This Non-provisional application claims priority under 35 U.S.C. §119(a) on Patent Application No(s). 102113997 filed in Taiwan, Republic of China on Apr. 19, 2013, the entire contents of which are hereby incorporated by reference.
1. Field of Invention
The invention relates to a stability analyzing apparatus and stability analyzing method and, in particular, to a stability analyzing apparatus and stability analyzing method of a direct current (DC) power system.
2. Related Art
Because the DC power system has advantages of high reliability, good modular design and easy maintenance, it has been widely applied to many appliances, such as a DC grid system or a telecommunication system. For the large-scale DC distributed power system, monitoring the stability thereof is very important in order to avoid potential power failure.
In general, a DC power system will be made equivalent to a dual-port module for monitoring its stability. As shown in
ZL denotes load impedance, Zs denotes the impedance of the dual-port power module by a view from the dual-port power module's output terminal, and Tm (impedance ratio) denotes the ratio of Zs to ZL (i.e. Tm=Zs/ZL).
According to the transfer function of the bus terminal impedance ZBus, it can be found that the impedance ZBus will be approximate to the infinity when the impedance ratio Tm equals −1, and therefore the DC power system will become unstable. When the DC power system becomes unstable, some bad influences will be caused, such as higher voltage stress, abnormal system operation or reduced system lifespan.
For monitoring the stability of the DC power system, the impedance ratio Tm needs to be analyzed in the conventional art. As shown in
However, when the DC power system includes a parallel connection of multiple modules as shown in
The load terminal current iL of the load module includes iL1, iL2, . . . , iLN, and the output terminal current is of the power module includes iSi, is2, . . . , isN. Therefore, for monitoring the stability of the DC power system 1, all the load terminal current iL (including iL1, iL2, . . . , iLN) and output terminal current is (including is1, is2, . . . , isN) need to be monitored to compute the impedance ratio Tm. However, there is a large number of the power modules 11 and load modules 12, so the complexity and difficulty for monitoring is increased a lot. Besides, this kind of monitoring belongs to an invasive manner, thus forbidden in the practical application.
Therefore, it is an important subject to provide a stability analyzing apparatus and stability analyzing method applied to a DC power system that can simplify the stability monitoring and analyzing of the DC power system to increase the efficiency of the stability analyzing.
In view of the foregoing subject, an objective of this invention is to provide a stability analyzing apparatus and stability analyzing method that can simplify the stability monitoring and analyzing of a DC power system for increasing the efficiency of the stability analyzing.
To achieve the above objective, a stability analyzing apparatus according to this invention is in cooperation with a DC power system having a bus terminal connected to at least a load. The stability analyzing apparatus comprises a perturbation signal generating module, a signal processing module and a determining module. The perturbation signal generating module generates a perturbation signal injected into the bus terminal to obtain a transfer function of the bus terminal impedance. The signal processing module is electrically connected to the perturbation signal generating module and calculates the slope of the transfer function of the bus terminal impedance to obtain a transfer function of the bus terminal impedance slope. The determining module is electrically connected to the signal processing module and determines the stability tendency of the DC power system according to the transfer function of the bus terminal impedance slope.
To achieve the above objective, a stability analyzing method according to this invention is in cooperation with a DC power system having a bus terminal connected to at least a load. The stability analyzing method comprises steps of: providing a perturbation signal injected into the bus terminal to obtain a transfer function of the bus terminal impedance; calculating the slope of the transfer function of the bus terminal impedance to obtain a transfer function of the bus terminal impedance slope; and determining the stability tendency of the DC power system according to the transfer function of the bus terminal impedance slope.
In one embodiment, the perturbation signal includes a step signal or a frequency sweep signal.
In one embodiment, the step of obtaining the transfer function of the bus terminal impedance further comprises a step of: obtaining a Bode diagram of the bus terminal impedance with different damping ratios of the DC power system according to the transfer function of the bus terminal impedance.
