Distributed robust optimization method, device and storage medium considering grid flexibility

Abstract

The application discloses a kind of distributed robust optimization method, equipment and storage medium considering railway power grid flexibility, for high-altitude area power grid access impact traction load and fluctuation new energy, the flexibility requirement uncertainty set based on Wasserstein distance is constructed by analyzing the flexible demand of high-altitude railway along power system, the potential risk size caused by flexibility requirement uncertainty to system is quantitatively evaluated, the risk cost when flexibility shortage is determined, according to the risk cost when flexibility shortage and flexibility resource operation cost, the distributed robust optimization model based on Wasserstein distance is constructed, the model is converted into processable optimization problem using the approximation framework based on conjugate function, with high reliability, improve the flexibility adjustment capability of circuit, improve the balance of robustness and economy of optimization scheduling of system by reducing the number of constraints.

Description

Technical Field

[0001] This invention relates to the field of power grid flexibility technology, and more specifically to a distributed robust optimization method, device, and storage medium that takes into account the flexibility of railway power grids. Background Technology

[0002] With the advancement of the Western Development Strategy, a large number of complex mountain railways have been planned and constructed. High-altitude mountain railways traverse extremely steep terrain, and their long gradients significantly alter their load characteristics compared to other lines. This results in loads that are not only subject to impulsive and random fluctuations but also potentially involve frequent and large-amplitude regenerative braking power, unlike conventional lines, exacerbating load uncertainty. Furthermore, the vigorous development of clean and renewable energy sources has led to the grid connection of numerous wind power projects along the railway lines. This combination not only increases the demand for system flexibility but also enhances its randomness and volatility, potentially leading to insufficient flexibility and placing higher demands on the grid's flexibility and regulation capabilities.

[0003] Power system flexibility is defined as the system's ability to respond promptly to load fluctuations and stochastic changes in renewable energy sources, while considering technical and economic constraints. Improving power system flexibility enhances its resilience to both source and load disturbances. Currently, addressing the insufficient flexibility risk caused by intensified source-load fluctuations in power grids along high-altitude mountain railway lines requires substantial investment to increase flexibility capacity. Existing methods for handling the uncertainty of flexibility requirements primarily focus on stochastic optimization and robust optimization. However, stochastic optimization typically requires obtaining precise probabilistic characteristics to mitigate potential operational risks, which is difficult to achieve in practice and cannot guarantee high reliability. Robust optimization often considers worst-case scenarios, resulting in overly conservative solutions that cannot avoid the risk of insufficient flexibility in power grids along high-altitude mountain railway lines. Furthermore, it suffers from computational efficiency issues due to the increasing number of constraints as historical data accumulates. Summary of the Invention

[0004] The technical problem this invention aims to solve is that existing methods for handling uncertainty in flexibility requirements suffer from low reliability, poor grid flexibility adjustment capabilities, and low computational efficiency due to the increasing number of constraints as historical data grows. The goal is to provide a distributed robust optimization method, device, and storage medium that considers the flexibility of railway power grids. By analyzing the flexibility requirements of the power system and considering the operating costs of flexibility resources and the risk costs of insufficient flexibility, a distributed robust model based on Wasserstein distance is constructed. An approximate transformation framework based on conjugate functions is used to transform this model into a tractable optimization problem, resulting in high reliability, strong grid flexibility adjustment capabilities, and improved computational efficiency by reducing the number of constraints.

[0005] This invention is achieved through the following technical solution:

[0006] The first aspect of this invention provides a distributed robust optimization method that takes into account grid flexibility, comprising the following specific steps:

[0007] S1. Obtain the load power and generation power, determine the net load based on the load power and generation power, and analyze the flexible demand of the power system based on the net load;

[0008] S2. Based on the analysis of the flexible demand of the power system, obtain the true distribution and empirical distribution of the forecast error of the flexible demand, and construct the uncertainty set of the flexible demand based on the Wasserstein distance based on the true distribution and empirical distribution.

