A Distributionally Robust Scheduling Method for Power Systems Against the Uncertainty of Atmospheric Pollutant Diffusion

Abstract

The present invention discloses a distributionally robust scheduling method for power systems aiming at the uncertainty of atmospheric pollutant diffusion, which includes the following steps: constructing a refined diffusion control model for atmospheric pollution emissions → establishing a distribution set of the uncertainty of meteorological conditions in the diffusion process of atmospheric pollution emissions → establishing a day-ahead unit commitment scheduling model for power systems considering the uncertainty of meteorological conditions → establishing a two-stage distributionally robust optimization method for the day-ahead unit commitment scheduling model of power systems. The present invention belongs to the technical field of day-ahead scheduling on the transmission side of power systems. Specifically, it can precisely describe the contribution of the pollutant emissions of units to the atmospheric pollutant concentration after a period of diffusion, thereby providing a basis for the control of atmospheric pollutants in power systems. At the same time, the unit commitment scheduling considers the uncertainty of meteorological conditions in the diffusion process, making the unit commitment scheduling plan have a certain green robustness, that is, the pollutant control effect can be guaranteed regardless of how the meteorological conditions change.

Description

Technical Field

[0001] The present invention belongs to the technical field of day-ahead scheduling on the transmission side of the power system, and specifically refers to a distributionally robust scheduling method for the power system aiming at the uncertainty of atmospheric pollutant diffusion. Background Art

[0002] Similar to climate warming, air pollution is also one of the main environmental problems caused by gaseous emissions. As a major energy consumption sector, the power industry emits a large amount of atmospheric pollutants such as SO2, NOx, and fine particulate matter, which has a significant impact on the regional air quality. Although the power industry has gradually deployed advanced and efficient desulfurization, denitrification, and dust removal facilities to reduce the emissions of atmospheric pollutants, full configuration or upgrading still requires a large amount of time and financial support. As one of the core tasks of the power system, optimal scheduling is an effective means to meet the load demand with efficient energy supply. By incorporating the impact of unit emissions on air pollution problems into the optimal scheduling of the power system, the power system can be guided to preferentially utilize low-pollution units, thereby improving the regional air quality. Summary of the Invention

[0003] In view of the above situation, to overcome the defects of the prior art, the present invention proposes a distributionally robust scheduling method for the power system aiming at the uncertainty of atmospheric pollutant diffusion. Since air pollution is mainly determined by the ground concentration of atmospheric pollutants in the region, the present invention first constructs a refined diffusion control model for atmospheric pollution emissions, which aims to reduce the increment of atmospheric pollutant concentration caused by the diffusion of power system emissions; for the uncertainty of meteorological conditions during the diffusion process of atmospheric pollution emissions, a distribution set is established based on K-means clustering and confidence sets, and the unit commitment scheduling decision needs to cope with the extreme distribution of meteorological condition uncertainty; finally, a unit commitment model for the power system considering meteorological condition uncertainty is established, and a two-stage distributionally robust optimization method is established for it to obtain the optimal unit commitment scheduling plan.

[0004] The technical solution adopted by the present invention is as follows: A distributionally robust scheduling method for the power system aiming at the uncertainty of atmospheric pollutant diffusion proposed by the present invention includes the following steps:

[0005] Construct a refined diffusion control model for atmospheric pollution emissions → Establish a distribution set for the uncertainty of meteorological conditions during the diffusion process of atmospheric pollution emissions → Establish a day-ahead unit commitment scheduling model for the power system considering meteorological condition uncertainty → Establish a two-stage distributionally robust optimization method for the day-ahead unit commitment scheduling model of the power system.

[0006] Implementing the distributionally robust scheduling method for the power system aiming at the uncertainty of atmospheric pollutant diffusion of the present invention includes the following contents:

[0007] Step 1: Construct a refined diffusion control model for air pollution emissions, considering pollutant settlement effects and ground reflection effects;

[0008] Step 2. For the uncertainty of meteorological conditions in the diffusion process of air pollution emissions, first, obtain the possible scenarios of this uncertainty based on Nataf-transformed Latin hypercube sampling. Secondly, establish a distribution set of the uncertainty of meteorological conditions in the diffusion process of air pollution emissions based on K-means clustering and confidence sets;

[0009] Step 3: Establish a day-ahead unit commitment scheduling model for the power system considering the uncertainty of meteorological conditions;

[0010] Step 4: Establish a two-stage distributionally robust optimization method for the day-ahead unit commitment scheduling model of the power system.

