A renewable energy period coupling schedulable area efficient representation and scheduling method based on binary coefficients and space-time decomposition

Abstract

The application discloses a renewable energy period coupling schedulable area efficient representation and scheduling method based on binary coefficients and space-time decomposition, and relates to the technical field of power system scheduling optimization. The method defines an infeasible distance through L1 norm minimization, constructs a maximum-minimum robust optimization problem to identify a maximum infeasible point, tightens continuous coefficients in a dual problem to binary values to generate a feasible cut, and avoids exponential growth of calculation complexity caused by introduction of complementary relaxation constraints. Meanwhile, a cardinality constraint strategy is adopted to increase the number of non-zero variables in stages to reduce branch and bound nodes and inhibit degenerate inequalities, and a space-time decomposition strategy is combined to parallelize and reduce dimensions of the problem in time and space dimensions. The method is suitable for multi-period scheduling of large-scale power systems containing multiple renewable energy units.

Description

Technical Field

[0001] This invention relates to the field of power system dispatch optimization technology, and in particular to an efficient characterization and dispatching method for renewable energy time-coupled dispatchable areas based on binary coefficients and spatiotemporal decomposition. Background Technology

[0002] Under the conditions of large-scale renewable energy grid integration, accurately characterizing the dispatchable region of the power system is crucial for assessing the system's ability to absorb the uncertainties of renewable energy. The dispatchable region is the set of all feasible renewable energy power injection vectors that satisfy system operating constraints. In actual power system operation, generator units are subject to time-coupled constraints such as ramp rate limits. Feasible variations in renewable energy output are not only spatially coupled between different units but also temporally coupled across multiple dispatch periods, making the characterization of the dispatchable region a complex computational problem involving high-dimensional convex polyhedral projections.

[0003] Existing adaptive constraint generation methods, when characterizing schedulable regions, require transforming the minimax problem into a mixed-integer linear programming form using KKT conditions. This transformation inevitably introduces complementary relaxation constraints and a large number of binary variables. Each iteration generates a new feasible cut, further expanding the scale of the subsequent problems. This leads to excessively long computation times or even non-convergence in real-world scenarios involving multiple renewable energy units and more than twenty-four scheduling periods. This computational bottleneck makes it difficult to implement time-coupled schedulable region representations in engineering practice. Summary of the Invention

[0004] To address the computational efficiency bottleneck of existing schedulable region characterization methods in scenarios involving multiple renewable energy units and multiple time periods coupled together, this invention provides an efficient characterization and scheduling method for renewable energy time-period coupled schedulable regions based on binary coefficients and spatiotemporal decomposition.

[0005] This invention provides an efficient representation and scheduling method for renewable energy time-coupled dispatchable regions based on binary coefficients and spatiotemporal decomposition, comprising the following steps: obtaining power system operating parameters and establishing an operating constraint model including time-coupled constraints to construct an initial time-coupled dispatchable region; defining the minimum infeasible distance based on the L1 norm minimization problem, constructing a two-stage robust optimization problem of minimax to identify the maximum infeasible point in the current dispatchable region, and transforming it into a single-stage dual problem through dual theory; tightening the continuous coefficient variables in the dual problem into binary integer variables with values ​​limited to negative one, zero, and positive one, reconstructing the dual problem into a mixed integer linear programming problem, iteratively generating binary coefficient feasible cuts to gradually shrink the current dispatchable region; using a cardinality constraint strategy to divide the generation of feasible cuts into multiple stages, gradually increasing the number of non-zero binary variables from the first-order cardinality constraint to the preset maximum order; using a spatiotemporal decomposition strategy, representing independently in a finite number of adjacent time periods in the time dimension, and gradually expanding from a single unit to a multi-unit combination in parallel representation in the spatial dimension, and then merging them step by step to obtain the overall time-coupled dispatchable region.

[0006] As a preferred embodiment of the present invention, the operational constraint model is established based on a DC power flow model and a power transfer distribution factor. The time-coupling constraint includes the ramp rate limit between adjacent time periods of conventional generator sets. The operational constraints are uniformly expressed as follows: The relationship between renewable energy power injection and operating variables is as follows: .

