A water, wind and solar energy system balanced scheduling model based on distribution robust optimization

Abstract

This invention relates to the field of short-term dispatching of hydro-wind-solar hybrid energy systems, specifically a balanced dispatching model for such systems based on partial Bruker bar optimization. This model represents a novel optimization approach for balancing reliability and economic efficiency in the short-term dispatching of hydro-wind-solar hybrid energy systems. The technical solution involves: using fuzzy sets based on Wasserstein distance to describe the uncertainties of renewable energy; constructing a partial Bruker bar optimization model for the hydro-wind-solar hybrid energy system; transforming the model into a MILP model using the ε-constraint method, strong duality theory, and linearization techniques; and finally solving for the short-term dispatching scheme of the hybrid energy system. This method is of great significance for maintaining the balance between reliability and economic efficiency in hydro-wind-solar hybrid energy systems.

Description

Technical Field

[0001] This invention belongs to the field of short-term scheduling of hydro-wind-solar hybrid systems, and relates to a balanced scheduling model for hydro-wind-solar energy systems based on distributed bar optimization. It is a new optimization model for solving the problem of balancing reliability and economy in the short-term scheduling of hydro-wind-solar hybrid energy systems. Background Technology

[0002] Driven by the goals of "carbon peaking and carbon neutrality," my country's power structure is shifting towards renewable energy. By 2020, my country's installed wind and solar power capacity had exceeded 530 GW, accounting for 24% of the total installed capacity. Furthermore, my country plans to increase wind and solar power capacity to over 1200 GW by 2030 and raise the share of non-fossil energy consumption to over 80% by 2060. On the path to decarbonization, renewable energy is gradually taking a dominant position in China's power system. However, the intermittent and uncertain output of wind and solar power significantly increases the volatility of the power system and reduces the flexibility of power dispatch. Grid dispatchers must ensure a balance between power supply and demand to maintain the reliability and stability of system operation, and the large-scale grid connection of wind and solar power exacerbates the complexity of power balance. Simultaneously, with the gradual phasing out of high-energy-consuming regulating power sources such as thermal power, the demand for power system flexibility will increase significantly. Hydropower, as a low-carbon, environmentally friendly, and flexible power source, can provide great flexibility through cascade control to mitigate the randomness caused by the large-scale integration of renewable energy into the grid. Therefore, hydropower plays an increasingly important role in the power system.

[0003] However, the forecasting of wind and solar power is uncertain and limited, leading to power supply risks in the short-term scheduling of hydro-wind-solar hybrid energy systems. Furthermore, the uncertainty of renewable energy sources also affects the economic operation of short-term scheduling of hybrid systems, including water consumption and energy storage. Therefore, how to balance the power supply risks and economic efficiency of hydro-power hybrid systems has become a challenging scientific problem. This invention utilizes a biblical optimization model based on Wasserstein distance to address the reliable-economic equilibrium scheduling problem of hydro-wind-solar hybrid energy systems. It considers not only the complex hydrological and power coupling relationships but also the multiple risks and economic aspects of hydropower operation, namely, minimizing risk, minimizing water consumption, maximizing energy storage, and minimizing hydropower station output adjustments. Meanwhile, Mixed Integer Linear Programming (MILP) is one of the most commonly used mathematical programming algorithms for reservoir power generation scheduling due to its good model scalability, global convergence, and the availability of numerous advanced open-source and commercial solvers. Therefore, this invention utilizes the ε-constraint method, strong duality theory, and linearization techniques to transform the above model into an easily tractable MILP model.

[0004] This invention is supported by the National Natural Science Foundation of China Major Program Key Project No. 52039002. Summary of the Invention

[0005] To address the balance between reliability and economy in the scheduling of hydro-wind-solar hybrid energy systems, this invention proposes a bibliometric optimization model based on Wasserstein distance.