[0011] Furthermore, the specific steps for generating the distribution set in Step 2 are as follows: First, for the historical scenario set of observed meteorological conditions, use the K-means clustering method to generate K clusters. Secondly, use Nataf-transformed Latin hypercube sampling to obtain a sampling scenario set and update the K clusters. Finally, based on the confidence set theory, construct a distribution set of the uncertainty of meteorological conditions.

[0012] Even further, the specific solution steps of Step 3 are as follows:

[0013] Step 3.1: Optimize the first-stage master problem to determine the unit commitment and send it to the second-stage sub-problem;

[0014] Step 3.2: Optimize the second-stage sub-problem to determine the extreme distribution of the uncertainty of meteorological conditions in the diffusion process of air pollution emissions and upload it to the first-stage master problem;

[0015] Step 3.3: Repeat Step 3.1 and Step 3.2 until the objectives of the master problem and the sub-problem are consistent, and output the unit commitment obtained in the last step of the master problem as the optimal scheduling strategy.

[0016] The beneficial effects achieved by the present invention with the above structure are as follows: The invention can accurately describe the contribution of the pollutant emissions of units to the atmospheric pollutant concentration after a period of diffusion, thereby providing a basis for the control of atmospheric pollutants in the power system; at the same time, the unit commitment scheduling considers the uncertainty of meteorological conditions in the diffusion process, making the unit commitment scheduling plan have a certain green robustness, that is, no matter how the meteorological conditions change, the determined unit commitment can ensure the pollutant control effect. Description of the Drawings

[0017] Figure 1 It is a flowchart for constructing a distribution set of the uncertainty of meteorological conditions for a distributionally robust scheduling method of a power system for the uncertainty of atmospheric pollutant diffusion proposed by the present invention;

[0018] Figure 2 This is a flowchart of a two-stage distributionally robust optimization method for a power system distributionally robust scheduling method targeting the uncertainty of atmospheric pollutant diffusion proposed by the present invention.

[0019] The accompanying drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention, and do not constitute a limitation to the present invention. Detailed implementation manners

[0020] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention and the accompanying drawings. The scheduling cycle of the unit commitment scheduling model of the power system involved in this project is one day, the scheduling time interval is one hour, and the scheduling time period index is t. For the description of the unit emission diffusion process, the scheduling cycle can be further subdivided, and the diffusion time period index is τ.

[0021] Step 1, construct a refined diffusion control model for atmospheric pollution emissions:

[0022] At a certain time period, the contribution value of a certain generator i to the atmospheric pollutant concentration at monitoring point j is equal to the sum of the contribution values of emissions in all previous time periods to the atmospheric pollutant concentration, and the contribution value of the power system to the atmospheric pollutant concentration at monitoring point j is equal to the sum of the contribution values of all generators;

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] In the formula, c j,τ (β) is the contribution of the power system to pollutant β at monitoring point j during the time period; G i,j,(τ’,τ) (β) is the diffusion function, indicating the influence of the pollutants emitted during the τ' time period on the concentration at the subsequent τ time period; Q i,τ’ (β) is the mass of pollutant β emitted by generator i during the τ' time period; Formulas (2) to (4) calculate the diffusion function G, which depends on two elements; one element is the movement of the plume, i.e., [x i,(τ',τ) , y i,(τ',τ) , z i,(τ',τ), which is the plume Q i,τ’ (β) position at time τ; Another element is the free diffusion of the plume, which is reflected in the diffusion factor σ x,(τ',τ) , σ y,(τ',τ) , σ z,(τ',τ) . The diffusion factor is related to the diffusion time and the diffusion constants a α,τ , b α,τ and is shown in formula (4); The position of the plume is related to the wind intensity V around the generator i i,s and the wind direction θ i,s and is shown in formulas (5) and (6); [vxi, s, vyi, s, vzi, s] is the average wind speed on the plume diffusion path;

[0030] Pollutant sedimentation effect correction: Pollutants have a certain gravity, that is, the plume has a certain sedimentation speed, so the wind speed is corrected:

[0031]

[0032] In the formula, v0(β) is the sedimentation speed of pollutant β;

