SCIENCE CHINA Technological Sciences • Article •
July 2015 Vol.58 No.7: 1162–1172 doi: 10.1007/s11431-015-5839-7
A calculation method for a power user’s CIC under specific conditions in smart distribution grid SUN Bing & YU YiXin* Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, China Received February 23, 2015; accepted May 14, 2015; published online June 9, 2015
This paper presents a practical method for calculating a power user’s customer interruption costs (CIC) under specific conditions. This novel method has been developed, based on the CIC results predicted by Lawrence Berkeley National Laboratory (LBNL), so that the key factors, such as customer type, customer size, interruption occurrence time and interruption duration can be considered. As compared to the LBNL method, the method proposed here is easy to understand and easy to execute with an acceptable error. It lays a solid foundation for further investigation of distributed generators and demand response in assessing reliability value of smart distribution grid (SDG). The effectiveness of the proposed method is confirmed through the assessment of RBTS-Bus2. smart distribution grid, reliability value, customer interruption costs, customer type, customer size, interruption occurrence time, interruption duration Citation:
Sun B, Yu Y X. A calculation method for a power user’s CIC under specific conditions in smart distribution grid. Sci China Tech Sci, 2015, 58: 11621172, doi: 10.1007/s11431-015-5839-7
1 Introduction Smart Grid is regarded as the key development strategy to resolve the energy problems in the 21st century [1]. But, scientific assessment of its benefits is challenging, especially the benefit of improved reliability, which is now the main concern of power consumers. In talking about drivers of smart grid, ref. [2] comments that “It is not the cost of electricity that drives our decisions. It is the cost of NOT having electricity”. This, in effect, means that the benefit of improved reliability is an important issue of the smart grid. Consequently, calculating the reduction in reliability costs that may result from implementing the smart grid becomes the core issue, while assessing the benefits of smart grid. In view of the fact that 80% or more of the recorded power failures are caused by distribution grid; 50% to 70%
of the total investments in power grid go to distribution grid; both the integration of increasing distributed generators (DGs) and demand response (DR) owing to the interactivity between power grid and power users occurred in distribution grid. This paper aims at assessing the benefits of smart distribution grid (SDG), but the uncertainties arising from DGs and DR make the assessment mission challenging. Putting a monetized value on reliability makes a traditionally implied value explicit. This supports explanation of benefits to key stakeholders and allows for a standard, objective mechanism to compare reliability investments. Customer outage costs (COC) are always referred to as the value [3]. Consequently, the research of appropriate valuation of COC becomes a hot issue. Existing methods fall broadly into three categories. Before presenting them, CIC and COC are defined below [4]. CIC: The perceived individual customer or average sector customer costs resulting from electricity interruptions.
*Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2015
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They are therefore system-independent. COC: The expected total costs incurred by all the customers connected to a particular network or service area. They are calculated from the CIC and take into consideration the network performance data and loading information. They are therefore customer mix and system dependent. Category 1. The product of unserved energy and average cost of unit unserved energy is regarded as COC. Dozens of indexes are being used as the average cost. For example, electricity price multiplied by a conversion factor [5]; economic output of unit electricity [6]; statistical value from past failures [7]. Category 2. Contingent valuation method (CVM) [8], based on customer surveys, is the cornerstone. Customer damage function (CDF), which describes the nonlinear relationship between CIC and interruption duration, is developed on the basis of survey data of CVM [9]. The concept of classification, which involves the following four steps, holds good for the whole assessment of COC. All the customers surveyed were grouped into different classes based on the Standard Industrial Classification (SIC), and each class was assigned an SIC code or other name. All SIC classes were generalized into different sectors, e.g. residential, industrial and commercial [4]. First, the entire survey data belonging to an SIC class was normalized with respect to either the customer’s annual energy consumption or his or her peak demand. These normalized CIC values were averaged or weighted to give corresponding SIC class values that form the so-called individual CDF (ICDF). Second, sector customer damage functions (SCDFs) were developed by weighting the above mentioned ICDFs, using annual energy consumption or peak demand. Here, the SCDFs can be geared to the needs of any supply region, e.g. a load point or a sub-distribution. Third, composite customer damage functions (CCDFs) were developed by weighting these SCDFs, following a similar procedure. Last, COC values of a network were calculated with CCDF. With further research, it was realized that more and more impact factors should be dealt with in developing CDFs. The significance of customer type is highlighted in [10]. The effect of interruption occurrence time is analyzed and time varying cost model developed in [11]. Ordinary CDF and CDF, under the assumption of normal distribution, are compared in [12] to explore the uncertainty of CIC. Seven impact factors of CDF and CIC are put forward in [13]. Category 3. Multiple surveys are integrated and then survey data normalized with the GDP deflator [14] (or other appropriate index). Based on this, the effect of customer size, i.e. the size of a power user’s annual electricity consumption, can be accounted for. Furthermore, exact expressions of CDF are developed in [15], instead of connecting several discrete points to obtain the desired CDF curves [4] as in category 2. So far, LBNL seems to be the only laboratory that can carry out this work. However, the existing methods have some drawbacks. 1)
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Although the methods of category 1 are easy to apply, neither the time-varying and nonlinearity characteristics nor the close relationship between COC and customer type is considered. 2) In spite of being clear in their thinking, the authors of category 2 papers generally analyzed only a single factor. Besides, they did not undertake any quantitative analysis of the effect of customer size on CIC/COC. 3) The method of category 3 is originally believed to greatly promote the development of reliability valuation, but because of its complexity, the achievements have not been adopted widely. In addition, it should be noted that, in the existing methods as those in [4], load point is by default the minimum unit for load shedding when interruption occurs. That is, all users under the same load point always experience the same interruption. However, the implementation of smart grid is expected to bring a plethora of new elements into traditional distribution grid [16,17]. A quintessential example of these elements is the advanced metering infrastructure (AMI) with smart meters for sensors, which facilitates DR and user-level (or even equipment-level) load management [18,19]. Against this background, user or even user’s equipment should play the role of minimum unit during load shedding in SDG, which will make the calculation of COC more complex as compared with previous practices. Additionally, time to failure and repair time of each element are burdened with probabilistic features; output of DGs is labeled with intermittent variability and uncertainty; both implementation degree of AMI and the relationship between DR and electricity price are uncertain in SDG. All these new elements make COC more elusive and little attention has been paid on their effects on COC valuation. In summary, probabilistic reliability valuation of SDG is a very complex issue. The natural solution, therefore, is to break down the issue into two sub-problems: Calculating 1) a power user’s CIC under specific conditions and 2) the COC of SDG, given the specific planning scheme. This paper focuses on solving sub-problem 1), which relates to the users experiencing interruption, and thus lays a solid foundation for solving sub-problem 2) .as a separate paper. With the outcome of this study, the uncertainties from load, DGs and DR are easy to overcome.
