Cascade frequency converters control features

The structures of systems with high-voltage cascade frequency converters containing multi-winding transformers and low-voltage low-power converters connected in series at each output phase of the load are considered. Lowvoltage blocks contain three-phase diode or active rectifiers, DC capacitor filters, single-phase stand-alone voltage inverters and block disconnecting devices in partial modes (in case of failure when part of the blocks are disconnected). The possibilities of operation of cascade converters are determined, equations for correcting tasks to units in partial modes are given, tables of correction of tasks with estimates of achievable load characteristics are proposed. The results of experiments on the model of a powerful installation with a cascade frequency converter are presented, confirming the possibility of ensuring the symmetry of the load currents when disconnecting part of the blocks and the asymmetry of the circuit.

If energy recovery of the motors through the CFC is not required to the supply network, then diode rectifiers are used in low-voltage TBC. To reduce distortion of currents and network voltages, a multi-winding transformer is used, in which the secondary windings are mutually shifted in phase. The drive circuit with a 10-winding transformer and a converter with nine low-voltage TBCs with diode rectifiers is shown in Fig.1.
In the circuit (Fig.1) in the phases of the power supply circuit of an induction motor (IM) three TBCs are connected in series. The mutual phase shift of the triples of the transformer secondary windings is performed at angles that are multiples of π/N, where N is the number of TBC in the CFC. In the circuit, every three secondary windings of the transformer coincide in phase, and these three windings are made with phase shifts relative to the network voltage by angles of -20, 0, +20 degrees, which corresponds to an 18-pulse rectification circuit. Each TBC contains a three-phase diode rectifier, a DC capacitor filter, a protection circuit against an increase in the rectified voltage with a chopper and a resistor, as well as a single-phase autonomous voltage inverter (AVI). As part of the TBC, fuses in the rectifier phases and a switching device at the output of the AVI can be used. With these elements, the unit is excluded from operation when it malfunctions. The remaining operating TBC provide the specified mode of operation of the CBC.
Recovery of IM energy into the supply network is not possible, since diode rectifiers are used in the CFC. However, part of the energy of IM can be returned through the AVI in the circuit of the rectified current and spent in the resistors of the protective circuits. If the drive requires recovery of significant energy (mine hoists, etc.), then in the TBC rectifiers are active, for example, on IGBT modules [2,[6][7][8][9][10].
CFC control algorithms in normal operation. Algorithms for controlling multilevel frequency converters are considered in many publications [8,13,14]. In the considered CFC control systems (CS) of automatic circuit breaker (ACB) and AVI can be performed with independent control from each other [2,7]. In the control system of single-phase AVIs, transistor control pulses are generated as a result of comparing the control voltage u y with the reference voltages u om (m is the number of BPC in the phase). If several TBCs are used in the load phase (for example, 2, 3, 4 or 5), then there are several reference voltages, as shown in Fig.2.
In the normal mode of operation of the CFC, all sawtooth voltages have the same amplitude of ripple. Moreover, they are offset in level relative to each other so that the minima of some of the saws correspond to the maxima of the other saws. The instantaneous values of all saws are within ±1 p.u. A single saw-tooth pulses family is used to control all TBCs. In each phase of the load, the control pulses of each AVI are assigned to a specific saw. The formation of transistor control pulses  of any AVI is carried out as a result of comparing the phase control voltage with the reference voltage system of this AVI. At each moment of time in the PWM mode, only one AVI operates in each phase of the load, other AVIs of this phase are in overmodulation mode. It is also possible that all AVIs of this phase are in overmodulation mode.
Features of the operation of the CFC when disconnecting part of the TBS. In the event of a failure of the part of the TBC, the remaining blocks in the work create a symmetrical three-phase system of load voltages. If the voltage or current reserves are not provided for in the CFC, then the voltage and load power are reduced.
If in each phase of a three-phase load the number of TBCs is equal to m, then the total number of states of the CFC during operation of all TBCs or their parts is determined by For a CFC with three TBCs in each phase of the load, the total number of CFC states is M = 64. Data on the CFC states, depending on the number of operational TBCs, are shown in Table 1. Table 1 Mutual phase shifts and CFC load voltage with nine TBCs depending on the number of serviceable units  The top row of the table shows the phase numbers. The second line at the top shows the designation of the angles of shift of the stress vectors of the 2nd and 3rd phases of the CFC relative to the 1st phase ( 12 and  13 ). Columns with the headings "N" indicate the status numbers of the CFC. In the other rows of Table 1, the number of operational BPFs in each load phase is indicated, as well as those phase shifts of the stress vectors (in degrees) relative to the 1st phase vector, at which the symmetry of the three-phase system of load voltages is ensured with the maximum use of operating TBC. The highest symmetrical load voltages, which are provided by serviceable TBCs, are also indicated. The operating states of the CFC are shown on a light background, the gray background shows the states from which it is necessary to switch to the operating states (for example, from state N 12 to state N 33), against a dark background -shutdown the unit (Stop).
