Distributed aggregate tracking of heterogeneous thermostatically controlled load clusters

Abstract

This paper proposes a distributed aggregate tracking strategy for multiple heterogeneous TCL (thermostatically controlled load) clusters under a bus load agent. Specifically, these heterogeneous TCLs are composed of lots of homogeneous load clusters and each one can be modeled by a TISO (third-input single-output) aggregate model with the aggregate power being the output, and the changes of ambient/setpoint temperature and the ramping rate of the setpoint temperature being inputs. According to the aggregate model of the TCL cluster, a distributed leader-following communication protocol is proposed such that each cluster just needs to communicate with its neighbors and partial clusters are connected to the load agent, and then the aggregate power tracking problem can be solved in a distributed way. Finally, numerical results are conducted to demonstrate the effectiveness and performance of the proposed aggregate tracking algorithm.

Keywords

Aggregate tracking distributed control thermostatically controlled loads (TCLs)

1 Introduction

Thermostatically controlled loads (TCLs), such as air conditioners, water heaters, heat pumps, ice thermal energy storage and refrigerators in civil or commercial loads, have already accounted for a great part of the total power consumption around the world [1 –4]. And these controllable loads in the demand side are often included in demand response (DR) programme, which in turn make them become active participants in the power system operations. The aggregated loads can provide different kinds of ancillary services, both in the real-time balancing and the planning stage, such as frequency regulation [5, 6], load following [7, 8], spanning reserve [9, 10]. On the other hand, these controllable loads can also be involved in the electricity market to become responsive loads under real-time pricing or critical peak pricing mechanism [11, 12], which is beneficial to the steady-state operation of power systems.

If the TCL is operated in a scenario that its local thermostat is free of outside intervention, then the internal temperature of the mass will converge to a steady period orbit with the corresponding cooling period and heating period [13]. The objective of the thermostat is to maintain the mass’s temperature near the customer’s setpoint value with a predefined temperature deadband. And the TCL switches its operational state (on and off) when the internal temperature hits the boundaries of the temperature deadband [14]. The power demand of the TCL over a period is determined by the initial temperature value, the temperature setpoint of the mass (or the on/off state) and the ambient temperature around the mass. The only one controllable variable is the temperature setpoint. There are mainly two control mechanisms for the TCLs under control: on/off control [15] and continuous setpoint control [16], which in turn can regulate the aggregate power consumption.

We will investigate the demand response regulation problem of a large population of thermostatically controlled loads and design a distributed control strategy to drive the aggregate power of numerous heterogeneous TCLs such that the aggregate power can track a reference power trajectory, i.e., second control mode in the power system. In the power grid, a large number of individual appliances are distributed dispersedly, which results in the control of these TCL become a technical challenge since the power grid is a distributed structure [15]. In order to calculate the aggregate power of all TCLs, the real time operation states of each TCL need to be measured, which is low efficient especially when there are a large number of TCLs in DR program. Therefore, the aggregate approximate modeling is necessary which is able to provide an estimation of the aggregate power based on an approximate aggregate model. Great effort has been devoted to the modeling of homogeneous or heterogeneous TCL clusters, such as state-queueing model [17], temperature setpoint model [18], a second-order dynamic model [19 –22], Markov switching model [23].

Here, we utilize the aggregated model proposed in our recent paper [7] to estimate the aggregate power of numerous homogeneous TCL clusters for aggregate tracking. Specifically, all heterogeneous TCLs are divided to multiple homogeneous clusters and each one is modeled by a TISO aggregate model. Such as all the homogeneous TCLs in a community can be modeled by a load cluster. Therefore, several heterogeneous clusters may emerge in each community. In our previous paper [7], we investigated the centralized load following control problem and the results are further extended to a distributed aggregate tracking scenario. Specifically, we utilize a distributed pinning consensus control algorithm [24] to drive the operation of multiple TCL clusters for performing the aggregate tracking problem.

