Large fluctuations in locational marginal prices

This paper investigates large fluctuations of locational marginal prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form P ( LMP ∉ ∏ i = 1 n [ α i − , α i + ] ) , where LMP is the vector of LMPs at the n power grid nodes, and α − , α + ∈ R n are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply–demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modelling uncontrollable renewable generation. We use techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations, and are validated numerically on the IEEE 14-bus test case. This article is part of the theme issue ‘The mathematics of energy systems’.

Partitioning Power Grid for the Design of the Zonal Energy Market while Preserving Control Area Constraints

The use of a zonal structure for energy markets across the globe is expanding; however the debate on how to effectively partition the grid into bidding zones is still open for discussion. One of the factors that needs to be addressed in the process of bidding zones’ delimitation is the transmission system operators control areas. Merging parts of different control areas into one bidding zone can lead to multiple problems, ranging from political, through grid security concerns, to reserve control issues. To address it, this paper presents a novel grid partitioning method aimed at bidding zones delimitation that is based on clustering the power grid using an extended version of the standard agglomerative clustering. The proposed solution adds additional clustering rules when constructing the dendrogram in order to take into account the control areas. The algorithm is applied to the data which represents the locational marginal prices obtained from optimal power flow analysis.

Cost implications of increased solar penetration and time-of-use rate interactions

Electricity-grid operators are facing new challenges in matching load and generation due to increased solar generation and peak-load growth. This paper demonstrates that time-of-use (TOU) rates are an effective method to address these challenges. TOU rates use price differences to incentivize conserving electricity during peak hours and encouraging use during off-peak hours. This strategy is being used across the USA, including in Arizona, California and Hawaii. This analysis used the production-cost model PLEXOS with an hourly resolution to explore how production costs, locational marginal prices and dispatch stacks (type of generation used to meet load) change due to changes in load shapes prompted by TOU rates and with additional solar generation. The modelling focused on implementing TOU rates at three different adoption (response) levels with and without additional solar generation in the Arizona balancing areas within a PLEXOS model. In most cases analysed, implementing TOU rates in Arizona reduced reserve shortages in the Western Interconnect and, in some cases, very substantially. This result is representative of the interactions that happen interconnection-wide, demonstrating the advantage of modelling the entire interconnection. Production costs were decreased by the additional solar generation and the load change from TOU rates, and high response levels reduced the production costs the most for high-solar-generation cases. Load change from TOU rates decreased locational marginal prices for a typical summer day but had inconsistent results on a high-load day. Additional solar generation decreased the usage of combustion turbines, combined cycles and coal-fired generation.