[0007] As a preferred technical solution of the present invention, in the step of constructing the initial time-coupled schedulable region, the maximum and minimum values ​​of the projection variables of each renewable energy unit in each scheduling period are obtained by solving a linear programming problem, thereby constructing a box-shaped region as the initial schedulable region.

[0008] As a preferred embodiment of the present invention, the objective function of the L1 norm minimization problem is: The constraints include , , , When its optimal objective value is zero, it indicates the running point. It is located within the actual time-coupled schedulable region.

[0009] As a preferred embodiment of the present invention, the form of the two-stage robust optimization problem of minimax is as follows: ,in The schedulable region is estimated for the current iteration; the dual theory transformation refers to replacing the inner minimization problem with its dual form, making the minimax problem a problem with respect to the dual variables. and The single-stage maximization problem DP2.

[0010] As a preferred embodiment of the present invention, in the step of compressing the continuous coefficient variable into a binary integer variable, the dual variable... Each component in Restricted to , In the mixed-integer linear programming problem BP2, the binary variables and the bilinear terms of continuous variables involved are equivalently transformed using the standard linearization method.

[0011] As a preferred embodiment of the present invention, the cardinality constraint strategy defines the k-th order cardinality constraint as follows: Within each stage, the BP2 with cardinality constraints is solved repeatedly until no infeasible points exist in that stage, then the next stage begins. The process continues until the order of the cardinality constraints reaches the preset maximum order. Convergence is determined when there are no infeasible points.

[0012] As a preferred technical solution of the present invention, in the spatiotemporal decomposition strategy, the number of adjacent time periods selected in the time dimension is two, the maximum unit combination scale in the spatial dimension is two, the representation process between each combination in the spatial dimension is executed in parallel, and the representation result of the previous combination stage is used as the input of the next combination stage.

[0013] As a preferred technical solution of the present invention, the method further includes a characterization result verification step: constructing a linear programming evaluation problem based on the time-coupled schedulable region obtained from the characterization, generating multiple sets of target coefficient vectors through Monte Carlo sampling, calculating the optimal target values ​​of the approximate schedulable region and the actual schedulable region respectively, and using relative error, average minimum infeasible distance and vertex coverage as evaluation indicators of characterization accuracy.

[0014] Compared with the prior art, the present invention has the following beneficial effects:

[0015] This invention generates feasible cut coefficients by tightening the dual variables to binary values, fundamentally eliminating the binary variable accumulation problem introduced by complementary relaxation constraints in traditional methods. This ensures that the computational complexity only increases linearly during the iteration process. At the same time, the cardinality constraint strategy effectively reduces branch and bound nodes and avoids degenerate inequalities by gradually increasing the number of non-zero variables in stages. The spatiotemporal decomposition strategy enables the representation of large-scale systems by parallelizing and reducing the dimensionality of the problem. The synergistic effect of these three factors allows this method to represent the time-coupled schedulable region in a large-scale power system containing multiple renewable energy units and 24-hour periods within ten minutes with an error of no more than 2%. Attached Figure Description

[0016] Figure 1A two-dimensional schematic diagram illustrating how cardinality constraints reduce degenerate inequalities;

[0017] Figure 2 A flowchart illustrating the spatiotemporal decomposition strategy;

[0018] Figure 3 This is an overall flowchart of the method of the present invention;

[0019] Figure 4 This is a schematic diagram of the iterative process under different cardinal constraint orders. Detailed Implementation

[0020] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] See Figure 3 As shown, this embodiment provides an efficient characterization and scheduling method for renewable energy time-coupled schedulable regions based on binary coefficients and spatiotemporal decomposition. The overall process of this method can be divided into four stages: obtaining operating parameters and constraint modeling, constructing the initial schedulable region, iterative characterization based on dynamic shrinkage of binary boundaries, and large-scale expansion based on spatiotemporal decomposition.