2 Profile of LBNL achievements and the new ideas of this paper By 2009, the U.S. LBNL integrated 28 investigation projects from 9 utilities through 16 years and obtained a wealth of primitive data. After multiple mathematical analyses and processing of the primitive survey data, LBNL fitted the “two-part model” with 80% of the mature data obtained, which enabled accounting for customer size [14]. The model is more precise than others with numerous multi-variables expressions of CDF. The remaining 20% data was used to
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contrast the predicting accuracy of the “two-part model” with that of other methods. The “two-part model” is proved to be the best and its CIC predicted results show that CIC is greatly influenced by customer size with a strong nonlinear effect. Regrettably, among all the achievements of LBNL, only the weight coefficients of all the impact factors of the “two-part model” and a small part of CIC predicted results have been made public [14]. Primitive survey data, intermediate results and detailed fitting methods are unavailable. Dr. Sullivan M J, the proponent of “two-part model, in one of his lectures published in 2010 (see ref. [15]), observed thus: “This methodology has been proven to provide more reliable estimates, but has not usurped other methodologies because it is more complicated”. “Two-part model” yields high accuracy, but introduces, in the process, high complexity. A host of mathematical analyses and lack of physical explanation are the main causes of complexity. One of the main manifestations of complexity is the number of weight coefficients in its expressions, which amazingly goes up to 46. In the absence of a detailed explanation for determining these coefficients and a clear depiction of each procedure, one finds it hard to understand the “two-part model” without getting to the bottom of LBNL research. The way to master and use it is full of barriers. Ref. [15] is devoted to the use of “two-part model”, but with little success. Additionally, while reproducing the announced CIC predicted results in [14], obtained by rigorously following the “two-part model” of [15], an error shows up as a result of coefficients’ precision or other unknown reasons. Figure 1 shows the reproductions of “Medium and Large Commercial and Industrial Customers US 2008$ Customer Damage Functions by Average kW—Summer Weekday Afternoon” (Figures 3–4 in [14]). Here, “US 2008$” means that all the interruption costs have been estimated at 2008 dollars by adjusting the original estimates using the US Bureau of Economic Analysis GDP deflator. The numbers in the legend box refer to users’ annual average powers, those preceded by blue dots to announced CIC predicted results in
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[14], and those preceded by red dots to reproductions. To provide a reliable estimate of CIC/COC, accounting for the impact factors is most critical, and this can be done in two ways. The first one is to consider these factors while fitting CDF and then calculate CIC/COC with the complex CDF (as in [15]). The second way is to consider these factors while fitting CDF, and then when enough CIC predicted results are produce under typical conditions, use these typical values to calculate CIC/COC. In the sense of promoting the excellent achievements of LBNL, the first way, as mentioned in [15], did not yield the desired result. As such, we decided to adopt the second way. Instead of involving ourselves in the complex fitting procedures, we relied on the CIC predicted results, announced in a report of LBNL [14], and carried out the subsequent assessment of reliability in SDG. The following work was carried out as a further step to what has already been done.[14]: Developing a method for calculating the power user’s CIC under specific conditions with clear meanings of both calculation steps and coefficients; solving the problem of “two-part model” that it’s hard to understand and the problem that available predicted results are inadequate.
3 A power user’s CIC under specific conditions 3.1 Calculation method for a power user’s CIC under specific conditions Departing from the categorization of customers into residential, industrial and commercial, as given in [4], the customers are grouped into three sectors in [14]: Medium and large commercial and industrial customers (MLCIC), small commercial and industrial customers (SCIC) and residential customers (RC). The average annual electricity consumption of each surveyed customer is shown in Table 1. Annual consumption of 50MWh is taken here as the boundary between MLCIC and SCIC. Both MLCIC and SCIC are finely subdivided into 9 industries by industry type, in the same way as the SIC classes in [4] are subdivided into construction, manufacturing and so on. The default load type is constant power load in [14] and the value is user’s annual average power. LBNL shows CIC predicted results in four units: cost per event, cost per average kW, CPUE and cost per annual kWh. The numeric values corresponding to these four units can be converted into each other through annual average power. As CPUE shows an obvious advantage in the calculation process of COC [13], we choose CUPE as our unit. Table 1 Average annual electricity consumption of the surveyed customers of MLCIC, SCIC and RC
Figure 1 The comparison of predicted CIC in [14] and reproductions according to [15].
