Holistic modeling framework of demand response considering multi-timescale uncertainties for capacity value estimation

Applied Energy 247 (2019) 692–702

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Holistic modeling framework of demand response considering multitimescale uncertainties for capacity value estimation

T

⁎

Bo Zenga, , Dongbo Zhaob, Chanan Singhc, Jianhui Wangd, Chen Chenb a

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China Energy Systems Division, Argonne National Laboratory, Lemont, IL 60439, USA c Department of Electrical Engineering, Texas A&M University, College Station, TX 77843, USA d Department of Electrical Engineering, Southern Methodist University, Dallas, TX 75275, USA b

H I GH L IG H T S

behavior-driven DR modeling framework is proposed. • AWemulti-timescale use analytical and data-driven approaches to model DR uncertainties. • The jointly uncertainties in the load recovery process are considered. • A capacity value evaluation algorithm considering DR operation is developed. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Demand response Capacity value Reliability analysis Uncertainty Demand-side behavior Regret matching

Demand response (DR) is regarded as an effective tool to mitigate the operational uncertainties and enhance the reliability of power supply in smart grids. However, with the time-varying attribute, to what extent DR could be committed is a major concern for utilities. This paper proposes a new approach to assess the capacity value (CV) of DR with a methodological framework developed for the uncertainty modeling of DR. The novelty of this framework is its inclusion of both physical and human-related analyses in DR programs, which allows the characterization of DR variability to be accurate for the CV estimation. To achieve this, the demand-side activities in DR are disaggregated into several modules as load usage, contract selection and actual performance. Based on their intrinsic properties, different parametric models are proposed to represent the impact of each technical/social factor on the availability of DR. The parameters of these models are determined using learningbased algorithms to adapt to various behavior patterns of consumers. The outputs of the framework will serve as the quantifiers of DR capability and are integrated into reliability-based CV evaluation. The results of case studies verify the effectiveness of the proposed methodology.

1. Introduction The unprecedented energy demand and increasing deficiencies of traditional power systems have provided a strong impetus for the development of smart grids (SG) throughout the world . As a distinguishing feature of SG, demand response (DR) plays an important role in the SG systems [1] . DR programs are dedicated for motivating customers to actively interact with the grid by voluntarily adjusting their energy consumption upon request when the system is in emergencies. In this sense, the wide spread of DR will greatly enhance the operational flexibility of power systems, which is expected to bring benefits to different stakeholders (e.g., users, utilities, etc.), if exploited

⁎

intelligently [2]. Among the numerous contributions of DR in SG, one of the most relevant aspects to utility companies could be its implication on the reliability of supply [3]. This is because, under a competitive electricity market, regulators normally impose mandatory limits on the frequency/duration of customer interruptions, this would put utilities under greater pressure to improve the reliability of their services as failing to deliver the required targets can incur severe penalties to themselves [4]. However, as a remedial resource, DR can be employed to modify the load demand and provide capacity supports to the system (like operating reserves) at times of contingencies. This would improve the adequacy of power supply and mitigate the outage risks in the

Corresponding author. E-mail address: [email protected] (B. Zeng).

https://doi.org/10.1016/j.apenergy.2019.03.121 Received 7 January 2019; Received in revised form 13 February 2019; Accepted 11 March 2019 Available online 28 April 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

z (Tcs )

Acronyms

Functions

AI CDF CL CS CV DA DR EENS EFC ENS FOR IL LR MSRE NKDA NLC OC RMM SG SL SMCS SO

G penalty function for the non-performance of DR customers L disutility function M (s, s’) regret function of the customer with respect to his CS actions s and s’ U benefit function W payoff function ΓB , ΓI probability distribution function for customer CS decisions with and without a priori information Γ final probability distribution for customers’ decisionmaking in the CS

actual implementation cumulative distribution function critical load contract selection capacity value demand analysis demand response expected energy not supplied equivalent firm capacity energy-not-supplied forced outage rate interruptible load load recovery load recovery nonparametric kernel density-based approach non-direct load control opportunity cost regret-matching mechanism smart grid shiftable load sequential monte-carlo simulation system operator

Parameters and variables

P drr PE P il ,P sl P il, −, P sl, − P sl,' + tt

demand reduction required by the SO, kW total load demand of DR customer under the emergency case, kW modified demand of ILs or SLs, kW power reduction of ILs or SLs, kW payback demand from period t’ to t, kW

P il, rat , P sl, rat , P cl, rat baseline demand of ILs/SLs/CLs in the normal case (without DR), kW xI, xB probability of the user for choosing a CS strategy δ maximum duration of LR process, hours δ pk delayed time for the peak rebound, hours λ weighting coefficient for the customer’s decision-making in the CS retail electricity price, $/kW ρ ω weighting coefficient for the customer’s decision-making in the AI ϖ up , ϖ dw slope of customers’ LR pattern

Indices (Sets) i, j k (ΩD) s (S) t, t’’ tz

time interval for a DR contract term

system buses system customers Candidate CS strategies of DR customer time period time periods in the interval z

predictions beforehand [12]. Because of this, the assumption previously described could become unjustified under the NLC case. To resolve this problem, the uncertainties of DR have been considered and examined in some studies, e.g., [13–17]. In these researches, most of works address the variability of demand responsiveness by using randomization methods, where stochastic characteristics in their availability are described through a constant probability model. In practice, such representation of DR will be fully effective if it is applied for operational purposes (i.e., load dispatch), where the time period is normally short enough that the behaviors of customers can be considered stable. However, if the study is aimed for long-term reliability issues, the model might be not applicable due to the volatility of system conditions. Specifically, in the long-term reliability studies, as the time-interval under concern is much longer (usually in years), consumers can adjust (modify) their strategies about DR participation (e.g., contractual setting) dynamically during operation, in order to obtain greater benefits from the system. As such, in this case, the behavior patterns of customers are not stable, but will change with the time and external conditions (e.g., economic returns). The constant probability models are in general not sufficient to capture such evolutionary properties of DR. Besides the above aspect, most of current works represent the LR effect in DR using deterministic approaches [10,11,15,18]. However, in actual situations, as the implementation of LR is mostly on an uncontrolled basis, individuals may choose different ways for initiating their demand payback. Thus, failing to consider such uncertainties in LR may lead to erroneous estimation on the potential of DR and their contribution to the capacity of SGs. In order to fill the research gap as presented above, in this paper, we

