Gas and Electric (PG&E) 's price-based DR tariffs. 2. Demand Response ..... (4) G. Wikler et al, âPacific Gas & Electric Company 2007 Auto-DR Program: Task 13 ...
Improvement of Classification of Electricity Customers by Demand Response Nobuyuki Yamaguchi＊, Member, Hiroshi Asano, Senior Member (CRIEPI), Junqiao Han, Girish Ghatikar, Sila Kilicotte, Mary Ann Piette, Non-Member (Lawrence Berkeley National Laboratory) system. One of the most advanced measures is “Automated Demand Response (Auto-DR).” Demand Response Research Center at the Lawrence Berkeley National Laboratory (LBNL) has developed the Auto-DR and analyzed effectiveness of its deployment in PG&E’s service territory [3], [4]. Auto-DR does not involve human intervention and pre-programmed DR strategies are executed by energy management control systems in a building or facility through receipt of an external communications signal. LBNL has recently published “Open Auto-DR Communications Specification (OpenADR)” [5]. OpenADR specification is being donated to standards development organizations for formal standards. The National Institute of Standards and Technology, in proposal to U.S. Department of Energy, has considered it for Smart Grid standards. 2.2 Calculation of Demand Reduction Demand reduction is the difference between an actual load and a customer baseline load (CBL). The CBL Li,d,t is defined as follows:
1. Introduction According to the 2008 Federal Energy Regulatory Commission (FERC) Survey on Demand Response (DR) in the U.S. [1], the number of utilities and ISOs that offered DR programs has increased since 2006. These circumstances would provide informative experiences of DR deployment for utilities and independent systems operators which are considering the introduction of DR programs and expecting to conduct better ex ante evaluation of programs. For estimate of demand reduction by DR programs, load profiles of each customer have been recently available because of a spread of interval meters. Since the load profile represents each customer’s load characteristic, acceptable estimates of the demand reduction would be achieved by using the load profile. The purpose of this study is for ex ante evaluation of the demand reduction by DR programs to examine whether the demand reduction can be explained by regression models, which employ the actual load profile and outside air temperature (OAT). In cluster analysis, each load profile is classified according to its load shape. Then, the index of the cluster is used as one of the explanatory variables of the regression models. Another explanatory variable is load sensitivity to OAT. In order to verify the proposed method, we apply the regression model to demand reduction performed in 2008 summer by customers who participated in Critical Peak Pricing (CPP) program, one of Pacific Gas and Electric (PG&E) ’s price-based DR tariffs.
Li , d ,t = Li′, d , t + Δ i , d ............................................................ (1) Li′,d ,t = Ci′,t + Α i , t ⋅ Ti , d , t + ε i′, d , t .......................................... (2) Where, L’i,d,t: the CBL i at period t on event day d before a morning adjustment [6], C’i, t: a constant, Ai,t: a load sensitivity to OAT at period t, Ti,d,t: OAT, ε i′, d , t : an error term, and Δ i, d : a shift term for the morning adjustment. The morning adjustment is to mitigate a difference between actual demand and the CBL before the morning adjustment. The shift term is calculated from the data from 9am to noon as follows:
2. Demand Response Program 2.1 PG&E’s CPP Program In PG&E’s CPP program [2], customers sign up on a tariff where all electric usage during summer on-peak and partial-peak hours is discounted on days when no CPP events are called. Contrarily, on CPP event days, maximum of 12 times during the summer season, higher “critical peak” energy charges are imposed for all electric usage that occurs weekdays, excluding holidays, as follows: -Moderate Price Period (MPP): Noon to 3 p.m. customers are charged approximately three times the partial-peak energy rate shown on their otherwise applicable rate schedule. -High Price Period (HPP): 3 p.m. to 6 p.m. customers are charged approximately five times the on-peak energy rate shown on their otherwise applicable rate schedule. Commercial and industrial customers must have peak demand of 200 kW or greater and equipped with an interval meter provided free of charge by PG&E. There are several ways to control the demand on the customer’s side. The most primitive way is a manual control. The second semi-automated control involves a pre-programmed demand reduction strategy initiated by a person via centralized control
Δi,d =
∑ AL
i , d ,t t ∈9 am to12 noon
−
∑L
.................................... (3)
i , d ,t t ∈9 am to12 noon
Where, ALi,d,t represents the actual demand on CPP event day d. In order to estimate Ai,t and C’i, t in (2), we used 10 previous business days’ data of event day d. We use OAT T i,d,t which is measured at the nearest weather station chose from 15 weather stations of National Oceanic and Atmospheric Administration. The demand reduction rate Ri,d,xPP is defined as follows:
Ri , d , xPP =
1 1 ⋅ ⋅ ∑ (Li , d ,t − ALi , d , t ) ......................... (4) N xPP PLi t∈xPP
Where, xPP represents HPP or MPP. NxPP means the number of period t in the xPP. Table 1 illustrates the descriptive statistics of demand reduction rate of sample participants in the CPP program. The number of sample participants is 99 accounts which include 27 Auto-DR accounts. The load sensitivity to OAT α i in table 1 is the mean value of Ai,t and defined as follows:
1
4. Numerical Results
Table 1. Descriptive Statistics Maximum Demand (kW) Num. of Obs. Mean Max. Min. Variance
99 960.61 10864.7 150.46 2164756
Demand Reduction Rate in MPP * 1182 0.024 0.714 -0.516 0.0115
Demand Reduction Rate in HPP * 1182 0.0278 0.875 -0.571 0.172
Load Sensitivity to OAT *
The examined model includes the load sensitivity to OAT and a dummy variable for Auto-DR enrollment (DAutoDR,i) and the index of the cluster (Dk,i) as explanatory variables.
