This paper considers demand side management in smart power grid systems containing significant numbers of thermostatically controlled loads such as air conditioning systems, heat pumps, etc. Recent studies have shown …
This paper considers demand side management in smart power grid systems containing significant numbers of thermostatically controlled loads such as air conditioning systems, heat pumps, etc. Recent studies have shown that the overall power consumption of such systems can be regulated up and down centrally by broadcasting small setpoint change commands without significantly impacting consumer comfort. However, sudden simultaneous setpoint changes induce undesirable power consumption oscillations due to sudden synchronization of the on/off cycles of the individual units. In this paper, we present a novel algorithm for counter-acting these unwanted oscillations, which requires neither central management of the individual units nor communication between units. We present a formal proof of convergence of homogeneous populations to desynchronized status, as well as simulations that indicate that the algorithm is able to effectively dampen power consumption oscillations for both homogeneous and heterogeneous populations of thermostatically controlled loads.
This paper considers demand side management in smart power grid systems containing significant numbers of thermostatically controlled loads such as air conditioning systems, heat pumps, etc. Recent studies have shown …
This paper considers demand side management in smart power grid systems containing significant numbers of thermostatically controlled loads such as air conditioning systems, heat pumps, etc. Recent studies have shown that the overall power consumption of such systems can be regulated up and down centrally by broadcasting small setpoint change commands without significantly impacting consumer comfort. However, sudden simultaneous setpoint changes induce undesirable power consumption oscillations due to sudden synchronization of the on/off cycles of the individual units. In this paper, we present a novel algorithm for counter-acting these unwanted oscillations, which requires neither central management of the individual units nor communication between units. We present a formal proof of convergence of homogeneous populations to desynchronized status, as well as simulations that indicate that the algorithm is able to effectively dampen power consumption oscillations for both homogeneous and heterogeneous populations of thermostatically controlled loads.
A collection of thermostatically controlled loads (TCLs) -- such as air conditioners and water heaters -- can vary their power consumption within limits to help the balancing authority of a …
A collection of thermostatically controlled loads (TCLs) -- such as air conditioners and water heaters -- can vary their power consumption within limits to help the balancing authority of a power grid maintain demand supply balance. Doing so requires loads to coordinate their on/off decisions so that the aggregate power consumption profile tracks a grid-supplied reference. At the same time, each consumer's quality of service (QoS) must be maintained. While there is a large body of work on TCL coordination, there are several limitations. One is that they do not provide guarantees on the reference tracking performance and QoS maintenance. A second limitation of past work is that they do not provide a means to compute a suitable reference signal for power demand of a collection of TCLs. In this work we provide a framework that addresses these weaknesses. The framework enables coordination of an arbitrary number of TCLs that: (i) is computationally efficient, (ii) is implementable at the TCLs with local feedback and low communication, and (iii) enables reference tracking by the collection while ensuring that temperature and cycling constraints are satisfied at every TCL at all times. The framework is based on a Markov model obtained by discretizing a pair of Fokker-Planck equations derived in earlier work by Malhame and Chong [21]. We then use this model to design randomized policies for TCLs. The balancing authority broadcasts the same policy to all TCLs, and each TCL implements this policy which requires only local measurement to make on/off decisions. Simulation results are provided to support these claims.
As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time-scale fluctuations in generated power. Recent numerical …
As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time-scale fluctuations in generated power. Recent numerical modeling of thermostatically controlled loads (TCLs) has demonstrated that such load following is feasible, but analytical models that satisfactorily quantify the aggregate power consumption of a group of TCLs are desired to enable controller design. We develop such a model for the aggregate power response of a homogeneous population of TCLs to uniform variation of all TCL setpoints. A linearized model of the response is derived, and a linear quadratic regulator (LQR) has been designed. Using the TCL setpoint as the control input, the LQR enables aggregate power to track reference signals that exhibit step, ramp and sinusoidal variations. Although much of the work assumes a homogeneous population of TCLs with deterministic dynamics, we also propose a method for probing the dynamics of systems where load characteristics are not well known.
Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency-control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior, which raises the …
Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency-control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior, which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e., simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this article, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions, which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared with existing implementations.
Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior which raises …
Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e. simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this paper, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared to conventional implementations.
Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior which raises …
Thermostatically controlled loads (TCLs) can provide ancillary services to the power network by aiding existing frequency control mechanisms. TCLs are, however, characterized by an intrinsic limit cycle behavior which raises the risk that these could synchronize when coupled with the frequency dynamics of the power grid, i.e. simultaneously switch, inducing persistent and possibly catastrophic power oscillations. To address this problem, schemes with a randomized response time in their control policy have been proposed in the literature. However, such schemes introduce delays in the response of TCLs to frequency feedback that may limit their ability to provide fast support at urgencies. In this paper, we present a deterministic control mechanism for TCLs such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we provide analytic conditions which ensure that synchronization is avoided. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small. Our analytical results are verified with simulations on the Northeast Power Coordinating Council (NPCC) 140-bus system, which demonstrate that the proposed scheme offers improved frequency response compared to conventional implementations.
We explore methods to use thermostatically controlled loads (TCLs), such as water heaters and air conditioners, to provide ancillary services by assisting in balancing generation and load. We show that …
We explore methods to use thermostatically controlled loads (TCLs), such as water heaters and air conditioners, to provide ancillary services by assisting in balancing generation and load. We show that by adding simple imbedded instructions and a small amount of memory to temperature controllers of TCLs, it is possible to design open-loop control algorithms capable of creating short-term pulses of demand response without unwanted power oscillations associated with temporary synchronization of the TCL dynamics. By moving a small amount of intelligence to each of the end point TCL devices, we are able to leverage our knowledge of the time dynamics of TCLs to shape the demand response pulses for different power system applications. A significant benefit of our open-loop method is the reduction from two-way to one-way broadcast communication which also eliminates many basic consumer privacy issues. In this work, we focus on developing the algorithms to generate a set of fundamental pulse shapes that can subsequently be used to create demand response with arbitrary profiles. Demand response control methods, such as the one developed here, open the door to fast, nonperturbative control of large aggregations of TCLs.
This paper focuses on the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the device bidding and market …
This paper focuses on the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the device bidding and market clearing strategies to motivate self-interested users to realize efficient energy allocation subject to a peak energy constraint. This coordination problem is formulated as a mechanism design problem, and we propose a mechanism to implement the social choice function in dominant strategy equilibrium. The proposed mechanism consists of a novel bidding and clearing strategy that incorporates the internal dynamics of TCLs in the market mechanism design, and we show it can realize the team optimal solution. A learning scheme is proposed to address the unknown load model parameters. Numerical simulations are performed to validate the effectiveness of the proposed coordination framework.
This paper focuses on the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the device bidding and market …
This paper focuses on the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the device bidding and market clearing strategies to motivate self-interested users to realize efficient energy allocation subject to a peak energy constraint. This coordination problem is formulated as a mechanism design problem, and we propose a mechanism to implement the social choice function in dominant strategy equilibrium. The proposed mechanism consists of a novel bidding and clearing strategy that incorporates the internal dynamics of TCLs in the market mechanism design, and we show it can realize the team optimal solution. A learning scheme is proposed to address the unknown load model parameters. Numerical simulations are performed to validate the effectiveness of the proposed coordination framework.
Thermostatically controlled loads (TCLs) have the potential to be flexible and responsive loads to be used in demand response (DR) schemes. With increasing renewable penetration, DR is playing an increasingly …
Thermostatically controlled loads (TCLs) have the potential to be flexible and responsive loads to be used in demand response (DR) schemes. With increasing renewable penetration, DR is playing an increasingly important role in enhancing power grid reliability. The aggregate demand of a population of TCLs can be modulated by changing their temperature setpoint. When and/or what proportion of the population sees the setpoint change determines the change in aggregate demand. However, since the TCL population is finite, not all changes in aggregate demand can be maintained for arbitrarily long periods of time. In this paper, the dynamic behavior of a TCL fleet is modeled and used to characterize the set possible changes in aggregate demand that can be reached and the corresponding time for which the demand change can be held, for a given change in setpoint. This set is referred to, in this paper, as the reach and hold set of a TCL fleet. Furthermore, the effect of the setpoint change and ambient temperature on the reach and hold are analyzed. The characterized set is then validated through simulation using both the population TCL models and individual TCL micro-models.
We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads. This is motivated by the problem of synthesizing the demand response for …
We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads. This is motivated by the problem of synthesizing the demand response for a load serving entity (LSE) serving a population of such customers. We show how the LSE can opportunistically design the aggregate reference consumption to minimize its energy procurement cost, given day-ahead price, load and ambient temperature forecasts, while respecting each individual load's comfort range constraints. The resulting synthesis problem is shown to be amenable to optimal control techniques, but computationally difficult otherwise. Numerical simulations elucidate how the LSE can use the optimal aggregate power consumption trajectory thus computed, for the purpose of demand response.