system. As such, to utilities, DR is regarded as an efficacious measure for addressing the reliability issue of power supply under the SG [5]. In recognition of the significant role of DR, a large amount of research efforts have been directed to investigate its implications on reliability. For example, a SCUC-based approach is presented by [6] to evaluate the effects of DR on supply adequacy. Using the Monte-Carlo simulation (MCS) method, the reliability contribution of DR in distribution networks is examined in [7]. Similar works can be also found in [8] and [9], considering different load characteristics and DR programs. In practice, as decrease in energy usage could cause detriments to users’ welfare, to compensate for such losses, customers tend to restore their load demand after the responses. This load recovery (LR) effect has also been studied by [10] and it is shown that the LR may largely offset the reliability benefits of DR in some cases. Based on the work of [10], the authors further propose a capacity value (CV) evaluation framework for DR resources [11]. Sequential MCS has been used to assess the system reliability in the presence of DR, accounting for the representation of inter-temporal constraints. For all the literatures mentioned above, a common hypothesis adopted is that the utilities have complete knowledge about the DR potential of all the system customers. Moreover, it is assumed that the DR resources are always available whenever they are dispatched during operation. In practice, such assumptions should be valid if DR is implemented via a direct-load-control program, in which customers have no choice to decide whether to respond when receiving DR calls from the grid. However, if the study is intended for the non-direct control (NLC) case, the situation would much differ as the responses of users will be of a “voluntary” nature to DR signals, thus making the available DR capacity to be highly volatile and may deviate from the utilities’ 693

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propose a holistic methodological framework for DR modeling and apply it to the CV analysis of DR. As distinct from the previous works, our framework could account for the effects of both technical and human-related aspects in DR programs; moreover, the uncertainties of demand-side performance and their potential interaction at different timescales are also explicitly captured. Compared with existing studies, the new contributions of this paper are in threefold:

overview of DR in the SG and its CV metrics is presented. Then, the proposed DR modelling framework is described in Section 3. The algorithm used for CV evaluation is given in Section 4. Section 5 provides the numerical studies and the conclusions of this work are finally given in Section 6.

(1) The multi-timescale uncertainties of DR are comprehensively formulated from the demand-side perspective. In existing researches, only short-term operational uncertainties of DR are concerned and examined. However, in this study, we model the effects of both contingent and long-term dynamic uncertainties in NLC-based DR programs and consider them simultaneously under the same framework. This makes the paper a pioneering work in this research area to incorporate the long-term evolutionary characteristics of demand-side behaviors in DR modeling, through which a more realistic/accurate estimation on the CV of DR could be achieved in real-world applications. (2) Unlike previous studies which represent DR with a single approach, the proposed framework incorporates the advantages of both analytical and data-driven approaches to derive the DR model. This makes our study generic and capable of assessing the DR characteristics of different types of customers, without the need of imposing any pre-assumptions on their behavior pattern/preference. (3) The uncertainties in the LR process and their influence on the performance of DR are also taken into account.

In this study, we consider a SG system where all the consumers have been equipped with smart meters that are embedded with the nonintrusive load monitoring technique [19], thus allowing the system operator (SO) to extract the appliance-level information, e.g., on/off status and hourly consumption, from the grossly metered data of individuals. Moreover, in such a configuration, it is assumed that customers can opt in or not subscribe to the DR program, according to their own interests. Subscribed users sign up and will be required by the SO to reduce their load when the system encounters contingencies during operation. The corresponding responses will modify the load level and hence improve the reliability of the system. To denote the CV of DR, four different metrics are developed in [11]. However, here, for simplicity, we only select one of them, namely the equivalent firm capacity (EFC) method, in this study. The EFC of DR is defined as the amount of firm generation capacity (which is 100% reliable) that needs to be installed to achieve the same system reliability level as provided by DR. For ease of exposition, the expected energy not supplied (EENS) is adopted as the reliability index of the system, which is consistent with [11].

2. Capacity value of DR resources

The remainder of this paper is organized as follows. In Section 2, an

Fig. 1. Modelling framework of DR. 694

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flexibility of usage, electric loads may roughly be classified into three categories, critical loads (CLs), interruptible loads (ILs), and shiftable loads (SLs) [25].

3. DR characterization 3.1. Rationales

• CLs refer to the loads whose operation should not be interrupted in

Sophisticated modeling of load characteristics and its inherent uncertainties is the prerequisite for effective estimation on the CV of DR. In general, the existing methodologies used for DR modeling can be roughly divided into two categories: analytical and data-based approaches [20]. The former mainly evaluates the demand responsiveness by formulating optimization models from a profit-driven perspective [21] while the latter predicts the DR capability by learning customer behaviors through historical data [22]. However, for CV studies under the NLC case, as DR is solicited on a voluntary basis and its performance is examined in a long-term horizon, this will bring about some additional issues which may make the above DR modeling approaches no longer applicable. The most substantial one is the heterogeneity in demand-side behaviors. In NLC, as loads are not directly controlled, individuals may act differently and not necessarily perform the DR calls from the grid in a rational manner [23]. However, in reality, it could be very difficult for the SO to have full knowledge about the idiosyncrasies of each individual, such as their rationality, consumption preferences, etc. Moreover, even if such information is attainable, the actual responsivity of users during operation can be also affected by various unpredictable factors [24]. Both of these would make it infeasible for SOs to represent DR using fully analytical approaches in real cases. Beyond this, for long-term analysis, since customers can sign up or opt out of DR programs dynamically, the available DR capacity in the system could be not stable but evolve with the demand-side participation over time. According to the study of [25], in practice, whether individuals are willing to participate in DR is not only dependent on their own preference, but could be also affected by some other criteria, such as their historical payoffs from the program. However, most of current DR modeling approaches cannot fully capture such evolutionary and dependent nature of customer behaviors. Driven by the above challenges, a holistic modeling framework for DR that is able to address all the discussed issues is proposed in this study. As shown in Fig. 1, the framework consists of a number of modules, which represent the modeling of influential factors of DR existing at different timescales (Fig. 2). Specifically, the physical characteristics of DR (load) resources are examined in the demand analysis (DA) block, whose outputs serve as the essential knowledge of the entire study. The human-related aspects in DR are analyzed in two different modules: contract selection (CS) and actual implementation (AI). The CS mainly represents users’ decision-making on DR subscription in the contract-signing phase, which generally involves a longterm horizon; whereas the AI is intended for evaluating the actual DR performance of consumers for the short-term operation horizon, while subject to the constraints of long-term CS decisions. By combining the outputs of these modules, the modified load profile by DR under different operating scenarios can be estimated. These data, as the final outputs of the framework, is used by the reliability evaluation algorithm to assess the DR CV.

