Keywords

1 Introduction

In present, adjustable speed drive system is applied to ship propelling, vehicle and industrial production to improve the performances [1,2,3,4,5]. Unfortunately, many factors result in power supply losses that usually lead to inverters shutting down. The shutting down of inverters usually brings about economic losses and accidents [6–9]. Therefore, the capability of power supply losses riding through (PSLRT) is required to improve the performance and reliability.

Many researchers are interested in PSLRT method for inverters. In [3], a riding through method using the ultra-capacitor is proposed. The energy is stored in the ultra-capacitor when the inverter operates under the normal mode or braking mode. The stored energy is applied to riding through the grid power supply loss. The other method of stabilizing inverter DC voltages is feeding electrical energy, which is generated by utilizing the inertia energy of the rotor and the connected mechanical loads, to inverters. Scholars who take interest in this area usually focus on designing and improving the control method of the motor that is working as a generator.

Most of the riding through method are designed for two-level or three-level inverters, in which only one DC voltage needs to be stabilized during the riding through process. At present, three-phase cascaded H-bridge multilevel inverters that consists of numerous H bridge cells, are widely used in high-voltage great-power ASDs. Unfortunately, few researcher pays attention to the PSLRT method of cascaded H-bridge multilevel inverters.

This paper focuses on the PSLRT method for cascaded H-bridge multilevel inverters. Since this type inverters usually includes three legs and each leg consists of numerous H-bridge cells. The PSLRT method includes three parts: (1) stabilizing the sum of all cell DC voltages (U DCΣ); (2) balancing three leg DC voltages (U DCA, U DCB, and U DCC), achieving U DCA = U DCB = U DCC = U DCΣ/3; (3) balancing the cascaded cell DC voltages in one leg, achieving U DC_1 = U DC_2 = …= U DC_N = UDCp/N (p = A, B and C). In this paper, three parts of the PSLRT method are designed. This paper is organized as follow. Section 2 introduces the simplified topology of cascaded H-bridge multilevel inverters during riding through peroids. Section 3 proposes the PSLRT method. Section 4 offers simulation results.

2 Simplified Topology of Cascaded H-Bridge Multilevel Inverters Under Power Supply Loss Riding Through Condition

Cascaded H-bridge multilevel inverters that are applied to adjustable speed drive systems, usually consists of three legs. Each leg is composed of N cascaded H bridge cells. Each cell includes an isolated DC source. The DC source usually consists of DC capacitor and three-phase rectifier that is connected to the output ports of a multi-winding transformer. Electrical energy flows into H-bridge cells by way of the multi-winding transformer and the rectifier when the grid voltage is normal. Under the condition of power supply losses, the rectifier usually shuts down.

On the other hand, the electrical power consumption of power electronic devices is mainly related to the magnitude of the output current, the output power factor, the carrier waveform frequency, the cell DC voltage. In practical applications, the carrier waveform frequency is constant. During the riding through period, the output current magnitude is nearly constant and the power factor is nearly equal to zero. Therefore, under the condition that the inverter DC voltages a little deviate from the required value, the electrical power consumption is almost constant.

The simplified topology of cascaded H-bridge multilevel inverters is shown in Fig. 1, during riding through periods. In Fig. 1, P cell-loss is the power consumption of the H-bridge cell.

Fig. 1.
figure 1

The simplified topology of cascaded H bridge multilevel inverters under the condition of riding through power supply loss

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3 The Proposed Method of Riding Through Power Supply Loss for Cascaded H-Bridge Multilevel Inverters

Since cascaded H-bridge multilevel inverters consists of three legs that includes several cascade-connected H-bridge cells, not only should the sum of all H-bridge cell DC voltages be stabilized, but also three leg DC voltages and the H-bridge cell DC voltages during the riding through period.