[0009] S3. Determine the risk cost of flexibility deficit based on the uncertainty set of flexibility requirements;

[0010] S4. Obtain the operating cost of flexible resources, and combine it with the risk cost of insufficient flexibility to construct a distributed robust optimization model based on Wasserstein distance;

[0011] S5. The distributed robust optimization model of Wasserstein distance is optimized using conjugate functions.

[0012] This invention addresses the impactful traction loads and fluctuating renewable energy sources affecting power grid integration in high-altitude regions. It analyzes the flexible demand of power systems along high-altitude railway lines, constructs a flexibility demand uncertainty set based on Wasserstein distance, quantitatively assesses the potential risks posed by this uncertainty, and determines the risk cost of flexibility deficits based on the uncertainty set. Based on the risk cost of flexibility deficits and the operating cost of flexibility resources, a distributed robust optimization model based on Wasserstein distance is constructed. To address the computational inefficiency of distributed robust optimization models with Wasserstein uncertainty sets, an approximation framework based on conjugate functions is used to transform the model into a manageable optimization problem. This model exhibits high reliability, strong grid flexibility adjustment capabilities, and improved computational efficiency by reducing the number of constraints, thus enhancing the balance between robustness and economy in optimal system scheduling.

[0013] Furthermore, S1 specifically includes:

[0014] S11. Obtain the normal load power and power generation at time t, and determine the net load at time t based on the normal load power and power generation at time t;

[0015] S12. Analyze the flexible demand of the power system based on the net load, including the following specific steps:

[0016] Obtain the net load power forecast at time t+τ and the net load power forecast at time t. Combine the net load at time t to determine the flexibility demand forecast at time t.

[0017] Obtain the net load power prediction error at time t+τ and the net load power prediction error at time t. Combine the net load at time t to determine the flexibility demand prediction error at time t.

[0018] The power system flexibility requirement is determined based on the predicted flexibility requirement at time t and the flexibility requirement prediction error.

[0019] Furthermore, S2 specifically includes:

[0020] S21. Obtain the true and empirical distributions of the forecasting error for flexibility requirements, and use Wasserstein distance to measure the distance between any two probability distributions.

[0021] S22. Construct a set of uncertainty for flexibility requirements based on the distance between any two probability distributions determined by the Wasserstein distance.

[0022] Furthermore, S3 specifically includes:

[0023] S31. Obtain the ramp rate and output value of hydropower units and thermal power units during time period t, and determine the flexibility of generator units during time period t.

[0024] S32. Obtain the deviation amount and risk coefficient cost of flexibility demand when there is a lack of flexibility, and obtain the risk cost caused by insufficient flexibility.

[0025] Furthermore, S32 specifically includes:

[0026] Based on the generator set's increased flexibility in time period t, obtain the deviation of the increased flexibility requirement when there is a flexibility shortfall;

[0027] By obtaining the wind curtailment risk cost coefficient and combining it with the deviation of increasing flexibility demand when there is a lack of flexibility, the load shedding risk cost caused by insufficient flexibility can be obtained.

[0028] Based on the reduction of generator unit flexibility in time period t, obtain the deviation of the reduction flexibility requirement when there is a flexibility shortage;

[0029] By obtaining the load shedding risk cost coefficient and combining it with the deviation of reducing flexibility demand when there is a lack of flexibility, the wind curtailment risk cost caused by insufficient flexibility is obtained.

[0030] Furthermore, S4 specifically includes:

[0031] S41. Obtain the coal consumption coefficient of the thermal power unit and the output of the thermal power unit at time t, and determine the minimum operating cost of the thermal power unit.

[0032] S42. Obtain the unit output cost of the hydropower unit and the output of the hydropower unit at time t, and determine the minimum operating cost of the hydropower unit.

[0033] S43. Construct a distributed robust optimization model based on Wasserstein distance, based on minimizing the operating costs of thermal power units, hydropower units, and the risk cost of insufficient flexibility.

[0034] Furthermore, S5 specifically includes:

[0035] S51. Based on strong duality theory and relaxation theorem, obtain the worst-case scenario expectation under Wasserstein distance fuzzy set;

[0036] S52. Using the definition of dual norm and the decomposability of functions, the worst-case scenario expectation under the Wasserstein distance uncertainty set is decomposed, and the risk cost of insufficient flexibility is decomposed into the risk of increasing insufficient flexibility and the risk of decreasing insufficient flexibility.