Summary We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads such as air conditioners. This is motivated by the need to …
Summary We consider the problem of determining the optimal aggregate power consumption of a population of thermostatically controlled loads such as air conditioners. This is motivated by the need to synthesize the demand response for a load serving entity (LSE) catering a population of such customers. We show how the LSE can opportunistically design the aggregate reference consumption to minimize its energy procurement cost, given day‐ahead price, load forecast, and ambient temperature forecast, while respecting each individual load's comfort range constraints. The resulting synthesis problem is intractable when posed as a direct optimization problem after Euler discretization of the dynamics, since it results in a mixed‐integer linear programming problem with number of variables typically of the order of millions. In contrast, in this paper, we show that the problem is amenable to continuous‐time optimal control techniques. Numerical simulations elucidate how the LSE can use the optimal aggregate power consumption trajectory thus computed, for the purpose of demand response.
This contribution is based on two talks given at the XIII Mexican School of Particles and Fields. We revisit some of the results presented in [19], concerning the rate of …
This contribution is based on two talks given at the XIII Mexican School of Particles and Fields. We revisit some of the results presented in [19], concerning the rate of energy loss of an accelerating quark in strongly‐coupled N = 4 super‐Yang‐Mills.
In the design of structure of experimental platform of helicopter's rotary-wing's dynamic balance,the great seasonal temperature difference in northeastern China causes the experimental platform to expand in summer and contract …
In the design of structure of experimental platform of helicopter's rotary-wing's dynamic balance,the great seasonal temperature difference in northeastern China causes the experimental platform to expand in summer and contract in winter, thereby producing stress, which leads the experimental platform to have hidden danger in safes. In order to meet the needs of application under special environment, the external loading conditions are analyzed (mainly those caused by templrature difference). ANSYS software is employed to attain the largest stress and the largest displacement in the wing. The analysis offers the foundation for the reliable design of the experimental flatform,and gives an aided method to reduce the influence of temperature difference as much as possible.
Compliant robotics have seen successful applications in energy efficient locomotion and cyclic manipulation. However, exploitation of variable physical impedance for energy efficient sequential movements has not been extensively addressed. This …
Compliant robotics have seen successful applications in energy efficient locomotion and cyclic manipulation. However, exploitation of variable physical impedance for energy efficient sequential movements has not been extensively addressed. This work employs a hierarchical approach to encapsulate low-level optimal control for sub-movement generation into an outer loop of iterative policy improvement, thereby leveraging the benefits of both optimal control and reinforcement learning. The framework enables optimizing efficiency trade-off for minimal energy expenses in a model-free manner, by taking account of cost function weighting, variable impedance exploitation, and transition timing -- which are associated with the skill of compliance. The effectiveness of the proposed method is evaluated using two consecutive reaching tasks on a variable impedance actuator. The results demonstrate significant energy saving by improving the skill of compliance, with an electrical consumption reduction of about 30% measured in a physical robot experiment.
This paper presents a fuzzy regression analysis method based on a general quadrilateral interval type‐2 fuzzy numbers, regarding the data outlier detection. The Euclidean distance for the general quadrilateral interval …
This paper presents a fuzzy regression analysis method based on a general quadrilateral interval type‐2 fuzzy numbers, regarding the data outlier detection. The Euclidean distance for the general quadrilateral interval type‐2 fuzzy numbers is provided. In the sense of Euclidean distance, some parameter estimation laws of the type‐2 fuzzy linear regression model are designed. Then, the data outlier detection‐oriented parameter estimation method is proposed using the data deletion‐based type‐2 fuzzy regression model. Moreover, based on the fuzzy regression model, by using the root mean squared error method, an impact evaluation rule is designed for detecting data outlier. An example is finally provided to validate the presented methods.
Recent studies on control of aggregate power of an ensemble of thermostatically-controlled-loads (TCLs) have been concentrated on shifting the temperature set points of each TCL in the population. A sudden …
Recent studies on control of aggregate power of an ensemble of thermostatically-controlled-loads (TCLs) have been concentrated on shifting the temperature set points of each TCL in the population. A sudden shift in the set point, however, is known to be associated with undesirable power oscillations which require closed-loop control strategies to regulate the aggregate power consumption of the population. In this article, we propose a new approach which we term as a "safe protocol" to implement the shift in temperature set point. It is shown analytically and verified numerically that by shifting the set point "safely" the aggregate power consumption can be changed to a different value within a time frame of the order of a TCL's cycle duration and avoid the undesired oscillations seen otherwise in a "sudden" shift. We discuss how the excess aggregate energy transferred under a safe shift in the set point could potentially mitigate the burden due to abnormal energy generation within a short time span.