1. Introduction
Several energy storage technologies have been developed including compressed air, pumped-storage power plant (PSPP), flywheels, high energy batteries, super capacitors, biofuels, and thermal energy storage. Among these, the PSPP is a mature technology in the category of large energy storage systems and is critical for power system flexibility [
1]. To comply with the Kyoto protocol, worldwide focus is on renewable energy sources like wind, solar, etc.; however, renewable energy generation is highly variable and intermittent in nature affecting the power system operations, especially power balancing; therefore, power grid operators are encouraged to connect the energy storage systems to the power system network. In addition, European countries have introduced regulations for stabilizing the power grid network wherein ‘energy storage systems are mandatory when more than 20% of the power is generated using solar and wind’ [
2].
Since the 1900s, synchronous machine-based fixed-speed PSPPs have been installed in European, American, and Asian continents, and more than 110 GW of them are in active operation worldwide [
3,
4]. Nowadays, variable speed PSPP is an emerging technology used in pumped-storage systems where it offers several benefits, specifically (i) increased efficiency in generation/pumping mode irrespective of water level in the dam, (ii) mode transition from pumping to generation and vice versa in short time, (iii) high dynamic stability against grid and speed fluctuations, (iv) high ramp rate compared to fixed-speed PSPP, (v) quick response in load balancing, and (vi) flywheel effect (inertia energy) [
5], etc. Variable speed PSPP was introduced in Japan in the early 1990s, and 18 PSPPs (i.e., 36 units) are installed/under construction worldwide with a total capacity of 9.425 GW [
4,
6].
The synchronous machine-based variable speed PSPPs (e.g., 100 MW Grimsel 2 at Switzerland) [
7] installed in various countries offer several benefits; however, this system is not yet accepted by the project authorities due to its limitations as listed here: (i) power converter with a rating similar to the machine is required, which is unfeasible due to the larger size (space requirement) and cost, especially in the case of an underground power house, (ii) hydro turbine requires only 10–15% speed variation from the rated speed for significant improvement in efficiency; therefore, focus is shifted to doubly fed induction machine (DFIM) for use in variable speed PSPP (400 MW Ohkawachi PSPP, Japan (1993); 250 MW Linthal PSPP, Switzerland (2015); 250 MW Tehri PSPP, India (under construction)), where power converters with a capacity lower than the rating of the machine are enough to achieve the required efficiency improvement and high dynamic stability [
8,
9].
Power converters connected on the rotor side of the DFIM ensures active and reactive power control for the drive. Since the 1990s, cycloconverters (e.g., 400 MW Ohkawachi PSPP, Japan (1993)) have been used on the rotor side of DFIM; however, they are now being phased out gradually due to high ripples in rotor current and reactive power consumption from grid (rotor side). Presently, the three-level back-to-back voltage source inverter (VSI) is preferred owing to its less THD and unity power factor on grid side (rotor). In the case of a large current on rotor side, multi-channel (MC) power converters are adopted, e.g., the five-channel, three-level back-to-back VSI (connected on rotor side) at 250 MW Tehri PSPP, India [
10] that handles 11,600 A.
It is reported that redundancy in power converter with control circuit is not yet adopted in multi-channel DFIM-fed drives in industries, especially in pumped-storage units, due to the operational challenges [
11,
12]. Also, faults are more likely in power converters of variable speed drives causing frequent plant shutdowns and huge generation losses [
13]; therefore, redundancy in power converters and control circuits, especially in pumped-hydro applications of large rating (>100 MW), is expected to be imposed as a statutory requirement by the regulatory body, e.g., Central Electricity Authority (CEA) of India (2007) [
14]. This creates uncertainties in decision-making for the policy makers and project authorities of the variable speed PSPP in view of reliability and availability of the unit.
Considerable research has been conducted in doubly fed induction machine drives with regard to motor control [
15,
16] grid disturbances, converter faults, sensor failures, fault detection, fault tolerant control, etc. [
17,
18,
19,
20,
21,
22,
23]. Particularly, references [
17,
18] discuss the impact of the VSI faults on induction drives. Likewise, faults in power converter, control circuits, and motor are detailed in [
19,
20]. Grid disturbances such as the unbalanced grid voltage and voltage sag are discussed in [
21,
22,
23]. Reliability of supply, motor, and components are analyzed in [
24,
25,
26,
27] for squirrel-cage induction and synchronous machine drives. Several publications discussed the reliability assessment techniques such as fault trees, Markov model, reliability block diagrams, etc., that are discussed in detail in [
28]. The Markov model is considered as the most powerful technique with better features such as (i) fault coverage, (ii) time-dependent failure rates, (iii) common mode failures, etc. compared to the fault trees and reliability block diagrams.
Reliability analysis is critical for effective development, maintenance, and operation of large-rated variable speed PSPPs.
Figure 1 shows the single line diagram of a 250-MW DFIM-fed variable-speed unit consisting of multi-channel VSI, control system, DFIM, phase shift transformer, unit transformer, inter phase reactors, etc. In this study, we analyze the reliability and availability of this system using Markov model in comparison with fixed-speed PSPP.
The rest of this paper is structured as follows.
Section 2 discusses the survivability of the test unit (250 MW DFIM) with regard to the converters, sensors, and rotor winding failures. The Markov reliability model and equations are detailed in
Section 3. The reliability components of a 250-MW variable-speed unit are presented in
Section 4, and the reliability estimation and comparative analysis are discussed in
Section 5. Finally, the concluding remarks are presented in
Section 6.
