Dynamic recursion-multi-stage robust risk scheduling method for new energy power system

Abstract

The invention discloses a dynamic recursion-multi-stage robust risk scheduling method for a new energy power system. The method comprises the following steps: establishing a system operation security constraint; establishing an operation risk model, wherein the operation risk comprises a new energy non-consumption risk and a load shedding risk; establishing a dynamic recursion-multi-stage robust optimization model by taking operation risk minimization as a target according to system operation security constraints and an operation risk model; and solving the model by adopting a fast robust dual dynamic programming algorithm to obtain an optimal scheduling strategy. The model of the invention follows the unpredictability of the scheduling decision and keeps the robustness, and the accuracy of the decision process description is improved. The model integrates a dynamic uncertainty set based on conditional value-at-risk, and can adaptively adjust the boundary of the uncertainty set according to the operation risk level of the system. A fast robust dual dynamic programming solving algorithm is provided, the dynamic recursion-multi-stage robust optimization model can be efficiently solved, and a high-quality decision result is obtained.

Description

Technical Field

[0001] The present invention relates to the technical field of energy scheduling, and in particular to a dynamic recursive-multi-stage robust risk scheduling method for a new energy power system. Background Art

[0002] Under the "dual carbon" initiative, renewable energy capacity is rapidly expanding to mitigate global warming caused by excessive fossil fuel consumption, as it can provide zero-carbon electricity. However, the inherent variability and uncertainty of renewable energy make it difficult for power systems to incorporate it. To address the uncertainty of renewable energy, previous studies have proposed modeling the power system optimal scheduling problem as a two-stage stochastic optimization model. However, due to the computational complexity and the requirement for precise distributions of random variables, stochastic optimization models are difficult to apply in practice. An alternative approach is to formulate the scheduling decision problem as a two-stage robust optimization model. This model uses a "max-min" operator to filter out the worst-case scenario, thereby reducing the computational burden. Due to this, two-stage robust optimization models are frequently used to model the operation of uncertain renewable energy power systems and have been used to provide robust scheduling decisions. However, scheduling methods based on two-stage robust optimization violate the unpredictability of decision-making under uncertain renewable energy evolution, which has been well-documented in previous studies. Simply put, the second-stage decision of the two-stage scheme is made with full knowledge of all uncertain future parameters. In practice, the power system dispatcher's decision depends solely on the uncertainty of the current period. Therefore, the two-stage plan overestimates the power system's ability to adapt to renewable energy.

[0003] To accommodate the unpredictability of scheduling decisions, existing research has expanded the two-stage robust optimization scheduling model into a multi-stage robust optimization model based on the timeline. Specifically, the number of stages is increased to equal the number of scheduling periods. This changes the scheduling paradigm from the single-layer "max-min" structure of the two-stage robust optimization to a nested, multi-layer "max-min" structure, exponentially increasing model complexity. Existing solutions use affine rules to map unit output to a linear function of the actual renewable energy power. To improve optimality, piecewise affine rules and polynomial affine rules have also been proposed. While various affine rules appear to offer a feasible approach to multi-stage robust optimization models, it should be emphasized that they are inherently conservative approximations that oversimplify the original model and reduce the quality of the decision results. Recent research in the field of operations research transforms the multi-stage robust optimization model into a dynamic recursive structure and solves it using a sequential decomposition method, which circumvents the imprecision of affine methods. However, this approach is designed for logistics problems and has been rarely explored in the field of uncertain optimal scheduling of power systems. Furthermore, existing robust optimization models for power system dispatch primarily employ predefined box-like uncertainty sets, making it difficult to arrive at dispatch decisions that balance robustness and economy. The question of how to set an uncertainty set that can be adaptively adjusted based on system state remains an urgent one. Summary of the Invention

[0004] The present invention mainly solves the problems that the existing scheduling methods do not follow the unexpectedness of scheduling decisions, reduce the quality of decision results, and fail to balance robustness and economy, and provides a dynamic recursive-multi-stage robust risk scheduling method for new energy power systems.