[0033] Ground reflection effect correction: When pollutants reach the ground, due to the low density of atmospheric pollutants, the ground has a large reflection effect on them; The "image method" can be used to calculate the contribution of the power system to the pollutant concentration at any point in space, which can be regarded as the superposition of two parts of the concentration, one part is the concentration contribution without considering the ground reflection, and the other part is the concentration contribution increased by the ground reflection effect; Therefore, the concentration contribution value at any point in space is corrected as:

[0034]

[0035]

[0036]

[0037] In the formula, G i,j,(τ’,τ) (β)' is the diffusion function generated by the ground reflection effect, and λ is the reflection coefficient of the ground for pollutants;

[0038] To adapt to unit scheduling, the contribution value c j,τ (β) of the atmospheric pollutant concentration is averaged, and the average value of the concentration contribution value for each scheduling period is obtained as:

[0039]

[0040] In the formula, NT is the number of diffusion periods included in each scheduling period;

[0041] Previously, unit commitment dispatch imposed constraints on the contribution value of atmospheric pollutant concentration. When this value exceeded a certain threshold, the system was given a certain penalty and added to the operating cost.

[0042] f air (β) = c(β)·λ(β), ∑ t ∑ j c j,t (β) ≤ Γ(β) + λ(β) (12)

[0043] In the formula, f air (β) is the penalty cost for pollutant β, c(β) is the penalty coefficient, Γ(β) is the concentration contribution value threshold, and λ(β) is the part exceeding the threshold;

[0044] Step 2: Establish the uncertainty distribution set of meteorological conditions during the diffusion process of air pollution emissions, such as Figure 1 and as shown in formulas (1) to (10), the uncertainties of meteorological conditions affecting pollutant diffusion include wind speed and wind direction;

[0045] Step 2.1: First, for the historical scenario set R of observed meteorological conditions, the K-means clustering method is used to generate K clusters, each cluster corresponding to a cluster center, and the reference probability density of each cluster scenario is p k,0 .

[0046] Step 2.2: Secondly, based on the historical scenarios, the Nataf transformation Latin hypercube sampling is used to obtain the sampling scenario set V. The sampling scenario set represents other scenarios where meteorological condition uncertainties may occur in addition to historical scenarios; The basic process of Nataf transformation Latin hypercube sampling is as follows: 1) First, for the independent standard normal distribution space, the original sampling matrix Z is obtained based on Latin hypercube sampling; 2) Based on the Nataf transformation, the sampling matrix Z in the independent standard normal distribution space is transformed into the sampling matrix X of meteorological conditions; The transformation formula is as follows:

[0047] ρ0 = L0L0 T (13)

[0048] Y = L0Z (14)

[0049] x i = C i -1 [Φ(y i )] (15)

[0050] In the formula, ρ0 is the correlation matrix of the sampling matrix Y, Y is the sampling matrix in the correlated standard normal distribution space, Φ() is the cumulative distribution function of the standard normal distribution, C i- 1is the inverse of the cumulative distribution function of the uncertainty variable of the i-th meteorological condition; the historical scenario set R of meteorological conditions is merged with the sampling scenario set V to obtain the total scenario set Ω = R ∪ V. Calculate the distance of each scenario in Ω from the clustering center in step 2.1, incorporate each scenario into the cluster with the closest distance, and update the K clusters.

[0051] Step 2.3, based on the confidence set theory, construct the distribution set Θ of the meteorological condition uncertainty ξ. The extreme distribution of the meteorological condition uncertainty includes the determination of scenarios and the determination of probability density. Each cluster will generate a scenario ξ k to form the extreme distribution, that is:

[0052]

[0053]

[0054] where ξ k,j is the scenario in the k-th cluster, and π k,j is a 0-1 variable. When π k,j equals 1, it means that the scenario is selected.

[0055] In addition, the extreme distribution of the meteorological condition uncertainty also needs to determine the probability density range of each cluster scenario:

[0056]

[0057]

[0058]

[0059] where p k is the probability density of the k-th scenario, M is the number of historical scenarios, and α is the confidence level.