Distributed control is inexpensive to be implemented compared with centralized control, and suitable for the distributed structure of TCLs in power grids, which has the good reliable, scalability, easy implementation, low complexity, and high robustness [25]. Distributed DR has became a hot research topic in the literature [26, 27]. Distributed optimization or control algorithms were utilized to solve the DR strategy for electric vehicles [28, 29]. The authors in [30] investigated the distributed DR real-time power balance problem in a neighborhood with a population of power customers and renewable energy sources. Distributed load shifting is investigated in [31] for an islanded microgrid (MG). However, few publications are concerned with distributed control of TCL clusters for load following service.

On the other hand, pinning control [32, 33] indicates that the global system information can be accessed only by a small fraction of terminals, and the rest of terminals access data each other based on a spare communication network. This idea can be utilized to handle the optimization or control problems with global constraints. For example, distributed pinning droop control mechanism has been introduced in the isolated converter-fed microgrids for active and reactive power sharing problem [34]. Secondary voltage pinning control strategy was proposed in [35] for an isolated microgrid, where pinning designs demonstrated satisfactory control performances. We will consider the distributed pinning load following control of multiple heterogeneous TCL clusters for DR regulation in smart grids. The proposed control design can drive the consumption of aggregate power of DR clusters with any size of TCLs and any initial states of each TCL.

The rest of this paper is organized as follows. The basic aggregate model of TCLs and problem formulation are illustrated in Section 2. In Section 3, the detailed distributed pinning load following control is designed for multiple heterogeneous TCL clusters. Simulation results on a typical distributed load cluster system are provided in Section 4. Discussions on the proposed distributed algorithm is shown in Section 5. Finally, Section 6 concluded our work.

Notations: The communication network among TCL clusters is modeled by a digraph $G = {V, E, A}$ with $V = {1, 2, \dots, N}$ being the nodes’ set (index of the TCL clusters) and $E$ being the links’ set (communication lines among clusters). The edge $e_{ij} = (i, j) \in E$ denotes the information flow if from jth unit to ith unit. A digraph degenerates to an undirected if $e_{ij} \in E$ implies $e_{ji} \in E$ . A directed spanning tree of $G$ is a directed tree (i.e., every node in the network, except the root node, has exactly one parent node) with the same node set $V$ and the edge set is a subset of $E$ . The adjacency matrix $A \in R^{N \times N}$ of a digraph $G$ is defined as a_ij ≥ 0, and $a_{ij} = 1 \Leftrightarrow e_{ji} (j ↪ i) \in E$ , while a_ij = 0 if $e_{ji} \notin E$ . Furthermore, self links are not allowed in the network, i.e., a_ii = 0. The Laplacian matrix $L = D - A$ , where matrix $D$ is a diagonal matrix with d_ii = ∑_j≠ia_ij. The maximal node in-degree of digraph $G$ is defined by d_max = max {d_ii}.

2 Primaries and problem formulation

2.1 Aggregation model for the TCL cluster

Suppose a population of heterogeneous TCLs under a common bus is grouped into several homogeneous clusters, where each cluster is approximated by a TISO bilinear system [7] as follows, ${\begin{matrix} \dot{x} (t) = A x (t) + B x (t) u (t), \\ y (t) = \tilde{C} x (t), u (t) = \frac{1}{C R} (Δ θ_{s e t} (t) - Δ θ_{a} (t)) + Δ {\dot{θ}}_{s e t} (t), \\ Δ θ_{a} (t) = θ_{a} (t) - θ_{b a s e}, \\ Δ θ_{s e t} (t) = θ_{s e t} (t) - θ_{s e t}^{d e s}, \end{matrix}$ (1) where $x (t) \in ℝ^{Q}$ is the state bin denoting the average number of off or on TCLs in each temperature subinterval of the temperature deadband; $y (t) \in ℝ$ is the estimated aggregate power output of the TCL cluster; $u (t) \in ℝ$ is an incorporated control input.

