CN108490791B - Temperature controlled load cost control strategy - Google Patents
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Abstract
The invention discloses a temperature control load cost control strategy, which adopts a temperature set value control strategy for polymerization temperature control loads, selects a bilinear model for function modeling, establishes a cost function model of a power company, consists of an adjusting cost and an dissatisfaction cost, combines the tracking precision of the adjusting cost and the comfort of the dissatisfaction cost by using a weight coefficient, and performs optimization solution by a recursion algorithm based on a tracking differentiator to minimize the cost; aiming at the problem of low tracking precision, the tracking precision is further improved by using a tracking differentiator control strategy, aiming at the reduction of tracking error and generated comfort level in the adjusting process, the change trend of the cost of the two parts under different weights and the relation between the tracking precision and the comfort level are considered, the tracking differentiator is applied to solve the problem of cost minimization, the algorithm is easy to realize, the tracking precision is considered, and the cost of an electric power company is minimized.
Description
Technical Field
The invention belongs to the technical field of smart power grids, and particularly relates to a temperature control load cost control strategy.
Background
Temperature-controlled loads are a class of temperature-regulated electrical devices whose switching action is controlled by a thermostat, such as: air conditioners, heat pumps, refrigerators, water heaters, and the like. As long as the temperature of the temperature control load does not exceed the temperature of the dead zone, the requirement of comfort level of users can be met, so that the temperature evolution dynamic state of the temperature control load can be changed, the conversion between heat energy and electric energy can be flexibly realized, the flexibility of a single temperature control load is relatively low, but the temperature control loads of a group (hereinafter referred to as aggregated temperature control loads) have high flexibility, can be applied to a smart grid, provide auxiliary service for the smart grid, realize the peak clipping and valley filling of the power grid, and track the power generation of renewable energy sources through frequency adjustment.
For an electric power company, a contract is made with a user aggregating temperature control load, and the user is encouraged to participate in frequency adjustment service, so that the operation cost of the electric power company is reduced, the cost is divided into two parts, the first part is payment cost determined according to the electric quantity adjustment quantity provided by the user and is defined as adjustment cost, and the larger the adjustment quantity is, the higher the cost is; the second part is the payment cost generated by the reduction of the comfort degree generated by the frequency adjustment, and is defined as dissatisfaction cost, the higher the dissatisfaction is, the larger the cost is, the total cost is the weighted sum of the two parts of the cost, and the proportion (weight) of the adjustment cost and the dissatisfaction cost in the total cost respectively represents different priorities for the tracking precision and the comfort degree.
In order to minimize the cost, it is necessary to control the adjustment cost and dissatisfaction cost of the temperature controlled load, and further, a control strategy of the temperature controlled load is studied, and a temperature controlled load switch control strategy and a temperature set value control strategy have been proposed in recent research work. The switch control strategy has the advantages that the power consumption of the polymerization temperature control load can be accurately adjusted, the accurate tracking of the frequency signal is realized, however, when the amplitude of the reference signal is too large, the temperature of the polymerization temperature control load is in the dead zone edge for a long time, the comfort requirement of a user cannot be met, or the effective tracking cannot be realized at all due to the limitation of the adjustable range of the polymerization power of the temperature control load. The temperature set point control strategy can solve the problems, and the adjustment range of the temperature control load aggregation power is changed by adjusting the set point, but the comfort of a user is greatly influenced. In recent years, a hybrid control strategy combining the above two strategies has been proposed, that is, a switching control strategy is used to achieve accurate tracking in a non-edge range of a temperature dead zone, and a temperature set value control strategy is used to expand a temperature-controlled load collective power regulation range in a dead zone edge range. Although the hybrid control strategy can effectively improve the tracking accuracy, the frequency tracking accuracy still needs to be improved, the cost problem of a power company is not considered in the process of frequency adjustment, the mutual restriction effect of the tracking accuracy and the comfort level is not comprehensively considered, the weight problem between the two parts of cost is not considered, and the cost of the temperature control load cannot be effectively controlled to be the lowest.
Disclosure of Invention
The invention aims to solve the technical problem of providing a temperature control load cost control strategy for controlling the aggregation temperature control load to track the power grid frequency regulation signal.
