Individual risk in mean-field control models for decentralized control, with application to automated demand response

Flexibility of energy consumption can be harnessed for the purposes of ancillary services in a large power grid. In prior work by the authors a randomized control architecture is introduced for individual loads for this purpose. In examples it is shown that the control architecture can be designed so that control of the loads is easy at the grid level: Tracking of a balancing authority reference signal is possible, while ensuring that the quality of service (QoS) for each load is acceptable on average. The analysis was based on a mean field limit (as the number of loads approaches infinity), combined with an LTI-system approximation of the aggregate nonlinear model. This paper examines in depth the issue of individual risk in these systems. The main contributions of the paper are of two kinds: Risk is modeled and quantified: (i) The average performance is not an adequate measure of success. It is found empirically that a histogram of QoS is approximately Gaussian, and consequently each load will eventually receive poor service. (ii) The variance can be estimated from a refinement of the LTI model that includes a white-noise disturbance; variance is a function of the randomized policy, as well as the power spectral density of the reference signal. Additional local control can eliminate risk: (iii) The histogram of QoS is truncated through this local control, so that strict bounds on service quality are guaranteed. (iv) This has insignificant impact on the grid-level performance, beyond a modest reduction in capacity of ancillary service.Comment: Publication without appendix to appear in the 53rd IEEE Conf. on Decision and Control, December, 201

State Estimation for the Individual and the Population in Mean Field Control with Application to Demand Dispatch

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it has been shown that local control can be carefully designed so that the aggregate of loads behaves as a controllable resource with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements,Comment: To appear, IEEE Trans. Auto. Control. Preliminary version appeared in the 54rd IEEE Conference on Decision and Control, 201

Opportunities for Price Manipulation by Aggregators in Electricity Markets

Aggregators are playing an increasingly crucial role in the integration of renewable generation in power systems. However, the intermittent nature of renewable generation makes market interactions of aggregators difficult to monitor and regulate, raising concerns about potential market manipulation by aggregators. In this paper, we study this issue by quantifying the profit an aggregator can obtain through strategic curtailment of generation in an electricity market. We show that, while the problem of maximizing the benefit from curtailment is hard in general, efficient algorithms exist when the topology of the network is radial (acyclic). Further, we highlight that significant increases in profit are possible via strategic curtailment in practical settings

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

Balancing California's Grid Without Batteries

International audienceDemand dispatch refers to a collection of distributed control techniques to obtain grid services from flexible loads. A carefully designed control architecture can enable a collection of loads to behave in aggregate as a large virtual storage device. Grid-level ancillary services can be provided with minimal communication, while guaranteeing quality of service to the consumer. This work expands on prior work in several directions: • A natural notion of energy capacity is proposed for the special case of thermostatically controlled loads (TCLs). It is shown that this quantity is closely approximated by thermal energy capacity, which is a component of the "leaky battery model" introduced in prior work. • Simulation experiments in a distributed control setting show that these energy limits, and accompanying power capacity limits, are reliable indicators of online capacity, even for a heterogeneous population of loads. • A feedforward/feedback control scheme is proposed for a large collection of heterogeneous loads. At the local level, control loops are used to create cooperative responses from each load in a given class of homogeneous loads. This simplifies control of the aggregate based on two pieces of information: aggregate power consumption from each class of loads and the state of charge surrogate that is a part of the leaky battery model. This information is required at a slow timescale (say, 5 minute sampling). • The paper concludes with economic implications. In particular, given that dispatchable loads are a form of virtual storage and not virtual generation, it is not surprising that the use of real time or time-of-use pricing has been problematic

Aggregate capacity for TCLs providing virtual energy storage with cycling constraints

International audienceThe coordination of thermostatically controlled loads (TCLs) is challenging due to the need to meet individual loads quality of service (QoS), such as indoor temperature constraints. Since these loads are usually on/off type, cycling rate is one of their QoS metrics; frequent cycling between on and off states is detrimental to them. While significant prior work has been done on the coordination of air conditioning TCLs, the question of cycling QoS has not been investigated in a principled manner. In this work we propose a method to characterize aggregate capacity of a collection of air conditioning TCLs that respects the loads cycling rate constraints (maximum number of cycles in a given time period). The development is done within the framework of randomized local control in which a load makes on/off decisions probabilistically. This characterization allows us to propose a reference planning problem to generate feasible reference trajectories for the ensemble that respect cycling constraints. The reference planning problem manifests itself in the form a Nonlinear Programming problem (NLP), that can be efficiently solved. Our proposed method is compared to previous methods in the literature that do not enforce aggregate cycling. Enforcing individual cycling constraint without taking that into account in reference generation leads to poor reference tracking

Opportunities for Price Manipulation by Aggregators in Electricity Markets

Aggregators of distributed generation are playing an increasingly crucial role in the integration of renewable energy in power systems. However, the intermittent nature of renewable generation makes market interactions of aggregators difficult to monitor and regulate, raising concerns about potential market manipulation by aggregators. In this paper, we study this issue by quantifying the profit an aggregator can obtain through strategic curtailment of generation in an electricity market. We show that, while the problem of maximizing the benefit from curtailment is hard in general, efficient algorithms exist when the topology of the network is radial (acyclic). Further, we highlight that significant increases in profit are possible via strategic curtailment in practical settings