[Paper Review] Decentralized Control via Dynamic Stochastic Prices: The Independent System Operator Problem

Rahul Singh, P. R. Kumar+1 more|arXiv (Cornell University)|May 28, 2016

Economic theories and models43 references3 citations

TL;DR

This paper proposes a decentralized dynamic stochastic pricing mechanism for Independent System Operators (ISOs) to maximize social welfare in power systems with uncertain renewable generation and demand. By iteratively exchanging bid and price signals, agents—without knowing each other’s models—achieve optimal system-wide outcomes equivalent to centralized control, yielding 53.5% cost savings in simulations under LQG assumptions and enabling optimal stochastic locational marginal pricing.

ABSTRACT

A smart grid connects wind or solar or storage farms, fossil fuel plants, industrialor commercial loads, or load serving entities, modeled as stochastic dynamical systems. In each time period, they consume or supply electrical energy, with the constraint that total generation equals consumption. Each agent's utility is either the benefit accrued from consumption, or negative of generation cost. The Independent System Operator has to maximize their sum, the social welfare, without agents revealing their dynamic models or utilities. It has to announce prices after interacting with agents via bids. If agents observe and know the laws of uncertainties affecting other agents, then there is an iterative price and bid interaction that leads to the maximum social welfare attainable if agents pooled their information. In the important case where agents are LQG systems not even knowing of the existence of other agents, the bid and price iteration is dramatically simple, exchanging time vectors of future prices and consumptions or generations at each time step. State dependent bidding is not needed. This solution of the decentralized stochastic control problem may be of economic importance in power systems, and of broader interest in general equilibrium theory of economics for stochastic dynamic agents.

Motivation & Objective

• To address the challenge of decentralized, dynamic, and stochastic coordination in power systems where agents (e.g., wind farms, loads) have private models and uncertain dynamics.
• To enable the Independent System Operator (ISO) to maximize social welfare without access to agents’ private information, including system states, utility functions, or dynamic models.
• To design a scalable, information-efficient mechanism where agents respond to time-varying stochastic prices without requiring knowledge of other agents’ behaviors or uncertainties.
• To demonstrate that iterative bid-price interactions can achieve the same optimal social welfare as a centralized control policy with full information.
• To extend general equilibrium theory to dynamic, stochastic settings with asymmetric information, particularly in power systems with renewable energy integration.

Proposed method

• The ISO uses an iterative price-bid mechanism where it announces dynamic stochastic prices and agents respond with optimal generation or consumption based on their private models and utility functions.
• Agents solve their own stochastic optimal control problems using the current price signals, treating future prices as random variables with known distributions.
• The system leverages the LQG (Linear Quadratic Gaussian) structure, enabling tractable and closed-form solutions where only time-varying vectors of future prices and generation/consumption levels are exchanged.
• The ISO updates prices based on aggregated bids, using sequential information to refine predictions of future system states and externalities.
• The mechanism incorporates DC power flow equations to derive optimal stochastic dynamic locational marginal prices (LMPs).
• The process converges to the global maximum of social welfare under compactness and convexity assumptions, or exactly under LQG conditions.

Experimental results

Research questions

• RQ1 Can a decentralized mechanism with only price feedback achieve the same social welfare as a centralized optimal control policy when agents have private, stochastic, dynamic models?
• RQ2 How can an ISO set dynamic stochastic prices in real time when agents do not reveal their system states, utility functions, or uncertainty models?
• RQ3 What is the structure of optimal dynamic prices in a stochastic power system with renewable generation and adjustable loads?
• RQ4 Under what conditions does iterative bid-price interaction converge to the global welfare optimum despite asymmetric information and uncertainty?
• RQ5 Can the proposed mechanism yield significant cost savings in real-world power system scenarios with wind and thermal generation?

Key findings

• The iterative bid-price mechanism achieves the same optimal social welfare as a centralized control policy with full information, under LQG assumptions.
• In a two-period scenario with wind and thermal loads, the optimal scheme reduced total system costs by 53.5% compared to a baseline, with net costs of $1.75×10⁵ vs. $3.76×10⁵.
• The optimal scheme predicted energy shortages in advance, allowing smoother generator response and earlier demand response, as shown in power generation and price trajectories.
• Prices in the optimal scheme clearly signaled future shortages or surpluses, enabling agents to adjust behavior proactively and reduce disutility.
• The method yields optimal stochastic dynamic locational marginal prices (LMPs) when DC power flow constraints are incorporated.
• The mechanism is computationally tractable for LQG systems, requiring only exchange of time-vectors of future prices and generation/consumption levels at each step.