Model predictive power tracking control method considering coupling characteristics among multi-stage compressors
By establishing a model predictive control method based on the coupling characteristics between multi-stage compressors, the problem that the coupling relationship in the multi-stage compressor system is not considered in the PID control method is solved, high-precision power tracking and flexible adjustment are achieved, and the control performance of the AA-CAES system is improved.
Patent Information
- Application Number
- CN202510657813.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-21
- Publication Date
- 2025-09-16
AI Technical Summary
In the existing technology, the coupling relationship between multi-stage compressors has not been fully considered, resulting in deviations in the PID control method when tracking power commands. In addition, an excessively large safety margin is used to ensure safety, which limits the adjustment range and flexibility of the AA-CAES system.
The model predictive control method is adopted to establish a dynamic model considering the coupling characteristics between multi-stage compressors. Through the principles of conservation of mass, momentum and angular momentum, combined with the ternary function form of the measured data fitting, an augmented nonlinear state space model is established, and linearization and discretization are performed to form a simplified power prediction model. The control strategy is optimized using the model predictive controller, and the constraints of state and control quantities are considered to achieve accurate power tracking.
The control flexibility and response speed of the AA-CAES system are significantly improved, high-precision power tracking performance is achieved under strict compliance with safe operation constraints, and the system's regulation capability is enhanced.
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Figure CN120653058A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a model prediction power tracking control method considering coupling characteristics between multi-stage compressors, and belongs to the field of new energy technology. Background Art
[0002] With the continued rise in renewable energy penetration and the integration of new loads, power systems are facing increasing volatility and randomness at both the source and load sides, placing higher demands on the system's flexible adjustment capabilities. Advanced adiabatic compressed air energy storage (AA-CAES) systems, with their large-scale energy storage capacity, adjustment flexibility, and rotational inertia, can effectively meet the flexibility requirements of new power systems, such as frequency regulation. However, in existing technologies, flexible adjustment of power plants is primarily focused on the energy release side, while the energy storage side is still considered an uncontrollable load connected to the grid. This is primarily due to the tight coupling between the compressor stages, which leads to complex interactions between the control variables. The widely used PID control method fails to account for these coupling effects, ignoring the interactions between control variables and the safe operation constraints during transitions. When a control variable reaches its safe operating limit and cannot be further adjusted, the decoupling control method cannot leverage the coupling relationships of other control variables to continue adjusting the system state, resulting in deviations in tracking power commands. Therefore, the limitations of PID control limit the flexible adjustment capabilities of AA-CAES systems, making them prone to breaching safety constraints during command tracking and operating condition changes. If an excessively large safety margin is used to ensure safety, the adjustment range of the system will be severely narrowed. Summary of the Invention
[0003] The present invention aims to provide a model-predictive power tracking control method that considers the coupling characteristics of multi-stage compressors. This method aims to improve the power tracking accuracy and control performance of multi-stage compressed energy storage systems. While ensuring safe operation, it effectively coordinates the various control variables on the energy storage side, thereby enhancing the flexible adjustment capabilities of the AA-CAES system. To this end, the present invention adopts the following technical solutions:
[0004] A model prediction power tracking control method for a multi-stage compressor system, characterized by comprising the following steps:
[0005] (1) Establishing a dynamic model of the multi-stage compressor system: The dynamic model is established based on the principles of conservation of mass, conservation of momentum, and conservation of angular momentum, and the dynamic model takes into account the coupling effect of each stage of the compressor and the pressure drop of the heat exchanger between each stage of the compressor; wherein the dynamic model is further parameterized by using the pressure ratio and isentropic efficiency in the form of a ternary function related to the working fluid flow rate, speed, and pressure obtained by fitting based on measured data; and the conversion process of the compressor shaft power to the motor power is modeled as a first-order inertia link;
[0006] (2) establishing a simplified power prediction model for model predictive control: based on the ideal gas assumption and the continuity principle, calculating the mass flow rate in the gas outlet pipeline of the multi-stage compressor system, and establishing an augmented nonlinear state space model of the multi-stage compressor system, wherein the augmentation is achieved by adding the electric power of the compressor drive motors of each stage as auxiliary state variables to the state variables of the dynamic model; and linearizing the augmented nonlinear state space model at a preset operating point using a first-order Taylor expansion and discretizing it using a bilinear transformation method to form the simplified power prediction model;
[0007] (3) Executing model predictive control: adopting the model predictive control (MPC) method, utilizing the simplified power prediction model, and optimizing the control strategy in the power tracking process by solving a constrained quadratic programming problem in each control cycle. The optimization process takes into account the preset state quantity constraints and control quantity constraints to achieve accurate tracking of the output power of the multi-stage compressor system to the target power instruction.
