CN114065561A - Control-oriented variable frequency air conditioner load aggregation modeling method - Google Patents
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Abstract
The invention discloses a control-oriented variable frequency air conditioner load aggregation modeling method, which comprises the following steps: (1) determining a controllable frequency range according to the comfort requirement of a user, and obtaining a frequency control model based on a variable slope coefficient; (2) establishing a polymerization variable frequency air conditioner dynamic response model and a forced response model according to the obtained frequency control model, and obtaining a corresponding frequency change rate; (3) and discretizing the working frequency of the compressor of the variable frequency air conditioner based on a finite difference method, and establishing a control-oriented aggregated variable frequency air conditioner load model under dynamic response and forced response. Finally, the effectiveness of the aggregated variable frequency air conditioner load model is verified through simulation, the unified scheduling and control of the large-scale variable frequency air conditioner are realized, and a theoretical basis is provided for the decision of a scheduling center and a load agent.
Description
Technical Field
The invention belongs to the field of auxiliary service and demand side response of a power system, and relates to a temperature control load aggregation modeling method, in particular to a control-oriented variable frequency air conditioner load aggregation modeling method.
Background
The large-scale network access of new energy represented by wind power and photovoltaic puts higher requirements on the adjustability of a power grid, and the traditional method for maintaining the balance of supply and demand of a power system by increasing the reserve capacity not only increases the operation cost of the system, but also has lower efficiency. With the development of the technology of the internet of things and the smart grid, demand side loads serve as excellent schedulable resources, and can play an increasingly greater role in improving the reliability and the economy of a power system by providing rapid load tracking, rotary standby and other auxiliary services.
The variable frequency air conditioner is a demand side resource with huge schedulable potential and has good energy storage characteristics. The variable frequency air conditioner maintains the room temperature to be stable through continuous change of frequency and power, the response speed is higher, and the energy consumption is lower at low frequency, so that the aggregation modeling of the large-scale variable frequency air conditioner is one of core technologies for researching that the variable frequency air conditioner provides various auxiliary services for a power system, and has an important role in realizing participation of the variable frequency air conditioner in demand response.
Disclosure of Invention
The invention aims to establish a control-oriented aggregation variable frequency air conditioner load model and solve the problem that the frequency operation characteristic of a variable frequency air conditioner group is neglected in the process of participating in demand response, namely, the temperature set value cannot be accurately tracked or the frequency change rate is regarded as a constant. The invention provides a frequency control model of a variable frequency air conditioner suitable for participating in demand response, and the control strategy not only considers the comfort level of a user, but also can avoid load rebound; and on the basis, a control-oriented converged variable frequency air conditioner load model is deduced and established, and finally the effectiveness of the converged variable frequency air conditioner load model is verified through simulation.
The problem of the invention is realized by the following technical scheme:
a control-oriented variable frequency air conditioner load aggregation modeling method comprises the following steps:
(1) determining a controllable frequency range according to the comfort requirement of a user, and obtaining a frequency control model based on a variable slope coefficient;
(2) establishing a polymerization variable frequency air conditioner dynamic response model and a forced response model according to the obtained frequency control model, and obtaining a corresponding frequency change rate;
(3) and discretizing the working frequency of the compressor of the variable frequency air conditioner based on a finite difference method, and establishing a control-oriented aggregated variable frequency air conditioner load model under dynamic response and forced response.
Specifically, in the step (1), the frequency control model based on the variable slope coefficient is:
wherein: f (Hz) is the working frequency of the compressor of the inverter air conditioner, fmax(Hz) is the maximum operating frequency thereof, u and v are constants, fset(Hz) compressor operating frequency for stable operation at a set temperature value, fmin＝((fmax-fset)/v)·u+fsetFor the minimum working frequency, k, of the variable-frequency air-conditioner compressorf＝(fmax-fset) The slope of a straight line,. DELTA.T (. degree.C.) is the indoor temperature TinAnd a set temperature TsetThe change of the temperature set value can influence the change of the slope, thereby changing the relation of f-delta T and rapidly changing the change of the frequency; when the frequency setting value is changed, the lowest operation frequency f accepted by the user is set according to the comfort requirement of the useruserThe frequency control model described by the formula (1) is changed into:
fuserdifferent values can be set according to comfort requirements of different users, and the slope of the frequency expression in the single variable-frequency air conditioner load model is not changed any more.