[0060] Step 3, establish a day-ahead unit commitment scheduling model for the power system considering meteorological condition uncertainty:

[0061]

[0062]

[0063] where x ∈ χ is the unit commitment variable, y ∈ Y is the unit output within the day, c T x is the unit start-stop cost, F(x, ξ) is the day-ahead optimal scheduling cost of the system when the unit commitment x and the meteorological condition uncertainty ξ are determined, f is the unit operation cost coefficient, A, B, C, d, U are constants, and G ξ is the diffusion function matrix when the meteorological condition uncertainty ξ is determined;

[0064] Step 4, Two-stage distributionally robust optimization method for establishing a day-ahead unit commitment scheduling model of a power system: As Figure 2 shown, this method is mainly divided into the solution of the master problem and the sub-problem. The master problem determines the unit commitment and sends it to the sub-problem. The sub-problem determines the extreme distribution of meteorological condition uncertainty and uploads it to the master problem. When the convergence condition is reached, the optimization ends and the optimal unit commitment plan is output;

[0065] Step 4.1, Optimize the first-stage master problem to determine the unit commitment and send it to the second-stage sub-problem:

[0066]

[0067]

[0068] where Ω R is the set of extreme distributions generated by the sub-problem, is each clustering scenario included in the s-th extreme distribution, is the probability density corresponding to each clustering scenario. The objective determined by the master problem is the lower bound LB;

[0069] Step 4.2, Optimize the first-stage sub-problem to determine the extreme distribution and upload it to the first-stage master problem:

[0070]

[0071] where x * is the unit commitment variable sent by the master problem, p ∈ P is the constraint on the probability density p in formulas (18) - (20), and π ∈ Q is the constraint on the 0-1 variable π in formula (17); The solution of this problem is divided into two steps. First, calculate the intraday scheduling cost of all scenarios in the scenario set Ω, and select the scenario with the largest cost in each clustering to form the extreme distribution, and its corresponding π k,j is equal to 1, that is, determine the optimization of the inner-layer π. Let the worst scenario of each clustering be ξ k ; Second, optimize p by taking the cost of the clustering scenario as a constant to maximize the cost expectation, that is, complete the optimization of the outer-layer p; Then the extreme distribution is composed of each clustering scenario ξ k and the corresponding probability density p k ; The objective determined by the sub-problem is the upper bound UB.

[0072] Step 4.3, When UB - LB ≤ εLB, where ε is a very small constant, that is, it means that the objectives of the master and sub-problems are consistent, the algorithm converges, and the unit commitment obtained in the last step is output as the optimal scheduling plan.

[0073] The above-described embodiments merely represent one implementation manner of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent for the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the patent for the present invention shall be subject to the appended claims.

