CN112003735B

CN112003735B - Risk-aware deep learning-driven limit transmission capacity adjustment method

Info

Publication number: CN112003735B
Application number: CN202010739587.3A
Authority: CN
Inventors: 邱高; 刘友波; 刘俊勇; 邱红兵
Original assignee: Sichuan University
Current assignee: Sichuan University
Priority date: 2020-07-28
Filing date: 2020-07-28
Publication date: 2021-11-09
Anticipated expiration: 2040-07-28
Also published as: CN112003735A

Abstract

The invention discloses a risk-aware deep learning-driven limit transmission capacity adjusting method, which comprises the following steps: embedding the limit transmission capacity predictor into the adjustment model to replace the most complex and time-consuming calculation part to obtain a deep confidence network agent-assisted double-layer model; constructing a prediction interval based on a deep belief network, adjusting the prediction interval according to the coverage probability of the prediction interval, the normalized average bandwidth of the prediction interval and the accumulated bandwidth deviation, and obtaining an optimal prediction interval through integrated learning training; obtaining the probability R of the TTC value falling in the interval based on the trained prediction interval, and evaluating the risk probability of the control failure according to the probability R; and introducing the probability R into an objective function of a double-layer model assisted by a deep confidence network agent, and adjusting the limit transmission capacity value. By means of the invention, a balance between adjustment costs and control risks can be achieved.

Description

Risk-aware deep learning-driven limit transmission capacity adjustment method

Technical Field

The invention relates to a risk-aware deep learning-driven limit transmission capacity adjustment method.

Background

The problem of preventive management of TTC requires not only a rapid perception of TTC, but also the formulation of TTC preventive adjustment strategies in minutes. Some researchers proposed using sensitivity techniques to adjust the cross-sectional flow state, however, the calculation of sensitivity is too coarse and many sets of predicted accidents are not considered in this study. In summary, there is currently little safe economic research on TTC prevention scheduling, and a new approach is needed to solve this problem. In recent years, some scholars have proposed a proxy-assisted (SA) optimization strategy. The strategy uses the agent rule of machine learning to replace high-dimensional nonlinear or complex differential equation constraint existing in the optimization model, thereby greatly reducing the solving complexity of the optimization model and being very suitable for the TTC prevention control model.

The TTC preventive control technology based on the SA will provide strong support for the dispatcher to make a power grid preventive control strategy, however, some inherent problems still need to be solved. For example, the machine learning rule embedded in the SA model cannot satisfy absolute accuracy, and its inherent error may cause the TTC control targeted for economic optimization to fail, and the system is still at an unstable operating point. In this regard, the scholars have proposed solutions. If research suggests that a certain margin is added into a control model, the system operation point is far away from a critical safety point, however, the scheme is difficult to ensure the economical efficiency of regulation and control, and the optimized convergence is reduced in practical application; there are also researchers who propose to quantify the prediction error with probability using ensemble learning, however, this scheme is only for classification type decision trees and the compatibility of machine learning methods and regression type problems remains to be studied.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a risk-aware deep learning-driven limit transmission capacity adjusting method, which comprises the following steps of;

embedding a limit transmission capacity predictor into an adjustment model to obtain a deep confidence network agent-assisted double-layer model;

step two, constructing a prediction interval based on a deep belief network, adjusting the prediction interval according to the coverage probability of the prediction interval, the normalized average bandwidth of the prediction interval and the accumulated bandwidth deviation, and obtaining the trained prediction interval through integrated learning training;

thirdly, obtaining the probability R of the TTC value falling in the interval based on the trained prediction interval, and evaluating the risk probability of control failure according to the probability R;

and step four, introducing the probability R into an objective function of a double-layer model assisted by the deep confidence network agent, and adjusting the limit transmission capacity value.

Further, the construction of the prediction interval comprises;

set training sample set

And PI, yielding the following formula:

adjusting the prediction interval through the prediction interval coverage probability, the prediction interval normalized average bandwidth and the accumulated bandwidth deviation; the prediction interval coverage probability indicates the probability that the target of the training sample set is covered by the prediction interval, and is calculated by adopting the following formula:

wherein, κ_iIs a boolean variable represented by the formula:

the normalized average bandwidth of the prediction interval is used for quantifying the degree of the deviation of the training target from the upper limit or the lower limit of the prediction interval, and is calculated by adopting the following formula:

the accumulated bandwidth deviation is calculated by the following formula:

wherein Z is a regularization factor.