[0005] The above technical problems of the present invention are mainly solved by the following technical solutions: A dynamic recursive multi-stage robust risk scheduling method for a new energy power system, comprising the following steps: Establishing system operation security constraints; Establish an operational risk model, which includes the risk of unabsorbed renewable energy and the risk of load shedding; Based on the system operation safety constraints and operation risk model, a dynamic recursive-multi-stage robust optimization model is established with the goal of minimizing operational risk; A fast and robust dual dynamic programming algorithm is used to solve the model and obtain the optimal scheduling strategy.

[0006] This paper proposes a dynamic recursive multi-stage robust optimization model that respects the unpredictability of scheduling decisions while maintaining robustness, improving the accuracy of the decision-making process compared to existing research. The dynamic recursive multi-stage robust optimization model integrates a dynamic uncertainty set based on conditional value at risk, which can adaptively adjust the boundaries of the uncertainty set based on the system's operational risk level. A fast robust dual dynamic programming solution algorithm is proposed, which can efficiently solve the dynamic recursive multi-stage robust optimization model and obtain high-quality decision results.

[0007] As an optimal solution, the system operation safety constraints include the power generation constraint model of dispatchable thermal power units, the output power model of new energy power generation, the charge state model of the energy storage system, and the power balance model of the entire network.

[0008] As an optimal solution, the power generation constraint model of dispatchable thermal power units includes upper and lower limits on power generation, as well as ramp restrictions. The start or shutdown status of the thermal power units is determined by the start and stop plan determined a day ago.

[0009] The power generation of dispatchable thermal power units is subject to upper and lower limits of power generation, as well as ramp restrictions. The start or shutdown status of the unit is determined by the currently determined start and stop plan.

[0010] As an optimal solution, the renewable energy power generation output power model includes a relationship between the predicted available renewable energy power and the uncertainty set boundary, the grid-connected wind power does not exceed the limit of the maximum available wind power, and the definition of the uncertainty set boundary of the actual measured wind power.

[0011] The output power of renewable energy generation is represented by the following relationship, which includes the relationship between the predicted available renewable energy power and the boundary of the uncertainty set, the relationship that restricts the grid-connected wind power to not exceed the maximum available wind power, which fluctuates within the uncertainty set, and the relationship between the actual measured wind power and the boundary of the uncertainty set.

[0012] As a preferred solution, the energy storage system state of charge model includes restrictions on the energy storage state of charge and a formula for energy storage state of charge transformation.

[0013] This solution uses a linear energy storage operation model to characterize the state of charge (SOC) of the energy storage system. This model approximates the SOC transitions and ignores the charging and discharging efficiency parameters of the energy storage. A correction function is used to refine the SOC deviation caused by ignoring efficiency. This correction function is not used as a constraint and is calculated within each adjacent stage of the established dynamic recursive multi-stage robust optimization model, without affecting the model's linearity.

[0014] As a preferred solution, the power balance model of the entire network includes the relationship between the phase angle difference and the power flow between the connection nodes, the power flow limit of each transmission line, and the node power balance formula.

[0015] The DC power flow is used to model the power balance of the entire network, including the relationship between the phase angle difference between the connected nodes and the power flow. The power flow restriction of each transmission line limits the power flow of each transmission line to within the capacity limit. The node power balance formula specifies the node power balance.

[0016] As a preferred option, the risk of non-absorption of new energy is that the test value of new energy power generation is between the upper limit of the uncertainty boundary and the upper limit of the available power generation of the new energy generator set, and the difference between the test value of new energy power generation and the upper limit of the uncertainty boundary is integrated and calculated.

[0017] Operational risk is defined as the expected value of the risk of non-absorption of renewable energy and the risk of load shedding. When the renewable energy power exceeds the uncertainty boundary of the system, it is usually established based on the probability distribution function of the renewable energy power, which is obtained through historical forecast error data.

[0018] The relationship between the uncertainty boundary and operational risk is that due to prediction errors, when the actual renewable energy power on a given day is greater than the upper limit of the uncertainty boundary, the renewable energy will not be absorbed.

[0019] As a preferred solution, the load shedding risk is that the test value of the renewable energy power generation is between zero and the lower limit of the uncertainty boundary, and the difference between the lower limit of the uncertainty boundary and the test value of the renewable energy power generation is integrated and calculated.