Specifically, in the step (2), the frequency change rate under the dynamic response of the variable frequency air conditioner is as follows:
wherein: k is a radical offA (kW/Hz) and b (kW) are the variable frequency air conditioner refrigerating capacity expression QACConstant coefficient in af + b, ToutAnd TinRespectively outdoor temperature and indoor temperature, R and C respectively are equivalent thermal resistance and equivalent thermal capacity of a room, and the increase rate of the load concentration can be obtained by dividing the difference between the inflow and the outflow by the change of the frequencyAnd the inflow is positive and the outflow is negative, so that a dynamic response lower aggregation variable frequency air conditioner load model can be obtained:
wherein: x (f, t) is the load number of the frequency down-conversion air-conditioning group at the moment t and f, and lambdafIs the rate of change of frequency under dynamic response; when the frequency is set to the value fsetWhen the change occurs, the frequency change rate under the forced response is:
wherein: f. ofsetWhen the frequency set value is changed, the forced response load model of the aggregated variable frequency air conditioner is as follows:
wherein: lambda [ alpha ]uTo force the rate of change of frequency under response.
Specifically, in the step (3), a finite difference method is used to establish a control-oriented aggregated variable frequency air conditioner load model under dynamic response and forced response, and the specific process is as follows:
discretizing the working frequency of the compressor of the inverter air conditioner, replacing the frequency of each discrete interval with the intermediate value of the frequency of the interval, and setting the initial value T of the temperatureset0Approximately represents TinUsing frequency setting value initial value fset0Approximate substitution of fsetFrom this, the discretized frequency rate of change can be obtained:
wherein: f. ofiIs the middle of the ith frequency intervalValue λfiAnd λuiRespectively representing the frequency change rate under a discretized dynamic response model and the frequency change rate under a forced response model;
in discrete processes, when the transmission rate of the load under forced response is negative with respect to the dynamic response process, i.e. λuIf the difference is less than 0, selecting the forward difference of the space quantity, otherwise selecting the backward difference of the space quantity, and establishing a control-oriented aggregation variable frequency air conditioner load model under different conditions;
the first condition is as follows: assuming a frequency set value fsetFalling on the Mth section, and according to the operation characteristics of the variable frequency air conditioner group, being at fmin，fset) The load flow direction in the range is positive and is at (f)set，fmax]The load flow direction in the range is negative, and the discretization (4) formula intermediate polymerization variable frequency air conditioner load model can obtain a control-oriented dynamic response lower polymerization variable frequency air conditioner load model expression:
wherein: m (kW/Hz) and n (kW) are power expressions P of the variable frequency air conditionerACConstant coefficient in mf + n, x (t) ═ x1(t)，x2(t)，…，xN(t)]TIs an Nx 1 order state vector, A1Is an NxN order state matrix, B1＝0，E＝[1，1，…，1]1×NIs an output vector of 1 XN, y (t) represents the total power of the aggregated variable frequency air conditioner, the matrix C is a state output matrix of NXN, A1And C is expressed as:
case two: when the demand response requires load reduction, in order to ensure the load reductionEffectively, the load flow direction is assumed to be all negative, i.e. λu< 0, discretizing the forced response model in the formula (6) to obtain the expression of the aggregated variable frequency air conditioner load model in the control-oriented forced response stage load reduction:
wherein A is2Is an NxN order state matrix, B2The matrix is an NxN-order input matrix, A2And B2Comprises the following steps:
case three: in contrast to the load shedding process, when the demand response requires an increase in load, to ensure the effectiveness of the load shedding, it is assumed that the load flow is all positive, i.e., λuWhen the forced response model in the formula (6) is discretized, the expression of the aggregated variable frequency air conditioner load model when the load is increased in the forced response stage facing the control can be obtained:
wherein A is3Is an NxN order state matrix, B3The matrix is an NxN-order input matrix, A3And B3The expression is as follows:
considering the user comfort requirement, the rate of change of the frequency setting value needs to be limited, when fmin＜fuserWhen the f- Δ T relation is changed to expression (2), expression (7) above should be updated according to the following expression:
wherein: lambda [ alpha ]fiAnd λuiAre respectively fmin＜fuserFrequency rate of change under a dynamic response model of time and under a forced response model.