Further, the prediction interval training comprises the following processes:

by integrationsTraining a prediction interval, adjusting the weight optimization prediction interval of the ensemble-based learner, wherein a decision variable is the weight of the ensemble-based learner and is defined as lambda,

wherein 2M represents the sum of the base learners participating in the prediction interval training; the training process of the prediction interval is an optimization process taking the following formula as a target:

by the importance factor

Converting the multi-objective optimization problem into a single-objective optimization problem:

further, the probability R is calculated by using the following formula:

introducing R into an objective function of a double-layer model assisted by a deep confidence network agent to obtain:

wherein, alpha is ∈ [0,1 ]]；

Is a normalized adjustment cost, an optimal integration weight lambda^*。

Further, the embedding of the extreme transmission capacity predictor into the two-layer model to obtain the two-layer model assisted by the deep confidence network agent includes the following processes:

the proxy assisted TTC adjusted two-layer model is represented by:

Lower level:β^*＝argmax(f(x,β))

wherein x and y are a control variable vector and a state variable vector, respectively; (x, y) represents a specific working condition; f (x) is the generator contribution adjustment cost; z (x, y) and H (x, y) are equality and inequality constraints, respectively;

representing a differential algebraic equation; -beta ^*0 or less represents a safety constraint based on the target feature value, where β^*The solved beta value is obtained;

target eigenvalue predictor Φ using deep belief-based network^e(x_e) Replacing the lower layer model to obtain a two-layer model assisted by the deep confidence network agent, which is shown as the following formula:

wherein the content of the first and second substances,

is the actual value of beta^*The predicted value of (2);

is a predicted value of the target value, i.e., a predicted target feature value.

The invention has the beneficial effects that: the interval prediction technology based on the DBN realizes the balance of adjustment cost and control risk.

Drawings

FIG. 1 is a schematic flow chart of a risk-aware deep learning driven extreme transmission capacity adjustment method;

FIG. 2 is a general framework of a proxy-assisted TTC adaptation model;

FIG. 3 is a schematic diagram of a description of control failure due to predictor error;

FIG. 4 is a schematic diagram of PIs-based control failure risk perception;

FIG. 5 shows a test scenario TC₁A power angle track diagram in the following optimization process;

FIG. 6 is a test scenario TC₂Power angle trace diagram in optimization process

FIG. 7 is a schematic view of a PIs curve;

FIG. 8 is a graphical comparison of adjustment cost and CFI index for a risk-aware method and an error-compensated method;

FIG. 9 is a graph of sensitivity for cost, risk balance for different methods.

Detailed Description

The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.

As shown in fig. 1, in most OPF problems, the transmission capacity is often regarded as a constant, so that the solution of the full linearization of the model can be facilitated. However, as the Operating Condition (OC) changes, the TTC also changes, which may cause a safety problem. In order to solve the problem, a feasible method is to use a double-layer model to solve, that is, a TTC calculation model is used as a lower layer model, and a TTC security constraint is added to an upper layer economic dispatch model. And the TTC safety constraint is that the TTC of the control section is always larger than the transmission power flow of the section. However, the convergence difficulty and heavy computational burden problems in solving the underlying TTC computational model make the TTC-adjusted two-layer model difficult to solve. Therefore, embedding the TTC predictor in the two-layer model instead of the underlying TTC computational model is a very efficient solution. The framework of this solution is shown in figure 2.

The proxy assisted TTC adjusted two-layer model may be represented by:

Lower level:β^*＝argmax(f(x,β)) (8b)

representing differential algebraic equations such as transient stability constraints and the like; -beta ^*0 or less represents a TTC-based safety constraint, where β^*Is obtained by solving the lower layer model, and the lower layer model is equivalent to the model (4). The last two equations in the model indicate that the profile transmission flow should be controlled not to exceed the TTC value.

