Negative Price in the Electricity Market: Pattern, Volatility and

Impact to Peak Load Demand

Kun Li (Corresponding)

Business School, Beijing Normal University,

Rear Main Building, 19 Xinjiekouwai Street, Beijing, China, 100875

Tel: +86-182-3033-2003

njulk@msn.com

Joseph D. Cursio

Stuart School of Business, Illinois Institute of Technology

565 W. Adams Street, Chicago, IL 60661, USA

jcursio@hawk.iit.edu

(The 5th International Association for Energy Economics Asian Conference

Proceeding Paper, 2016)

Abstract

This study explores how the performance of negative pricing affects the price volatility comparing

to peak load pricing. We analyze the 2014 real-time pricing data from the PJM electricity market

including 11,574 transmission lines. Through a Principal Component Analysis, we find that the

position and dispersion of peak load prices have the largest explanatory power to the variation of

data. By contrast, components dominated by negative pricing have much smaller explanatory

power. Our results implies that fulfilling the occasional over-demand is the resolution to reduce

price volatility.

Key Words: Price Volatility; Principal Component Analysis; PJM electricity market; Peak Load;

Negative Electricity Pricing

1. Introduction

Price volatility emerges frequently during the recent years along with the development of

wholesale electricity markets restructuring and sophisticated auction mechanisms. Numerous prior

studies suggest that extreme price swings are one of the distinct characteristics for electricity

markets (Engle and Patton, 2001; Hadsell et al, 2004; Knittel and Roberts, 2005; Xiao et al 2014;

Zareipour et al, 2007). There has been a growing interest in this issue with various focuses

discussed in the prior studies. A group of studies attribute the price swings to the prevalence of

peak load pricing (Hadsell and Shawky, 2006; Joskow and Wolfram, 2012; Spees and Lave, 2008).

Another group of studies consider negative pricing (Baradar and Hesamzadeh, 2014; Genoese et

al, 2010; Zhou et al, 2014) as the trigger of price volatility and consequently discuss potential

economic opportunities for electricity storage plants under the electricity (Barbour et al, 2014;

Sioshansi et al, 2009).

In this study, we study factors related to the price volatility from two kinds of electricity

prices: negative and peak load. As two inverse phenomena, both kinds of prices are often observed

in wholesale electricity markets as the constituents of extreme values that lead to price swings. We

compare which kind of prices accounts for more cross-sectional price volatility. We analyze the

2014 real-time pricing (RTP) data from the wholesale Pennsylvania, New Jersey and Maryland

(PJM) electricity market. It includes over 11,000 transmission lines, and their RTP records update

hourly (24 hours × 365 days = 8760 RTP records). We define the price volatility as the

standard deviation of RTPs by transmission line.

To compare the effects on price volatility from negative prices and peak load prices, we

construct a Principal Component Analysis (PCA) model instead of the traditional multivariate

regression. We find that PCA provides more useful outcomes. The principal component which

represents the position and dispersion of peak load prices has the largest explanatory power to the

variation of data. By contrast, components dominated by negative pricing have much smaller

explanatory power to the variation of data. Our results show that the performance and distribution

of peak load prices account for more price volatility than those of negative prices. As an

implication, fulfillment of over-demand issues should be the resolution to reduce price swings.

The remainder of this paper is organized as follows. Section 2 introduces background

information of our research methodology. Section 3 describes the data and covariates. Section 4

presents results of our PCA model. Section 5 concludes.

2. Research Methodology

PCA is one of the most widely used techniques in multivariate statistical inference. PCA is

popularly applied to studies relevant to ours. For example, Egloff, et al. (2010) suggest a two-

factor model in order to capture the long and short-term fluctuations of the volatility term structure

for the stock index. Besides volatility, many recent studies apply PCA to research questions in

electricity markets and relevant areas, such as Borovkova and Geman (2006), Chelmis et al.

(2015), Evans et al. (2008), Hong and Wu (2012), Kheirkhah, et al. (2013), Lam et al. (2008),

Ndiaye and Gabriel (2011), and Zhang et al. (2012). The large number of literatures indicates that

PCA is an efficient and reliable tool for studies about electricity markets.

First, PCA can identify a smaller number of principal components to which electively

summarize a previously large part of the variation of the data, and consequently reduce the

dimensionality of the multivariate statistical problems. For example, Baek et al. (2015) measure

risk in common stocks at the Korean market and find that only one risk component extracted from

PCA has sufficient accuracy for risk measures. PCA is applied to determine the number of factors

as discussed in studies including Bai (2003), Bai and Ng (2002), and Stock and Watson (1998,

2002).

