CN114069599A - Polymerization temperature control load improvement model prediction control under preset performance condition - Google Patents

Polymerization temperature control load improvement model prediction control under preset performance condition Download PDF

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CN114069599A
CN114069599A CN202010754960.2A CN202010754960A CN114069599A CN 114069599 A CN114069599 A CN 114069599A CN 202010754960 A CN202010754960 A CN 202010754960A CN 114069599 A CN114069599 A CN 114069599A
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余洋
权丽
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North China Electric Power University
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Abstract

The method for providing the load tracking auxiliary service by using the aggregated temperature control load on the demand side to stabilize the power fluctuation of the new energy is an economic and effective method. The invention discloses an improved model predictive control strategy with a preset performance based on aggregation temperature control load balancing new energy power fluctuation. Firstly, expanding an original temperature control load bilinear polymerization model through a second-order equivalent thermodynamic parameter model to obtain an improved temperature control load bilinear polymerization model so as to optimize the influence of the accumulated error of the original bilinear polymerization model; then, in order to ensure the specified performance of the output tracking error, an error transformation method is utilized, a preset performance controller is designed for the improved temperature control load bilinear polymerization model based on model prediction control of a Lyapunov function, and the stability of the control strategy is proved; finally, simulation results show that the improved temperature control load bilinear model has higher precision, the proposed control method has high convergence rate, and the tracking error can be controlled within the limit of the prediction performance function.

Description

Polymerization temperature control load improvement model prediction control under preset performance condition
Technical Field
The invention belongs to the field of power grid auxiliary service and demand response control, and particularly relates to an improved model predictive control strategy with preset performance based on aggregated temperature control load balancing new energy power fluctuation.
Background
The large-scale grid connection of the intermittent new energy sources brings challenges to the maintenance of power balance between a power source and a load of a power system. Usually, a controllable power supply such as thermal power supplies provides auxiliary services, but on one hand, the operation efficiency of the system is reduced, and on the other hand, the operation cost is increased due to deep peak shaving of the thermal power unit. Previous researches show that Thermal Controlled Loads (TCLs) of demand side resources such as air conditioners, electric water heaters and the like have large regulation potential after a large amount of polymerization. In addition, the Aggregation Thermal Controlled Load (ATCL) has the advantages of large energy storage capacity, quick response and the like, and becomes an ideal choice for providing auxiliary service for the power grid on the demand side.
The establishment of an accurate and practical temperature control load aggregation model is the basis for researching the participation of the temperature control load in the regulation and control of the power system. The current temperature control load aggregation model for control mainly comprises a state space model, a state sequence model, a Fokker-Planck equation model, a bilinear model and the like. The bilinear model which adopts the finite difference method to disperse the temperature in the finite range is a method which has higher precision and is easy to combine with the dispatching of the power system. The output power is adjusted by changing the temperature set point. Most of the temperature-controlled load bilinear polymerization models in the prior art are based on a first-order Equivalent Thermal Parameter (ETP) model to simulate the thermodynamic process, and the material temperature is ignored. Obviously, due to the coupled thermodynamic characteristics of the material temperature and the indoor temperature, the first-order equivalent thermodynamic parameter model is not accurate enough in practical application. Therefore, it is necessary to introduce the material temperature to obtain an aggregation model which accurately reflects the transient and steady-state response of the cluster temperature control load.
At present, many documents research control methods based on temperature-controlled load polymerization models. Such as back-thrust control, sliding mode control, Model Predictive Control (MPC), and the like. MPC is widely used due to its robustness and control accuracy. However, the conventional MPC is optimized repeatedly each time sampling, which requires a large amount of calculation, and causes a certain execution delay, which may reduce the control performance. Moreover, the above-mentioned aggregate temperature-controlled load power control method hardly enables the tracking error to be converged quickly according to a preset performance range. With respect to predetermined performance control, this method has been widely used in other fields. Here, predetermined properties are applied to the polymerization temperature-controlled load control.
Disclosure of Invention
In order to solve the problems, the invention improves a primary TCL Bilinear Aggregation Model (TBAM) and provides an improved MPC control strategy with preset performance. The problem that the traditional MPC is large in calculation amount is solved, and the tracking error is made to be converged in a pre-designed performance range.
The innovation points are embodied in the following two aspects: (1) an original temperature control load bilinear model is improved by introducing the material temperature, and a more accurate improved temperature control load bilinear aggregation model (ITBAM) in practical application is obtained; (2) based on an improved temperature control load bilinear polymerization model, an MPC control scheme with a preset performance and based on a Lyapunov function is designed, and transient and steady-state performances required by a tracking error are guaranteed.