In order to solve the problems, the technical scheme adopted by the invention is as follows:
a temperature controlled load cost control strategy, characterized by: adopting a temperature set value control strategy for the polymerization temperature control load, selecting a bilinear model for function modeling, establishing a cost function model of the power company, wherein the cost function consists of an adjusting cost and an dissatisfaction cost, combining the tracking precision of the adjusting cost and the comfort of the dissatisfaction cost by using a weight coefficient, and performing optimization solution by a recursion algorithm based on a tracking differentiator to minimize the cost; the cost function solving process is as follows:
1) firstly, calculating a power signal to be tracked according to a frequency adjusting signal downloaded from a power market and a baseline value calculated by external temperature prediction, wherein the power signal to be tracked is used as the input of a cost function;
2) calculating a tracking error by a bilinear model according to a power signal to be tracked and initialized polymerization power, calculating an initial cost value by a cost function according to the tracking error, wherein the variable quantity of an initial temperature set value is zero, and extracting the initial cost value and the initial temperature set value as the input of a tracking differentiator;
3) the tracking differentiator respectively obtains corresponding differential signals according to the received initial cost value signal and the temperature set value signal, and iteratively updates the differential signals by adopting a recursion algorithm to obtain the variation of the temperature set value of the next step, wherein the variation of the temperature set value, namely the updating of an independent variable, enables the cost to gradually approach to a minimum value;
4) taking the updated independent variable as a control signal of the bilinear model, and calculating the cost value of the next step;
5) and circularly executing the steps 3) and 4) until an iteration termination condition is met, finishing the tracking of the first power signal to be tracked, obtaining an optimal cost function value, and then tracking the next power signal to be tracked until all the power signals to be tracked are tracked.
Further, the cost function is:
c＝(1-v)cf+vct(1)
wherein, cfTo adjust the cost, ctFor dissatisfaction cost, v is the weighting factor and v ranges from [0,1 ].
Further, the calculation formula of the adjustment cost is as follows:
wherein p isf，pr，psFor forecasting price, adjusting price and spot price, x, respectivelyeIs the power regulation error, is the power to be tracked PtargetAnd the polymerization power PtotalDifference of (a), xrIs the temperature-controlled load-regulating capacity, Δ TsIs the period of change of the frequency adjustment signal; the dissatisfaction degree cost is calculated according to the formula:
wherein p istIs a price of a degree of discomfort,
is the temperature set point for the k-th step,
is the temperature set point at the initial time.
Further, the cost function is constrained by:
wherein the temperature control load model
For a bilinear model, a, B, C are each constant matrices, and assuming that the temperature dead zone interval is divided equally into a plurality of temperature intervals, x represents a state variable representing the number of "on" or "off" state loads in each temperature interval,
is the derivative of x, u (t) is the input of the model, represents the variation of the temperature set value, y represents the temperature control load aggregate power, is the output of the model; the temperature set-point of the user being adjusted within a certain range, i.e.
Is the temperature set point for the k-th step,
is the lower limit of the temperature set point,
is the upper limit of the temperature set value, and is a constant; the temperature-controlled load aggregate power is in a certain range, i.e.
The power is aggregated for the upper temperature controlled load when the load is fully on,
for the lower limit temperature control when the load is completely closedPolymerization power of charge, Ptotal,kPower when part load is on; the amount of power regulation that the temperature controlled load can provide is in the capacity range, i.e. | xa|≤xr，xaIs the amount of power regulation, x, that the temperature controlled load can providerIs the temperature controlled load regulation capacity.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
aiming at the problem of low tracking precision, the tracking precision is further improved by using a tracking differentiator control strategy, aiming at the tracking error in the adjusting process and the generated comfort level reduction, the adjusting cost and the dissatisfaction cost of the power company are modeled, the weight problem between the two parts of cost is considered, the tracking differentiator is applied to solve the cost minimization problem according to the variation trend of the two parts of cost under different weights and the relation between the tracking precision and the comfort level, the algorithm is easy to realize, the tracking precision is considered, and the cost of the power company is minimized.