In one embodiment, the step of obtaining the transfer function of the bus terminal impedance slope further comprises a step of: obtaining a Bode diagram of the bus terminal impedance slope with different damping ratios of the DC power system according to the transfer function of the bus terminal impedance slope.
In one embodiment, the Bode diagram of the bus terminal impedance slope includes a gain Bode diagram and a phase Bode diagram.
In one embodiment, when the impedance slope in the gain Bode diagram of the bus terminal impedance slope is larger than 20 dB/decade or less than −20 dB/decade, the DC power system tends to instability.
In one embodiment, when the damping ratio in the Bode diagram of the bus terminal impedance slope is larger than 0.707, the DC power system tends to stability.
In one embodiment, the step of determining the stability tendency of the DC power system further comprises a step of: obtaining a Nyquist diagram of the bus terminal impedance slope with different damping ratios of the DC power system according to the Bode diagram of the bus terminal impedance slope.
In one embodiment, the step of obtaining the Nyquist diagram of the bus terminal impedance slope further comprises a step of: determining the stability tendency of the DC power system according to the Nyquist diagram of the bus terminal impedance slope.
In one embodiment, when the Nyquist contour in the Nyquist diagram of the bus terminal impedance slope exceeds the circle of the damping ratio equal to 0.707, the DC power system tends to instability.
As mentioned above, in the stability analyzing apparatus and method of this invention, a perturbation signal is injected into the bus terminal for obtaining the transfer function of the bus terminal impedance, and then the slope of the transfer function of the bus terminal impedance is calculated for obtaining the transfer function of the bus terminal impedance slope. Subsequently, the stability tendency of the DC power system can be determined according to the transfer function of the bus terminal impedance slope. In comparison with the prior art, the stability tendency of the DC power system can be determined in the invention just by injecting a perturbation signal into the bus terminal, which is a non-invasive method for the stability monitoring. Besides, in the invention, measuring all the output terminal and load terminal currents of the DC power system is not required, and therefore the stability monitoring and analyzing can be simplified a lot and the efficiency of the stability analyzing also can be increased. Besides, in one embodiment of the invention, the stability tendency of the DC power system can be determined by the gain Bode diagram of the bus terminal impedance slope, the phase Bode diagram of the bus terminal impedance slope, or the Nyquist diagram of the bus terminal impedance slope. So, this invention provides a more intuitive manner to determine the stability tendency of the DC power system.
The invention will become more fully understood from the detailed description and accompanying drawings, which are given for illustration only, and thus are not limitative of the present invention, and wherein:
The present invention will be apparent from the following detailed description, which proceeds with reference to the accompanying drawings, wherein the same references relate to the same elements.
In
The stability analyzing method of this embodiment is applied to the stability analyzing apparatus 2. As shown in
The stability analyzing method includes the steps S01 to S03.
The step S01 is to provide a perturbation signal ip that is injected into the bus terminals T1 and T2 for obtaining the transfer function of the bus terminal impedance ZBus. As shown in
Tn denotes admittance ratio, ξ denotes damping ratio, s=jω, ω denotes angular velocity (ω=2πf), and ωn denotes natural resonance frequency.
