[Paper Review] Need-based Communication for Smart Grid: When to Inquire Power Price?

Husheng Li, Robert C. Qiu|arXiv (Cornell University)|Mar 10, 2010

Smart Grid Energy Management7 references3 citations

TL;DR

This paper proposes an optimal communication strategy for smart grid appliances to decide when to inquire power prices, balancing communication costs against penalties from using outdated prices. Using a Markov decision process (MDP) with probabilistic locational marginal pricing (LMP) forecasting, it formulates the inquiry timing as a dynamic programming problem, achieving up to 40% reduction in total cost compared to always-inquiring, while a simple myopic strategy closely approximates optimality.

ABSTRACT

In smart grid, a home appliance can adjust its power consumption level according to the realtime power price obtained from communication channels. Most studies on smart grid do not consider the cost of communications which cannot be ignored in many situations. Therefore, the total cost in smart grid should be jointly optimized with the communication cost. In this paper, a probabilistic mechanism of locational margin price (LMP) is applied and a model for the stochastic evolution of the underlying load which determines the power price is proposed. Based on this framework of power price, the problem of determining when to inquire the power price is formulated as a Markov decision process and the corresponding elements, namely the action space, system state and reward function, are defined. Dynamic programming is then applied to obtain the optimal strategy. A simpler myopic approach is proposed by comparing the cost of communications and the penalty incurred by using the old value of power price. Numerical results show the significant performance gain of the optimal strategy of price inquiry, as well as the near-optimality of the myopic approach.

Motivation & Objective

• To address the overlooked cost of communication in smart grid power price inquiry, which is typically ignored in existing studies.
• To model the stochastic evolution of power prices based on load dynamics using a Brownian motion-like process and LMP-load mapping.
• To formulate the decision of when to inquire power prices as a Markov decision process (MDP) to minimize the total cost of power consumption and communication.
• To develop and evaluate both an optimal dynamic programming-based strategy and a simpler myopic strategy for practical deployment.
• To quantify the performance gain of optimal inquiry policies across different grid buses with varying price volatility.

Proposed method

• Models the load dynamics as a stochastic process resembling Brownian motion, with the power price derived via a known LMP-load mapping curve.
• Defines a Markov decision process (MDP) with state space representing time since last inquiry, action space including 'inquire' or 'wait', and reward function based on utility of power consumption minus communication and penalty costs.
• Applies value iteration in dynamic programming to compute the optimal policy that minimizes the discounted sum of total costs.
• Proposes a myopic strategy that compares the immediate cost of communication with the expected penalty of using outdated price information.
• Uses a PJM five-bus system for numerical simulation with parameters including discount factor β=0.99, utility function U(x)=100logx, and adjustable communication cost c.
• Evaluates performance using cost ratios between optimal strategy and baseline strategies (always-inquire, no-inquiry, myopic).

Experimental results

Research questions

• RQ1 What is the optimal timing policy for an appliance to inquire power prices in a smart grid, considering both communication cost and penalty from outdated prices?
• RQ2 How does the performance of the optimal MDP-based strategy compare to always-inquiring or never-inquiring in terms of total cost reduction?
• RQ3 How close is a simple myopic strategy—based on immediate cost-benefit comparison—to the optimal solution?
• RQ4 How does price volatility at different buses affect the necessity and effectiveness of price inquiry?
• RQ5 How do varying communication costs influence the trade-off between inquiry frequency and total cost?

Key findings

• The optimal MDP-based strategy reduces total cost by 20% to 40% compared to always-inquiring, with the highest gains observed in buses with low price volatility (e.g., bus E).
• For bus D, where prices change most radically, the performance gain is smaller due to higher demand for frequent inquiries.
• Even in low-volatility scenarios (e.g., bus E), the optimal strategy achieves significant cost reduction, demonstrating the necessity of inquiry despite minimal price changes.
• The myopic strategy closely approximates the optimal policy, with cost ratios between optimal and myopic strategies consistently near 1.0 across different θ and communication costs.
• As communication cost increases, the performance gain of the optimal strategy relative to always-inquiring increases, while its gain over no-inquiry decreases, reflecting a shift in optimal inquiry frequency.
• The cost ratio between the optimal strategy and the always-inquiry strategy ranges from 0.6 to 0.8 across most buses, indicating substantial savings from optimized inquiry timing.