[0037] S53. Using characteristic functions and conjugate functions, and by strengthening constraints and relaxing them, we obtain the Bruker model for increasing the risk score of insufficient flexibility and the Bruker model for decreasing the risk score of insufficient flexibility.

[0038] Furthermore, the optimization process also includes constraints on grid operating conditions and actual power source operating characteristics, including constraints on power balance, thermal power units, and hydropower units.

[0039] A second aspect of the present invention provides a distributed robust optimization method that takes into account grid flexibility, and an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a distributed robust optimization method that takes into account grid flexibility.

[0040] A third aspect of the present invention provides a distributed robust optimization method that takes into account grid flexibility, and a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is used to implement a distributed robust optimization method that takes into account grid flexibility.

[0041] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0042] 1. This invention analyzes the flexibility requirements of power systems, considers the flexibility requirements of power grids along high-altitude railways based on the operating costs of flexibility resources and the risk costs of insufficient flexibility, improves the flexibility regulation capability of power grids, and provides a basis for the optimized planning of power grid flexibility resources.

[0043] 2. This invention adopts a distributed robust optimization model based on Wasserstein distance, which effectively balances the robustness and economy of the system's optimization scheduling.

[0044] 3. This invention uses an approximate transformation framework based on conjugate functions to transform the model into a tractable optimization problem. By transforming the objective function through conjugate transformation, the optimization efficiency of the nonlinear model is greatly improved, the reliability is high, and the power grid's flexibility and regulation capability are strong. The computational efficiency is improved by reducing the number of constraints. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0046] Figure 1 This is a flowchart of the optimization method in this embodiment;

[0047] Figure 2 This is a diagram of the power grid topology along a high-altitude railway in this embodiment;

[0048] Figure 3 This is a schematic diagram illustrating the principle of flexibility balance in this embodiment;

[0049] Figure 4 This is a diagram illustrating the impact of sample size and risk coefficient on cost in this embodiment.

[0050] Figure 5 The solution time curves for the model under different samples in this embodiment are shown. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0052] Example 1

[0053] like Figure 1As shown, this embodiment provides a distributed robust optimization method that takes into account grid flexibility, including the following specific steps:

[0054] S1. Obtain the load power and generation power, determine the net load based on the load power and generation power, and analyze the flexible demand of the power system based on the net load;

[0055] S2. Based on the analysis of the flexible demand of the power system, obtain the true distribution and empirical distribution of the forecast error of the flexible demand, and construct the uncertainty set of the flexible demand based on the Wasserstein distance based on the true distribution and empirical distribution.

[0056] S3. Determine the risk cost of flexibility deficit based on the uncertainty set of flexibility requirements;

[0057] S4. Obtain the operating cost of flexible resources, and combine it with the risk cost of insufficient flexibility to construct a distributed robust optimization model based on Wasserstein distance;

[0058] S5. The distributed robust optimization model of Wasserstein distance is optimized using conjugate functions.

[0059] To address the impactful traction loads and fluctuating renewable energy sources affecting power grid integration in high-altitude regions, this paper analyzes the flexible demand of power systems along high-altitude railway lines. A flexible demand uncertainty set based on Wasserstein distance is constructed to quantitatively assess the potential risks posed by this uncertainty. Based on the uncertainty set, the risk cost of flexibility deficits is determined. Then, a distributed robust optimization model based on Wasserstein distance is constructed, taking into account both the risk cost of flexibility deficits and the operating cost of flexibility resources. To address the computational inefficiency of distributed robust optimization models with Wasserstein uncertainty sets, an approximation framework based on conjugate functions is adopted to transform the model into a tractable optimization problem. This model exhibits high reliability and strong grid flexibility adjustment capabilities. By reducing the number of constraints, computational efficiency is improved, enhancing the balance between robustness and economy in optimal system scheduling.