Drawings
Fig. 1 is a diagram of a typical frequency adjustment service;
FIG. 2 is a simulation diagram of the temperature control load cost control strategy based on a tracking differentiator according to the present invention;
FIG. 3 is a flowchart of the solving procedure of the k-th step of the cost function according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
FIG. 1 is a schematic diagram of a typical temperature controlled load for grid frequency regulation services, where PAGCThe frequency regulation signal of the power grid downloaded from the PJM power market in the United states is a series of power signals with positive and negative changes, the positive value represents that the power grid frequency is higher than a standard value (50Hz), the negative value represents that the frequency is lower than the standard value, and the frequency regulation service is used for regulating the power of a temperature control load to regulate the power grid frequency so that the frequency is stabilized near the standard value. PBLIs a baseline, which is a predicted value, P, of the power consumption of the temperature controlled load for the next daytargetIs the power signal to be tracked, PtotalIs to aggregate the total power of the temperature-controlled load by designing or controlling a controllerThe algorithm adjusts the total power of the aggregated temperature control load, accurately tracks a power signal to be tracked and keeps the frequency of the power grid stable.
The method adopts a temperature set value control strategy for the polymerization temperature control load, selects a bilinear model for function modeling, establishes a cost function model of the power company, combines the tracking precision of the adjustment cost and the comfort level of the dissatisfaction cost by using a weight coefficient, and performs optimization solution by a recursion algorithm based on a tracking differentiator to minimize the cost.
The tracking differentiator is originated from the PID controller and is the basis in the active disturbance rejection technology for obtaining the tracking signal and the differentiated signal. The method applies the characteristic of solving the extreme value of the function by a tracking differentiator, adopts a recursion algorithm to carry out optimization solution on the cost function, and realizes the minimization of the cost function. The derivative value of the dependent variable relative to the independent variable is needed in the recursion algorithm, the two costs (adjustment cost and dissatisfaction cost) are functions of the temperature set value, the selected temperature control load model is a bilinear model, so that the relation between the dependent variable and the independent variable becomes complex, the derivative value cannot be directly solved, the derivative form needs to be converted into differential signals of the two variables, and therefore a tracking differentiator is used for solving the differential signals and then is brought into the recursion algorithm to obtain the extreme value of the cost function. The premise of optimizing the function by the recursion algorithm is that the optimized function is a convex function, the value of the independent variable in the next step is updated according to the value of the independent variable in the previous step, the recursion algorithm comprises a derivative value and an iteration step length, and the iteration step length is set to be a constant value for simplifying calculation. Because the cost function of the invention is not necessarily a single-peak convex function, the cost function is divided into a plurality of convex functions by a forward method, the extreme value of each convex function is obtained, and finally the optimal extreme value is found out from all the extreme values and is used as the extreme point of the cost function.
The cost function of the present invention is as follows:
c＝(1-v)cf+vct(1)
the cost function is divided into two parts, the first part being called the frequency adjustment cost, i.e. c in equation (1)fThe formula for the calculation is:
wherein p isf，pr，psFor forecasting price, adjusting price and spot price, x, respectivelyeIs the power regulation error and xe＝Ptotal-Ptarget，xrIs the temperature-controlled load-regulating capacity, Δ TsIs the period of change of the frequency adjustment signal when the frequency adjustment error xeIn the temperature-controlled load-regulating capacity range xrInternal time (| x)e|≤xrIn time), the user can provide normal frequency adjustment service, and the cost at this time is adjusting price and electric quantity adjusting quantity (| x)e|ΔTs) When the frequency adjustment error xeRegulating capacity x beyond temperature-controlled loadrIn the meantime, the user cannot provide the normal frequency adjustment service, which shows that the purchased power of the power company is remained (x)e<-xrTime) or deficiency (x)e>xrTime), the power cost at that time is the maximum adjustment (x) provided by the customerrΔTs) Cost and wasted power ((-x)e-xr)ΔTs) Or the amount of electricity to repurchase ((x)e-xr)ΔTs) The sum of the costs of (a).
The second part cost is called the discomfort cost, i.e. c in the formulatThe calculation formula is as follows:
wherein p istIs a price of a degree of discomfort,
is the temperature set point for the k-th step,
is the temperature set point at the initial moment, it can be seen that the discomfort cost and the temperature during the conditioning processThe amount by which the temperature set point deviates from the temperature set point initially set by the user is relevant.
