# A Latent-Factor System Model for Real-Time Electricity Prices in Texas
## 1 Introduction  
Information about energy prices is known in the day-ahead market, but actual real-time prices will deviate from the day-ahead prices for many \"hidden\" reasons; see [1]. For example, an error in load forecasts, wind forecasts, solar output forecasts, or the outage of a power plant or transmission line, and many other unforeseen events will cause real-time prices to deviate from day-ahead prices. These latent factors are difficult to measure and adjust in real-time, and yet their impact on prices can be significant. This reveals itself in the fact that the new real-time price is set at most every five minutes. A typical approach to explaining real-time prices is to start with the ex-post day-ahead price, and model deviations of the real-time price from the day-ahead price as a function of forecasting errors. While this approach may be helpful, it fails to consider the myriad of unobserved latent factors. Also, system-wide hidden factors are difficult to forecast in single-equation models that are used to explain real-time prices. One of the two main aims of this paper is to present a novel methodology that uses unobserved latent factors and exogenous variables to explain energy prices in Texas by modeling these prices as endogenous, multivariate time-series. This system-wide approach then leads to estimating the attendant merit-order effects of baseload generation (nuclear energy) as well as renewable energy generation (wind and solar). The hourly real-time market (RTM) energy price used in our analysis originates from the 5-min real-time energy prices based on the real-time operation of the Electric Reliability Council of Texas (ERCOT). ERCOT uses a security-constrained economic dispatch model (SCED) to simultaneously manage energy, system power balance, and network congestion,yielding 5-min locational marginal prices (LMPs) for each electrical bus within the market. The SCED process seeks to minimize offer-based costs, subject to power balance and network constraints. The zonal settlement price for a load-serving entity's real-time energy purchase is a load-weighted average of all 5-min LMPs in a load zone, which is converted to 15-min values or hourly values by ERCOT. Economic merit order effects attributable to renewable energy generation have been analyzed for many of the world's competitive wholesale markets using linear regression models. These include studies of the market in Spain [2], Germany [3; 4; 5; 6], Denmark [7; 8], Italy [9], Australia [10], Ireland [11], the U.S. mid-continent or MISO [12; 13], Texas [14; 15; 16], PJM [17], the Pacific Northwest [18; 19], and California [20]. Also, quantile regression approaches have been employed to study merit-order effects in Turkey [21] and Germany [22]. _Methodological Contribution_. We explore this topic using hourly real-time price data for the years 2015-2018 from the ERCOT market. Divided into eight zones--North, Houston, South, West, Austin Energy, CPS Energy, Lower Colorado River Authority, and Rayburn Electric Cooperative--ERCOT serves the electrical needs of the largest electricity-consuming state in the U.S.; it accounts for about 8% of the nation's total electricity generation, and is repeatedly cited as North America's most successful attempt to introduce competition in both generation and retail segments of the power industry (Distributed Energy Financial Group, 2015). In the interests of brevity, we report the findings for Houston, Austin, and West regions, since the results from the other regions are similar. To the best of our knowledge, this study is the first attempt at developing a latent-factor system-wide model for estimating the merit-order effects of baseload and renewable energy generation. While we use the Texas energy market to exemplify the methodology, the models developed here are readily applicable to other markets as well. Moreover, while we focus on real-time prices, the methodology readily lends itself to the study of day-ahead prices as well. Section 2 describes the data and variables used in the study.