[0008] Furthermore, the dynamic model established for each stage of the compressor in step (1) is a third-order dynamic model that at least describes the rate of change of the gas pressure in the compressor of that stage, the rate of change of the mass flow rate through the compressor of that stage, and the rate of change of the rotor speed of the compressor of that stage.
[0009] Furthermore, the ternary function of pressure ratio and isentropic efficiency in step (1) is obtained by fitting a semi-empirical formula in combination with measured data, and is used to calculate the pressure ratio and isentropic efficiency under the current working conditions in real time in the dynamic model.
[0010] Furthermore, the nonlinear parts included in the augmented nonlinear state space model established in step (2) are specifically: a function for characterizing the impeller pressure, a function for characterizing the compressor torque, a function for characterizing the outlet pipe mass flow rate, and a function for characterizing the electric power of the drive motor.
[0011] Furthermore, the state quantity constraints considered in step (3) include at least one of the following for each stage compressor in the multi-stage compressor system: power constraint, mass flow rate constraint, outlet pressure constraint, speed constraint, and outlet temperature constraint.
[0012] Furthermore, the control quantity constraints considered in step (3) include adjustment limits on the driving torque of each compressor stage in the multi-stage compressor system and adjustment limits on the inlet guide vane angle.
[0013] Furthermore, the objective function of the constrained quadratic programming problem solved in step (3) aims to minimize the deviation between the predicted trajectory of the output power of the multi-stage compressor system and the target power command.
[0014] The core technical solution of this invention lies in establishing a third-order dynamic model for a multi-stage compressor system based on the principles of conservation of mass, momentum, and angular momentum, taking into account the coupling effects between compressor stages and the pressure drop across the interstage heat exchanger. This model is parameterized using the pressure ratio and isentropic efficiency as three-variable functions related to working fluid flow rate, speed, and pressure, fitted based on measured data. The conversion process from compressor shaft power to motor power is modeled as a first-order inertial link.
[0015] On this basis, an augmented nonlinear state-space model of the system is established by using the electric power of each compressor drive motor as an auxiliary state variable. This augmented model is then locally linearized at a preset operating point (e.g., the equilibrium operating point) using a first-order Taylor expansion and converted into a standard linear state-space deviation form. The linearized model is then discretized using methods such as bilinear transformation, ultimately forming a simplified power prediction model for model predictive control (MPC). Its output is a signal representing the total system output power (e.g., the total electric power consumed by each drive motor), which is used to track power commands.
[0016] In terms of control strategy, the present invention employs a model predictive control (MPC) approach. This approach aims to accurately track system output power, using the drive torque and inlet guide vane (IGV) angles of each compressor stage as control variables. During each control cycle, the MPC controller utilizes the simplified power prediction model described above and, while fully considering system state and control variable constraints (i.e., safe operation constraints), solves a constrained quadratic programming (CQP) problem to obtain the optimal control sequence.
[0017] By accurately modeling and applying an MPC strategy that considers coupling characteristics, this invention effectively leverages the coupling relationship between compressor stages, significantly improving the system's control flexibility and response speed. Compared to traditional multi-loop PID decoupling control strategies, this control strategy achieves higher-precision power tracking while strictly adhering to safe operating constraints. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] Figure 1 This is the MPC control framework diagram of the AA-CAES system.
[0019] Figure 2 This is a comparison chart of the MPC and PID power tracking control effects. DETAILED DESCRIPTION
[0020] Referring to the accompanying drawings, the present invention provides a model predictive power tracking control method considering the coupling characteristics between multi-stage compressors, comprising the following steps:
[0021] (1) Establishing a fine state space dynamic model for the energy storage side
[0022] First, a mathematical model of the multi-stage centrifugal compressor system is established based on the principles of conservation of mass, momentum, and angular momentum. The mass conservation equation is used to describe the relationship between the rate of change of the gas pressure p in the compressor volume chamber and the mass flow rate m in and out of the volume chamber:
[0023]
[0024] Where R is the gas constant, T is the gas temperature, V is the volume of the volume chamber, m in and m out are the mass flow rates entering and out of the volume chamber, respectively.
