Multi-objective mid-term scheduling method for cascade hydro-photovoltaic-storage considering photovoltaic uncertainty

Abstract

The present application relates to the technical field of comprehensive energy system optimization operation, and discloses a cascade water-light-storage multi-objective medium-term scheduling method considering water inflow and photovoltaic uncertainty. A cascade water-light-storage medium-term complementary power generation model is established by taking the maximum system total power generation and the minimum system residual load variance as the target and combining various types of unit output constraints, thereby guaranteeing the economy, safety and stability of the system. The vibration area constraint of the water turbine unit and the power transmission constraint of the direct current tie line are considered, thereby guaranteeing the safe operation of the cascade water turbine unit and fully playing the power optimization role of the direct current tie line. In view of the seasonal change of natural water inflow and the daily scale fluctuation of photovoltaic output, the information gap decision theory is used to construct a scheduling model considering water and light uncertainty, so that the scheduling method can better avoid the risk brought by water and light uncertainty. For the multi-objective model constructed, the epsilon constraint method is used for solving, and the compromise solution is selected based on the fuzzy decision method, so that the comprehensive satisfaction is maximized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optimal operation of integrated energy systems, in particular to a cascade water-light-storage multi-objective medium-term scheduling method considering water inflow and photovoltaic uncertainty. BACKGROUND

[0002] Photovoltaic power stations have the advantages of low carbon, short construction period, and continuously declining investment cost, which have promoted the rapid increase of installed capacity in recent years. However, solar energy is greatly affected by environmental temperature and weather conditions, and has great volatility in space and time, and shows intermittency and randomness. The increasing popularity of solar energy poses a threat to the stable and safe operation of power systems. In order to accelerate the large-scale integration of renewable energy other than solar energy, multi-energy complementary power generation has emerged in recent years. Hydropower has the characteristics of flexibility and adjustability, and the water turbine can realize from start-up to full load within a few minutes, so it becomes a perfect complementary power source to smooth the fluctuation of photovoltaic energy.

[0003] In addition to cascade hydropower, pumped storage power stations are another important power source to safely and stably alleviate the intermittency and fluctuation of renewable energy. When the renewable energy generation exceeds the system regulation capacity, curtailment of electricity will occur. Therefore, exploring the energy time-shifting capability of system components with energy storage capability (such as pumped storage with medium and long-term energy storage capability) is crucial to reduce the curtailment rate of renewable energy and the corresponding economic loss.

[0004] In the modeling process of cascade hydropower stations, the influence of the vibration zone is often ignored. However, when the water turbine runs in the vibration zone for a long time, it is easy to cause damage to the turbine shaft and blades, so it is necessary to consider the vibration zone constraint in the modeling process of hydropower units.

[0005] China's renewable energy centers are far away from load centers, which leads to the need for long-distance and large-capacity energy transmission. However, there are few studies on the influence of DC tie lines on the operation of multi-energy complementary power generation systems in existing research. In addition, single-objective multi-energy complementary power generation models cannot balance economic benefits and system stability and safety, so it is necessary to establish a multi-objective scheduling model.

[0006] The intensity of light and natural inflow are greatly affected by natural conditions such as climate and temperature, which inevitably causes uncertainty in the scheduling results and poses a great challenge to the efficient use of renewable energy. Domestic and foreign scholars have conducted extensive research on methods for dealing with uncertainty, and current research results mostly use robust optimization or stochastic optimization to deal with uncertainty problems. However, the results of robust optimization are often conservative, and the computational load of stochastic optimization will increase significantly with the increase of uncertain scenarios. In addition, it is quite difficult to determine the probability distribution and membership relationship of variables in many cases.

[0007] Therefore, considering vibration zone constraints, DC tie-line power transmission constraints, and multiple scheduling objectives is of great significance in the cascade hydro-solar-storage complementary power generation model. In the modeling process where photovoltaic output and natural water inflow are uncertain, the use of non-probabilistic and non-fuzzy information gap decision theory can effectively address the complex internal mechanisms and limited known information of hydro-solar-storage complementary power generation systems. Summary of the Invention

[0008] To address the aforementioned problems, the present invention aims to provide a multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems that considers the uncertainty of incoming water photovoltaic power, while simultaneously taking into account the system's economic and safety stability requirements. This method fully leverages the power optimization capabilities of hydropower units and DC tie lines, reducing the risks to system economy caused by the uncertainty of hydropower-solar power. The technical solution is as follows:

[0009] A multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems that considers the uncertainty of incoming water photovoltaic power includes the following steps:

[0010] Step 1: Determine the objective function of the multi-objective medium-term scheduling model for cascade hydropower, solar power, and energy storage: maximize the total power generation of the system and minimize the variance of the remaining load;

[0011] Step 2: Determine the constraints of the cascade hydropower stations, including output constraints, water balance and reservoir capacity constraints, and vibration zone constraints;

[0012] Step 3: Establish constraints for the pumped storage power station, including reservoir capacity constraints, state constraints, output constraints, and start-up / shutdown frequency constraints;

[0013] Step 4: Establish output constraints for photovoltaic power plants;

[0014] Step 5: Establish DC tie-line power transmission constraints, including upper and lower limit constraints, regulation rate constraints, and regulation number constraints;

[0015] Step 6: Further consider the uncertainties of natural water inflow and photovoltaic power output, and establish a robust model based on information gap decision theory;

[0016] Step 7: Solve the model using the ε-constraint method, and select a compromise solution using the fuzzy decision-making method;

[0017] Step 8: Input the equipment parameters and operating parameters of the cascade hydro-solar-storage complementary power generation system, and use the commercial solver Gurobi to solve the multi-objective model to obtain the scheduling results.