Note that the underlying model is difficult to compute, so the DBN-based TTC predictor Φ is used^e(x^e) Instead of the lower layer model, a DBN surrogate-assisted bi-level model (DBN-SBM) may be obtained as shown in the following formula:

wherein the content of the first and second substances,

is the actual value of beta^*The predicted value of (2);

is a predicted value of the target value, i.e., a predicted TTC value.

2) Optimization solver of DBN-SBM:

on one hand, in order to ensure the accuracy of the final optimal scheme on the nonlinear power system; on the other hand, since the DBN is a typical large nonlinear system including multiple layers of nonlinear neurons, it is difficult to solve the DBN-SBM using a linear solver (e.g., Cplex, etc.), a new evolutionary computing algorithm, the symbiont search (SOS), will be used to solve the two-layer model. The flow of the SOS procedure can be summarized as the following steps: i) initializing; ii) global evolution (including three stages of symbiosis, commensalism and parasitism); iii) termination conditions. Based on the underlying SOS procedure, some improvements will be introduced into the SOS to improve its stability and robustness. The modified SOS algorithm for solving the TTC adjustment model is as follows:

i) improved initialization: in order to prevent the convergence rate from being reduced due to the randomly generated initial ecosystem, the initial ecosystem is generated by adopting a sweet spot set (GPS) Caizian;

ii) parallelized ecosystems: in order to improve the optimization performance of the SOS and ensure the diversity of the ecosystem, a classical ring migration parallel strategy is adopted to evolve the ecosystem in parallel;

iii) improved evolution strategies:

a) and (3) self-adaptive symbiosis stage: in the initial phase of evolution, the fitness of organisms is generally low. Therefore, a more global search strategy should be employed to efficiently explore the solution space near the optimal solution. After the evolution reaches a certain number of generations, the SOS needs to increase the randomness of searching so as to prevent the searching from falling into local optimum only in a certain limited space. Therefore, SOS at this stage employs the symbiotic mechanism as follows:

wherein ω ∈ [0,1 ]]Is an adaptive scalar factor; MV is a symbiotic vector, equal to (X)_i+X_j)/2；BF₁And BF₂Is a reciprocal factor whose value is randomly determined to be 1 or 2.

b) A co-habitation stage introducing random disturbance terms: the adaptive symbiotic phase will increase the convergence rate, however the global search capability of the SOS will also decrease. In order to achieve a balance between search rate and global search capability, while preventing SOS from falling into local optima, random perturbation terms are introduced to increase the randomness of SOS search in the co-habitation stage:

X_inew＝X_i+ψ(X_best-X_j)+ψ(X_k-X_i),k≠i≠j (10)

where ψ is a random scalar within the interval (-1, 1); x_kIs a randomly selected organism that serves to increase the diversity of the ecosystem.

iv) parasitic phase: the parasitic mechanism is mainly used to prevent the SOS algorithm from falling into local optima. First, a random selection of a creature X in the initial ecosystem is made_iBy randomly modifying X_iOne dimension of (a) produces a parasitic factor (PV). Then PV and X are mixed_iAnd (4) comparing, and preferentially retaining.

TTC adjustment of deep belief network driven perceptual risk:

the DBN-SBM is able to adjust the system from an unstable operating domain to a stable operating domain under the guidance of the TTC rules of the DBN mining, however, using only the DBN-SBM model may result in unreliable data-driven preventive control decisions and even completely erroneous preventive control decisions due to unavoidable errors of the conventional point prediction method.

As shown in FIG. 3, the initial condition of the system is operating in the unsafe region (when the power flow is greater than TTC, as shown on the left in FIG. 2), and DBN-SBM optimization is performed. After the optimization is completed, a preventive control strategy is implemented, and the result shows that the TTC predicted by the DBN is larger than the power flow (as shown in the right side of the figure 3). However, due to the presence of prediction error ζ, the actual TTC value (i.e., the

) Lower than the tidal flow value PF_l(λ′₀) I.e. in fact the system does not enter the secure operating domain. Therefore, to prevent control failures, system dispatchers prefer to employ conservative preventive control strategies while also being economical. One possible solution is to introduce the positive threshold tool TTC constraint directly, i.e. to rewrite the TTC safety constraint to