For a CPC with nine TBCs, some states of the system are shown in Fig.3 in the form of phase voltage diagrams during the formation of a three-phase symmetric system of load voltages (depending on the number of operational BPCs).
If the CFC contains 15 TBCs (5 each in the load phases), then the state of the system, depending on the number of operational TBCs in phases, is presented in Table 2. The system states are numbered, the permissible ones for operation are indicated (on a light background). Figure 4 under N 1 shows a vector diagram of the phase voltages during operation of all TBCs. Angles of mutual shift of vectors is 120 deg. The stress phase vector of the load is formed as the sum of the stress vectors of the operating AVI. The lines connecting the ends of the phase voltage vectors form a symmetrical three-phase system of load voltages (100 %). Fig.4 under N 37 shows the voltage diagram when disconnecting one TBC in the 1st phase of the load. The creation of a symmetric system of linear load voltages is provided by changing the phases of the 2nd and 3rd stress vectors (the angle of mutual shift of the 2nd and 3rd vectors is shown in Fig.4 -107 electric degrees). In this case, the effective value of the symmetric system of linear load stresses decreases to approximately 93 %.
Equations for a symmetric three-phase linear load voltage system: , , where U 12 , U 23 , U 31 -Line voltages RMS values.
Equations (2) can be written using phase voltages U 1 , U 2 , U 3 and the angles between them α, β, γ (phase voltages are proportional to the number of operating TBC): The system of equations (3) can be solved with respect to unknown angles α, β, γ by iterative methods, for example, in the next record of equations: where n -iteration number; Z -parameter ensuring stability of the calculation process.
Not all CFC states can determine the angles α, β, and γ. For example, in case of a malfunction of all TBCs in two load phases in accordance with Table 1, system states N 16, 32, 48, 52, 56, 60, 61, 62, 63, 64 are impossible.
As a result of solving equations (4), using the known phases α, β, and γ and CFC voltages U 1 and U 2 , the highest load stresses with zero point 0 are determined (Fig.5, b): The voltages defined by expressions (5) should be considered as the voltage limitations at the output of the CFC that acts in the control system. Actual voltages may be less and are determined by the regulation system. The task of iterative calculation of phases and stresses by formulas (4) and (5) is solved in Excel.
Coordination of the characteristics of the CFC and the load in partial modes. If the load of the CFC is a synchronous motor, and the CFC does not provide a margin for output voltage, then when a part of the TBC is turned off, the motor voltage should be reduced, for example, by reducing the magnetic flux of the motor. While maintaining the load power, this leads to an increase in the currents at the output of the CFC, i.e. the equipment must have a current margin.  In particular, the voltages of the 1st and 2nd phases are mutually shifted by less than 90 deg. (instead of 120 electric degrees in symmetrical modes).
It should be noted that in the asymmetric mode of operation of the CFC, the phase currents of the supply network are distorted. It should be expected that with a larger number of TBCs as part of the CFC, disconnection of one unit will lead to less distortion of the grid current.
Conclusions. Cascade frequency converters make it possible to create high-voltage systems using low-voltage power units. They have small distortions of currents and voltages at the input and output, provide galvanic isolation of power networks and loads, have high survivability, and allow adjusting the engine speed in the full range. Due to these advantages, cascade converters are widely used in the drives of gas line compressors, mine fans, pumps, in mine hoists, and in many other installations.
To implement effective control algorithms and increase the reliability and survivability of drives with cascade frequency converters, the analysis of the operating modes and characteristics of the converters in partial modes (in case of failure and disconnection of a different number of power units) is performed. It was revealed that for the formation of a symmetric system of load currents, it is necessary to correct tasks for the mutual shift of the phase voltage vectors depending on the number of working blocks. The state tables of converters are proposed, which determine the tasks by phase of the voltages, characterizing the possibilities of creating a symmetric three-phase system of load voltages in partial modes. The algorithm for calculating the settings for the phases of the voltage was mathematically determined.
On the breadboard installation with an asynchronized generator-motor with a power of 2530 kVA and an active cascade frequency converter of comparable power, experiments were performed confirming the effectiveness of the considered technical solutions. The converter control system uses a relatively simple algorithm for adjusting the phases of the output voltage in partial modes, based on the conversion of a part of the control voltage that goes beyond the reference voltage into a zero-sequence component and in the subtraction of this component from all phase control voltages. The implementation of this algorithm made it possible to ensure an almost sinusoidal shape of the phase currents at a PWM frequency of the converter 4000 Hz.