[0018] Furthermore, the objective function of the multi-objective medium-term scheduling model for cascade hydropower-solar-storage systems described in step 1 is as follows:

[0019]

[0020] C γ,t =L γ,t-P γ,loc,t

[0021]

[0022] In the formula: I, S, R, and T represent the number of cascade hydropower units, photovoltaic power stations, pumped storage power stations, and time periods, respectively; γ is the typical day index; P γ,i,t and P γ,s,t These represent the output of the cascade hydropower unit i and the photovoltaic power station s, respectively. and These represent the output of pumped-storage unit r when it is in power generation and pumping mode, respectively; Δt is the time period length; N γ This is the typical number of days; L γ,t C γ,t and These represent the local load, remaining load, and average remaining load of γ during time period t on a typical day; P γ,d,t and P γ,loc,t d represents the power transmitted and the power absorbed locally by the DC tie line d during the time period t of a typical day γ, respectively; D represents the number of DC tie lines; W represents the total power generation of the system; and C represents the variance of the remaining load.

[0023] Furthermore, the constraints of the cascade hydropower stations mentioned in step 2 are as follows:

[0024] (1) Output constraint:

[0025]

[0026] h γ,i,t ·P i min ≤P γ,i,t ≤h γ,i,t ·P i max

[0027] -ΔP i max ≤P γ,i,t -P γ,i,t-1 ≤ΔP i max

[0028] In the formula: Q γ,i,t It is the power generation flow of the cascade hydropower station i during time period t; It is the average water consumption rate of hydropower conversion; c i P represents the conversion factor; i min and P i max Represents the minimum and maximum output values ​​of cascade hydropower station i; 0-1 variable h γ,i,tΔP represents the start-up and shutdown state variables of hydropower unit i during time period t on a typical day γ. i max This represents the maximum climbing ability of the cascade hydropower unit i.

[0029] (2) Water balance and reservoir capacity constraints:

[0030]

[0031] q γ,i,t =Q γ,i,t +S γ,i,t

[0032] V i min ≤V γ,i,t ≤V i max

[0033]

[0034] In the formula: V γ，i,t The reservoir capacity of cascade hydropower station i during the t-hour period of a typical day γ; q γ,i,t and S γ,i,t Each represents the predicted natural inflow, outflow, and discharge of the cascade hydropower unit i during the t-hour period of a typical day γ; V i min and V i max Each represents the minimum and maximum reservoir capacity of cascade hydropower station i; and Each represents the minimum and maximum power generation flow of cascade hydropower station i;

[0035] (3) Vibration zone constraint:

[0036]

[0037] u i,k ∈{0,1}

[0038] In the formula: M is a sufficiently large positive number; and The range of vibration zone k represents the area of ​​the cascade hydropower station i; u i,k It is a 0-1 variable, indicating that the unit output is less than the lower limit of the vibration zone or higher than the upper limit of the vibration zone. It is 1 when it is less than the lower limit of the vibration zone and 0 when it is higher than the upper limit of the vibration zone.

[0039] Furthermore, the specific constraints of the pumped storage power station mentioned in step 3 are as follows:

[0040] (1) Reservoir capacity constraints:

[0041]

[0042] In the formula: V γ,u,t and V γ,d,t Each represents the upper and lower reservoir capacity of a pumped storage power station during the t-hour period of a typical day γ; and This represents the lower and upper limits of the reservoir's capacity; and Represents the lower and upper limits of the reservoir's capacity; η p and η g Each represents the hydroelectric conversion coefficient in the pumping state and the power generation state, respectively;

[0043] (2) State constraints:

[0044]

[0045]

[0046] In the formula: 0-1 variables and These are the power generation and pumping state variables of the unit; and Each represents the start-up variables for the unit's power generation and pumping status; and Variables indicating the shutdown status of power generation and pumping; and This represents the power generation and pumping state variables of the entire power station;

[0047] (3) Output constraint:

[0048]

[0049] In the formula: and Each represents the maximum output of unit r under pumping and power generation conditions; and Each represents the ramp limit of the unit under power generation and pumping conditions;

[0050] (4) Start-stop frequency constraint:

[0051]

[0052] In the formula: and Each represents the maximum number of times unit r can be started in both power generation and pumping modes during the dispatch period.