•

•

any circumstances. In reality, CLs include refrigerators, cooking and lighting facilities. Since the use of CLs is normally related to the livelihood of individuals, hence they have no responsivity to external signals in most cases. ILs refer to the loads whose consumption can be curtailed at the time of system emergencies. Typical ILs include heating, ventilation and air conditioning appliances, etc.. For ILs, if a power reduction P il, − is initiated in a period t, their modified demand can be derived as Pkil, t = Pkil,,trat − Pkil,,t−, where Pkil,,trat is the normal consumption (baseline) of ILs at t. SLs are the loads whose demand can be flexibly settled in a timehorizon subject to the total energy constraint. The most common SLs include water heaters, and plug-in electric vehicles, etc. To SLs, if a DR is initiated during operation, their resulted energy reduction must be paid back sometime after the DR period, which is controlled by customers.

To represent this, a generalized technology-agnostic model is adopted, taking into account of both the LR and the relevant uncertainties with SLs. The method characterizes the demand reduction and recoveries of SLs by using two straight lines, as shown in Fig. 3. The upward line models the load pick-up after the DR, while the downward line describes the restoration of consumption back to the pre-DR level while considering the fading effect of LR process [26]. It is worth mentioning that, in practice, although individuals may have different patterns of demand payback in ILC-based DR programs theoretically, the two-line-based model as depicted by Fig. 3 has been mostly commonly used in DR studies [14], since it could properly capture the compensatory nature of shiftable loads and its correlation with customers’ relative satisfaction. Because of this, in this study, we adopt the same approach to model the recovery pattern of SLs, whereas other possible dynamic characteristics (e.g., oscillation process) in the LR were not taken into account. However, it should be noted that, from a technical perspective, the proposed DR modeling framework could be extended and incorporate SLs with different LR characteristics, if needed. The detailed discussion on such issue is beyond the scope of this study. Each time a load reduction Pksl, t, − is initiated, say in period t, the corresponding restored demand at a subsequent period t′ (Pksl, tt, +' ) can be uniquely determined as up pk sl ⎧ bk,0 + ϖk (t ′ − t − 1), t '∈ {t + 1,⋯,t + δk } ⎪ Pksl,, tt+′ = bksl,1 − ϖkdw (t ′ − t − δ pk ), t '∈ {t + δ pk + 1,⋯,t + δk } k k ⎨ ⎪ 0, else ⎩

(1)

where

3.2. Demand analysis module

bksl,0 = [2Pksl,, t− + ϖkup (δkpk − 1)(δkpk − 2δk ) + ϖkdw (δk − δkpk )2]/2δk

(2)

bksl,1 = [2Pksl,, t− + ϖkup δkpk (δkpk − 1) + ϖkdw (δk − δkpk )2]/2δk

(3)

ϖkup ,

ϖkdw ,

δkpk

δk and are characteristic parameters, which define and the shape of user’s LR pattern. Under ILC, since customers implement LR in an uncontrolled mode,

From a physical perspective, the potential of DR is mainly dictated by the operational characteristics of load demand. According to the

Fig. 2. Timescale for different modules.

į

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Fig. 3. Characterization of demand payback for SLs.

incorporate such with a priori information case. In reliability-based DR, consumers reduce their demand upon request and in return they get financial rewards from the grid. For an interval z, the compensation received by a customer k due to DR actions can be computed based on a benefit function Uk: R+ → R. Generally, the composition of Uk is related to both capacity and energy contribution of DR [27]. In some DR programs, penalty policies may also exist for the violation of contract obligation. In this case, if a customer fails to meet the DR request, a penalty charge Gk will incur where the value of Gk increases with the violation degree of the user [13]. On the other hand, performing load reduction (shifting) will also cause inconveniences to consumers. In DR studies, such discomfort can be normally represented using a disutility function Lk: R+ → R+, which is considered as the input information in our model. Lk(.) is a function which maps each customer’s load response level (i.e., Pkil,,t− and Pksl, t, −) to his corresponding disutility value. In this function, since both independent variables (Pkil,,t− and Pksl, t, −) and the dependent variable (user’s disutility) involved are positive real numbers, we can notate it as “Lk(.):R+ → R+”, where “R+ → R+” specifies the mathematical nature of the function Lk(.), i.e., it is a mapping of the data existed in a positive real-number domain to a new positive real-number domain. Given the above definitions, the users’ total payoff (Wk) from DR participation in interval z can be then expressed as:

the parameters in (1) could be uncertain to the SO. In practice, to determine these parameter values, a load survey is required. The statistical characteristics of these quantities can be identified based on longterm observation of customers’ LR due to DR. However, here for simplicity, we assume ϖkup , ϖkdw , δk and δkpk are normally distributed variables, which are determined using random sampling in the CV calculation. Combining both the power reduction and payback, the demand of SLs under DR can be expressed as: t−1