Besides, the step S01 of obtaining the transfer function of the bus terminal impedance can further include a step of obtaining a Bode diagram of the bus terminal impedance of the DC power system 1 with different damping ratios ζ by the signal processing module 22 according to the transfer function of the bus terminal impedance. Herein, the Bode diagram of the bus terminal impedance includes a gain Bode diagram and a phase Bode diagram. According to the transfer function of the bus terminal impedance, the Bode diagram and Nyquist diagram of the admittance ratio Tn and bus terminal impedance ZBus with different damping ratios ζ can be plotted. The frequency characteristics of the system in the s-domain can be analyzed by the Bode and Nyquist diagrams. By the Bode diagram, the system gain and the phase variation at different frequencies can be found. The Nyquist diagram is a complex plane, and the system's stability can be determined according to the system transfer function (i.e. admittance ratio Tn). Besides, by making the absolute value of the admittance ratio Tn equal to 1, the crossover frequency can be derived, and also the phase margin PM of the admittance ratio ζ can be obtained. When the damping ratio ζ is larger than 0.707 and the phase margin PM of the admittance ratio Tn is larger than 65°, the DC power system 1 tends to stability. The related equations are as follows:
Then, the step S02 is to calculate the slope of the transfer function of the bus terminal impedance for obtaining the transfer function of the bus terminal impedance slope. Herein, the slope of the transfer function of the bus terminal impedance is calculated by the signal processing module 22 according to the transfer function of the bus terminal impedance. In other words, the signal processing module 22 differentiates the transfer function of the bus terminal impedance to obtain the transfer function of the bus terminal impedance slope. After differentiating the transfer function of the bus terminal impedance, the transfer function of the bus terminal impedance slope can be obtained as follows:
Besides, the step S02 of obtaining the transfer function of the bus terminal impedance slope can further include a step of obtaining a Bode diagram of the bus terminal impedance slope of the DC power system 1 with different damping ratios ζ according to the transfer function of the bus terminal impedance slope. Herein, the Bode diagram of the bus terminal impedance slope of the DC power system 1 with different damping ratios is obtained by the signal processing module 22 according to the transfer function of the bus terminal impedance slope. The Bode diagram of the bus terminal impedance slope includes a gain Bode diagram and a phase Bode diagram.
Then, the step S03 is to determine the stability tendency of the DC power system 1 according to the transfer function of the bus terminal impedance slope. Herein, the stability tendency of the DC power system 1 is determined by the determining module 23 according to the Bode diagram of the bus terminal impedance slope generated by the transfer function of the bus terminal impedance slope. In the Bode diagram of the bus terminal impedance slope, when the impedance slope is larger than 20 dB/decade or less than −20 dB/decade, the DC power system 1 tends to instability. In other words, when the slope of the ascending curve is larger than 20 dB/decade, the system tends to instability. Likewise, when the slope of the descending curve is less than −20 dB/decade, the system also tends to instability. Besides, in the Bode diagram of the bus terminal impedance slope, when the damping ratio ζ is larger than 0.707, the DC power system 1 tends to stability. On the contrary, when the damping ratio ζ is less than 0.707, the DC power system 1 tends to instability. When the maximum slope is larger than 20 dB/decade, the damping ratio ζ is less than 0.707 and the phase margin is less than 65°, and therefore the DC power system 1 tends to instability. Furthermore, the maximum bus terminal impedance slope can be obtained according to the transfer function of the bus terminal impedance slope, and the curve of the maximum bus terminal impedance slope versus the damping ratio ζ can be plotted. When the maximum slop of the impedance curve is larger than 20 dB/decade, the damping ratio ζ is less than 0.707.
The step S03 of determining the stability tendency of the DC power system 1 can further include a step of obtaining a Nyquist diagram of the bus terminal impedance slope of the DC power system 1 with different damping ratios ζ according to the Bode diagram of the bus terminal impedance slope. Herein, the Nyquist diagram of the bus terminal impedance slope with different damping ratios ζ is obtained by the determining module 23. The determining module 23 plots the Nyquist diagram of the bus terminal impedance slope according to the gain Bode diagram and phase Bode diagram of the bus terminal impedance slope. In the Nyquist diagram, different circles denote different damping ratios ζ and different gains. For example, the circle of the damping ratio ζ equal to 0.707 has a radius (gain) equal to 20 dB in this embodiment.
To be noted, in this invention, the stability tendency of the DC power system 1 can be intuitively determined by the Nyquist diagram of the bus terminal impedance slope. In the Nyquist diagram of the bus terminal impedance slope, if the Nyquist contour exceeds the circle of the damping ratio ζ equal to 0.707, the DC power system 1 tends to instability. On the contrary, if the Nyquist contour doesn't exceed the circle of the damping ratio ζ equal to 0.707, the DC power system 1 tends to stability. The stability analyzing method of this invention is further illustrated as below by two practical circuits. However, the stability analyzing method of this invention can be applied to other DC distributed power systems, such as a more complicated power system.