And coefficients C [kWh/°C] and R [°C/kW] are the thermal capacitance and thermal resistance of the TCL. θ_a (t) is the time-varying ambient temperature; θ_base is the base value of the ambient temperature; θ_set (t) is the temperature setpoint; and $θ_{set}^{des}$ is the preferred setpoint temperature. $| Δ θ_{set} (t) | \leq Δ θ_{set}^{\max}$ , i.e., bounded by the comfort levels of customers; $Δ {\dot{θ}}_{set}$ is the changing rate of the temperature setpoint, which must lie in the interval $[{\bar{α}}_{on}, {\bar{α}}_{off}]$ so as to make the aggregate bilinear model (1) make senses, the illustration can be found in the aggregate model proposed in [18] similarly;

Parameters ${\bar{α}}_{on}$ , ${\bar{α}}_{off}$ are functions with the independent variables θ_base and $θ_{set}^{des}$ , given as ${\begin{matrix} {\bar{α}}_{o n} (θ_{b a s e}, θ_{s e t}^{d e s}) = \frac{1}{C R} (θ_{b a s e} - θ_{s e t}^{d e s} - R P_{r}), \\ {\bar{α}}_{o f f} (θ_{b a s e}, θ_{s e t}^{d e s}) = \frac{1}{C R} (θ_{b a s e} - θ_{s e t}^{d e s}), \end{matrix}$ where P_r [kW] is the energy transfer rate to or from the thermal mass.

Remark 1. The temperature deviation Δθ_a (t) is always bounded. Therefore, the incorporated control input is also a bounded variable as well. As for the time-varying ambient temperature θ_a (t), we introduce a base value θ_base, which is predefined according to the practical experience. Hence, the time-varying θ_a (t) is transformed to the sum of a fixed value and a deviation value, i.e., θ_a (t) = θ_base + Δθ_a (t). The main reason lies in that the coefficient matrix A of Eq.(1) is a fixed one once the value of θ_base is fixed. Meanwhile, the time-varying division Δθ_a (t) is transformed to be an input.

The coefficient matrices for system (1) are given by $A = A ({\bar{α}}_{on}, {\bar{α}}_{off}) \in ℝ^{Q \times Q}$ , $B \in ℝ^{Q \times Q}$ , and $\tilde{C} = [\underset{N}{\underset{︸}{0, \dots, 0}}, \underset{Q - N}{\underset{︸}{P_{r} / η, \dots, P_{r} / η}}]$ . The matrix A is a sparse matrix, which can be rewritten as the following block structure, $\begin{matrix} A ({\bar{α}}_{on}, {\bar{α}}_{off}) = [\begin{matrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{matrix}], \end{matrix}$ where $A_{11} \in ℝ^{N \times N}$ and $A_{22} \in ℝ^{(Q - N) \times (Q - N)}$ are given as $\begin{matrix} A_{11} = [\begin{matrix} - {\bar{α}}_{off} \\ {\bar{α}}_{off} & - {\bar{α}}_{off} \\ ⋱ & ⋱ \\ {\bar{α}}_{off} & - {\bar{α}}_{off} \\ ⋱ & ⋱ \\ {\bar{α}}_{off} & - {\bar{α}}_{off} \end{matrix}], \\ A_{22} = [\begin{matrix} {\bar{α}}_{on} & - {\bar{α}}_{on} \\ ⋱ & ⋱ \\ {\bar{α}}_{on} & - {\bar{α}}_{on} \\ ⋱ & ⋱ \\ {\bar{α}}_{on} & - {\bar{α}}_{on} \\ {\bar{α}}_{on} \end{matrix}], \end{matrix}$ and other elements of matrices A₁₂, A₂₁ are zeroes. The matrix B = A (-1, - 1) can be obtained by setting ${\bar{α}}_{on}$ $= {\bar{α}}_{off} = - 1$ in matrix A.