A weight coefficient v is introduced into the cost function, and the significance of the weight coefficient v is that the requirement of a user on the comfort level weight is met by changing the weight of the two parts of cost. v ranges from [0,1), when v is 0, it means that the comfort level of the user is not considered, only the accuracy of the frequency adjustment is considered, and as v increases, the comfort level of the user increases in weight and the accuracy of the frequency adjustment decreases in weight, however, v can only approach 1 and cannot be equal to 1, because when v is 1, the frequency adjustment is not considered.
Fig. 2 is a simulation diagram of the temperature control load cost control strategy based on the tracking differentiator according to the present invention, in which some constraints are added to the cost function, as shown in equation (4),
four constraints are included, specifically as follows: a. the temperature control load model is a bilinear function model
Wherein A, B, C are constant matrixes respectively, x represents a state variable representing the number of on or off state loads in each temperature interval on the assumption that the temperature dead zone interval is divided into a plurality of temperature intervals in an average manner,
is the derivative of x, u (t) is the model input, represents the change in temperature set point, and y represents the temperature controlled load aggregate power, is the model output. b. The temperature set-point of the user being adjusted within a certain range, i.e.
Is the temperature set point for the k-th step,
is the lower limit of the temperature set point,
the upper limit of the temperature set value can be reasonably set and is constant; c. the temperature-controlled load aggregate power is in a certain range, i.e.
The power is aggregated for the upper temperature controlled load when the load is fully on,
for the lower temperature-controlled load aggregate power, P, at which the load is completely switched offtotal,kPower when part load is on; d. the amount of power regulation that the temperature controlled load can provide is in the capacity range, i.e. | xa|≤xr，xaIs the amount of power regulation, x, that the temperature controlled load can providerIs the temperature controlled load regulation capacity.
As can be seen from fig. 2, the temperature control load model is a bilinear model, the input quantity (independent variable) of the model is the temperature setting value variable u (t), and the output is the temperature control load aggregate power y, and it can be seen that the bilinear model contains a state space equation instead of a general linear equation. The method is solved by using a classical recursive algorithm, the derivative of the cost relative to the variation of the temperature set value is needed in the algorithm, and the cost c can be regarded as a function of the variation u of the temperature set value through the analysis. As shown in figure 2 of the drawings, in which,
can be converted into
So that derivatives with respect to time can be obtained as long as c and u are available in real time, the tracking differentiator isThe practical tool for solving the differential signal can obtain the corresponding differential signal only by inputting a reference signal, so that the derivation problem in the classical recursion algorithm can be simplified by utilizing two tracking differentiators.
PtargetIs a series of power signals to be tracked, and in the simulation process, the variation period Delta T of the signals is definedsDefining k as the number of simulation steps, each step lasting Δ TsDefining the total simulation step number as N (N, k is a positive integer, k is less than or equal to N), that is, there are N power signals to be tracked in total, and performing a solution once in a variation period of the power signals to be tracked.
Fig. 2 represents the solving process of the k-th step, and it should be noted that each value of k corresponds to a solving process, and a solving process needs to be cycled for many times to solve the optimal cost value c.
Is available in real time (since PAGCIs data provided in real time according to the imbalance of supply and demand of the power grid, PBLIs a predicted value of power consumption in the future day, is specific data predicted in advance), at the k-th step,
inputting the reference value to the k step of the optimization function model, initializing a temperature set value variable u at each step k, and calculating the sum of the initialized u and the initialized u
Corresponding cost c can be calculated, then the obtained cost c and initialized u are input into respective tracking differentiators to obtain respective derivatives with respect to time, u is updated according to a recursion algorithm, and the updated u and the kth step are kept unchanged
Re-entering cost modelAnd repeating iteration by analogy until a convergence condition is met, ending the cycle of the k step, wherein c and u at the moment are the optimal cost and the temperature set value variable u of the k step, then, k is k +1, and carrying out the next cycle until the cycle of the N step is finished, and ending the program. J. the design is a squarekIs an objective function, i.e. a cost function, and the purpose of the optimization is to make the objective function obtain the minimum value under specific constraint conditions. The convergence condition is set to
That is, the absolute value of the derivative in the recursion formula is converged when the absolute value of the derivative is smaller than a certain small constant value epsilon, and the convergence condition is a common convergence condition in the recursion algorithm, and the redelification is not needed in the invention. λ is the update step in the recurrence formula, and is a positive constant value.