[0006] The technical solution of the present invention is as follows:

[0007] A balanced scheduling model for a hydro-wind-solar energy system based on distributed bar optimization is as follows:

[0008] (1) Using fuzzy sets based on Wasserstein distance to describe the uncertainty of renewable energy:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] in, This indicates the forecasting error or net load uncertainty of renewable energy. and These represent the prediction errors for wind power and solar power output, respectively. For simplicity, the time index t is omitted below. Yes True distribution The estimate, i.e. Historical wind and solar power prediction error data are used in formula (2). Calculate the corresponding Dirac measure Therefore, it can be concluded that Represents the Wasserstein distance; and They respectively follow the distribution and distribution ||·|| denotes the norm; ∏ denotes... and The joint distribution; The Wasserstein sphere is represented by an empirical distribution. Centered on, ∈ N The radius restricts the sum of fuzzy sets. The distance between them; β is the confidence level of the fuzzy set; D is a constant obtained by solving formula (7), where... ρ represents the sample mean; ρ is the auxiliary decision variable.

[0017] (2) Constructing a partial Bruker optimization model for a hydro-wind-solar hybrid energy system:

[0018] Due to meteorological factors, wind and solar power have limited load tracking and dispatch capabilities, leading to increased system load volatility and a greater demand for system flexibility. Cascade hydropower stations, on the other hand, can provide flexibility through reservoir storage capacity and rapid ramp-up response, mitigating the volatility and uncertainty brought by wind and solar power. Therefore, hydropower can proactively adjust its output to reduce power shortages and curtailment caused by insufficient system flexibility. While pursuing high returns is a fundamental requirement for power generation companies, in a hydro-wind-solar complementary dispatch model, hydropower can provide flexibility to compensate for the volatility and uncertainty of wind and solar power. This, in turn, affects the economic efficiency of hydropower dispatch itself, thus creating a balance between system reliability and hydropower economics. Water consumption and energy storage losses can be viewed as the generation costs of cascade hydropower from two different perspectives, i.e., the economic efficiency of hydropower. Generally, the minimum water consumption tends to be achieved by utilizing power stations with higher head, while the maximum energy storage tends to be achieved by utilizing power stations with lower head. Therefore, the minimum water consumption and maximum energy storage are inherently in equilibrium. However, the grid connection of wind and solar power not only increases the reliability of power supply but also adds complexity to improving the economic efficiency of hydropower. Taking all the above factors into account, this invention also considers the above three aspects as optimization objectives.

[0019] 1) Quantify the three risks of water wastage, power shortage, and power wastage, and use them as the objective function to ensure the reliable operation of the hydro-wind-solar hybrid system:

[0020]

[0021] in, This represents the abandoned power of the i-th type of renewable energy source during time period t; This represents the power shortage in the hybrid power system during time period t; RES is the renewable energy number, including wind and solar power, RES = 2; s m,t η represents the water discharge from hydropower station m during time period t; m The energy conversion coefficient of hydropower station m is obtained from historical dispatch data; s m,t / η m Let M represent the energy wasted by hydropower station m; M and T represent the set of hydropower stations and the set of time periods, respectively. This objective comprises two phases: Phase 1... The first stage aims to reduce the risk of "three abandonments" (abandonment of wind, solar, and organic power) and improve the reliability of the hybrid system. This stage involves decisions based on predicted wind and solar power output. The second stage prioritizes minimizing adjustments to hydropower output, utilizing hydropower regulation capabilities to mitigate the interference caused by prediction errors related to renewable energy uncertainties, thus ensuring the stable operation of the cascade hydropower stations. This represents the output adjustment function for the second stage, where x, These represent the decision variables and uncertain sample parameters for the second stage, respectively.

[0022] 2) Incorporate the economic efficiency of the hydropower station into the objectives, namely, minimizing water consumption (minf2) and maximizing energy storage (maxf3):

[0023]

[0024]

[0025]

[0026] Among them, R m,t Δt represents the total discharge of hydropower station m during time period t; Δt represents the length of the time period; ES m This represents the stored energy of hydropower station m at the end of the dispatch period, which is equal to the energy generated by power generation from the final water level to the dead water level; v m,T+1 and minV m These represent the storage capacity at the end of the time period and the dead storage capacity, respectively.