Customer sector type Average annual consumption (kWh)
MLCIC 7140501
SCIC 19214
RC 13351
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3.1.1 Set of specific conditions Ci , j ,( m, n, r ) ( S , t ) is the formulation of customer’s CPUE in this paper, where the subscript variables i, j, (m,n,r) and the variables S, t within brackets denote the so-called specific conditions. In the following description, {} is to be used as a set consisting of elements . The indicator variables of customer type include i and j. i {1, 2,3} represents the 3 sectors, i.e. MLCIC, SCIC and RC. j {0,1, ,10} represents customer industry type, the numbers 1 to 9 correspond to 9 industries respectively (as in Figure 2 where the curves are labeled 1 to 9 from bottom to top). When industry information is unknown, let j 10 represent “integrated type”. To ensure that the expression is tidy, let j 0 represent RC, which is not subdivided further. To set it apart from the customer type, we call variable j customer industry type. The indicator variables of interruption occurrence time include m, n and r. m {1, 2} represents summer and winter, n {1, 2} weekday and weekend, and r {1, 2,3, 4} morning, afternoon, evening and night. By combining m , n and r, 16 vectors in the form of (m, n, r ) can be generated, which make up the set I, I {1, 2} {1, 2} {1, 2,3, 4} , where is the operation symbol of direct product. S is the indicator of customer size, S R , and represents the annual electricity consumption, where R is the positive real set. t is the indicator of interruption duration, t T : {1, 2, ,17}
Z , where Z is positive integer. t 1 represents momentary; t 2, ,17 corresponds to 0.5, 1, 1.5,…, 8 h respectively. Figure 2 shows some predicted results of MLCIC ( i 1 ) given in [14]. The curve cluster in this figure includes nine curves, each corresponding to an industry of j {1, 2, , 9} {0,1, ,10} . At any point on these curves, customer size S and interruption occurrence time (m, n, r ) are constant. Specifically, S is 7140501 kWh, which is the average
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consumption of MLCIC in Table 1 and (m, n, r ) (1,1, 2) , meaning afternoon of summer weekday. According to the above expression, all the discrete points, t T , on the 9 curves can be written as C1, j ,(1,1,2) (7140501, t ) , j {1, 2, , 9} .
3.1.2 Essential CIC predicted results This subsection lists the essential inputs for calculating a power user’s CIC under specific conditions. To any i {1, 2,3} , CIC predicted results are narrated in such a way that only a single factor is variable, while the others remain constant [14]. In Figure 2, customer industry type is variable, traversing the 9 industries; the customer size and interruption occurrence time are constant as stated above. For simplicity, we call the single variable as cluster variable and name the corresponding curve cluster with the name of the cluster variable. A cluster consists of multiple curves and each curve is regarded as a CDF [14]. As a result, Figure 2 is named “MLCIC CIC predicted results with the variable of customer industry type”. To differentiate between the cluster variables, we call abscissa variable (interruption duration) and ordinate variable (CIC) as independent variable and dependent variable respectively. According to the set of specific conditions, the following CIC predicted results are required. (1) For any i {1, 2} , the figure of curve cluster, with the variable of customer industry type j {1, ,10} , consisting of 10 curves accordingly; the figure of curve cluster with the variable of customer size S R , coupled with the solution to continuous change of S ; the figure of curve cluster, with the variable of interruption occurrence time (m, n, r ) I , consisting of 16 curves accordingly. There are six figures in all, and for each curve in these figures, the independent variable is interruption duration in hour and the dependent variable is CIC predicted results in CPUE. (2) For i 3 , the figure of curve cluster with the variable of customer size S R , coupled with the solution to continuous change of S ; the figure of curve cluster, with the variable of interruption occurrence time (m, n, r ) I , consisting of 16 curves accordingly. There are two figures in all, and the style of each curve is the same as that of (1). 3.1.3 Original data [14] and detail tasks The original data available from [14] is as follows. Consequent to the above mentioned essential inputs, the detailed tasks emerged finally. It is to be noted that, because CPUE is the unit of CIC, we converted all CIC predicted results available from [14] to data in CPUE. (1) For any i {1, 2} {1, 2,3} , CIC predicted results (figure of CPUE curve cluster) with the variable of customer industry type j {1, 2, , 9} {0,1, ,10} , i.e.
Figure 2 MLCIC US 2008$ CIC predicted results by industry-summer weekday afternoon.