[0060] Step S1 specifically includes:

[0061] like Figure 2 As shown, the load on this line not only exhibits strong impulsiveness and random fluctuations, but also possesses frequent and large-amplitude regenerative braking power, unlike conventional line loads. Therefore, the load-side volatility increases after connection to the grid along the line. To better characterize the combined effect of renewable energy generation and load power in the system, it can be represented by net load:

[0062] To obtain the conventional load power and generating power at time t, and to determine the net load at time t based on the conventional load power and generating power at time t, the calculation steps include:

[0063]

[0064] in, Let be the normal load power of the system at time t. Let t be the conventional wind power output of the system at time t. Let be the net load power of the system at time t.

[0065] System flexibility requirements are typically predetermined based on net load fluctuations and their forecasting errors. To address uncertainties in net load, the power system flexibility requirements are analyzed based on the obtained net load, including the following specific steps:

[0066] Obtain the net load power forecast at time t+τ and the net load power forecast at time t. Combine the net load at time t to determine the flexibility demand forecast at time t.

[0067] Obtain the net load power prediction error at time t+τ and the net load power prediction error at time t. Combine the net load at time t to determine the flexibility demand prediction error at time t.

[0068] The power system flexibility requirement is determined based on the predicted flexibility requirement at time t and the flexibility requirement prediction error.

[0069] The steps for calculating power system flexibility requirements include:

[0070]

[0071] Where τ is the sampling time interval, The predicted net load power of the system at time t+τ Let be the predicted net load power of the system at time t. The value for the predicted flexibility requirement at time t; The net load power prediction error at time t+τ of the system. Let be the net load power prediction error at time t, and its value should be the difference between the wind power prediction error and the load power prediction error. Let be a random variable, representing the error in forecasting flexibility requirements.

[0072] Step S2 specifically includes:

[0073] S21. Obtain the true and empirical distributions of the flexibility demand prediction error, and use the Wasserstein distance to measure the distance between any two probability distributions. The measurement steps include:

[0074] Obtain the marginal distributions of any two probability distributions to obtain the joint probability distribution of the two probability distributions;

[0075] Determine the distance between any two probability distributions based on the marginal distribution and the joint probability distribution;

[0076] The true distribution P of the forecast error for flexibility demand is fuzzy, but random samples can be obtained from historical data. Therefore, empirical distribution It can be regarded as an estimate of the true distribution P, where for The Dirac measure, in order to more accurately measure the difference between the true distribution P and the empirical distribution... The distance between them is measured using the Wasserstein distance, which measures the distance between any two probability distributions. The calculation steps include:

[0077]

[0078] Where dξ1 and dξ2 represent the marginal distributions of P1 and P2 respectively, π(dξ1,dξ2) is the joint probability distribution of dξ1 and dξ2, ||·|| represents the arbitrary norm and ||ξ1-ξ2|| represents the unit cost of moving ξ1 to ξ2;

[0079] S22. Based on the distance between any two probability distributions determined by the Wasserstein distance, a set of uncertainty for flexibility requirements is constructed. In the bibliometric optimization problem, the 1-norm is used in this paper because it has good numerical tractability. The calculation steps include:

[0080]

[0081] The radius ε(N) has a significant impact on the bibru bar model based on Wasserstein distance. The larger the radius, the more probability distributions are included in the uncertain set, and the more conservative the optimization result will be. The radius δ(N) can be solved by the following formula:

[0082]

[0083] Where χ represents the confidence level; σ is the sample mean; ρ and ρ are auxiliary variables.