The technical scheme provided by the invention has the beneficial effects that:
the frequency control model based on the variable slope coefficient can accurately track the temperature set value on the basis of changing the f-delta T electrical quantity relation, the change of the slope can obviously adjust the output of power, and the demand response effect can be effectively improved. A dynamic response and forced response aggregated variable frequency air conditioner load finite-dimension state space model is established, and the comfort level of a user is considered to update model parameters, so that the control of the variable frequency air conditioner load in a wide frequency range is realized.
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The invention will be further described with reference to the accompanying drawings in which:
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a variable slope coefficient frequency model;
FIG. 3 is a schematic diagram of an uncontrolled free response process;
FIG. 4 is a schematic diagram of a load shedding process in the forced response phase;
FIG. 5 is a schematic diagram of a forced response phase load increase process;
FIG. 6 is a comparison graph of a load model of an aggregated inverter air conditioner and Monte Carlo simulation.
Detailed description of the preferred embodiments
As shown in fig. 1, the present invention provides a control-oriented aggregation modeling method for variable frequency air conditioner loads, which is specifically described by the following steps in conjunction with fig. 2 to 6. The theoretical derivation of the present invention is explained in detail in the following description, but the present invention can be implemented in many different ways than those described herein, and thus the present invention is not limited by the specific implementation disclosed below.
The method comprises the following steps: and determining a controllable frequency range according to the comfort requirement of a user, and obtaining a frequency control model based on a variable slope coefficient.
As shown in FIG. 2, for example, the frequency setting value f is used to reduce the loadsetMoving downwards along the vertical line Δ T-0, curve i1Becomes curve l2The frequency reduction amount corresponding to the variable frequency air conditioner load running on the curve comprises two parts: 1) from A to B, the thermodynamic change process is described, with a reduction Δ f1(ii) a 2) From B to C, the process characterizes fsetIs changed by a frequency of Δ f2Therefore, the frequency control model based on the variable slope coefficient is obtained as follows:
wherein: f (Hz) is the working frequency of the compressor of the inverter air conditioner, fmax(Hz) is the maximum operating frequency thereof, u and v are constants, fset(Hz) compressor operating frequency for stable operation at a set temperature value, fmin＝((fmax-fset)/v)·u+fsetFor the minimum working frequency, k, of the variable-frequency air-conditioner compressorf＝(fmax-fset) The slope of a straight line,. DELTA.T (. degree.C.) is the indoor temperature TinAnd a set temperature TsetThe change of the temperature set value can influence the change of the slope, thereby changing the relation of f-delta T and rapidly changing the change of the frequency; when the frequency setting value is changed, the lowest operation frequency f accepted by the user is set according to the comfort requirement of the useruserThe frequency control model described by the formula (1) is changed into:
fuserdifferent values can be set according to comfort requirements of different users, and the slope of the frequency expression in the single variable-frequency air conditioner load model is not changed any more.
Step 2: the dynamic change process of the variable frequency air conditioner load is described through an Equivalent Thermodynamic Parameter (ETP) model, and a single variable frequency air conditioner load model is established according to a frequency control strategy based on a variable slope coefficient.
Wherein: refrigerating capacity QACAnd air conditioning efficiency power PACThe frequency f can be obtained according to the formula (1) and the formula (2) for a linear function of the working frequency of the compressor, a, b, m and n are constant coefficients, and the thermodynamic dynamic characteristics of the variable frequency air conditioner are simulated according to an Equivalent Thermodynamic Parameter (ETP) model:
wherein: t isoutAnd TinOutdoor and indoor temperatures, R and C equivalent thermal resistance and equivalent thermal capacity of a room, respectively, and the compressor operates at a minimum frequency f when Δ T < uminOperating, at Δ T > u, the compressor at the highest frequency fmaxAnd operating, wherein the variable frequency air conditioner load participates in response by the following method in the demand response stage:
wherein, Δ PupAnd Δ PdnTarget power, f, to be increased and decreased during demand response, respectivelytargerTo correspond to Δ PupAnd Δ PdnThe target frequency of (c).