[0022] In the operational parameter acquisition and constraint modeling phase, all parameters required for system operation are first obtained from the power system dispatch center. For conventional generating units, the required parameters include baseline output. , output upper limit and lower limit Climbing speed and uphill and downhill speed For renewable energy generator sets, required parameters include predicted output. Prediction error The range of values ​​and installed capacity In addition, the load power of each node needs to be obtained. and transmission capacity limitations of power transmission lines The power transfer distribution factor is also considered. Power system operating constraints are described using a DC power flow model, specifically including four types of constraints. The first type is the output constraint of conventional generating units, requiring that the actual output of each unit in each time period does not exceed its upper and lower limits. The second type is the time-coupled ramping constraint, requiring that the change in the rescheduled amount of conventional generating units between adjacent time periods does not exceed the ramping rate limit, i.e. The third type is power balance constraint, which requires the total rescheduled amount of conventional generating units in the system to match the total prediction error of renewable energy. The fourth type is transmission line capacity constraint, which calculates the power flow changes of each line based on the power transfer distribution factor and limits them to not exceeding the transmission capacity. The actual output of renewable energy units must also meet the physical limit from zero to installed capacity. All the above constraints are then organized into a matrix form. And establish a mapping relationship between renewable energy power injection and operating variables. The power balance equality constraint can be equivalently represented as two inequality constraints in opposite directions. Since the high-dimensional feasible region defined by the linear constraints is a convex polyhedron, and its projection onto the renewable energy power injection vector is also a convex polyhedron, the time-coupled schedulable region can be represented as... In the form of, and This refers to the coefficient matrix and right-hand vector that need to be determined through iterative solutions.

[0023] In the initial schedulable region construction phase, a box-shaped region is used as the initial time-coupled schedulable region estimate. The box-shaped region is constructed as follows: for each renewable energy unit... In each scheduling period projection variables , respectively With the goal of maximizing and minimizing, under constraints , Solving the two linear programming problems yields the following results. The feasible range and upper and lower bounds. The upper and lower bounds of the ranges of all projected variables together form a hyperrectangular region, which serves as the initial schedulable region. The initial region necessarily contains the actual time-coupled schedulable region, but because the coupling relationship between different projection variables is not considered, its volume is usually much larger than the actual schedulable region. Subsequent iterations shrink this initial region by continuously adding feasible cuts. It is worth noting that the box initialization method can also be regarded as a special case when the cardinality constraint is first-order; therefore, in subsequent iterations, the first-order cardinality constraint stage usually does not generate new infeasible points.

[0024] The iterative representation based on the dynamic shrinkage of binary boundaries is the core stage of the method of this invention, and its specific execution process is as follows.

[0025] For a given run point The distance between the schedulable region and the actual schedulable region is evaluated by solving an L1 norm minimization problem. This problem introduces auxiliary variables. and , represent the components that need to be adjusted in the positive and negative directions in each dimension of the running point, respectively, and the objective function is . The constraints are , , , When the optimal objective value is zero, it means... It is already within the actual schedulable area and requires no adjustment; otherwise, the optimal target value represents the minimum infeasible distance of the running point.

[0026] To find the maximum infeasibility point in the current schedulable region estimate, a minimax problem is constructed: the outermost point is within the current schedulable region. Search running point The inner layer solves for the minimum infeasibility distance at the run point. Using duality theory, the inner layer problem is replaced with its dual form, resulting in the single-stage dual problem DP2. In DP2, the dual variables... With projection variables The product terms make the problem non-convex. The traditional approach is to transform DP2 into a mixed-integer linear programming form using KKT conditions. However, the complementary relaxation constraints introduced by this transformation mean that each new feasible cut generates an additional set of binary variables and Big M constraints, leading to a rapid increase in the problem size and solution difficulty in subsequent iterations. When the projection dimension exceeds seven, this method becomes practically infeasible, and the projection dimension of multi-unit, multi-time-period problems is often much higher.