Ci , j ,(1,1,2) ( S0,i , t ) ,
j {1, 2, , 9} , t T ,where customer
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size is the average in Table 1. As a result, the S0,i here is identified by Table 1, e.g. S0,1 is 17140501 kWh for i 1 ; interruption occurrence time is constant (m, n, r ) (1,1, 2) as in Figure 2. (2) For any i {1, 2} and j 10 , CIC predicted results (figure of CPUE curve cluster) with the variable of customer size, i.e. Ci ,10,(1,1,2) ( S1,i , t ) , Ci ,10,(1,1,2) ( S2,i , t ) , Ci ,10,(1,1,2) ( S3,i , t ) and Ci ,10,(1,1,2) ( S 4,i , t ) , t T ; for i 3
and j 0 , CIC predicted results (figure of CPUE curve cluster) with the variable of customer size, i.e. C3,0,(1,1,2) ( S1,3 , t ) , C3,0,(1,1,2) ( S2,3 , t ) , C3,0,(1,1,2) ( S3,3 , t ) and C3,0,(1,1,2) ( S4,3 , t ) , t T .
Where four kinds of customer size Si ( S1,i , S2,i , S3,i , S 4,i ) , i {1, 2,3} are assumed values, {S1, S2 , S3}
R 4 , and where R 4 represents 4-dimensional real space, S1 (175.2 MWh,876 MWh, 4.38 GWh, 21.9 GWh), S2 (2.19 MWh,8.76 MWh, 26.28 MWh, 43.8 MWh) , S3 (2.19 MWh,8.76 MWh, 21.9 MWh,35.04 MWh) . (3) For any i {1, 2} and j 10 , CIC predicted results (figure of CPUE curve cluster and CPUE table) with the variable of interruption occurrence time. CPUE curve cluster consists of four CPUE curves corresponding to summer weekday morning, summer weekday afternoon, winter weekday morning and winter weekday afternoon: Ci ,10,( m, n, r ) ( S0,i , t ) , (m, n, r ) I , t T , where I {(1,1,1), (1,1, 2),(2,1,1),(2,1, 2)} I ; CPUE table consists of 16 rows corresponding to 16 vectors (m, n, r ) I : Ci ,10,( m, n, r ) ( S0,i , t ) , (m, n, r ) I , t T : {1, 2,3, 9,17} T .
For i 3 and j 0 , CIC predicted results (figure of CPUE curve cluster and CPUE table) with the variable of interruption occurrence time: CPUE curve cluster consists of 4 CPUE curves corresponding to summer weekday morning, summer weekday afternoon, winter weekday morning and winter weekday afternoon: C3,0,( m, n, r ) ( S0,3 , t ) , (m, n, r ) I , t T ; CPUE table consists of 16 rows corresponding to 16 vectors (m, n, r ) : C3,0,( m, n, r ) ( S0,3 , t ) , (m, n, r ) I , t T . Therefore, for meeting the essential CIC predicted results, the following tasks are to be carried out. Task 1: Replenish the CPUE curve of j 10 to CIC predicted results with the variable of customer industry type j. Task 2: Replenish the solution to continuous change of S to CIC predicted results with the variable of customer size S. Task 3: Replenish discrete CPUE points, t T \ T , to CIC predicted results (CPUE table) with the variable of interruption occurrence time (m, n, r ) , where \ is the op-
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eration symbol of set difference. Based on these discrete points, the other 12 curves, (m, n, r ) I \ I , can be replenished to CIC predicted results (figure of CPUE curve cluster) with the variable of interruption occurrence time. 3.1.4 Four steps for CIC calculation The CIC is calculated through four steps, which correspond to the ways they deal with the four impact factors of Ci , j ,( m, n, r ) ( S , t ) : Customer type (i, j ) , customer size S, interruption occurrence time (m, n, r ) , and interruption duration t. (1) Accounting for customer type (i, j ) , based on CIC predicted results with the variable of customer industry type j. When the customer to be estimated is MLCIC or SCIC, i {1, 2} and j 10 , proceed as follows. First, determine variable i by judging whether his annual consumption is more than 50 MWh, and embody variable j according to his industry type. Then, find the curve corresponding to j from the CPUE curve cluster with the variable of customer industry type corresponding to i. Lastly, extract 17 discrete values Ci , j ,(1,1,2) ( S0,i , t ) , t T , from the curve. If j 10 or i 3 , then go to the next step directly. (2) Accounting for customer size S based on CIC predicted results with variable of customer size S. For any i {1, 2} {1, 2,3} and j 10 , 4 discrete CPUE values can be extracted from CIC predicted results with the variable of customer size for any t T : Ci ,10,(1,1,2) ( S1,i , t ) , Ci ,10,(1,1,2) ( S2,i , t ) , Ci ,10,(1,1,2) ( S3,i , t ) and Ci ,10,(1,1,2) ( S 4,i , t ) .
According to the principle of polynomial function, four points determine the only cubic function. As a result, the cubic function f i ,t ( S ), S R can be fitted with the follow-
ing 4 points: ( S1,i , Ci ,10,(1,1,2) ( S1,i , t )) , ( S2,i , Ci ,10,(1,1,2) ( S2,i , t )) , ( S3,i , Ci ,10,(1,1,2) ( S3,i , t )) and ( S 4,i , Ci ,10,(1,1,2) ( S4,i , t )) . Consid-
ering that S1,i , S2,i , S3,i and S 4,i increase exponentially leading to a very uneven distribution of the 4 points, annual electricity consumptions are converted logarithmically. At last, cubic function f i ,t (lg S ), S R is fitted with (lg S1,i , Ci ,10,(1,1,2) ( S1,i , t )) , (lg S2,i , Ci ,10,(1,1,2) ( S2,i , t )) , (lg S3,i , Ci ,10,(1,1,2) ( S3,i , t )) and (lg S 4,i , Ci ,10,(1,1,2) ( S 4,i , t )) . In
the same way, f 3,t (lg S ), S R can be fitted according to C3,0,(1,1,2) ( S1,3 , t ) , C3,0,(1,1,2) ( S2,3 , t ) , C3,0,(1,1,2) ( S3,3 , t ) and C3,0,(1,1,2) ( S 4,3 , t ) .