[0084] Step S3 specifically includes:

[0085] S31. Obtain the ramp rate and output value of the hydropower unit and thermal power unit during time period t, and determine the flexibility of the generator unit during time period t. The calculation formula is as follows:

[0086]

[0087] Where, N g N represents the number of thermal power units. h This refers to the number of hydroelectric generating units;

[0088] Let i be the output of thermal power unit i during time period t. Let i be the upper limit of the output of thermal power unit i during time period t. This represents the lower limit of the output of thermal power unit i during time period t;

[0089] Let i be the output of hydropower unit i during time period t. Let be the upper limit of the output of hydropower unit i during time period t. This represents the lower limit of the output of hydropower unit i during time period t;

[0090] Let be the uphill speed of thermal power unit i. Let i be the downhill ramp rate of thermal power unit i;

[0091] Let i be the uphill climbing rate of hydropower unit i. Let i be the downhill climbing rate of hydropower unit i;

[0092] The upward adjustment flexibility provided for thermal power unit i The upward adjustment flexibility provided for thermal power unit i The upward adjustment flexibility provided for thermal power unit i The upward adjustment flexibility provided for thermal power unit i;

[0093] To improve the system's flexibility in time period t, The system's flexibility is adjusted downwards for time period t.

[0094] S32. Obtain the deviation amount and risk coefficient cost of flexibility demand when there is a lack of flexibility, and obtain the risk cost caused by insufficient flexibility.

[0095] like Figure 3 As shown, the renewable energy output forecasting errors and load forecasting errors contained in flexibility demand will cause it to fluctuate randomly within a certain range, easily leading to a mismatch between system flexibility supply and demand. When the upward fluctuation range of flexibility demand exceeds the upward adjustment of flexibility supply configured by the system, there will be a risk of load shedding; conversely, there will be a risk of wind curtailment. To quantitatively assess the potential risks to the system caused by the uncertainty of flexibility demand, a flexibility shortage penalty cost is introduced to quantify the flexibility deficit, including the following specific steps:

[0096] Based on the generator set's increased flexibility in time period t, obtain the deviation of the increased flexibility requirement when there is a flexibility shortfall;

[0097] By obtaining the wind curtailment risk cost coefficient and combining it with the deviation of increasing flexibility demand when there is a lack of flexibility, the load shedding risk cost caused by insufficient flexibility can be obtained.

[0098] Based on the reduction of generator unit flexibility in time period t, obtain the deviation of the reduction flexibility requirement when there is a flexibility shortage;

[0099] By obtaining the load shedding risk cost coefficient and combining it with the deviation of reducing flexibility demand when there is a lack of flexibility, the wind curtailment risk cost caused by insufficient flexibility is obtained.

[0100] The calculation steps include:

[0101]

[0102] δ l δ represents the risk cost coefficient for wind curtailment. w The load shedding risk cost coefficient, To adjust the difference between the increase in flexibility demand and the increase in flexibility supply when there is a flexibility shortage. When there is a shortage of flexibility, the deviation between reducing the demand for flexibility and reducing the supply of flexibility, f risk_l To increase the cost of load shedding risk due to insufficient flexibility, f risk_w To reduce the cost of wind curtailment risks caused by insufficient flexibility, f risk Due to insufficient flexibility and associated risks and costs.

[0103] Step S4 specifically includes:

[0104] S41. Obtain the coal consumption coefficient and output of the thermal power unit at time t, and determine the minimum operating cost of the thermal power unit. The calculation steps include:

[0105]

[0106] Among them, a g,i b g,i c g,i All are the coal consumption coefficients of thermal power unit i;

[0107] S42. Obtain the unit output cost of the hydropower unit and the output of the hydropower unit at time t, and determine the minimum operating cost of the hydropower unit. The calculation steps include:

[0108]

[0109] Among them, c h,i c h,i Let T be the unit output cost of hydropower unit i, and T be the total number of time periods within the scheduling cycle.

[0110] S43. Based on minimizing the operating costs of thermal power units, hydropower units, and the risk cost of insufficient flexibility, construct a distributed robust optimization model based on Wasserstein distance. The calculation steps include:

[0111]

[0112] Here, x represents each decision variable, which can be adjusted using affine rules.

[0113] Step S4 aims to minimize the operating costs of each flexible resource in the system and the risk costs of insufficient flexibility. Taking into account flexibility constraints, a distributed robust optimization model based on Wasserstein distance is constructed to meet the flexibility requirements under all possible probability distributions. The model collaboratively optimizes the real-time power of thermal power units, hydropower units, controllable loads, and energy storage to ensure the reliable and economical operation of the system.