[0053] Furthermore, the specific output constraints of the photovoltaic power station mentioned in step 4 are as follows:

[0054]

[0055] In the formula: This represents the predicted value of photovoltaic power plant s in time period t.

[0056] Furthermore, the DC tie-line power transmission constraints described in step 5 are as follows:

[0057]

[0058]

[0059] In the formula: P γ,d,t It is the power transmitted by the DC tie line during time period t on a typical day γ; and Represents the lower and upper limits of power transfer; 0-1 variables. and Indicates whether the power has been adjusted upwards or downwards; and Indicates the power rise and fall limits for adjacent time periods; n d This represents the maximum number of times the power can be adjusted.

[0060] Furthermore, the robust model based on information gap decision theory described in step 6 is as follows:

[0061] (1) Description of uncertainty

[0062] The relationship between the predicted and actual values ​​of photovoltaic power output and natural water inflow is as follows;

[0063]

[0064] In the formula: s represents the actual value of photovoltaic power plant s in time period t; e represents the predicted deviation of photovoltaic output, e max and e min β represents the upper and lower limits of the photovoltaic power output prediction deviation; β is the photovoltaic power output deviation coefficient. This represents the deviation in water inflow forecast. and The upper and lower limits of the inflow forecast deviation are represented by α; α is the deviation coefficient of the inflow forecast; U S and U I These are the uncertain sets of photovoltaic output and water inflow, respectively; I γ,i,t The actual value of the natural inflow of the cascade hydropower unit i during the t-period of a typical day γ;

[0065] (2) Construct a robust model based on information gap decision theory;

[0066] Rewrite the original deterministic model in matrix form;

[0067] min B(X,d0)

[0068] stF(X,d0)=0,G(X,d0)≤0

[0069] In the formula: X represents the decision variable; d0 represents the uncertain parameter, including natural water inflow and photovoltaic power output; F and G represent equality and inequality constraints, respectively; B represents the original objective function;

[0070] In information gap decision theory, the uncertainty of uncertain parameters is considered as the deviation between the predicted and actual values. The uncertainty set is as follows:

[0071] d0∈U(d * ,D0)

[0072]

[0073] In the formula: d * U(d) represents the predicted value of the uncertain parameter. * D0) is the set of uncertainties that indicate the deviation of the uncertain parameter from the predicted range; D0 is the maximum fluctuation range of the uncertain parameter;

[0074] The relevant constraints are modified as follows after considering the uncertainties of water-optical processes;

[0075] V γ,i,t =V γ,i,t-1 +I γ,i,t +q γ,i-1,t -q γ,i,t

[0076]

[0077] In the formula: I γ,i,t and They belong to the uncertain set U of incoming water. I And the uncertain set U of photovoltaic output S ;

[0078] The robust model based on the information gap decision theory is described as follows;

[0079] maxα,β

[0080] maxC=C(X,d0)≤(1+λ C )·C0

[0081] minW=W(X,d0)≥(1-λ W )·W0

[0082]

[0083] g(x)≤0,f(x)=0

[0084] In the formula: C and W represent the variance of the remaining load and the total power generation; C0 and W0 represent the variance of the remaining load and the total power generation obtained under the deterministic model, which are called the base quantities; λ C and λ W The coefficients represent the deviation between the remaining load and the total power generation; g(x) and f(x) represent the remaining inequalities and equality constraints.

[0085] Furthermore, the specific steps in step 7 for solving the model using the ε-constraint method and selecting a compromise solution using the fuzzy decision method are as follows:

[0086] Step 7.1: Solve using the ε-constraint method

[0087] The uncertainties regarding water inflow and photovoltaic power in the robust model are simplified as follows:

[0088]

[0089] The simplified information gap decision theory model is as follows:

[0090] maxα,β

[0091] maxC=C(X,d0)≤(1+λ C )·C0

[0092] minW=W(X,d0)≥(1-λ W )·W0

[0093]

[0094] g(x)≤0,f(x)=0

[0095] The specific steps for solving multi-objective models using the ε-constraint method are as follows;

[0096] 1) Calculate the optimal value for each single objective and obtain their optimal solutions, which represent the optimal solutions under a single objective;

[0097] 2) Calculate the payoff matrix: Substitute the optimal solution of a single objective into the payoff matrix for other objectives;

[0098] 3) Selecting the primary objective: Select the primary objective based on the decision-maker's preferences;

[0099] 4) Determine the ε constraint: Treat the other objective as a constraint, and the original multi-objective model is transformed into the following model;

[0100] maxα(X)

[0101] g(x)≤0,f(x)=0

[0102] C=C(X,d0)≤(1+λ C )·C0

[0103] W=W(X,d0)≥(1-λ W )·W0

[0104]

[0105] β≥ε i

[0106]

[0107] In the formula: n represents the number of equal parts; ε i Let α(X1) and β(X2) be the lower limit of the objective value included in the constraints during the i-th solution, and let β(X1) and β(X2) be the values ​​of β(X) when considering the objectives α(X) and β(X) separately.