In this embodiment, the perturbation signal ip is a step current from 0 A to 1 A.
As an embodiment, after the perturbation signal ip is injected into the bus terminals T1 and T2 of the DC power system 3, a gain-phase frequency response analyzer (e.g. PSM1735) is used to measure the bus terminals T1 and T2 so as to obtain the transfer function of the bus terminal impedance (s-domain), and thereby the Bode diagram of the bus terminal impedance can be plotted. In other words, in this invention, the frequency response analyzer directly measures the transfer function of the bus terminal impedance, and thus the Bode diagram of the bus terminal impedance can be plotted as shown in
However, since the stability tendency of the DC power system 3 can not be intuitively known from
As shown in
However, for the general users,
As shown in
By injecting the step current of 0 A˜1 A into the bus terminals T1 and T2 of the DC power system 4, the transient response of the output voltage Vo in t-domain can be obtained. From the step response waveform of the output voltage with different load resistances Ro (the damping ratio ζ is inversely proportional to the load resistance Ro), it can be observed that the overshoot is less and the DC power system 4 tends to stability if the load resistance Ro is less (i.e. the damping ratio ζ is larger) and, contrarily, that the overshoot is larger and the DC power system 4 tends to instability if the load resistance Ro is larger (i.e. the damping ratio ζ is less).
A gain-phase frequency response analyzer (e.g. PSM1735) is used to measure the bus terminals T1 and T2 for obtaining the transfer function of the bus terminal impedance (s-domain), and thereby the Bode diagram of the bus terminal impedance can be plotted as shown in
As shown in
However, for the general users,
As shown in
To be noted, in this invention, no matter how complex the DC power system is and no matter how many DC power systems are connected in parallel to form a DC distributed power system, the transfer function of the bus terminal impedance can be obtained as long as a perturbation signal is injected into the bus terminal of the DC power system. Besides, the transfer function of the bus terminal impedance slope can be further obtained by differentiating the transfer function of the bus terminal impedance. Then, by plotting the Bode diagram (including a gain Bode diagram and a phase Bode diagram) of the bus terminal impedance slope of the DC power system with different damping ratios, the stability tendency of the DC power system can be determined. Furthermore, the Nyquist diagram of the bus terminal impedance slope with different damping ratios of the DC power system can be plotted according to the gain Bode diagram and phase Bode diagram of the bus terminal impedance slope. Then, the stability tendency of the DC power system can be determined just by observing if the impedance slope curve exceeds the circle of the damping ratio equal to 0.707. Therefore, this invention provides a more intuitive manner to determine the stability tendency of the DC power system.
In summary, in the stability analyzing apparatus and method of this invention, a perturbation signal is injected into the bus terminal for obtaining the transfer function of the bus terminal impedance, and then the slope of the transfer function of the bus terminal impedance is calculated for obtaining the transfer function of the bus terminal impedance slope. Subsequently, the stability tendency of the DC power system can be determined according to the transfer function of the bus terminal impedance slope. In comparison with the prior art, the stability tendency of the DC power system can be determined in the invention just by injecting a perturbation signal into the bus terminal, which is a non-invasive method for the stability monitoring. Besides, in the invention, measuring all the output terminal and load terminal currents of the DC power system is not required, and therefore the stability monitoring and analyzing can be simplified a lot and the efficiency of the stability analyzing also can be increased. Besides, in one embodiment of the invention, the stability tendency of the DC power system can be determined by the gain Bode diagram of the bus terminal impedance slope, the phase Bode diagram of the bus terminal impedance slope, or the Nyquist diagram of the bus terminal impedance slope. So, this invention provides a more intuitive manner to determine the stability tendency of the DC power system.
Although the invention has been described with reference to specific embodiments, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed embodiments, as well as alternative embodiments, will be apparent to persons skilled in the art. It is, therefore, contemplated that the appended claims will cover all modifications that fall within the true scope of the invention.
Number | Date | Country | Kind |
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102113997 | Apr 2013 | TW | national |