Optimal Ensemble Control of Loads in Distribution Grids with Network Constraints

Flexible loads, e.g. thermostatically controlled loads (TCLs), are technically feasible to participate in demand response (DR) programs. On the other hand, there is a number of challenges that need to be resolved before it can be implemented in practice en masse. First, individual TCLs must be aggregated and operated in sync to scale DR benefits. Second, the uncertainty of TCLs needs to be accounted for. Third, exercising the flexibility of TCLs needs to be coordinated with distribution system operations to avoid unnecessary power losses and compliance with power flow and voltage limits. This paper addresses these challenges. We propose a network-constrained, open-loop, stochastic optimal control formulation. The first part of this formulation represents ensembles of collocated TCLs modelled by an aggregated Markov Process (MP), where each MP state is associated with a given power consumption or production level. The second part extends MPs to a multi-period distribution power flow optimization. In this optimization, the control of TCL ensembles is regulated by transition probability matrices and physically enabled by local active and reactive power controls at TCL locations. The optimization is solved with a Spatio-Temporal Dual Decomposition (ST-D2) algorithm. The performance of the proposed formulation and algorithm is demonstrated on the IEEE 33-bus distribution model.Comment: 7 pages, 6 figures, accepted PSCC 201

Mean Field Control for Efficient Mixing of Energy Loads

We pose an engineering challenge of controlling an Ensemble of Energy Devices via coordinated, implementation-light and randomized on/off switching as a problem in Non-Equilibrium Statistical Mechanics. We show that Mean Field Control} with nonlinear feedback on the cumulative consumption, assumed available to the aggregator via direct physical measurements of the energy flow, allows the ensemble to recover from its use in the Demand Response regime, i.e. transition to a statistical steady state, significantly faster than in the case of the fixed feedback. Moreover when the nonlinearity is sufficiently strong, one observes the phenomenon of "super-relaxation" -- where the total instantaneous energy consumption of the ensemble transitions to the steady state much faster than the underlying probability distribution of the devices over their state space, while also leaving almost no devices outside of the comfort zone.Comment: 7 pages, 5 figure

An online disaggregation algorithm and its application to demand control

National audienceThe increase of renewable energy has made the supply-demand balance of power more complex to handle. In [1], the authors designed randomized controllers to obtain ancillary services to the power grid by harnessing inherent flexibility in many loads. However these controllers suppose that we know the consumption of each device that we want to control. This introduce the cost and the social constraint of putting sensors on each device of each house. Therefore, our approach was to use Nonintrusive Appliance Load Monitoring (NALM) methods to solve a disaggregation problem. The latter comes down to estimating the power consumption of each device given the total power consumption of the whole house. We started by looking at the Factorial Hierarchical Dirichlet Process-Hidden Semi-Markov Model (Factorial HDP-HSMM) introduced in [2]. In our application, the total power consumption is considered as the observations of this state-space model and the consumption of each device as the state variables. Each of the latter is modelled by an HDP-HSMM which is an extension of a Hidden Markov Model. However, the inference method used in [2] is based on Gibbs sampling and has a complexity of O(T 2 N +T N 2) where T is the number of observations and N is the number of hidden states. As our goal is to use the randomized controllers with our estimations, we wanted a method that does not scale with T. Therefore, we developed an online algorithm based on particle filters. Because we worked in a Bayesian setting, we had to infer the parameters of our model. To do so, we used a method called Particle Learning which is presented in [3]. The idea is to include the parameters in the state space so that they are tied to the particles. Then, for each (re)sampling step, the parameters are sampled from their posterior distribution with the help of Bayesian sufficient statistics. We applied the method to data from Pecan Street. Using their Dataport, we have collected the power consumption of each device from about a hundred houses. We selected the few devices that consume the most and that are present in most houses. We separated the houses in a training set and a test set. For each device of each house from the training set, we estimated the operating modes with a HDP-HSMM and used these estimations to compute estimators of the priors hyperparameters. Finally we applied the particle filters method to the test houses using the computed priors. The algorithm performs well for the device with the highest power consumption, the air compressor in our case. We will discuss ongoing work where we apply the "Thermo-statically Controlled Loads" example of [1] using our estimations of this air compressor's operating modes

Control oriented modeling of TCLs

Thermostatically controlled loads (TCLs) have the potential to be a valuable resource for the Balancing Authority (BA) of the future. Examples of TCLs include household appliances such as air conditioners, water heaters, and refrigerators. Since the rated power of each TCL is on the order of kilowatts, to provide meaningful service for the BA, it is necessary to control large collections of TCLs. To perform design of a distributed coordination/control algorithm, the BA requires a control oriented model that describes the relevant dynamics of an ensemble. Works focusing on solely modeling the ensemble date back to the 1980's, while works focusing on control oriented modeling are more recent. In this work, we contribute to the control oriented modeling literature. We leverage techniques from computational fluid dynamics (CFD) to discretize a pair of Fokker-Planck equations derived in earlier work [1]. The discretized equations are shown to admit a certain factorization, which makes the developed model useful for control design. In particular, the effects of weather and control are shown to independently effect the system dynamics.Comment: 9 pages, 5 figure

Kullback-Leibler-Quadratic Optimal Control

This paper presents advances in Kullback-Leibler-Quadratic (KLQ) optimal control: a stochastic control framework for Markovian models. The motivation is distributed control of large networks. As in prior work, the objective function is composed of a state cost in the form of Kullback-Leibler divergence plus a quadratic control cost. With this choice of objective function, the optimal probability distribution of a population of agents over a finite time horizon is shown to be an exponential tilting of the nominal probability distribution. The same is true for the controlled transition matrices that induce the optimal probability distribution. However, one limitation of the previous work is that randomness can only be introduced via the control policy; all uncontrolled (natural) processes must be modeled as deterministic to render them immutable under an exponential tilting. In this work, only the controlled dynamics are subject to tilting, allowing for more general probabilistic models. Another advancement is a reduction in complexity based on lossy compression using transform techniques. This is motivated by the need to consider time horizons that are much longer than the inter-sampling times required for reliable control. Numerical experiments are performed in a power network setting. The results show that the KLQ method enables the aggregate power consumption of a collection of flexible loads to track a time-varying reference signal, while simultaneously ensuring each individual load satisfies its own quality of service constraints

Distributed control of a fleet of batteries

International audienceBattery storage is increasingly important for grid-level services such as frequency regulation, load following, and peak-shaving. The management of a large number of batteries presents a control challenge: How can we solve the apparently combinatorial problem of coordinating a large number of batteries with discrete, and possibly slow rates of charge/discharge? The control solution must respect battery constraints, and ensure that the aggregate power output tracks the desired grid-level signal. A distributed stochastic control architecture is introduced as a potential solution. Extending prior research on distributed control of flexible loads, a randomized decision rule is defined for each battery of the same type. The power mode at each time-slot is a randomized function of the grid-signal and its internal state. The randomized decision rule is designed to maximize idle time of each battery, and keep the state-of-charge near its optimal level, while ensuring that the aggregate power output can be continuously controlled by a grid operator or aggregator. Numerical results show excellent tracking, and low stress to individual batteries