3.1 The Method of Stabilizing the Sum of All H-Bridge Cell DC Voltages

Since cascaded H-bridge multilevel inverters consists of numerous H-bridge cell that needs an isolated DC voltage, riding through power supply by using storage device or specially designed circuits is very complex and costly. Therefore, utilizing the inertia energy of the rotor and the mechanical loads and feeding the energy back to the inverter is a feasible method to stabilizing the sum of all cell DC voltages. This method is inexpensive because it needs no additional devices and circuits. During the riding through period, the induction motor operate as a generator and the electrical energy is feeding back to the inverter. The relationship among the sum of all cell DC voltages and the feed-back power should be analyzed to design the controller at first. When the field orientated control (FOC) method is utilized, the feed-back power can be expressed as:

$$ P_{\varSigma } = - 1.5n_{\text{p}} i_{\text{sq}} \varphi_{\text{sd}} \omega_{\text{r}} - P_{{{\text{e}}\_{\text{loss}}}} $$
(1)

In Eq. (1), P Σ is the feed-back power, n p is the number of pole pair, i sq is the current component of q axis, φ sd is the stator magnetic field component of d axis, ω r is the rotor speed, P e_loss is the electrical power consumption of the motor. Since the magnitude of the motor current is nearly constant, P e_loss can be treated as a constant value, during the riding through period. Under the condition that the sum of all cell DC voltages (U DCΣ) is a little deviating from the static value (U DCΣ0). The relationship among P Σ, U DCΣ and the inverter power consumption (ΣP cell_loss) can be expressed as:

$$ P_{\Sigma } - \sum {P_{{{\text{cell}}\_{\text{loss}}}} } = C_{\Sigma } U_{{{\text{DC}}{\Sigma} 0}}^{{}} \frac{{{\text{d}}U_{{{\text{DC}}{\Sigma} }}^{{}} }}{{{\text{d}}t}} $$
(2)

In Eq. (2), C Σ is the equivalent capacitor of the inverter. The value of C Σ is equal to all H-bridge cell capacitors are connected in series. Based on Eqs. (1) and (2), the relationship between i sq and U DCΣ can be expressed as:

$$ G_{{{\text{isq}}\_{\text{UDC}}\Sigma }} \left( s \right) = - \frac{{1.5n_{\text{p}} \varphi_{\text{sd}} \omega_{\text{r}} }}{{C_{\Sigma } U_{{{\text{DC}}\Sigma 0}}^{{}} s}} $$
(3)

It can be observed from Eq. (3) that a proportional controller can be used to stabilize U DCΣ. But the static error is inevitable when the proportional controller is utilized without compensation. Considering that the electrical power consumption of the motor and the inverter can be measured or calculated easily, a compensation (i sq_com) can be added to the controller to reduce the static error. The picture that describes the control system are shown in Fig. 2.

Fig. 2.
figure 2

The control system for stabilizing UDCΣ

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3.2 The Method of Balancing Three Leg DC Voltages

Since there are usually no zero sequence current way between the inverter and the motor, injecting a zero sequence voltage in the inverter output AC voltage little affects the motor. Regulating the leg feed-back electrical energy and balancing three leg DC voltages by injecting a zero sequence voltage in the inverter output AC voltage is a valuable method. The positive sequence voltage (fundamental waveform) and the zero sequence voltage of the inverter output voltages can be expressed as:

$$ u_{\text{A}} = U_{{p{\text{m}}}} \sin \omega_{\text{m}} t + u_{ 0} $$
(4)
$$ u_{\text{B}} = U_{{p{\text{m}}}} \sin \left( {\omega_{\text{m}} t - \frac{{2\uppi}}{3}} \right) + u_{ 0} $$
(5)
$$ u_{\text{C}} = U_{{p{\text{m}}}} \sin \left( {\omega_{\text{m}} t + \frac{{2\uppi}}{3}} \right) + u_{ 0} $$
(6)
$$ u_{ 0} = U_{{0{\text{m}}}} \sin \left( {\omega_{\text{m}} t + \theta_{0} } \right) $$
(7)

In Eqs. (4)–(7), Upm is the magnitude of the positive sequence phase-voltage waveform, ω m is the frequency of the output voltage fundamental waveform, θ is the difference between the voltage phase and the current phase, U 0m is the magnitude of the zero sequence voltage waveform, θ 0 is the difference between the zero sequence voltage phase and u A phase. In common application, there is no way for zero sequence current between inverters and motors. The inverter output current can be expressed as:

$$ i_{\text{A}} = I_{{p{\text{m}}}} \sin \left( {\omega_{\text{m}} t - \theta } \right) $$
(8)
$$ i_{\text{B}} = I_{{p{\text{m}}}} \sin \left( {\omega_{\text{m}} t - \theta - \frac{{2\uppi}}{3}} \right) $$
(9)
$$ i_{\text{C}} = I_{{p{\text{m}}}} \sin \left( {\omega_{\text{m}} t - \theta + \frac{{2\uppi}}{3}} \right) $$
(10)