Second, since PCA is able to reduce the dimensionality of multivariate analysis, it becomes a

preferable approach especially for studies with large data sizes, as stated by Ross (1976),

Chamberlain and Rothschild (1983). One important reason is that PCA is performed by the

estimation of the eigenvalues which is calculated by the sample covariance matrix. According to

Anderson (1958, 1963), eigenvalues are proved as consistent and asymptotically normal

estimators to represent the population. Another reason is that PCA is able to be employed under

weaker assumptions as stated by Chamberlain and Rothschild (1983). These properties are

beneficial for big data studies, e.g. Ait-Sahalia and Xiu (2015).

Third, PCA helps construct latent common structure of factors and discover the structural

meaning. This point is very important to our study. Principal components are constituted of

factors, but factors perform differently in each component. For those which perform with

significant coefficients, those factors have powerful explanations to the corresponding component.

By interpreting the difference of factor performance across components, we can infer the

summarized implication of each principal components, which is generally qualitative and

unobserved. As an example, Chakrabarty and Tyurin (2011) have explicit interpretations on the

principal components of execution and cancellation probabilities in the stock market. Besides,

PCA is widely employed for this purpose especially in studies about dynamic factor models, such

as in Forni et al (2000, 2004), and Forni and Lippi (2001), in which PCA helps disclose discrete-

time lagged values of the unobserved factors and their effects on the observed dependent

variables.

3. Data and Covariates

We use the dataset from the PJM electricity market. As a Regional Transmission

Organization (RTO), PJM coordinates the movement of power within its region. As a clearing

house, PJM matches bids and offers and thus gives the market-clearing price for each service area.

Areas served by PJM are divided by the transmission lines which are referred to as the pricing

nodes (Pnode). The market-clearing price is referred to as the locational marginal price (LMP) and

updated hourly. We use the whole Year 2014 hourly LMP data including 11,574 Pnodes. 92% of

the Pnodes have hourly LMPs over the whole 365 calendar days in 2014 and there are a total of

97,229,531 LMP records across all the Pnodes in our data. We filter out the non-positive LMPs as

the negative LMPs. Using a customized filtering rule across Pnodes, we distinguish the peak load

as the LMPs which are at least twice higher than the average values of LMPs at the same Pnode

during 2014. This distinguishing rule is more reasonable than simply setting up a threshold on the

whole population. It can figure out the relatively higher price periods and thus capture the large

price swing for each specific Pnode.

Table 1 presents the descriptive statistics of negative and peak load LMPs. There are over

560,000 negative records and over five million peak load records in our dataset. The mean of

negative LMP is -23.58 and the mean of the peak load is 216.38. The standard deviation of

negative LMPs is 53.42 while the standard deviation of peak load is 209.12. The ranges of both

groups are wide: negative LMPs spread between -2240.3 and 0 whereas the peak load LMPs

spread between 43.02 and 4643.74.

We sort these negative and peak load LMPs by their Pnode IDs. For each Pnode, we calculate

the descriptive statistics for both LMP groups, including mean, standard deviation, skewness,

kurtosis, minimum, and maximum. We calculate the percentage of occurrence for each LMP group

across Pnodes. For Pnode i, the percentage of negative LMPs is defined as

𝑁𝑒𝑔_𝑃𝑒𝑟𝑖 =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐿𝑀𝑃𝑠

𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐿𝑀𝑃𝑠 𝑓𝑜𝑟 𝑖 (1)

And the percentage of peak load LMPs is defined as

𝑃𝑒𝑎𝑘_𝑃𝑒𝑟𝑖 =𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 𝑜𝑓 𝑃𝑒𝑎𝑘 𝐿𝑜𝑎𝑑 𝐿𝑀𝑃𝑠

𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐿𝑀𝑃𝑠 𝑓𝑜𝑟 𝑖 (2)

We use 13 covariates listed in Table 2. We exclude the maximum of negative LMPs after

observing all the values are zero. We use them to measure the cross-sectional variation for our

PCA model in the next section.

4. Results

Table 3 shows the correlation matrix for the selected covariates from Section 3. We observe

many correlation values greater than 50 percent. Given this, we apply principal component

analysis to effect a dimension reduction. By definition, the principal components are constructed

as linear combinations of covariates with orthonormal loading coefficients. The first component,

PC1, is chosen to explain the largest proportion of variation in the covariates. The second

component PC2 explains the second largest proportion of the variation that is left unexplained.

And PC3 continues explaining the remaining, and so forth.