Pksl, t = Pksl,rat − Pksl,, t− + ,t

∑

Pksl,, t ′+t

(4)

t ′= t − δk

Pksl, t, rat

where is the power demand of SLs in normal conditions (without DR) at period t. 3.3. Contract selection module To model demand-side behaviors in the CS phase, let ΩD denote the set of system customers, and for each user k ∈ ΩD, we assume all his probable actions/decisions for CS constitute a finite set Sk = {sk1, sk2, ⋯, skM } , where each element in Sk is a percentage value representing the ratio between the user’s contracted (load reduction) level and his total DR potential Pkil,,trat + Pksl, t, rat . In addition, a time-interval set Tcs = {1, 2, ⋯, z , ⋯} is defined representing the contract terms/ time-horizons for CS decision. Thus, each time-slot t in z ∈ Tcs can be denoted by tz = mod(t , z ) . Given the above notations, the major problem to address in CS is how to determine the users’ liability for choosing different actions in Sk at each interval z ∈ Tcs . For this, let us first consider the case without a priori information. In this case, since individuals have barely any conception about the DR program they enroll in, their decisions for CS have to be made only based on their own judgment (which can be instinctive and subjective). Thus, for user k, the probability of each strategy sk' ∈ Sk to be selected can be described using an empirical distribution ΓIk : ={xkI,0 (sk' )} , where xkI,0 (sk' ) denotes the probability value for sk' and ∑s ' ∈ Sk xkI,0 (sk' ) = 1.

(

)

Wk sk, z , Pkil,, t−z , Pksl,, tz− = Wk0 (sk, z ) +

∑ Wk′ (Pkil,,t−z , Pksl,,tz−) tz ∈ z

(

) ∑ Uk′ (Pkil,,t−, Pksl,,t−)

Wk0 (sk, z ) = Uk sk, z , Pkil,, t−z , Pksl,, tz− −

z

z

(5)

tz ∈ z

(6)

Wk′ Pkil,, t−z , Pksl,, tz− = ℘ (Uk′, Gk , Lkil , Lksl )

(7)

(

)

According to (5), the customer payoff from DR is the summation of two components, i.e., availability payment Wk0 and utilization payment Wk' . Wk0 generally involves the availability of DR which is dictated by the user’s contracted level at interval z (i.e., CS decisions sk, z ) as represented by (6); while Wk' corresponds to the energy curtailment, which depends on the users’ actual performance during operation Pkil,,t−z

k

ΓIk indicates the customer’s inherent belief about the prospect of such a DR program. For example, if a customer is cordial and believes that participating in DR could bring reasonable rewards, he should orient at choosing high contract-level strategies; otherwise, the lowlevel strategies might be preferred. As ΓIk is established on the inherent propensity of users, it remains constant and does not change with time. Although the above formulation seems reasonable, it might be not sufficiently precise for CV studies, due to the negligence of users’ learning capabilities. In actual conditions, for long-term analysis, as consumers can potentially ‘forecast’ the profitability of DR program based on their previous observations and take this into account in their future decisions; therefore, the probability of the customer for selecting a certain CS strategy could be not a constant, but evolve with the time. This means the performance of customers at the CS will not follow their inherent pattern (ΓIk ) consistently. As such, next we will describe how to extend our model to

and Pksl, t,z− and is a result from Uk' , Gk , Lkil , and Lksl , as represented by (7). In normal conditions, since customers at the demand side can hardly assess information about the system aside from their own observations/ experiences in history, hence their decision-making at CS tends to follow a “reflex-response” paradigm in praxeology [28]. This can be explained as: at each interval, a user may switch from his current action to other actions if those can be proved able to yield more pleasurable results (higher payoff) once taken earlier; moreover, the ‘better’ an alternative strategy as being perceived, the higher likelihood it will be chosen. To properly model this “reflex-response” effect, a behavioral economics based theory, regret-matching mechanism (RMM), is introduced in this study. RMM is originally designed to address the local decisionmaking problem under the incomplete information of environment 696

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payoff is the normalized value of users’ total payoff Wk (.) with respect to all the concerned intervals z. When the payoff with the strategy sk'' is lower than that of sk' , the user will not regret his decision and hence Mk, z (sk' , sk'') is 0. To calculate the regret measure, the SO needs to know what the user’s payoffs would have been, if their actions in the past have been different from what they actually were, i.e., Wk (sk'', τ ) in (9). However, in practice, since it is not always feasible for the SO to obtain such information from users, Eq. (8) is not directly applicable. To resolve this issue, the formulation of Ek, z has to be converted. For long-term studies, if the probability of a strategy s '' being selected is a times that of strategy s ' , according to the law of large numbers, s '' will be played a times as often as s ' . Because of this fact, the total payoff over intervals when s’’ is taken can be estimated by multiplying the s ' -payoff by a frequency term 1/a; the modified form of s '' -payoff (i.e., the first term in (9)) is then rewritten as

[29]. Due to its distributed nature, RMM is highly suitable for representation of users’ adaptive behaviors, like the CS case discussed here. On the other hand, as RMM is established on the bounded rationality assumption of human, therefore it can more effectively model the behavior patterns of customers in real-world conditions. Note that the proposed RMM is also distinct from the common “opportunity cost” (OC) concept in microeconomics, due to the following aspects: (1) In OC theory, the potential loss/gain of the customer for taking an action instead of an alternative one is quantified by using ‘opportunity cost’. To calculate the OC of a scheme over another, it is assumed that the decision-maker could perfectly estimate the potential value with respect to each of his options, before making such decisions. In this case, the OC belongs to a “look-ahead” approach, which can be only used for the contexts where corresponding forecast data is available. By contrast, in RMM, the potential loss/gain of the customer for taking an action instead of an alternative is quantified by using a ‘regret value’. As distinct from the OC, the RMM assumes that the decisionmaker concerned could not have perfect foresight about the potential value of his action before selecting it; instead, the decision-maker could only learn the profitability of his strategy/action gradually from the previous observations/experiences in history. Because of this, the RMM belongs to a “look-back” approach, which is particularly suitable for representing the behaviors of individuals under the incomplete information of environment. (2) Besides, another difference between the two theories pertains to the fact that the OC concept is mainly used for one-time decision-making, whereas the RMM focuses explicitly on the dynamics (evolutionary characteristics) in customers’ decision-making process. Specifically, in the RMM framework, the customers are considered to derive his decision not only based on the information in the current phase, but also the available knowledge (experiences) obtained in history. (3) Finally, the two theories also differ in terms of their outputs. In the OC framework, the output results are single and deterministic decisions (selections); but for RMM, the outputs are a collection of probability distribution functions, which indicate the possibility of the customer for choosing each strategy option in the current time. Based on the above explanations, the justification for using regretmatching theory in this study can be summarized as follows: first, in real-world applications, since customers have freedom to decide whether to sign up for the DR program dynamically upon each contract term, and moreover, in most cases, these individuals cannot know the expected payoff of his action until it is actually realized at a later time. These features make the decision-making of customers on DR participation more consistent with the rationale of RMM model, as compared to the OC framework. Second, unlike OC, the RMM utilize a probabilistic model to represent the behaviors of customers. Thus, it can properly capture the bounded rationality and stochastic nature of humanbeing in the DR modeling, which is more consistent with the situation as it turned out in real-world conditions. Additionally, since the proposed RMM approach combines the advantages of both analytical and data-based techniques to derive the DR model, it can identify the behavior pattern for different types of customers without making any presumption on their preferences. In this regard, our proposed approach could be more universal and practical in actual implementations, as compared with the OC-based approach. In RMM, for every interval z ∈ Tcs , the regret of a customer Mk, z (sk' , sk'') for not having chosen a different strategy sk'' ∈ Sk relative to the present action sk' is defined as

Mk, z (sk′, sk″) = max {Yk, z (sk′, s″), 0} Yk, z (sk′, sk″) =

1 z

[ ∑ τ ⩽ z : sk , τ = sk′

Wk (sk″, τ ) −

∑

∑

Wk (sk′, τ )

∑

xk, τ (sk′)·Wk (sk′, τ )/ xk, τ (sk″) (10)

τ ⩽ z : sk , τ = sk″

where xk, τ (sk ) denotes the probability for the action sk to be chosen at interval τ ≤ z . In practice, since the value of xk, τ (.) can be readily determined from the historical data of customers, Eq. (10) thus becomes tractable for the SO. With the modified regret measure, the propensity of customer k ∈ ΩD over his decisions at CS can be then defined, according to the RMM. If let sk' ∈ Sk be the action chosen by k at time-interval z, the likelihood of the user to take strategy sk'' ∈ Sk at z + 1 follows the probability distribution ΓBk, z + 1 below

ΓBk, z + 1 =

⎧ xkB, z + 1 (sk″) = min

{M 1 γ

k , z (sk′, sk″)

, ς

}

⎨ x B (s ′) = 1 − ∑ x B (s ″) k, z + 1 k sk″∈ Sk : sk″≠ sk′ k , z + 1 k ⎩

(11)

where xkB, z + 1 (sk' ) and xkB, z + 1 (sk'') denote the probability of the user for choosing strategy sk' and sk'' , respectively; γ is the proportionality factor; ζ is a predetermined small constant which guarantees that the sum of all the proposed probabilities does not exceed 1. Eq. (11) states that at each interval z, a customer can either continue using the same strategy as in the previous interval z-1 sk' , or switch to a new action sk'' ∈ Sk , sk'' ≠ sk' with probabilities that are proportional to their regret value Mk, z (sk' , sk'') . Besides, taking ζ as a minimum ensures there is always a positive chance for every strategy of Sk to be taken in the decision-making. Thus, the provided model in (11) is fully consistent with the core idea of reflex-response.■ So far we have modeled the customer decision-making for CS with and without a priori information. However, in the real-world, as most of individuals can be not fully adaptable nor incorrigibly obstinate, thus their actual performance (behavioral pattern) at the CS tends to be intervenient between the estimates of the two models. As such, by combining the distributions ΓIk and ΓBk proposed above, the final formulation of customer CS model can be then derived as:

Γk, z + 1 =

⎧ xk, z + 1 (sk″) = (1 − λk ) min

{M 1 γ

k , z (sk′, sk″)

}

, ς + λk xk,0 (sk″)

⎨ xk, z + 1 (s ′) = 1 − ∑ x (s ″) k sk″∈ Sk : sk″≠ sk′ k , z + 1 k ⎩ (12)

As shown in (12), the final probability for a user to choose an action sk'' ( xk, z + 1 (sk'') ) is a weighted average of two probability vectors, where the first term with weight 1 − λk represents the effect of users’ adaptability, while the second term with weight λk reflects the impact of customer intrinsic preference on their selections. The weighting coefficient 0 ≤ λk ≤ 1 reflects the relative importance of historical experiences to the customer. In practice, to identify the value of λk , the SO needs to collect the information about users’ CS actions (sk ) in history. Then, statistical techniques can be used to determine the differences

(8)

τ ⩽ z : sk , τ = sk′

Wk (sk″, τ ) =

τ ⩽ z : sk , τ = sk′

] (9)

As observed, the regret is calculated as the variation of user’s average payoff for every time if the actually used action sk' were replaced by a different one sk'' ∈ Sk in the history up to z. The average 697

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In (14), ρk is the retail electricity price and ρk Pkil,,t−z represents the user’s savings in electricity bill due to the load curtailment. 0 ≤ ωk ≤ 1 is a weighting coefficient indicating the relative importance of incentive rewards and comfort to the individual at time-slot tz . For the ILC program, as the compliance of users to DR signals could be highly uncertain, thus ωk is a random variable which can be described using a probability distribution Ψ(ωk ) . In practice, as the form and coefficients of Ψ(ωk ) are unknown to the SO, they need to be learned from the historical data of customers. For this, a nonparametric kernel density-based approach (NKDA) [30] has been used in this study. Compared to traditional methods, NKDA does not rely on parameter estimates and a-priori knowledge about the variables. In this regard, it has ability to fit any shape of probability distributions and thus can recognize different behavior patterns of customers in actual situations. In CV assessment, the value of ωk will be determined by using randomly sampling, according to Ψ(ωk ) . Then, the expected response level (load reduction) of customer k ∈ ΩD for the time period tz can be estimated by solving the optimization problem given below:

between the observed data and estimation results provided by the two component models. As the obtained distances indicate the ‘closeness’ of users’ behavior pattern to the ΓIk and ΓBk in statistics, the value of λk can be quantified by normalizing the calculation of these distance measures. In the CV estimation, the SO can update and obtain Γk, z for each customer k ∈ ΩD at interval z ∈ Tcs by using Algorithm 1. Then, for a given sk' , z ∈ Sk , the available DR capacity of the user at time-slot tz can be determined according to (13). These results are namely the outputs of CS module.

