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Energy Storage From Aggregate Deferrable Demand: Fundamental Trade-Offs and Scheduling Policies
Abstract
We investigate the ability of a collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive explicit bounds on the battery capacity that can be offered, and show that there is a fundamental trade-off between the abilities of collective load to absorb and release energy at high aggregate rates. Finally, we introduce a new class of dynamic priority-driven feedback policies that balance these abilities, and characterize the batteries that they can emulate.
... There are a number of papers that provide closed-form inner approximations for the aggregate flexibility set as a function of the individual load parameters [16], [17], [19], [24]. While these inner approximations are trivial to compute, they have been observed to be very conservative when there is considerable heterogeneity between the individual flexibility sets [18]. ...
... The resulting collection of homothets are then summed to yield a structure-preserving inner approximation to the aggregate flexibility set given by the AH-polytope i∈N γ i + i∈N α i U 0 . Clearly, the restriction to homothetic transformations in (19) will result in overly conservative approximations if the individual flexibility sets differ significantly in shape from the given base set U 0 . This limitation is perhaps most pronounced in settings where an individual flexibility set is of lower dimension than the base set (i.e., dim U i < dim U 0 ). ...
... This limitation is perhaps most pronounced in settings where an individual flexibility set is of lower dimension than the base set (i.e., dim U i < dim U 0 ). In such settings, the only feasible homothetic transformations satisfying the containment constraint in (19) are those having a zero scaling factor α i = 0, resulting in internal approximations that are singletons. ...
Plug-in electric vehicles (EVs) are widely recognized as being highly flexible electric loads that can be pooled and controlled via aggregators to provide low-cost energy and ancillary services to wholesale electricity markets. To participate in these markets, an EV aggregator must encode the aggregate flexibility of the population of EVs under their command as a single polytope that is compliant with existing market rules. To this end, we investigate the problem of characterizing the aggregate flexibility set of a heterogeneous population of EVs whose individual flexibility sets are given as convex polytopes in half-space representation. As the exact computation of the aggregate flexibility set -- the Minkowski sum of the individual flexibility sets -- is known to be intractable, we study the problems of computing maximum-volume inner approximations and minimum-volume outer approximations to the aggregate flexibility set by optimizing over affine transformations of a given convex polytope in half-space representation. We show how to conservatively approximate the pair of maximum-volume and minimum-volume set containment problems as linear programs that scale polynomially with the number and dimension of the individual flexibility sets. The class of approximations methods provided in this paper generalizes existing methods from the literature. We illustrate the improvement in approximation accuracy achievable by our methods with numerical experiments.
... This paper focuses on the design of this closed-loop system and, in particular, the design of real-time feedback signal from the aggregator to the ISO quantifying the available flexibility. The design of the aggregate flexibility feedback signal is complex and has been the subject of significant research over the last decade, e.g., [3], [4], [5], [6], [7], [8], [9], [10], [11]. Any feedback design must balance a variety of conflicting goals. ...
... The assessment and enhancement of aggregate flexibility are often considered independent of the operational objectives. For instance, in a reserve market, an aggregator will report to the ISO a day in advance an offline notion of aggregated flexibility based on forecast for the ISO to compute a energy and reserve schedule for the following day, e.g., [3], [29], [8], [7], with notable exceptions, such as [12], which considered charging and discharging of EV fleets batteries for tracking a sequence of automatic generation control (AGC) signals. However, this approach has several limitations. ...
... It is often a "simplified" summary of the constraints in (2b)-(2d), as we reviewed in Section I-B. Notably, existing aggregate flexibility definitions (for instance, in [3], [4], [5], [6], [7], [8], [9], [10]) all focus on the offline version of (2). It remains unclear that first, what is the right notion of realtime aggregate flexibility? ...
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. To be used effectively, an aggregator must be able to communicate the available flexibility of the loads they control, as known as the aggregate flexibility to a system operator. However, most of existing aggregate flexibility measures often are slow-timescale estimations and much less attention has been paid to real-time coordination between an aggregator and an operator. In this paper, we consider solving an online optimization in a closed-loop system and present a design of real-time aggregate flexibility feedback, termed the maximum entropy feedback (MEF). In addition to deriving analytic properties of the MEF, combining learning and control, we show that it can be approximated using reinforcement learning and used as a penalty term in a novel control algorithm – the penalized predictive control (PPC), which modifies vanilla model predictive control (MPC). The benefits of our scheme are (1). Efficient Communication. An operator running PPC does not need to know the exact states and constraints of the loads, but only the MEF. (2). Fast Computation. The PPC often has much less number of variables than an MPC formulation. (3). Lower Costs We show that under certain regularity assumptions, the PPC is optimal. We illustrate the efficacy of the PPC using a dataset from an adaptive electric vehicle charging network and show that PPC outperforms classical MPC.
... This paper focuses on the design of this closed-loop system and, in particular, the design of the signal quantifying the available flexibility sent from the aggregator to the ISO. The question of how to design the signal providing information on aggregate flexibility of the aggregator to the operator, namely the aggregate flexibility feedback signal, is complex and has been the subject of significant research over the last decade, e.g., [3], [4], [5], [6], [7], [8], [9], [10], [11]. Any feedback design must balance between a variety of conflicting goals. ...
... The assessment and enhancement of aggregate flexibility are often considered independent of the operational objectives today. For instance, the notion of aggregated flexibility is reported to an ISO participating in a reserve market a day ahead and the scheduling is then conducted the next day after receiving the flexibility representation as defined in [3], [26], [8], [7], with notable exceptions, such as [12], which considered charging and discharging of EV fleets batteries for tracking a sequence of automatic generation control (AGC) signals. However, this approach has several limitations. ...
... It is often a "simplified" summary of the constraints in (2b)-(2d), as we reviewed in Section I-B. Notably, existing aggregate flexibility definitions (for instance, in [3], [4], [5], [6], [7], [8], [9], [10]) all focus on the offline version of (2). It remains unclear that first, what is the right notion of realtime aggregate flexibility? ...