And step 3: and establishing a dynamic response model and a forced response model of the polymerization variable-frequency air conditioner, and obtaining a corresponding frequency change rate.
Wherein X (F, t) is the load quantity of the frequency down-conversion air conditioning group at the moment t, F (F, t) is the load flow,
for the change of frequency with time, called the flow rate of the load, the frequency change rate under the dynamic response model is:
the increase rate of the load concentration can be represented by dividing the difference value of the inflow and the outflow by the frequency change, and the inflow is defined to be positive, and the outflow is defined to be negative, so that a dynamic response lower polymerization variable frequency air conditioner load model can be obtained:
wherein: lambda [ alpha ]fIs the rate of change of frequency under dynamic response; when the frequency is set to the value fsetWhen a change occurs, the increment of X (f, t) is determined by the net increment and external factors according to the conservation relation, and the load flow can be written as follows:
the rate of change of frequency under forced response is:
it can be derived that when the frequency set value is changed, the forced response load model of the aggregated variable frequency air conditioner is:
wherein: lambda [ alpha ]uTo force the rate of change of frequency under response.
And 4, step 4: and discretizing the working frequency of the compressor of the variable frequency air conditioner based on a finite difference method, and establishing a control-oriented aggregated variable frequency air conditioner load model under dynamic response and forced response.
The working frequency of the compressor of the inverter air conditioner is discretized to obtain:
wherein: n is [ f ]min，fmax]The number of upper discretization intervals is df is the interval length, the frequency of the interval is replaced by the intermediate value of each frequency interval in the formula (12), and the initial value T set by the temperature is usedset0Approximately represents TinUsing frequency setting value initial value fset0Approximate substitution of fsetFrom this, it can be obtained that the frequency change rate after discretization is:
wherein: f. ofiIs the median value of the ith frequency interval, λfiAnd λuiRespectively representing the frequency change rate under a discretized dynamic response model and the frequency change rate under a forced response model;
in discrete processes, when the transmission rate of the load under forced response is negative with respect to the dynamic response process, i.e. λuIf the difference is less than 0, selecting the forward difference of the space quantity, otherwise, selecting the backward difference of the space quantity, and establishing a control-oriented polymerization variable frequency air conditioner load model under different conditions;
the first condition is as follows: as shown in fig. 3, assume a frequency setting value fsetFalls on the Mth section, and is at the moment according to the running characteristics of the variable frequency air conditioner group[fmin，fset) The load flow direction in the range is positive and is at (f)set，fmax]The load flow direction in the range is negative, and the load model of the variable frequency air conditioner with the polymerization in the formula of dispersion (8) can be obtained:
xi(t) represents the load quantity of the ith segment at the time t, and deltaf is the discretization frequency length according to the flow conservation, x1And x2At this time, the node only flows out, the node M only flows in, that is, all loads finally flow to the frequency setting value, and the boundary conditions of the uncontrolled dynamic response model can be obtained as follows: a
Therefore, a control-oriented dynamic response lower polymerization variable frequency air conditioner load model expression can be obtained:
wherein x (t) ═ x1(t)，x2(t)，…，xN(t)]TIs an Nx 1 order state vector, A1Is an NxN order state matrix, B1＝0， E＝[1，1，…，1]1×NIs an output vector of 1 XN, y (t) represents the total power of the aggregated variable frequency air conditioner, the C matrix is a state output matrix of NXN, A1And C is expressed as:
case two: as shown in FIG. 4, to ensure the effectiveness of load shedding when demand response requires load shedding, it is assumed that the load flow direction is all negative, i.e., λu< 0, discretizing the forced response model in the formula (11) can obtain:
according to conservation of flow, x1Node only flows in traffic, xNThe node only flows out, that is, all loads finally flow to the node with the minimum frequency value, and the boundary conditions of the load reduction model in the forced response stage can be obtained as follows:
therefore, a control-oriented load model expression of the aggregated variable frequency air conditioner during load reduction in the forced response stage can be obtained:
wherein A is2Is an NxN order state matrix, B2The matrix is an NxN-order input matrix, A2And B2Comprises the following steps:
case three: as shown in FIG. 5, in contrast to the load shedding process, when the demand response requires an increase in load, to ensure the effectiveness of the load shedding, it is assumed that the load flow direction is all positive, i.e., λuAnd > 0, discretizing the forced response model in the formula (11) to obtain the following model:
according to conservation of flow, xNNode only flows in traffic, x1The node only flows out, that is, all loads finally flow to the node with the maximum frequency value, and the boundary conditions of the model for forcing the load increase in the response stage can be obtained as follows:
therefore, a control-oriented load model expression of the aggregated variable frequency air conditioner during load increase in the forced response stage can be obtained:
wherein A is3Is an NxN order state matrix, B3The matrix is an NxN-order input matrix, A3And B3The expression is as follows:
considering the user comfort requirement, the rate of change of the frequency setting value needs to be limited, when fmin＜fuserIn this case, the f- Δ T relation is changed to expression (2), and expression (13) is updated according to the following expression.