(

sl,rat Pkav, tz = sk′, z Pkil,rat , tz + Pk , tz

)

(13)

Algorithm 1 (Derivation of the dynamic probability distribution Γk,z for customer CS decision).

Input: Set of CS strategies Sk ; payoff function Wk ; Empirical distribution Γ Ik ; Historical DR records sk, τ , Pkil,,t−τ , Pksl, t,τ− , Pkdrr , tτ , ∀ τ < z

maximize Wk′

Output: The probability distributionΓk, z , ∀ k ∈ ΩD (1) (2) (3) (4) (5)

Pkil,, t−, Pksl,, t−

sk'

z

Select an initial action from Sk and set τ = 1 Loop t=1 Repeat Check whether there is a DR at user k in slot t If yes, retrieve the data of

(6)

Pkil,,t−τ

and

Pksl, t,τ− ,

subject to

and record

(7) Else, continue (8) t ← t+1 (9) Check if t ∈ τ (10) If yes, go back to (4) (11) Else

0 ⩽ Pkil,, t−z ⩽ Pkil,rat , tz

(16)

0 ⩽ Pksl,, tz− ⩽ Pksl,rat , tz

(17)

Pkil,, t−z

(12)

Quantify user’s payoff Wk under sk'' and sk' , (5) Compute the regret measure Mk, τ (sk' , sk'' ) (8) End for

+

Pksl,, tz−

⩽

Pkdrr , tz

(18)

Here, constraints (16) and (17) are used to ensure that the power reduction obtained from ILs and SLs not exceed their available capacity in the period. Also, considering that the emergency-DR is performed only upon the request of the SO, thus the total DR level of the customer should not be greater than the required value. This is ensured by (18). Since the formulation (15)–(18) is a linearly constrained nonlinear programming problem, it can be solved using interior point method [26]. The calculation of the model will indicate the optimal level of power curtailment with respect to ILs and SLs from the perspective of customer, Pkil,,t−z and Pksl, t,z−, while subject to the DR requirement of the grid

for ∀ sk'' ∈ Sk |sk'' ≠ sk' do (13) (14)

(15)

z

(15) Determine Γ Bk, τ , according to (11) (16) Check whether τ = z (17) If yes, combine Γ Bk, τ and Γ Ik to derive Γk, z based on (12) (18) Else, τ ← τ + 1 (19) Go back to (2) (20) End loop

(Pkdrr , tz ). These results, as the outputs of AI module, will be fed back to DA to determine the value of P sl, + ' in (1), which are used in the CV evak , tz t

luation of DR. 3.4. Actual implementation module 3.5. Outputs module During operation, each time upon receipt of DR calls, customers will face the problem of how to reschedule their loads to respond to the request. Such a decision-making problem is formulated by the AI module. To do so, let Pkdrr , tz denote the demand reduction required by the SO at slot tz , then users’ expected incomes from DR and the penalty payment for non-compliance can be calculated based on the benefit function Uk' and penalty function Gk , where Uk' and Gk are proportional functions of the users’ responses Pkil,,t−z + Pksl, t,z− and its deviation from the request level

Pkdrr , tz

−

Pkil,,t−z

Pksl, t,z−,

−

Combining the load reduction and LR effects, the total demand of a DR user under the emergency condition PkE, tz can be derived accordingly as il sl PkE, tz = Pkcl,rat , tz + Pk , tz + Pk , tz t −1

z il,rat sl,rat il, sl, sl, + = Pkcl,rat , tz + Pk , tz + Pk , tz − Pk , tz − Pk , tz + ∑t ′= tz − δk Pk , t ′tz ⏟ ⏟ of AI Outputs ⏟of DA Outputs Outputs

of DA

respectively. Also, the inconvenience costs caused

(

Pksl,, tz−

Uk′ Pkil,, t−z

) = ωk [ −

(

,− Gk Pkdrr , tz

(

+

Pksl,, tz−

−

Pkil,, t−z

)+

is the power demand of CLs at time-slot tz . where In this study, since we assume SO can possess the appliance-level and information of all its customers (as stated in Section 2), Pkcl, t,zrat , Pkil,,trat z

Pksl, t,zrat are deterministic values in (19). 3.6. Summary on the value of proposed framework

ρk Pkil,, t−z

The holistic framework presented above have various theoretical properties, making it structurally differ and outperform the existing DR modeling approaches in the following aspects: (1) As the proposed framework accounts for the uncertainties of customer performance in

− Pksl,, tz−)]

− (1 − ωk ) [Lkil (Pkil,, t−z ) + Lksl (Pksl,, tz−)]

(19)

Pkcl, t,zrat

by DR are denoted by the disutility functions Lkil and Lksl , which increase with the actual response level/frequency of customers. Based on the above functions, the total payoff of customer for demand modification at slot tz (Wk' ) can be defined, which is computed as the weighted difference between its expected revenues and the discomfort cost:

Wk′ Pkil,, t−z ,

(dependent variable of AI outputs)

(14) 698

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(TS) and validation set (VS). TS, which is constituted by 130 random samples from the 180 datasets, is used to learn users’ behavior pattern and determine the parameters of AI model (i.e., Ψ(ωk ) ), while VS, with the remaining 50 samples, serves as the reference data to check the goodness-of-fit for the produced model. To achieve the best performance of NKDA, we examine the effect of various kernel functions and an optimization technique [30] is also used to determine the best bandwidth for the model. The goodness-offit is assessed using the mean-square-root error (MSRE) index [30]. The kernel function with the smallest MSRE is considered as the best-fit and will be finally selected. Following this way, the forecasted results based on the fitted Ψ(ωk ) from NKDA is visualized via cumulative distribution function (CDF) in Fig. 6. As observed, for both customers, the area between the estimated and actual observed CDFs is rather small, implying that there is good consistency for the prediction and actual measurements in statistics. To verify this numerically, the well-known chi-square ( χ 2 ) test is further conducted. In the χ 2 test, the variance between envisaged distribution and actual samples is measured through the χ 2 statistic, where a smaller value represents a higher forecast precision. For a given significance level αα, the hypothesis of a distribution model will be rejected if its χ 2 is found larger than the threshold value α χα2 at significance level α; otherwise, the model will be accepted. According to the simulation, the χ 2 statistic of the fitted Ψ(ωk ) and the threshold value under different significance levels are summarized in Table 1. As is shown, the obtained χ 2 for both users are smaller than the threshold value at significance level of 0.01. This implies that the fitted Ψ(ωk ) passed the tests with a high accuracy. Thus the proposed AI model is valid and capable of representing users with divergent behavior patterns in real-world applications.