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. To be used effectively, an aggregator must be able to communicate the available flexibility of the loads they control, as known as the aggregate flexibility to a system operator. However, most of existing aggregate flexibility measures often are slow-timescale estimations and much less attention has been paid to real-time coordination between an aggregator and an operator as a closed-loop control system. In this paper, we present a design of real-time aggregate flexibility feedback based on maximization of entropy, termed the maximum entropy feedback (MEF). The design provides a concise and informative signal that can be used by the system operator to perform online cost minimization, while provably satisfying the constraints of the loads. In addition to deriving analytic properties of the MEF, we show that it can be generated efficiently using reinforcement learning and used as a penalty term in model predictive control (MPC), which gives a novel algorithm -- the penalized predictive control (PPC). The benefits of the PPC are (1). Efficient Communication. An operator running PPC does not need to know the exact states and constraints of the loads on the aggregator's side, but only the MEF sent by the aggregator. (2). Fast Computation. The PPC is an unconstrained online optimization and it often has much less number of variables than the optimization formulation of an MPC. (3). Lower Costs. We illustrate the efficacy of the PPC using a dataset from an adaptive electric vehicle charging network and show that PPC outperforms classical MPC by achieving lower costs.
... This paper focuses on the design of this closed-loop system and, in particular, the design of the signal quantifying the available flexibility sent from the aggregator to the ISO. The question of how to design the signal providing information on aggregate flexibility of the aggregator to the operator, namely the aggregate flexibility feedback signal, is complex and has been the subject of significant research over the last decade, e.g., [3], [4], [5], [6], [7], [8], [9], [10], [11]. Any feedback design must balance between a variety of conflicting goals. ...
... The assessment and enhancement of aggregate flexibility are often considered independent of the operational objectives today. For instance, the notion of aggregated flexibility is reported to an ISO participating in a reserve market a day ahead and the scheduling is then conducted the next day after receiving the flexibility representation as defined in [3], [25], [8], [7], with notable exceptions, such as [12], which considered charging and discharging of EV fleets batteries for tracking a sequence of automatic generation control (AGC) signals. However, this approach has several limitations. ...
... It is often a "simplified" summary of the constraints in (2b)-(2d), as we reviewed in Section I-B. Notably, existing aggregate flexibility definitions (for instance, in [3], [4], [5], [6], [7], [8], [9], [10]) all focus on the offline version of (2). It remains unclear that first, what is the right notion of realtime aggregate flexibility? ...
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. To be used effectively, an aggregator must be able to communicate the available flexibility of the loads they control, as known as the aggregate flexibility to a system operator. However, most of existing aggregate flexibility measures often are slow-timescale estimations and much less attention has been paid to real-time coordination between an aggregator and a system operator to allow the system operator to send control signals to the aggregator that lead to optimization of system-level objectives, such as online cost minimization, and do not violate private constraints of the loads, such as satisfying specific load demands. In this paper, we present a design of real-time aggregate flexibility feedback based on maximization of entropy, termed the maximum entropy feedback (MEF). The design provides a concise and informative signal that can be used by the system operator to perform online cost minimization, while provably satisfying the constraints of the loads. In addition to deriving analytic properties of the MEF, we show that it can be generated efficiently using reinforcement learning and used as a penalty term in model predictive control (MPC), which gives a novel algorithm -- the penalized predictive control (PPC). The benefits of the PPC are (1). Efficient Communication. An operator running PPC does not need to know the exact states and constraints of the loads on the aggregator's side, but only the MEF sent by the aggregator. (2). Fast Computation. The PPC is an unconstrained online optimization and it often has much less number of variables than the optimization formulation of an MPC. (3). Lower Costs. We illustrate the efficacy of the PPC using a dataset from an adaptive electric vehicle charging network and show that PPC outperforms classical MPC by achieving lower costs.
... This paper focuses on the design of this closed-loop system and, in particular, the design of the signal quantifying the available flexibility sent from the aggregator to the ISO. The question of how to design the signal providing information on aggregate flexibility of the aggregator to the operator, namely the flexibility feedback signal, is complex and has been the subject of significant research over the last decade, e.g., [2,5,8,11,13,17,21,22,28]. Any feedback design must balance between a variety of conflicting goals. ...
... The assessment and enhancement of aggregate flexibility are often considered independent of the operational objectives and constraints today. For instance, the notion of aggregated flexibility is reported to an ISO participating in a reserve market a day ahead and the scheduling is then conducted the next day after receiving the flexibility representation as defined in [5,6,11,17], with notable exceptions, such as [27], which considered charging and discharging of EV fleets batteries for tracking a sequence of automatic generation control (AGC) signals. However, this approach has several limitations. ...
... Every function in this collection is causal in that it depends only on information available to the aggregator at time t. In contrast to most aggregate flexibility notions in the literature [5,8,11,13,17,21,22,28], the flexibility feedback here is specifically designed for an online feedback control setting. ...
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. However, to be used effectively, aggregators must be able to communicate the available flexibility of the loads they control to the system operator in a manner that is both (i) concise enough to be scalable to aggregators governing hundreds or even thousands of loads and (ii) informative enough to allow the system operator to send control signals to the aggregator that lead to optimization of system-level objectives, such as cost minimization, and do not violate private constraints of the loads, such as satisfying specific load demands. In this paper, we present the design of a real-time flexibility feedback signal based on maximization of entropy. The design provides a concise and informative signal that can be used by the system operator to perform online cost minimization and real-time capacity estimation, while provably satisfying the private constraints of the loads. In addition to deriving analytic properties of the design, we illustrate the effectiveness of the design using a dataset from an adaptive electric vehicle charging network.
... This paper focuses on the design of this closed-loop system and, in particular, the design of the signal quantifying the available flexibility sent from the aggregator to the ISO. The question of how to design the signal providing information on aggregate flexibility of the aggregator to the operator, namely the flexibility feedback signal, is complex and has been the subject of significant research over the last decade, e.g., [2,5,8,11,13,17,21,22,28]. Any feedback design must balance between a variety of conflicting goals. ...
... The assessment and enhancement of aggregate flexibility are often considered independent of the operational objectives and constraints today. For instance, the notion of aggregated flexibility is reported to an ISO participating in a reserve market a day ahead and the scheduling is then conducted the next day after receiving the flexibility representation as defined in [5,6,11,17], with notable exceptions, such as [27], which considered charging and discharging of EV fleets batteries for tracking a sequence of automatic generation control (AGC) signals. However, this approach has several limitations. ...
... Every function in this collection is causal in that it depends only on information available to the aggregator at time t. In contrast to most aggregate flexibility notions in the literature [5,8,11,13,17,21,22,28], the flexibility feedback here is specifically designed for an online feedback control setting. ...
Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. However, to be used effectively, aggregators must be able to communicate the available flexibility of the loads they control to the system operator in a manner that is both (i) concise enough to be scalable to aggregators governing hundreds or even thousands of loads and (ii) informative enough to allow the system operator to send control signals to the aggregator that lead to optimization of system-level objectives, such as cost minimization, and do not violate private constraints of the loads, such as satisfying specific load demands. In this paper, we present the design of a real-time flexibility feedback signal based on maximization of entropy. The design provides a concise and informative signal that can be used by the system operator to perform online cost minimization and real-time capacity estimation, while provably satisfying the private constraints of the loads. In addition to deriving analytic properties of the design, we illustrate the effectiveness of the design using a dataset from an adaptive electric vehicle charging network.
... And system operator barely cares about the diverse and enormous intrinsic properties (e.g., temperature, route path) of VES, but external properties (e.g., power and energy state) are highly concerned. Therefore, a storage-like baseline model was proposed in [8][9], which realized the equivalent transformation between physical parameters and VES parameters by using first-order energy dynamics but without considering the time-varying and stochastic features. The above researches are suitable under the contract market with mandatory control of power and duration of customers. ...
... The main contributions are threefold: i) Modeling: GES is modeled in a data-driven framework, which enhances the generality and parameter realization. Compared with deterministic models [8][9], the proposed strategy outperforms its rivals in considering real-time SOC constraints. Compared with CCO-DIUs model [12][13][14], detailed uncertainty description is established considering both the exogenous and endogenous uncertainties of VES. ...
Aggregated and coordinated generic energy storage (GES) resources provide sustainable but uncertain flexibilities for power grid operation and renewable energy integration. To optimally cope with multi-uncertainties, this paper proposes a novel chance-constrained optimization (CCO) model for economic dispatch of GES in the day-ahead energy market. We present a novel data-driven model and detailed uncertainty description for commonly used GESs, especially considering decision-dependent uncertainties (DDUs) in uncertain SOC boundaries determined by incentive price and accumulated discomfort. Two tractable solution methodologies (i.e., robust approximation and iteration algorithm) are developed to effectively solve the proposed CCODDUs. Reliability indexes (i.e., LORP and ERNS) are produced to verify the reliability and applicability of the proposed approach. Comparative results show that the proposed method can provide conservative but reliable strategies by data-driven initialization and considering DDUs, which eventually reduces the requirement for real-time power balance and extra costs for the reserve market.
... The storage of heat/cool can be equivalent to the energy storage, and the heating/cooling power can be equivalent to charging and discharging power. Further, the aggregated TCLs can consequently be viewed as an equivalent energy storage (EES) model [18]. Several EES models for TCLs are proposed in Ref. [19]-Ref. ...
... where () xt is the state vector for the TCL at time t, and the matrices A and B can be easily derived from equation (18) and equation (19). s(t) is the switching state of each individual TCL, which is typically regulated by a simple hysteretic controller based on a temperature dead-band, and s(t) can be defined as following: ...
Among various kinds of flexible loads resources in power system, the thermostatically con-trolled loads (TCLs) are considered as the excellent candidates for the demand response (DR) programs due to the heat/cool storage characteristics. Effective operation and coordination of TCLs in DR programs re-quires an accurate model to capture the aggregate power. One appealing approach is the equivalent energy storage (EES) method, which describes the change of aggregate power offered by the TCLs as the dynamic of an energy storage model with limits on the output power and the energy capacity. In this paper, an EES model with the second-order equivalent thermal parameters (second-order ETP) model is established for interpretation of TCLs dynamic characteristics. Considering the internal and external heat exchange of the TCLs, the relationships between the heat exchange power and energy storage of the TCLs EES model are redefined. In order to exert the actual potential of TCLs in day-ahead scheduling, the time-varying charg-ing-discharging power and energy storage constraints of the TCLs EES model are developed. By this way, more feasible scheduling results can be obtained. The performance of the proposed method is verified by the testing results.
... There are various types of flexible loads with different properties, which have a great potential for the improvement of VPP's flexibility and economy. Flexible loads can be mainly divided into the following categories: storage-like loads [4], air conditioning loads [5], [6], deferrable loads (DLs) [7], etc. Currently, flexible loads have been exploited in many power system applications, such as economic dispatch, renewable energy generation accommodation, frequency control, energy balance and auxiliary services [4], [5], [8], etc. Results of these studies jointly demonstrate that the utilization of flexible loads can effectively improve the power system flexibility. ...
... (3). Storage approximation methods [5], [7], [17]. This kind of method approximates the characteristics of a collection of flexible loads by a virtual energy storage. ...
To unlock the potential of flexible resources, a multi-time-scale economic scheduling strategy for the virtual power plant (VPP) to participate in the wholesale energy and reserve market considering large quantity of deferrable loads (DLs) aggregation and disaggregation is proposed in this paper. For the VPP multi-time-scale scheduling including day-ahead bidding and real-time operation, the following models are proposed, namely, DLs aggregation model based on clustering approach, economic scheduling model considering DLs aggregation, and DLs disaggregation model satisfying consumers' requirements, respectively. The proposed strategy can realize the efficient management of massive DLs to reduce the energy management complexity and increase the overall economics with high computation efficiency, which indicate its promising application in the VPP economic scheduling.
... [25] extends [24] by suggesting a detailed analysis of necessary and sufficient conditions of the application of polytopes for the purposes of combining devices. [26] and [27] explore the boundary values for the solution space and discuss its effect on the ability of deferrable loads to provide grid services. ...
The increasing number of intelligent electrical appliances and home energy management systems provide a big opportunity for demand response services from residential and small commercial buildings to the grid. Simultaneously, direct control of individual devices by utilities can cause communication bottlenecks, as well as coordination and privacy concerns. These challenges can be addressed by combining the constituent devices into a single house battery equivalent for the purposes of demand response, using Minkowski sum and a 2d bin packing problem. However, the well-studied traditional problems have not been tested in a real house, as implementation carries significant challenges of its own. We deploy the packing problem on residential devices in a controllable house. We report the barriers we found, such as charge forecast and scalability of the algorithm, and discuss our solutions. The study serves as an intermediate step between existing theoretical research and possible future steps, such as prototype deployments of systems that provide residential demand response.