[0020] The relationship between the uncertainty boundary and operational risk also includes that when the actual renewable energy power is less than the lower limit of the uncertainty boundary, load shedding will occur, and emergency scheduling will be required to restore the operational feasibility of the system.

[0021] As a preferred solution, a dynamic recursive multi-stage robust optimization model is established, including: By minimizing the expected operational risk brought by unacceptable wind energy and considering the worst case scenario to ensure operational feasibility, a multi-level optimization problem is established, which is restated in a compact problem and equivalently converted into a dynamic recursive form.

[0022] According to the system operation security constraints and operation risk model, the multi-period dispatch decision problem of the power system is modeled as a dynamic recursive-multi-stage robust optimization model.

[0023] As a preferred solution, a fast robust dual dynamic programming algorithm is used to solve the model, specifically including: Upper and lower bounds are introduced for the operating cost function of stage t. By refining the upper bound, the worst uncertainty of new energy involved in the lower bound is screened out, and the global optimal solution of the multi-stage robust optimization model is achieved. The lower bound is corrected by adding Benders cutting planes, and the upper bound is corrected by approximate convex hull.

[0024] Because the dynamic programming framework is employed, the model is converted into a dynamic recursive form that can be recursively solved in a hierarchical manner. For traditional dynamic recursive multi-stage problems, nested Benders cuts and random sequence decomposition can be used to achieve a global optimal solution, constructing the lower bound of the cost function using the cutting plane. However, in the dynamic recursive multi-stage robust optimization model of the present invention, using only the lower bound of the cost function cannot handle the nested max operator, which represents the worst-case uncertainty realization.

[0025] To solve the dynamic recursive multi-stage robust optimization model, a fast robust dual dynamic programming algorithm is proposed. This algorithm first introduces upper and lower bounds on the running cost function of stage t, constructed using a convex hull and a hyperplane, respectively. This dual-bound solution effectively identifies the worst-case scenarios involving new energy uncertainty in the lower bound by refining the upper bound, thereby achieving a global optimal solution for the multi-stage robust optimization model. The upper and lower bounds are iteratively refined until the difference between them is smaller than a criterion. This is achieved by recursively solving the lower and upper approximation problems. The lower bound is corrected by adding Benders cutting planes, while the upper bound is corrected using an approximate convex hull.

[0026] Therefore, the advantages of the present invention are: 1. A dynamic recursive-multi-stage robust optimization model is proposed, which respects the unpredictability of scheduling decisions and maintains robustness, and improves the accuracy of decision-making process description compared with existing research.

[0027] 2. Based on the dynamic recursive-multi-stage robust optimization model, a dynamic uncertainty set based on conditional value at risk is integrated, which can adaptively adjust the boundary of the uncertainty set according to the operating risk level of the system.

[0028] 3. A fast robust dual dynamic programming solution algorithm is proposed, which can efficiently solve the dynamic recursive-multi-stage robust optimization model and obtain high-quality decision results. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a schematic diagram comparing the geometric forms of the upper boundary correction using the approximate convex hull method and the traditional convex hull method in the present invention.

[0030] Figure 2 This is a topology diagram of a test system exemplified in an embodiment of the present invention.

[0031] Figure 3 It is a graphical comparison diagram of the method of the present invention and the method that does not follow the unexpected scheduling.

[0032] Figure 4 It is a schematic diagram of the uncertainty set and scheduling decision as well as the total unconsumed new energy and load shedding conditions in the simulation of an embodiment of the present invention. DETAILED DESCRIPTION

[0033] The technical solution of the present invention will be further specifically described below through embodiments and in conjunction with the accompanying drawings.

[0034] Example: This embodiment provides a new energy power system dynamic recursive multi-stage robust risk scheduling method, such as Figure 1 As shown, the following steps are included: S1. Establish system operation security constraints; System operation safety constraints include the power generation constraint model of dispatchable thermal power units, the output power model of new energy power generation, the charge state model of the energy storage system, and the power balance model of the entire network.