Ci , j ,(1,1,2) ( S , t ) Ci , j ,(1,1,2) ( S0,i , t ) kt ( S ), i {1, 2}, j {1, 2, , 9}, f i ,t (lg S ), i {1, 2}, j 10, (1) i 3, f 3,t (lg S ),
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C3,0,( m, n, r ) ( S0,3 , t ) C3,0,( m,1,2) ( S0,3 , t ) * kt (t ),
(S , t ) C1,10,(1,1,2) , C1,10,(1,1,2) ( S0,1 , t ) kt ( S ) (S , t ) C2,10,(1,1,2) , C 2,10,(1,1,2) ( S0,2 , t ) f1,t (lg S ) , S (50 MWh, +), f1,t (lg S0,1 ) f 2,t (lg S ) , S (0,50 MWh ], f t (lg S ) 0,2 2,
i 3, t T \ T ,
(2)
(3)
[Ci ,10,(1,1,2) ( S1,i , t ), Ci ,10,(1,1,2) ( S2,i , t ), Ci ,10,(1,1,2) ( S3,i , t ), Ci ,10,(1,1,2) ( S 4,i , t )], i {1, 2}, C : (4) [C3,0,(1,1,2) ( S1,3 , t ), C3,0,(1,1,2) ( S2,3 , t ), C3,0,(1,1,2) ( S3,3 , t ), C3,0,(1,1,2) ( S 4,3 , t )], i 3.
The physical meaning of kt ( S ) in eq. (1) refers to the influence coefficient of customer size to CPUE. Eq. (2) represents that kt ( S ) is the ratio of corresponding CPUE calculated by f i ,t (lg S ) . Eq. (3) represents that f i ,t (lg S ) is the output of POLYFIT function of software
MATLAB, where C on the right side is defined by eq. (4) and 3 represents a polynomial of degree three. So far, tasks 1 and 2 are completed. At this point, to the CPUE Ci , j ,(1,1,2) ( S0,i , t ) from step (1), customer size S can be any positive real number, i.e. Ci , j ,(1,1,2) ( S , t ) , S R . (3) The following methods are proposed to solve task 3. t max{x T , x t}, t T \ T ,
(5)
t min{x T , x t}, t T \ T ,
(6)
Ci ,10,( m, n, r ) ( S0,i , t ) , i {1, 2}, Ci ,10,( m,1,2) ( S0,i , t ) kt C3,0,( m, n, r ) ( S0,3 , t ) , i 3, C 3,0,( m,1,2) ( S0,3 , t )
(7)
Ci ,10,( m, n, r ) ( S0,i , t ) , i {1, 2}, Ci ,10,( m,1,2) ( S0,i , t ) kt C3,0,( m, n, r ) ( S0,3 , t ) , i 3, C 3,0,( m,1,2) ( S0,3 , t ) (t t ) kt(t ) kt (kt kt ), (t t )
t T \ T ,
Ci ,10,( m, n, r ) ( S0,i , t ) Ci ,10,( m,1,2) ( S0,i , t ) * kt (t ), i {1, 2}, t T \ T ,
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(10-2)
where t and t are discrete values in set T with smallest distance to t in relation to the directions given below and above respectively. Eqs. (7) and (8) represent the ratios of CPUE corresponding to t and t . kt(t ) in eq.
f i ,t (lg S ) : polyfit ([lg S1,i , lg S2,i , lg S3,i , lg S4,i ], C ,3), t T , i {1, 2,3}, S R ,
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(9) is the result of linear interpolation to kt and kt . The unknown discrete CPUE values are calculated through influence coefficient kt(t ) in eqs. (10-1) and (10-2). With this, task 3 completes. Accounting for interruption occurrence time (m, n, r ) , based on CIC predicted results with the variable of interruption occurrence time (m, n, r ) . Assuming that one interruption arises on article hourth hour: (m, n, r ) g (hourth), hourth [0,8760],
(11)
Ci , j ,( m , n, r ) ( S , t ) Ci , j ,(1,1,2) ( S , t ) kt(hourth), t T , (12)
Ci ,10,( m , n , r ) ( S0,i , t ) , i {1, 2}, Ci ,10,(1,1,2) ( S0,i , t ) kt(hourth) C3,0,( m , n, r ) ( S0,3 , t ) , i 3, C 3,0,(1,1,2) ( S0,3 , t )
(13)
where g in eq. (11) represents a program written to identify (m, n, r ) with hourth . The simple program operates because of calendar and will not be unfolded here. The physical meaning of kt(hourth) in eq. (12) is the influence coefficient of interruption occurrence time to CPUE. All the CPUE on the right side of eq. (13) are from CPUE curve cluster with variable of interruption occurrence time. At this point, to the CPUE Ci , j ,(1,1,2) ( S , t ) from step (2), interruption occurrence time (m, n, r ) can be any vector in I, i.e. Ci , j ,( m, n, r ) ( S , t ) , (m, n, r ) I . (4) Accounting for interruption duration. R , Ci , j ,( m, n, r ) ( S , t ) is calculated by To any t (0,8h] linear interpolation to 17 discrete values Ci , j ,( m, n, r ) ( S , t ) , t T . To any t (8h, ) R , CPUE is believed to
reach a stable number:
(8)
Ci , j ,( m, n , r ) S , t Ci , j ,( m, n, r ) S ,17 , t 8 h.