... To address this issue, an aggregator is urgently required to formulate an approximate aggregation model for a large number of TCRs, which can realize a win-win situation between the system operator and individual TCRs: On the one hand, the system operator can efficiently utilize the TCRs' flexibility without imposing excessive computational burden [28]. On the other hand, individual TCR owners can obtain more financial reward by providing services to the superior CHP system operator [29]. In [30], a first-order linear virtual battery model is proposed to capture the flexibility of residential HVAC systems, which can be utilized as an accurate and simple model to represent the overall dynamical characteristic of the HVACs. ...
Thermal controllable residents possess great potential of thermal inertia to improve the system renewable generation accommodation capability. Nevertheless, a high-dimensional optimization problem with huge computational burden emerges if a large number of small thermal controllable residents are modeled individually. In light of this, a polytope-based inner approximate aggregation approach for thermal controllable residents with heterogeneous parameters is proposed, which can unlock the potential operational flexibility offered by numerous small thermal controllable residents and satisfy their various operational constraints. Moreover, a day-ahead economic dispatch framework for combined heat and power systems coordinating with thermal controllable residents’ aggregation and disaggregation processes is proposed to further utilize the thermal controllable residents’ flexibility and promote the wind energy accommodation. The object is to reduce the overall operation cost while ensuring users’ comfort and diversified system operational constraints. Simulation analyses are conducted on the 14-bus electric system and 7-node district heating system, which substantiate that the proposed approach can efficiently improve the system economy and relieve the wind power curtailment through aggregate management of numerous thermal controllable residents.
... In [9], machine learning methods are used along with a direct load control scheme to parameterize a low-order VB model that works well for small-scale aggregations of less than 300 electic water heaters (EWHs) and air conditioners (ACs). The temporal flexibility or slack inherent to deferrable DERs, such as electric vehicles (EVs), are characterized as a VB in [7], where online control policies are developed to dispatch the DERs within local and VB constraints. ...
... (2). It is unrealistic to model the DRs separately due to the large quantity, which will impose huge computation and communication burdens to the system operator [26], [27]. ...
Controllable distributed resources can offer great potential benefits to the power systems since they possess considerable operation flexibility. However, a high-dimensional mathematical problem is emerged when modeling the massive distributed resources (DRs) with heterogeneous parameters. In light of this, based on the aggregation and disaggregation of massive DRs of small capacity, a model predictive control (MPC) based strategy considering incremental operation cost of various controllable devices is proposed for the real-time secondary frequency regulation in an islanded microgrid. The proposed strategy is implemented in a distributed framework using a neurodynamic-based approach, which only requires the information exchange among neighboring units. Simulation results illustrate that the proposed strategy can efficiently manage massive DRs to maintain the system frequency and achieve a satisfactory economic performance, which indicates its promising application value in the field of microgrid frequency regulation.
... Numerous researches illustrate that VPP has provided an effective way to accommodate the high penetration level of renewable energy sources (RESs) that have brought great technical challenges to the economic operation of the distribution network. Thus, VPP techniques have been implemented in many fields of the power systems, such as demandside management [4], flexible load [5], RESs utilisation [6] etc. which have achieved significant economic values. ...
Abstract: Virtual power plant (VPP) has become a promising technique to facilitate distributed energy resources (DERs) to participate in the power markets. Considering the respective interests of the VPP agent and distribution system operator (DSO), a bi-level optimization model for VPP bidding in multiple retail markets (including active power, reactive power and spinning reserve market) as price-maker is formulated. In the upper layer, taking into account various DERs, the VPP agent aims to develop hourly bidding prices and quantities of multiple market commodities to maximize its operation profits. In the lower layer, DSO conducts the retail market clearing to minimize the system operation cost considering the network constraints and bidding plans of the market participants. Moreover, the quadratic coupling constraints among different market commodities due to capacity limitation of DGs and branches are formulated explicitly in the proposed model. The hybrid simulated annealing-genetic algorithm (SA-GA) with self-adaptive parameters is adopted to cope with the nonlinearity and compute the economic bidding plans for VPP. The effectiveness of the proposed approach is verified under different scenarios through case studies, which indicate its superiority and great potential for implementation.
... While the core concepts underpinning autonomous demand response (ADR) can be traced back to the early 1980s [6,7], the VESS technology available today is still in the early stages, but advancing rapidly. Recently, researchers have developed generalized energy-based models for aggregating and coordinating DERs that are very similar to that of a classic charge/discharge battery model [2,[8][9][10][11][12][13][14]. The VESS model presented herein adapts the general, first-order energy dynamics found in [9], including the box constraints on the energy state and (charge/discharge) power dispatch bounds. ...
High penetrations of intermittent renewable energy resources in the power system require large balancing reserves for reliable operations. Aggregated and coordinated behind-the-meter loads can provide these fast reserves, but represent energy-constrained and uncertain reserves (in their energy state and capacity). To optimally dispatch uncertain, energy-constrained reserves, optimization-based techniques allow one to develop an appropriate trade-off between closed-loop performance and robustness of the dispatch. Therefore, this paper investigates the uncertainty associated with energy-constrained aggregations of flexible, behind-the-meter distributed energy resources (DERs). The uncertainty studied herein is associated with estimating the state of charge and the capacity of an aggregation of DERs (i.e., a virtual energy storage system or VESS). To that effect, a risk-based chance constrained control strategy is developed that optimizes the operational risk of unexpectedly saturating the VESS against deviating generators from their scheduled set-points. The controller coordinates energy-constrained VESSs to minimize unscheduled participation of and overcome ramp-rate limited generators for balancing variability from renewable generation, while taking into account grid conditions. To illustrate the effectiveness of the proposed method, simulation-based analysis is carried out on an augmented IEEE RTS-96 network with uncertain energy resources and temperature-based dynamic line ratings.
... However, using the constraints for reference planning requires a simulation of TCLs, making the capacity dependent on the coordination algorithm. In addition to TCLs, there is work on characterizing the capacity of deferrable loads [21]. ...
