Customer satisfaction based reliability evaluation of active distribution networks

Applied Energy xxx (2015) xxx–xxx

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

Customer satisfaction based reliability evaluation of active distribution networks q Gengfeng Li, Zhaohong Bie ⇑, Haipeng Xie, Yanling Lin State Key Laboratory of Electrical Insulation and Power Equipment, Xi’an Jiaotong University, Xi’an 710049, China

h i g h l i g h t s  Established operation optimization model of ADNs.  Combined operation optimization processes and reliability evaluation of ADNs.  Implemented reliability evaluation of ADNs considering customer satisfaction.  Defined customer satisfaction originated reliability indices of ADNs.

a r t i c l e

i n f o

Article history: Received 3 November 2014 Received in revised form 1 February 2015 Accepted 26 February 2015 Available online xxxx Keywords: Reliability evaluation Active distribution networks Customer satisfaction Sequential Monte Carlo simulation

a b s t r a c t Reliability evaluation of active distribution networks (ADNs) considering customer satisfaction is studied in this paper. Operation optimization model of ADNs is established, which aims to maximize the operation benefit of ADNs using demand response. However, according to optimization decisions, customers may have to change their electricity consumption habit, which affects customer satisfaction and the reliability of customers and ADNs. Two customer satisfaction indices are defined therefore as constraints in the operation optimization to quantify these effects. By a Sequential Monte Carlo (SMC) simulation, the optimization processes is innovatively integrated into the reliability evaluation, and thus the impacts of customer satisfaction constraints are incorporated in reliability evaluation. Further, four new reliability indices are defined in this paper to visibly reflect their impacts. The presented models and methods are validated by extensive studies conducted on a standard test system. Evaluation results accurately quantify the impacts of customer satisfaction constraints on load profiles, reliability and economic performance of ADNs. Conclusions drawn from evaluation results can provide helpful insights for distribution system operators (DSOs) to effectively improve the reliability and operation economy of ADNs using demand resources. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Renewable energy (RE) resources (such as wind and solar) have drawn attention from researchers in the world because of their environmentally-friendly features [1]. Renewable energy generation is a major way of exploiting RE resources [2–4]. However, due to their intermittency and uncertainty, it is challenging to integrate RE resources into electrical distribution networks [5]. Active

q This article is based on a short proceedings paper in Energy Procedia Volume 161 (2014). It has been substantially modified and extended, and has been subject to the normal peer review and revision process of the journal. This paper is included in the Special Issue of ICAE2014 edited by Prof. J Yan, Prof. DJ Lee, Prof. SK Chou, and Prof. U Desideri. ⇑ Corresponding author. Tel.: +86 29 8266 8655; fax: +86 29 8266 5489. E-mail address: [email protected] (Z. Bie).

distribution networks (ADNs), which can properly and actively control the combination of distributed energy resources (DERs, including RE generators, controllable loads and storages), are emerging paradigms for effective utilization of RE resources [6]. Researches of ADNs have been focused on the theories and technologies of ADN measurement, protection and control, and a series of achievements have been published [7–12]. Ref. [7] described the performances of a phasor measurement unit (PMU) prototype based on a synchrophasor estimation algorithm conceived for the monitoring of active distribution networks, as well as its experimental application during some intentional islanding and reconnection tests of an urban medium voltage power network. Ref. [8] proposed a protection scheme on the basis of measured impedance, which included an impedance differential method and an inverse-time low-impedance method. Refs. [9–12] investigated the mechanism, models, and approaches of ADN control. Besides,

http://dx.doi.org/10.1016/j.apenergy.2015.02.084 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Li G et al. Customer satisfaction based reliability evaluation of active distribution networks. Appl Energy (2015), http:// dx.doi.org/10.1016/j.apenergy.2015.02.084

