Assessing capacity credit of demand response in smart distribution grids with behavior-driven modeling framework

Electrical Power and Energy Systems 118 (2020) 105745

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Assessing capacity credit of demand response in smart distribution grids with behavior-driven modeling framework

T

Bo Zenga, , Xuan Weia, Bo Suna, Feng Qiua, Jianhua Zhanga, Xuanrong Quanb ⁎

a b

State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China State Grid Beijing Electric Power Company, Beijing 100031, China

ARTICLE INFO

ABSTRACT

Keywords: Capacity credit Demand response Smart distribution grid Reliability Z-number

In smart grid, demand response (DR) provides the utilities with a new alternative to mitigate the operational uncertainties and achieve the power balance target. However, unlike conventional generation units, the performance of DR is strongly dependent on behavioral pattern of customers. As such, to what extent DR programs could be utilized to provide capacity support and contribute to the adequacy of the supply turns out to be an important concern for the utilities. In order to resolve this issue, this paper presents a new methodological framework for assessing the reliability value of DR in a context of distribution grid. The proposed approach is developed on the generation-oriented concept of capacity credit (CC) and it extends the CC application to a DR setting. As the major contribution of this work, the proposed framework accounts for the impacts of both physical and human-related factors on the availability of DR; furthermore, the uncertainty issue that associated with demand-side performances is also explicitly considered in our study. To properly handle the ambiguities of customers’ willingness for DR participation, a novel Z-number-based technique is introduced. Through such an approach, not only the inherent randomness accruing from the demand-side could be captured, but the impact of information creditability would also be accounted for, which could allow a more realistic characterization of DR as compared with existing studies. By jointly using fuzzy-expectation technique and the centroid method, the different types of uncertain variables (probabilistic and Z-numbers) involved in our analysis can be normalized into comparable quantities and then used for the CC evaluation of DR. The proposed framework is illustrated based on both a small test case and a real distribution system, and the obtained results verify the significant role of DR in enhancing the reliability of supply, as well as its sensitivity to different influencing factors.

1. Introduction As an emerging element of smart-grid, demand response (DR) offers utilities an innovative solution to manage the operation of future power systems by exploiting the flexibilities of energy usage at the demand side [1]. DR programs can decrease consumer electricity consumption when contingencies, like unpredictable variations in demand or generation unit outages take place [2]. In this regard, efficient use of DR would significantly conduce to preventing the imbalance of supply and demand, and thus improving the reliability performance of future power systems [3,4]. To effectively determine the potential reliability benefits achievable from DR, it is essential to undertake a quantitative assessment in order to indicate to what extent demand side resources may displace conventional generation and thus fairly estimate their capability in terms of contribution to system adequacy. Recently, some research efforts have

already been made to investigate such a topic. For example, based on the Monte-Carlo simulation technique, Safdarian et al. [5] studied the potential contribution of DR to the reliability of smart grid. Gazijahan et al. [6] proposed a comprehensive multi-stage programming model to investigate the potential capability of DR for ensuring reliable operation of distribution grid. Aghaei et al. [7] and Nikzad et al. [8] performed similar studies with consideration of different types of DR programs. Molavi et al. [9] discussed the effects of D-TOU (day-of-use) tariff on DR program operation with thermal energy storage, and the simulation results indicate that the use of D-TOU together with energy storage can bring about higher DR benefits to the system during peak hours. Besides, Wang et al. [4] investigated the potential value of market-based demand response for the reliability of supply under extreme disasters based on a case study of PJM (Pennsylvania-Jersey-Maryland)*1 market. Zhou et al. [10] also proposed a capacity value conceptual

Corresponding author. E-mail address: [email protected] (B. Zeng). 1 PJM is a regional transmission organization that coordinates the movement of wholesale electricity in all or parts of Delaware, Illinois, Indiana, Kentucky, Maryland, Michigan, New Jersey, North Carolina, Ohio, Pennsylvania, Tennessee, Virginia, West Virginia and the District of Columbia. ⁎

https://doi.org/10.1016/j.ijepes.2019.105745 Received 11 July 2019; Received in revised form 19 November 2019; Accepted 27 November 2019 0142-0615/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature

c inc C rl I N sm P P cl P cl, rated P gen P il P il, ava P il, curt P il, rated P sl P sl, ava P sl, curt P sl, rated P sl, rec P te P tn P usd Q Q gen r V

Acronyms CC CL DR EENS EFC ENS FOR IF IL LR PDF PJM SDG SL SMCS SO

capacity credit critical load demand response expected energy not supplied equivalent firm capacity energy-not-supplied forced outage rate involvement factor interruptible load load recovery probability distribution function Pennsylvania-Jersey-Maryland smart distribution grid shiftable load sequential Monte-Carlo simulation SDG operator

Indices (Sets)

k( ij( t

D)

F)

load points/customers network feeders time periods

µ

Parameters and Variables

C bm c cp C egn

capacity of benchmark unit availability payment for DR participants total capacity of available generation units

ζ

framework for quantifying the potential reliability benefits of DR in the power grid. In addition, Muireann et al. [11] demonstrated that the DR resources could have a significant capacity value, which may reduce equilibrium levels of generation capacity and yielding consumer savings. However, in the above literatures, it is generally assumed that the demand responsivity of customers is fixed, which can be fully determined by the utilities before the evaluation. But in reality, owing to the idiosyncrasy of human behaviors, DR cannot be trusted to provide stable reserve capacity all the time. In view of the above problem, the uncertainty issue of DR has been noticed and investigated by some researches. For example, Gao et al. [12] developed a new approach to evaluate the impacts of DR on the generation adequacy of wind-integrated power systems, wherein the stochastic nature of demand-side participation is explicitly considered by using a variant Roth-Erev algorithm. Yu et al. [13] discussed the uncertainty issue of DR in a context of optimal rate-making study. Also, Kopsidas et al. [14] presented a probabilistic modeling approach to maximize network’s reliability with uncertainties by utilizing the available demand response at emergencies. Kwag et al. [15] examined the reliability benefits of DR, wherein the randomness of customer performance was considered using a multi-state Markov model. In addition, Zeng et al. [16] also put forward a novel probabilistic-possibilistic approach to represent the uncertainty of DR in their studies, which captures both aleatory and epistemic uncertainties that associated with DR programs. In addition, Wu et al. [17] also proposed a chance-constrained stochastic model for network congestion management in the day-ahead power market, with consideration of DR effects. However, for all the literatures described above, the uncertain nature of DR were

incentive rate for DR participation total capacity of DR loads in the SDG current-carrying in the network feeder number of simulation years in the SMCS active power flow in the network power demand of CL baseline demand of CL active power output of generation units in the system power demand of IL available IL capacity in DR program reduced demand that realized by IL baseline power demand of IL power demand of SL available SL capacity in DR program reduced demand that realized by SL baseline demand of SL payback demand of SL total load demand of customers under the DR case total load demand of customers under the normal case load shedding/loss-of-load reactive power flow in the network reactive power output of generation units in the system resistance value of feeder nodal voltage time duration of SL energy restoration process fading coefficient energy compensation ratio ratio of user’s contracted DR capacity to the total responsiveness tolerance threshold value for CC calculation reactance value of feeder impedance value of feeder

mostly described using a simple probabilistic model. Although such DR representation might be suited for some specific settings (e.g., shortterm operational studies), they could be not necessarily applicable for long-term reliability studies, due to neglecting the possible effects of demand-side preferences. In real-world applications, DR activities imply that customers have to change their original energy usage pattern; as such, whether the individuals could be willing to accept these changes and opt in DR program becomes a critical issue for deciding the benefits of DR. If an individual does not subscribe to DR program, then he/she cannot make any contribution to the system reliability, no matter how much flexible loads he/she possesses. In practice, to represent the uncertainties concerning customers’ willingness for DR participation is not without difficulty. This is because, under a liberalized environment, whether an electricity user would be willing to participate in the DR program depends on a wide spectrum of factors, such as rewarding rate, education degree and personal preference, etc. [18]. As such, it could always be very difficult (even impossible) for the utility to have sufficient data (complete knowledge) for estimating the likelihood of each customer to involve in DR. Even if such information can be accessible, in actual situations, whether customers would really opt in DR program can still be influenced by many other issues, such as impulsive decision, propagation effect, and so on [19]. All of these would make it impracticable for utilities to describe the stochastic nature of DR using fully statistical approaches. In this study, a new methodological framework for quantifying the potential benefits of DR to the reliability of smart distribution grid (SDG) is proposed. The proposed method is based on the concept of capacity credit (CC), which was initially developed to estimate the contribution of

