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Extremum Seeking Library (ESL) v1.0

The software developed is a library for the Modelica language. The library includes different extremum seeking control algorithms and examples of possible usecases. It is also intended to export the models as so called Functional Mock-up Units, which are models supported by any kind of software which supports the Functional Mock-up Interface standard.

Mueller, Joscha↗

Hierarchical Management of Distributed Energy Resources Using Chance-Constrained OPF and Extremum Seeking Control: Preprint

Distributed energy resources (DERs) are becoming an important part of distribution systems because of their economic and environmental benefits. Although their inherent intermittency and volatility introduce uncertainties into the system, they have potential to provide controllability to the system under proper coordination. In this paper, we propose a hierarchical control algorithm for distribution systems with DERs so that they have controllability similar to that of a generator bus. The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head. The proposed algorithm is tested on a modified IEEE 13-node feeder, demonstrating its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Hierarchical Management of Distributed Energy Resources Using Chance-Constrained OPF and Extremum Seeking Control

Distributed energy resources (DERs) are becoming an important part of distribution systems, because of their economic and environmental benefits. Although their inherent intermittency and volatility introduce uncertainties into the electric power system, they have the potential to provide controllability to the system under proper coordination. In this paper, we propose a hierarchical control algorithm for distribution systems with DERs so that they have controllability similar to a generator bus. The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head. The proposed algorithm is tested on a modified IEEE 13-node feeder, demonstrating its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Batch Measurement Extremum Seeking Control of Distributed Energy Resources to Account for Communication Delays and Information Loss

Distributed Energy Resources (DER) have great potential to enhance the operation of electric power distribution systems. Previously, we explored the use of 2 Dimensional Extremum Seeking (2D-ES) control algorithms to enable model-free optimal control of DER to provide grid services to both the distribution and transmissions systems. Motivated by preliminary deployments of DER managed by 2D-ES algorithms in hardware-in-the-loop tests and in operational distribution grids, in this work, we extend the control scheme to accommodate communication delays and information loss. We propose a modification to the 2D-ES scheme to allow for the processing of batches of possibly noncontiguous objective function measurements at unknown and possibly uneven intervals. We provide a proof of the convergence of the batch 2D-ES (2D-BES) scheme when optimizing a generic convex objective function, as well as simulation results that demonstrate the suitability of the approach for substation active and reactive power target tracking.

Sankur, Michael↗

Extremum seeking control of distributed energy resources with decaying dither and equilibrium-based switching

Embodiments relate to an operating system coupled to and controlling at least one Distributed Energy Resource (DER) in a smart grid and includes an electricity distribution network and a 2-dimensional Extremum Seeking (2D-ES) controller coupled to network. The electricity distribution network has first and second inputs and one output and maps all active power and reactive power inputs to the smart grid providing measurements of an objective function. The 2D-ES controller controls the DER and includes an active power loop and a reactive power loop. The active power loop is in communication with the first input and the output, governs active power contribution, and receives measurements of the objective function which contain static and oscillatory components. The reactive power loop is in communication with the second input and the output, governs reactive power contribution, and receives measurements of the objective function which contain static and oscillatory components.

Arnold, Daniel↗

Black-box optimization of a closed-circuit reverse osmosis system for desalination through extremum seeking control

We study the minimization of the cost function of a closed-circuit desalination reverse osmosis (CCRO) system, which is used for producing drinking water. The cost function is a trade-off between the specific energy consumption and the specific brine management cost. The extremum-seeking controller (ESC) manipulates the critical electric conductivity of the brine to minimize the cost function. Experiments were designed in which the composition of the feed salinity is increased to test the controller’s ability to converge to a new optimum. The ESC was able to shift the critical conductivity to a new optimum, which resulted in a 9% improvement in the cost function.

Chowdhury, Dhruba↗

Extremum Seeking Control of Smart Inverters for VAR Compensation

Reactive power compensation is used by utilities to ensure customer voltages are within pre-defined tolerances and reduce system resistive losses. While much attention has been paid to model-based control algorithms for reactive power support and Volt Var Optimization (VVO), these strategies typically require relatively large communications capabilities and accurate models. In this work, a non-model-based control strategy for smart inverters is considered for VAR compensation. An Extremum Seeking control algorithm is applied to modulate the reactive power output of inverters based on real power information from the feeder substation, without an explicit feeder model. Simulation results using utility demand information confirm the ability of the control algorithm to inject VARs to minimize feeder head real power consumption. In addition, we show that the algorithm is capable of improving feeder voltage profiles and reducing reactive power supplied by the distribution substation.

Arnold, Daniel↗

Extremum seeking for optimal control problems with unknown time-varying systems and unknown objective functions

We consider the problem of optimal feedback control of an unknown, noisy, time-varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. In this paper, we present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time-varying systems.

42 ENGINEERING↗

Extremum seeking-based optimization of high voltage converter modulator rise-time

We digitally implement an extremum seeking (ES) algorithm, which optimizes the rise time of the output voltage of a high voltage converter modulator (HVCM) at the Los Alamos Neutron Science Center (LANSCE) HVCM test stand by iteratively, simultaneously tuning the first 8 switching edges of each of the three phase drive waveforms (24 variables total). We achieve a 50 μs rise time, which is reduction in half compared to the 100 μs achieved at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. Considering that HVCMs typically operate with an output voltage of 100 kV, with a 60Hz repetition rate, the 50 μs rise time reduction will result in very significant energy savings. The ES algorithm will prove successful, despite the noisy measurements and cost calculations, confirming the theoretical results that the algorithm is not affected by noise whose frequency components are independent of the perturbing frequencies.

43 PARTICLE ACCELERATORS↗