[0108] 5) Solve the nth-degree single-objective model to obtain the Pareto solution set;

[0109] Step 7.2: Select the Pareto compromise solution using the fuzzy decision-making method. The specific steps are as follows;

[0110] 1) Determine the satisfaction level of each Pareto solution:

[0111]

[0112] In the formula: A v This represents the satisfaction level of the Pareto solution v; This represents the value of the Pareto solution; and Indicates upper and lower limits;

[0113] 2) Determine the target weights

[0114] The weight ω of the objective is determined based on the decision-maker's preferences. v ;

[0115] 3) Determine overall satisfaction

[0116]

[0117] In the formula: A represents the overall satisfaction level, and V represents the number of Pareto solutions;

[0118] According to the fuzzy decision-making method, the solution with the highest overall satisfaction is selected as the compromise solution; the weights of the two objectives, total system power generation W and residual load variance C, are both set to 0.5; then the overall satisfaction is calculated using the following formula:

[0119]

[0120] In the formula: W max and W min C represents the upper and lower limits of the system's total power generation;max and C min These are the upper and lower limits of the residual load variance.

[0121] Furthermore, the equipment parameters of the cascade hydro-solar-storage complementary power generation system mentioned in step 8 include the upper and lower limits of unit output, hydro-electricity conversion coefficient, maximum reservoir capacity, maximum gradient and upper and lower limits of vibration range, as well as load data, inflow water and photovoltaic output prediction data.

[0122] The beneficial effects of this invention are:

[0123] 1) This invention aims to maximize the total power generation of the system and minimize the variance of the system's remaining load, and establishes a medium-term complementary power generation model of cascade hydro-solar-storage power generation by combining the output constraints of various units, while ensuring the economic efficiency and safety and stability of the system.

[0124] 2) This invention takes into account the vibration zone constraints of hydropower units and the power transmission constraints of DC tie lines, thereby ensuring the safe operation of cascade hydropower units and giving full play to the power optimization effect of hydropower units and DC tie lines;

[0125] 3) This invention addresses the seasonal variations in natural water inflow and the daily fluctuations in photovoltaic output by employing information gap decision theory to construct a scheduling model that considers the uncertainties of water and solar power, thereby enabling the scheduling method to better mitigate the risks brought about by the uncertainties of water and solar power.

[0126] 4) For the constructed multi-objective model, this invention uses the ε-constraint method to solve it, and selects a compromise solution based on the fuzzy decision method to maximize the overall satisfaction. Attached Figure Description

[0127] Figure 1 This is a flowchart of the steps of the method described in this invention.

[0128] Figure 2 This is a schematic diagram of the vibration zone of a hydroelectric generator unit.

[0129] Figure 3 This is the system architecture diagram for the simulation test.

[0130] Figure 4 It is a multi-timescale water-light uncertainty diagram. Detailed Implementation

[0131] To provide a detailed explanation of the technical solutions disclosed in this invention, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0132] This invention discloses a multi-objective medium-term scheduling method for cascaded hydropower-solar-storage systems that considers the uncertainties of natural water inflow and photovoltaic power generation. The specific implementation steps are as follows: Figure 1 As shown, the technical solution of the present invention includes the following steps:

[0133] Step 1: Determine the objective function of the multi-objective medium-term scheduling model for cascade hydropower, solar power and energy storage: maximize the total power generation of the system and minimize the variance of the remaining load.

[0134]

[0135] C γ,t =L γ,t -P γ,loc,t

[0136]

[0137] In the formula: I, S, R, and T represent the number of cascade hydropower units, photovoltaic power stations, pumped storage power stations, and time periods, respectively. γ is a typical day index. P γ,i,t P γ,s,t , and N represents the output of the cascade hydropower unit i, the photovoltaic power station s, and the pumped storage unit r, which is in both power generation and pumping operation. Δt is the time period length, set to 1 hour. γ This is a typical number of days. L γ,t C γ,t and P represents the local load, remaining load, and average remaining load of γ during time period t on a typical day. γ,d,t and P γ,loc,t These represent the power transmitted and the power absorbed locally by the DC tie line d during time period t on a typical day γ. D represents the number of DC tie lines. W represents the total system power generation, and C represents the variance of the remaining load.

[0138] Step 2: Determine the output constraints of the cascade hydropower stations, mainly including output constraints, water balance and reservoir capacity constraints, and vibration zone constraints.

[0139] (2.1) Output constraints:

[0140]

[0141] h γ,i,t ·P i min ≤P γ,i,t ≤h γ,i,t ·P i max

[0142] -ΔP i max ≤P γ,i,t -P γ,i,t-1 ≤ΔP i max

[0143] In the formula: Q γ,i,tIt is the power generation flow of the cascade hydropower station i during time period t; It is the average water consumption rate of hydropower conversion; c i P represents the conversion factor; i min and P i max Represents the minimum and maximum output values ​​of cascade hydropower station i; 0-1 variable h γ,i,t This represents the start-up and shutdown state variables of hydropower unit i during time period t on a typical day γ. ΔP i max This represents the maximum climbing ability of the cascade hydropower unit i.