A flexible load can vary its power consumption to perform grid support services. This flexibility is naturally limited by the Quality of Service (QoS) requirements at the load. A widely examined class of flexible loads is Thermostatically Controlled Loads (TCLs), which include air conditioners, water heaters, and refrigerators. A TCL is designed to maintain a temperature within a preset band, and the actuation to achieve this is on/off. Temperature, cycling rate, and the energy bill are three main QoS metrics: exceeding the temperature limits, frequent cycling between on and off, and a high energy bill must be avoided. How the temperature constraint affects the capacity of an ensemble of TCLs to provide grid support is a well studied problem. However, how the cycling constraint effects the capacity is often neglected. In this work we present a characterization of the capacity of a collection of TCLs that takes into account not only temperature, but also cycling and energy constraints. Our characterization of capacity is consistent with its most practical utility: a grid authority can use this characterization to plan a reference signal that the TCLs can track without violating any of their QoS constraints. Additionally, the proposed characterization is independent of the algorithm used to coordinate the TCLs (to provide grid support) and leads to a convex and feasible optimization problem for the grid authority's reference planning.
... Wenzel et al. studies realtime charging strategies for electric vehicles to provide ancillary services with minimum tracking error [11]. Madjidian et al. discovers the trade-off between absorbing and releasing energy for collective loads under causal allocation policies [12]. In all of these works, the quantity of available resources is fixed. ...
This paper studies the problem of procuring diverse resources in a forward market to cover a set of uncertain demand signals . We consider two scenarios: (a) is revealed all at once by an oracle (b) reveals itself causally. Each scenario induces an optimal procurement cost. The ratio between these two costs is defined as the {\em price of causality}. It captures the additional cost of not knowing the future values of the uncertain demand signal. We consider two application contexts: procuring energy reserves from a forward capacity market, and purchasing virtual machine instances from a cloud service. An upper bound on the price of causality is obtained, and the exact price of causality is computed for some special cases. The algorithmic basis for all these computations is set containment linear programming. A mechanism is proposed to allocate the procurement cost to consumers who in aggregate produce the demand signal. We show that the proposed cost allocation is fair, budget-balanced, and respects the cost-causation principle. The results are validated through numerical simulations.
This paper investigates the problem of enhancing the energy efficiency of buildings which eventually contributes to the carbon neutrality and sustainability. To achieve that, two strategies are proposed based on the exploitation of the functioning of building windows for thermal losses prevention and renewable power generation. More specifically, the first strategy proposes an integrated control scheme for lighting and heating, ventilation, and air conditioning (HVAC) systems under controllable blinds or curtains. Numerical simulations and calculations are then carried out to show the effectiveness of this strategy. Next, in the second strategy, it is proposed to employ the so-called solar windows to obtain clean power generation via solar cells attached to building windows. A realistic experiment is performed for an office building, which reveals the viability of such solar power generation strategy.
Among various kinds of flexible loads resources in power system, the thermostatically controlled loads are considered as the excellent candidates for the demand response programs due to the heating/cooling storage characteristics. Market-orientated demand-side management has become a new focus, and the participation of the thermostatically controlled loads in the electricity market requires an accurate cost model. In this paper, a cost model is established based on the response characteristics of the thermostatically controlled loads in day-ahead scheduling, and considering the impact of non-monotonic bidding for thermostatically controlled loads on market clearing is considered, then the augmented constraints of the thermostatically controlled loads bidding are introduced into the traditional clearing method. By this way, proper sequence of bid quantity of each segment and the economic revenue can be guaranteed. The numeral testing results verify the effectiveness of the proposed method.
Smart buildings have been proven to be a kind of flexible demand response resources in the power system. To maximize the utilization of the demand response resources, such as the heating, ventilating and air-conditioning (HVAC), the energy storage systems (ESSs), the plug-in electric vehicles (PEVs), and the photovoltaic systems (PVs), their controlling, operation and information communication technologies have been widely studied. Involving human behaviors and cyber space, a traditional power system evolves into a cyber-physical-social system (CPSS). Lots of new operation frameworks, controlling methods and potential resources integration techniques will be introduced. Conversely, these new techniques urge the reforming requirement of the techniques on the modeling, structure, and integration techniques of smart buildings. In this paper, a brief comprehensive survey of the modeling, controlling, and operation of smart buildings is provided. Besides, a novel CPSS-based smart building operation structure is proposed, and the integration techniques for the group of smart buildings are discussed. Moreover, available business models for aggregating the smart buildings are discussed. Furthermore, the required advanced technologies for well-developed smart buildings are outlined.
Numerous small-capacity distributed energy re-sources (DERs) pose technical challenges and increase the man-agement complexity for power system operators. This article proposes an aggregate operation model to efficiently manage a large number of DERs with heterogeneous parameters. The aggregate operation model includes the approximate feasible region and the equivalent operational cost function. First, con-sidering the coupling of power, energy, and regulation service, the operational flexibility of multiple categories of DERs is modeled by a general polytope. Second, by scaling and translating a basic homothetic polytope, a maximum inner aggregation approach is formulated to exploit the potential flexibility of DERs and guar-antee solution feasibility. The uncertainty of DERs is modeled by the distributionally robust chance-constrained program (DRCCP), and the equivalent cost function of the DER aggregator is rigidly derived. Last, this study theoretically explains that the aggregate feasible region can be enlarged by introducing the DER clustering process, and a spectral clustering algorithm based on the multi-scale similarity metric method is developed to classify DERs into different aggregators. Numerical simulation results indicate the great potential of the proposed method to enhance system operational flexibility with high computational efficiency.
In this paper, we study the problem of procuring diverse resources in a forward market to cover a set
of uncertain demand signals
. We consider two scenarios: (a)
is revealed all at once by an oracle (b)
reveals itself causally. Each scenario induces an optimal procurement cost. The ratio between these two costs is defined as the price of causality. It captures the additional cost of not knowing the future values of the uncertain demand signal. We consider two application contexts: procuring energy reserves from a forward capacity market, and purchasing virtual machine instances from a cloud service. An upper bound on the price of causality is obtained, and the exact price of causality is computed for some special cases. The algorithmic basis for all these computations is set containment linear programming. A mechanism is proposed to allocate the procurement cost to consumers who in aggregate produce the demand signal. We show that the proposed cost allocation is fair, budget-balanced, and respects the cost-causation principle. The results are validated through numerical simulations.