[0027] (3) Model transformation:

[0028] Step 1: The model in step (2) was modified using the ε-constraint method, transforming the multi-objective problem into a single-objective problem. While ensuring the ideality of a certain objective, other objectives were also fully considered. To ensure the normal development of society, this invention takes power supply risk as the main objective and economic objective as the constraint condition, transforming the original objective function into:

[0029]

[0030] Where α m,t This represents the adjustment factor for the uncertainty of new energy response in hydropower station m during time period t, where... That is, the adjustment amount of hydropower output.

[0031] Step 2: The second stage in the objective function involves the fuzzy set as a function variable in the worst-case scenario, which is more difficult to handle. This invention utilizes strong duality theory for re-transformation:

[0032]

[0033] Where κ represents the relationship with In Related dual variables.

[0034] Step 3: Introduce the auxiliary variable τ k Formula (13) can be transformed into:

[0035]

[0036] in, It is a convex function. The optimal solution can be found in the maximum value of the samples in Ξ. or sample minimum value ω It can be obtained from there.

[0037] Step 4: Based on the results of Step 3, it can be further transformed into:

[0038]

[0039] Step 5: Transform the model from Step 4 into a standard MILP model, making it more flexible, efficient, and easier to solve using commercial solvers. Furthermore, this invention utilizes an approximation framework to reduce the dimensionality of the problem. The objective function (15) is transformed into:

[0040]

[0041] Here, λ and μ represent Lagrange multipliers.

[0042] By following the steps above, the multi-objective optimization problem of this hybrid energy system can be solved.

[0043] The beneficial effects of this invention are as follows: This invention addresses the reliability and economic issues in the complementary scheduling of hydropower, wind power, and solar power. It proposes a reliable-economic equilibrium scheduling model based on biblical optimization, which describes the wind and solar power prediction errors using the Wasserstein distance uncertainty set. This model can solve the problems of stochastic programming relying on specific distributions and the overly conservative solution strategies of robust optimization, providing system decision-makers with a reliable-economic equilibrium scheduling strategy. At the same time, it can provide corresponding scheduling strategies based on the decision-maker's risk preferences. Attached Figure Description

[0044] Figure 1 The optimal target value is determined for different sample sizes during the dry season.

[0045] Figure 2 The optimal target value under different sample sizes during the flood season;

[0046] Figure 3 The Pareto result is for the optimal scheduling model during the dry season;

[0047] Figure 4The Pareto result is for the optimal scheduling model during the flood season.

[0048] Figure 5 The optimal scheduling result for a hydro-wind-solar hybrid energy system during the dry season;

[0049] Figure 6 The optimal scheduling result for a hydro-wind-solar hybrid energy system during the flood season;

[0050] Figure 7 To provide power to various hydropower stations during the dry season;

[0051] Figure 8 To contribute to the hydropower stations during the flood season. Detailed Implementation

[0052] The present invention will be further described below with reference to embodiments.

[0053] The specific operation methods for each step are implemented according to the following ideas (a)-(f):

[0054] (a) Describing the uncertainty of renewable energy

[0055] The uncertainty of renewable energy is described by using fuzzy sets based on Wasserstein distance, and the specific steps are described in the invention description.

[0056] (b) Basic Model Setup

[0057] objective function

[0058] To ensure normal social development, the hydro-wind-solar hybrid energy system should prioritize reliability during its operation, meaning minimizing power supply risk should be the primary objective. The other two economic objectives should be transformed into constraints, and the problem should be modeled accordingly.