Wherein: lambda [ alpha ]fiAnd λuiAre respectively fmin＜fuserUnder the dynamic response model of time andforcing the rate of change of frequency under the response model.
In order to verify the effectiveness of the load model of the aggregated variable frequency air conditioner, the Monte Carlo method is adopted to simulate the actual operation condition of a variable frequency air conditioner group consisting of 3000 variable frequency air conditioners, and the aggregated variable frequency air conditioner can be changed at any time by changing fsetThe output power is changed, the frequency set value excitation signal in the simulation is reduced by 1.8Hz at the rate of 0.1Hz/h within 0.1h and then is restored to the original frequency set value at the same rate within 0.3h, the comparison of the load model of the variable frequency air conditioner and the Monte Carlo simulation result is shown in FIG. 6, and the parameters used in the simulation are shown in Table 1:
TABLE 1 variable frequency air conditioner and user Room parameter settings
From the simulation result of fig. 6, in the forced response process of reducing or increasing the load, the aggregated variable frequency air conditioner load model not only has better response speed, but also has higher model precision and small error of reducing and increasing the power, and completely meets the precision requirement of the demand response of the power system. Due only to the approximation in equation (13), | λuI is slightly smaller than the true value, in the uncontrolled dynamic response process, the power change is slightly delayed compared with the Monte Carlo simulation, but the final power curve is still stable near the Monte Carlo simulation result, and no load rebounds after the recovery frequency is set to the initial value.
Claims (4)
1. A control-oriented variable frequency air conditioner load aggregation modeling method is characterized in that: the method comprises the following steps:
(1) determining a controllable frequency range according to the comfort requirement of a user, and obtaining a frequency control model based on a variable slope coefficient;
(2) establishing a polymerization variable frequency air conditioner dynamic response model and a forced response model according to the obtained frequency control model, and obtaining a corresponding frequency change rate;
(3) and discretizing the working frequency of the compressor of the variable frequency air conditioner based on a finite difference method, and establishing a control-oriented aggregated variable frequency air conditioner load model under dynamic response and forced response.
2. The control-oriented variable frequency air conditioner load aggregation modeling method according to claim 1, characterized in that: in the step (1), the frequency control model based on the variable slope coefficient is as follows:
wherein: f (Hz) is the working frequency of the compressor of the inverter air conditioner, fmax(Hz) is the maximum operating frequency thereof, u and v are constants, fset(Hz) compressor operating frequency for stable operation at a set temperature value, fmin＝((fmax-fset)/v)·u+fsetIs the minimum working frequency k of the compressor of the inverter air conditionerf＝(fmax-fset) The slope of a straight line,. DELTA.T (. degree.C.) is the indoor temperature TinAnd a set temperature TsetThe change of the temperature set value can affect the change of the slope, thereby changing the relation of f-delta T and rapidly changing the change of the frequency; when the frequency setting is changed, the lowest operation frequency f accepted by the user is set according to the comfort requirement of the useruserThe frequency control model described by the formula (1) is changed into:
fusetdifferent values can be set according to comfort requirements of different users, and the slope of the frequency expression in the variable frequency air conditioner load model is not changed at the moment.