(14)
At this point, to the CPUE Ci , j ,( m, n, r ) ( S , t ) from step (2),
(9)
interruption duration t can be any number in R , i.e. Ci , j ,( m, n, r ) ( S , t ) , t R .
(10-1)
When the load model is time-varying power injection curve of 8760 hours, the cost of one power user experiencing the interruption is
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hourth t
Cfault Ci , j ,( m , n , r ) ( S , t ) *
Pt1 dt1 ,
(15)
hourth
where Pt1 is the user’s active power on t1 . 3.1.5 Remark (1) Eqs. (2) and (10-1) have the tacit assumption that the influence coefficients of customer size and interruption occurrence time identified by integrated type j 10 are suitable to any other industry type j {1, 2, , 9} {0,1, ,10} . (2) If the set of specific conditions is expanded to include an additional factor x , we can calculate the influence coefficients of x in the same way as the one given above. By multiplying the influence coefficients of x with Ci , j ,( m, n, r ) ( S , t ) , the final CIC can account for x . 3.2
Modification method of CIC
It is observed in [4] and [20] that the CIC of long interruption duration is closely related to unserved energy, but the CIC of short interruption duration is even more closely related to peak power. For interruptions longer than 1 hour, CIC can be well assessed with eq. (15), and for those shorter than 1 hour, it is necessary to ensure smooth and continuous growing of CIC along with the increase of interruption duration, besides satisfying the law in [4] and [20]. As such, CPUE values corresponding to momentary, 0.5 and 1 h, are calculated for a duration of less than 1 hour, instead of t. Then three CIC values, corresponding to the above three CPUE values, are achieved. Then, the CIC corresponding to t is calculated by linear interpolation of the above three CIC values. 3.3
Adjustment method of CIC
It is to be noted that both CIC predicted results and CDF are closely related to the primitive survey data. As a result, the subsequent assessment based on CIC predicted results or CDF suits only to the cradle of survey data. Simply put, although the method proposed in this paper is universally applicable, the concrete figures can be used only for assessment in USA. Most of the countries in the world have not undertaken the required investigations because large-scale surveys of CVM are very expensive and time-consuming. For instance, this type of survey is seldom carried out in China. Moreover, digitization is poised to increase gradually in the near future, and the CIC led by the same interruption will increase correspondingly. Consequently, the achievements of LBNL will have to be adjusted, although they are now used with their cradle in the USA. In this context, it may be helpful to create a conversion factor to solve the problems arising from regional differences and time variations. The conversion factor is inevitably related to the industry structure and the degree of digiti-
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zation. The following are the two suggestive indicators : 1) index reflecting electric efficiency, i.e., the energy consumption per 10,000¥/$ GDP for each j {0,1, ,10} ; 2) index reflecting digitization, i.e.,. the number of employees per 10,000¥/$ GDP for each j {0,1, ,10} . Reliability value increases with the decrease of the two indexes. Conversion factor results from weighting of these two indexes. In the current society with big data, it is not hard to touch these statistical indexes.
4 Case studies For any system, the procedure for calculation of COC depends on the system model, the load model and the cost model. System model: The topology of RBTS-Bus2 is shown in Figure 3. The details given therein refer to those given in [21]. All the feeders are cables and their maximum current is set at 334A. The reliability parameters of [21] are modified as follows. 1) The components of repair time tre and load transition time tsw are lognormal distributed, with the expectation that the numbers are consistent with the numbers given in [21] and their standard deviations are 1/3 of the corresponding expectations. Fault isolation time tis is 1/2 of tsw . 2) Failure rates of buses and breakers are the same as those of eq. (16) in [22]. 3) Failure rates of cables and transformers are as eq. (17) referring to [23]. Load model: Load model with constant power factor of 0.95 is extracted from [24]. Customer industry types are as Table 2. Cost model is obtained using the calculation method given in Section 3. Assessment period is 20 years.
break er (t2 ) y (t2 T y ) 1 1.1y 0.00155 0.00155 3 (t2 y ) 2 ,
bus (t2 ) y (t2 T y ) 1
(16)
1.1 0.000259 0.000259 3 (t2 y ) , y
2
y {0,1, ,19}, t2 [ y, y 1),
Figure 3
Network topology of RBTS-Bus2.
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Table 2 Customer industry type of each load point of RBTS-Bus2 Customer industry type Load point
RC 1/2/3/10/11 /12/17/18/19
Public Admin. 4/5/13/ 14/20/21
Trade & Retail
Services
Fin., Ins. & R. E.
Manufacturing
6/15
7/16
8/22
9
cable (t2 ) 0 t2 15, 0.0026, 2 0.0026 0.0026 3 (t2 15) , 15 t2 20, transformer (t2 ) 0.0021, 2 0.0021 0.0021 3 (t2 15) ,
(17)
0 t2 15, 15 t2 20.