In order to achieve the above object, the present invention provides a method for predictive control of a polymerization temperature-controlled load improvement model under a preset performance condition, comprising the steps of:
(1) expanding the original temperature control load bilinear polymerization model through a second-order equivalent thermodynamic parameter model to obtain an improved temperature control load bilinear polymerization model;
(2) aiming at the improved temperature control load bilinear polymerization model, a preset performance controller is designed based on model prediction control of a Lyapunov function.
According to the step (1), the original TCL bilinear polymerization model is expanded through a second-order ETP model to obtain an improved TCL bilinear polymerization model:
Figure BSA0000215552550000031
wherein,
Figure BSA0000215552550000032
x (t) is the number of temperature control loads in each temperature interval, A is the state matrix, B is the input matrix, C is the output matrix, U (t) is the control input, CaIs the heat capacity of indoor air, RaIs the thermal resistance of indoor air, CmIs the heat capacity of indoor material, RmIs the thermal resistance of the indoor substance,
Figure BSA0000215552550000033
as a derivative of the temperature set point, TsetIs a temperature set value, and is used as a temperature setting value,
Figure BSA0000215552550000034
to a desired temperature set point, Tm0Is the initial room temperature, PT(T) Total output Power of the aggregate temperature controlled load,. DELTA.TsetFor variation of the temperature setting, Δ TmIs the change of the temperature of the indoor material u1(t) and u2(t) respectively reflecting the real-time influence and the accumulated influence of the temperature set value change on the dynamic process of the temperature control load, u3(t) reflects the influence of heterogeneity on the dynamic process of temperature-controlled load,
Figure BSA0000215552550000035
as an estimate of the temperature of the room mass, Tm(t) is the room temperature.
Due to the temperature T of the indoor materialm(t) is not easily obtained in practical applications, and its estimated value can be used
Figure BSA0000215552550000036
Instead of this, the user can,
Figure BSA0000215552550000037
the calculation can be made using the following formula:
Figure BSA0000215552550000038
the step (2) is based on an improved temperature control load bilinear polymerization model, and a preset performance controller is designed based on model prediction control of a Lyapunov function:
Figure BSA0000215552550000039
wherein,
Figure BSA00002155525500000310
Figure BSA0000215552550000041
ρ(t)＝(ρ0-ρ∞)e-rt+ρ∞，-δ1ρ(t)＜ey(t)＜δ2ρ(t)，ρ0p (0), u (t) is the resulting optimal control input, Pref(t) is a given power reference value, s is a converted error variable, α is a virtual control quantity, ξ is an intermediate variable, ey(t) is the tracking error, X (t) is the number of temperature control loads in each temperature interval, A is the state matrix, B is the input matrix, C is the output matrix, xi is the intermediate variable and xi > 0, epsilon is a constant greater than 0, rho (t) is the selected predetermined performance function, rho (0) is the value of rho (t) at zero time, k is the value of1、δ1And delta2Are predetermined performance parameters and are all greater than 0, r is a time coefficient, rho0For a predetermined performance function initial value, p∞Is a steady state value of a predetermined performance function, and p0＞ρ∞，
Figure BSA0000215552550000042
Are the transition variables.
Drawings
FIG. 1 is a comparison of Monte Carlo simulations of a second order ETP model and a first order ETP model;
FIG. 2 is a comparison of simulation results of TBAM, ITBAM and second order ETP Monte Carlo models;
FIG. 3 is a schematic view of an embodiment;
FIG. 4 is a diagram of an improved MPC algorithm power tracking error with predetermined performance;
FIG. 5 is an MPC algorithm power tracking error based on a Lyapunov function;
FIG. 6 is a system power generation and utilization curve;
fig. 7 is a tracking error curve for different control algorithms.