[0059]

[0060] The model transformation for the second item in the objective is as follows:

[0061]

[0062] in, This represents the amount of electricity discarded by the i-th renewable energy source during time period t; This represents the power shortage in the hybrid power system during time period t; RES is the number of renewable energy sources, including wind and solar power, RES = 2; s m,t η represents the water discharge from hydropower station m during time period t; m The energy conversion coefficient of hydropower station m is obtained from historical dispatch data; s m,t / η m Let m be the energy wasted by hydropower station m; M and T represent the set of hydropower stations and the set of time periods; α m,tThis represents the adjustment coefficient of hydropower station m in response to uncertainties in renewable energy; The error in the prediction of renewable energy output is represented by λ and μ, which represent Lagrange multipliers, and κ is the dual variable.

[0063] Constraint settings

[0064] (1) Power balance constraints:

[0065]

[0066] in, This represents the output of hydropower station m during time period t; C represents the output of the i-th renewable energy source during time period t; t This represents the system's load demand during time period t.

[0067] (2) Reserve capacity constraints:

[0068]

[0069]

[0070]

[0071]

[0072] in, and r m,t These represent the upper and lower reserve capacities of hydropower station m during time period t, respectively. and These represent the maximum output and maximum reserve capacity of hydropower station m, respectively.

[0073] (3) Water balance constraint:

[0074]

[0075] R m,t =q m,t +s m,t (25)

[0076] Among them, v m,t Indicates the reservoir capacity of hydropower station m during time period t; I m,t s m,t and q m,t τ represents the inflow, discharge, and power generation of hydropower station m during time period t; j,m This indicates the water flow delay time from hydropower station j to hydropower station m.

[0077] (4) Storage capacity constraint:

[0078]

[0079]

[0080] in, V m and These represent the lower and upper limits of the reservoir capacity m of the hydropower station, respectively; This represents the initial storage capacity of the reservoir.

[0081] (5) Downflow constraint:

[0082]

[0083]

[0084] in, Q m and These represent the lower and upper limits of the power generation flow rate of the hydropower station m, respectively. O m and These represent the lower and upper limits of the total discharge flow of the hydropower station m, respectively.

[0085] (6) Clean water head constraint:

[0086]

[0087]

[0088]

[0089]

[0090] in, Indicates the relationship between water level and reservoir capacity; This represents the functional relationship between the tailwater level and discharge rate. This represents the functional relationship between power generation flow and head loss. and These represent the upstream water level and the tailrace water level of hydropower station m during time period t, respectively. and These represent the head loss and net head of the hydropower station m during time period t, respectively.

[0091] (7) Output constraints of hydropower stations:

[0092]

[0093] in, This represents the functional relationship between the power output, power generation flow, and net head of hydropower station m during time period t.

[0094] (8) Hydropower station output ramping constraints:

[0095]

[0096]

[0097] in, and These represent the upper and lower limits of the hydropower station's m-output ramp-up capability, respectively.

[0098] (9) Transmission constraints:

[0099]

[0100] in, and These represent the lower and upper limits of transmission line l, respectively; ι m,l This indicates the proportion of the power output of hydropower station m that is transmitted through transmission line l.

[0101] (10) Power shortage and power abandonment logic constraints:

[0102]

[0103] This formula indicates that power shortages and power abandonment cannot occur simultaneously.

[0104] (c) Transformation of multi-objective problems

[0105] The multi-objective optimization problem is transformed into a single-objective optimization problem using the ε-constraint method. The specific steps are described in the invention description.

[0106] (d) Transform the objective into a manageable form

[0107] The strong duality theory is used to process the part of the objective function that contains fuzzy sets. The specific steps are described in the invention description.

[0108] (e) Model linearization

[0109] The objective function and nonlinear constraints are linearized, a MILP model is established and solved, and the steps for linearizing the objective function are described in the invention description. For the nonlinear constraints, the following method is used.

[0110] Two-dimensional and three-dimensional nonlinear constraints are handled using two mature and effective methods: the multiple choice (MC) model and the decomposition convex combination (DCC) model. Logical constraints are handled by introducing 0-1 auxiliary variables, i.e.:

[0111]

[0112]

[0113] in, and These represent the upper limits for power curtailment and power shortage, respectively. hour, when hour, and This ensures that power shortages and power curtailment do not occur simultaneously, thus achieving the linearization of constraints.