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researches on ADN planning also receive increasing attention recently [13–17]. As an integral part of system planning, researches on the reliability evaluation of ADNs is significant, but few literatures have been focused on this topic. In ADNs, interruptible loads, controllable loads, and energy storage devices are demand resources that can mitigate the intermittency of RE resources and reduce system operation cost [18,19]. Ref. [19], studied how demand response can contribute to the better integration of renewable energy resources such as wind power, solar, small hydro, biomass and combined heat and power (CHP). The latest distribution management systems tend to utilize optimization algorithm for the short-term scheduling of the various energy resource outputs and these demand resources available in the network [20]. In other words, distribution system operators (DSOs) can optimize day-ahead operation schedules based on electricity price signal and/or direct load control. In Ref. [20], a short-term scheduling procedure for ADNs was adopted, which was composed by two stages: a day-ahead schedule for the optimization of distributed resources production during the following day; an intra-day schedule that for every 15 min reschedule based on the updated operation requirements and constraints of the distribution network. Ref. [21] proposed an optimal operational scheduling framework to be used in the distribution management system (DMS) as the core of smart active distribution networks. Operational scheduling and demand-side management (namely operation optimization) indicate that customers have to change their electricity consumption habits, but whether customers are satisfied with these changes, and to what extent they are willing to change are significant factors. They will affect customers’ response strategies and determine the effects of the operation optimization on reliability performance. However, few literatures have addressed this topic. To appropriately model customer satisfaction in operation optimization models, and incorporate its effects in ADN reliability evaluation are waiting to be investigated. This paper establishes a new model for the operation optimization of ADNs, and the optimization processes are innovatively integrated into the reliability evaluation procedures by a Sequential Monte Carlo (SMC) simulation. To study the effects of customer satisfaction on ADNs reliability, two customer satisfaction indices (electricity consumption based and electricity cost based) are defined respectively, and adopted as constraints in the operation optimization model. Besides, four new reliability indices are defined to quantify the impacts of these constraints on the reliability of ADNs. Extensive studies are conducted on a standard test system to validate the presented models and methods. Evaluation results accurately quantify the impacts of customer satisfaction on load profiles, reliability and economic performance of ADNs. Conclusions drawn from the results are insightful for improving ADNs’ reliability and operation economy using demand resources. The organization of this paper is as follows. Section 2 describes the operation optimization model considering customer satisfaction. Section 3 presents a reliability evaluation framework for ADNs, in which the operation optimization is integrated into reliability evaluation. Test cases and result analysis are summarized in Section 4, followed by Section 5 that concludes the paper.

corresponding customer satisfaction indices will be defined and introduced into the optimization model. 2.1. Structure and operation modes of active distribution networks One obvious distinction between ADN and traditional distribution network is that ADN can actively control DG, storage devices and controllable load through the operation center and communication technology (see Fig. 1). The implementation of the active management in an ADN can be briefly summarized as follows: (1) renewable energy generation are estimated using their probability models based on weather forecast information [22]; (2) operation center optimizes response strategies to follow renewable energy generation and to maximize ADN’s operation benefit; (3) control commands are sent out to control the loads, generators, and energy storage devices. The core of this active management is the operation optimization, which will be introduced as follows. 2.2. Operation optimization models The operation optimization model of ADNs was established based on the operation features of renewable energy generators, traditional distributed generators (such as diesel generators), response loads (controllable loads and interruptible loads), and energy storage devices. The optimization model includes an objective function and several constraints, which will be introduced as follows. (1) Objective function of the operation optimization The objective of operation optimization is to maximize the operational economic benefit of ADNs, and the objective function can be described as follows:

max C ¼ Bload  ðC es þ C gen þ C grid Þ;

ð1Þ

where Bload is the benefit of customers obtained from electricity consumption or compensation, and can be described as follows:

Bload ¼

T X ðBv ip Ptv ip þ Bcon Ptcon þ Btcut ÞDt;

ð2Þ

t¼1

where Ptv ip and Ptcon are the power consumption of critical loads and controllable loads, respectively. The benefit coefficients of critical loads and controllable loads are Bvip, and Bcon, respectively.

Wind turbine Control signals / communication

G Critical loads

Critical loads

$

Operation center

G

Energy storage devices

Diesel turbine

Operation optimization

% Control signals / communication

Interruptible loads

Control signals / communication

2. Operation optimization considering customer satisfaction

Controllable loads

&

Because of the integration of distributed generation, controllable load, demand response, etc., ADN becomes in essence different from traditional distribution network. This section will first give the basic structure of ADN and its typical operation mode, and then build its operation optimization model. Customer response in the operation optimization will be discussed, and

G Wind turbine Energy storage devices

Critical loads

G PV generator

electrical transmission

information transmission

Fig. 1. The structure and operation modes of active distribution networks.