[0035] The generation capacity constraint model for dispatchable thermal power units includes upper and lower limits on generation capacity, as well as ramping restrictions. The startup or shutdown status of the thermal power units is determined by the start-up and shutdown plan determined the day before. The generation capacity of dispatchable thermal power units is subject to upper and lower limits on generation capacity, as well as ramping restrictions. The startup or shutdown status of the units is determined by the currently determined start-up and shutdown plan. The model is specifically expressed using the following formula: in, represents the upper limit of the power generation capacity of thermal power unit g, P g Indicates the lower limit of the power generation of thermal power unit g, I g,t Indicates the switching state of thermal power unit g during period t, P g,t represents the power generation of thermal power unit g during period t, Indicates the rising rate limit of the thermal power unit g, Indicates the drop rate limit of thermal power unit g, g represents the thermal power unit index,

[0036] The output power model of renewable energy power generation includes the relationship between the predicted available renewable energy power and the uncertainty set boundary, the restriction that the grid-connected wind power does not exceed the maximum available wind power, the relationship between the power fluctuation within the uncertainty set, and the definition of the uncertainty set boundary of the actual measured wind power. The model is specifically expressed by the following formula: Among them, Aw q,t Indicates the available wind power, represents the upper limit of available wind power output predicted a day ago, It represents the lower boundary of available wind power output predicted a day ago. Indicates the upper limit of the available power generation capacity of the new energy unit q, q represents the index of the new energy unit, Pw q,t represents the power generation of the new energy unit q during period t, The output of the new energy unit q during period t is an uncertain variable that can obtain the lower bound of the wind power forecast value. It represents the output of the new energy unit q in period t as an uncertain variable that is the upper bound of the wind power forecast value.

[0037] Formula (13) defines the relationship between the predicted available renewable energy power and the uncertainty set boundary. Formula (14) limits the grid-connected wind power to no more than the maximum available wind power, which fluctuates within the uncertainty set. Formula (15) defines the boundary of the uncertainty set for the measured wind power.

[0038] The energy storage system state of charge model includes the energy storage state of charge limit and the energy storage state of charge transformation formula. The specific expression is as follows: Among them, Soc e,t Indicates the charging state of energy storage e during period t, Indicates the upper limit of the energy storage e charging state, Soc e Indicates the lower limit of energy storage e charging state, Pe e,t represents the charging and discharging power of the energy storage e during period t, represents the energy storage charging efficiency, Indicates the energy storage discharge efficiency, C e Represents the total capacity of energy storage e, e represents the energy storage index,

[0039] The energy storage system state of charge model uses a linear energy storage operation model to characterize the state of charge of the energy storage system, where Pe e,t The positive or negative value of represents the charge or discharge of the energy storage e. The state of charge of the energy storage is limited by formulas (16) and (17). Formula (18) is an approximate calculation for modeling the change of the state of charge of the energy storage, ignoring the charging and discharging efficiency parameters of the energy storage. The correction function is used to refine the state of charge deviation caused by ignoring the efficiency. The correction function is expressed as follows: The correction function is not used as a constraint, but is calculated within the interval of each adjacent stage of the dynamic recursive-multi-stage Luban optimization model established later, so the max and min operators will not affect the linearity of the model.

[0040] The power balance model for the entire network includes the relationship between the phase angle difference between connected nodes and the power flow, the power flow limit of each transmission line, and the node power balance formula. The specific expression is as follows: Among them, θ h,t represents the phase angle of node h during period t, θ k,t represents the phase angle of the grid node k during period t, x hk represents the impedance of the grid line hk, represents the upper limit of the node phase angle, θ represents the lower limit of the node phase angle, F hk,t represents the power flow of line hk during period t, represents the upper limit of the transmission line hk capacity, F hk represents the lower limit of the transmission line hk capacity, L d,t represents the load demand of node d during period t, h, k represent the grid node index, hk represents the transmission line index, d represents the load index, represents the set of lines from node h, represents the set of routes to node h, represents the positive unbalanced power of the grid node h during period t, represents the negative unbalance power of the grid node h during period t, The set of units connected to the grid node h, The energy storage set connected to the grid node h, The set of wind turbines connected to the grid node h, Represents the set of loads connected to the grid node h.

[0041] The DC power flow is used to model the power balance of the entire network. Formulas (20) and (21) characterize the relationship between the phase angle difference between the connected nodes and the power flow. Formula (22) limits the power flow of each transmission line to the capacity limit. Formula (23) stipulates the node power balance.