In Eqs. (8)–(10), I pm is the magnitude of the phase-current waveform. The active-power adjustments by injecting the zero sequence voltage can be expressed as:

$$ \Delta P_{\text{A}}^{0} = 0.5U_{{ 0 {\text{m}}}} I_{{p{\text{m}}}} \cos \left( {\theta_{0}^{{}} + \theta } \right) $$
(11)
$$ \Delta P_{\text{B}}^{0} = 0.5U_{{ 0 {\text{m}}}} I_{{p{\text{m}}}} \cos \left( {\theta_{0}^{{}} + \theta + \frac{{2\uppi}}{3}} \right) $$
(12)
$$ \Delta P_{\text{C}}^{ 0} = 0.5U_{{ 0 {\text{m}}}} I_{{p{\text{m}}}} \cos \left( {\theta_{0}^{{}} + \theta - \frac{{2\uppi}}{3}} \right) $$
(13)

Based on the principle of the capacitor storing electrical energy, the relationship of the active-power adjustment and the leg DC voltage can be expressed as:

$$ G_{{\Delta P_{p} \_U_{DCp} }} (s) = \frac{1}{{C_{p} U_{{{\text{DC}}p0}} s}}\quad (p = {\text{A}},{\text{B}},{\text{C}}) $$
(14)

In Eq. (14), C p is the equivalent capacitor of the leg. The value of C p is equal to the leg H-bridge cell capacitors are connected in series. U DCp is the leg DC voltage, and U DCp0 is the static value. On the other hand, under the condition that U DCΣ is stabilized, if U DCA and U DCB are adjusted to U DCΣ/3, U DCC is U DCΣ/3. Therefore only two controller are required to balancing three leg DC voltages. It can be observed from Eq. (14) that proportional controllers can be used to control U DCA and U DCB. But the static error is inevitable when the proportional controller is utilized. In practical applications, small static error is permitted. The picture that describes the control system are shown in Fig. 3. The zero sequence voltage is calculated by (11), (12) and (13).

Fig. 3.
figure 3

The control system for controlling U DC_p

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3.3 The Method of Balancing the H-Bridge Cell DC Voltage in One Leg

It is well known that the cell DC voltage can be controlled by regulating the active power that is fed in the cell. The cell active power without regulation is expressed as:

$$ P_{\text{cell}} = U_{\text{cell}} I_{\text{cell}} \cos \theta $$
(15)

In Eq. (15), cosθ is the power factor, U cell and I cell are the RMS of the cell output AC voltage and current without regulations, respectively. If an AC voltage is injected, the active power can be expressed as:

$$ P_{\text{cell}} + \Delta P_{\text{cell}} = U_{\text{cell}} I_{\text{cell}} \cos \theta + \Delta U_{\text{cell}} I_{\text{cell}} \cos \theta_{1} $$
(16)

Since the riding through is required to operate well under the condition that the rotor speed is high. In some special conditions, the regulation of magnetic field is forbidden. The magnitude of output voltage is proportional to rotor speed and the magnitude of the magnetic field. Therefore, the method of controlling and balancing the H-bridge cell DC voltages is required to operate well when the cell output voltage is high. Unfortunately, the higher the output voltage magnitude, the smaller the AC voltage magnitude that is injected to regulate the cell feed-back active power without over-modulation. The method of this paper needs smaller injecting AC voltage and achieves better performance. It can be observed that △U cell is smallest when cosθ 1 is zero, under the condition that △U cell and I cell is constant. Therefore, injecting an AC voltage of which the phase is equal to the current, can regulate the active power and the magnitude is smallest. This method fits to the condition that small magnitude AC voltage is permitted to inject without over-modulation.