2. Survivability Analysis of a 250-MW Variable-Speed Unit
This section discusses the survivability status of the 250-MW DFIM-fed variable-speed unit [
29] with regard to power converters, sensors, and rotor winding faults. A 250-MW DFIM with five-channel three level neutral point back-to-back converter (3L-NPC) is designed in Matlab/Simulink tool to observe the drive behavior. A field-oriented vector control system is designed to control the active (real)/reactive power of the unit, and an active current sharing control is embedded in the controller for proper sharing of rotor currents among the converters. The detailed control circuit and equations are detailed in [
29]. Faults are simulated in the system using the multi-port switch and breaker in Matlab/Simulink. The switching frequencies of the grid-side and machine-side converters are selected as 500 Hz and 300 Hz, respectively, considering the switching losses.
The active and reactive powers of the 250-MW DFIM at normal operating condition are shown in
Figure 2. Stator current of the machine is shown in
Figure 2c. It is inferred that magnitude of the stator current changes with respect to the change in real and reactive power delivery, and frequency of the stator current is constant at grid frequency. In case of rotor currents, both magnitude and frequency are changed (shown in
Figure 2e). Frequency of the rotor currents depends on slip frequency. In addition, it is noted that the rotor voltage also depends on the slip of the machine. In the case of faults, the machine is instructed to operate at 0.96 p.u. (221.5 rpm), and the shaft power is considered as 240 MW. Furthermore, the power factor is set as 0.95 through the reactive power control system. The test results show that: (i) the line current in stator winding is 9157 A (0.814 p.u.), (ii) the voltage (P-P) applied to the rotor winding by the rotor-side converter is 1255 V (0.38 p.u.), (iii) the line current in rotor winding is 10,360 A (0.893 p.u.), (iv) the reactive power consumption of the machine is 15.3 MVAr (0.05 p.u.), and (v) the frequency of rotor current is 2 Hz.
2.1. Converter Faults
A single-switch gate-drive open-circuit fault (upper switch) is injected into one of the parallel connected grid-side converter (GSC) at 160 s, and the results are shown in
Figure 3. During the fault, the phase current corresponding to the faulty leg is distorted in upper half cycle, and the negative half cycle is found to be omitted, resulting in variation of phase and magnitude of the other two phase currents (
Figure 3a); however, the current flowing through the other healthy converters are not affected as shown in
Figure 3b. From the test results, it is inferred that: (i) the dc-link voltage fluctuates marginally in the faulty converter as shown in
Figure 3c (oscillation at grid frequency), (ii) variation in both capacitor dc-link voltages as shown in
Figure 3d, (iii) the power factor on grid side (rotor) fluctuates (
Figure 3e) due to the variation in reactive power consumption, and (iv) the speed of the machine is constant as set by the machine-side control system. In the case of an open-circuit fault in lower switch, the results are similar to the upper switch; however, it is observed that (i) the phase current of the faulty leg is disturbed in lower half cycle, while it is omitted in upper half cycle, (ii) the variations in the dc-link capacitor voltages are reversed when compared to the open-circuit fault of the upper switch.
2.2. Sensor Faults
Single rotor current sensor omission fault is injected at 410 s, and the results are shown in
Figure 4. During the fault, one of the current sensor reads zero value, resulting in changes in Iqr (q-axis (torque) component of machine). The changes in Iqr distort the electro-magnetic torque of the machine, resulting in fluctuations in the real power delivery and speed. From the results, it is observed that (i) the speed of the machine marginally fluctuates (
Figure 4f), resulting in changes in the active power delivery (
Figure 4c) and (ii) there are variations in rotor and stator currents (
Figure 4a,b). Despite these variations, the machine is observed to be in continuous operation, and Idr maintains the controlled reactive power at grid (stator side). It is observed that all controllers are in regular operation in the grid-side converters, and the dc-link voltage is maintained.
2.3. Rotor Winding Faults
Simulation study is repeated for single-phase rotor winding fault that is injected into machine side converter (MSC) at 410 s, and the results are shown in
Figure 5. When a fault occurs, one of the rotor phase current goes to zero (
Figure 5a), and the conduction mode is equivalent to the single-phase mode with other two healthy phases. During the fault, the magnitude of the rotor and stator phase transient currents increase to a level of 2.96 p.u. (
Figure 5a) and 4.15 p.u. (
Figure 5b), respectively. Consequently, the active and reactive powers of the machine are affected (
Figure 5c,d). From the test results, it is observed that: (i) the healthy phase rotor currents undergo deviations in phase, and they produce transients at meeting point of these two phase currents, (ii) both stator and rotor currents increase to the levels above the rated value, (iii) there are fluctuations in dc-link voltage and speed of the machine, (iv) there is instability in active and reactive power delivery, and (v) the rotor side converter (both GSC and MSC) control system falls out of action. Likewise, all the power converter and sensor faults are injected, and the results are summarized in
Table 1 and
Table 2, respectively.
3. Markov Reliability Model
Reliability is a term used to measure the successful rate of operation of equipment/components in a given period. Let us assume that an equipment is in successful operation in the interval from time t
1 to time t
2. Then, ‘F’ is a variable denoting time to failure in an equipment, and reliability of the equipment is mathematically defined as,
.
Mean Time to Failure (MTTF) is given by,
In general, a component failure is exponentially distributed in reliability analysis. Therefore, reliability is given by
Failure rate over the period, and it is reported as constant. Time period between initial commissioning and the instant of susceptibility to fail.
Exponential distribution shows that the reliability decays to zero when the component ages. For a single component, MTTF is also given by,
In a series system, with ‘n’ components having failure rates λ
1, λ
2, …, λ
n and reliability functions R
1(t), R
2(t), …, Rn(t), the overall reliability function and MTTF are given by,
Reliability for ‘n’ paralleled systems is given by,
Availability of an equipment is considered by the time to repair and number of failures. System availability is mathematically given by,
; ; .