[0027] The key technical steps of this invention lie in utilizing The bounded property in DP2 tightens each component from the continuous domain to the discrete domain, specifically limiting its values ​​to... Under this binary coefficient assumption, DP2 is approximately reconstructed as a mixed-integer linear programming problem BP2, which involves... Bilinear products with continuous variables can be linearized equivalently by introducing auxiliary variables and adding linear inequalities. A key property of BP2 is that the feasible cut coefficients generated by solving BP2 in each iteration are... Since it is itself in binary form, this feasible cut, when added as a new constraint to the schedulable region, does not introduce additional complementary relaxed binary variables as in traditional methods. Therefore, the structure and size growth of BP2 in subsequent iterations are controllable. When the optimal objective value of BP2 is greater than zero, its corresponding solution... and the right-hand side constant Constitutes feasible cutting Add the feasible cut to the current schedulable region. After contraction When the optimal objective value of BP2 is zero, there are no longer any infeasible points in the current schedulable region, and the iteration terminates. It should be noted that although the binary coefficient assumption is an approximation, because the coefficient values ​​are determined through optimization rather than being fixed manually, it can generate a compact and accurate approximation of the schedulable region.

[0028] The cardinality constraint strategy plays a crucial role in accelerating the above iteration process. This is achieved by adjusting the coefficient vector in BP2. Analyzing the structure allows us to establish a correspondence between the number of non-zero elements and the types of physical constraints. When there is only one non-zero element, the corresponding feasible cut represents the upper or lower bound of the output of a renewable energy unit during a given time period. When there are two non-zero elements with opposite signs, the corresponding feasible cut represents a ramp-up constraint across time periods; when the two non-zero elements have the same sign, it corresponds to a cumulative power boundary constraint. Feasible cuts corresponding to three or more non-zero elements reflect more complex multi-time period, multi-unit coupling relationships. Based on this physical intuition, we define... Order cardinality constraint The entire feasible cut generation process is divided into several stages based on the number of non-zero elements, from fewest to most. In the first stage... In this stage, the solution to BP2 is supplemented with The constraint is used to iterate repeatedly until no more infeasible points are found, and then proceed to the next step. The phase. The effectiveness of this strategy can be understood on two levels. For example... Figure 1 As shown, at the computational level, cardinality constraints significantly reduce the search space for branch and bound, decreasing the number of nodes to be explored, thus drastically shortening the solution time for a single BP2 iteration. At the algorithmic level, gradually increasing the complexity of feasible cuts from lower orders effectively avoids the generation of degenerate inequalities. Degenerate inequalities refer to constraints that only intersect the schedulable region at a vertex or low-dimensional face without substantially contributing to boundary shaping. While these constraints do not affect the correctness of the final result, they increase the size of the constraint set and the burden of subsequent solutions. In the two-dimensional example, without cardinality constraints, the feasible cut generated in the first iteration passes through a vertex of the actual schedulable region and requires three iterations to complete the representation. However, first-order cardinality constraints allow for the generation of effective boundary constraints and convergence within the first two iterations. Actual calculations show that without cardinality constraints, even in a small-scale system containing two renewable energy units, directly applying the binary boundary dynamic shrinkage method cannot complete the representation within one hour, while introducing cardinality constraints allows convergence in just a few seconds.

[0029] like Figure 2 As shown, the spatiotemporal decomposition strategy is used to address the dimensionality problem when there are a large number of renewable energy units. In the time dimension, all... Each scheduling period is divided into several time windows consisting of a finite number of adjacent time periods. In this embodiment, each time window contains two adjacent time periods. Within each time window, the aforementioned binary boundary dynamic shrinkage method is run independently to characterize the schedulable region of all renewable energy units. The characterization between different time windows can be executed in parallel. In the spatial dimension, the characterization process adopts a step-by-step expansion strategy. First, the time-coupled schedulable region of each renewable energy unit is independently characterized, resulting in... The results for a single unit. Then, the process moves to the combination of two units, from... Take all from the Taiwan machine group Each pair of combinations is used to characterize its joint time-coupled schedulable region. In this stage, the computations between combinations are independent and can be executed in complete parallel. After the two-unit stage is completed, the results can be used as input for higher-level combination stages; however, in practice, a maximum combination size of two is usually sufficient to meet accuracy requirements. Finally, the characterization results of each window in the time dimension are merged and integrated with the characterization results of each level in the spatial dimension to obtain the overall time-coupled schedulable region covering all units and all time periods.

