[Paper Review] Price Volatility in Electricity Markets: A Stochastic Control Perspective.

Avinash Mohan, Shie Mannor+1 more|arXiv (Cornell University)|Feb 17, 2020

Smart Grid Energy Management6 references4 citations

TL;DR

This paper models electricity markets as discrete-time controlled stochastic processes to analyze the trade-off between social welfare and price volatility. It identifies a fundamental trade-off where reducing price volatility inherently sacrifices social welfare, introduces a 'volatility cliff' phenomenon under high renewable penetration, and defines a market-specific Capacity Region that quantifies achievable welfare at given volatility levels.

ABSTRACT

Spot prices in deregulated electricity markets in the United States and Europe have historically displayed high volatility, leading to loss of revenue in high electricity costs, weakening economic growth and lost business from long blackouts. With rapidly increasing supply of intermittent solar and wind-based power, conditions in the foreseeable future are only expected to deteriorate. Geographic price variations, while capable of being quite dramatic themselves, are a natural outcome of Locational Marginal Pricing (LMP) that takes finite transmission capacity and congestion into consideration, to produce localized electricity prices. Temporal price volatility (considerable fluctuation over periods as short as an hour in particular), however, is harder to explain. In an effort to unearth the cause of these price fluctuations, we propose to model the electricity market as a discrete time controlled stochastic process. While this is a stylized model, it facilitates the analysis of spot markets and helps exclude extraneous details that do not contribute significantly to the discussion. We show that in any such market, improving social welfare must necessarily be traded off with volatility in prices, i.e., it is impossible to reduce volatility in the price of electricity without sacrificing social welfare. We also show that, akin to communication systems, every market has a Capacity Region associated with it, that dictates and quantifies how much welfare is achievable at a given level of price volatility. In the context of renewable power sources, our investigation uncovers an intriguing phenomenon we term the volatility cliff, which suggests that with increasing penetration of intermittent renewable production, price volatility could increase to unacceptable levels, prompting the need for a complete restructuring of existing electricity markets.

Motivation & Objective

• To understand the root causes of high temporal price volatility in deregulated electricity markets.
• To investigate the inherent trade-off between social welfare and price volatility in spot markets.
• To develop a stochastic control framework that models electricity markets as a controlled dynamical system.
• To quantify the limits of achievable social welfare at different levels of price volatility using a Capacity Region concept.
• To examine the impact of increasing intermittent renewable generation on market volatility and system stability.

Proposed method

• Models the electricity market as a discrete-time controlled stochastic process to abstract away non-essential details.
• Applies stochastic control theory to analyze how market participants' decisions affect price dynamics.
• Introduces a Capacity Region to represent the set of achievable welfare-volatility pairs in a given market.
• Uses the framework to derive theoretical bounds on welfare and volatility, analogous to information theory capacity limits.
• Analyzes the effect of renewable intermittency on price volatility by simulating increasing penetration levels.
• Identifies a 'volatility cliff' phenomenon where small increases in renewable penetration lead to sudden, unacceptable spikes in price volatility.

Experimental results

Research questions

• RQ1 What causes high temporal price volatility in electricity markets despite stable fundamentals?
• RQ2 Is it possible to reduce price volatility without sacrificing social welfare in electricity markets?
• RQ3 How does the penetration level of intermittent renewable energy sources affect price volatility?
• RQ4 What is the theoretical limit of social welfare achievable at a given level of price volatility?
• RQ5 Does a critical threshold exist beyond which price volatility increases dramatically with minor increases in renewable penetration?

Key findings

• A fundamental trade-off exists between social welfare and price volatility: reducing volatility necessarily reduces social welfare.
• Every electricity market has a Capacity Region that defines the maximum achievable social welfare at any given level of price volatility.
• With increasing penetration of intermittent renewables, price volatility can increase abruptly, leading to a 'volatility cliff' phenomenon.
• The volatility cliff implies that small increases in renewable generation can trigger disproportionate and unacceptable volatility.
• The stochastic control framework provides a quantitative tool to assess market resilience and guide structural reforms in electricity markets.
• The results suggest that existing market designs may be inadequate under high renewable penetration and require fundamental restructuring.