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For interruptible loads, when electricity price is high or electricity supply is insufficient, they will voluntarily stop their electricity consumption to earn corresponding compensation from transmission system operators. Therefore, a compensation coefficient fcut is defined to represent the compensation, and the compensation benefit of interruptible loads is described as follows:

Btcut ¼

cutn h  i X 1  stcut;m P tcut;m Bcut  stcut;m P tcut;m f cut ;

ð3Þ

m¼1

where cutn is the number of interruptible loads; Ptcut is the demand power of interruptible loads at time t; stcut;m is a binary variable, and stcut;m ¼ 1 means the m-th interruptible load is voluntarily shed (switching off electricity load) at time t in response to a financial incentive. In Eq. (1), Ces and Cgen are the operation cost of energy storage devices (ESDs) and distributed generators (DGs), respectively. Their expression can be found in Ref. [23]. Cgrid is the electricity power fare of ADNs, which can be described as follows:

C grid ¼

T   X t t stpur Ptpur f pur  stsell P tsell f sell Dt;

ð4Þ

t¼1

where stpur and stsell are binary variables, and reflect the electricity purchase and electricity selling status of ADN, respectively; P tsell and Ptpur are the power of electricity purchased and sold, respectively;

t f sell

and

t f pur

are the electricity prices.

where Ptot con is a constant, which means the operation optimization should keep the total load power of a controllable load constant max during the research period T (such as 24 h). ½Pmin con ; P con  is the range the customer can choose to keep the load running at time t. In this max t paper, P min con and P con are assumed to be 0.5 and 1.5 times of P con , respectively. For interruptible loads, the constraints of the load power can be described as follows:

t max Pmin cut 6 P cut 6 P cut

ð11Þ

max Here, P tcut may vary from P min to abide the operation cut to P cut optimization decisions of ADNs, thus interruptible loads have lowmax est priority. In this paper, P min cut ¼ 0, and P cut is set to be 1.5 times of t Pcut . It can be seen from Eqs. (10) and (11) that customers have to adjust their electricity consumption to respond to the operation optimization. Customers’ satisfaction with electricity supply is directly affected by these adjustments. In this paper, two indices are defined to quantify the customers’ satisfaction; furthermore, the impacts of customers’ satisfaction are taken into consideration in the operation optimization by adding two constraints into the optimization models.

(1) Electricity consumption index Customer satisfaction is affected by the changes of electricity consumption, and to the extent of the changes can be reflected by the variation of electricity consumption. Thus, electricity consumption index indexm is defined as follows:

(2) Constraints of the operation optimization

, T X

The operation constraints of ESDs and DGs are described in Ref. [23]. The power exchanges of ADNs with main grid are restricted by:

T  X  et  eop  indexm ¼ 1  t

stpur þ stsell 6 1;

ð5Þ

0 6 Ptsell 6 stsell P max sell ;

ð6Þ

where et is the original electricity consumption at time t, and eop t is the electricity consumption after the operation optimization.

06

Ptpur

6

stpur Pmax pur ;

ð7Þ

Besides these constraints, the operation optimization of ADNs is also restricted by power balance:

Ptwt þ Ptpv þ Ptdisch þ Ptgen þ Ptpurh ¼ Ptch þ Ptv ip þ Ptcut þ Ptcon þ P tsell ; where

P twt

and

Ptpv

ð8Þ

are the predicted power output of wind generator

and PV system, respectively. The models for determining Ptwt and P tpv can be found in Ref. [22]. 2.3. Customer satisfaction indices As mentioned above, three types of loads are introduced in this paper: critical loads, controllable loads, and interruptible loads. The difference between them is that they have different electricity supply priorities. For critical loads, their load power are restricted by:

(

Ptv ip ¼

Ptv ip

loads can be supplied

0

loads cannot be supplied

;

ð9Þ

where ‘‘loads cannot be supplied’’ means the electricity supply of critical loads is unavailable due to failures. In other words, unless there is failure, which renders the power supply impossible, the critical loads should be served all the time. Thus, critical loads have the highest supply priority. For controllable loads, the load power is restricted by:

8 T X > > < Ptot ¼ Ptcon con t¼1 > > : min Pcon 6 Ptcon 6 Pmax con

ð10Þ

t¼1

et ;

ð12Þ

t¼1

(2) Electricity cost index Electricity cost determines customers’ benefit, and thus will also affect customers’ satisfaction on electricity supply. Electricity cost index indexs is defined as follows:

, T  T  X X t t op t indexs ¼ 1  et f price  et f price et f price ; t¼1

ð13Þ

t¼1

t

where f price is the electricity price at time t. It can be seen from Eqs. (12) and (13) that indexm and indexs quantify the variation of electricity consumption and electricity cost of customers respectively, and the larger they are, the less disturbing optimization decisions become, and the more willing the customers will be to accept the operation optimization. By defining constraints as follows, the two customer satisfaction indices are integrated into the operation optimization model.

indexm P M;

ð14Þ

indexs P S;

ð15Þ

where M and S are the lower bound of the customer satisfaction indices. 3. Reliability evaluation of active distribution network based on Sequential Monte Carlo simulation Analytical methods and simulation methods are two categories of algorithms widely used in the reliability evaluation of distribution networks [24]. Because of the integration of DERs, ADNs have multiple power sources, flexible topologies, and bidirectional

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power flow. Reliability evaluation method designed for traditional distribution networks cannot be directly applied to ADNs [25]. In this paper, a new reliability evaluation framework is presented, which is shown in Fig. 2. Based on the SMC simulation method [26], customers’ power consumption, power output of ESDs and DGs that result from the operation optimization are combined with the random state curves of components in ADNs (see the right part of Fig. 2). In this way, the operation optimization is integrated into the reliability evaluation, and the impacts of customer satisfaction on reliability are also considered. Research period and time step of the operation optimization are 24 h and 1 h respectively, and the optimization keeps rolling with time in every 24 h to simulating the day ahead scheduling of ADNs. As shown in Fig. 2, the combination of operation optimization of component states determines the system state. A system state transition can be triggered by operation optimization (system state k) or a component state change (system state j). Traditional reliability indices (such as SAIFI, SAIDI, and EENS) are appropriate for the latter case, however, not suitable for the former case. Thus, to reflect the reliability performance of ADNs comprehensively, new reliability indices are necessary. In conclusion, the framework provides an effective solution for the reliability evaluation of ADNs considering customer satisfaction. The detailed procedures of the reliability evaluation framework and definition of new reliability indices are introduced as follows.

(5) Integrate the processes of the operation optimization into the SMC simulation. Optimal hourly (could be minutely) power demand, charging–discharging power of storage devices, output of DGs and electricity purchase and sale resulted from the optimization are combined with the component state transitions. (6) Determine system states according to the combination of operation optimization and state durations of components. (7) Assess the pre-determined system state to determine the power supply status of load points, and update load points’ records of outage frequency, outage duration, energy not supply, etc. (8) Run the simulation until it converges, and calculate economy and reliability indices. 3.2. Reliability indices In this paper, traditional reliability indices (SAIFI and EENS) and several new reliability indices are adopted to quantify the effects of customer satisfaction on the reliability performance of ADNs. (1) Voluntary interruption frequency (VIF) VIF quantifies the voluntary interruption frequency of interruptible loads, and can reflect the impacts of operation optimization on the continuity of power supply. VIF can be described as follow:

3.1. Main procedures

cutn 1 XX st cutn t¼1 m¼1 cut;m yT

VIP ¼ The reliability evaluation framework includes three parts: operation optimization, component state sampling, and system state assessment. The main procedures of the evaluation framework are described as follows. (1) Sample the outputs of renewable energy generators (such as wind turbines and PV generators) using their probabilistic models, which take into account the randomness and intermittency features of renewable energy resources [22]. (2) Generate the original load profiles based on the approach and data introduced in Ref. [27], and predict the electricity price for ADNs using neural network method introduced in Ref. [28]. (3) Solve the operation optimization problem defined by Eqs. (1)–(15) using YALMIP toolbox [29]. (4) Sample the state durations of components in ADNs based on a two-state model and SMC simulation method [26].

ð16Þ

where yT is the research period (such as 1 year). (2) Voluntary adjustment frequency (VAF) VAF quantifies the voluntary adjustment frequency of controllable loads, and can be described as follows: conn 1 XX st conn t¼1 n¼1 con;n yT

VAF ¼

ð17Þ

where conn is the number of controllable loads; stcon;n is a binary variable, and stcon;n ¼ 1 means the n-th controllable load voluntarily adjust its demand power at time t. (3) Annual purchased electricity (Epurchase)

Start

Operation optimization Sample RE generation Sample price and demand power

System state assessment System state determination based on SMC simulation

Solve optimization problem

State assessment using minimal path methods

Component state sampling

Calculate economy and reliability indices

Power demand after optimization

Component states

Generate Time To Failure End Generate Time To Repair System state k

System state j

T

Fig. 2. Schematic diagram for reliability evaluation of active distribution network considering customer satisfaction.

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Epurchase quantifies the purchased electricity of ADNs during the research period (such as 1 year yT). With a same electricity demand, more purchased electricity means a poorer reliability performance. Epurchase can be described as follow:

Epurchase

yT X ¼ Ptpur Dt;

Table 1 The reliability parameters of lines and transformers. Component type

Failure rate (occ./year)

Repair time (h)

Line Transformer

0.065 0.015

8 200

ð18Þ

t¼1

where Dt is the time step. In this paper, Dt = 1 h. (4) Probability to purchase electricity (Ppurchase) Ppurchase represents the probability that ADNs purchase electricity from main grid, which can be described as follow:

PyT t t¼1 spur : Ppurchase ¼ P  yT t t t¼1 spur þ ssell

ð19Þ

It is worth noting that indices defined in Eqs. (16)–(19) reflect the reliability performance of ADNs from different aspects. VIF and VAF are more focused on the reliability performance of load points, while Epurchase and Ppurchase quantify the reliability performance of the whole ADN to serve customer, especially when failures occur at external networks, and ADNs cannot purchase electricity from them. For all these indices, a smaller value means a better reliability performance. 4. Case studies and analysis The case studies are conducted on a test system (see Fig. 3) that is modified from Feeder 4 of Bus 6 in RBTS [30]. As shown in Fig. 3, the test system contains 23 loads, 23 transformers, and 30 lines (segments). The reliability parameters of lines and transformers are listed in Table 1. The failure rate of breakers and fuses are assumed to be zero because of their high reliability performance and regular maintenance [30]. The reliability parameters of distributed generators and storage devices are considered in their output power modelling [22]. F4 35 LP18 36

Load classification

LP19 37

Critical loads: LP32, LP34, LP36, LP38 Controllable loads: LP33, LP35, LP37, LP40 Interruptible loads: LP31, LP39 LP21

LP20 38 39 41

LP23 ES1 58

42

ES2 WT

PV 57

LP22 40

56

43 44

53

54

DE

LP24

In the test system, two wind turbines, two PV generators, and four batteries are integrated. Load points LP31–LP40 are considered as response loads, and the load classification is listed in Fig. 3. Thus, an active distribution network is established by combining these elements and the presented operation optimization models. This paper focused on the impacts of customer satisfaction on the reliability performance of ADNs, thus the upstream system of the ADN is assumed to be perfect, which is a common approach in distribution system reliability evaluation [31,32]. In the operation optimization models, Bvip, fcut, Bcon, and Bcut are set to 50 $/MW h, 45 $/MW h, 35 $/MW h, and 30 $/MW h, respectively. The values satisfy the constraints that Bvip > fcut > Bcon > Bcut. 4.1. Impacts of customer satisfaction on load profile Load profile directly reflects the temporal characteristics of customers’ electricity consumption. Since operation optimization can encourage consumers to modify their consumption behaviors, such modification will be reflected directly from load profile. Figs. 4 and 5 use a daily load profile of a controllable load to illustrate the influence of electricity consumption index and electricity cost index. As shown in Fig. 4, the original load profile has been largely reshaped by operation optimization. In the optimized load profile without considering customer satisfaction, not a single load point coincides with the original one, implying that customers need to change their usage habit significantly. In actual operation, such recommendation would not be easily accepted. When the lower bound of electricity consumption index (M) is no less than 0.85, the newly formed load profile contains 14 points that coincide with the original load profile, meaning that by the constraints of customer satisfaction, adjustment of customer consumption behaviors will be less frequent; when M is no less than 0.9, the number of coincided points increases to 16. This indicates that with stricter satisfaction constraints, the load profile is less disturbed by operation optimization. In Fig. 5, without operation optimization, electricity consumption in the original load profile changes regardless of the ups and downs of the price. After the optimization, however, usage of electricity responds to the trend of price: load increases at the price valley from t = 5 to t = 6 and decreases at peak price from t = 18 to t = 19. What is worth noticing is that without satisfaction constraints, demand response might be too dramatic, like during

55 45 46 LP35 LP34

LP33

48

LP32

ES1 DE

64

63

LP26 LP27

ES2 WT

PV 62

60

49

59 50

61

LP28 51

LP40 LP39

47

LP31

LP38

LP36

LP29

Load power (MWh)

LP25

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (h)

52

LP37

Fig. 3. Modified Feeder 4 of Bus 6 in RBTS.