[0042] S2. Establish an operational risk model. Operational risks include the risk of unabsorbed new energy and the risk of load shedding.

[0043] Operational risk is defined as the expected value of the risk of unabsorbed renewable energy and the risk of load shedding. When renewable energy power exceeds the uncertainty boundary of the system, it is usually established based on the probability distribution function of renewable energy power, which is obtained from historical forecast error data. The relationship between uncertainty boundary and operational risk is as follows. Due to forecast error, the actual renewable energy power on that day is greater than the upper limit of the uncertainty boundary. On the contrary, when the actual power of new energy is less than When the load is cut off, emergency dispatch is required to restore the operational feasibility of the system. According to the definition of operational risk, the risk of non-absorption of new energy is the difference between the test value of new energy power generation and the upper limit of the uncertainty boundary when the test value is between the upper limit of the uncertainty boundary and the upper limit of the available power generation of the new energy generator set, and the integral calculation is performed on the difference between the test value of new energy power generation and the upper limit of the uncertainty boundary. The risk of load shedding is the difference between the test value of new energy power generation and the lower limit of the uncertainty boundary when the test value is between zero and the lower limit of the uncertainty boundary, and the integral calculation is performed on the difference between the lower limit of the uncertainty boundary and the test value of new energy power generation. Specifically, the risk of non-absorption of new energy and the risk of load shedding are calculated using the following formulas respectively: in, Indicates the risk coefficient of new energy consumption operation. Indicates the load shedding risk factor for absorbing operation, Represents the measured value of renewable energy power generation, represents the probability of power generation.

[0044] Since the operational risk definitions (1) and (2) contain complex integral terms, a piecewise linear approach is introduced to reformulate them into a tractable model. Since operational risk is always convex for different types of probability density functions, this tractable operational risk model is valid for any wind energy probability density function. Taking the case of unabsorbed renewable energy as an example, the first step is to relax formula (1) into an inequality: Since the objective function is to minimize operational risk, after optimization, formula (3) will be equal, that is, formula (1) and formula (3) are equivalent. Formula (3) is further piecewise linearized as follows: Where γ represents the ordinal number of the piecewise linearization method, represents the operational risk constant coefficient, which is calculated as follows: in, and They represent the intermediate parameters of the piecewise linearization method, and κ represents the auxiliary variable.

[0045] Similarly, the load shedding risk can be reformulated using the following tractable formula: S3. Based on the system operation safety constraints and operation risk model, a dynamic recursive-multi-stage robust optimization model is established with the goal of minimizing operational risks.

[0046] Based on the above system operation security constraints and operation risk model, the multi-period dispatch decision problem of the power system is modeled as a dynamic recursive-multi-stage robust optimization model.

[0047] By minimizing the expected operational risk brought by unacceptable wind energy and considering the worst case scenario to ensure operational feasibility, a multi-level optimization problem is established, which is restated in a compact problem and equivalently converted into a dynamic recursive form.

[0048] Specifically, the WAC range can be obtained by minimizing the expected operational risk caused by unacceptable wind energy. This requires considering the worst case scenario to ensure operational feasibility, which leads to a multi-level optimization problem as shown in the following formula: in, In the multi-level optimization problem (24), the outer “min” problem ensures the optimality of the uncertainty bound in terms of the system operation risk. The inner “max-min” problems are nested sequentially in t∈[1:T], which guarantees that within the acceptable uncertainty set w t Within the system, any output of new energy will not cause system power imbalance.

[0049] For the sake of brevity, the above recursive-multi-stage robust optimization scheduling problem can be restated in a compact problem as follows: in, w、 A, B1, D t 、E t 、F t They represent the coefficient matrices in the compact form of the optimization model, p1(ξ1) is the scheduling decision variable, ξ1 is the uncertain variable, Ω represents the operational risk boundary level set, Φ represents the feasible set of scheduling decisions, Ξ represents the uncertain set of energy generation, Represents a set of n-dimensional real variables.

[0050] The aforementioned "max-min" operator screens out the worst-case renewable energy generation scenarios to determine sufficiently safe uncertain boundary results and ensure system feasibility. Compared to the two-stage robust optimization model, the "max-min" operator is sequentially expanded into multiple stages, following the unexpected evolution of uncertainty realization.

