1. Comparing the Synchronous and Virtual Electrical Inertia Arising from Induction Motors and Motor Drives.
Vince J. Wilson, Taylor Short, Leon Tolbert
University of Dayton, The University of Tennessee Knoxville
BACKGROUND: GRID FREQUENCY AND TYPES OF INERTIA
Introduction
For most of its history, alternating current (AC) power generation has been dominated by the use of synchronous generators (SG). A key feature of AC power is that it follows a sinusoidal waveform and so voltage and current switch direction at a regular frequency. When large amounts of SG are connected in parallel to form an AC power grid, the rotational speed of SG will determine the frequency of the grid using the following equation
𝑝∗ 𝑛 𝑠 =120∗𝑓 (1)
Where p is the number of magnetic poles in the generator rotor, ns is the speed of the rotor or synchronous speed in RPM, and f is the resulting frequency of AC power in Hz.
Grid frequency is meant to be kept constant at 60 Hz in the United States and 50 Hz in Europe. Frequency can fluctuate due to imbalances between generation and load, faults in transmission lines, or loss of connection in the grid. If frequency begins to fluctuate to rapidly or exceeds safety margins, machinery can be damaged, loads may be cut-off, and blackouts may occur. Thus, it is of the utmost importance grid frequency be kept stable
Synchronous inertia
By nature of being large rotating objects, SG can store kinetic energy in the form of inertia. When there is a power imbalance in the grid, the SG will automatically inject or absorb energy from its inertia to make up for the deficiency. This in turns slows down or speeds up the rotor, allowing the grid to maintain constant frequency during disturbances. This form of inertia is known as synchronous inertia (SI) and is quantified with two values: the inertia constant H and the rate of change of frequency (RoCoF). H is the number of seconds a SG can supply its rated power before its inertia is exhausted. H is usually around 2-10 seconds and is calculated using the following equation
𝐻= 𝐽∗ 𝜔 𝑚 2 2∗𝑆 (2)
Where J is the moment of inertia of the rotor in kg/m2, ωm is the rotor speed in radian/sec, and S is power in V-A. RoCoF in Hz/sec can be calculated using
𝑅𝑜𝐶𝑜𝐹= 𝑓 0 2∗𝐻∗𝑆 ∗ 𝑃 𝑚 − 𝑃 𝑒 (3)
Where f0 is the original frequency, Pm is the mechanical power to the rotor in watts and Pe is the electrical power demand in watts.
Virtual inertia
In the modern era, increasing amounts of renewable energy sources (RES) and smart loads are being connected to the grid via power converters. Power converters are switch based power electronics devices that can control the various properties of the power a device will receive or output. As a result, converter connected devices are electrically decoupled from the grid and have low to non-existent SI, threating grid stability. To remedy this, many power converters are capable of mimicking the inertia response of SG, creating virtual inertia (VI) for both loads and generation sources.
VI production relies on two main techniques: deloading and energy storage system (ESS) moderation. Deloading involves using the power converter to control how much power a device produces or consumes from the grid, letting it respond to disturbances by altering its power needs. ESS moderation uses an ESS to act as a SG rotor equivalent; the ESS absorbs excess energy from the grid and injects energy into the grid when there is an under-generation event. Since there are varying methods of producing VI, there is no standard way to calculate H for VI. Instead a simple derivative form of RoCoF shown below is used.
𝑅𝑜𝐶𝑜𝐹= 𝑑𝑓 𝑑𝑡 (4)
METHODS: EXPLANATION OF SIMULINK MODELS AND TEST PARAMETERS
Model explanations
The grid fed model (Fig.1) begins by creating voltage signal using the voltage source initialization block (gray). These signals are then fed into current source blocks (green) and the resulting signals are then fed into the induction motor (red). The three-phase fault (yellow) is placed on the line between the current sources and induction motor. Various measurement blocks are extended out from the main model to collect data.
The V/f drive model is very similar to the grid fed model except for the motor drive made up of the voltage source converter (VSC) and V/f drive blocks (blue and purple) and which is controlled by the VSC controller and frequency control blocks (not shown). In total, these four blocks control V and f so the V/f ratio in equation. 5 is kept constant. With some additional programming, a V/f drive can also act to balance out grid frequency by altering the voltage consumed by the motor, providing VI support.