[0144] (2.2) Water balance and reservoir capacity constraints:

[0145]

[0146] q γ,i,t =Q γ,i,t +S γ,i,t

[0147] V i min ≤V γ,i,t ≤V i max

[0148]

[0149] In the formula: V γ，i,t The reservoir capacity represents the cascade hydropower station i during the t-hour period of a typical day γ. q γ,i,t and S γ,i,t Each represents the predicted natural inflow, outflow, and discharge of the cascade hydropower unit i during the t-hour period of a typical day γ; V i min and V i max Each represents the minimum and maximum reservoir capacity of cascade hydropower station i. and Each represents the minimum and maximum power generation flow of cascade hydropower station i.

[0150] (2.3) Vibration zone constraints:

[0151]

[0152] u i,k ∈{0,1}

[0153] In the formula: M is a sufficiently large positive number; and The range of vibration zone k represents the area of ​​the cascade hydropower station i. i,kIt is a 0-1 variable.

[0154] A schematic diagram of the vibration zone of a hydroelectric generator unit is shown below. Figure 2 As shown.

[0155] Step 3: Establish constraints for the pumped storage power station, mainly including reservoir capacity constraints, state constraints, output constraints, and start-up / shutdown frequency constraints.

[0156] (3.1) Reservoir capacity constraints:

[0157]

[0158] In the formula: V γ,u,t and V γ,d,t Each represents the upper and lower reservoir capacity of a pumped storage power station during the t-hour period of a typical day γ. and This represents the lower and upper limits of the reservoir's capacity. Similarly, and This represents the lower and upper limits of the reservoir's capacity. η p and η g Each represents the hydroelectric conversion coefficient in the pumping and power generation states, respectively.

[0159] (3.2) State constraints:

[0160]

[0161] In the formula: 0-1 variables and These are the power generation and pumping state variables of the unit; and Each represents a variable indicating the generator unit's power generation and pumping status at startup. Similarly, and This variable represents the shutdown status of power generation and pumping. and This represents the power generation and pumping state variables of the entire power plant.

[0162] (3.3) Output constraints:

[0163]

[0164] In the formula: and Each represents the maximum output of unit r under pumping and power generation conditions, respectively. and Each represents the ramp limit of the unit under power generation and pumping conditions.

[0165] (3.4) Start-stop frequency constraint:

[0166]

[0167] In the formula: and Each represents the maximum number of times unit r can be started in both power generation and pumping modes during the dispatch period.

[0168] Step 4: Establish output constraints for photovoltaic power plants.

[0169]

[0170] In the formula: This represents the predicted value of photovoltaic power plant s in time period t.

[0171] Step 5: Establish DC tie-line power transfer constraints. This mainly includes upper and lower limit constraints, adjustment rate constraints, and adjustment number constraints.

[0172]

[0173]

[0174] In the formula: P γ,d,t It is the transmission power of the DC tie line during time period t. and Represents the lower and upper limits of power transfer. 0-1 variables. and This indicates whether the power is adjusted upwards or downwards. and This indicates the power increase and decrease limits for adjacent time periods. d This represents the maximum number of times the power can be adjusted.

[0175] Step 6: Further consider the uncertainties of natural water supply and photovoltaic power output, and establish a robust model based on information gap decision theory.

[0176] (6.1) Information Gap Decision Theory

[0177] Information gap decision theory does not require probability distribution functions and membership functions, making it suitable for uncertainty modeling of systems with complex internal mechanisms and limited known information. Information gap decision theory comprises three parts: the original system model, the uncertainty set, and the pre-defined objective. Information refers to the factors introducing uncertainty parameters, and gaps refer to the deviation between the actual value and the predicted value of the uncertain parameter. The uncertainty set is the set of all possible values ​​of the uncertain parameter. The uncertainty introduced by the uncertain parameter can have two possible effects on the original objective: increasing the risk of the objective becoming worse or increasing the probability of achieving a better objective. A model built based on the former is called a risk-averse robust model, which sets a worst-case objective value and seeks the maximum fluctuation range of the uncertain parameter that is no worse than that case. A model built based on the latter is called an opportunity model, which sets a better objective value and seeks the minimum fluctuation range of the uncertain parameter that allows the objective to be achieved. The choice of model depends on the decision-maker's preference; this invention chooses a robust model.

[0178] (6.2) Description of uncertainty.

[0179] Due to the influence of rainfall and climate conditions, the natural inflow of cascade hydropower stations exhibits seasonal uncertainty. Unlike photovoltaic power stations, cascade hydropower stations have a certain water storage capacity, so the impact of inflow uncertainty on power generation is not relatively independent over time. Photovoltaic power generation exhibits daily uncertainty. The specific relationship between the predicted and actual values ​​of photovoltaic output and natural inflow is as follows.