[0114] Step S5 specifically includes:

[0115] S51. Based on strong duality theory and relaxation theorem, obtain the worst-case scenario expectation under Wasserstein distance fuzzy sets. The calculation steps include:

[0116]

[0117] Where λ is the dual variable, s i It is an auxiliary variable.

[0118] S52. Using the definition of dual norm and the decomposability of functions, the worst-case expectation under the Wasserstein distance uncertainty set is decomposed, and the inflexibility risk cost is decomposed into upward and downward inflexibility risk. The calculation steps include:

[0119]

[0120] S53. Using characteristic functions and conjugate functions, and through strengthening constraints and relaxation, we obtain the Bruker model for increasing the risk score of insufficient flexibility and the Bruker model for decreasing the risk score of insufficient flexibility. The calculation steps include:

[0121] Using dual norms, equation (11) is finally transformed into equation (13):

[0122]

[0123] Where, ||θ ki || * Represents the original norm The dual norm of equation (13) still represents an infinite-dimensional problem encompassing all distributions, and the number of constraints increases with the increase of variables. A general transformation of this equation results in a linear increase in computation time with the increase of historical data. Therefore, this invention employs an approximation framework to transform θ in equation (13). ki Replace with θ k Introducing the conjugate function, we obtain the following equation:

[0124]

[0125] in, In box-type uncertain set The characteristic function under the given condition can be solved using Lagrange duality. The specific steps for solving are as follows:

[0126]

[0127] As the conjugate function, taking the risk cost of insufficient flexibility (k=1) as an example, the specific calculation steps are as follows:

[0128]

[0129] Substituting equations (15) and (16) into equation (14), we obtain the following equation:

[0130]

[0131] Here, α1 and β1 are auxiliary variables.

[0132] However, due to the existence of constraint 1 in equation (17), the number of constraints will also increase with the increase of the number of variables, and constraint 1 contains an optimization problem, which is difficult to solve in the model. By strengthening the constraints and relaxing them, the model with insufficient flexibility risk is finally obtained as a Blue Bar model:

[0133]

[0134] Similarly, the sub-bar model under the risk of insufficient adjustment flexibility is obtained as follows:

[0135]

[0136] In the formula, α2 and β2 are auxiliary variables.

[0137] In some possible embodiments, to ensure the basic reliable operation of the power grid, constraints need to be imposed on the power grid operating conditions and the actual operating characteristics of the power sources during the optimization process, specifically including:

[0138] Power balance constraints:

[0139]

[0140] Thermal power unit constraints:

[0141]

[0142] Hydropower unit constraints:

[0143]

[0144] in, Let be the power difference between the i-th thermal power unit at time t and time t-τ;

[0145] χ h,i , and V represents the output coefficient of hydropower unit i at time t. min V is the minimum available hydropower generation capacity for the day. max This represents the maximum available water generation capacity for the day.

[0146] The second aspect of this embodiment provides a distributed robust optimization method that takes into account grid flexibility. An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a distributed robust optimization method that takes into account grid flexibility.

[0147] The third aspect of this embodiment provides a distributed robust optimization method that takes into account grid flexibility, and a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is used to implement a distributed robust optimization method that takes into account grid flexibility.

[0148] Example 2

[0149] This embodiment is based on Embodiment 1, and analyzes and compares the optimized scheduling results:

[0150] 1. Impact Analysis of High-Speed ​​Rail Load and Flexibility on System Optimization: To verify the effectiveness of considering the uncertainty of flexibility requirements and the impact of high-speed rail load on system optimization, the following four scenarios will be analyzed:

[0151] Scenario 1: System optimization solution without considering the uncertainty of flexibility requirements, where high-speed rail load is not connected;

[0152] Scenario 2: System optimization solution for high-speed rail load access without considering the uncertainty of flexibility requirements;

[0153] Scenario 3: System optimization solution considering the uncertainty of flexibility requirements, where high-speed rail load is not connected;

[0154] Scenario 4: High-speed rail load access, system optimization solution considering the uncertainty of flexibility requirements.