Table 4 presents the variation explained by the eigenvalues of PCA. PC1, the component that

has the largest eigenvalue 4.00, contributes 31% explanatory power to the variation of data. PC2

has the second largest eigenvalue (2.47) and explains 19% of the variation. The cumulative

explanatory contribution by PC1 and PC2 has reached 50% as shown in the cumulative column.

Including the first six components, the cumulative explanatory contribution by PC1 – PC6 already

reaches up to 92%. Therefore, PCA helps reduce the dimensionality.

We extract the first six components. They are constructed as linear combinations of

covariates so that they have orthonormal loading coefficients. Table 5 presents how these PCs

relate to our covariates and lists the coefficients of covariates for each PC in the columns. For

example, PC1 is related to our covariates by the following equation:

PC1 = -0.2112 Neg_Per + 0.1884 Neg_Sku - 0.077 Neg_Std + 0.1499 Neg_Min - 0.2055 Neg_Kur

+ 0.0167 Neg_Mean + 0.3565 Peak_Std + 0.1405 Peak_Max + 0.4723 Peak_Mean -0.3043

Peak_Sku + 0.4457 Peak_Min - 0.3011 Peak_Kur + 0.3118 Peak_Per (3)

As we discussed in Section 2.2, one advantage of PCA is that it helps discover the latent and

structural meaning constructed by covariates. We can summarize the implication of each PC,

which is generally qualitative and unobserved from direct regression by covariates. In Equation

(3), among the covariates, three of them have significantly larger coefficients: Peak_Mean

(0.4723), Peak_Min (0.4457) and Peak_Std (0.3565). These three covariates are the dominant

power to affect PC1. According to their concepts, they suggest an interpretation for PC1 as the

position and dispersion of peak load LMP records. The mean and the minimum control the

position of peak load LMPs, while the standard deviation quantifies the extent of dispersion.

We have found that as the foremost component, PC1 contributes 31% explanatory power to

the variation of data. As the dominant composition for PC1, all the three covariates above belong

to the peak load group. Therefore, we can infer that the variation of peak load LMPs accounts for

the population’s variation more than negative LMPs.

In PC2’s column at Table 5, we find that two covariates have significantly larger absolute

values of coefficients: Neg_Std (0.4092) and Neg_Min (-0.4901). Both covariates are different

from the dominant covariates for PC1, and they both are from the negative LMP group. Similar to

PC1, PC2 can be interpreted as the position and dispersion of negative LMPs. By contrast, PC2’s

explanatory power is 19% and much smaller than PC1’s.

For PC3, three covariates are dominant as observed in Table 5: Peak_Max (0.4639),

Peak_Sku (0.4504) and Peak_Kur (0.3969). They are not repeated as dominant in PC1 or PC2,

and all three are from the peak load side again. PC3 can be interpreted as the extent of

concentration of peak load LMP group. Similarly, PC4’s dominant covariates are also the

skewness and kurtosis of negative LMP group (Neg_Sku and Neg_Kur). Compared with PC2, the

explanatory powers of PC3 and PC4 become even weaker (16% and 13%). But PC3’s value is

greater than PC4’s, implying again that peak load LMPs still account for the variation more than

negative LMPs.

There is only one covariate that dominates in PC5 and PC6 respectively. In PC5, the only

covariate is Neg_Mean (0.9815), and in PC6 it is Neg_Per (0.7223). As shown in Table 4, PC5

and PC6 have only 8% and 5% explanatory power. They are supplementary variation affected by

negative LMPs.

In summary, through the result of PCA we select six components and interpret their

implication related to the covariates. We find that components highly related to dimensions of

peak load LMPs account for the variation of our data more than dimensions of negative LMPs.

5. Conclusion

As two frequently-observed phenomena and the constituents of extreme values, peak load

and negative prices have opposite economic meanings. Negative prices indicate over-supply while

peak load prices indicate over-demand. This study explores how the performances of negative

pricing and peak load pricing affect the price volatility. We define the standard deviation of RTPs

by transmission line as the price volatility from a cross-sectional perspective. We analyze the 2014

RTP data from the PJM electricity market including 11,574 transmission lines which update their

RTP records hourly. For both negative and peak load price groups, we calculate 13 covariates by

transmission lines. These covariates capture the distributions of peak load prices and negative

prices.

To compare the importance between negative prices and peak load prices price volatility, we

employ a PCA model. First, the principal component which represents the position and dispersion

of peak load prices has the largest explanatory power to the variation of data. By contrast,

components dominated by negative pricing has much smaller explanatory power to the variation

of data. Our results indicate that the performance and distribution of peak load prices account for

more price volatility than those of negative prices. As an implication, fulfillment of over-demand

issues should be the resolution to reduce price swings.