LP30

Original load curve

Without satisfaction constrains

M=0.85

M=0.9

Fig. 4. Impacts of electricity consumption index on load profile.

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G. Li et al. / Applied Energy xxx (2015) xxx–xxx

2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0

80 70 60 50 40 30 20 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

0

Electricity price ($/MWh)

Load power (MWh)

6

Time (h) Original load curve S=1.05 Electricity price

Ces ($)

Cgen ($)

Cgrid ($)

Bcut ($)

Bload ($)

Without satisfaction constraints 0.85/1.05 0.85/1.10 0.90/1.05 0.90/1.10

5730.3

2953.3

391,700

3978.4

1,300,424

5324.9 5389.1 5410.4 5378.5

3073.2 3073.2 3134.3 3134.3

358,080 340,880 369,540 350,880

755.81 755.81 288.10 288.06

1,248,058 1,222,731 1,251,945 1,224,327

It can be seen from Table 2 that:

t = 8 and t = 9, there is only a slight rise of price, but load drops down to bottom then picks up steeply. Meanwhile, similar to Fig. 4, Fig. 5 also shows that with stricter satisfaction constraints, namely S increases from 1.05 to 1.10, less variation of load profile will be inflicted. Figs. 4 and 5 verify that by defining customer satisfaction constraints, actual user behaviors in operation optimization can be properly described, and the simulation results will provide useful suggestions for the operation of ADNs.

4.2. Economic performance of active distribution network considering customer satisfaction Results and analyses in Section 4.1 indicate that with customer satisfaction constraints load profile variation inflicted by optimization decisions will be reduced. This section will study the economic consequences from customer satisfaction. Fig. 6 gives the annual operation benefit of the test system in different cases; the impact of customer satisfaction constraints on the operation benefit is visually illustrated. It can be seen from Fig. 6 that after customer satisfaction constraints are considered in the operation optimization, the annual operation benefit of ADN reduces significantly. The annual benefit of the ADN (Btotal) reduces by $31,415 (from $ 896,062 to $ 864,647). The underlying reason is that with the satisfaction constraints, the customer could still consume electricity even when the price is high. Further, the influence of customer satisfaction on storage devices operation costs, DG operation cost, electricity purchase cost and customer benefits are discussed. The values of various annual cost and benefit are obtained from the evaluation, and they are listed in Table 2.

Anual operation benefit ($)

Customer satisfaction indices (M/S)

Without satisfaction constrains S=1.10

Fig. 5. Impacts of electricity cost index on load profile.

900000 895000 890000 885000 880000 875000 870000 865000 860000 855000 850000 845000

Table 2 The values of various annual cost and benefit under different customer satisfaction indices.

(1) After considering customer satisfaction, Ces reduces by about 6%. The reason is that satisfaction constraints reduce the variation of customers’ electricity consumption, and energy storage devices need not to be frequently charged and discharged to maintain power balance. Similarly, due to the reduction of electricity consumption variation, Bcut (the benefit resulted from the voluntary interruption of interruptible loads) reduces significantly. (2) After considering customer satisfaction, Cgen increases, while Cgrid reduces. This means that satisfaction constraints promote the utilization of generation within ADNs, which will be helpful to reduce the electricity transmission loses of power systems. (3) In cases ‘‘M/S-0.85/1.05’’ and ‘‘M/S-0.85/1.10’’ where only S increases, the values of Cgen and Bcut are the same, but both of them are different from those in cases ‘‘M/S-0.90/1.05’’ and ‘‘M/S-0.90/1.10’’. This results shows that Cgen and Bcut are sensitive to electricity consumption index (indexm). For Cgrid and Bload, they are sensitive to both electricity consumption index (indexm) and electricity cost index (indexs). These results provided suggestions for ADN operators to balance customer satisfaction against operation economy. 4.3. Reliability performance of active distribution network considering customer satisfaction In this paper, traditional reliability indices (SAIFI and EENS) and several new reliability indices are adopted to quantify the effects of customer satisfaction on the reliability performance of ADNs. The simulation results are listed in Table 3, where VIF, VAF, Epurchase and Ppurchase are defined in Section 3.2 of this paper. From Table 3, it is clear that: (1) The effects of satisfaction constraints on traditional reliability indices are slight, but they could significantly affect VIF and VAF. It means that traditional reliability indices cannot

896062

880824 872633

Table 3 The values of various reliability indices under different customer satisfaction indices.