[0030] like Figure 4 As shown, in a medium-sized system comprising ten conventional generator units and three renewable energy units, the scheduling cycle is twenty-four time periods. After obtaining the operating parameters, the initial box-shaped region is constructed in a seventy-two-dimensional space. The maximum order of the cardinality constraint is set to six. In the spatiotemporal decomposition strategy, the maximum combination size of the spatial dimension is two, and the window width of the time dimension is two time periods. Under the second-order cardinality constraint, a large number of infeasible points are identified, while only a small number of additional iterations are required under the third to sixth-order cardinality constraints. The entire representation process is completed within approximately thirty seconds. To verify the representation accuracy, 20,000 sets of target coefficient vectors are uniformly sampled using the Monte Carlo method, with each component of each set of coefficients uniformly distributed within the range of negative one to positive one. For each set of coefficients, a linear programming problem is solved with constraints on the approximate schedulable region and the actual schedulable region, respectively, and the relative error of the optimal target values ​​for both is calculated. The results show that the maximum relative error is 0.59%, the average relative error is only 0.03%, the average minimum infeasible distance is 0.24 MW, and the vertex coverage reaches 93%.

[0031] In larger-scale systems, comprising 54 conventional generator units and 6 renewable energy units, the projected variable dimension reaches 144 dimensions. Directly representing the globally time-coupled schedulable region presents significant computational challenges. A spatiotemporal decomposition strategy divides the spatial dimension into two stages: six parallel computations of a single generator unit and fifteen combined parallel computations of two generator units. Under this configuration, the final representation result is obtained by merging and integrating all parallel tasks after completion. The entire process is completed in approximately 590 seconds. Validated with 20,000 Monte Carlo samples, the maximum relative error is 0.41%, the average relative error is 0.04%, and the vertex coverage reaches 96.5%. In contrast, methods that do not consider temporal coupling require over an hour to represent the schedulable region for a single time period. Furthermore, due to neglecting temporal coupling, their results are overly optimistic in assessing the system's ability to absorb the uncertainty of renewable energy, with a maximum relative error reaching 7.56%.

[0032] Regarding the impact of system operating constraints on representation accuracy, when the transmission capacity limits of transmission lines are reduced by 10% and 20% respectively, the system operating space is subject to stricter constraints. The representation time increases slightly, but the accuracy improves. This phenomenon is because the tighter operating constraints make the boundaries of the schedulable region more regular, and the binary coefficient feasible cut approximates it better.

[0033] Regarding the impact of the number of renewable energy units, as the number of units increases from three to five, the computation time required for characterization increases from approximately twenty-eight seconds to approximately one hundred and fifty-two seconds, a growth trend consistent with the increase in projection dimensions. The characterization accuracy under different unit number configurations does not exhibit a monotonic change trend, because different configurations correspond to different baseline power injection scenarios, and the geometry of their schedulable regions varies.

[0034] Regarding the impact of the number of scheduling periods, when the number of periods increased from eight to twenty-four, the computation time for medium-sized systems increased from approximately seven seconds to approximately twenty-eight seconds, while the increase in computation time was more pronounced for large-scale systems. When the number of periods was small, the computation times for systems of different sizes were similar, indicating that the method's sensitivity to the number of periods was low when the number of periods was small, but gradually increased with the increase in the number of periods, and this sensitivity was closely related to the system size.

[0035] The parameter configurations and numerical results in the above embodiments are merely illustrative of specific implementations of the method of the present invention and do not constitute a limitation on the scope of protection of the present invention. Those skilled in the art can adjust parameters such as the maximum order of the cardinality constraint, the width of the time window, and the maximum combined size of the spatial dimensions according to factors such as the scale of the actual system, the number of renewable energy units, and the length of the scheduling period. Different linear programming or mixed-integer linear programming solvers can be used as needed to execute the optimization problems involved in the algorithm. Reasonable changes to the above parameters and implementation details, while maintaining the core technical concept of the present invention, are all within the scope of protection of the present invention.