[0114] (f) Application

[0115] (1) Project background and parameter selection

[0116] This embodiment selects the hydro-wind-solar hybrid energy system in the Beipanjiang River basin in southwest China as the research object. The Beipanjiang River basin possesses abundant hydropower, wind power, and solar power resources. Four cascade hydropower stations have been built, and a large amount of wind and solar power has been integrated to construct the Beipanjiang Clean Energy Base. Due to the rapid growth of wind and solar power, the volatility of the power system has increased dramatically, and the difficulty of dispatch and management has continued to rise. Researching the coordinated operation of renewable energy and cascade hydropower can alleviate the burden and play an important role in achieving the 2060 carbon neutrality target.

[0117] This watershed exhibits distinct flood and dry seasons. Representative scenarios were selected to test the performance of this invention. In this embodiment, the hour is used as the day-ahead scheduling unit for the hydro-wind-solar hybrid energy system, and the confidence level of the fuzzy set based on Wasserstein distance is set to 95%. Using the method proposed in the invention, the final MILP model was developed using Pyomo in Python 3.6 and solved using Gurobi 9.0. All programs ran on a personal computer equipped with an Intel Core i7-9750H CPU with a 2.6GHz CPU and 16.0MB of RAM. Iteration was terminated when the step size reached 0.001 or the solution time exceeded 600 seconds.

[0118] (2) Analysis of Calculation Results

[0119] Figure 1 and Figure 2The impact of different numbers of historical samples on the target value is presented for both dry and flood seasons. It can be seen that, regardless of the season, the more historical samples, the smaller the optimal target value. Specifically, as the number of historical samples varies between 1000 and 10000, the power supply risk decreases from 4136.45MW to 1606.39MW during the dry season and from 1334.09MW to 118.08MW during the flood season. According to the calculated Wasserstein radius, the radius for 1000 samples is 0.0334, and for 10000 samples it is 0.0004. This is because the ambiguity set decreases with the increase in the number of historical samples, indicating that as the number of historical samples increases, the unknown distribution gradually approaches the true distribution. In summary, two case studies under different hydrological conditions demonstrate that the proposed Wasserstein distance-based ambiguity optimization model can provide options for selecting the size of the ambiguity set based on the Wasserstein metric, thereby enabling decision-makers to adopt a risk-averse approach. Meanwhile, with the increase in historical data, the understanding of the uncertainty of renewable energy in the decision-making process is also increasing, which further improves the ability of the Wasserstein distance-based bibliometric optimization model to hedge against renewable energy fluctuations.

[0120] Figure 3 and Figure 4 The Pareto results for the economic-reliable equilibrium optimal scheduling model during the dry and flood seasons explain the trade-offs between minimum power supply risk, minimum water consumption, and maximum energy storage. From the results, we can draw the following conclusions: Under different hydrological conditions, the water consumption and energy storage of cascade hydropower stations affect power supply risk; the conflict between the two economic objectives of minimum water consumption and maximum energy storage further increases the power supply risk caused by the uncertainty of renewable energy. With fixed energy storage conditions, a gradual decrease in hydropower water consumption leads to higher power supply risk, while hedging against this risk reduces the economics of cascade hydropower stations (increasing water consumption or reducing energy storage); under different hydrological conditions, maintaining a large water consumption and low energy storage becomes less important for reducing the power risk of the hydrological ecosystem. (See details...) Figure 3 , Figure 4 The horizontal area in the 3D diagram represents the area with the lowest risk.

[0121] Figure 5 and Figure 6 This is an operational plan diagram for a hybrid hydro-wind-solar energy system during the dry and flood seasons, including load demand, output of each power source, and situations of power curtailment and power shortage. Figure 7 and Figure 8 It can be seen that the total power output of the water-wind-solar hybrid system follows the trend of system scheduling.