ε>0, and further can enable the DBN-SBM to obtain a larger TTC value after being optimized

The purpose of compensating the error zeta is achieved. However, the problem with this approach is that it is very difficult to find a value of ε that can just compensate for ζ, i.e., ε ═ ζ, due to uncertainty in ζ. Obviously, setting a relatively large value of ε can ensure that ε>ζ is a solution to this problem, however, an increase in the value of ε would obviously lead to an increase in the cost of tuning. Moreover, the value of ε may also require repeated experimental determinations for different operating conditions, which may result in additional computational costs. In summary, it is difficult to reasonably formulate a DBN-based interval prediction technique for epsilon values applicable to all scenes:

a typical Prediction Interval (PI) is a range of predicted intervals within which the actual target value will fall with a certain probability (i.e., confidence level). PI is limited by a lower limit

An upper limit

And a particular probability of 100 x (1-c)% composition, where c is the significance level and 100 x (1-c)% is the confidence level.

i) Indices of PIs:

suppose there is a set of training samples

And a special featureThe PI is defined as follows:

some criteria need to be proposed to optimally adjust the prediction interval. Generally, three indexes are used to calculate the quality of interval prediction, namely, a Predicted Interval Coverage Probability (PICP), a predicted interval normalized average bandwidth (PINAW), and an Accumulated bandwidth deviation (AWD).

a) PICP: the PICP index indicates the probability that the target of the training sample set is covered by the prediction interval, which can be calculated by the following formula:

wherein, κ_iIs a boolean variable, the definition of which is shown in equation (13). A higher value of PICP indicates a higher quality of the prediction interval.

b) AWD: the AWD is used to quantify the degree to which the training target deviates from the upper or lower limit of PI, and can be calculated by equations (14) and (15). A lower AWD indicates a higher quality prediction interval.

c) PINAW: psi (x) for a given set of samples^t) A prediction interval with an upper limit of positive infinity and a lower limit of negative infinity is selected, and the PICP and AWD values can be optimized. However, such a prediction interval cannot be usedProviding any useful information. Therefore, in order to construct a PI with high information degree, a PINAW needs to be introduced, as shown in formula (16). The smaller the PINAW value, the higher the quality of the prediction interval PI.

Where Z is a regularization factor.

ii) prediction interval PIs training:

the present patent trains PIs through ensemble learning, i.e., optimizes PIs by adjusting the weights of a large number of integrated base learners. PIs training is theoretically a multi-objective optimization problem, where the decision variables are the weights of the ensemble learner, defined as λ,

(where 2M represents the sum of the base learners participating in the training of PIs). The goal of PIs training is to construct the best quality PIs given c, whose training process can be defined as an optimization process targeting equation (17):

by some importance factor

The multi-objective optimization problem can be converted into a single-objective optimization problem:

the above problem can be solved using Particle Swarm Optimization (PSO). Additionally, ensemble learning is used to improve robustness and quality of PI. The pseudo code is as follows:

iii) TTC scheduling based on perceived risk of PIs:

it is mentioned above that it is difficult to determine whether the preventive control strategy obtained by solving the DBN-SBM model based on point estimation can successfully implement the system safety control. PIs can effectively solve this problem. The PIs can give a confidence level of the predictor, in other words, the PIs can give probability information that the actual TTC value falls within the interval, which can in turn be used to assess the risk of preventive control failure.

The DBN proxy-assisted bi-level model (DBN-SBM) is shown as follows:

wherein the content of the first and second substances,

is the actual value of beta^*The predicted value of (2);

is a predicted value of the target value, i.e., a predicted TTC value.

2) Optimization solver of DBN-SBM:

iii) improved evolution strategies:

X_inew＝X_i+ψ(X_best-X_j)+ψ(X_k-X_i),k≠i≠j (10)

where ψ is a random scalar within the interval (-1, 1); xk is a randomly selected organism used to increase ecosystem diversity.