Claims

1. A method for efficient characterization and scheduling of renewable energy time-coupled schedulable regions based on binary coefficients and spatiotemporal decomposition, characterized in that, Includes the following steps: Obtain power system operating parameters and establish an operating constraint model that includes time-coupled constraints, and construct an initial time-coupled schedulable region; Based on the L1 norm minimization problem, the minimum infeasibility distance is defined, and a two-stage robust optimization problem of minimax and minimax is constructed to identify the maximum infeasibility point in the current schedulable region. It is then transformed into a single-stage dual problem through dual theory. The continuous coefficient variables in the dual problem are tightened into binary integer variables with values ​​limited to negative one, zero, and positive one. The dual problem is reconstructed into a mixed integer linear programming problem, and the binary coefficient feasible cut is iteratively generated to gradually shrink the current schedulable region. The feasible cut generation is divided into multiple stages by adopting a cardinality constraint strategy, gradually increasing the number of non-zero binary variables from the first-order cardinality constraint to the preset maximum order. A spatiotemporal decomposition strategy is adopted, which represents the time dimension independently in a finite number of adjacent time periods, and expands from a single unit to a multi-unit combination and parallel representation in the spatial dimension and then merges them step by step to obtain the overall time-coupled schedulable region.

2. The method according to claim 1, characterized in that: The operational constraint model is established based on the DC power flow model and the power transfer distribution factor. The time-coupling constraints include ramp rate limits between adjacent time periods of conventional generator sets. The operational constraints are uniformly expressed as follows: The relationship between renewable energy power injection and operating variables is as follows: .

3. The method according to claim 1, characterized in that: In the step of constructing the initial time-coupled schedulable region, the maximum and minimum values ​​of the projection variables of each renewable energy unit in each scheduling period are obtained by solving a linear programming problem, and a box-shaped region is constructed as the initial schedulable region.

4. The method according to claim 1, characterized in that: The objective function of the L1 norm minimization problem is: The constraints include , , , When its optimal objective value is zero, it indicates the running point. It is located within the actual time-coupled schedulable region.

5. The method according to claim 1, characterized in that: The form of the minimax two-stage robust optimization problem is as follows: ,in The schedulable region is estimated for the current iteration; the dual theory transformation refers to replacing the inner minimization problem with its dual form, making the minimax problem a problem with respect to the dual variables. and The single-stage maximization problem DP2.

6. The method according to claim 1, characterized in that: In the step of compressing continuous coefficient variables into binary integer variables, the dual variable... Each component in Restricted to , In the mixed-integer linear programming problem BP2, the binary variables and the bilinear terms of continuous variables involved are equivalently transformed using the standard linearization method.

7. The method according to claim 1, characterized in that: The cardinality constraint strategy defines a k-th order cardinality constraint as follows: The problem is solved repeatedly in each stage, involving mixed-integer linear programming with cardinality constraints, until no infeasible points exist in that stage. Then, the problem proceeds to the next stage. The process continues until the order of the cardinality constraints reaches a preset maximum order. Convergence is determined when there are no infeasible points.

8. The method according to claim 1, characterized in that: In the spatiotemporal decomposition strategy, the number of adjacent time periods selected in the time dimension is two, the maximum unit combination size in the spatial dimension is two, the representation process between each combination in the spatial dimension is executed in parallel, and the representation result of the previous combination stage is used as the input of the next combination stage.

9. The method according to claim 1, characterized in that: In the aforementioned base constraint strategy, the first-order base constraint corresponds to the upper and lower bounds of the output of renewable energy units in a specific time period, the second-order base constraint corresponds to the ramp-up constraint or cumulative power boundary constraint across time periods, and the higher-order base constraint corresponds to the coupling boundary of multiple time periods and multiple units.

10. The method according to claim 1, characterized in that: The method also includes a characterization result verification step: constructing a linear programming evaluation problem based on the time-coupled schedulable region obtained from the characterization, generating multiple sets of target coefficient vectors through Monte Carlo sampling, calculating the optimal target values ​​for the approximate schedulable region and the actual schedulable region respectively, and using relative error, average minimum infeasible distance and vertex coverage as evaluation indicators of characterization accuracy.

Images