[0051] In order to p t and ξ t From the complex affine relation p t (ξ t ), and convert the problem (25) into a dynamic recursive form equivalently, as follows: Where h represents the constant term on the right side of the compact form of the optimization model, It is the pre-stage question Q P The worst-case operating cost function is used to measure the overall operating risk of the uncertainty set boundary w on the entire intraday system operation.

[0052] Calculated by the following formula:

[0053] According to the dynamic recursive paradigm, w is sent as a state variable to the system to run the problem (Q1 to Q T ), starting from the first stage problem, the formula is as follows: Among them, ω1 represents the auxiliary variable that copies w into the relaxed form, and e1 represents the selection matrix that selects w1 from w.

[0054] Operation cost function of system operation problem Where t≥2 represents the worst case operation strategy and uncertainty set decision (ω t-1 ,p t-1 ) can be calculated by the following formula: where Q t (ω t-1 ,p t-1 ξ t ) is defined as follows: In equations (27) and (29), the constraints ω1 = w and will solve for Q P The obtained uncertainty boundary decision w is copied into the state space of each stage problem. This means that in the proposed scheduling model, not only the variables p representing the system operating state (such as the unit ramping state)t , and the auxiliary variable ω t It is also a state variable.

[0055] S4. Use the fast robust dual dynamic programming algorithm to solve the model and obtain the optimal scheduling strategy.

[0056] Upper and lower bounds are introduced for the operating cost function of stage t. By refining the upper bound, the worst uncertainty of new energy involved in the lower bound is screened out, and the global optimal solution of the multi-stage robust optimization model is achieved. The lower bound is corrected by adding Benders cutting planes, and the upper bound is corrected by approximate convex hull.

[0057] Due to the dynamic programming framework, problems (26)-(29) can be solved recursively by decomposition. For traditional dynamic recursive multi-stage problems, nested Benders cuts and random sequence decomposition can be used to achieve the global optimal solution, and the cost function can be constructed by cutting planes. However, in the dynamic recursive-multi-stage robust optimization model of the present invention, only using the lower bound of the cost function cannot handle the nested "max" operator, which represents the worst-case uncertainty realization.

[0058] In order to solve the dynamic recursive-multi-stage robust optimization scheduling model, the present invention adopts a fast robust dual dynamic programming algorithm. First, the operating cost function of stage t is Introducing upper and lower boundaries and satisfy and Constructed by convex hull and hyperplane respectively, this solution method based on double boundaries can effectively screen out The uncertainty of the new energy involved is the worst, and the global optimal solution of the multi-stage robust model is achieved. and are iteratively refined until the gap between them is smaller than a criterion, which is achieved by recursively solving the lower and upper approximation problems Q t and to be completed.

[0059] The upper approximation problem is as follows: The following approximation problem is as follows: The implementation of the fast robust dual dynamic programming algorithm consists of two processes: forward pass and backward pass. In the forward pass, from the pre-stage (Q P ) to stage T(Q T ), solve the problem To generate the worst-case uncertainty realization ξ t and by in the scene ξ t Solve the following problem Q t (ξ t ) to determine the decision sampling point [ω t ;p t ]. The backward pass generates valid interior points and cutting planes to correct and Once the upper bound reaches the lower bound, the algorithm terminates. Correct this by adding a Benders cut: in, ω t and p t They are the ones obtained from the forward pass just completed Q t (ξ t ) is the optimal solution. This is the problem in the backward pass Q t+1 (ξ t+1 ), Indicates a problem Q t+1 (ξ t+1 )middle[ ω t ; p t ]’s shadow price.

[0060] For the upper bound in problem (30) The correction method uses the approximate convex hull method. In the upper bound correction process of the traditional sequence method, the convex hull method is generally used. This method requires enumeration This time-consuming process is difficult to apply in the dispatch of actual large-scale power grids. In the approximate convex hull method, an approximate method is proposed to speed up the upper bound approximation problem. The solution to the problem of , by constructing an approximate convex hull, avoids the enumeration of extreme points. The specific form is as follows: Among them, λ s represents the target value of the approximation problem at the number of iterations s, represents auxiliary variables, λ s represents the number of iterations s convex combination coefficient, represents the slack variable penalty coefficient, represents the sampling point corresponding to the decision variable, s represents the effective iteration of stage t, s∈Λ t .