It should be noted that the constructed cost model is not a convex function, and a multi-peak function is divided into a plurality of unimodal functions by combining with a forward method, and then a classical recursion algorithm is applied to solve the unimodal functions. The solving program block diagram of the function model at the k step is shown in fig. 3, the program operation starts, the setting parameters are initialized, then the multi-peak function is divided into a single-peak interval, the recursive algorithm is applied to the single-peak interval to solve, the convergence condition is met, and the program operation is finished.
Claims (4)
1. A temperature controlled load cost control strategy, characterized by: adopting a temperature set value control strategy for the polymerization temperature control load, selecting a bilinear model for function modeling, establishing a cost function model of the power company, wherein the cost function consists of an adjusting cost and an dissatisfaction cost, combining the tracking precision of the adjusting cost and the comfort of the dissatisfaction cost by using a weight coefficient, and performing optimization solution by a recursion algorithm based on a tracking differentiator to minimize the cost; the cost function based solution process is as follows:
1) firstly, calculating a power signal to be tracked according to a frequency adjusting signal downloaded from a power market and a baseline value calculated by external temperature prediction, wherein the power signal to be tracked is used as the input of a cost function;
2) calculating a tracking error by a bilinear model according to a power signal to be tracked and initialized polymerization power, calculating an initial cost value by a cost function according to the tracking error, wherein the variable quantity of an initial temperature set value is zero, and extracting the initial cost value and the initial temperature set value as the input of a tracking differentiator;
3) the tracking differentiator respectively obtains corresponding differential signals according to the received initial cost value signal and the temperature set value signal, and iteratively updates the differential signals by adopting a recursion algorithm to obtain the variation of the temperature set value of the next step, wherein the variation of the temperature set value, namely the updating of an independent variable, enables the cost to gradually approach to a minimum value;
4) taking the updated independent variable as a control signal of the bilinear model, and calculating the cost value of the next step;
5) and circularly executing the steps 3) and 4) until an iteration termination condition is met, finishing the tracking of the first power signal to be tracked, obtaining an optimal cost function value, and then tracking the next power signal to be tracked until all the power signals to be tracked are tracked.
2. The temperature controlled load cost control strategy of claim 1, wherein: the cost function is:
c＝(1-v)cf+vct(1)
wherein, cfTo adjust the cost, ctFor dissatisfaction cost, v is the weighting factor and v ranges from [0,1 ].
3. The temperature controlled load cost control strategy of claim 2, wherein: the calculation formula of the adjustment cost is as follows:
wherein p isf，pr，psFor forecasting price, adjusting price and spot price, x, respectivelyeIs the power regulation error, is the power to be tracked PtargetAnd the polymerization powerPtotalDifference of (a), xrIs the temperature-controlled load-regulating capacity, Δ TsIs the period of change of the frequency adjustment signal; the dissatisfaction degree cost is calculated according to the formula:
wherein p istIs a price of a degree of discomfort,
is the temperature set point of the k-th step, T0 setIs the temperature set point at the initial time.
4. The temperature controlled load cost control strategy of claim 2 or 3, wherein: the cost function is constrained by the following conditions:
wherein the temperature control load model
For a bilinear model, a, B, C are each constant matrices, and assuming that the temperature dead zone interval is divided equally into a plurality of temperature intervals, x represents a state variable representing the number of "on" or "off" state loads in each temperature interval,
is the derivative of x, u (t) is the input of the model, representing the variation of the temperature set value, y represents the total power output of the temperature control load; the temperature set-point of the user being adjusted within a certain range, i.e.
Is the temperature set point for the k-th step,
is the lower limit of the temperature set point,
is the upper limit of the temperature set value, and is a constant; the temperature-controlled load aggregate power is in a certain range, i.e.
The power is aggregated for the upper temperature controlled load when the load is fully on,
for the lower temperature-controlled load aggregate power, P, at which the load is completely switched offtotal,kPower when part load is on; the amount of power regulation that the temperature controlled load can provide is in the capacity range, i.e. | xa|≤xr，xaIs the amount of power regulation, x, that the temperature controlled load can providerIs the temperature controlled load regulation capacity.
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