Deferrable power-driven demands such as water and thermal ones possess a capability of energy storage which can be exploited to further optimize electric systems. This paper proposes a new optimized scheduling framework for electric grids by simultaneously exploiting the high-inertia thermal dynamics and lossless water storage. Unlike previous ideas in the literature, both water and thermal demands are managed to realize the long-term and short-term load-shifting strategies, respectively. First, distributed water/thermal loads are aggregated where the virtual storage can be represented by battery models. Then, a further optimized scheduling framework is proposed with a mixed-integer nonlinear programing problem. Comparative studies show that the water storage offers outstanding flexibility for electric system via pumps scheduling, especially for the electric load-shifting strategy in a long time-horizon thanks to the lossless water-storage process. Meanwhile, the thermal storage can directly support short-term electric load-shifting to avoid price spikes of electricity. Numerical results show that the proposed method can reduce the total cost of micro-grids by maximizing the usage of renewable energy sources, avoiding price spikes, and reducing dependence on high-cost centralized energy-storage facilities provided that the critical water-energy demands are preserved.
Different from most existing studies that focus on off-line demand side management (DSM) in microgrids (MGs) while neglecting forecasting errors of uncertain renewable generations (URGs), this paper studies on-line DSM. A two-stage real-time DSM (RDSM) method for an MG including different time scales, integrated with schedulable ability (SA) and uncertainties, is proposed. In the first stage, a novel internal pricing model is developed. On this basis, a model predictive control-based dynamic optimization is applied to minimize the operation cost and maintain the power balance considering the uncertainties imposed by both supply and demand sides in the MG system. In the second stage, we define the concept of SA for response executors (REs) and also establish an SA evaluation system taking the real-time and history information of the REs into account. In doing so, a faster-time scale on-line power allocation among REs is carried out in the framework of dynamic optimization to further compensate for the uncertainties in real-time, based on the evaluated SA values of the REs and the required compensation power. Numerical simulations on a residential MG show the reasonableness and effectiveness of the proposed method.
Aggregation of a large number of responsive loads presents great power flexibility for demand response. An effective control and coordination scheme of flexible loads requires an accurate and tractable model that captures their aggregate flexibility. This paper proposes a novel approach to extract the aggregate flexibility of deferrable loads with heterogeneous parameters using polytopic projection approximation. First, an exact characterization of their aggregate flexibility is derived analytically, which in general contains exponentially many inequality constraints with respect to the number of loads. In order to have a tractable solution, we develop a numerical algorithm that gives a sufficient approximation of the exact aggregate flexibility. Geometrically, the flexibility of each individual load is a polytope, and their aggregation is the Minkowski sum of these polytopes. Our method originates from an alternative interpretation of the Minkowski sum as projection. The aggregate flexibility can be viewed as the projection of a high-dimensional polytope onto the subspace representing the aggregate power. We formulate a robust optimization problem to optimally approximate the polytopic projection with respect to the homothet of a given polytope. To enable efficient and parallel computation of the aggregate flexibility for a large number of loads, a muti-stage aggregation strategy is proposed. The scheduling policy for individual loads is also derived. Finally, an energy arbitrage problem is solved to demonstrate the effectiveness of the proposed method.
This paper develops a strategy to coordinate the charging of autonomous plug-in electric vehicles (PEVs) using concepts from non-cooperative games. The foundation of the paper is a model that assumes PEVs are cost-minimizing and weakly coupled via a common electricity price. At a Nash equilibrium, each PEV reacts optimally with respect to a commonly observed charging trajectory that is the average of all PEV strategies. This average is given by the solution of a fixed point problem in the limit of infinite population size. The ideal solution minimizes electricity generation costs by scheduling PEV demand to fill the overnight non-PEV demand "valley". The paper's central theoretical result is a proof of the existence of a unique Nash equilibrium that almost satisfies that ideal. This result is accompanied by a decentralized computational algorithm and a proof that the algorithm converges to the Nash equilibrium in the infinite system limit. Several numerical examples are used to illustrate the performance of the solution strategy for finite populations. The examples demonstrate that convergence to the Nash equilibrium occurs very quickly over a broad range of parameters, and suggest this method could be useful in situations where frequent communication with PEVs is not possible. The method is useful in applications where fully centralized control is not possible, but where optimal or near-optimal charging patterns are essential to system operation.
It is widely accepted that thermostatically controlled loads (TCLs) can be used to provide regulation reserve to the grid. We first argue that the aggregate flexibility offered by a collection of TCLs can be succinctly modeled as a stochastic battery with dissipation. We next characterize the power limits and energy capacity of this battery model in terms of TCL parameters and random exogenous variables such as ambient temperature and user-specified set-points. We then describe a direct load control architecture for regulation service provision. Here, we use a priority-stack-based control framework to select which TCLs to control at any time. The control objective is for the aggregate power deviation from baseline to track an automatic generation control signal supplied by the system operator. Simulation studies suggest the practical promise of our methods.
The thermal storage potential in commercial buildings is an enormous resource for providing various ancillary services to the grid. In this paper, we show how fans in Heating, Ventilation, and Air Conditioning (HVAC) systems of commercial buildings alone can provide substantial frequency regulation service, with little change in their indoor environments. A feedforward architecture is proposed to control the fan power consumption to track a regulation signal. The proposed control scheme is then tested through simulations based on a calibrated high fidelity non-linear model of a building. Model parameters are identified from data collected in Pugh Hall, a commercial building located on the University of Florida campus. For the HVAC system under consideration, numerical experiments demonstrate how up to 15% of the rated fan power can be deployed for regulation purpose while having little effect on the building indoor temperature. The regulation signal that can be successfully tracked is constrained in the frequency band , where minutes and seconds. Our results indicate that fans in existing commercial buildings in the U.S. can provide about 70% of the current national regulation reserve requirements in the aforementioned frequency band. A unique advantage of the proposed control scheme is that assessing the value of the ancillary service provided is trivial, which is in stark contrast to many demand-response programs.
This paper explores methods to coordinate aggregations of thermostatically controlled loads (TCLs; including air conditioners and refrigerators) to manage frequency and energy imbalances in power systems. We focus on opportunities to centrally control loads with high accuracy but low requirements for sensing and communications infrastructure. We compare cases when measured load state information (e.g., power consumption and temperature) is 1) available in real time; 2) available, but not in real time; and 3) not available. We use Markov chain models to describe the temperature state evolution of populations of TCLs, and Kalman filtering for both state and joint parameter/state estimation. A look-ahead proportional controller broadcasts control signals to all TCLs, which always remain in their temperature dead-band. Simulations indicate that it is possible to achieve power tracking RMS errors in the range of 0.26%-9.3% of steady state aggregated power consumption. We also report results in terms of the generator compliance threshold which is commonly used in industry. Results depend upon the information available for system identification, state estimation, and control. Depending upon the performance required, TCLs may not need to provide state information to the central controller in real time or at all.
Renewable energy sources such as wind and solar power have a high degree of
unpredictability and time-variation, which makes balancing demand and supply
challenging. One possible way to address this challenge is to harness the
inherent flexibility in demand of many types of loads. Introduced in this paper
is a technique for decentralized control for automated demand response that can
be used by grid operators as ancillary service for maintaining demand-supply
balance.
A Markovian Decision Process (MDP) model is introduced for an individual
load. A randomized control architecture is proposed, motivated by the need for
decentralized decision making, and the need to avoid synchronization that can
lead to large and detrimental spikes in demand. An aggregate model for a large
number of loads is then developed by examining the mean field limit. A key
innovation is an LTI-system approximation of the aggregate nonlinear model,
with a scalar signal as the input and a measure of the aggregate demand as the
output. This makes the approximation particularly convenient for control design
at the grid level.
The second half of the paper contains a detailed application of these results
to a network of residential pools. Simulations are provided to illustrate the
accuracy of the approximations and effectiveness of the proposed control
approach.
Responsive load is the most underutilized reliability resource available to the power system today. It is currently not used at all to provide spinning reserve. Historically there were good reasons for this, but recent technological advances in communications and controls have provided new capabilities and eliminated many of the old obstacles. North American Electric Reliability Council (NERC), Federal Energy Regulatory Commission (FERC), Northeast Power Coordinating Council (NPCC), New York State Reliability Council (NYSRC), and New York Independent System Operator (NYISO) rules are beginning to recognize these changes and are starting to encourage responsive load provision of reliability services. The Carrier ComfortChoice responsive thermostats provide an example of these technological advances. This is a technology aimed at reducing summer peak demand through central control of residential and small commercial air-conditioning loads. It is being utilized by Long Island Power Authority (LIPA), Consolidated Edison (ConEd), Southern California Edison (SCE), and San Diego Gas and Electric (SDG&E). The technology is capable of delivering even greater response in the faster spinning reserve time frame (while still providing peak reduction). Analysis of demand reduction testing results from LIPA during the summer of 2002 provides evidence to back up this claim. It also demonstrates that loads are different from generators and that the conventional wisdom, which advocates for starting with large loads as better ancillary service providers, is flawed. The tempting approach of incrementally adapting ancillary service requirements, which were established when generators were the only available resources, will not work. While it is easier for most generators to provide replacement power and non-spinning reserve (the slower response services) than it is to supply spinning reserve (the fastest service), the opposite is true for many loads. Also, there is more financial reward for supplying spinning reserve than for supplying the other reserve services as a result of the higher spinning reserve prices. The LIPAedge program (LIPA's demand reduction program using Carrier ComfortChoice thermostats) provides an opportunity to test the use of responsive load for spinning reserve. With potentially 75 MW of spinning reserve capability already installed, this test program can also make an important contribution to the capacity needs of Long Island during the summer of 2003. Testing could also be done at ConEd (â30 MW), SCE (â15 MW), and/or SDG&E (â15 MW). This paper is divided into six chapters. Chapter 2 discusses the contingency reserve ancillary services, their functions in supporting power system reliability, and their technical requirements. It also discusses the policy and tariff requirements and attempts to distinguish between ones that are genuinely necessary and ones that are artifacts of the technologies that were historically used to provide the services. Chapter 3 discusses how responsive load could provide contingency reserves (especially spinning reserve) for the power system. Chapter 4 specifically discusses the Carrier ComfortChoice responsive thermostat technology, the LIPAedge experience with that technology, and how the technology could be used to supply spinning reserve. Chapter 5 discusses a number of unresolved issues and suggests areas for further research. Chapter 6 offers conclusions and recommendations.
Distribution Automation and Control (DAC) systems have potentially major effects on costs, social impacts, and even on the nature of the power system itself, especially as dispersed storage, generation, and customer interaction become more prevalent. However, at the present time, it is not clear which particular modes of control will best exploit the capabilities of DAC. Homeostatic Utility Control is an overall concept which tries to maintain an internal equilibrium between supply and demand. Equilibrating forces are obtained over longer time scales (5 minutes and up) by economic principles through an Energy Marketplace using time-varying spot prices. Faster supply-demand balancing is obtained by employing "governor-type" action on certain types of loads using a Frequency Adaptive Power Energy Rescheduler (FAPER) to assist or even replace conventional turbine-governed systems and spinning reserve. Conventional metering is replaced by a Marketing Interface to Customer (MIC) which, in addition to measuring power usage, multiplies that usage by posted price and records total cost. Customers retain the freedom to select their consumption patterns. Homeostatic control is a new, untried concept. It is discussed in this paper because its great potential makes it a vehicle for interesting discussions of where the future may actually evolve.
The problems of hard-real-time task scheduling in a multiprocessor
environment are discussed in terms of a scheduling game representation
of the problem. It is shown that optimal scheduling without a priori
knowledge is impossible in the multiprocessor case even if there is no
restriction on preemption owing to precedence or mutual exclusion
constraints. Sufficient conditions that permit a set of tasks to be
optimally scheduled at run time are derived
We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive bounds on the battery capacity that can be realized and show that there are fundamental trade-offs between battery parameters. By characterizing the state trajectories under scheduling policies that emulate two illustrative batteries, we show that the trade-offs occur because the states that allow the loads to absorb and release energy at high aggregate rates are conflicting.
We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive bounds on the battery capacity that can be realized and show that there are fundamental trade-offs between battery parameters. By characterizing the state trajectories under scheduling policies that emulate two illustrative batteries, we show that the trade-offs occur because the states that allow the loads to absorb and release energy at high aggregate rates are conflicting.
With the advent of renewable sources and Smart-Grid deployments, it is increasingly common to control demands in order to reduce power consumption variability and thus the need for regulation, with load aggregators now exploiting the deferability of some power loads to smooth the consumption profile. In this paper, we analyze the impact of service deferrals and scheduling on power consumption variability using tools from queueing theory. We consider a generic model for a load aggregator that receive job requests, involving a certain amount of energy to be provided and a deadline. We analyze different scheduling policies and examine the impact of service deferrals, quantifying the tradeoff between variance reduction and attained deadlines.
