Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs
Abstract
:1. Introduction
- A self-triggered control scheme is applied to the frequency regulation of the power grid;
- An online optimization method is used to extend the triggering period for reducing communication cost; and
- Communication cost and parameters of control system for power grid are estimated and optimized, so that the cost of control system can be guaranteed under a required level.
2. System Model of Power Grid
2.1. Dynamic Model of Power Grid
- and are TBC gain and frequency bias, respectively.
- and are the governor and gas turbine constant, respectively.
- and D are the inertia and damping constant, respectively.
- and are the regulation and synchronizing constant, respectively.
- is a governor input of a gas turbine generator.
- is an output of the gas turbine generator.
- is an output of wind power generation.
- is the load fluctuation except controllable load.
- is an output of the battery electric storage system.
- and is the tie-line power low deviation.
- is the output power of area i, which is delivered to area j.
- in Equation (1) shows the electric power generation of subsystem i and the supply error margin of power consumption.
2.2. The Self-Triggered Controller
- First, obtain the system state of each subsystem, when the time for triggering is up;
- Second, calculate the time for the next triggering;
- Finally, apply the new control output, which is calculated by using the system state obtained in step 1.
2.3. Exponential Stability and Cost Function
3. The Self-Triggered Controller Design
3.1. Function for Self Triggering
3.2. The Selection of Feedback Gain for Controller
- For a given , is calculated by conventional discrete robust control technique;
- The upper bound of cost function is obtained by Theorem 4, and can be calculated;
- Update by numerical optimization algorithms (such as GA optimization algorithm) with obtained in previous step;
- Return to the first step until the stop criteria is satisfied.
3.3. Event-Triggered Control Algorithm
4. Simulation Results
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Proof of Theorem 1
Appendix B. Proof of Theorem 3
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Parameters ($) | Symbols (Unit) ($) | Values | ||
---|---|---|---|---|
Subsystem 1 | Subsystem 2 | Subsystem 3 | ||
Inertia constant | M (puMw s/Hz) | 0.20 | 0.14 | 0.16 |
Damping constant | D (puMw/Hz) | 0.26 | 0.26 | 0.23 |
Governor constant | (s) | 0.20 | 0.20 | 0.12 |
Gas turbine constant | (s) | 5.0 | 4.5 | 5.0 |
Regulation constant | (Hz/pu Mw) | 2.5 | 2.5 | 1.5 |
Synchronizing constant | (pu Mw) | 0.50 | 0.5 | 0.5 |
TBC gain | 0.1 | 0.08 | 0.1 | |
Frequency bias | (Mw/Hz) | 0.1 | 0.1 | 0.08 |
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Zhu, Z.; Sun, J.; Qi, G.; Chai, Y.; Chen, Y. Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs. Appl. Sci. 2017, 7, 688. https://doi.org/10.3390/app7070688
Zhu Z, Sun J, Qi G, Chai Y, Chen Y. Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs. Applied Sciences. 2017; 7(7):688. https://doi.org/10.3390/app7070688
Chicago/Turabian StyleZhu, Zhiqin, Jian Sun, Guanqiu Qi, Yi Chai, and Yinong Chen. 2017. "Frequency Regulation of Power Systems with Self-Triggered Control under the Consideration of Communication Costs" Applied Sciences 7, no. 7: 688. https://doi.org/10.3390/app7070688