both CS and AI phases, it can capture the stochastic nature of DR under multi-timescales, which is in contrast to most of the current DR representations that solely consider the uncertainties of DR in a shortterm horizon [18]. (2) The presented CS model is established on an empirical (ΓIk ) and a learning-based component (ΓBk ), by which both static and dynamic feature in customers’ DR decisions could be considered and properly examined as they occur in the real world. (3) Since the proposed AI formulation combines the advantages of both analytical and data-based approaches, it can identify the behavior pattern for different types of customers without making any presumption on their preferences. In this regard, our hybrid model can be more practical in actual implementations, as compared with the existing analytical approaches [21]. 4. Assessment method In this section, the evaluation algorithm for the CV of DR is presented based on the metrics in Section 2 and the developed models in Section 3. As explained earlier, evaluation of DR’s CV (EFC) is implemented based on assessing and comparing system adequacy levels (EENS) with and without DR. To this end, the sequential Monte-Carlo simulation (SMCS) method has been used in this study. Figs. 4 and 5 demonstrate the major procedures of the algorithm. 5. Case study In this section, the effectiveness of the proposed DR framework will be first verified. Then, specific case studies are conducted to demonstrate its application for CV evaluation of DR. 5.1. Validation of proposed DR models

5.1.2. CS To test the CS model, a fuzzy logic approach is used to generate the virtual data with a similar process as in [22]. For this, we consider DR customers classified into two categories, namely empirical users (EU) and learning-based users (LU). It is assumed that EUs make CS decisions solely depending on their personal propensities, whereas LUs consider not only the preference issue but also the profitability of DR. The membership functions and fuzzy logic rules used for both customers are shown in Fig. 7 and Table 2. The required data behind Fig. 7 and Table 2 were obtained based on the distributed questionnaires among 500 units from a real commercial-based DR program in China. To enable the test, 300 sets of chronological CS data have been created for both customers. Similar to the AI case, we use the first 200 sets to derive the parameters of the CS model and the rest 100 datasets for the validation. The effectiveness of the derived model is evaluated by comparing the 1st raw moment (mean) and 2nd central moment

5.1.1. AI To validate the proposed AI model, the actual data collected from a real reliability-driven DR program in China is used. Two specific customers with diverse consumption patterns are arbitrarily selected and considered in this test. User 1 has a total capacity of CLs/ILs/SLs with 124.8/38.4/28.8 kW while User 2 corresponds to 82.3/24.4/18.3 kW, respectively. The historical DR data for each customer is collected over 2 years, which has 180 data samples overall. Each sample is characterized as P hdr = {P drr , P il, −, P sl, −} , which records the historical performance of the individual in each of 180 DR events. In this DR program, the incentive and penalty rate adopted corresponds to $ 0.18/kWh and $ 0.25/kW, respectively. The energy price ρk is equal to $ 0.14/kWh. To perform the verification, all the data are divided into training set

Start Data input

Set Cmax=Crat and Cmin=0

B

Add benchmark unit with capacity Cbm=(Cmax+Cmin)/2

Create state-duration time series for CG and REG units Determine power output curve of REG and CG units

A

Compute system reliability level (EENSdr) with DR using SMCS

Cmin=C

bm

Cmax=C

bm

Run SMCS to determine EENS v of the adjusted system EENSv>EENSdr? N

Y

Remove DR from the system

B

N

Search for EFC Export EFC value as DR CV

Update Cbm=(Cmax+Cmin)/2

Bisection method

|EENSv-EENSdr|/EENSdr<ζ? Y EFC=Cbm

Fig. 4. Flowchart of the algorithm for evaluating the CV (EFC) of DR. 699

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Fig. 5. Procedures for evaluating system adequacy with DR based on SMCS.

Fig. 6. CDFs for forecasted distribution model and actual measurements in TS. Table 1 Chi-square test results. χ2 statistic

User 1 User 2

9.425 11.631

Threshold value α = 0.1

α = 0.05

α = 0.01

α = 0.005

7.779

9.488

13.277

14.860

(variance) of the observed data and estimation results. As shown in Fig. 8, for both customer groups, the difference in the mean and variance value is rather small during the concerned intervals. This indicates that the estimation provided by our model has good statistical consistency with respect to those observation data. Therefore, the proposed CS model can be effective to represent DR customers with

Fig. 7. Fuzzy membership functions.

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Table 2 Fuzzy logic rules of customers. Rules

#1 #2 #3 #4 #5 #6 #7 #8 #9

Table 3 Scenario settings for CV assessment.