The increasing prevalence of technologies such as advanced metering and controls and continuously variable power electronic devices are enabling a radical shift in the way frequency regulation is performed in the bulk power system. This is a welcome development in light of the increase of unpredictable and variable generation. The idea of active participation of loads in frequency markets is not new, but the rapidly changing landscape of the power grid requires new techniques for successful integration of new types of resources; this paper works towards that end. Previously, it has been shown that residential HVAC systems can be aggregated and used to provide frequency regulation by utilizing their thermal energy capacity and flexibility of energy consumption. The virtual battery model—a first-order linear dynamical model—was analytically shown to be an accurate and simple model to capture the flexibility of residential HVAC systems. This paper presents a technique for creating the same battery-type models for many other types of systems, which can be much more complex. Our technique is based on stress testing detailed software models of physical systems. A realistic case study involving the terminal building of a small airport is presented as evidence of the effectiveness of the proposed techniques.
We propose a least laxity first (LLF) scheduling algorithm for a heterogeneous population of thermostatically controlled loads (TCL), aimed at providing regulation services for the power grid. TCLs periodically switch between on and off states in order to keep their monitored temperature in a certain comfort band. In our scheme, TCLs inform a central controller of their anticipated deadlines to switch states, allowing for their switching events to be scheduled. An LLF policy schedules these transitions to provide regulation with minimum deviation from the autonomous evolution of the TCLs. To manage large populations, we bundle requests with similar laxity values in a limited number of clusters, considerably reducing computational and communication costs, and preserving the privacy of participants.
We consider a collection of flexible loads. Each load is modeled as requiring energy E on a service interval [a; d] at a maximum rate of m. The collection is serviced by available generation g(t) which must be allocated causally to the various tasks. Our objective is to characterize the aggregate flexibility offered by this collection. In the absence of rate limits, we offer necessary and sufficient conditions for the generation g(t) to service the loads under causal scheduling without surplus or deficit. Our results show that the flexibility in the collection can be modeled as electricity storage. The capacity Q(t) and maximum charge/discharge rate m(t) of the equivalent storage can be computed in real time. Ex ante, these parameters must be estimated based on arrival/departure statistics and charging needs. Thus, the collection is equivalent a stochastic time-varying electricity storage. We next consider the case with charging rate limits. Here, we offer bounds on the capacity and rate of the equivalent electricity storage. We offer synthetic examples to illustrate our results.
Constrained charging control of large populations of Plug-in Electric Vehicles (PEVs) is addressed using mean field game theory. We consider PEVs as heterogeneous agents, with different charging constraints (plug-in times and deadlines). The agents minimize their own charging cost, but are weakly coupled via a common electricity price. We propose an iterative algorithm that, in the case of an infinite population, converges to the Nash equilibrium of a related decentralized optimization problem. This allows us to approximate the centralized optimal solution, which in the unconstrained case fills the overnight power demand valley, via a decentralized procedure. The benefits of the proposed formulation in terms of convergence behavior and overall charging cost are illustrated through numerical simulations.
A method for certifying exact input trackability for constrained discrete
time linear systems is introduced in this paper. A signal is assumed to be
drawn from a reference set and the system must track this signal with a linear
combination of its inputs. Using methods from robust model predictive control,
the proposed approach certifies the ability of a system to track any reference
drawn from a polytopic set on a finite time horizon by solving a linear
program. Optimization over a parameterization of the set of reference signals
is discussed, and particular instances of parameterization of this set that
result in a convex program are identified, allowing one to find the largest set
of trackable signals of some class. Infinite horizon feasibility of the methods
proposed is obtained through use of invariant sets, and an implicit description
of such an invariant set is proposed. These results are tailored for the
application of power consumption tracking for loads, where the operator of the
load needs to certify in advance his ability to fulfill some requirement set by
the network operator. An example of a building heating system illustrates the
results.
We investigate the potential for aggregations of residential thermostatically controlled loads (TCLs), such as air conditioners, to arbitrage intraday wholesale electricity market prices via non-disruptive load control. We present two arbitrage approaches: 1) a benchmark that gives us an optimal policy but requires local computation or real-time communication and 2) an alternative based on a thermal energy storage model, which relies on less computation/communication infrastructure, but is suboptimal. We find that the alternative approach achieves around 60%–80% of the optimal wholesale energy cost savings. We use this approach to compute practical upper bounds for savings via arbitrage with air conditioners in California's intraday energy market. We investigate six sites over four years and find that the savings range from 2–37 per TCL per year, and depend upon outdoor temperature statistics and price volatility.
We consider a collection of distributed energy resources [DERs] such as electric vehicles and thermostatically controlled loads. These resources are flexible: they require delivery of a certain total energy over a specified service interval. This flexibility can facilitate the integration of renewable generation by absorbing variability, and reducing the reserve capacity and reserve energy requirements. We first model the energy needs of these resources as tasks, parameterized by arrival time, departure time, energy requirement, and maximum allowable servicing power. We consider the problem of servicing these resources by allocating available power using real-time scheduling policies. The available generation consists of a mix of renewable energy [from utility-scale wind-farms or distributed rooftop photovoltaics], and load-following reserves. Reserve capacity is purchased in advance, but reserve energy use must be scheduled in real-time to meet the energy requirements of the resources. We show that there does not exist a causal optimal scheduling policy that respects servicing power constraints. We then present three heuristic causal scheduling policies: Earliest Deadline First [EDF], Least Laxity First [LLF], and Receding Horizon Control [RHC]. We show that EDF is optimal in the absence of power constraints. We explore, via simulation studies, the performance of these three scheduling policies in the metrics of required reserve energy and reserve capacity.
We consider an aggregator managing a portfolio of ON/OFF demand-side devices. The devices are able to shift consumption in time within certain energy limitations; moreover, the devices are able to measure the system frequency and switch ON and OFF accordingly. We show how the aggregator can manage the portfolio of devices to collectively provide a primary reserve delivery in an unbundled liberalized electricity market setting under current regulations. Furthermore, we formulate a binary linear optimization problem that minimizes the aggregator's cost of providing a primary reserve delivery of a given volume, and demonstrate this method on numerical examples.