1. Exploring Optimal Control Strategies for Enhanced Grid Frequency Regulation
Chris Briere, Hector Pulgar-Painemal, Seddik M. Djouadi
Dept. of Electrical Engineering and Computer Science
University of Tennessee - Knoxville

2. The Problem
Adequate grid frequency regulation is important for ensuring Power System Stability.
The goal of this research is to address the problem of Primary Frequency Regulation though the use of Discrete Control mechanisms.
This approach has the potential to unlock new possibilities for addressing the frequency regulation problem.

3. The Differential Algebraic System:
The Model
The Differential Algebraic System:

4. Optimal Pulse Control
An interior point optimization algorithm was used to determine the optimal pulse signal which minimizes the maximum frequency excursion.
Critical Injection
Window
Lpulse
Fig. 3. Contour plot and level sets of the maximum frequency deviation, Lpulse, scaled by a factor of 1000 for a 0.15 pu pulse of injected power, Pinj.
Fig. 4. Response of the system with the with optimal pulse of injected power, u*.

5. Linearizing the DAE System
The linearized system can be represented in a more compact form where ‘x’ represents the differential variables, ‘y’ the algebraic, ‘u’ the control variable, and ‘w’ the disturbance.
The algebraic variables can be solved for explicitly yielding a single set of ordinary differential equations.
Linearizing the Differential Algebraic System:

6. Optimal Control Formulation
Optimal Control Problem:
The objective of the optimal control problem is to determine the optimal control input which minimizes the integral of an objective function plus a penalty term.
The optimal control problem was solved in Matlab using the Forward-Backward Sweep Method.
Hamiltonian of the ODE-OCP:
Objective Function and Penalty Term:

7. Forward-Backward Sweep Method
Convergence Satisfied!

8. Optimal Control Results
The Lloyd algorithm was used to quantize the optimal control signal into a pulse signal.
Results of the optimal control show a significant improvement in reducing the maximum frequency excursion.
Quantization level
Switching threshold
Fig. 5. Response of the system with the with optimal control input, u*, and the quantized optimal control input, uq*.

9. Acknowledgements
This work was supported primarily by the National Science Foundation under Grant No , the Engineering Research Center Program of the National Science Foundation and the Department of Energy under NSF Award No. EEC and the CURENT Industry Partnership Program.
Other US government and industrial sponsors of CURENT research are also gratefully acknowledged.

10. Thanks for your attention! Questions?

11. Extra Slides…
Effectiveness of discrete control with increased renewable energy penetration…
The primary problem is the slow response of thermal power plants which can exhibit significant frequency excursions when there is a rapid change in electric generation or demand. As renewable energy penetration increases the impact on the fewer remaining thermal plants is likely to be more severe (i.e. lower frequency nadir). We believe that this type of discrete control has great potential for alleviating this problem.

12. Extra Slides…
Why is a linear model enough when the real power system contains nonlinearities?
In order for a control approach to be feasible for real-time implementation, it will be necessary to make certain simplifying assumptions. Linearization is one such strategy which has shown great potential with other challenging models.
It has been shown that governor deadband could be a key nonlinearity to consider, an insight which has been validated with actual FNET data for the Eastern Interconnection.
G. Kou, P. Markham, S. Hadley, T. King and Y. Liu, "Impact of Governor Deadband on Frequency Response of the U.S. Eastern Interconnection," in IEEE Transactions on Smart Grid, vol. 7, no. 3, pp , May 2016.

13. Extra Slides…
What components can be targeted for this type of discrete control?
Demand response: large industrial loads or aggregated commercial and residential loads
Energy storage systems: Batteries, flywheels, pumped hydroelectric, ect.

14. Extra Slides…

15. Extra Slides…
IEESGO Governor Model

16. Extra Slides… Future Work
Application to a more realistic grid model with a larger, more interconnected system.
Refine the method of frequency excursion measurement with the goal of maintaining a fast, reliable control response while mitigating the effect of measurement noise and unwanted control action due to electromechanical modes.
Consider coordinated control with multiple actuation mechanisms