[0061] The approximate convex hull method adopted in the present invention is compared with the traditional convex hull method. Figure 1 (a) represents the traditional convex hull method, Figure 1 (b) represents the approximate convex hull method. The convex hull method is obtained by enumerating After that, the convex hull method collects a decision sample point for each iteration to update the convex hull, and the convex hull gradually approaches the actual residual cost function from above. In contrast, the approximate convex hull method uses a slope of The boundary line of is replaced by the top of the extreme point to construct the approximate convex hull. If the optimal solution falls within the approximate convex hull (such as Figure 1 The shaded area in b), then will be represented as a historical interior point If the optimal solution is outside the approximate convex hull, then Will be affected by large numbers penalties and is located on the border line.

[0062] The following uses a practical example to illustrate the dynamic recursive multi-stage robust risk scheduling method for the new energy power system of the present invention. For example, a test is conducted in a real system connecting Jiashan, Pinghu and Nanhu areas in Zhejiang Province, China. The system topology is as follows: Figure 2 Figure 1 shows a thermal power unit, Figure 2 shows an emergency unit, Figure 3 shows a renewable energy unit, and Figure 4 shows energy storage equipment. The three interconnected regions in the system have 39, 18, and 44 nodes, respectively, and their interconnection lines are marked with bold lines. The number of transmission lines, renewable energy units, and wind farms involved in the three regions is shown in Table 1. area Jiashan Pinghu South Lake Number of nodes 39 18 44 thermal power units 7 4 7 Energy storage equipment 4 2 3 transmission line 46 26 52

[0063] Table 1 Test system information The power imbalance penalty coefficient M is set to 10 6 $ / MWh, risk factor for unabsorbed renewable energy and load shedding and Set to 50$ / MWh and 10 4 $ / MWh. The minimum start-up and shutdown time of the fast-start unit is 1 hour, and the startup and fuel costs are 4×10 3 $ and 10 3 $ / MWh. Assume that the actual available power of each renewable energy unit follows a normal distribution with a standard deviation σ equal to 0.1AW q,t. The test code is implemented on the JuMP.jl toolkit of the Julia language, and the optimization problem is solved using Gurobi Optimizer 8.1.1 on a server with CPU Xeon E5–2678 and 64Gb RAM. In the system, the 31-day actual renewable energy and load data from 00:00 on August 1, 2021 to 23:45 on August 31, 2021, which were actually observed in the region, are used. The total installed capacity of renewable energy is 36% of the thermal power installed capacity, of which the proportions of renewable energy units 1-3 are configured at 33.60%, 23.92%, and 42.48%, respectively. The original load data is expanded in the same proportion as the wind power capacity and evenly distributed to each bus.

[0064] In order to illustrate the impact of considering or not considering unexpected factors on the scheduling results, a typical one-day available wind power generation scenario (dashed line) is selected to compare the scheduling decision results based on the traditional two-stage robust optimization and the proposed dynamic recursive-multi-stage robust optimization scheduling results. The scheduling decision results of the two are shown as follows: Figure 3 (a) and Figure 3 (b) As shown. When the available renewable energy power is at a higher level, such as the 5-9 hour and 13-18 hour periods, the dynamic recursive-multi-stage robust optimization model only absorbs the renewable energy power at the upper boundary of the uncertainty set, because the allowed range cannot cover the total renewable energy power generation. On the other hand, the traditional two-stage model assumes that the system can fully absorb all available renewable energy power because it overestimates the adjustable capacity of the thermal power units, and thus obtains a larger uncertainty set to cover all available renewable energy power, which leads to serious non-absorption of renewable energy. In the method of the present invention, since the actual renewable energy power generation is lower than the limit of the uncertainty set, more thermal power unit output is increased during periods of low renewable energy power generation (such as 10-12 hours and 22-24 hours) to meet the load. However, the traditional two-stage model mistakenly assumes that the renewable energy power generation is within the uncertainty set range and the load does not need to be met by increasing the thermal power output, resulting in load reduction.