For the TCLs in a load cluster, the real time temperature setpoint θ_set (t) can be obtained by $θ_{set} (t) = θ_{set}^{des} + Δ θ_{set} (t)$ . According to the generated temperature setpoint control signal, each TCL regulate the inner temperature of the mass and change the active power consumption over an operational period.

Suppose there are N_L homogeneous TCLs (i.e., they have the same parameters C, R, P_r, η) in a common load cluster. The electrical model [36] of each TCL is shown in Fig. 1.

Fig.1

The simplified electrical model of a TCL.

Then, the dynamical model of the ith TCL can be easily derived, given by the following differential equation [37]:

$\frac{d θ_{i} (t)}{d t} = \frac{1}{CR} (θ_{a} (t) - θ_{i} (t) - s_{i} (t) {RP}_{r}),$ (2) for i = 1, …, N_L, where θ_i (t) is the inner temperature of ith TCL and P_r is defined the same as previously. As for cooling TCLs, P_r > 0; and P_r < 0 for heating TCLs. s_i (t) is the operation state, which is governed by a thermostatic switching law with predetermined temperature deadband δ_db,i. For example, the switching law of s_i (t) for the cooling TCLs is provided as follows: $\begin{matrix} s_{i} (t) = {\begin{matrix} 0 & if s_{i} (t - ɛ) = 1 & θ_{i} (t) < θ_{i}^{-} \\ 1 & if s_{i} (t - ɛ) = 0 & θ_{i} (t) > θ_{i}^{+} \\ s_{i} (t - ɛ) & otherwise \end{matrix} \end{matrix}$ in which, ɛ is the sampling period, and $θ_{i}^{-}, θ_{i}^{+}$ are the boundaries of the temperature deadband:

$θ_{i}^{-} = θ_{set, i} - \frac{δ_{db, i}}{2}; θ_{i}^{+} = θ_{set, i} + \frac{δ_{db, i}}{2} .$ (3)

Therefore, the direct physical aggregate power output of all TCLs can be derived as:

$P_{T} (t) = \sum_{i = 1}^{N_{L}} \frac{1}{η} s_{i} (t) P_{r},$ (4) where η denotes the power energy’s transmission efficiency.

The approximated aggregate power derived from the TISO model is highly identical with the physical aggregate power from the physical-based model (4). Besides, the model is more accurate especially when the temperature deadband is divided with a thinner partition [7]. In the following, we mainly focus on the distributed aggregate load following problem of multiple heterogenous TCL clusters.

3 Distributed pinning control of multiple aggregated TCLs

This section is to propose a distributed load control strategy such that the aggregate TCLs can provide the load following service, i.e., tracking a given reference power trajectory. Under a bus load agent, there are numerous heterogeneous TCL clusters and each cluster is constituted of multiple homogeneous TCLs. The function of flexible load agents is similar to the negative generating units, which can provide min-min ancillary services.

Due to the flexibility of the TCL cluster, they may plug-in or plug-out based on their own enabling conditions. The distributed technique is suitable for this scenario of multiple interactive units, which enable the participants can be plugged-in and plugged-out flexibly. In the following, we consider the real time aggregate tracking P_ref (t) problem of N TCL clusters and the ith cluster is given by the following TISO bilinear model, ${\begin{matrix} {\dot{x}}_{i} (t) = A_{i} x_{i} (t) + B_{i} x_{i} (t) u_{i} (t), \\ u_{i} (t) = \frac{1}{C_{i} R_{i}} (Δ θ_{s e t, i} (t) - Δ θ_{a} (t)) \\ + Δ {\dot{θ}}_{s e t, i} (t), y_{i} (t) = C_{i} x_{i} (t), \\ i = 1, 2 \dots, N . \end{matrix}$ (5)