Detailed Description
The invention is realized by the following technical scheme:
modeling of TCL bilinear polymerization model
1.1 thermodynamic model of monomer TCL
Most literature often describes thermodynamic processes using a first-order ETP model, which can be described as:
Figure BSA0000215552550000051
because the second-order dynamic effect caused by the temperature of the substance is neglected, the first-order ETP model cannot accurately describe the real TCL dynamic process caused by the change of the temperature set value. Therefore, TCL is described using a second order ETP model, also known as a two-mass model, which takes changes in air temperature and mass temperature as observed two state variables. The specific differentiation process is as follows:
Figure BSA0000215552550000052
wherein,
Figure BSA0000215552550000053
wherein T is the indoor temperature, C is the indoor average heat capacity, R is the indoor average heat resistance, TaIs the temperature of the indoor air, TmIs the temperature of the indoor material, T∞Is the outdoor ambient temperature, P is the TCL rated power of the monomer, TmaxAnd TminRespectively, the upper and lower limits of the temperature limit, TsetIs the temperature set point, δdbM (t) is a temperature dead zone, m (t) is a switching variable, Δ t is a time interval, CaFor heat capacity of indoor air，RaIs the thermal resistance of indoor air, CmIs the heat capacity of indoor material, RmIs the thermal resistance of the indoor substance,
1.2 improved bilinear temperature control load aggregation model
A control-oriented temperature control load bilinear polymerization model (TBAM) established based on a first-order ETP model is as follows:
Figure BSA0000215552550000054
wherein X (t) is the number of temperature control loads in each temperature interval, A is a state matrix, B is an input matrix, C is an output matrix, u (t) is a control input, PT(t) is the total output power of the aggregate temperature control load.
The TBAM model is only suitable for a scene with a small change range of the load temperature set value, and once the temperature set value deviates from the expected value to be too large, the bilinear polymerization model fails under long-time operation. Therefore, the TBAM model is extended by using a second-order ETP model, and a more accurate improved temperature-controlled load bilinear aggregation model (ITBAM) is obtained as follows:
Figure BSA0000215552550000061
wherein,
Figure BSA0000215552550000062
x (t) is the number of temperature control loads in each temperature interval, A is the state matrix, B is the input matrix, C is the output matrix, U (t) is the control input, CaIs the heat capacity of indoor air, RaIs the thermal resistance of indoor air, CmIs the heat capacity of indoor material, RmIs the thermal resistance of the indoor substance,
Figure BSA0000215552550000063
as a derivative of the temperature set point, TsetIs a temperature set value, and is used as a temperature setting value,
Figure BSA0000215552550000064
to a desired temperature set point, Tm0Is the initial room temperature, PT(T) Total output Power of the aggregate temperature controlled load,. DELTA.TsetFor variation of the temperature setting, Δ TmIs the change of the temperature of the indoor material u1(t) and u2(t) respectively reflecting the real-time influence and the accumulated influence of the temperature set value change on the dynamic process of the temperature control load, u3(t) reflects the influence of heterogeneity on the dynamic process of temperature-controlled load,
Figure BSA0000215552550000065
as an estimate of the temperature of the room mass, Tm(t) is the room temperature.
2. Polymerization temperature control load improvement model prediction control under preset performance condition
2.1 control problem description
The control object of the invention is to adjust the ATCL output power to track the given reference power by using the proposed MPC control scheme based on Lyapunov function with the predetermined performance based on the improved temperature controlled load bilinear polymerization model.
2.2 error conversion
Defining a tracking error ey(t)＝PT(t)-Pref(t), the predetermined property of which can be described as:
-δ1ρ(t)＜ey(t)＜δ2ρ(t) (5)
wherein, PT(t) Total output Power of the aggregate temperature controlled load, PrefIs the reference power. ρ (t) ═ p (ρ0-ρ∞)e-rt+ρ∞For a selected performance function, δ1，δ2A predetermined performance parameter greater than 0; rho0ρ (0) is a value at time ρ (t) 0. r is a time coefficient, ρ0For a predetermined performance function initial value, p∞Is a steady state value of a predetermined performance function, and p0＞ρ∞。
The constrained tracking error is converted to an unconstrained error variable. In particular, we can define:
ey(t)＝ρ(t)φ(s(t)) (6)
wherein s is a conversion error; phi(s) belongs to (-delta)1，δ2) Is a smooth monotonically increasing function.
From φ(s), s can be defined as:
Figure BSA0000215552550000071
Figure BSA0000215552550000072
wherein,
Figure BSA0000215552550000073
is an intermediate variable and xi > 0,
Figure BSA0000215552550000074
are the transition variables.
As long as s (t) is bounded, ey(t) satisfies the predetermined property described in the above formula (6).
2.3 Lyapunov function based MPC controller design with predetermined Performance
Using the state space model of equation (4) as the prediction model, it is rewritten as:
Figure BSA0000215552550000075
wherein X (t) is the number of temperature control loads in each temperature interval, A is a state matrix, B is an input matrix, C is an output matrix, U (t) is a control input, PT(t) is the total output power of the aggregate temperature control load.