2

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The remainder of this paper is organized as follows. The CC metrics of DR are introduced in Section 2. The representation of DR characteristics is presented in Sections 3. Section 4 elaborates on the evaluation method used for CC approximation of DR. Numerical studies are performed in Section 5, and the conclusions are drawn in Section 6.

a generation resource to the adequacy of supply. In this study, this concept is extended to a DR context. As distinct from existing researches, the proposed work paid explicit attention to the role of human-related uncertainties in DR programs and their potential effects to the operation benefits of DR. To achieve this, in this study, we consider the available DR capacity from the demand-side as a synthesized outcome of two facets, i.e., operation characteristics of load appliances and participation rate of customers, and different models are presented to describe the effect of each component. To properly consider the uncertainties of customer participation in DR program, a novel Z-number-based technique is introduced. Unlike traditional uncertainty handling approaches, the proposed Z-number model can not only describe the inherent stochasticity associated with demand-side performance but also incorporate the impact of information reliability, thus allowing more realistic representation of DR effects as they occur in the actual situations. By jointly using fuzzy-expectation technique and the centroid method, the different types of uncertain variables (probabilistic and Z-numbers) involved in our study can be transformed into equivalent quantities. The relevant results are then considered as input data and utilized to enable the CC approximation of DR by using reliability analysis algorithms Compared with existing works, the main contributions of this study are as follows:

2. Capacity credit of DR 2.1. Overview of SDG with DR The study presented in this paper is based on an SDG consisting of various distributed generation units, transmission lines, and customers, as shown in Fig. 1. For this system, it is assumed that smart metering devices with non-intrusive load monitoring functionality [20] have been deployed in all the households. This enables SDG operators (SO) to obtain the device-level information from the gross measurement data of customers, such as on/off status and hourly consumption. Under an open-access market environment, it is supposed that customers have freedom to decide whether participate in the DR program based on their own preferences. For those who are willing to enroll, they need to sign up with the SO and specify how much DR capacity (load curtailment) they could provide, i.e., daily DR availability profile, at different time of a day. During operation, when the SDG encounters contingencies of the system, the SO will dispatch DR as virtual operating reserves to ensure the reliability of supply. In this study, it is assumed that all the DR activities discussed are implemented through direct-load-control (DLC) programs. DLC program refers to the DR activity in which the grid utility has full control over the operating status (including ON/OFF and power consumption) of registered loads based on remote control equipment, assuming that the customer has given permission for supervisory control of their loads. In such program, the system operator can remotely control the power demand of customer customer’s electrical equipment on short notice when the grid reliability is jeopardized or merely if the operator feels necessary to do so. The corresponding DR calls are broadcasted to the DR subscribers via communication infrastructures. These DR actions would modify the load profile of SDG and hence affect the reliability of the system accordingly. Due to space limitations, more detailed introduction about the DLC program can be found in [21]. After each DR event, the SO will keep a record on the participation history of each individual; and based on their actual performance, the SO pays rewards to these customers. This information will be kept in SO’s database for future references.

1) A new evaluation framework based on the CC concept is proposed for assessing the potential contribution of DR to the reliability of SDG. Unlike the existing works [4–11], the proposed approach provides a fair and visualized playfield for comparing the value of generation-side and demand-side resources in the context of reliability. As such, with such framework, the utility operator could expediently estimate the potential reliability benefits arising from DR program under different scenarios, without involving excessive computational complexities. 2) A comprehensive DR model is developed to estimate the flexibility of customer load consumption during operation, wherein the effects of both technical- and human-related factors that attended with the DR program are simultaneously considered in our analysis. Thus, compared with conventional DR representations [12–17], the proposed model could provide a more realistic estimation for the DR performances as they occur in real-world situations, which would lead to more convincing estimation of DR’s capacity value. 3) A novel Z-number-based approach is utilized to handle the uncertainties of customers about DR participation. This is fundamentally distinct from most of existing researches [4–17] in which the information creditability issue for DR modeling was not fully considered, and hence it could enable more accurate and comprehensive characterization for the stochastic nature of DR program.

Fig. 1. Architecture of a typical SDG with DR users. 3

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2.2. CC metrics

Specifically, from a technical viewpoint, the available capability of DR, which is defined as the amount of power consumption that can be curtailed or transferred to other time periods, is primarily tied to the load composition of customers and their usage patterns. In practice, the potential flexible loads for a customer can be identified through analyzing their performance and purposes for which they are to be used [23]. For example, to a residential customer, the operation of an air conditioner can be simply interrupted for a certain period as long as the ambient temperature is within a tolerable range; hence it can be regarded as a potential DR resource. However, for an industrial user (e.g., pharmaceutical factory), interrupting the air conditioner operation may lead to the production of non-conforming products. Thus, the air conditioner belongs to an inelastic load. In addition, the demand responsivity of customers is also affected by the physical properties of their loads. For example, for some particular loads (e.g., water heaters), once they were involved in a demand reduction event, these loads cannot be used for DR purpose in subsequent time periods until the previous curtailed energy was fully restored. In this case, the CC of DR would be directly affected by the operational constraints of loads. Synthesizing the above facts, it is essential to consider the heterogeneous nature of customers’ load demands when analyzing the reliability value of DR. Besides the abovementioned issue, the behaviors/preference of customers can be another factor influencing the potential benefits of DR. As stated earlier, under a context of the liberalized market, the demander customers can decide whether to enroll in DR program based on their own preference. Therefore, to the SO, a potential flexible load in the SDG can be eligible for DR operation only if its owner agreed to do so [24]. According to the studies of [18,25], in practice, whether an electricity user would be willing to participate in the DR program may depend on various factors, such as rewarding rate, education degree, and inconveniences to be caused. Furthermore, for long-term analysis, it has also been reported that the participation of customers for DR program tends to be not constant, but it could evolve with the expected profitability level of customers during operations [26]. In actual situations, to properly consider the uncertainties arising from the demand-side, the utilities normally conduct a field survey and represent the stochastic variability of customer behaviors by using a statistical approach, e.g., probabilistic [27] or possibilistic model [28] that derived from the obtained survey data. Regardless of any statistical-based methods, all the existing uncertainty handling techniques require that the basic data used for the modelling must be completely reliable. However, in real-world situations, the willingness for DR participation is strongly tied to the personal preference of customers and is very individual-specific; but it tends to be arduous (even impossible) for the utility to have fully reliable information about the personal traits of each user. Furthermore, even if the information mentioned above can be accessible, in reality, the actual performance of users pertaining to DR could be still affected by some other unpredictable factors [19], for instance, unexpected events or impromptu cognition. This would make the obtained statistics may not necessarily reflect the characteristics of customer decisions in future cases. All of these would make great difficulties to represent the humanrelated issues in DR programs using a statistical approach. Based on the above explanations, a new DR reliability model which can systematically consider the impacts of all the abovementioned issues is developed in this paper. As illustrated in Fig. 2, the proposed method regards the available DR capacity in the SDG as a comprehensive outcome of two independent facets, that is, the load characteristics and the involvement level of customers during operation. In this study, considering that sufficient data about the customer consumption can be obtained through the smart meters deployed in the SDG, we use a probabilistic method to model the operation pattern of different types of loads. Based on this, the potential impacts of human factors are further incorporated. In practice, since it is often difficult for utilities to get fully reliable information about the idiosyncrasies of each individual, a novel Z-number-based approach is introduced and employed to describe the potential dynamics in the demand-side