Table 1: Descriptive Statistics of Negative and Peak Load LMPs

variable Negative LMP Peak Load LMP

Number of

Occurrence 560,244 5,923,637

mean -23.58 216.38

Std. Dev. 53.42 209.12

skewness -11.04 4.48

kurtosis 249.01 29.88

min -2240.30 43.02

p5 -96.59 87.60

p25 -26.07 112.11

p50 -6.92 147.13

p75 -0.04 238.97

p95 0 523.28

max 0 4643.74

Table 2: Covariates of PCA

variable Negative

LMPs

Peak Load

LMPs

Percentage of Occurrence Neg_Per Peak_Per

mean Neg_Mean Peak_Mean

Std. Dev. Neg_Std Peak_Std

skewness Neg_Sku Peak_Sku

kurtosis Neg_Kur Peak_Kur

min Neg_Min Peak_Min

max Peak_Max

Table 3: Correlation Matrix of Covariates

Neg_Per Neg_Mean Neg_Std Neg_Sku Neg_Kur Neg_Min Peak_Per Peak_Mean Peak_Std Peak_Sku Peak_Kur Peak_Min

Neg_Mean 0.0192

Neg_Std 0.3076 -0.0276

Neg_Sku 0.0156 0.0407 -0.0159

Neg_Kur 0.2365 -0.0168 0.1295 -0.9141

Neg_Min -0.4926 0.0187 -0.8747 0.2556 -0.4600

Peak_Per -0.0426 -0.0229 0.2409 0.2018 -0.1388 -0.1816

Peak_Mean -0.2800 0.0343 -0.0215 0.1898 -0.1658 0.0817 0.6430

Peak_Std -0.2976 0.0469 -0.1110 0.0340 -0.0380 0.1304 0.3143 0.8084

Peak_Sku 0.1220 0.0114 0.0205 -0.1567 0.1754 -0.0975 -0.2824 -0.5327 -0.0961

Peak_Kur 0.1741 0.0104 0.0757 -0.1181 0.1599 -0.1477 -0.1852 -0.5209 -0.1559 0.9801

Peak_Min -0.2585 0.0466 -0.0260 0.2428 -0.1949 0.0828 0.7037 0.9307 0.6876 -0.4238 -0.3808

Peak_Max -0.2451 -0.0124 0.0743 -0.1104 0.0575 -0.0273 0.2525 0.3662 0.7217 0.3707 0.3087 0.2450

Table 4: Variations explained by the eigenvalues of PCA

Component Eigenvalue Difference Proportion Cumulative

PC1 4.00 1.53 31% 31%

PC2 2.47 0.34 19% 50%

PC3 2.13 0.49 16% 66%

PC4 1.64 0.63 13% 79%

PC5 1.01 0.31 8% 87%

PC6 0.70 0.10 5% 92%

PC7 0.61 0.31 5% 97%

PC8 0.30 0.23 2% 99%

PC9 0.07 0.04 1% 99%

PC10 0.03 0.01 0% 100%

PC11 0.02 0.01 0% 100%

PC12 0.01 0.01 0% 100%

PC13 0.01 . 0% 100%

Table 5: Covariate Coefficients of six PCs

Covariate PC1 PC2 PC3 PC4 PC5 PC6

Neg_Per -0.2112 0.1651 -0.3013 0.1981 0.134 0.7223

Neg_Sku 0.1884 -0.2851 -0.0762 0.6063 0.0022 0.0337

Neg_Std -0.077 0.4092 -0.3298 0.2938 -0.0558 -0.4791

Neg_Min 0.1499 -0.4901 0.3293 -0.1284 -0.0047 0.1688

Neg_Kur -0.2055 0.3717 -0.0165 -0.5186 0.0559 0.1814

Neg_Mean 0.0167 -0.0119 0.0236 0.0361 0.9815 -0.1471

Peak_Std 0.3565 0.2396 0.3076 -0.0672 0.05 0.0437

Peak_Max 0.1405 0.342 0.4639 0.0899 -0.0566 -0.166

Peak_Mean 0.4723 0.1727 -0.0075 -0.0598 0.0295 0.0975

Peak_Sku -0.3043 0.1498 0.4504 0.2584 0.0066 0.0973

Peak_Min 0.4457 0.156 -0.0095 0.024 0.0424 0.2128

Peak_Kur -0.3011 0.1651 0.3969 0.3095 0.0056 0.1562

Peak_Per 0.3118 0.2594 -0.1228 0.2018 -0.0631 0.2155

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