[0155] Set the load shedding risk factor δ W = $45 / (MW·h) -1 The wind curtailment risk coefficient δ1 = 160 $ / (MW·h) -1 The calculation results for the four scenarios are shown in Table 1:

[0156] This shows that the overall operating costs and wind curtailment of scenarios three and four, which take into account the uncertainty of flexibility requirements, are lower than those of scenarios one and two. The main reasons are as follows: From the perspective of flexibility deficit, the risk of insufficient upward adjustment of flexibility in scenarios three and four is reduced by US$16,583.99 and US$23,013.31 respectively compared with scenarios one and two. This indicates that when the actual net load output is greater than its forecast value, the potential load shedding caused by insufficient upward adjustment of flexibility is significantly reduced.

[0157] The risks of insufficient downsizing flexibility in scenarios three and four are reduced by $16,835.83 and $15,775.59 respectively compared to scenarios one and two. This indicates that when the actual net load output is less than its forecast, the potential wind curtailment due to insufficient downsizing flexibility is less. From the perspective of actual dispatch costs...

[0158] Compared to scenarios one and two, the operating costs of thermal power in scenarios three and four are reduced, while the operating costs of hydropower are increased accordingly. The increases in hydropower costs are 16.18% and 17.60%, respectively. This is because in order to cope with the fluctuations in flexibility demand, it is necessary to reasonably balance the adjustment capacity of flexibility resources.

[0159] Table 1 Optimization results under different scenarios

[0160]

[0161] (2) Analysis of the influence of model parameters and time complexity

[0162] To analyze the impact of different sample sizes and risk coefficients on the scheduling cost of the model in this paper, the confidence level of the Wasserstein distance was fixed at 0.9, and different sample sizes and risk coefficients were varied. The results are as follows. Figure 4 As shown. From Figure 4As can be seen, the overall operating cost decreases with the increase of the sample size. This is mainly because as the sample size increases, the radius of the uncertainty set based on the Wasserstein distance becomes smaller, the conservatism decreases, and the operating cost decreases. The overall operating cost exhibits a high-low-high pattern with increasing risk coefficient. This is because using a lower risk coefficient requires the system to provide higher flexibility capacity, increasing the actual operating cost of the system; a higher risk coefficient means that the system faces a greater flexibility deficit, resulting in a greater risk cost due to insufficient flexibility. Therefore, operators can balance economics by selecting different sample sizes and risk coefficients.

[0163] To verify the computational efficiency of this paper, a stochastic optimization model and a DRCC model were selected for comparison. The average solution time was obtained by conducting 15 experiments on each model. The results are as follows: Figure 5 As shown, the computation time of the three models increases with the number of samples, but the growth rates differ significantly. The DRCC model shows the fastest growth, while the computation time of the method proposed in this invention increases the slowest with the number of samples. This is because the computation time is mainly affected by the number of constraints. After transformation, the number of constraints of the objective function in the DRCC-CT model remains at k+6 and does not increase with the number of samples. Therefore, the proposed model has better computational advantages, and online real-time computation can be achieved by selecting an appropriate number of samples.