The CC concept is initially developed for evaluating the potential of generation resources to provide capacity support for power systems. However, to examine the reliability benefits that might be incurred from the flexibility of demand-side consumption, the definition of CC has been extended to a DR scenario by [10]. To denote the CC of DR, four metrics have been proposed and recommended in [10], which are effective load carrying capability (ELCC), equivalent firm capacity (EFC), equivalent conventional capacity (ECC) and equivalent generation capacity substitution (EGCS). These four metrics define the CC of DR from different perspectives, hence they are generally applicable for different engineering purposes. Specifically, the ELCC is defined from the perspective of demand-side, while the other three metrics are defined from the generation-side. In this respect, the ELCC metric should be more suitable to be used for system expansion planning in the presence of load growth; EFC and ECC metrics are more suitable to be used for the purposes of investment portfolio comparison, i.e., to value DR’s reliability contribution with conventional generation resources; finally, the EGCS metric is suitable to be used for indicating the capability of DR for substituting existing generation capacity. Among these metrics, since the EFC method defines the DR’s CC in the light of comparing its reliability contribution with a conventional (100% reliable) generation unit, it can better illustrate the virtual generation characteristics of DR resources and hence providing a more clear and straightforward manner to value the DR’s CC in real-world applications. Therefore, in this paper, to avoid excessive complexity, we only employ the EFC method to estimate the CC of DR, although other metrics can also be used in a similar manner, if needed. According to the EFC approach, the CC of DR is defined as the capacity of additional generation that must be deployed to achieve the same system reliability as the situation with DR. In practice, to determine the EFC of DR, the reliability of the system is first assessed when DR effect is incorporated: (1)

E1efc = [(C egn + C rl ); D]

where D denotes the system load profile; denotes the capacity of available DR resources; C egn represents the total capacity of available generation units in the discussed SDG. Also, E1efc is the system reliability index. In this work, the well-known expected energy not supplied (EENS) [22] is adopted since it could allow our results explicitly comparable to previous works in [10]. Subsequently, the concerned DR resource will be removed, and a benchmark unit with the capacity C bm and a zero forced outage rate (FOR) is added. This modification will lead to a new EENS of the system, as expressed

C rl

E2efc = [(C egn + C bm ); D]

(2)

The value of will be adjusted continuously until the reliability level of the system is equal to that of the DR case, i.e., E1efc = E2efc . Then, the required generation capacity C bm at this time is considered to be the CC (EFC) of DR.

C bm

3. Reliability modeling of DR 3.1. Overview Effective representation of demand-side performance and its related characteristics is the prerequisite for implementing CC analysis of DR. As aforementioned, unlike conventional generation resources, the capacity benefits of DR are virtually exploited from the changes of energy consumption pattern by customers. As such, to what extent DR activities could contribute to the reliability of system, therefore, would not only depend on the technical properties of end-use load appliances, but also on the behavioral preference of individuals at the demand side. 4

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Load characteristics Section 3.2

Probabilistic method

Participation level of customers Section 3.3

Z-number-based method

3.2.3. Shiftable loads SLs refer to the loads whose energy usage can be flexibly settled during certain periods as long as their total consumption remains constant. In practice, typical SLs include washing machines and PEVs. During operation, if a demand curtailment is called from an SL at bus k, the reduced energy usage will be restored over a certain time interval with temporal adjacency after the load reduction event [26,30]. In reliability studies, such DR characteristics of SLs with intertemporal constraints can be described by using a generic linearized model, as suggested by [27]. The discussed approach considers the demand reduction and recoveries of SLs as a load-redistribution process, where the energy payback due to a load curtailment event is assumed to be linearly distributed in the subsequent time-periods at a diminishing rate. According to this model, if a demand reduction event occurs at a time period t, the DR effects of SLs as modified demands can be mathematically described as:

Available DR capacity

Fig. 2. Framework of the proposed DR model.

participation for DR program. The indication concerning users’ participation willingness, together with the operation pattern of their loads, defines the actual available capacity of DR for each time period in the SDG. The obtained results, which are seen as the output data of the proposed DR model, are regarded as input parameters and applied in the procedures of CC approximation. 3.2. Load characteristics

Pksl, t = Pksl,rated ,t t+ k

D,

sl,curt Pksl,rec , t t = Pk, t

Pkusd ,t

3.2.2. Interruptible loads ILs are defined as the loads whose energy consumption could be partially or even totally curtailed if the system were in the emergency state. In practice, typical ILs may include heating ventilation and air conditioning equipment, home entertainment devices, etc.. During operation, for a specific time-period t, the quantity of power reduction that could be exploited from an IL may vary from zero up to their energy demand at t. Thus, in the CC calculation, the final load power of ILs can be expressed as

Pkil, t = Pkil,rated ,t

Pkil,curt ,t

k

D,

t

t

(5)

k

D,

t

(6)

k

k (t

t

1)

k

D,

t, t

[t + 1, t +

k]

(7)

where D is the set of load buses; and are the normal power demand of the CL at t and the potential load shedding occurred, respectively. In our CC evaluation, Pkusd , t is input data, which is determined by solving an optimal DR scheduling model as given in the Appendix. Here, it is worth mentioning that the ‘load shedding’ in (3) is fundamentally different from the conventional concept of ‘load reduction’. The latter refers to the adjustment of consumption for flexible loads; whereas the former refers to the compelled interruption of customers’ inflexible loads. As such, the CL shedding can be seen as a kind of forced load curtailment, which could bring about much greater discomfort/ disutility to customers than the conventional “load reduction” case.

Pkcl,rated ,t

k

D,

where Pksl, t, rated and Pksl, t, curt represent the regular power demand of the SL at bus k and the quantity of load curtailment that performed in timeperiod t. In the CC calculation, Pkil,,tcurt is an input data, which is determined by solving an optimal DR scheduling model as presented in the Appendix. Also, Pksl, tt, rec ' denotes the payback demand that exerted to period t, because of the DR event in the previous time t’; furthermore, k represents the time duration of SL energy restoration process while k and k are the fading coefficient and the payback ratio. The values of k , k and k collectively define the recovery pattern of SLs [27]. In the above model, Eq. (5) states that, for a SL, its modified load demand due to DR in a period t (Pksl, t ) can be computed as the baseline demand (Pksl, t, rated ) minus the curtailed power by the SO (Pksl, t, curt ) plus the total recovered demand that imposed to t ( Pksl, tt, rec ' ). Also, for SLs, their overall energy consumption must remain constant across the operation cycle. This energy conservation constraint is described by (6). Finally, equation (7) is dedicated to calculating the load recovery (LR) pattern of SLs as the result of DR. By using (7), the SO may determine the payback demand of SLs with respect to each period t ' [t + 1, t + k ], given the previous load reduction value Pksl, t, curt . These outcomes will be used as input parameters in the DR CC approximation. In practice, since DR customers implement their demand payback on an uncontrolled basis, hence for a demand reduction from SLs, its resulting energy payback pattern could be highly heterogeneous among different individuals. Because of this, some parameters in the above model (including k , k and k ) should be uncertain to the SO. However, for an SDG containing massive independent users, the aggregated behavior of the individuals will exhibit statistical regularity, as guaranteed by the law of large numbers. Therefore, the stochastic variability of these parameters can be modeled using a probabilistic approach, based on long-term observation of customers’ load recovery patterns. In this paper, without loss of generality, we assume that k , k and k all conform to a Gaussian distribution. Then, in the CC estimation, the values of these uncertain parameters can be determined by random sampling, according to their probability distributions.

(3)

t

sl,curt Pksl,rec , t t = Pk , t

k

k

t =t+1

3.2.1. Critical loads CLs refer to the loads whose consumption cannot be reduced under any circumstances; otherwise it would have a negative impact on the well-being of customers. In practice, the most common examples of CLs are cooking facilities, freezers and lighting equipment. In practice, unless the contingencies in the SDG render power supply impossible, the energy demand of CLs should be served all the time. Thus, for any time period t, the power consumption of CLs yields.

k

Pksl,rec , tt t =t

In practice, according to the operation characteristics, the electric loads in the SDG can be categorized into 3 basic groups, namely critical loads (CLs), interruptible loads (ILs), and shiftable loads (SLs) [26,29]. In our study, the mathematical models used to represent the demand pattern of each load type are presented.