[0025] The momentum conservation equation (pipeline part) describes the rate of change of mass flow entering the compressor and the compressor impeller outlet pressure p out and the relationship between the volume chamber pressure p:
[0026]
[0027] Where ρ is the gas density, A is the cross-sectional area of the pipe, and u is the gas flow rate.
[0028] The angular momentum conservation equation is used to describe the change rate of the compressor speed and the driving torque T d and impeller braking torque T b The relationship between:
[0029]
[0030] Where J is the moment of inertia and ω is the compressor speed.
[0031] Secondly, in order to more accurately describe the nonlinear characteristics of the compressor, a semi-empirical formula combined with the measured data was used to fit the ternary function of the pressure ratio and isentropic efficiency. The conversion process of the compressor shaft power to the drive motor electric power was further simplified to a first-order inertia link. Through the above process, a complete compressor dynamic model was established.
[0032] Furthermore, based on the continuity principle of mass flow rate, pressure and temperature, assuming that the gas is an ideal gas, the mass flow rate m in the pipeline is calculated. pipe :
[0033]
[0034] Where, Indicates the mass flow rate in the pipe. A pipe Indicates the cross-sectional area of the pipe. pipe,in and p pipe,out Indicates the pressure at the inlet and outlet of the pipe. C f,pipe Indicates the flow coefficient, R g is the ideal gas constant, T pipe is the temperature of the gas in the pipeline.
[0035] And considering the pressure drop of the heat exchanger between each stage of compressor, further by establishing the pressure change rate of the volume chamber of each stage of compressor Mass flow rate change rate and speed change rate Construct a nonlinear state space model of the aerodynamic-maneuvering part of the multi-stage compression coupling system, and set the state variables x=[p1,m1,ω1,p2,m2,ω2,…,p n ,m n ,ω n ] T , control variable u=[T d1 ,α1,T d2 ,α2,…,T dn ,α n ] T , where T di is the driving torque of the i-th stage compressor, α i is the angle of the inlet guide vane of the i-th stage, the nonlinear state space model can be expressed as: Where f(x,u) is a nonlinear function vector that contains the above equations of conservation of mass, conservation of momentum, conservation of angular momentum, etc., and its specific form is:
[0036]
[0037] Finally, the model is simplified by linearizing and discretizing the differential equations in vector form.
[0038] (2) Model predictive power tracking control considering safe operation constraints
[0039] First, the electric power P of each level of driving motor elec1 ,P elec2 ,…,P elecn As the augmented state variable, let the augmented state variable x a =[x T ,P elec1 ,P elec2 ,…,P elecn ] T , then the augmented state space model is where f a (x a ,u) is a function vector containing the original state space model and the electric power related dynamic equations.
[0040] The augmented model consists of four main nonlinear parts: impeller pressure function, torque function, outlet pipe mass flow function and the electric power of the drive motor. Secondly, based on the linearization principle, the nonlinear system is linearized using the first-order Taylor expansion at the rated operating point. The linearized system is:
[0041]
[0042] in, They are the state matrix and input matrix respectively, and f a (x a ,u) is obtained by taking the partial derivative at the rated operating point.
[0043] Since the state variables of the system remain constant under rated operating conditions, that is, the rated operating point is also the equilibrium point of the system, the derivative of each state variable is 0. In order to transform the linearized affine system into a linearized system, the deviation of the state variables and the control quantity from the equilibrium point is defined, and the augmented state space model is further approximately linearized and radially transformed into a standard linear state space deviation form. The model output is the total electric power consumed by each level of the drive motor to track the power tracking instruction. Finally, the model is discretized using bilinear changes. The discretized state space model is
[0044] x a (k+1)=Φx a (k)+Γu(k),(1b)
[0045] in, I is the unit matrix. Based on the simplified power prediction model above, the output of the compressor at the next moment is predicted, and the error between the power and the reference power is calculated and used as the objective function:
[0046]
[0047] Where N is the prediction time domain, and the control target is to minimize the deviation between the system's power change trajectory and the target power command. In the process of energy storage side power tracking, the system's state quantity constraints and control quantity constraints are mainly considered. Among them, the former includes the power constraints P of each level of compressor min ≤P i ≤P max , mass flow rate constraint m min ≤m i ≤m max , outlet pressure constraint p out,min ≤p out,i ≤p out,max , speed constraint ω min ≤ω i ≤ω max and outlet temperature constraint T out,min ≤T out,i ≤T out,max , the latter includes the driving torque T of each stage compressor d,min ≤T d,i ≤T d,max and the adjustment limit of the inlet guide vane angle α min ≤α i ≤α max .
