Dynamic optimization of boiler for minimizing energy consumption in the intentionally transient process operation: effect of different interval number
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Fakhrony Sholahudin Rohman
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Ashraf Azmi
Abstract
Certain manufacturing or industrial processes may involve variable conditions, and intentionally transient boiler operation allows optimal adaptation to these variations. This helps maintain efficiency and reduce energy consumption during different process phases. Transient operation is inherent during the start-up and intermittent phases in reaching the pressure required for boiler operation. Optimizing these transient states can reduce energy consumption. Dynamic optimization of boilers is crucial for several reasons, especially in industrial and power generation settings. Boilers are used to produce steam or hot water for various processes, and optimizing their performance can lead to increased efficiency, reduced energy consumption, and improved overall system reliability. The dynamic optimization problems were solved using the orthogonal collocation method. Three problem optimizations were considered in this study: minimize process time (P1), minimize energy consumption without optimized final time (P2), minimize energy consumption with optimized final time (P3). The control/decision variables applied were firing rate, Q, and water feed flowrate, q f. From the simulation results, the control trajectories of P3 were chosen to be the most effective control operation to achieve the minimum energy consumption for reaching target pressure, i.e., 10.2 MPa, with a reasonable intermittent unit time. In practice, the selection of the number of intervals is often determined through a combination of domain knowledge, computational resources, and the desired level of accuracy. Sensitivity analysis and testing with different interval sizes can help in understanding the impact of this parameter on the optimization results. A greater interval time will decrease energy consumption.
Funding source: Universiti Teknologi Malaysia
Award Identifier / Grant number: Q.J130000.3046.04M49
Funding source: Universiti Teknologi Malaysia
Award Identifier / Grant number: Q.J130000.21A2.07E17
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Research ethics: Not applicable.
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Author contributions: Fakhrony S Rohman contributes on conceptualization, methodology, data curation, formal analysis, writing-original draft, writing-review & editing; Sharifah Rafidah Wan Alwi contributes on conceptualization, writing-review & editing, supervision, funding acquisition; Siti Nor Azreen Ahmad Termizi contributes on writing-review & editing; Hong An Er contributes on formal analysis, writing-review & editing; Ashraf Azmi contributes on conceptualization, methodology, data curation.
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Competing interests: The authors declare no competing interests.
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Research funding: The authors greatly acknowledge the financial grants from Universiti Teknologi Malaysia Professional Development Research University Grant (UTM-PDRU) with Vote number Q.J130000.21A2.07E17 and UTM Matching Grant entitled MG1 – 11.1: Facilities Energy Minimisation using P-Graph and RENKEI control strategies with Vote number Q.J130000.3046.04M49.
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Data availability: Datasets used and/or analysed in this study are available upon reasonable request.
Figures of steam and water property.
Pseudocode of dynamic optimization using orthogonal collocation method.
# Define the dynamic system and the objective function.
function system_dynamics(t, x, u):
#Implement the system dynamics.
return dxdt.
function objective_function(x, u):
#Implement the objective function.
return objective.
#Define parameters and initial conditions.
N = number_of_collocation_points.
T = time_horizon.
x0 = initial_state.
xf = final_state.
initial_guess_control = u0.
initial_guess_state = x_guess.
# Choose collocation points (e.g., Legendre-Gauss-Lobatto points).
collocation_points = get_collocation_points(N).
# Initialize optimization variables.
# These include the state and control at each collocation point.
optimization_variables = initialize_variables(collocation_points, initial_guess_state, initial_guess_control).
#Define the constraints.
constraints = []
# Add boundary constraints.
constraints.append(initial_state_constraint(optimization_variables, x0)).
constraints.append(final_state_constraint(optimization_variables, xf)).
#Add collocation constraints.
for i = 0 to N+1:
t = collocation_points[i].
state = get_state(optimization_variables, t).
control = get_control(optimization_variables, t).
if i = < = N+1:
next_t = collocation_points[i + 1].
next_state = get_state(optimization_variables, next_t).
# Compute state derivative using system dynamics.
dxdt = system_dynamics(t, state, control).
# Approximate the state at the next collocation point.
h = next_t - t
collocation_constraint = next_state - (state + dxdt * h).
constraints.append(collocation_constraint).
# Define the objective function to be minimized.
objective = 0.
for i = 0 to N+1:
t = collocation_points[i]
state = get_state(optimization_variables, t)
control = get_control(optimization_variables, t)
objective + = objective_function(state, control)
# Solve the optimization problem.
solution = solve_optimization(optimization_variables, objective, constraints).
# Extract the optimal state and control trajectories.
optimal_state_trajectory = extract_state_trajectory(solution, collocation_points).
optimal_control_trajectory = extract_control_trajectory(solution, collocation_points).
# Output the results
return optimal_state_trajectory, optimal_control_trajectory.
# Auxiliary Functions
function get_collocation_points(N):
# Implement the method to get collocation points (e.g., Legendre-Gauss-Lobatto).
return points.
function initialize_variables(collocation_points, x_guess, u_guess):
# Initialize state and control variables at collocation points.
return variables
function get_state(variables, t):
#Extract the state at time t from optimization variables.
return state.
function get_control(variables, t):
#Extract the control at time t from optimization variables.
return control.
function initial_state_constraint(variables, x0):
# Constraint ensuring initial state matches x0
return constraint.
function final_state_constraint(variables, xf):
# Constraint ensuring final state matches xf.
return constraint
function solve_optimization(variables, objective, constraints):
# Implement optimization solver (e.g., IPOPT, SNOPT).
return solution.
function extract_state_trajectory(solution, collocation_points):
#Extract the state trajectory from the optimization solution.
return state_trajectory.
function extract_control_trajectory(solution, collocation_points):
#Extract the control trajectory from the optimization solution.
return control_trajectory.
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Artikel in diesem Heft
- Frontmatter
- Research Articles
- Energy cost prediction for chromium removal by nanofiltration membrane
- Forecasting gasification sustainability through enhanced K-nearest neighbour models for hydrogen and nitrogen amount
- Applying machine learning for biomass gasification prediction: enhancing efficiency and sustainability
- Enhancing prediction of elemental composition through machine learning decision tree models for biomass gasification optimization
- Nonlinear model predictive controller of hydrogenation of dimethyl oxalate for ethylene glycol production
- Dynamic optimization of boiler for minimizing energy consumption in the intentionally transient process operation: effect of different interval number
- Heat transfer efficiency in gas–solid fluidized beds with flat and corrugated walls
- Ant lion based optimization for performance improvement of methanol production
- Boundary Element Method for Viscous Flow through Out-phase Slip-patterned Microchannel under the Influence of Inclined Magnetic Field
- Artificial neural network models for forecasting the extracted yield of essential oils from Curcuma longa L. by hydro-distillation