[0122] Overall, the model enhances the ability of cascade hydropower stations to compensate for uncertainties in renewable energy and to resist power risks in hybrid energy systems.

Claims

1. A balanced scheduling model for a hydro-wind-solar energy system based on distributed bar optimization, characterized in that, The specific steps are as follows: (1) Using fuzzy sets based on Wasserstein distance to describe the uncertainty of renewable energy: in, This indicates the forecasting error or net load uncertainty of renewable energy. and These represent the prediction errors for wind power and solar power output, respectively. For simplicity, the time index t is omitted below. Yes True distribution The estimate, i.e. Historical wind and solar power prediction error data are used in formula (2). Calculate the corresponding Dirac measure Therefore, it can be concluded that Represents the Wasserstein distance; and They respectively follow the distribution and distribution ||·|| represents the norm; Π represents... and The joint distribution; The Wasserstein sphere is represented by an empirical distribution. Centered on, ∈ N The radius restricts the sum of fuzzy sets. The distance between them; β is the confidence level of the fuzzy set; D is a constant obtained by solving formula (7), where... ρ represents the sample mean; ρ is an auxiliary decision variable. (2) Constructing a partial Bruker optimization model for a hydro-wind-solar hybrid energy system: 1) Quantify the three risks of water wastage, power shortage, and power wastage, and use them as the objective function to ensure the reliable operation of the hydro-wind-solar hybrid system: in, This represents the abandoned power of the i-th type of renewable energy source during time period t; This represents the power shortage in the hybrid power system during time period t; RES is the renewable energy number, including wind and solar power, RES = 2; s m,t η represents the water discharge from hydropower station m during time period t; m The energy conversion coefficient of hydropower station m is obtained from historical dispatch data; s m,t / η m Let m be the energy wasted by hydropower station m; M and T represent the set of hydropower stations and the set of time periods; the objective consists of two stages: the first stage The first stage aims to reduce the risk of "three abandonments" (abandonment of wind, solar, and organic power) and improve the reliability of the hybrid system. This stage involves decisions based on predicted wind and solar power output. The second stage prioritizes minimizing adjustments to hydropower output, utilizing hydropower regulation capabilities to mitigate the interference caused by prediction errors related to renewable energy uncertainties, thus ensuring the stable operation of the cascade hydropower stations. This represents the output adjustment function for the second stage, where x, These represent the decision variables and uncertain sample parameters for the second stage, respectively. 2) Incorporate the economic efficiency of the hydropower station into the objectives, namely, minimizing water consumption (minf2) and maximizing energy storage (maxf3): Among them, R m,t Δt represents the total discharge of hydropower station m during time period t; Δt represents the length of the time period; ES m This represents the stored energy of hydropower station m at the end of the dispatch period, which is equal to the energy generated by power generation from the final water level to the dead water level; v m,T+1 and minV m These represent the storage capacity at the end of the time period and the dead storage capacity, respectively. (3) Model transformation: Step 1: Modify the model in step (2) using the ε-constraint method, transforming the multi-objective problem into a single-objective problem. While ensuring the ideality of a certain objective, other objectives are also fully considered. Power supply risk is taken as the primary objective, and economic objective as the constraint condition. The original objective function is transformed into: Where α m,t This represents the adjustment factor for the uncertainty of new energy response in hydropower station m during time period t, where... That is, the adjustment amount of hydropower output; Step 2: The second stage in the objective function is the function variable of the fuzzy set in the worst case, which is then re-transformed using strong duality theory: Where κ represents the relationship with In Related dual variables; Step 3: Introduce the auxiliary variable τ k Equation (13) can be transformed into: in, It is a convex function. The optimal solution can be found in the maximum value of the samples in Ξ. or sample minimum value ω Where can it be obtained? Step 4: Based on the results of Step 3, continue to transform it into: Step 5: Transform the model from Step 4 into a standard MILP model and use an approximation framework to reduce the dimensionality of the problem; the objective function (15) is transformed into: Here, λ and μ represent Lagrange multipliers.

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