Learning-based customers

Empirical-based customers

Regret

Preference

Fitness

Regret

Preference

Fitness

High High High Middle Middle Middle Low Low Low

High Middle Low High Middle Low High Middle Low

High Little high Middle Little high Middle Little low Middle Little low Low

High High High Middle Middle Middle Low Low Low

High Middle Low High Middle Low High Middle Low

High Middle Little low High Middle Low Little high Middle Low

Energy reward ($/kWh) Capacity reward ($/kW) Penalty rate ($/kW)

#1

#2

#3

#4

#5

#6

0.05 0.45 0.25

0.18 0.45 0.25

0.32 0.45 0.25

0.18 0.45 0

0.18 0.45 0.37

0.18 0 0.25

Scheme 1 (I): DR is modeled by using a fully deterministic approach, as similar to [6]. In this scheme, the DR capacity of customers and their compliance during operation are considered to be both fixed, where for the AI module and ωk ≡ 1, ∀ k ∈ ΩD sk, z ≡ 1, ∀ k ∈ ΩD , ∀ z ∈ Tcs for the CS. Scheme 2 (II): DR is modeled considering long-term uncertainties only. In this scheme, the compliance of customers during operation is assumed to be fixed, where ωk ≡ 1, ∀ k ∈ ΩD ; while their participation level for DR is considered to be stochastic, which conforms to the proposed CS model. Scheme 3 (III): DR is modeled considering short-term uncertainties only, as similar to [13]. In this scheme, the participation level of customers for DR is assumed to be fixed, where sk, z ≡ 1, ∀ k ∈ ΩD , ∀ z ∈ Tcs ; while their performance during operation is considered to be stochastic, which conforms to the proposed AI model. Scheme 4 (IV): Proposed holistic DR modeling approach.

different behavioral patterns in the actual implementations.

5.2. CV assessment To demonstrate the applicability of proposed framework for CV evaluation of DR, the Roy Billinton Test System (RBTS) system [31] is used. The system has a total generation capacity of 240 MW and the peak demand of 185 MW. A 20-MW wind farm is assumed to be added at Bus-3. Each wind turbine has a FOR of 0.04 and cut-in/rated/cut-out speeds of 7.2, 46.8, and 90 m/s [13]. The wind speed is represented using an autoregressive moving average model [25], which is developed based on real meteorological records from China. Also, in this study, we consider that users’ CS strategies and their benefit/penalty/ disutility functions are the same as those used in Section 5.1. The weighting factor λk for CS is assumed to be 0.1. ωk is considered as a normally distributed variable, which has a mean of 0.7 and a standard deviation of 1. Moreover, it is assumed that users sign DR contracts with the SO on a monthly basis and their participation level is 100% at the start of SMCS. To analyze the CV of DR, the benchmark unit is considered connected from Bus 5 of the system. Six scenarios representing DR programs based on different incentive mechanism have been considered as in Table 3. The incentive/penalty rates used here are based on the same datasource as that of previous studies in Section 5.1 and some modifications are also made to allow the settings better fit for the purpose of our test. To quantify the CV of DR, four different DR modeling schemes are considered, and comparative analysis is conducted to show the advantage of proposed framework over other existing approaches.

As can be seen from Table 4, neglecting either short- or long-term uncertainties of DR could result in a higher estimation of CV as compared to that with the proposed case. This indicates that, under the ILC, the uncertainties associated with the demand side could play an important role in determining the reliability benefits of DR program. As such, realistically modeling these uncertainties is critical for effective evaluation of the DR CV. Otherwise, the SO might overestimate the DR contribution and make suboptimal decisions in the system strategic planning. In this regard, the advantage of the proposed holistic modeling framework over the existing approaches can be clearly manifested. 6. Conclusion This paper analyzes the capacity value of DR with a new methodological framework developed for the uncertainty modeling of DR. As distinct from existing works, the proposed framework is built on modularized structure and incorporates both technical and human-related aspects in DR programs. Various uncertainties associated with the

Fig. 8. Comparison of E(sk) and D(sk) for the estimated and observed data. 701

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Table 4 CV estimates under different DR models. DR modeling scheme

−15% MW

#1

I II III IV

#2

Original capacity

+15%

pct. (%)

MW

pct. (%)

MW

pct. (%)

20.63 14.31 16.23 12.88

30.85 21.41 24.27 19.26

33.07 26.06 28.92 24.14

42.04 33.13 36.77 30.69

39.78 33.75 34.02 30.96

43.98 37.31 37.61 34.23

I II III IV

20.63 17.76 18.52 15.18

30.85 26.56 27.70 22.70

33.07 30.92 31.65 29.68

42.04 39.31 40.23 37.74

39.78 36.59 37.69 33.21

43.97 40.45 41.66 36.72

#3

I II III IV

20.63 19.56 20.13 19.07

30.85 29.26 30.11 28.53

33.07 32.22 32.95 31.66

42.03 40.96 41.88 40.25

39.78 38.08 39.52 37.65

43.98 42.10 43.69 41.62

#4

I II III IV

20.63 13.39 15.58 11.87

30.85 20.03 23.30 17.75

33.07 26.62 27.58 22.86

42.04 33.85 35.05 29.06

39.78 29.22 33.57 27.89

43.97 32.30 37.11 30.84

#5

I II III IV

20.62 14.78 19.67 12.69

30.85 22.11 29.42 18.98

33.07 28.27 32.08 25.26

42.04 35.93 39.25 32.11

39.78 32.49 38.06 29.87

43.97 35.92 42.07 33.03

#6

I II III IV

20.63 15.39 16.43 13.61

30.85 23.02 24.58 20.36

33.07 28.76 29.86 27.61

42.04 36.56 37.96 35.09

39.78 34.04 35.00 30.69

43.97 37.63 38.69 33.93

Scenario

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demand-side at different timescales are systematically considered in our analysis. The numerical studies verify the effectiveness of the proposed framework and demonstrate the significant potential of DR in enhancing the reliability of power systems. In this regard, the developed framework proves significant not only in its capability of providing complete information about DR but also for its serving as a tool to guide utility companies on the exploitation of DR based on more accurate assessment for the potential of demand-side flexibilities in future power grids. It should be noted that the whole methodological framework presented in this study is utterly proposed from an international perspective rather than focusing on the issues of one country. In fact, in our paper, we only depend on some real data gathered from China (as an example) in the case study to verify the effectiveness the proposed model, but this does not mean our proposed framework is only applicable in China; instead, it could be universal for different applications and different countries, if the relevant data needed is available. Acknowledgements This work was supported by the National Natural Science Foundation of China (51507061, 71601078) and the Fundamental Research Funds for the Central Universities (2017MS007, 2018ZD13). References [1] Siano P. Demand response and smart grids—a survey. Renew Sustain Energy Rev 2014;30(2):461–78. [2] Palensky P, Dietrich D. Demand side management: demand response, intelligent

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