the falling edge of the current pulse), the energy stored in the electromagnet winding is returned to the machine, which at that instant operates as a motor. The speed of the machine increases, and the energy is again accumulated for the next cycle.

For a triangular current pulse, the switched power is equal to

\[ P_{\mathrm{k}} = \frac{4}{\tau} Q = \frac{4}{0.084}\cdot 880 \cdot 10^{3} = 42\ \text{MVA}. \]

In accelerators whose electromagnets are supplied from motor-generators with a rectifier-inverter, the nominal power of the generators is taken to be approximately equal to the maximum switched power (see Table 2). If, for the synchrotron under consideration, the generator is also chosen on the basis of this condition, then its power should be 40–50 MW. The cost of synchronous generators, in particular TGV-30 turbogenerators with a power of 30 MW and TV-60-2 units with a power of 60 MW, is respectively 132.0 and 209.0 thousand rubles [11].

Table 2

If, for supplying the electromagnet of the 1.5 GeV TPI synchrotron, the TVS-30 turbogenerator is even selected, then the cost of the power-supply circuit will be no less than 132.0 thousand rubles, i.e., 1.7 times higher than the cost of the capacitor version of the electromagnet supply.

Table 3 gives the technical data and cost data for several turbogenerators manufactured by our industry [11].

Table 3

Figure 1 shows the dependences of the cost of storing 1 J of energy in electric machines with a rectifier-inverter and in a capacitor bank on the magnitude of the stored energy. In the calculations, the maximum commutated power was taken to be equal to the rated power of the generators \((P_k=P_n)\). The amount of energy stored in the generator for a triangular current pulse in the load was determined by the formula \(Q=\frac{\tau P_n}{4}\). The cost of 1 J stored in the turbogenerator was determined as

\[ C_{1\,\mathrm{J}}=\frac{C_{\mathrm{tg}}}{Q}, \]

where \(C_{\mathrm{tg}}\) is the cost of the turbogenerator.

The dependences of the cost of 1 J of energy stored in electric machines in Fig. 1 are presented for three values of the duration

Fig. 1. Dependences of the cost of storing 1 J of energy in electrical machines with a rectifier-inverter (1--3) and in a capacitor bank (4) on the amount of stored energy.

current pulse in the electromagnet windings: 0.01, 0.1, and 1.0 sec. The durations of current pulses in accelerator electromagnets vary approximately within this range.

The cost of the energy stored in capacitors does not depend on the magnitude of the energy or on the duration of the current pulses in the electromagnet. In the calculations we used IM 3-100 pulse capacitors as a reference; each of them can store an energy of 450 J. With the price of an IM 3-100 capacitor equal to 40 rubles [1], the cost of 1 J stored in such capacitors is \(C_{1\text{J}} = 0.089\) rub/J.

It is seen from Fig. 1 that, from the economic point of view, the electric-machine version of the power supply for accelerator electromagnets proves advantageous at large values of the energy stored in the magnetic field of the accelerators (above \(10^7\) J at \(\tau = 0.1\) sec and above \(10^5\) J at \(\tau = 1\) sec).

In addition to the cost of the equipment, when choosing a variant of the electromagnet power-supply circuit it is also necessary to take into account other factors, namely the operating conditions of the power-supply system as a reliable power installation, and especially the conditions for acceleration of charged particles.

Accelerator power-supply circuits must create a magnetic field that periodically increases from zero to the maximum value and repeats from cycle to cycle with the specified accuracy and stability. In the magnetic field of an accelerator, undesired time harmonic components close to the frequency of the synchrotron oscillations of the accelerated particles, and spatial harmonic components of azimuthal field asymmetry close to the frequency of the betatron oscillations of the particles, are undesirable. The electromagnet power-supply circuit of an accelerator is usually required to provide the possibility of reducing and regulating the rate of rise of the magnetic field.

field during the injection of particles into the accelerator chamber. This is necessary both for reducing distortions of the magnetic field due to the influence of eddy currents and for selecting the optimum conditions for particle capture into acceleration.

The operation of the power-supply system of the electromagnet of a high-power accelerator is usually accompanied by the periodic accumulation and expenditure of electrical energy, the magnitude of which is substantially greater than the irreversible energy losses. Therefore, in designing power-supply systems for high-power accelerators, provision is made for energy recovery and for eliminating the loading of the supply power system by reactive power.

When choosing one or another version of the electromagnet power-supply system, the operating conditions of the power-supply system must also be taken into account. With the motor-generator version of the power supply, it is necessary to take into account the considerable cost of machine halls with powerful foundations for the machines, the need to use crane equipment, the vibration of foundations and the building, and the required higher qualifications of the maintenance personnel.

The requirements indicated above are most simply satisfied by accelerator electromagnet power-supply systems using capacitor banks.

All cyclic electron accelerators, in whose electromagnets a comparatively small reactive energy is stored in comparison with proton accelerators and which operate with short durations of electromagnet current, use capacitor banks as energy-storage devices.

For the 1.5 GeV TPI synchrotron, power supply of the electromagnet from a capacitor bank has likewise been adopted.

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