1188 0.0057 0.025 -0.013 0.26E-4
Ri ,d , xPP = C + ∑k =1 β k ⋅ (1 − D AutoDR ,i )⋅ α i ⋅ Dk ,i 8
8 + ∑k =1 β k ⋅ D AutoDR ,i ⋅ α i ⋅ Dk ,i + ε 3 .................................... (9)
Where, C represents a constant. β * and γ ∗ express coefficients to be estimated. ε x means an error term.
*: dimensionless parameter
Table 2. Estimate results for MPP with Correlation distance function
β6
7.15
1.23
5.84**
0.00
β7
2.79
1.01
2.76**
0.01
β8
-2.05
3.94
-0.52
0.60
γ1
0.64
31.85
0.02
0.98
γ2
-271.14
695.93
-0.39
0.70
Table 2 shows estimate results of the examined model which is applied Correlation distance function for explaining demand reduction in MPP. Of 16 estimates, 10 coefficients are statistically significant in a confidential level of 95%. Similarly, the model employed Squared Euclidean distance function has 11 estimates which are statistically significant. These results imply that the explanatory variables in this model would be suit for explaining demand reduction. Then, adjusted R-squared of Correlation model is 0.156. This is slightly better than adjusted R-squared of Squared Euclidean model (0.151). Hence, Correlation would be better as distance function. In comparison of demand reduction of the enrolled customers, because statistically significant estimates for customers with Auto-DR ( β * ) tend to be larger than customers withoutAuto-DR ( γ ∗ ). Therefore, customers with Auto-DR
γ3
9.48
2.09
4.54**
0.00
generally achieved better than without Auto-DR.
γ4
26.56
17.54
1.51
0.13
γ5
15.83
4.70
3.37**
0.00
γ6
4.31
0.88
4.88**
0.00
γ7
8.23
1.13
7.25**
0.00
17.33 2.09 8.30** Adjusted R-squared: 0.156291
0.00
Parameter C
Estimate -0.01
Std. Error 0.00
t Statistic -1.17
P value 0.24
-7.91
5.12
-1.54
0.12
β1 β2
-9.51
9.43
-1.01
0.31
β3
1.92
0.97
1.97*
0.05
β4 β5
γ8
20.35
3.16
6.43**
0.00
11.30
2.04
5.53**
0.00
5. Conclusions This paper presents the regression models which employ indices derived from cluster analysis and load sensitivity to OAT as explanatory variables. The numerical results suggest that Combination of load sensitivity and cluster analysis improve the performance of the regression models. In term of distance function, Correlation performs better estimates than Squared Euclidean. Nevertheless, the goodness of fit of regression models, which is expressed by the coefficient of determination, adjusted R squared, is still not enough. Future study would include tests on other methods of clustering and other years’ experiments of DR events.
** and * represent statistically significant level of 99% and 95% respectively.
αi =
6× 4 1 1 ⋅ ⋅ ∑ Α i , t ............................................... (5) PLi 6 × 4 t∈PP
Where, PLi: the hourly maximum demand for typical summer season, PP: a set of observations from noon to 6pm (in HPP and MPP). It is 6 hours an event day and each hour has 4 observations because of a 15-minute interval meter.
References
3. Regression Models of Demand Reduction (1)
FERC, 2008 Assessment of Demand Response and Advanced Metering, Staff Report, 2008. (2) Critical Peak Pricing (CPP) Program, PG&E web site (3) M.A. Piette, D. Watson, N. Motegi, and S. Kiliccote, “Automated Critical Peak Pricing Field Tests: 2006 Pilot Program Description and Results”, California Energy Commission (CEC), PIER program, LBNL 62218, 2007. (4) G. Wikler et al, “Pacific Gas & Electric Company 2007 Auto-DR Program: Task 13 Deliverable: Auto-DR Assessment Study”, 2008. (5) M. A. Piette, G. Ghatikar, S. Kiliccote, E. Koch, D. Hennage, P. Palensky, and C. McParland,“Open Automated Demand Response Communications Specification”. CEC, PIER Program, CEC-500-2009-063, 2009. (6) K. Coughlin et al, “Estimating Demand Response Load Impacts: Evaluation of Baseline Load Models for Non-Residential Buildings in California”, CEC PIER, LBNL 63728, 2008. (7) S. Valero et al, “Methods for Customer and Demand Response Policies Selection in New Electricity Markets”, IET Gener. Trans. Distrib., Vol. 1, No. 1, Jan., 2007. (8) G. Chicco et al, “Customer Characterization Options for Improving the Tariff Offer”, IEEE Trans. on Power Systems, Vol. 18, No. 1, Feb., 2003. (9) G. Chicco et al, “Load Pattern-Based Classification of Electric Customers”, IEEE Trans. on Power Systems, Vol. 19, No. 2, May., 2004. (10) F. van der Heihden et al, Classification, Parameter Estimation and State Estimation, UK: Wiley, 2004, p232.
The proposed method includes two steps. First, explanatory variables are derived from load profiles. We use CBL before the morning adjustment L’i,d,t as the load profiles. The CBLs are categorized by cluster analysis. The load sensitivity to OAT is also applied as explanatory variable. The next step is to fit the regression models (section 4). Cluster analysis which is applied in the first step has been recently studied [7-9]. In this study, k-means clustering [10], which is not hierarchical, instead partitions the data set into K number of categories or clusters designated beforehand, are applied. In this paper, the number of cluster is eight (K=8). Distance function in k-means clustering should be chosen in accordance with problems. In this study, we examine Squared Euclidean distance and Correlation. The former is a popular distance function. The later is expected to reflect the coincidence of each customer’s load pattern on this clustering.
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