3. The control-oriented variable frequency air conditioner load aggregation modeling method according to claim 1, characterized in that: in the step (2), the frequency change rate under the dynamic response of the variable frequency air conditioner is as follows:
wherein: k is a radical offA (kW/Hz) and b (kW) are the variable frequency air conditioner refrigerating capacity expression QACConstant coefficient in af + b, ToutAnd TinRespectively outdoor temperature and indoor temperature, R and C respectively are equivalent thermal resistance and equivalent thermal capacity of a room, the increase rate of the load concentration can be represented by dividing the difference value of inflow and outflow by the frequency change, and the inflow is positive and the outflow is negative, so that a dynamic response lower polymerization variable frequency air conditioner load model can be obtained:
wherein: x (f, t) is the load number of the frequency down-conversion air-conditioning group at the moment t and f, and lambdafIs the rate of change of frequency under dynamic response; when the frequency is set to the value fsetWhen the change occurs, the frequency change rate under the forced response is:
wherein: f. ofsetFor the change rate of the frequency set value, when the frequency set value is changed, the forced response load model of the aggregated variable frequency air conditioner is as follows:
wherein: lambda [ alpha ]uTo force the rate of change of frequency under response.
4. The control-oriented variable frequency air conditioner load aggregation modeling method according to claim 1, characterized in that: in the step (3), a finite difference method is used for establishing a control-oriented aggregated variable frequency air conditioner load model under dynamic response and forced response, and the specific process is as follows:
discretizing the working frequency of the compressor of the inverter air conditioner, replacing the frequency of each discrete interval with the intermediate value of the frequency of the interval, and setting the initial value T of the temperatureset0Approximately represents TinUsing frequency setting value initial value fset0Approximate substitution of fsetFrom this, the frequency change rate after discretization can be obtained:
wherein: f. ofiIs the median value of the ith frequency interval, λfiAnd λuiRespectively representing the frequency change rate under a discretized dynamic response model and the frequency change rate under a forced response model;
in discrete processes, when the transmission rate of the load under forced response is negative with respect to the dynamic response process, i.e. λuIf the difference is less than 0, selecting the forward difference of the space quantity, otherwise selecting the backward difference of the space quantity, and establishing a control-oriented aggregation variable frequency air conditioner load model under different conditions;
the first condition is as follows: assuming a frequency set value fsetFalling on the Mth section, and according to the operation characteristics of the variable frequency air conditioner group, being at fmin，fset) The load flow direction in the range is positive and is at (f)set，fmax]The load flow direction in the range is negative, and the discretization (4) formula intermediate polymerization variable frequency air conditioner load model can obtain a control-oriented dynamic response lower polymerization variable frequency air conditioner load model expression:
wherein: m (kW/Hz) and n (kW) are power expressions P of the variable frequency air conditionerACConstant coefficient in mf + n, x (t) ═ x1(t)，x2(t)，…，xN(t)]TIs an Nx 1 order state vector, A1Is an NxN order state matrix, B1＝0，E＝[1，1，…，1]1×NIs an output vector of 1 XN, y (t) represents the total power of the aggregated variable frequency air conditioner, the matrix C is a state output matrix of NXN, A1And C is expressed as:
case two: when demand response requires load shedding, to ensure load shedding effectiveness, it is assumed that the load flow direction is all negative, i.e., λu< 0, discretizing the forced response model in the formula (6) to obtain the expression of the aggregated variable frequency air conditioner load model in the control-oriented forced response stage load reduction:
wherein A is2Is an NxN order state matrix, B2The matrix is an NxN-order input matrix, A2And B2Comprises the following steps:
case three: in contrast to the load shedding process, when the demand response requires an increase in load, to ensure the effectiveness of the load shedding, it is assumed that the load flow is all positive, i.e., λuGreater than 0, in the formula (6)The discretization of the forced response model can obtain a load model expression of the aggregated variable frequency air conditioner when the load is increased in a forced response stage facing the control:
wherein A is3Is an NxN order state matrix, B3The matrix is an NxN-order input matrix, A3And B3The expression is as follows:
considering the user comfort requirement, the rate of change of the frequency setting value needs to be limited, when fmin＜fuserWhen the f- Δ T relation is changed to expression (2), expression (7) above should be updated according to the following expression:
wherein: lambda [ alpha ]fiAnd λuiAre respectively fmin＜fuserFrequency rate of change under a dynamic response model of time and under a forced response model.
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