Both models are using the following base parameters. Source voltage has line to neutral peak value of 3396 volts and a base frequency of 60 Hz. The three-phase faults have a base resistance and inductance of Ω and H. A constant zip load (light blue) is placed on the drive fed model to stabilize transmission line signals.
Testing purpose and methodology
While inertia response and VI production using generation sources has been well investigated, less work has been done on investigating the inertia response of converter connected loads. As such, we built and tested two models in Simulink to compare the inertia responses of direct grid fed and voltage frequency (V/f) drive fed induction motor. To initiate a disturbance, a three-phase fault is activated on the transmission lines between the voltage source and motor/motor drive. This causes a disturbance of frequency, voltage, and current in the system, necessitating an inertia response from the motor or motor drive.
Fault resistances were varied from Ω to 10 Ω. Faults were activated at 2 seconds simulation time and deactivated at 3 seconds simulation time; total simulation time is 5 seconds. The absolute values of RoCoF, rate of change of Te, and rate of change of ωrotor were calculated from seconds to give the motors ample time to stabilize.
Induction motor dynamics
Induction motor (IM) are similar to SG in that their rotation is also related to frequency, but instead of producing power they consume it to createe torque. IM work by applying a three-phase AC voltage to the outer windings (stator). This fluctuating voltage creates a magnetic field that rotates at the same speed as ns. This field then induces another voltage to flow in the rotor, creating a second magnetic field. The interaction between the two magnetic fields causes the rotor to be torqued and begin rotating at speed nrotor.
The electromagnetic torque in N-m generated by the motor is given by
𝑇 𝑒 = 3∗ 𝑉 1 2 ∗ 𝑅 2 ∗𝑠∗60∗𝑝 2∗𝜋∗120∗𝑓∗[ 𝑅 1 ∗𝑠+ 𝑅 𝑋 1 + 𝑋 ∗ 𝑠 2 ] (5)
Where f and p are the frequency of the applied voltage and number of poles in the rotor. The slip factor, s, is the percent difference between ns and nrotor. V is voltage, R is resistance, and X is reactance. 1 and 2 denote a stator or rotor value. R, X, p, and s are all constant values, so Te is dependent only on V1 and f.
Fig .1 grid fed IM model
Fig .2 V/f drive fed IM model
RESULTS AND CONCLUSION
Conclusion
The grid fed model is able to maintain a much lower RoCoF than the V/f drive model by several orders of magnitude as RoCoF for the grid-fed model is neglible. This is due to the time delay inherent in the V/f control programming which allows frequency to have an initial spike and begin fluctuating. After roughly a tenth of a second, the V/f drive is able to stabilize frequency and RoCoF ceases to fluctuate. The V/f drives inertia response is inferior to the grid-fed model but it is still extremely effective in limiting RoCoF. The V/f drive has the additional benefit of having much higher torque control as demonstrated the less extreme swings in Te and ωrotor. Overall, V/f drives present an attractive option for those concerned with frequency and load stability.
Fault value and model type
Average RoCoF (Hz/sec)
Maximum RoCoF (Hz/sec)
Average RoCoTE
(N-m/sec)
Maximum RoCoTe (Nm/sec)
Average RoCoωrotor
(radian/sec2)
Maximum RoCoωrotor
0.001 Ω V/f
2.7344
0.0888
0.001 Ω grid fed
5.3058e-08
9.3602e-07
6.0686
0.1946
0.01 Ω V/f
2.7382
0.0890
0.01 Ω grid fed
6.0819
0.1951
0.1 Ω V/f control
2.7734
0.0915
0.1 Ω Grid fed control
6.2022
0.1989
1 Ω V/f
2.9946
0.1146
1 Ω grid fed
7.0796
0.2373
10 Ω V/f
1.3363
0.0595
10 Ω grid fed
3.7869
0.1369
Acknowledgments
This work was supported primarily by the ERC Program of the National Science Foundation and DOE under NSF Award Number EEC and the CURENT Industry Partnership Program.
I would like to thank my graduate mentor, Taylor Short and faculty advisor, Dr. Leon Tolbert for their assistance and efforts in teaching me this summer and introducing me to the world of electrical engineering and power systems. I would also like to thank the CURENT staff and the National Science Foundation for choosing me to participate in the CURENT REU program and granting me the opportunity to show my skills in an academic research setting.