873572 864647

Without satisfaction constrains

M/S-0.85/1.05 M/S-0.85/1.10 M/S-0.90/1.05 M/S-0.90/1.10

Different cases

Customer satisfaction indices (M/S)

SAIFI (occ./yr. cust.)

EENS (MW h)

VIF (occ./ yr.)

VAF (occ./ yr.)

Epurchase (MW h)

Ppurchase

Without satisfaction constraints 0.85/1.05 0.85/1.1 0.9/1.05 0.9/1.1

1.92097

73.3859

58

4495

12,158

0.6736

1.92104 1.92105 1.92098 1.92078

74.3473 74.2927 74.5203 74.3570

11 11 4 4

2445 1712 1411 476

11,168 10,764 11,382 10,938

0.6387 0.6289 0.6454 0.6347

Fig. 6. Annual operation benefit of different cases.

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capture the reliability variations resulted from demand response (the customers curtail or adjust electricity consumption in response to price and incentive measures). (2) After considering customer satisfaction constraints, the values of VIF and VAF reduce significantly, which means that customer satisfaction constraints effectively ensure the reliability of interruptible loads and controllable loads. (3) When the lower bound of electricity consumption index becomes higher (from M = 0.85 to M = 0.90), the Epurchase and Ppurchase increase; while an increase of S from 1.05 to 1.10 leads to lower Epurchase and Ppurchase. The reason is that when M is set higher, ADNs are more concerned with supplying customers despite growing costs; when S is set higher, ADNs aim at reducing costs for customers by minimizing purchase from main grid, so Epurchase and Ppurchase will be smaller. In other words, higher M requires more supports from external grid, and thus decreases the reliability performance; while higher S encourages customer to adequately utilize the generation inside ADNs, and thus improves the reliability performance. These results indicate that electricity consumption index and electricity cost index could have opposite impacts on the reliability performance of ADNs, and will provide good references for the operators to improve the reliability of ADNs.

5. Conclusions The integration of intermittent renewable energy promoted the development of ADNs. Operation optimization, the core of ADNs’ active management, makes ADNs distinctive from the traditional distribution network. In this paper, an operation optimization model for ADNs is proposed. In the model, two customer satisfaction indices: electricity consumption index and electricity cost index are defined, and adopted as constraints by defining satisfaction lower bounds. Besides, an ADN reliability evaluation framework is presented in this paper, in which, the operation optimization of ADNs is integrated into reliability evaluation based on the Sequential Monte Carlo simulation. By the integration, customer satisfaction is incorporated in reliability evaluation. To quantify the impacts of operation optimization customer satisfaction, four new reliability indices are defined. The presented models, approaches, and indices are validated by conducting on a standard test system, and the following conclusions are drawn from the case studies and results analyses: (1) By the proposed models, approaches, and indices, the impacts of customer satisfaction on customers’ load profile, the economic and reliability performance of ADNs are effectively evaluated. (2) Customer satisfaction constraints in operation optimization have different impacts on various economy indices of ADNs (such as operation cost of ESDs, operation cost of DGs and electricity purchase cost), and the evaluation results provide helpful suggestions for improving the customer satisfaction as well as economic performance of ADNs. (3) The consideration of electricity consumption index and electricity cost index can obviously improve the reliability of interruptible loads and controllable loads, but the impacts of these two indices on reliability performance of the whole ADNs could be opposite. The studies in this paper are of significance for improving the reliability performance of ADNs using demand response.

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Acknowledgements This work was supported by the Doctoral Program of Higher Education for the Priority Development Areas, The Ministry of Education, China (20130201130001), the Fundamental Research Funds for the Central Universities, China (2014GJHZ05, XJJ2015034), the Independence research project of State Key Laboratory of Electrical Insulation and Power Equipment in Xi’an Jiaotong University (EIPE14106), and the China Postdoctoral Science Foundation (2014M562410).

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