Combined Heat and Power State Estimation Using Lagrangian Multipliers
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for estimating the state of combined heat and power systems do not adequately consider the dynamic characteristics of pipes and energy transmission delays, leading to inaccuracies in multi-energy flow management and real-time scheduling.
Innovation Solution
A two-stage state estimation method using Lagrangian multipliers to establish objective functions and constraints, accounting for power flow, hydraulic, and thermal steady-state constraints, and dynamic characteristics of pipes, with energy transmission delay calculations to update the Lagrange function for dynamic-state estimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If steady-state constraints are used for state estimation, then computational simplicity is improved, but estimation accuracy deteriorates due to ignoring dynamic characteristics of pipes
Solution Approach 1:
The patent transitions from static steady-state constraints to dynamic constraints that incorporate the dynamic characteristics of pipes. The dynamic constraint equations include time-dependent terms and energy transmission delays, allowing the state estimation to adapt to changing system conditions while maintaining computational tractability through the structured formulation.
Solution Approach 2:
The patent pre-calculates energy transmission delays for each pipe based on steady-state conditions, then uses these pre-computed delay values in the dynamic constraint equations. This preliminary calculation of delay parameters enables the dynamic model to run efficiently without requiring real-time solution of complex transient equations.
2Measurement precision
If dynamic characteristics of pipes are incorporated, then estimation accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent divides the heating system into individual pipe segments, each with its own dynamic constraint equation and energy transmission delay. By segmenting the system, the complex dynamic behavior is broken down into manageable local models that can be combined systematically, reducing the overall computational burden compared to a monolithic dynamic model.
Solution Approach 2:
The patent introduces energy transmission delay as an intermediary parameter that mediates between the physical dynamic characteristics of pipes and the state estimation algorithm. These delay parameters act as intermediaries that capture the essential dynamic behavior without requiring full transient heat transfer simulations, thus simplifying the computational complexity.
3Measurement precision
If energy transmission delay is calculated, then tracking accuracy of state variables is improved, but measurement and calculation difficulty increases
Solution Approach 1:
The patent makes the state estimation algorithm self-sufficient by calculating energy transmission delays directly from available system data (pipe lengths, fluid velocities, specific heats) without requiring external measurements or complex experimental calibration. The algorithm uses its own estimated state variables to compute the delay parameters, creating a self-contained estimation system.
Solution Approach 2:
The patent transforms the difficult-to-measure dynamic characteristics of pipes into easily computable parameter changes. By expressing energy transmission delays in terms of fundamental parameters (pipe length L, fluid velocity v, specific heat cp, density ρ) that can be obtained from standard system data, the patent converts a complex measurement problem into a simple parameter substitution and calculation task.
Data Source
AI summary
A method for estimating a state of a combined heat and power system is provided. The method include: establishing an objective function; establishing constraints under a steady-state operating stage; converting the objective function and the constraints by utilizing a Lagrangian multiplier to obtain a Lagrange function; obtaining a steady-state estimation result of the combined heat and power system based on the Lagrange function; calculating an energy transmission delay produced by each pipe; establishing a dynamic constraint of each pipe based on the steady-state estimation result and the energy transmission delay; converting the objective function, the constraints, and the dynamic constraint by utilizing the Lagrangian multiplier to update the Lagrange function; obtaining a dynamic-state estimation result of the combined heat and power system during a dynamic-state operating stage of the combined heat and power system based on the updated Lagrange function.