Therefore, the estimated aggregate power P_est (t) of the load agent is obtained by $P_{est} (t) = \sum_{i = 1}^{N} y_{i} (t)$ , which can be measured by the transformer terminal unit (TTU) of the bus load agent. By utilizing the distributed pinning consensus control, the incorporated control input u_i (t) is synchronized to a common reference control variable U_ref, which is generated by a virtual centralized pinner regulated by the response variation P_est (t) - P_ref (t) between the estimated aggregated power and the reference power. The dynamics of the reference input is modeled by the following first-order regulation differential equation:

$\begin{matrix} {\dot{U}}_{ref} (t) = & μ_{1} (P_{est} (t) - P_{ref} (t)) \\ + μ_{2} \int_{t_{0}}^{t} (P_{est} (t) - P_{ref} (t)) d t, \end{matrix}$ (6) where the coefficients μ₁ and μ₂ are approximate positive regulation gains and the initial value is set by U_ref (t₀) =0; U_ref (t) is bounded by the $U_{ref}^{\max}$ and the control structure of the centralized pinner is given in Fig. 2.

Fig.2

Control structure for the centralized pinner (6).

For all TCLs under the bus load agent, the aggregate power is changed by regulating the temperature setpoint continuously. The reference input variable is calculated at the load agent, which can drive the aggregate power of the load agent track the reference power trajectory orderly. Since the TCLs are distributed decentralized in different control area in the smart grids, we consider the distributed pinning cnsensus control for all TCL clusters in the load agent such that all clusters can achieve the expected aggregate tracking in a cooperative way. Here, distributed pinning control can deal with the global constraint of multiple interactive units, which is given as:

$\begin{matrix} u_{i} (t) ≜ {\dot{U}}_{i} (t) = & β \sum_{j = 1}^{N} a_{ij} (U_{j} (t) - U_{i} (t)) \\ - β d_{i} (U_{i} (t) - U_{ref} (t)), \end{matrix}$ (7) where the initial value U_i (t₀) =0; a_ij is the element of the adjacent matrix $A$ of the communication network among the TCL clusters; a_ij = 1 if there exists a communication link between ith node and jth node, otherwise a_ij = 0; d_i = 1 if the ith TCL cluster is pinned by the pinner of the load agent, otherwise d_i = 0. And U_ref (t) is the reference control input, which is generated by the response error of the clusters. Generally, the communication topology needs to be a connected one for an undirected communication network and to have a directed spanning tree for a directed communication network.

Next, the detailed control strategy is provided for each cluster, based on which the temperature setpoint variable of this cluster can be updated.

$\begin{matrix} Δ {\dot{θ}}_{set, i} (t) = & \frac{1}{C_{i} R_{i}} (Δ θ_{a} (t) - Δ θ_{set, i} (t)) \\ + u_{i} (t), \end{matrix}$ (8) where $Δ θ_{set, i} (t_{0}) = θ_{set, i} (t_{0}) - θ_{set, i}^{des}$ .

Then, the practical temperature setpoint signal is generated by $θ_{set, i} (t) = θ_{set, i}^{des} + Δ θ_{set, i} (t)$ , according to which the aggregate power can be guided towards the expected moving direction.

Remark 2. As for the distributed feedback control, it is different from the traditional output feedback control. This paper focused on the consensus of the input of each TCL cluster, i.e., the average trends and ranges of the real time temperature setpoints are converged to the same amplitude. This strategy is coincide with the practical application since it is fair for all TCL clusters.

4 Case study

The performance of the proposed distributed load following strategy is validated. Here, we discuss 10 heterogeneous TCL clusters (composed of ten smart buildings or communities) with 14667 cooling air conditioners. By utilizing the distributed pinning consensus control strategy, the reference power trajectory of the load agent can be tracked by the active power of TCLs. The communication topology among the clusters is provided in Fig. 3, by which one can derive the communication matrix ( $A$ ) and only the first TCL cluster is connected to the load agent, i.e., pinned by the load agent.

Fig.3

The communication topology among TCL clusters.