Claims

1. A distributionally robust scheduling method for power systems against the uncertainty of atmospheric pollutant diffusion, characterized in that: It includes the following steps: Step 1: Construct a refined diffusion control model for air pollution emissions, considering pollutant settlement effects and ground reflection effects: During a certain time period, the contribution value of generator i to the concentration of air pollutants at monitoring point j is equal to the sum of the contribution values of emissions in all previous time periods to the concentration of air pollutants, and the contribution value of the power system to the concentration of air pollutants at monitoring point j is equal to the sum of the contribution values of all generators; where c j,τ (β) is the contribution of the power system to pollutant β at monitoring point j during a time period; G i,j,(τ’,τ) (β) is the diffusion function, representing the influence of pollutants emitted during τ' on the concentration during the subsequent τ; Q i,τ’ (β) is the mass of pollutant β emitted by generator i during τ'; Formulas (2) to (4) calculate the diffusion function G, which depends on two elements; one element is the movement of the puff, i.e., [x i,(τ',τ) , y i,(τ',τ) , z i,(τ',τ) , which is the position of the puff Q i,τ’ (β) at time τ; the other element is the free diffusion of the puff, which is reflected in the diffusion factors σ x,(τ',τ) , σ y,(τ',τ) , σ z,(τ',τ)； The diffusion factors are related to the diffusion time and diffusion constants a α,τ , b α,τ as shown in formula (4); the position of the puff is related to the wind speed V i,s and wind direction θ i,s around generator i, as shown in formulas (5) and (6); [vxi,s, vyi,s, vzi,s] is the average wind speed on the puff diffusion path; Pollutant settlement effect correction: Pollutants have a certain gravity, that is, the smoke plume has a certain settlement speed, so the wind speed is corrected: In the formula, v0(β) is the settlement speed of pollutant β; Ground reflection effect correction: When pollutants reach the ground, due to the low density of air pollutants, the ground has a great reflection effect on them; the "mirror image method" can be used to calculate the contribution value of the power system to the concentration of pollutants at any point in space, which can be regarded as the superposition of two parts of concentrations. One part is the concentration contribution without considering ground reflection, and the other part is the increased concentration contribution due to ground reflection; therefore, the concentration contribution value at any point in space is corrected as: where G i,j,(τ’,τ) (β)' is the diffusion function generated by the ground reflection effect, and λ is the reflection coefficient of the ground for pollutants; To adapt to unit scheduling, the contribution value c of atmospheric pollutant concentration j,τ (β) is averaged, and the average value of the concentration contribution value for each scheduling period is obtained as: In the formula, NT is the number of diffusion time periods included in each scheduling time period; The day-ahead unit commitment scheduling constrains the contribution value of air pollutant concentration. When its value exceeds a certain threshold, a certain penalty is given to the system and added to the operating cost; f air (β) = c(β)·λ(β), ∑ t ∑ j c j,t (β) ≤ Γ(β) + λ(β) (12) where f air (β) is the penalty cost for pollutant β, c(β) is the penalty coefficient, Γ(β) is the concentration contribution value threshold, and λ(β) is the part exceeding the threshold; Step 2: For the uncertainty of meteorological conditions in the air pollution emissions diffusion process, first, based on the Nataf transformation Latin hypercube sampling, obtain the possible scenarios of this uncertainty. Secondly, based on K-means clustering and confidence sets, establish a distribution set of the uncertainty of meteorological conditions in the air pollution emissions diffusion process; Step 3: Establish a day-ahead unit commitment scheduling model for the power system considering the uncertainty of meteorological conditions; Step 4: Establish a two-stage distributionally robust optimization method for the day-ahead unit commitment scheduling model of the power system: Step 4.1, optimize the first-stage master problem to determine the unit commitment and send it to the second-stage sub-problem; where, Ω R is the set of extreme distributions generated by sub-problems, is each clustering scenario included in the sth extreme distribution, is the probability density corresponding to each clustering scenario; the objective determined by the main problem is the lower bound LB; Step 4.2, optimize the first-stage sub-problem to determine the extreme distribution and upload it to the first-stage master problem; where x * is the unit commitment variable issued by the master problem, p ∈ P is the constraint on the probability density p in formulas (18)-(20), and π ∈ Q is the constraint on the 0-1 variable π in formula (17); The solution of this problem is divided into two steps. First, calculate the intraday scheduling cost of all scenarios in the scenario set Ω, and select the scenario with the maximum cost from each cluster to form the extreme distribution, and the corresponding π k,j is equal to 1, that is, determine the optimization of the inner layer π, and let the worst-case scenario of each cluster be ξ k ; Second, optimize p with the cost of the clustered scenarios as a constant to maximize the expected cost, that is, complete the optimization of the outer layer p; Then the extreme distribution is composed of the clustered scenarios ξ k and the corresponding probability density p k ; The objective determined by the sub-problem is the upper bound UB. Step 4.3, when UB - LB ≤ εLB, where ε is a very small constant, that is, it means that the objectives of the master and sub-problems are consistent, the algorithm converges, and the unit commitment obtained in the last step is output as the optimal scheduling plan.

2. A distributionally robust scheduling method for a power system against the uncertainty of air pollutant diffusion according to claim 1, characterized in that: The specific steps for generating the distribution set in Step 2 are as follows: First, for the historical scenario set of observed meteorological conditions, use the K-means clustering method to generate K clusters; secondly, use the Nataf transformation Latin hypercube sampling to obtain the sampling scenario set and update the K clusters; finally, based on the confidence set theory, construct a distribution set of the uncertainty of meteorological conditions.

3. A distributionally robust scheduling method for a power system against the uncertainty of atmospheric pollutant diffusion according to claim 1, characterized in that: The specific solution steps of Step 3 are as follows: Step 3.1: Optimize the first-stage master problem to determine the unit commitment and send it to the second-stage sub-problem; Step 3.2: Optimize the second-stage sub-problem to determine the extreme distribution of the uncertainty of meteorological conditions in the air pollution emissions diffusion process and upload it to the first-stage master problem; Step 3.3: Repeat Step 3.1 and Step 3.2 until the goals of the main problem and the sub-problems are consistent, and output the unit commitment obtained from the main problem in the last step as the optimal scheduling strategy.

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