# (485b) Addressing the Placement of Sensors in IGCC Power Plants through An Efficient Stochastic Mixed Integer Nonlinear Programming Algorithm

- Conference: AIChE Annual Meeting
- Year: 2010
- Proceeding: 2010 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Wednesday, November 10, 2010 - 12:55pm-1:20pm

The optimal sensor placement problem involves determining the most effective locations to place a network of sensors across an array of measurable signals, in accordance with a set of specified objectives and constraints, such as cost, performance, and sensitivity to uncertainty variations. In advanced power systems, such as in Pulverized Coal (PC) and Integrated Gasification Combined Cycle (IGCC) power plants, on-line sensors can be used to measure process variables within the power generation process. However, placing a sensor to measure each and every one of these process variables can become expensive, or even be technically infeasible due to certain harsh environments. Through advanced modeling techniques, it is possible to closely simulate the behavior of the power system. Then, by introducing variability into the process inputs, it is possible to simulate the resulting variance of the process variables downstream in the system. This variability can be analyzed using techniques from estimation and information theory to determine which signals can be observed using a network of virtual sensors, and which should be physically measured using a set of on-line sensors. In an effort to reduce the purchase costs associated with the network of sensors, an optimal sensor placement problem for advanced power systems can be defined. The objective is to find the set of sensors, along with their locations, such that the power system meets specified controllability, environmental, and cost constraints. Within this application, a measure of observability is proposed using Fisher information. Fisher information is a statistical measure established the field of information theory, used to capture the amount of information contained in the set of observations, resulting from the set of observations obtained from all measured process variables. It can be viewed as a statistical measure of dynamic system order that quantifies the variability in a process variable as a function of changes in the mean value of the process variable. As a result of its local property, lower (higher) Fisher information values correspond to a lower (higher) level of observability in regards to estimating the true parameter value. The Fisher information quantity is then used within a stochastic programming problem to obtain a sensing solution comprised of a combination of on-line and virtual sensors, where the uncertainty lies within the system and measurement variability. The optimization problem is designed to address elements such as the purchase cost of on-line sensors, as well as the plant performance and environmental factors that result from estimating process variables through virtual sensing algorithms. The nonlinear, stochastic programming problem is formulated as a two-stage mixed integer nonlinear programming problem recourse problem, where the objective is to maximize the overall Fisher information, subject to the costs associated with placing the network of on-line sensors. A solution is obtained using the L-shaped method combined with the efficient nonlinear programming algorithm, Better Optimization algorithm for Nonlinear Uncertain Systems (BONUS). The key contribution of using Fisher information as a metric for observability is that it generalizes the Gaussian assumption on representing process and measurement variability for systems governed by nonlinear dynamics.