Pkcl, t = Pkcl,rated - Pkusd ,t ,t

t 1

Pksl,curt + ,t

(4)

where denotes the baseline power demand of the IL at bus k in time period t; Pkil,,tcurt refers to the volume of demand curtailment that accomplished by the IL k at time-period t. In our CC evaluation, Pkil,,tcurt is an input data, which is determined by the SO according to an optimal DR scheduling model as presented in the Appendix.

Pkil,,trated

3.3. Customer participation Besides the abovementioned aspect, the capacity benefits of DR could also be related to the willingness of end-users to participate in DR 5

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program. In real-world, since unexpected load reductions/curtailments tend to degrade the comfort of individuals and cause a disutility cost to them [25], this would make some customers not want their electric loads to be used for DR purposes. As such, in practice, how much demand-side (load) resources can be solicited and used for DR should be regarded as an uncertain variable to the SO in the DR CC evaluation. In actual applications, to effectively describe the uncertainties pertaining to customer participation for DR, a thorough demand-side survey is normally required. Then, based on the obtained data, the stochastic variability in demand-side behaviors can be represented through different statistical models, such as probabilistic [13] or possibilistic approaches [16]. To apply the above uncertainty handling techniques, a critical prerequisite that must be concerned pertains to that the information used for the uncertainty modelling must be fully accessible and credible. However, in our study, since the willingness of customers for DR participation is very individual-specific, thus unlike load characteristics, it is usually difficult (even impossible) for the SO to obtain sufficient data about the preference of each user. Taking a step back, even if such information is attainable, in actual situations, whether customers would opt in DR program can be still affected by various unknown factors, such as impulsive selection, propagation effect, etc., which would render the obtained data not fully reliable and creditable. For these reasons, the traditional uncertainty handling methods (like probabilistic or possibilistic approaches) might be not applicable for our concerned case since the basic data needed for customer-willingness modelling could be unavailable or not credible. In order to resolve the above challenges, in our study, a novel uncertainty handling technique named the ‘Z-number’-based approach has been introduced, and we apply it to address the randomness issue pertaining to demand-side participation of DR program. The Z-number is a new-type uncertainty handling technique, which was originally developed by L. Zadeh in 2011 [32]. Compared with conventional statistical-based methods, the salient advantages/features of the Z-number approach are summarized in Table 1. In this study, the major rationality for choosing the Z-number technique to handle the relevant human-related uncertainties in DR can be summarized as follows:

for subscription of DR program. Specifically, the IF is defined as the ratio of customers’ contracted DR capacity to their total load flexibility, which can be mathematically expressed as: il,rated µk = (Pkil,ava + Pksl,ava + Pksl,rated ) ,t , t ) (Pk , t ,t

k

D,

t

(8)

where and represent the capacity of ILs and SLs at bus k that can be used for DR operation in time-period t. Apparently, the IF indicates the interests of individuals for the involvement of DR program. Customers with a greater IF are more likely to opt in DR program, as compared to those with a lower IF. For particular cases, if µk = 1, it means that the customer would like to dedicate all his potential flexible loads for DR operation; conversely, if µk = 0, it means that the user chooses to not enroll in the DR program and cannot make any contribution to the reliability of SDG. As explained above, in practice, since the willingness of customers for DR participation mainly depends on their own preference, thus the value of µk in (8) could be uncertain to the SO. In our work, for considering such uncertainties, the Z-number-based method is utilized. According to the Z-number approach, for any uncertainty variable ~ , its effect can be represented by an ordered pair of fuzzy-numbers ( A , ~ ~ ~ B ), where A is a supposed restriction on , and B is the measure of certainty degree which indicates the confidence of decision-maker ~ ~ ~ about the reliability of obtained data on A . In practice, A and B are usually perception-based and described by using fuzzy numbers or possibility distributions. Based on the above explanations, if we consider the IF value of a customer ( µk ) to be low, but the SO is not quite sure about the credibility of this information, then the corresponding Z-valuation for µk can be expressed as ( µk , low, probably). In actual applications, depending on the obtained data, different membership functions can be used to describe the distribution of fuzzy ~ ~ variables A and B in their respective numerical domains. For this study, without losing generality, we arbitrarily assume that the IF value of customers and their information reliability were subject to a trapezoidal distribution and a triangular distribution, respectively. Thus, the Znumber formulation for a customer’s IF can be mathematically re~ ~ ~ ~ (µk , A , B ) , presented as: where A A (x ) = (x1, x2 , x3 , x 4 ) , ~ ~ B B (x ') = (x '1, x '2 , x '3) , while x1 - x 4 and x'1 - x'3 being the characteristic parameters that define the shape of the relevant possibilistic distributions ( ~A (x ) and B~ (x ') ). In such a Z-number model, A~ (x ) describes the possibility of a customer to opt in the DR program, pertaining to his IF value; whereas B~ (x ') indicates the membership of the applied data to be reliable. As can be seen, the suggested Z-number method is established on the conventional fuzzy-set (possibilistic) theory. But fundamentally differing from the classical possibilistic approach, the most distinguishing feature of Z-number lies in its capability for incorporating the impact of information creditability issue in the process of uncertainty characterization. Specifically, in the conventional fuzzy-set case, the decision-maker only possesses the information with respect to the restriction part of ~ uncertain data, namely A in the Z-valuation; meanwhile, it is also assumed by default that the decision-maker has 100% certainty that the all the obtained data about are completely reliable and trust-worthy, i.e., fully conform to the corresponding the statistical characteristics of ~ model A . However, in the Z-number approach, the uncertainties in are ~ represented in the form of a combination of A together with a certainty ~ measure B which indicates the creditability of the applied data. As such,

Pkil,,tava

1) The conventional statistical models can only describe the characteristics of uncertainties depending on the historical data, thus they would fail to consider the impact of future influential factors. 2) The Z-number-based approach can account for the effects of both uncertain factors and the information credibility in the characterization of DR. Thus, it can provide a more accurate and comprehensive estimation on the human-related effects in actual DR operations. 3) As the Z-number model describes the uncertain information and their associated reliability in a natural language, it can reflect both the historical experience and the cognition of human beings in the presented DR model. In this way, the challenges for modelling demand-side participation due to the lack of reliable data can be properly addressed. In this work, to describe the impact of customer performance on DR capability, we introduce a variable μk (0 ≤ μk ≤ 1), which is called as involvement factor (IF), to indicate the willingness level of customers

Pksl, t, ava

Table 1 Comparison between Z-number and other uncertainty handling approaches. Approach

Data form

Pros

Cons

Probabilistic Possibilistic/fuzzy Interval Z-number

PDF Membership function Interval number Z-valuation

Statistical and informative Full use of human knowledge Simple and less demanding on data Considering both uncertain factor and data creditability

High requirement of historical data High requirement of data reliability Not informative and practical Computationally expensive

6

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the Z-number model can properly capture the impact of source-data credibility and make full use of the experiences of human beings in the uncertainty modelling, especially in the context of insufficient or

incomplete measurement data. Therefore, the Z-number approach can be used as an efficacious tool for handling the relevant randomness due to customer behavioural idiosyncrasies as concerned in this study.