[0180]

[0181] In the formula: s represents the actual value of photovoltaic power plant s in time period t; e represents the predicted deviation of photovoltaic output, e max and e min β represents the upper and lower limits of the photovoltaic power output prediction deviation; β is the photovoltaic power output deviation coefficient. This represents the deviation in water inflow forecast. and The upper and lower limits of the inflow forecast deviation are represented by α; α is the deviation coefficient of the inflow forecast; U S and U I These are the uncertain sets of photovoltaic power output and water inflow, respectively; I γ,i,t The actual natural inflow rate of the cascade hydropower unit i during the t-period on a typical day γ.

[0182] (6.3) Construct a robust model based on information gap decision theory.

[0183] The original deterministic model can be written in matrix form.

[0184] min B(X,d0)

[0185] stF(X,d0)=0,G(X,d0)≤0

[0186] In the formula: X represents the decision variable; d0 represents the uncertain parameters, including natural water inflow and photovoltaic power output. F and G represent the equality and inequality constraints, respectively.

[0187] In information gap decision theory, the uncertainty of an uncertain parameter is considered as the deviation between the predicted and actual values. The uncertainty set is as follows:

[0188] d0∈U(d * ,D0)

[0189]

[0190] In the formula: d * U(d) represents the predicted value of the uncertain parameter. * D0) is the set of uncertainties that indicates the deviation of the uncertain parameter from the predicted value range; D0 is the maximum fluctuation range of the uncertain parameter.

[0191] The relevant constraints are modified as follows after considering the uncertainties of water and light.

[0192] V γ,i,t =V γ,i,t-1 +I γ,i,t +q γ,i-1,t -q γ,i,t

[0193]

[0194] In the formula: I γ,i,t and They belong to the uncertain set U of incoming water. I And the uncertain set U of photovoltaic output S .

[0195] The robust model based on the information gap decision theory is described as follows.

[0196] maxα,β

[0197] maxC=C(X,d0)≤(1+λ C )·C0

[0198] minW=W(X,d0)≥(1-λ W )·W0

[0199]

[0200] g(x)≤0,f(x)=0

[0201] In the formula: C and W represent the variance of the remaining load and the total power generation; C0 and W0 represent the variance of the remaining load and the total power generation obtained under the deterministic model, which are called the base quantities; λ C and λ W The coefficients represent the deviation between the remaining load and the total power generation; g(x) and f(x) represent the remaining inequalities and equality constraints.

[0202] Step 7: Solve the model using the ε-constraint method, and select a compromise solution using the fuzzy decision method.

[0203] (7.1) Introduction to the ε-constraint method.

[0204] The robust model established in step (6) is a bilevel programming model, which is difficult to solve directly. Considering that the power generation and surplus load constraints are easier to satisfy when there is more incoming water, for a hydro-solar-storage system with sufficient regulation capacity, the greater the photovoltaic output, the easier it is to satisfy the power generation and surplus load constraints in the model. Therefore, the uncertain constraints of incoming water and photovoltaic power in the robust model are simplified as follows:

[0205]

[0206] The simplified information gap decision theory model is as follows:

[0207] maxα,β

[0208] maxC=C(X,d0)≤(1+λ C )·C0

[0209] minW=W(X,d0)≥(1-λ W )·W0

[0210]

[0211] g(x)≤0,f(x)=0

[0212] The specific steps for solving multi-objective models using the ε-constraint method are as follows:

[0213] 1) Calculate the optimal value for each individual objective to obtain their optimal solutions. represents the optimal solution for each individual objective;

[0214] 2) Calculate the payoff matrix. The payoff matrix can be obtained by substituting the optimal solution of a single objective into the solutions of other objectives.

[0215] 3) Select the primary objective. Select the primary objective based on the decision-maker's preferences.

[0216] 4) Determine the ε constraint. By treating the other objective as a constraint, the original multi-objective model is transformed into the following model.

[0217] maxα(X)

[0218] g(x)≤0,f(x)=0

[0219] C=C(X,d0)≤(1+λ C )·C0

[0220] W=W(X,d0)≥(1-λ W )·W0

[0221]

[0222] β≥ε i

[0223]

[0224] In the formula: n represents the number of equal parts. ε i Let α(X1) and β(X2) be the lower limit of the objective value included in the constraints during the i-th solution, and let β(X1) and β(X2) be the values ​​of β(X) when considering the objectives α(X) and β(X) separately.

[0225] 5) Solving the nth-order single-objective model yields the Pareto solution set.

[0226] (7.2) The specific steps for selecting the Pareto compromise solution using the fuzzy decision-making method are as follows.

[0227] 1) Determine the satisfaction level of each Pareto solution:

[0228]

[0229] In the formula: A v This represents the satisfaction level of the Pareto solution v; This represents the value of the Pareto solution. and Indicates the upper and lower limits.

[0230] 2) Determine the target weights

[0231] The weight ω of the target v The choice of weights can be determined based on the decision-maker's preferences, and the selection of weights can directly affect the choice of compromise solutions.