[0048] Furthermore, the obtained control variable is used for prediction and calculation in the next time step.
[0049] Finally, the designed MPC controller is used to perform closed-loop simulation verification on a fine dynamic mathematical model, and the MPC controller parameters are continuously adjusted based on the test results until the expected control effect is achieved.
[0050] The effects of two different closed-loop controls, MPC and multi-loop PID, are compared. The two represent the control ideas of taking into account and ignoring the coupling relationship between compressors at each stage, respectively.
[0051] Depend on Figure 2As can be seen, during power tracking, the performance of PID control under tight constraints in Scenario 1 is far inferior to that under loose constraints in Scenario 2. Under loose constraints, PID control allows the system to quickly reach a new steady-state within 5 seconds and subsequently tracks both falling and rising power signals without steady-state error. However, under tight constraints, which are closer to actual engineering applications, PID tracking of falling power signals exhibits significant oscillation and, due to the limited controller adjustment range, is unable to track rising power signals, resulting in significant deviation. In contrast, MPC control achieves similar control performance in both scenarios. Under loose constraints, the system under MPC control takes 50 seconds to reach a new steady-state, slower than PID control in this case. However, even after reaching steady-state, it can still track the power command without steady-state error. Under tight constraints, MPC control is far superior to PID, tracking both rising and falling commands without steady-state error.
[0052] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.
Claims
1. A model predictive power tracking control method for a multi-stage compressor system, characterized in that: The following steps are involved: (1) Establishing a dynamic model of the multi-stage compressor system: The dynamic model is established based on the principles of conservation of mass, conservation of momentum, and conservation of angular momentum, and the dynamic model takes into account the coupling effect of each stage of the compressor and the pressure drop of the heat exchanger between each stage of the compressor; wherein the dynamic model is further parameterized by using the pressure ratio and isentropic efficiency in the form of a ternary function related to the working fluid flow rate, speed, and pressure obtained by fitting based on measured data; and the conversion process of the compressor shaft power to the motor power is modeled as a first-order inertia link; (2) establishing a simplified power prediction model for model predictive control: based on the ideal gas assumption and the continuity principle, calculating the mass flow rate in the gas outlet pipeline of the multi-stage compressor system, and establishing an augmented nonlinear state space model of the multi-stage compressor system, wherein the augmentation is achieved by adding the electric power of the compressor drive motors of each stage as auxiliary state variables to the state variables of the dynamic model; and linearizing the augmented nonlinear state space model at a preset operating point using a first-order Taylor expansion and discretizing it using a bilinear transformation method to form the simplified power prediction model; (3) Executing model predictive control: adopting the model predictive control (MPC) method, utilizing the simplified power prediction model, and optimizing the control strategy in the power tracking process by solving a constrained quadratic programming problem in each control cycle. The optimization process takes into account the preset state quantity constraints and control quantity constraints to achieve accurate tracking of the output power of the multi-stage compressor system to the target power instruction.
2. The method according to claim 1, characterized in that The dynamic model established for each stage of the compressor in step (1) is a third-order dynamic model that at least describes the rate of change of the gas pressure in the compressor of that stage, the rate of change of the mass flow rate through the compressor of that stage, and the rate of change of the rotor speed of the compressor of that stage.
3. The method according to claim 1, characterized in that The ternary function of pressure ratio and isentropic efficiency in step (1) is obtained by fitting a semi-empirical formula in combination with measured data, and is used to calculate the pressure ratio and isentropic efficiency under the current working conditions in real time in the dynamic model.
4. The method according to claim 1, wherein The nonlinear parts included in the augmented nonlinear state space model established in step (2) are specifically: a function for characterizing the impeller pressure, a function for characterizing the compressor torque, a function for characterizing the outlet pipe mass flow rate, and a function for characterizing the electric power of the drive motor.
5. The method according to claim 1, wherein The state quantity constraints considered in step (3) include at least one of the following for each stage compressor in the multi-stage compressor system: power constraint, mass flow rate constraint, outlet pressure constraint, speed constraint, and outlet temperature constraint.
6. The method according to claim 1, wherein The control variable constraints considered in step (3) include adjustment limits on the driving torque of each compressor stage in the multi-stage compressor system and adjustment limits on the inlet guide vane angle.
7. The method according to claim 1, characterized in that The objective function of the constrained quadratic programming problem solved in step (3) is to minimize the deviation between the predicted trajectory of the output power of the multi-stage compressor system and the target power command.