Firstly, some basic simulation parameters are provided in the following Table 1, including N_L (the number of TCLs in each Cluster), R [°C/kW] (thermal resistance), C [kWh/°C] (thermal capacitance), output cooling energy P_r [kW], energy’s transmission efficiency η, preferred setpoint $θ_{set}^{des}$ .

Table 1

The private parameters of TCL clusters.

Agg.	N _L	R	C	P _r	η	$θ_{set}^{des}$	δ _db	pr _off
A1	1080	5.4	11.6	16.9	2.8	23.25	1	0.512
A2	1800	5.4	10.8	17.9	2.9	23.75	1	0.576
A3	972	5.1	9.8	16.6	2.9	24.25	1	0.635
A4	1235	5.1	9.3	17.6	2.7	24.75	1	0.691
A5	2120	5.2	9.4	19.4	2.9	24.45	1	0.557
A6	1120	5.4	8.8	16.1	2.8	23.15	1	0.842
A7	1420	4.6	8.7	16.4	2.7	23.95	1	0.815
A8	1800	4.9	8.8	19.7	2.9	24.35	1	0.591
A9	1200	4.7	9.6	17.2	2.7	24.65	1	0.635
A10	1920	5.2	11.8	19.9	2.8	24.15	1	0.516

Secondly, the initial temperature of each air conditioning in the cluster is set uniformly in the first temperature deadband. The initial off proportion pr_off of TCLs in each cluster are given in the table as well, and the tracking performance bound is set to be ɛ = 5%.

Thirdly, the regulation capacities and ramping rates of the load agent are: $P_{L}^{\min} = 14 MW$ , $P_{L}^{\max} = 67 MW$ , $R_{L}^{dn} = - 76 MW / \min$ , and $R_{L}^{up} = 125 MW / \min$ . Note that the reference power trajectory bidding from the load agent must satisfy the constraints of bounds and rates such that the load agent can follow the reference trajectory.

In the following, a two hours’ short-term load following service is tested. For example, the air conditioning loads in the summer day always account for a large population of electrical loads. Therefore, such a pear load period can be reduced by the proposed distributed pinning consensus strategy. Suppose the real time ambient temperature curve during a two hours’ period is provided in Fig. 4 and the base value θ_base = 37 . 5°C. Suppose the maximal length of the comfortable interval of users is 4°C, i.e., $Δ θ_{set}^{\max} = 2^{\circ} C$ and the dimension Q of the aggregate model (1) is Q = 100 for all clusters in the simulation.

Fig.4

The ambient temperature θ_a (t) and the incorporated input u_i (t) for each TCL cluster.

By calculations, it is easy to derive the upper and lower bounds of the control input u_i (t), denoted by -48.5737 ≤ u_i (t) ≤8.9018. The reference active power trajectory is provided by the load agent every 5min and the values are transformed to a more detailed reference power trajectory by the cubic spline interpolation method (shown in Fig. 4). The sampling period of the TCL clusters is 10s for a cycle.

By setting the control gains μ₁ = μ₂ = 1.25 and the coupling strength β = 6 and running the simulation, it is easy to obtain the real time control inputs u_i (t) (see Fig. 4) and the controlled temperature setpoint curves θ_set,i (t) for each cluster (see Fig. 5).

Fig.5

The controlled temperature setpoints’ curves for each TCL cluster.

Finally, the physical aggregate power (derived by Monte-Carlo method) and the approximated aggregate power (derived by TISO approximate model) and the reference power trajectory (provided by the load agent) are given in Fig. 6.

Fig.6

The aggregate active power curves for the load agent.

In order to illustrate the tracking performance, we utilize the relative errors given by the following computational formulas to describe the percentage error, $\begin{matrix} T_{e 1} (k) = \frac{| P_{est}^{(k)} - P_{ref}^{(k)} |}{P_{ref}^{(k)}}, T_{e 2} (k) = \frac{| P_{T}^{(k)} - P_{ref}^{(k)} |}{P_{ref}^{(k)}}, \end{matrix}$ and the tracking error and the relative error curves are provided in Figs. 7 and 8. As can be seen from the error curves, the tracking performance is feasible in proportionately either for the simulation model or for the real Monte-Carlo statistical results, i.e., T_e1 (k) ≤ ɛ, T_e2 (k) ≤ ɛ. Since the system is a nonlinear system and the controller is designed by the output feedback. The simulation results shows that the algorithm provided in this paper can be realized in reality.

Fig.7

The power tracking error curves for the load agent by the TISO model.

Fig.8

The real power tracking relative error curves for the load agent by the Monte-Carlo.

As can be seen from the tracking errors and the tracking curves: (1) the approximated power response well with the reference power trajectory based on the TISO estimation model and the distributed pinning consensus control; (2) the real physical aggregate power derived by the Monte-Carlo method in the simulation follows the reference trajectory successfully. Therefore, it is feasible for the aggregate tracking of the TCLs in the demand side via the proposed distributed pinning consensus control strategy.

5 Discussion

Aggregate tracking strategy of TCLs based on the temperature setpoint is able to provided various kinds of ancillary services. This manuscript investigated the distributed load following service provided by the flexible load agent, which can reduce the capacity of traditional spanning reserve units. We will discuss the distributed technique in the following two aspects:

Implementation: Along with the development of wireless communication technology, it is easy to implement the distributed control based on a distributed communication system. Note that the communication network can be an undirected connected one or a directed one with a directed spanning tree rooted at the centralized pinner (connected to the load agent).

Applications: the exploitable capacity of the TCL groups is pretty large since a small change in the temperature setpoint of users’ equipments can give rise to an observable change of the active power of the aggregated TCLs; On the other hand, the comfort level of the users will not be changed greatly under a small change of the temperature setpoint. Therefore, the aggregate flexibility of TCLs could provide different kinds of ancillary services, such as load following service, frequency regulation service, spinning reserve capacity.

In the load following application, when tracking a lower reference power trajectory, the temperature setpoint of the TCLs will be increased and vice versa. While in the scenario of the renewable power tracking (absorption or filling up of wind or photovoltaic power), temperature setpoint can be increased or decreased slightly via the fluctuation of the reference power, which may be upper or lower than the steady-state aggregate power compared with the uncontrolled case.

As for the real time control of TCL cluster, the control commands can be issued to the terminal TCLs every 20 s, which can be ensured by the advanced communication technology. And the DR response module embedded in the temperature setpoint regulation actuator will respond to the issued control commands.

In summary, TCLs in the demand side could provide adequate ancillary service capacity. The distributed load following strategy proposed in this paper is able to guide the power consumption of TCLs by regulating the temperature setpoints, which can reduce the total consumption TCLs in the peak period or increase the power consumption in the valley period to store energy.

6 Conclusion

This paper presented a distributed load following algorithm for coordinating the operation of multiple TCL clusters in smart grids. Meanwhile, the aggregate control implementation for the TCLs in the cluster is provided by tuning the temperature setpoint of the terminal TCls slightly. As one demonstration, the proposed control strategy is applied to a typical ten smart buildings’ TCLs’ control system with multiple heterogeneous TCL clusters and the simulation results indicate that the load following strategy is effective in guiding the power consumption of TCLs.

Future directions to extend the current work include a switched communication topology which can enable the plug-in and play of TCL clusters. Additionally the flexility of the TCL groups can also be utilized to follow the variability of wind or photovoltaic power generation under demand side real-time pricing (RTP).

Footnotes

Acknowledgments

This work was supported in part by the National Nature Science Foundation of China under Grants 61703095 and 51677173; in part by the Natural Science Foundation of Jiangsu Province of China under Grant BK20170697; in part by the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence under Grant No. BM2017002; in part by the Key Project of Natural Science Foundation of China (No. 61833005); in part by the Fundamental Research Funds for the Central Universities of China.

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