As shown in FIG. 5, the light red-yellow squares represent a prediction interval

The actual TTC value will fall within this interval with a probability of 100 × (1-c)%. Even though the TTC prediction has been controlled to be greater than the tidal current by the DBN-SBM optimization program (as in the figure, of the right coordinate system)

Shown), the actual TTC value still falls into the unstable region with a certain probability R (as shown in the right coordinate system by the light red square region R). In other words, the risk probability of failure of preventive control can be perceived to some extent by calculating the magnitude of R. From FIG. 5, R can be calculated from the following equation:

to account for the balance of risk and cost, R is introduced into the objective function of DBN-SBM:

where α is a user-defined factor, α ∈ [0,1 ]]；

Is the normalized adjustment cost. For conservative preventive control, the model tends to set an α value greater than 0.5. Theoretically, setting α to 1 can ensure the success of the preventive control, however, leads to a high cost.

Note that because the control risk is added to the objective function, the original DBN-SBM model will be reconstructed as a new model that does not contain the underlying model, and therefore the risk-aware SA model can be expressed as (21):

the proposed DBN-integrated based PIs of this patent, BPNN, MLR and DBN based PIs will be used for comparative experiments. In particular, to ensure unbiased testing, the 4 PIs learning methods will be based on the same training sample set Ψ and test sample set Ψ^eTraining and testing are performed. Each PIs training algorithm is executed for 10 times, and the average value of PIs quality indexes is taken to evaluate the performance of each algorithm; the results after testing on the test sample set are shown in fig. 6.

The ACE index will be used to evaluate the quality of each prediction interval. As can be seen from fig. 6, it is evident that the prediction interval performance of TTC based on MLR is the worst, and its three performance indicators ACE, PINAW and AWD are 6.8e-3, 0.6931 and 0.0098, respectively. For DBN-based PIs, the performance levels were 5.1e-3, 0.6656, and 0.0096, respectively. For DBN integrated PIs, the performance levels were 3.4e-3, 0.6191, and 0.0076, respectively. From these performance index comparisons, it can be seen that DBN integrated PIs perform optimally. Therefore, DBN integrated PIs will be used in risk-aware TTC tuning models.

Cost and risk balance:

although the above tests demonstrate that the DBN-SBM can successfully control TTC at a particular OC, the DBN-SBM cannot guarantee successful implementation of preventive control when the system is operating at other unstable points. Thus, two methods that enable conservative control of TTC-i.e., a PIs-based risk-aware TTC tuning algorithm (PIs-based risk-aware method) and a epsilon-value-based predictive error compensation algorithm (the fixed-epsilon method) -will be used to optimally balance the tuning cost and the tuning risk. The reliability of the proposed method is evaluated using the Control Failure Index (CFI). CFI is calculated by the following formula:

wherein the content of the first and second substances,

indicating that the ith destabilized OC failed control after TTC regulation. If the actual value of TTC after adjustment is lower than the power flow, then

Otherwise, the reverse is carried out

Before verifying the TTC safety criteria, steady state constraints (e.g., generator contribution constraints) will first be verified. If these steady state constraints are out of limit, this control will also be considered to have failed, then

S^UIndicating the number of destabilizing conditions tested. In this example, an additional 200 destabilizing conditions, therefore S, are generated by random sampling^U＝200。

By stepping up the user-defined coefficient α from 0 to 1, the relationship between α, cost and risk is clearly shown. The results of risk-aware algorithm adjustment TTC are shown in fig. 7. In particular, cost

Is the average accommodation cost for all successfully controlled OCs. As shown in FIG. 7, the CFI decreases but at the same time as more weights favor reducing the risk of control failure

And (4) rising. It is worth noting that when α is 0, the method of perceived risk is equivalent to the cost-dominated DBN-SBM, so the tuning strategy cost is the lowest (i.e., $700.12) at this time, but the risk of control failure reaches 11.5%, indicating that such a control strategy is too risky for practical preventive control. When alpha is increased to 0.25, CFI reaches an acceptable value for the first time, namely CFI is 1.5%<2% at the same time

To rise to $1,888.99. By raising α to 1, the risk-dominated model will result in the system operating at an operating point that is too conservative. Although the CFI reached 1.5%, the cost was too high to reach $8,017.86, indicating that this strategy is not feasible. Therefore, in order to make a strategy with low cost and risk, the interval [0.2,0.5 ] is]The internal selection α is appropriate. Furthermore, it is worth noting that CFI cannot reach 0% because at some extremes OC the generator's adjustable capacity is so severely insufficient that system stability cannot be maintained by generator rescheduling alone.