Based on the principle of the capacitor storing electrical energy, the relationship of the active-power adjustment and the cell DC voltage can be expressed as:

$$ G_{{\Delta U_{cell} \_U_{DCcell} }} (s) = \frac{1}{{C_{cell} U_{{{\text{DC}}cell0}} I_{\text{cell}} s}} $$
(17)

In Eq. (17), C cell is cell capacitor. U DCcell is the cell DC voltage, and U DCcell0 is the static value. It can be observed from Eq. (17) that proportional controllers can be used to control U DCcell because small static error is permitted in practical applications. The picture that describes the control system are shown in Fig. 4.

Fig. 4.
figure 4

The control system for controlling U DCcell

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4 Simulation

To verify the proposed PSLRT method, a mathematic model of the cascaded H-bridge multilevel inverter and the induction motor is established by means of MATLAB/Simulink. Each H-bridge cell is mainly composed of an H-bridge inverter, a capacitor (9.8 mF) and a three-phase rectifier, of which the input ports are connected to a multi-winding transformer. Each leg includes five H-bridge cells. The inverter consists of three legs, of which the topologies are identical. The nominal RMS value of the inverter output voltage is 6000 V. The nominal output power of the inverter is 1000 kW. Each cell DC voltage is approximately 1000 V, and each leg DC voltage is nearly 5000 V when the grid voltage is normal. Since the cell DC voltage is one of the criteria of detecting the power supply loss and the recovery of the power supply, the stabilized cell DC voltage should be lower than 850 V (0.85 times the nominal value) during the riding through period. On the other hand, because the cell is required to output nominal AC voltage during the riding through period, the cell DC voltage should be greater than 800 V (0.80 times the nominal value). Therefore, the stabilized value of the cell DC voltage is nearly 820 V (0.82 times the nominal value). The stabilized value of the leg DC voltage that is the sum of five cascaded cell DC voltages, is approximately 4100 V. The stabilized value of U DCΣ is 12300 V. To simulate the cell power consumption the resisters are placed in the cells and connected with the capacitor (10 mF) in parallel. The resisters of three legs are not equal to simulate the differences of three leg power consumptions. The resisters placed in the cells of A phase leg are 1000 Ω. The resisters placed in the cells of B and C phase leg are 1075 Ω and 925 Ω respectively.

The nominal voltage and power of the motor are 6000 V and 300 kW respectively. The nominal rotor speed is 750 r/min. The load of the motor is a synchronous generator of which the output ports are connected to the great-power resisters. When the rotor speed is 500 r/min and the proposed method of stabilizing U DCΣ is utilized, the waveform of U DCΣ is shown in Fig. 5. Because the inverter cannot ride through power supply losses without stabilizing U DCΣ, the simulation result of no stabilizing U DCΣ is invaluable and is not provided in this paper.

Fig. 5.
figure 5

The waveform of U DCΣ when the proposed method of stabilizing U DCΣ is utilized

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The waveform of U DCA, U DCB and U DCC are shown in Fig. 6 when the method of balancing three leg DC voltage is not used. The simulation result of the proposed balancing three leg DC voltages is shown in Fig. 7. The waveform of five cell DC voltages in A phase is shown in Fig. 8 without the proposed method of balancing cascaded H-bridge cell DC voltages. The simulation results of the proposed method of controlling and balancing cell DC voltages is shown in Fig. 8.

Fig. 6.
figure 6

The waveform U DCA, U DCB and U DCC without the proposed method of balancing three leg DC voltages

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Fig. 7.
figure 7

The waveform U DCA, U DCB and U DCC with the proposed method of balancing three leg DC voltages

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Fig. 8.
figure 8

The waveform of five cell DC voltages without the proposed method of balancing cell DC voltages in one leg

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It can be observed from Fig. 5 that the proposed method of stabilizing U DCΣ can control and stabilize U DCΣ rapidly. From Fig. 6, it obvious that three leg DC voltages deviates from the required value quickly. It can be observed from Fig. 7 that the proposed method of balancing U DCA, U DCB and U DCC can balancing three leg DC voltages quickly. It can be observed from Figs. 8 and 9 that five cell DC voltages deviates from the required value quickly without the proposed method and the proposed method can balance five cell DC voltages quickly.

Fig. 9.
figure 9

The waveform of five cell DC voltages with the proposed method of balancing cell DC voltages in one leg

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