[0065] like Figure 4 As shown in Figure 2, the system scheduling decisions for the 31-day simulation are shown. Figure 4 (a) It can be seen that the actual new energy output is within the uncertainty set in most periods. Figure 4 As shown in (b), if the actual renewable energy power generation cannot reach the permitted lower limit, the unavailable power will be compensated by load shedding. Figure 4 As shown in (c), when the actual wind power generation exceeds the uncertainty set range, the excess renewable energy generation will not be successfully absorbed. Overall, the proposed risk-based uncertainty set and scheduling method has achieved good results because Figure 4 The proportion of unabsorbed renewable energy and load shedding in (d) is less than 9.35% and 4.22% respectively.

[0066] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

[0067] While this article frequently uses terms such as system operational safety constraints, risk of unabsorbed renewable energy, load shedding risk, and dynamic recursive multi-stage robust optimization model, the use of other terms is not excluded. These terms are used solely to more conveniently describe and explain the essence of the present invention; interpreting them as any additional limitations would be contrary to the spirit of the present invention.

Claims

1. A dynamic recursive multi-stage robust risk scheduling method for a new energy power system, characterized in that: The following steps are involved: Establishing system operation security constraints; Establish an operational risk model, which includes the risk of unabsorbed renewable energy and the risk of load shedding; Based on the system operation safety constraints and operation risk model, a dynamic recursive-multi-stage robust optimization model is established with the goal of minimizing operational risk; A fast and robust dual dynamic programming algorithm is used to solve the model and obtain the optimal scheduling strategy.

2. The dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to claim 1 is characterized by: System operation safety constraints include the power generation constraint model of dispatchable thermal power units, the output power model of new energy power generation, the charge state model of the energy storage system, and the power balance model of the entire network.

3. The dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to claim 2 is characterized by: The power generation constraint model of dispatchable thermal power units includes upper and lower limits on power generation, as well as ramp restrictions. The start or shutdown status of the thermal power units is determined by the start and stop plan determined a day ago.

4. The method for dynamic recursive multi-stage robust risk scheduling of a new energy power system according to claim 2 is characterized by: The renewable energy power generation output power model includes the relationship between the predicted available renewable energy power and the uncertainty set boundary, the grid-connected wind power does not exceed the limit of the maximum available wind power, and the definition of the uncertainty set boundary of the actual measured wind power.

5. The dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to claim 2 is characterized by: The energy storage system state of charge model includes the energy storage state of charge restrictions and the energy storage state of charge transformation formula.

6. The method for dynamic recursive multi-stage robust risk scheduling of a new energy power system according to claim 2 is characterized by: The power balance model of the entire network includes the relationship between the phase angle difference and the power flow between the connected nodes, the power flow limit of each transmission line, and the node power balance formula.

7. A dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to any one of claims 2 to 6, characterized in that: The risk of non-absorption of new energy is that the test value of new energy power generation is between the upper limit of the uncertainty boundary and the upper limit of the available power generation of the new energy generator set, and the difference between the test value of new energy power generation and the upper limit of the uncertainty boundary is calculated by integrating.

8. The dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to claim 7 is characterized by: The load shedding risk is when the test value of renewable energy power generation is between zero and the lower limit of the uncertainty boundary, and the difference between the lower limit of the uncertainty boundary and the test value of renewable energy power generation is integrated and calculated.

9. A dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to any one of claims 1 to 6, characterized in that: Establish a dynamic recursive multi-stage robust optimization model, including: By minimizing the expected operational risk brought by unacceptable wind energy and considering the worst case scenario to ensure operational feasibility, a multi-level optimization problem is established, which is restated in a compact problem and equivalently converted into a dynamic recursive form.

10. A dynamic recursive multi-stage robust risk scheduling method for a new energy power system according to any one of claims 1 to 6, characterized in that: The model is solved using a fast robust dual dynamic programming algorithm, which includes: Upper and lower bounds are introduced for the operating cost function of stage t. By refining the upper bound, the worst uncertainty of new energy involved in the lower bound is screened out, and the global optimal solution of the multi-stage robust optimization model is achieved. The lower bound is corrected by adding Benders cutting planes, and the upper bound is corrected by approximate convex hull.

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