4.1 Accuracy verification
For the assumption “influence coefficients of customer size identified by integrated type j 10 are suitable to any other industry type j {1, 2, , 9} {0,1, ,10} ” in Remark 1) above, it is necessary to verify the calculations of some arbitrary values of customer size S . According to customer size (as in [21]) and customer industry type (as in Table 2), there are six kinds of customers on feeders F1 and F2, i.e. LP1-LP9. Their sizes are significantly different from each other, and can be used as verification objects. To be consistent with the contents of [14], the active power of each kind of customer is temporarily set at annual average power. Their CIC values in summer weekday afternoons, denoted as Ehtwo part (t ) and Ehsection 3 (t ) , t T , are calculated with “two-part model”, following the method given in Section 3, where h {1, 2,3, 4, 5, 6} represents six kinds of customers. As the magnitude orders of six kinds of CIC calculations are different, it is inconvenient to put them into one figure. Figure 4(a) shows the relative error (RE): RE section 3
Ehtwo part (t ) Ehsection 3 (t ) 100%, Ehtwo part (t )
(18)
t T , h {1, 2,3, 4, 5, 6}.
For an exact estimate of the magnitude of error, Figure 4(b) shows the RE of the 4 pairs of curves in Figure 1: RE ref .[14]
Eatwo part (t ) Earef .[14] (t ) 100%, Eatwo part (t )
(19)
t T , a {20,100, 500, 2500},
where a represents the four kinds of active power in Figure 1; Eatwo part (t ) represents the reds and Earef .[14] (t ) the blues. From Figure 4(a), it’s obvious that while most of the REs are within the range of 5%, there is some difference between Ehtwo part (t ) and Ehsection 3 (t ) . RE reaches its maximum of about 15% after about 1 hour. From Figure 4(b), it’s
Figure 4 (a) REs of CIC discrete values of six kinds of customer; (b) REs of reproductions from “two-part model” with respect to announced results in [14].
obvious that there are some differences between Eatwo part (t ) and Earef .[14] (t ) also, and most of them are within the range of 5%. RE reaches its maximum of about 25% after about 1 hour. It can be concluded from Figure 4(b) that what we get from [14] and [15] are not the exact expressions of “two-part model”. Yet, we considered the announced predicted results in [14] as our original data, but not the calculations of “two-part model” introduced in [15]. Therefore, it is inappropriate to regard REs in Figure 4(a) as the REs of the method in Section 3. The REs led by the method proposed in this paper should be smaller when the exact expression of “two-part model” is used. Besides, most of the numbers in Figure 4(a) are within the allowable range of engineering. So, the above assumption is valid. Similar conclusions to the assumption “influence coefficients of interruption occurrence time identified by integrated type j 10 are suitable to any other industry type j {1, 2, , 9} {0,1, ,10} ” are summarized from the
analysis of Appendix. All the calculations prove that the assumption in Section 3 is acceptable and valid. 4.2
Calculations of COC
As CIC is system-independent, it is necessary to apply the
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CIC calculation method proposed in Section 3 for the assessment of COC, which is system-dependent. In RBTSBus2, feeders F1 and F2 constitute a hand-in-hand one ring, and so do F3 and F4 in another ring. Reliability valuations (COC calculations) are carried out for the two rings through Monte Carlo simulation. Probability distribution histograms are shown in Figure 5, wherein the red in each figure represents the contour fitting curve, blue the normal distribution curve, and green the lognormal distribution curve. The statistical results can be seen between the blue and the green. The estimations provide an insight into the general trends of COC distribution. As precise calculation of COC distribution is very hard, if not impossible, we can use these estimations for interval estimation, e.g. the interval estimation of COC expectation. Consequently, the CIC calculation method proposed in this paper can estimate reliability value effectively.
5 Conclusions A method for calculating a power user’s customer interruption costs (CIC), under specific conditions, is proposed. The following are its characteristics. (1) It is based on CIC predicted results in [14] and can account for customer size, one of the core impact factors of CIC. (2) Each step is coupled with clear physical sense and the
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relative error is within the allowable range of engineering. (3) It is easy to apply. The calculation of a power user’s CIC under specific conditions, sub-problem 1) in Section 1, is split into two parts. Part 1): Fitting customer damage function with survey data by contingent valuation method and producing enough CIC predicted results under several typical conditions with the obtained customer damage function. Part 2): Calculating a power user’s CIC under specific conditions based on the typical CIC values obtained in part 1). This splitting of calculation is very much necessary as explained below. Part 1) can be done without much professional knowledge of power system, although it is a heavy task requiring a lot of time and effort. As a result, it needs the support from many departments and hence the calculation model obtained could be complex with poor physical sense. There are barriers on the way to calculating customer outage costs (COC) of smart distribution grid, given the specific planning scheme, sub-problem 2) in Section 1. The method proposed in this paper completes with part 2), which eliminates the barriers. It is built on past achievements, and strives for future progress. It lays a solid foundation for further investigation of distributed generators and demand response in assessing reliability value of smart distribution grid.
1 (a)
2
3 4 5 6
7 (b)
8
9
10
11 Figure 5 (a) Probability distribution histograms of COC values of hand-in- hand one ring of F1 and F2; (b) probability distribution histograms of COC values of hand-in- hand one ring of F3 and F4.