[0232] 3) Determine overall satisfaction

[0233]

[0234] In the formula: A represents overall satisfaction, and V represents the number of Pareto solutions. According to the fuzzy decision-making method, the solution with the highest overall satisfaction is selected as the compromise solution. This invention considers power generation and surplus load variance to be equally important, with each objective having a weight of 0.5. Overall satisfaction is calculated using the following formula:

[0235]

[0236] The effects of the present invention will be described in detail below through specific embodiments.

[0237] (1) Example introduction.

[0238] like Figure 3 The diagram shown illustrates the system architecture of the simulation test system. The system includes a photovoltaic power station, a cascade hydropower system with upstream and downstream power stations, an equivalent pumped storage power station, and an equivalent high-voltage direct current (HVDC) interconnection line. Figure 4 The multi-timescale water-light uncertainty diagram shown uses three typical days to represent the normal water period (first stage, 24 hours), the high water period (second stage, 24 hours), and the low water period (third stage, 24 hours).

[0239] Considering the complementarity of hydropower and solar power, this study investigates the vibration zone of cascade hydropower units, the connection of pumped storage power stations, DC tie-line power optimization, and the impact of uncertainties in hydropower and solar power. The settings for the examples are shown in Table 1. It is worth noting that the DC tie-line power transmission plans in Examples 2 and 3 are consistent with those in Example 1.

[0240] Table 1: Setup of Examples 1 to 5

[0241]

[0242] (2) Analysis of the results of the implementation examples.

[0243] Table 2 presents the solution results for Examples 1-5. It can be seen that after considering the vibration zone constraint, the power generation in Example 2 decreased by 21.62 MWh compared to Example 1, and the curtailment rate increased to 24.59%. This indicates that considering the vibration zone constraint slightly worsened the system's economics, but it avoided the units operating in the inefficient and life-damaging vibration zone. Example 3, based on Example 2, incorporates a pumped-storage power station. Considering the same residual load variance, the total power generation in Example 3 increased to 1,703,094.81 MWh, and the curtailment rate decreased to 21.11%. After considering the power optimization effect of the DC tie line, the total system power generation further increased to 1,882,375.42 MWh, and the curtailment rate decreased to 14.88%. Both the pumped-storage power station and the DC tie line contribute to improving system economics and renewable energy utilization.

[0244] Table 2 Comparison of results for different examples

[0245]

[0246] Table 3 shows the variance of the output curves of the cascade hydropower units in Examples 1-4. After considering the effect of the pumped storage power station, the variance of the output curves of the cascade hydropower units is significantly reduced, and the output becomes smoother, alleviating the peak-shaving pressure on the units. However, after considering the effect of the DC tie line, the output variance of the two units increases to 1227.81 MW. 2 and 2147.82MW 2 This sacrifices, to some extent, the regulation capacity of the cascade hydropower units.

[0247] Table 3 shows the variance (MW) of the output curves of the cascade hydropower units in Examples 1-4. 2 )

[0248]

[0249] Example 5, building upon Example 4, considers the uncertainties of natural water inflow and photovoltaic output, and employs information gap decision theory for modeling. Table 4 shows a comparison of the results before and after considering these uncertainties, with the deviation coefficients for power generation and surplus load both set to 0.02. Clearly, after considering these uncertainties, the total power generation in Example 5 is 1,844,727.92 MWh, higher than the 1,842,028.73 MWh in Example 4. This demonstrates that uncertainty modeling based on information gap decision theory has a significant advantage in addressing the adverse effects of water and photovoltaic uncertainties on the system.

[0250] Table 4 Comparison of results before and after considering the uncertainty of water and light.

[0251]

[0252] The above description constitutes a specific embodiment of the present invention, but does not limit the scope of patent protection of the present invention. Any equivalent changes or substitutions made using the content of the present invention specification and drawings, or any direct or indirect application to other related technical fields, should be included within the scope of protection of the present invention.