Fig. 3. Procedures of DR CC evaluation (A. Main process; B. Reliability analysis without DR; C. Reliability analysis with DR). 7

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Fig. 3. (continued)

Notice that, in practice, if the decision-maker considers that the information data used for the uncertainty modelling is fully reliable, then the part B in the proposed Z-number formulation will equate to null (i.e., B~ (x ') 1), which renders the Z-number model turned back into a conventional fuzzy-set (possibilistic) formulation. Furthermore, it is also worth mentioning that, as consistent with conventional probabilistic model, our proposed Z-number-based method could not be applicable without any historical data. Conversely, the historical data about the uncertain factors (customer load demand) is also needed to ~ establish the final Z-number model (i.e., A in the Z-number validation).

where Pktn, t and Pkte, t denote the total expected load demand of customer k under the normal and DR mode, respectively. The above equations indicate that, under the normal operation case, the total power consumption of a customer in period t is the summation of the energy demand from his CLs, ILs, and SLs. However, for the DR case, their total consumption would be the original demand of different loads (including both responsive and non-responsive) minus the reduced loads plus the relevant energy payback from the SLs. In (10), the available DR capacity of customers is considered as the product of their potential responsive load demand (Pkil,,trated and Pksl, t, rated ) and the IF value of individuals ( µk ). As IF indicates the willingness of customers to opt in the DR program, hence an individual with a greater IF is supposed to have a larger available DR capability than those having a smaller IF. Besides, in this study, for simplicity, we assume that the power factor of system customer loads remains constant for both the regular and the DR case. In this sense, the reactive power demand and the reactive power flow balance in the system can be determined according to the variation of active power of customers’ loads. The presence of Z-numbers makes our proposed DR model (3)–(10) incorporates different types of uncertain variables (i.e., probabilistic: k , k , k and Z-numbers: µk ) simultaneously. In order to apply such model in our CC evaluation, a probabilistic-based normalization technique is utilized, as presented in the following section.

3.4. Determination of available DR capacity By synthesizing the outputs from the above load characteristics and demand-side participation models, the final load demand of customers under the regular and the DR case can be determined as:

Pktn, t = Pkcl,rated + Pkil,rated + Pksl,rated ,t ,t ,t Pkte, t = [Pkcl,t + (1

k

µk )(Pkil,rated + Pksl,rated ) ,t ,t

D,

t

(9)

Pkusd ,t ]

Non - responsive load demand

+[(µk Pkil,rated ,t

Pkil,curt ) + (µk Pksl,rated ,t ,t

Pksl,curt )] ,t

Responsive load demand

+ (

t k P sl,rec ) t = t 1 k, tt

Recovered load demand

k

D,

t

(10) 8

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4. Evaluation algorithm

hardware availability of distributed generation units in the SDG [16]; and for renewable-based generation units, the energy supply profiles (e.g., wind speed) are created using time-series prediction models [35] and these chronological data are combined with the mechanical state (up/down) of the unit to determine their available power output at each time-period. On the other hand, for the demand-side, the IF of customers (µk ) is randomly determined according to their equivalent PDF that derived from (16). Then, based on these results, the available DR capacity that can be exploited from customers can be determined according to (8)–(10). To determine the EFC of DR, the SMCS is first conducted to evaluate the reliability of system containing DR. For this, power flow analysis is carried out for each slot in order to check the operation status of the system. (by using Newton-Raphson method). If no constraint violations (e.g., overload, undervoltage, etc.) are identified, it means the system is operating under a normal condition in the current period, thus the energy-not-supplied (ENS) of the system is equal to zero. Otherwise, it means the system is in an emergency. When the situation happens, we assume that the SO will implement the supply-side remedial strategies first, e.g., capacitor switching or transformer tap changing, etc., to mitigate the violations. DR resources, as the final corrective resort, will be invoked only if all the supply-side options are put into use and proved insufficient to remove the violations. In practice, to fully exploit the potential benefits of DR, the SO normally determines its DR operation strategy via an optimal power flow analysis [5]. The models to optimize DR operations have been widely suggested in many existing literatures [6,14]. However, in this study, since we mainly focus on the reliability contribution of DR, it is assumed the SO would utilize DR resources in a way simply for minimizing the system loss-of-load and improving the reliability of supply during contingencies. The mathematical formulation of this model is given by (A1)–(A12) in the Appendix. The calculation of the model (A1)–(A12) will lead to the modified load profile of system in the corresponding period t (Pkte, t ). Then, during the period t, the ENS of the system can be determined as follows:

4.1. Uncertainty normalization Since our presented DR model in last section contains both probabilistic and Z-number variables, to perform CC analysis, it requires that the different types of uncertain parameters must be converted into congeneric quantities first. For this purpose, in this study, a fuzzy-expectation method [33] is employed, through which the Z-numbers in our model could be changed into conventional fuzzy quantities; then, the well-known centroid method [34] is further adopted to transform the obtained fuzzy variables into corresponding probabilistic variables. The detailed steps for implementation of the above uncertainty propagation are presented below. ~ ~ For a given Z-number-type variable H = (A , B ) , where ~ ~ ~ ~ ~ A = { ( x ) [0, 1]} { < x ', ( x ') > [0, 1]} , and B = A A B B (x ')

~ 1) Perform defuzzification onto B to change it to into a crisp number , by following B + B

=

x

(x dx )

B

+ B

(x dx )

(11)

~ 2) Plug the obtained outcome B into A to derive its weighted form ~ H , which incorporates the impact of information credibility H = (A ,

B

(x ) =

B

A

a

)

A A

(x )

(12) (13)

(x )

~ ~ 3) Normalize H into the regular fuzzy value H by using the equal fuzzy-expectation theorem [33], as given H = (A , 1)

A

A

(x )

ENStdr =

(14)

x

(x ) =

A

B

+

A

(x )

A

(x ) dx

(17)

D

After each DR event, the customers’ load profile for the following time-periods (in the SL energy payback session [t + 1, t + k]) will be updated according to (5)-(7) to incorporate the LR effect. As the SMCS keeps rolling over time, the EENS of the system under the case in presence of DR can be eventually obtained by summarizing the historical ENS results as follows:

(15)

4) Determine the corresponding equivalent probability density func~ tion (PDF) with respect to H , according to the centroid method [34]

f (x ) =

Pkusd ,t k

(16)

EENS dr =

Through the above transformation, the Z-number-type variables involved in our study can be converted into their equivalent probabilistic forms, which can be then directly manageable for the CC evaluation.

1 N sm

8760 × N sm

ENStdr t=1

(18)

where denotes the number of simulation years. Subsequently, DR will be removed and another SMCS is performed to assess the system reliability with the benchmark unit only. This calculation will lead to a new EENSv. Then, a comparison can be made about the system reliability for the DR and the benchmark case (i.e., EENSdr vs. EENSv). Based on these results, the capacity of benchmark unit envisaged in the system (i.e., C bm in (2)) would be adjusted using a bisection method [16]. The overall searching terminates when the relative difference of EENS in the two cases become less than a tolerance threshold value ζ, i.e., |EENSv-EENSdr|/EENSdr ≤ ζ. In this study, we set ζ to be 5%, as consistent with [10]. Then, the capacity of benchmark generation found so far is then regarded as the CC (EFC) of DR.

N sm

4.2. Procedures In this section, the numerical algorithm for determining DR CC is described on account of the suggested metrics in Section 2.2 and the DR model in Section 3. In our study, without losing generality, the wellknown sequential Monte-Carlo simulation (SMCS) [22] method has been utilized for assessing the reliability performance of SDG with and without DR programs. The detailed procedures of the proposed CC evaluation algorithm are illustrated in Fig. 3. As can be seen, the evaluation starts with a random generation of the sequence of state duration for each of system components. In this study, since the capacity characteristics of DR program is the focus, we only take account of the uncertainties associated with generators. Other uncertainties that may affect DR CC, such as transmission failures, security of communication infrastructures, and information latency, are not considered. The two-state (up/down) Markov model has been used to represent the

5. Numerical study 5.1. Simulation settings To prove the effectiveness of the proposed CC evaluation framework, a practical 67-feeder distribution system is utilized as an illustrative test 9