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Yu Y X, Qin C. Explanation on the basic ideas of smart grid (in Chinese). Sci China Inf Sci, 2014, 44: 694–701 Pullins S W. The NETL modern grid initiative: What will the US modern grid cost? In: Power Engineering Society General Meeting. Tampa, FL: IEEE PES, 2007 Sullivan M J, Keane D. Outage Cost Estimation Guidebook. EPRI Report, 1995 Kariuki K K, Allan R N. Evaluation of reliability worth and value of lost load. IEE Proc Gener Transm Distrib, 1996, 143: 171–180. Guo Y J. Power System Rreliability Analysis (in Chinese). 1st ed. Beijing: Tsinghua University Press, 2003. 244–255 Zhou J H. Power System Planning With Large-scale Wind Power Based on Value Evaluation (in Chinese). Tianjin: Tianjin University, 2011. 102–103 Yu Y X, Wang J R, Lv X Y. Security value based expansion planning of power system with integration of large-scale wind power (in Chinese). Sci China Tech Sci, 2012, 55: 1908–1922 EPRI. Cost-benefit analysis of power system reliability: Determination of interruption costs-Vol. I: Measurement methods and potential applications in reliability cost-benefit analysis. EPRI Report EL-6791, 1990 Goel L, Billinton R. Determination of reliability worth for distribution system planning. IEEE Trans Power Delivery, 1994, 9: 1577– 1583 Billinton R, Ali S, Wacker G. Rural distribution system reliability worth evaluation using individual customer outage cost characteristics. Int J Elec Power, 2004, 26: 235–240 Wang P, Billinton R. Time sequential distribution system reliability worth analysis considering time varying load and cost models. IEEE Trans Power Delivery, 1999, 14: 1046–1051 Jonnavithula A, Billinton R. Features that influence composite power system reliability worth assessment. IEEE Trans Power Syst, 1997,
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15
16
17
18 19
20
21
22
23
24
Sci China Tech Sci
12: 1536–1541 Neudorf E G, Bhavaraju M P, Billinton R, et al. Cost-benefit analysis of power system reliability: Two utility case studies. IEEE Trans Power Syst, 1995, 10: 1667–1675 Sullivan M J. Estimated value of service reliability for electric utility customers in the united states. Ernest Orlando LBNL Report 2132E, 2009 Sullivan M J, Mercurio M G, Schellenberg J A, et al. How to estimate the value of service reliability improvements. In: Power and Energy Society General Meeting. Minneapolis, MN: IEEE PES, 2010 Yu Y X, Zeng Y, Liu H, et al. Challenges and R&D opportunities of smart distribution grid in China. Sci China Tech Sci, 2014, 57: 1588–1593 Mei S W, Chen L J. Recent advances on smart grid technology and renewable energy integration. Sci China Tech Sci, 2013, 56: 3040– 3048 Yu Y X, Luan W P. Smart grid and its implementations (in Chinese). Proc CSEE, 2009, 29: 1–8 Yu Y X, Ma S Q. 1-Neighbour knapsack problem and prospective greedy algorithm of intentional islanding in active distribution network. Sci China Tech Sci, 2014, 57: 568–577 Billinton R, Oteng A J, Ghajar R. Comparison of two alternate methods to establish an interruption assessment rate. IEEE Trans Power Syst, 1987, 2: 751–757 Allan R N, Billinton R, Sjarief I, et al. A reliability test system for educational purposes-basic distribution system data and results. IEEE Trans Power Syst, 1991, 6: 813–820 Duan D L, Wu X Y, Deng H Z. Reliability evaluation of distribution systems based on time-varying failure rate and service restoration time model (in Chinese). Proc CSEE, 2011, 31: 57–64 Srinivas N, Nishioka T, Sanford K, et al. Non-destructive condition assessment of energized cable systems. In: Power Engineering Society General Meeting, Montreal. Que: IEEE PES, 2006 Reliability Test System Task Force. IEEE reliability test system. IEEE T Power Apparatus Syst, 1979, 1: 2047–2054
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Appendix Calculate “Medium and Large Commercial and Industrial Customers US 2008$ Customer Damage Functions by Season and Time of Day” (Figures 3–5 in [14]) with “two-part model” and the method in Section 3, respectively. The calculations are shown in Figure A1. Sixteen curves, corresponding to 16 vectors (m, n, r ) I , are divided into four groups for detailed consideration. Solid lines represent reproductions of “two-part model” (similar to the description to Figure 1); dotted lines represent the results of the method in Section 3; discrete markers represent announced predicted results from [14]. Regarding the calculations, we can conclude that the fitting effects by the method in Section 3 are very good and the reproductions are slightly smaller than the announced predicted results. Taking the customer of LP8 on feeder F2 of RBTS-Bus2 as an example, the error resulting from the assumption that “influence coefficients of interruption occurrence time identified by integrated type j 10 are suitable to any other industry type j 7 {1, 2, , 9} ” is analyzed. CIC calculations, corresponding to 16 vectors (m, n, r ) I , are shown in Figure A2. Solid lines are the results of “two-part model”, and dotted lines are the results of the method given in Section 3. We find that the error is small and the solid lines are slightly below the dotted lines. It precisely offsets a part of the error shown in Figure A1.
Figure A1 The contract of CIC of MLCIC. (a) when interruption occurred in the morning; (b) when interruption occurred in the afternoon; (c) when interruption occurred in the evening; (d) when interruption occurred at night.
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Figure A2 The contract of CIC of LP8. (a) when interruption occurred in the morning; (b) when interruption occurred in the afternoon; (c) when interruption occurred in the evening; (d) when interruption occurred at night.