From equations (8) and (9), it is possible to obtain:
Figure BSA0000215552550000081
according to the Lyapunov theory, the Lyapunov function of the system is made to be
Figure BSA0000215552550000082
The derivative of V is:
Figure BSA0000215552550000083
in the formula, s is an error variable,
Figure BSA0000215552550000084
for the derivative of the error variable, X (t) is the number of temperature control loads in each temperature interval, A is the state matrix, B is the input matrix, C is the output matrix, U (t) is the control input, Pref(t) is reference power, ey(t) is the tracking error, ρ (t) is the performance function,
Figure BSA0000215552550000085
is the derivative of the performance function.
The optimal control law is designed as follows:
Figure BSA0000215552550000086
wherein,
Figure BSA0000215552550000087
by using the theorem 1, s ξ cx (t) u (t) in the formula (11) is represented as:
sξCX(t)U(t)≤|sξCBX(t)U(t)|≤ε-sα。 (13)
where ε is a constant greater than 0, s is an error variable, X (t) is the number of temperature control loads in each temperature interval, A is a state matrix, B is an input matrix, C is an output matrix, U (t) is a control input,
Figure BSA0000215552550000088
is the derivative of the reference power, ey(t) is the tracking error, ρ (t) is the performance function,
Figure BSA0000215552550000089
is the derivative of the performance function, xi is the intermediate variable, k1Is a parameter greater than 0.
The theory 1 is as follows:
for any x ∈ R and a constant ε > 0, the following holds:
Figure BSA00002155525500000810
substituting the above formula (12) into the above formula (11) can obtain:
Figure BSA0000215552550000091
in the formula, k1Is a parameter greater than 0, η ═ k1ε is a constant greater than 0 and s is the error variable.
As can be obtained from equation (15) above, s is bounded, thus ey(t) satisfies the above-specified properties.
3. Improved TCL bilinear polymerization model accuracy analysis
In order to verify the accuracy of ITBAM, 1000 TCL devices are selected, and a first-order ETP model, a second-order ETP model, TBAM and ITBAM are simulated and compared through Monte Carlo. The simulation parameters are shown in table 1. The simulation results are shown in fig. 1-2.
Figure BSA0000215552550000092
As shown in fig. 1, when the temperature setting value is changed, the second-order ETP model has a longer response period and a larger fluctuation amplitude than the first-order ETP model under the same parameters, which is caused by the thermal capacitance and thermal resistance properties exhibited by the introduced indoor substance. The coupling characteristic of the indoor air temperature and the indoor substance temperature is considered, and the second-order ETP model can reflect the real use condition better.
As shown in fig. 2, the ITBAM effectively improves the accumulated error of the bilinear model under long-time operation, improves the accuracy of model description, and proves that the proposed ITBAM can more accurately describe the dynamic process of aggregating TCLs.
4. Simulation analysis of control strategies
To verify the effectiveness of the proposed control strategy, a schematic diagram of an example of a multi-level hierarchical architecture is adopted, as shown in fig. 3. Including conventional generator sets, renewable energy sources such as wind farms and photovoltaic generation and TCL aggregates containing 10000 devices. The dispatching plan is directly issued by the dispatching center of the upper layer; the distributed reference power is adjusted and tracked by the TCL aggregate of the middle layer; the lower layer aggregates a large number of TCLs to participate in the load tracking service using the proposed controller.
The effectiveness of the control strategy for stabilizing the power fluctuation provided by the invention is further analyzed and verified in two calculation examples implemented below by using MPC based on Lyapunov function as a comparison algorithm.
Example 1: tracking of a given power value
The goal was to provide 40MW of power in 30 minutes, with 6 initial states e selected separatelyy(0)＝[0.0175，0.0451，0.0947，-0.0239，-0.0515，-0.0929]With a design parameter of rho0＝0.1009，δ1＝1，δ21, r 0.9 and ρ∞0.009. The simulation results are shown in fig. 4-5. As can be seen from fig. 4-5, the control method proposed herein can adjust the tracking error to zero and can adapt to the predetermined performance requirements at different initial conditions. In particular, compared with a model prediction control algorithm based on the Lyapunov function, the control method has faster transient convergence and can control the tracking error within the limit of a prediction performance function.
Example 2: stabilizing new energy power fluctuation
The ATCMs are utilized to carry out power fluctuation stabilization, and reference power (expected ATCMs power) is provided by a dispatching center and can be expressed as the total generated power containing new energy minus rigid load required power. The electricity generation and utilization in the system within two hours is shown in fig. 6.
As can be seen from fig. 6, the total load power demand of the system in the first two hours is greater than the total power generation power, because the uncontrollable load power demand is greater, even if the conventional energy generator set is adjusted, the load demand cannot be met due to the randomness of new energy power generation, and at this time, the ATCLs needs to be reduced to achieve the balance of the power consumption; and in the last two hours, the total generated power is larger than the total load power, because the new energy power generation is suddenly increased and is far larger than the load power demand, the new energy power generation can be consumed by increasing the ATCL power so as to meet the demand and supply balance. The desired ATCLs power is expressed as the total generated power containing new energy minus the demanded power without TCL loads.
To track the reference power, a parameter ρ is selected0＝0.12，δ1＝1，δ21, r 0.9 and ρ∞0.007. The simulation results are shown in fig. 7.
As can be seen from fig. 7, the proposed control method has a smaller steady-state error (about 0.002p.u) and faster convergence performance compared to the Lyapunov function-based MPC method with a steady-state error of about 0.005 p.u.

Claims (3)

1. The method is characterized by comprising the following steps of:
(1) expanding the original temperature control load bilinear polymerization model through a second-order equivalent thermodynamic parameter model to obtain an improved temperature control load bilinear polymerization model;
(2) aiming at the improved temperature control load bilinear polymerization model, a preset performance controller is designed based on model prediction control of a Lyapunov function.
2. The method for predicting and controlling the aggregated temperature-controlled load improvement model under the preset performance condition of claim 1, wherein: in the step (1), the original bilinear polymerization model is expanded, and the improved temperature control load bilinear polymerization model is obtained by:
Figure FSA0000215552540000011
wherein,
Figure FSA0000215552540000012
x (t) is the number of temperature control loads in each temperature interval, A is the state matrix, B is the input matrix, C is the output matrix, U (t) is the control input, CaIs the heat capacity of indoor air, RaIs the thermal resistance of indoor air, CmIs the heat capacity of indoor material, RmIs the thermal resistance of the indoor substance,
Figure FSA0000215552540000013
as a derivative of the temperature set point, TsetIs a temperature set value, and is used as a temperature setting value,
Figure FSA0000215552540000014
to a desired temperature set point, Tm0Is the initial room temperature, PT(T) Total output Power of the aggregate temperature controlled load,. DELTA.TsetFor variation of the temperature setting, Δ TmIs the change of the temperature of the indoor material u1(t) and u2(t) respectively reflecting the real-time influence and the accumulated influence of the temperature set value change on the dynamic process of the temperature control load, u3(t) reflects the influence of heterogeneity on the dynamic process of temperature-controlled load,
Figure FSA0000215552540000015
as an estimate of the temperature of the room mass, Tm(t) is the room temperature.
Due to the temperature T of the indoor materialm(t) is not easily obtained in practical applications, and its estimated value can be used
Figure FSA0000215552540000016
Instead of this, the user can,
Figure FSA0000215552540000021
can be calculated by：
Figure FSA0000215552540000022
3. The method for predicting and controlling the aggregated temperature-controlled load improvement model under the preset performance condition of claim 1, wherein: the step (2) is based on an improved temperature control load bilinear polymerization model, and a preset performance controller is designed based on model prediction control of a Lyapunov function:
Figure FSA0000215552540000023
wherein,
Figure FSA0000215552540000024
Figure FSA0000215552540000025
ρ(t)＝(ρ0-ρ∞)e-rt+ρ∞，-δ1ρ(t)＜ey(t)＜δ2ρ(t)，ρ0p (0), u (t) is the resulting optimal control input, Pref(t) is a given power reference value, s is a converted error variable, α is a virtual control quantity, ξ is an intermediate variable, ey(t) is the tracking error, X (t) is the number of temperature control loads in each temperature interval, A is the state matrix, B is the input matrix, C is the output matrix, xi is the intermediate variable and xi > 0, epsilon is a constant greater than 0, rho (t) is the selected predetermined performance function, rho (0) is the value of rho (t) at zero time, k is the value of1、δ1And delta2Are predetermined performance parameters and are all greater than 0, r is a time coefficient, rho0For a predetermined performance function initial value, p∞Is a steady state value of a predetermined performance function, and p0＞ρ∞，
Figure FSA0000215552540000026
Are the transition variables.
CN202010754960.2A 2020-07-29 2020-07-29 Polymerization temperature control load improvement model predictive control under preset performance condition Active CN114069599B (en)

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