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case in this paper. The structure of this system is shown in Fig. 4. We conduct our analysis on such a test case because the system as concerned has a typical form of radial topology which is the most commonplace in China; moreover, this system has been widely used in many existing studies in the reliability field [36–38], thus it could ensure the reproducibility of the relevant results derived from this work. As can be seen, the concerned system comprises 67 feeders, and 26 load buses, which is connected to the external grid via a distribution substation at Bus-1, with the total transforming capacity of 20 MVA. Also, in this study, we assume that two gas turbine units with the total capacity of 2 MW have been allocated at Bus-15, serving as a distributed generation unit in the system. The reliability data of the system components are extracted from [36–38] and summarized in Table 2. For the sake of simplicity, in this study, we assume that all the distributed generation units of our system are working at the constant power factor of unity, which means that they only provide active power for the grid, instead of reactive power. The system is comprised of four service areas and has an annual peak load demand of 16.3 MW. The details about the annual peak load data at each bus are presented in Table 3 [36]. Due to the lack of relevant supporting data, we assume that the customers in this system have the identical consumption pattern as shown in Fig. 5. The relevant data is determined according to [26], in which the annual load profiles for typical residential/commercial/industrial users were provided. For simplicity, in this study, we assume that all the users have similar LR characteristics, and the probabilistic models used to represent the variability of each uncertain parameter are shown in Table 4 according to the real statistics in China. In the CC calculation, we assume that the benchmark unit is installed at Bus 18 of the system. To ensure a meaningful evaluation, the CC of DR is examined through performing a group of comparative analysis. For this aim, four scenarios which represent the implementation of DR with different incentive settings are considered, as shown in Table 5. Specifically, in #2, we consider that the financial reward

Area 1 3

6

4 1

Mean time to repair (h)

Network feeder Transformer Gas turbine

2584 4900 1250

12 100 60

Table 3 Load data. Load point

kVA

Load point

kVA

Load point

kVA

M1 M2 M3 M4 M5 M6 M7 M8 M9

4381.01 160 10 216 822 1355 768 19 20

M10 M11 M12 M13 M14 M15 M16 M17 M18

150 170 25 1050 305 660 205 150 130

M19 M20 M21 M22 M23 M24 M25 M26

610 655 215 50 60 2280 585 1210

offered for DR subscribers ckinc corresponds to $0.18/kWh, along with a fixed availability payment ckcp equal to $0.45/time. Such incentive settings are adopted based on a real commercial DR program in China. On the basis of #2, for comparison purpose, we assume that there is a reduction in ckinc by 50% and an increase by 50%, which constitute Case #1 and #3, respectively. Finally for Case 4, the same setting about ckinc as Case 2 is considered, but the availability payment ckcp is assumed to be zero. We use the comparative analysis of Case 2 and Case 4 to illustrate the impact of different incentive designs/schemes on the effectiveness of DR deployment. To understand the willingness of customers for DR participation under each of the above scenarios (i.e., different incentive schemes), we conducted a field survey and a total amount of 50 questionnaires was sent to some residential customers that arbitrarily selected in Beijing,

GT 16

14

5

M3

13 M9

10

7 9

11

15

12 M10

8

17 18

Substation

Mean time to failures (h)

M5

M1

2 M2

Component

M8

M7 M4

Table 2 Reliability data of system components.

M12

M11

M6 M21

Area 2 M22 M24

41

40 39

38

35

Area 3

19

32

37 M23

R1

34 20

23

33

21

M26

36

M25

M14 M16 M17

Closer

M18

Breaker GT

25

30 29

M20

Fig. 4. 67-feeder distribution system. 10

28

27

M15

31

M19

Gas turbine

24

26

Area 4

22

M13

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p.u.

p.u.

p.u.

B. Zeng, et al.

capacity of the system, i.e., max[

Area 1

1.0 0.5 0.0

t

1000

2000

3000

4000

5000

6000

7000

8000

1000

2000

3000

4000

5000

6000

7000

8000

5000

6000

7000

8000

5000

6000

7000

8000

Area 3

1.0 0.5 0.0

1000

2000

3000

4000 Area 4

1.0 0.5 0.0

1000

2000

3000

4000 Time(h)

CL

SL

IL

Fig. 5. Annual load profile at each bus. Table 4 Characterization of LR. Uncertain parameter

Form of probability function

Specification

δk ωk υk

Gaussian distribution

Mean = 3; Variance = 0.4 Mean = 0.8; Variance = 0.2 Mean = 1.2; Variance = 0.5

#1

#2

#3

#4

Incentive reward ($/kWh) Availability payment ($/time)

0.05 0.45

0.18 0.45

0.32 0.45

0.18 0

(Pkcl, t, rated + Pksl, t, rated)].

denotes the value of lost load at system bus k. In this test, ckvoll is taken to be $2.99/kW according to [40]; also, the penetration rate of flexible loads in the SDG is assumed to be 30% and the four incentive cases as defined in Table 5 are considered for this study. As can be seen, before the implementation of DR program, the total cost of the utility is only comprised by the system outage cost, which reaches up to $46.16 M/year. Then, after introducing DR, the outage cost of the system and the total cost of the utility go down as the reliability of supply is improving; however, when the incentive is high enough, the DR operation cost increases dramatically because of the growth of payment used for DR incentives. Specifically, in #1, the total cost of the utility is computed as $44.39 M/year. However, with the increase of DR incentive, this value rises to $55.48 M/year in #3, which can be translated into a growth by 1.25 times and 1.2 times with reference to #1 and the no-DR case, respectively. In practice, as such a rise in system operation cost would greatly decrease the revenue of utilities, it may make the DR option less preferable and competitive to be used for capacity purposes, as compared with other supply-side solutions. Finally, according to Fig. 6, the result comparison between #2 and #4 show that, the CC of DR might decrease if the capacity payment is absent in a reliability-based DR program. This suggests that the design of incentive mechanism could have an important effect on the CC estimation of DR. Unlike kW-based reward, capacity remuneration provides consumers with supplemental payments that depend on the number of times they were invoked during operation. Therefore, the use of capacity payment will give users stronger incentives to opt in the DR program and help to reduce the variability in the participation of

Table 5 Scenario settings. Scenario

D

As observed, regardless of the scenarios considered, the DR CC increases with the growth of customer responsivity and becomes saturated when the DR penetration in the system reaches a certain threshold. Such results prove that the intrinsic flexibility of load demand can be a fundamental issue affecting the CC of DR. This finding is in line with our expectation because enabling higher responsivity implies a greater load regulation capability achievable in the demand side; thus it could help mitigate system shortages more significantly during emergencies. However, as the reliability of the system improves, since the addition of DR capacity cannot consistently reduce loss-of-load (generation shortfalls), as constrained by inherent properties of loads (i.e., LR effect), thus the marginal CC of DR decreases with the rise of customers’ demand responsivity. Besides, the results in Fig. 6 also demonstrate that the CC of DR could be strongly linked to the participation level of demand-side customers. In our analysis, #3 (with the highest incentive rate) always results in the highest CC estimate, while #1 (with the lowest incentive) possesses the lowest CC. Such contrast implies that a higher incentive provides users stronger impetus (i.e., financial return) for subscription of DR programs, it would enable larger capacity benefits for DR implementation. However, in practice, factitiously improving the CC of DR may QJ/>be not necessarily cost-effective to the SO. To reveal this, Fig. 7 presents the total cost of the utility before and after applying the DR program. The total cost of the utility is computed as the summation of system outage cost and the annual DR operation cost, i.e., usd c voll Pk, t + t k D [ckcp + ckInc (Pkil,,tcurt + Pksl, t, curt )], where ckvoll t k D k

Area 2

1.0 0.5 0.0

k

from which useful information about the willingness of individuals for DR and its correlation with the stimulus that imposed can be obtained. Based on these data, the Z-number valuation for the discussed IF of customers in each scenario can be determined accordingly. The detailed information is shown in Table 6. As can be seen, when a lower incentive rate was concerned (in Case 1), consumers showed fewer interests towards the participation of DR program. However, with the increase of expected reward (from Case 2 to 3), individuals would have greater interests/willingness to get involved in the DR program. Such formulation is fully consistent with our expectation in real-world situations. Moreover, in this test, we also ~ assume that the second part of the derived Z-number valuations, B , to be identical for all the scenarios, so as to ensure the final CC approximation results can be directly comparable under the same benchmark. The simulation is programmed in the MATLAB environment and executed on a PC. The optimization problem embedded in the model is solved by use of commercial solver, CPLEX [39]. 5.2. Results and analysis

Table 6 Z-number valuation of customers’ IF.

To perform our evaluation, we consider that the demand responsivity of system users (i.e., DR penetration), which is defined as the proportion of responsive loads (Pkcl, t, rated + Pksl, t, rated) to its total consumption Pktn, t at the period, varies discretely from 0 to 45%. Then, the CC of DR is examined under different settings as given in Table 5 and the final calculation results are presented in Fig. 6. Here, to facilitate a fair comparison, the CC results are reported in both MW and percentage values with reference to the annual peak DR

Scenario

#1 #2 #3 #4

11

Participation willingness

Low Medium High Low

A

(x )

B

(x ')

x1

x2

x3

x4

x'1

x'2

x'3

0.4 0.3 0.2 0.4

0.7 0.5 0.4 0.6

1 1 1 1

1 1 1 1

0.7 0.7 0.7 0.7

0.9 0.9 0.9 0.9

1 1 1 1

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Fig. 6. DR CC versus demand-side responsivity in MW and pct. values.

case, the IF of customers is assumed to be a normally distributed random variable in the interval [0,1] with the 0.5 mean and the variance of 1. The scenario represents what has been done in the published works [13] and [15]. Case 3: DR is modeled considering the uncertainties in both DR participation and LR. In this case, the IF setting is the same to Case 2, while the LR parameters are assumed to be uncertain which complies with Table 4. This scenario describes what has been done in the published work [14]. Case 4: DR is modeled with consideration of both IF and LR uncertainties. In this case, it is assumed that the IF of customers and their LR pattern are stochastic and can be represented using a possibilistic model (trapezoid-based membership function). This scenario resembles what has been done in the existing work [16]. Case 5: Proposed DR modeling framework in this paper. In this case, the relevant uncertainties associated with both customer participation (i.e., IF) and their LR behaviors are considered in the DR characterization collectively. The obtained CC estimation results under each of the above scenarios are depicted in Fig. 8. As can be seen, there is a significant discrepancy in the obtained CC results between different cases. More specifically, Case-1 always leads to the highest CC estimation of DR whereas the lowest value occurs in Case 5 with both LR- and human-related uncertainties in DR are considered. These results suggest that, in actual implementations, the uncertainties concerning individuals’ performance during operation could play a significant role in determining the potential reliability benefits of DR. Therefore, to obtain effective CC estimation of DR, taking into account the impacts of these uncertainties should be essential in the mathematical representation of DR. Although in some particular cases, the CC results obtained in Case 5 are occasionally similar to those from

Fig. 7. Total utility cost before and after performing DR program.

demand side, which thus allows a higher CC with respect to the benchmark Case 2 (where the only kW-based reward is considered). 5.3. Result comparison with existing works The above studies are conducted based on the proposed DR modelling method in this study. Next, we will make a comparison of these obtained results with those presented in other published works (where different DR representations were considered), in order to validate the contribution of this study with respect to the current state of arts. For this aim, five scenarios have been defined and considered in this section, which represent the different DR modeling approaches as used in extant works. The detailed information about each scenario is given in Table 7. Case 1: In this case, the effect of DR is described using a fully deterministic approach, where the uncertainties pertaining to both customers’ participation and their LR activities in the DR program are excluded. The characteristic parameters in the DR model are considered to be constant which are equal to the mean of their respective probability distribution. This scenario is considered as the reference case in our analysis, since it represents the conventional DR modelling approach which has been widely adopted in [5,6,8–11]. Case 2: DR is modeled with consideration of DR participation uncertainties only, while the randomness about LR is neglected. In this

Table 7 Scenario setting used for the validation of results with other published works. Scenario

12

Method

Uncertainty IF

LR

#1 #2 #3 #4

Deterministic Probabilistic Probabilistic Possibilistic

× √ √ √

× × √ √

#5

Z-number

√

√

Data representation

Published work

Constant PDF PDF Membership function Z-valuation

[5,6,8–11] [13,15] [14] [16] Present work

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comparison, the contribution of the proposed method can be clearly demonstrated, as compared with the current state of arts. 5.4. Effectiveness of Z-number formulation In this study, we introduced a novel uncertainty handling technique, namely ‘Z-number’, to describe the randomness of customers’ participation in DR program, through which the impact of information reliability/credibility issue can be explicitly considered. To illustrate the practicability of the applied ‘Z-number’ approach in real-world scenarios, in this section, we consider four scenarios which represent the Z-number valuations of customer’s IF with different in~ formation credibility settings (i.e., B part in the Z-number model), as shown in Table 8. Specifically, in #1, we assume that the information used for IF modelling is completely reliable. That is to say, for this case, the Znumber formulation of DR reverts to the conventional possibilistic (fuzzy-number) model, which has been widely adopted in many existing works [16,28]. On the contrary, in #2, #3, and #4, we consider that the relevant data about the demand-side is not fully trustworthy, and corresponds to ‘low-’, ‘medium-’, and ‘high-’ creditability, respectively. Three Z-number valuations with different settings of B are utilized to make this characterization. The CC of DR is assessed for each of the above scenarios, and the comparison of the obtained results will illustrate the impact of information credibility on the evaluation of DR. The relevant calculations are presented in Table 9. As can be seen, there is an obvious disparity in the CC approximation results obtained from the above scenarios. More specifically, with the improvement of data credibility, the CC estimates of DR increase accordingly. Through this comparative analysis, it can be seen that the reliability of the obtained information has an important impact on the CC estimation of DR since it determines the effectiveness of the derived DR model. In this study, the proposed DR modeling framework, due adoption of Z-number technique, can properly reflect the cognition of decision-makers about future information, therefore, it may allow a more realistic and comprehensive evaluation on the potential benefits of DR, as compared with conventional uncertainty handling approaches, such as probabilistic or possibilistic method in [13–16].

Fig. 8. Comparison of obtained CC results with other published works.

Table 8 Z-number valuation of customers’ IF considering different settings. Scenario

#1 #2 #3 #4

Information effect

No Yes Yes Yes

Credibility of information

– Low Medium High

A

(x )

B

(x ')

x1

x2

x3

x4

x'1

x'2

x'3

0.2 0.2 0.2 0.2

0.4 0.4 0.4 0.4

1 1 1 1

1 1 1 1

1 0.5 0.7 0.8

1 0.9 0.9 0.9

1 1 1 1

Table 9 DR CC estimations under different information credibility settings. Scenario

CC (MW)

CC (%)

#1 #2 #3 #4

4.08 2.75 3.26 3.75

20.43 13.74 16.32 18.79

5.5. Applications in large-scale test case

other models, such numerical deviations could be substantial for the rest of cases. As such, neglecting these intrinsic uncertainties would lead to misestimation on the capacity value of DR program. In addition, compared with extant works, the proposed model can not only account for the both uncertainties about DR participation and LR characteristics, but also consider the information credibility in the characterization of DR. Therefore, it can provide more accurate and comprehensive CC estimation results in real-world applications. Through such

In order to verify the validity of the proposed CC evaluation framework in real-world applications, in this section, we carry out a further study based on a real large-scale distribution system in Beijing. The concerned system includes 91 load buses, 103 transmission lines, 2 gas turbines, and 3 wind farms, and has a nominal voltage level of 10 kV, as shown in Fig. 9. The annual peak load of the system corresponds to 106.4 MW and Table 10 provides the load profiles of customers. These load data are obtained from the real customer survey by the local utility.

Fig. 9. A real regional distribution system. 13

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Table 10 Statistical data about system load demand.

Residential Government Industrial Office Commercial

AAPR (%)

CRSD (%)

AVPR (%)

PCL (%)

PIL (%)

PSL (%)

42.01–59.76 51.75–58.37 85.03–90.29 67.78–71.92 72.50–78.61

35.87–43.92 32.59–36.43 17.92–21.16 35.69–40.23 27.85–33.62

88.74–92.36 82.35–87.29 60.02–67.55 75.21–80.17 51.69–56.84

75.73–87.13 92.44–96.17 52.64–76.05 77.94–87.84 78.16–83.93

3.72–8.83 1.17–2.35 8.46–19.51 4.31–9.79 6.90–12.22

9.15–15.44 2.66–5.21 15.33–27.85 7.85–12.27 9.17–17.93

*AAPR: annual average-to-peak ratio; CRSD: corrected rational standard deviation (standard deviation*100% /peak value); AVPR: annual valley-to-peak ratio; PCL: percentage of CLs in the total load demand; PIL: percentage of ILs in the total load demand; PSL: percentage of SLs in the total load demand.

Fig. 10. CC estimation results. Fig. 11. CC estimation results under different DR models.

To quantify the CC of DR, we assume that the benchmark unit is connected into the system from Bus 11. The variability of wind speed is assumed to follow a Weibull distribution with the shape coefficient of 1.33 and the scale coefficient of 2.28, according to the real meteorological data in Beijing. In the evaluation, the wind speed is sampled by using MonteCarlo simulations and then the potential power output of wind turbines can be determined according to their operational characteristics [31]. The total available power from dispatchable DG and renewable-based DG would be combined with the load curve of customers to determine the system reliability level with and without DR. In addition, in this study, the incentive rate for DR customers is taken to be $0.18/kWh and the budget for DR operation is confined to $0.45/time. The other settings remain the same as those used in the previous studies (Section 5.1). To verify the effective of the proposed approach, we compare the CC estimates of DR based on the three different DR modeling schemes as described in Section 5.3, with the demand responsivity of customers being fixed to be 30%. The calculation results are shown in Fig. 10. As can be seen from Fig. 10, the obtained results of CC exhibit a similar trend as those in the previous study (Section 5.3), wherein neglecting the potential uncertainties of DR leads to a greater CC estimate as compared to other cases. More specifically, when the proposed DR model is considered, the CC of DR is derived as 32.69%, based on the EFC metric. This value is significantly lower than the corresponding value if the DR uncertainties were completely neglected (43.77%). In this paper, a novel Z-number technique is used to handle the uncertainties of customers for participation of DR program. Unlike conventional possibilistic method, the proposed Z-number model could account for the potential impact of information credibility, thus it would lead to a more realistic representation of DR effects. To illustrate the advantages of the Z-number method, a comparison of the DR CC estimates with conventional possibilistic approach is conducted and the corresponding results are shown in Fig. 11. As can be seen from Fig. 11, with the growth of demand-side responsiveness, the CC values obtained by both methods increase.

However, due to the consideration of information creditability effect, the results obtained by using the Z-number case are always slightly lower than the possibilistic model. Through this analysis, it can be seen that, the quality of concerned data tends to have a critical impact on the effectiveness of DR characterization. As such, neglecting the potential unreliability in the data acquisition could lead to overestimation of the DR’s CC. In this regard, the advantage of the Z-number technique over possibilistic approach could be clarified since it may properly allow for such impacts. 6. Conclusion This paper presents a new methodological framework to estimate the contribution of DR program to the reliability of supply in the future SDG. The proposed methodology is established on the concept of CC, whereby the benefits that can be produced by DR program to system adequacy are compared on a level playfield with conventional generation resources. To properly describe the availability of DR resources and their associated uncertainties during operation, we propose a compound model, wherein the effects of both technical- and humanrelated issues that attended with the DR program are systematically considered under the same framework. In this formulation, a novel uncertainty handling technique, Z-number, has been introduced and utilized to model the ambiguities about customers’ willingness for DR participation. Unlike traditional approaches, the proposed Z-number model does not only focus on the uncertainties in demand-side performance itself, but may also account for the potential impact of information creditability issue on the DR valuation; thus it could provide a more comprehensive/realistic estimation for the DR performances as they occur in real-world implementations. By using fuzzy-expectation technique and the centroid method, we transform the different types of uncertain variables in our developed DR model into comparable 14

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quantities; and then based on this, the CC evaluation of DR can be implemented by using a reliability analysis algorithm with SMCS. To verify the effectiveness of the presented method, numerical studies are performed based on a 41-bus test case and a real distribution network in Beijing, respectively. The simulation results show that the inherent flexibility of customer consumption may bring about significant benefits to the SDG, by improving the adequacy of supply. Furthermore, the CC of DR can be influenced by various issues, including the physical characteristics of load appliances, customers’ preference for DR involvement, and the composition of loads in the demand side. In general, a larger penetration of flexible loads and a higher level of customer participation would allow for a greater CC estimate of DR, but this could also bring about a significant increase in the operation cost of SDG. In addition, through the results of comparative study, it is also found that the uncertainties in demand-side behaviors could have an important impact on the reliability benefits of DR. In the real-world, due to potential difficulties in acquiring sufficient data about the demand side, incorporating such human-related uncertainties in the DR modeling tends to be a great challenge for the SO. However, the proposed framework, due to the adoption of the Znumber technique, can properly account for the impact of information reliability, thus it could provide a more convincing estimation on the potential value of DR.

CRediT authorship contribution statement Bo Zeng: Conceptualization, Methodology, Investigation, Writing original draft, Writing - review & editing. Xuan Wei: Validation, Formal analysis, Data curation, Writing - review & editing. Bo Sun: Writing - review & editing. Feng Qiu: Resources. Jianhua Zhang: Resources. Xuanrong Quan: Resources. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was supported by the National Natural Science Foundation of China (71601078, 51507061), the Fundamental Research Funds for the Central Universities (2018ZD13), and the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (Grant No. LAPS18009).

Appendix A. Optimization model for DR scheduling

Pkusd ,t

Minimize

Pkil,curt , Pksl,curt , Pkusd ,t ,t ,t k

(A1)

D

subject to

0

Pkil,curt ,t

µk Pkil,rated ,t

k

D,

t

0

Pksl,curt ,t

µk Pksl,rated ,t

k

D,

t

(A2) (A3) t

Pkusd [Pkcl,rated + (1 ,t ,t

0

µk )(Pkil,rated + Pksl,rated )+ ,t ,t

k

Pksl.rec , tt ]

k

D,

t

t =t 1

(j, k )

Qjgen ,t

Qjk, t + Qte j, t (j , k )

rij Pij, t +

ij Qij, t

V j, t )

Vmin

Vmax Iij,max

(i,j )

ij

F,

(5)

(A5)

(i , j )

F,

t

(A6) (A7) (A8)

t

(A9)

i, t (i,j )

F,

(A10)

t

[ckcp + ckinc (Pkil,curt + Pksl,curt )] ,t ,t k

t

i, j, t

V0, t

Iij, t = (Vi, t

Iij, t

F,

F

Vi, t = Vj, t +

Vi, t

(i , j )

F

Qij, t =

0

P jgen ,t

Pjk, t + Pjte, t

Pij, t =

bud

t

(A1)

D

(A12)

(7)

Qkte, t = Pkte, t tan

(A4)

k

k

D,

(A13)

t

Constraints (A2) and (A3) define the limits on the maximum DR capacity that can be invoked from the ILs and SLs at each bus of the system. Constraint (A4) represents the restriction on the capacity of load shedding that implemented at the demand side. Formulas (A5)-(A8) are linearized DistFlow equations, which are commonly used to describe the complex power flows in distribution systems [41]. To guarantee the security of the system, the limits concerning nodal voltage deviation and the current-carrying ability of feeders are enforced by (A9) and (A10). The budget constraint for DR implementation is considered in (A11). The constraints about the LR characteristics of SLs, i.e., (5)-(7), must also be satisfied in this optimization, as represented by (A12). Finally, constraint (A13) states the relationship between the customers’ action and reactive power demand in the DR scenario, wherein tan k is regarded to be a constant for every customer k. 15

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gen In the above formulation, P jgen , t and Qj, t are the active/reactive power output of generation units at system bus j; Pij, t , Qij, t , and Iij, t denote the active/reactive power flow and current in the network feeder ij; F is the set of system feeders; Vi, t and V0, t are the voltage magnitude at system bus i and slack bus in period t; rij , ij , and ij are the resistance, reactance, and impedance value of feeder ij. Additionally, ckinc and ckcp represent the incentive rate/availability payment for DR participant k, in $/kW, and $/time. The decision variables of above problem correspond to Pkil,,tcurt , Pksl, t, curt , and Pkusd ,t .

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