Similarly, the error compensation method can be tested by increasing the value of ε step by step, and the test results are shown in FIG. 8. The increase of the value of epsilon leads to cost

But does not result in a monotonic decrease in CFI as expected. The error compensation method can only reach the minimum CFI of 3%, which is 1.5% higher than the method capable of sensing the risk. Furthermore, the CFI did not decrease when the ε value was increased from 0.1p.u. to 0.5p.u., but instead increased from 3% to 8.5%. We also found that most optimizers are difficult to converge when the value of epsilon is higher than 0.1p.u. That is, setting a higher value of ε may result in a reduced convergence of the error compensation method, but setting a smaller value of ε may not guarantee successful TTC adjustment. In other words, selecting an optimal value of ε may also require trial and optimization, which may place additional computational burden. Assuming that an optimal value of epsilon has been obtained, the error compensation method still has difficulty reaching the specific sensible windThe risk method has better CFI index. In general, risk-aware methods perform better than error-compensated methods in conservatively adjusting TTC. Figure 9 shows the comparison between the economics of the two methods, and the sensitivity to cost and risk.

As can be seen in fig. 9, when both methods reach the same CFI of 3% for the first time, the perceived risk method has an adjustment cost of $943.67, while the error compensation method has an adjustment cost of $1,244.94. The cost of using the risk-aware approach is reduced by a relative $ 301.27. Thus, the economic performance of the sensible risk method is also due to the error compensation method.

And (3) calculating the overhead:

the computation times for the different algorithms are shown in table 2:

TABLE 2 computational overhead of different methods

The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. A risk-aware deep learning driven limit transmission capacity adjustment method is characterized by comprising the following steps;

thirdly, obtaining the probability R that the limit transmission capacity value falls in the interval based on the trained prediction interval, and evaluating the risk probability of control failure prevention according to the probability R;

2. The risk-aware deep learning-driven extreme transmission capacity adjustment method according to claim 1, wherein the prediction interval construction comprises;

set training sample set

(ii) a And PI, yielding the following formula:

wherein the content of the first and second substances,

is a boolean variable represented by the formula:

wherein the PI is a prediction interval,

is the number of the samples and is the number of the samples,

in order to train the variables of the training,

is the target variable, c is the level of significance,

for the (i) th training variable,

is the ith target variable;

the accumulated bandwidth deviation is used for quantifying the degree of the deviation of the training target from the upper limit or the lower limit of the prediction interval, and is calculated by adopting the following formula:

the normalized average bandwidth of the prediction interval is calculated by adopting the following formula:

wherein the content of the first and second substances,

is a regularization factor.

3. The method of claim 1, wherein the prediction interval training comprises the following steps:

training a prediction interval through ensemble learning, adjusting the weight optimization prediction interval of the ensemble-based learner, wherein a decision variable is the weight of the ensemble-based learner and is defined as

Wherein, in the step (A),

represents the sum of the base learners participating in the prediction interval training; the training process of the prediction interval is an optimization process taking the following formula as a target:

by the importance factor

the PICP is the coverage probability of a prediction interval, the PINAW is the normalized average bandwidth of the prediction interval, and the AWD is the accumulated bandwidth deviation.

4. The method of claim 1, wherein the probability R is calculated by the following formula:

will be provided withRIntroducing an objective function of a double-layer model assisted by a deep confidence network agent to obtain:

wherein the content of the first and second substances,

；

is to normalize the adjustment cost and optimize the integration weight

And c is the significance level.

5. The method as claimed in claim 1, wherein the step of embedding the threshold transmission capacity predictor into the two-layer model to obtain the two-layer model assisted by the deep-confidence network agent comprises the following steps:

the proxy assisted limit transmission capacity adjustment two-layer model is represented by: