Standby Losses Reduction Method for Flywheels Energy Storage System Based on Hybrid Space Vector Pulse Width Modulation

The flywheel energy storage system (FESS) can operate in three modes: charging, standby, and discharging. The standby mode requires the FESS drive motor to work at high speed under no load and has the longest operating time. Therefore, reducing the standby losses is of great significance for further promoting the application of FESS. In the paper, a novel modulation technique based on hybrid space vector pulse width modulation (HSVPWM) is proposed to reduce the standby losses of the FESS. By the reasonable arrangement of the zero vectors and non-zero vectors, the proposed method can reduce the switching frequency and eliminate the dead time, which reduces the standby losses of the FESS effectively. The modeling, simulation, and analysis verify the effectiveness of this method in reducing the standby loss of the FESS.


Introduction
As residents' awareness of environmental protection increases, the proportion of clean energy generation, including wind and solar power, is gradually increasing in total power generation.However, the instability of wind and solar energy poses challenges for ensuring the quality of the power grid [1][2].In order to provide high-quality and continuous electricity to the power grid, energy storage systems (ESS) play a crucial role.The FESS can store mechanical energy from flywheel rotation, which has the advantages of short charge-discharge time, low maintenance cost, high power density, long service life, high energy conversion efficiency, fast response, environmental friendliness, and no geographical limitations [3].
At present, the FESS is widely applied in new energy power stations, uninterruptible power supplies (UPS), artificial satellites, and vehicles.It has further enhanced its competitiveness by reducing losses, increasing power density, and improving conversion efficiency [4].The FESS can operate in three modes: standby, discharging, and charging.In standby mode, the flywheel can slowly decelerate due to losses or be driven by the motor at a low power to overcome standby losses and maintain a constant speed.During discharging, the flywheel decelerates, and the motor operates as a generator to convert mechanical energy into electrical energy [5].During the charging process, the flywheel is driven by an electric motor to accelerate rotation and store electrical energy as mechanical energy.
Some researchers have investigated the standby and operating losses of FESS.Most of the researchers focused on motor-related losses or aerodynamic losses, and less attention has been paid to losses related to magnetic bearings or power converters.FESS has been found to be a viable solution for UPS applications [6], especially in sensitive loads such as manufacturing and medical systems that require continuous power supply [7].FESS offers infinite charging/discharging cycles and requires minimal maintenance, making flywheel a perfect option in UPS applications compared to traditional battery solutions.Besides, FESS needs to operate in standby mode for long periods, where the motor drives the flywheel at high speed to overcome standby losses.Usually, in well-designed FESS systems, the proportion of standby loss in a total loss is not significant, but as the flywheel continues to operate, energy loss cannot be underestimated.Reducing the no-load losses of PMSM in FESS can further improve the performance and increase the reliability and efficiency of the system [8].
With the advancement of power electronics and digital microcontroller technology, there have been many improvements in motor drives.In addition to control strategies, pulse width modulation (PWM) methods are often an effective way to improve system performance [9].Space vector PWM (SVPWM) is the most popular modulation method, which has the advantages of high utilization of DC voltage and low harmonic distortion.Traditional SVPWM uses two alternating symmetrical switch sequences in each sampling interval and has been widely used in industry.Usually, the difference between different SVPWM strategies lies in the different types of switching sequences by utilizing space vector notation.By deliberately adjusting the switching sequence, SVPWM techniques can be designed specifically for a particular purpose.Recently, optimization methods for reducing switching loss and line current harmonic distortion through different switching sequence selections have been shown advantages over traditional SVPWM [10].
Focused on the PMSM-based FESS in the UPS system, the paper proposes an improved HSVPWM method to reduce the converter losses.A simplified FESS control model for UPS is also introduced, which contains only two working modes, charging and standby.Energy flows in the FESS through a bi-directional converter in this model.In this case, the FESS will be charged to its rated speed and maintained while the critical load is powered by the power grid.A simulation of the charging and standby processes is performed to observe the standby losses, and the correctness of the proposed improved modulation method is verified.

SVPWM
Typically, PMSM is driven by a two-level three-phase voltage source inverter.Figure 1 shows its circuit diagram.In the SVPWM, the reference vector is sampled in a sub-period T S .The inverter generates different voltage vectors, which are averaged over time to produce the average vector.Figure 2 shows the diagram of the space vector.Each phase of the three-phase inverter bridge in the inverter circuit mentioned above has eight possible switch combinations, where '0' represents the on-state of the lower bridge arm switch and '1' represents the on-state of the upper bridge arm switch.Figure 2 illustrates all eight voltage vectors that can be generated by the eight possible states of the voltage source inverter.It can be seen that two zero magnitude voltage vectors (named U 0 and U 7 ) are Bi-directional Power Converter produced by two zero states (000 and 111) through short-circuiting the motor's three-phase terminals, while the other six non-zero states apply voltage to the stator windings.These effective vectors (named U 1 , U 2 , U 3 , U 4 , U 5 , and U 6 ) are equal in magnitude.The space vector plane is cut into six sectors (named I, II, III, IV, V, and VI) by these active vectors.The mean value equivalence principle is the mathematical basis of the SVPWM algorithm, which uses a linear combination of the eight basic vectors to approximate any required voltage space vector.At any time, the required voltage space vector U ref is located in a certain sector, composed of two adjacent active vectors that make up the sector.It fills the remaining time of a switching cycle with zero vectors.Figure 3 shows a schematic diagram of space vector synthesis when the reference vector is located within the sector I. Figure 3. Diagram of vector synthesis using space vector when reference vector is located in sector Ⅰ.
Based on the principle of average value equivalence, we can obtain the following.
T 1 , T 2 , and T 0 represent the durations of the applied voltage space vectors U 1 , U 2 , and the zero vector U 0 (or U 7 ).The duration of each vector within a given sub-period T S is determined using the parallelogram rule for vectors illustrated in Figure 3. Specifically, the duration of each voltage vector can be calculated using the following formula.
The formula shows that θ is the angle between the synthesized reference vector U ref and vector U 1 , where 0 60 θ °≤ < ° , and T s is the switching period.After obtaining the operating time of each sub- vector through calculation, the corresponding switching devices can be driven according to the time.
The reference vector U ref in the formula is normalized relative to the DC bus voltage U DC .Of course, the duration of T 1 , T 2 , and T 0 must not be negative, so the magnitude of U ref is limited within the hexagon formed by the active vectors in Figure 2. The switching sequence of the six sectors in the traditional SVPWM method is shown in Figure 4.The characteristic of this modulation method is that the conduction states of the lower and upper bridge arms in the same phase are opposite, and all switching devices operate twice in each given sub-period.

HSVPWM
Unlike traditional SVPWM control that uses complementary switching, the hybrid space vector modulation employs non-complementary switching for both lower and upper bridge arms.This means there are switching states where neither the lower nor upper bridge arms are conducting.The conductive state of the lower bridge arm is represented by '-1' and the upper bridge arm by '1', while the non-conductive state of both is represented by '0'.As a result, there are 27 possible combinations of switch states for the three-phase inverter.These different switch combinations correspond to 27 basic voltage space vectors, including 12 active vectors and 15 zero vectors.The voltage space vector maps of 12 sectors can be obtained from the basic space voltage vectors of these 27 combinations, as shown in Figure 5 [11].
The 12 active vectors are composed of 6 active voltage vectors for the 180° conduction mode and 6 effective voltage vectors for the 120° conduction mode.The voltage vectors for the two conduction modes are separated by an angle of 30°, and the magnitude of the voltage vector for the 120° conduction mode is 3 / 2 times that of the 180° conduction mode.When synthesizing mixed space vectors, the calculation formula for the duration of each sub-vector differs from that of traditional SVPWM because the magnitudes of the two adjacent non-zero vectors are different.It should be noted that when calculating the duration of the voltage vector for the 120° conduction mode, no amplitude transformation is required.Figure 6 shows a schematic diagram of space vector synthesis when the reference vector is located within the sector I. Figure 6.Diagram of vector synthesis using hybrid space vector when reference vector is located in sector Ⅰ.
Similarly, based on the principle of equivalent average values, it can be obtained that: Due to the presence of up to 15 zero vectors, the selection and distribution of zero vectors are more flexible for hybrid space vector modulation.By appropriate selection, the number of switching events and switching losses can be minimized to the greatest extent possible.

Minimum switching loss modulation method based on HSVPWM
The allocation principle of the basic vector action sequence is selected as follows: at each switch state transition, only one of the lower and upper bridge arms of the same phase is changed, the PWM waveform is symmetrical within a switching cycle, the switch state is not changed during switching cycle alternation, and the zero vector is evenly allocated in time.The proposed switching sequence for the 12 sectors is shown in Figure 7.
As shown in Figure 7, when the reference voltage vector passes through each sector from Sector I to Sector XII, each switch device operates 16 times.However, if the traditional SVPWM method is used to let the reference voltage vector pass through each sector from sector I to sector VI at the same speed, each switch device needs to operate 24 times.According to this figure, the proposed method has an average of only 4/3 switch changes per switch device in one switching cycle, which reduces the number of switch changes by 33.3% compared to the traditional SVPWM method.In addition, there is no simultaneous conduction of the same phase in the lower and upper bridge arms when the switch state changes.Thus, there is no need to set a dead time, avoiding the influence of the dead time effect.

System model and simulation
The two working states of FESS, including motor-driven flywheel rotation and flywheel-driven motor power generation, are essentially achieved by controlling the motor that is mechanically connected to the flywheel.In this paper, only the state of the motor-driven flywheel is considered.Simply put, adding additional inertia to the PMSM rotor can be simulated as a flywheel [5,12].A complete system model of the PMSM driver was established using SIMULINK to test the effectiveness of the proposed modulation method.The operation under two modulation methods was also studied.Only the charging and standby modes of the FESS were simulated.A MOSFET-based inverter and a PMSM with i d = 0 control jointly constitute the simulation model [13].The motor control diagram is shown in Figure 8.
Simulation was conducted from the start of the flywheel at rest to the steady state at rated speed, during which the FESS was switched to standby mode and remained in that mode.During this period, the conduction and switching losses of the six switching devices were recorded.The traditional SVPWM method was used for acceleration and then switched to the proposed HSVPWM method during standby mode for comparison.The simulation model parameters remained unchanged throughout the process.
Figure 9 shows the start-up and steady-state process of FESS.During the period from 0 to 8 seconds, the PMSM is controlled by traditional SVPWM, and the flywheel is steadily accelerated at a speed of 1000 rpm/s.
When the flywheel reaches a speed of 8000 rpm at 8 seconds, it switches to standby mode and continues to rotate for 4 seconds.It can be seen that the PI parameters of the controller work well at this time.
At 12 seconds, the proposed HSVPWM modulation is adopted, and the effect of PI parameters deteriorates, resulting in significant fluctuations in speed.Figure 10 shows the phase current of the motor under traditional SVPWM modulation in standby mode.Figure 11 shows the current under the improved HSVPWM modulation.The power consumption of FESS in standby mode is very small, and the motor phase current is relatively small regardless of which modulation method is used.Moreover, there is no high requirement for the dynamic performance of the motor at this time, and the proposed modulation method is suitable for use.
When observing Figures 10 and 11, it can be observed that there are some differences in the motor phase currents between the traditional SVPWM modulation and the proposed HSVPWM modulation in the standby state.Specifically, compared to traditional SVPWM modulation, the proposed method exhibits smaller values in motor phase current, but the degree of current distortion increases.A-H in Table 4 represents the high-side switching device of phase A, and so on.Analyzing the data in the table, it can be observed that the number of switch actions has significantly reduced, with an average reduction of 32.31%.The switch losses have also significantly decreased, with an average reduction of 82.80%.Although the conduction losses have increased, the overall inverter losses have decreased by 60.77%.It is evident that the proposed modulation method is very suitable for reducing the inverter losses in the standby mode of the FESS.However, if this modulation method is applied to the charging or discharging state of the FESS, it may reduce the dynamic performance of the flywheel and bring significant electrical pollution to the DC bus.

Conclusion
This article proposes a novel HSVPWM switching sequence based on the concept of hybrid space vectors, which can significantly reduce the switching frequency of power electronic devices.When applied to the standby state of the FESS in the UPS, this method can significantly reduce standby power losses.On the basis of describing the FESS control algorithm, the application position and the implementation principle of the improved method are shown in detail with a comprehensive block diagram.The simulation results compare the power losses of the motor drive under standby conditions.The simulation results also verify the effectiveness of the improved switching sequence modulation method.In the future, more research can be conducted on the characteristics of this modulation method to expand application scenarios.

Figure 1 .
Figure 1.Inverter circuit of the FESS in UPS.

Figure 2 .
Figure 2. Diagram of space vector.Figure3.Diagram of vector synthesis using space vector when reference vector is located in sector Ⅰ.

Figure 5 .
Figure 5. Diagram of hybrid space vector.Figure6.Diagram of vector synthesis using hybrid space vector when reference vector is located in sector Ⅰ.

Table 1 .
Figure 8. Configuration of the simulation model.The UPS technical specifications, PMSM parameters, and MOSFET parameters in the system are shown in Table 1, Table 2, and Table 3, respectively.The parameters of the MOSFET are set with reference to the silicon carbide MOSFET product CAB450M12XM3 of CREE Corporation.Parameter of UPS.

Table 4 .
Simulation losses are calculated over 15 complete electrical cycles to obtain the switching frequency and losses of the six switches during the standby state, as shown in Table4.Switching frequency and loss during standby mode. 9