[0164] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A distributed robust optimization method considering power grid flexibility, characterized in that, The specific steps include the following: S1. Obtain the load power and generation power, determine the net load based on the load power and generation power, and analyze the flexible demand of the power system based on the net load; S2. Based on the analysis of the flexible demand of the power system, obtain the true distribution and empirical distribution of the forecast error of the flexible demand, and construct the uncertainty set of the flexible demand based on the Wasserstein distance based on the true distribution and empirical distribution. S3. Determine the risk cost of flexibility deficit based on the uncertainty set of flexibility requirements; S4. Obtain the operating cost of flexible resources, combine it with the risk cost when there is a lack of flexibility, and construct a distributed robust optimization model based on Wasserstein distance; S5. The distributed robust optimization model of Wasserstein distance is optimized using the conjugate function; S4 specifically includes: S41. Obtain the coal consumption coefficient and the output of the thermal power unit at time t, and determine the minimum operating cost of the thermal power unit, as shown in the following formula: Among them, a g,i b g,i c g,i All are the coal consumption coefficients of thermal power unit i; f g To minimize the operating costs of thermal power units; Let i be the output of thermal power unit i during time period t; S42. Obtain the unit output cost of the hydropower unit and the output of the hydropower unit at time t, and determine the minimum operating cost of the hydropower unit, as shown in the following formula: Among them, c h,i Let f be the unit output cost of hydropower unit i, and T be the total number of time periods within the scheduling cycle; h To minimize the operating costs of hydropower units; Let i be the output of hydropower unit i during time period t; S43. Based on minimizing the operating costs of thermal power units, hydropower units, and the risk cost of flexibility deficit, a distributed robust optimization model based on Wasserstein distance is constructed, as shown in the following formula: Where x represents each decision variable, which is adjusted using affine rules; f risk The risk cost of inadequate flexibility; S5 specifically includes: S51. Based on strong duality theory and relaxation theorem, obtain the worst-case scenario expectation under Wasserstein distance fuzzy set; S52. Using the definition of dual norm and the decomposability of functions, the worst-case expectation under the Wasserstein distance uncertainty set is decomposed, and the risk cost of insufficiency of flexibility is decomposed into the risk of increasing insufficiency of flexibility and the risk of decreasing insufficiency of flexibility. S53. Using characteristic functions and conjugate functions, and by strengthening constraints and relaxing them, we obtain the Bruker model for increasing the risk score of insufficient flexibility and the Bruker model for decreasing the risk score of insufficient flexibility.

2. The distributed robust optimization method considering grid flexibility according to claim 1, characterized in that, S1 specifically includes: S11. Obtain the normal load power and power generation at time t, and determine the net load at time t based on the normal load power and power generation at time t; S12. Analyze the flexible demand of the power system based on the net load, including the following specific steps: Obtain the net load power forecast at time t+τ and the net load power forecast at time t. Combine the net load at time t to determine the flexibility demand forecast at time t. Obtain the net load power prediction error at time t+τ and the net load power prediction error at time t. Combine the net load at time t to determine the flexibility demand prediction error at time t. The power system flexibility requirement is determined based on the predicted flexibility requirement at time t and the flexibility requirement prediction error.

3. The distributed robust optimization method considering grid flexibility according to claim 1, characterized in that, S2 specifically includes: S21. Obtain the true and empirical distributions of the forecasting error for flexibility requirements, and use Wasserstein distance to measure the distance between any two probability distributions. S22. Construct a set of uncertainty for flexibility requirements based on the distance between any two probability distributions determined by the Wasserstein distance.

4. The distributed robust optimization method considering grid flexibility according to claim 1, characterized in that, S3 specifically includes: S31. Obtain the ramp rate and output value of hydropower units and thermal power units during time period t, and determine the flexibility of generator units during time period t. S32. Obtain the deviation amount and risk coefficient cost of flexibility demand when there is a lack of flexibility, and obtain the risk cost caused by insufficient flexibility.

5. The distributed robust optimization method considering grid flexibility according to claim 4, characterized in that, Specifically, S32 includes: Based on the generator set's increased flexibility in time period t, obtain the deviation of the increased flexibility requirement when there is a flexibility shortfall; By obtaining the wind curtailment risk cost coefficient and combining it with the deviation of increasing flexibility demand when there is a lack of flexibility, the load shedding risk cost caused by insufficient flexibility can be obtained. Based on the reduction of generator unit flexibility in time period t, obtain the deviation of the reduction flexibility requirement when there is a flexibility shortage; By obtaining the load shedding risk cost coefficient and combining it with the deviation of reducing flexibility demand when there is a lack of flexibility, the wind curtailment risk cost caused by insufficient flexibility is obtained.

6. The distributed robust optimization method considering grid flexibility according to claim 1, characterized in that, It also includes constraints on grid operating conditions and actual power source operating characteristics, including constraints on power balance, thermal power units, and hydropower units.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a distributed robust optimization method that takes into account grid flexibility as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements a distributed robust optimization method that takes into account grid flexibility, as described in any one of claims 1 to 6.

Images