Claims

1. A multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems that considers the uncertainty of incoming water photovoltaic power, characterized in that, Includes the following steps: Step 1: Determine the objective function of the multi-objective medium-term scheduling model for cascade hydropower, solar power, and energy storage: maximize the total power generation of the system and minimize the variance of the remaining load; Step 2: Determine the constraints of the cascade hydropower stations, including output constraints, water balance and reservoir capacity constraints, and vibration zone constraints; Step 3: Establish constraints for the pumped storage power station, including reservoir capacity constraints, state constraints, output constraints, and start-up / shutdown frequency constraints; Step 4: Establish output constraints for photovoltaic power plants; Step 5: Establish DC tie-line power transmission constraints, including upper and lower limit constraints, regulation rate constraints, and regulation number constraints; Step 6: Further consider the uncertainties of natural water inflow and photovoltaic power output, and establish a robust model based on information gap decision theory; Step 7: Solve the model using the ε-constraint method, and select a compromise solution using the fuzzy decision-making method; Step 8: Input the equipment parameters and operating parameters of the cascade hydro-solar-storage complementary power generation system, and use the commercial solver Gurobi to solve the multi-objective model to obtain the scheduling results; The robust model based on information gap decision theory described in step 6 is as follows: (1) Description of uncertainty The relationship between the predicted and actual values ​​of photovoltaic power output and natural water inflow is as follows; ； ； ； ； ； ； ； ； In the formula: This represents the actual value of photovoltaic power plant s in time period t; This represents the deviation in photovoltaic power output forecast. and Represents the upper and lower limits of the photovoltaic power output prediction deviation; It is the photovoltaic output deviation coefficient; This represents the deviation in water inflow forecast. and Represents the upper and lower limits of the deviation in water inflow forecast; It is the deviation coefficient for water inflow prediction; and These are the uncertain sets of photovoltaic power output and water inflow, respectively; For typical days The actual value of the natural inflow of the cascade hydropower unit i during time period t; This represents the predicted value of photovoltaic power plant s in time period t; Representative on typical day The predicted natural inflow rate of the cascade hydropower unit i during the t-period; (2) Construct a robust model based on information gap decision theory; Rewrite the original deterministic model in matrix form; ； In the formula: X represents the decision variable; d0 represents the uncertain parameters, including natural water inflow and photovoltaic power output; F and G represent equality and inequality constraints, respectively; B represents the original objective function. In information gap decision theory, the uncertainty of uncertain parameters is considered as the deviation between the predicted and actual values. The uncertainty set is as follows: ； In the formula: This represents the predicted value of the uncertain parameter. It is an uncertain set that indicates that the uncertain parameters deviate from the predicted range; It represents the maximum fluctuation range of the uncertain parameter; The relevant constraints are modified as follows after considering the uncertainties of water-optical processes; ； ； In the formula: and They belong to the uncertain set of incoming water. Uncertain set of photovoltaic output ; Representing a cascade hydropower station i in a typical day The storage capacity during the t-period; Representative on typical day The discharge flow of the cascade hydropower unit i during time period t; Representative photovoltaic power station s in a typical day The output during time period t; The robust model based on the information gap decision theory is described as follows; ； ； ； ； ； In the formula: and This represents the variance of the remaining load and the total power generation; and The variance of the remaining load and the total power generation obtained from solving the deterministic model are called the base quantities; and This represents the deviation coefficient between the remaining load and the total power generation; and This represents the remaining inequalities and equality constraints.

2. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming water photovoltaic power, as described in claim 1, is characterized in that... The objective function of the multi-objective medium-term scheduling model for cascade hydropower, solar power, and energy storage described in step 1 is as follows: ； ； ； ； ； In the formula: , , and These represent the number of cascade hydropower units, photovoltaic power stations, and pumped storage power stations, as well as the number of time periods, respectively. It is a typical daily index; and These represent the output of the cascade hydropower unit i and the photovoltaic power station s, respectively. and These represent the output of the pumped storage unit r when it is in power generation and pumping mode, respectively. It refers to the length of the time period; This is a typical number of days; , and Representing typical days Local load, remaining load, and average remaining load during time period t; and Representing typical days The power transmitted by DC tie line d during time period t and the power consumed locally; D indicates the number of DC tie lines; This represents the total power generation of the system. This represents the variance of the remaining load.

3. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming photovoltaic power, as described in claim 2, is characterized in that... The specific constraints of the cascade hydropower stations mentioned in step 2 are as follows: (1) Output constraint: ； ； ； In the formula: It is the power generation flow of the cascade hydropower station i during time period t; It is the average water consumption rate of hydropower conversion; Indicates the conversion factor; and Represents the minimum and maximum output values ​​of cascade hydropower station i; 0-1 variables. Indicates that hydropower unit i is in a typical day The start / stop status variables during time period t; This represents the maximum climbing ability of the cascade hydropower unit i. (2) Water balance and reservoir capacity constraints: ； ； ； ； In the formula: Representing a cascade hydropower station i in a typical day The storage capacity during the t-period; , and Each representative on a typical day The predicted natural inflow, outflow and wastewater discharge of the cascade hydropower unit i during the t-period; and Each represents the minimum and maximum reservoir capacity of cascade hydropower station i; and Each represents the minimum and maximum power generation flow of cascade hydropower station i; (3) Vibration zone constraints: ； ； ； In the formula: M is a sufficiently large positive number; and The range of vibration zone k represents the range of the cascade hydropower station i. It is a 0-1 variable, indicating that the unit output is less than the lower limit of the vibration zone or higher than the upper limit of the vibration zone. It is 1 when it is less than the lower limit of the vibration zone and 0 when it is higher than the upper limit of the vibration zone.

4. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming photovoltaic power, as described in claim 3, is characterized in that... The specific constraints of the pumped storage power station mentioned in step 3 are as follows: (1) Reservoir capacity constraints: ； ； ； ； ； ； In the formula: and Each represents a pumped storage power station on a typical day The upper and lower reservoir capacities during time period t; and This represents the lower and upper limits of the reservoir's capacity; and This represents the lower and upper limits of the reservoir's capacity; and Each represents the hydroelectric conversion coefficient in the pumping state and the power generation state, respectively; (2) State constraints: ； ； ； ； ； ； ； ； In the formula: 0-1 variables and These are the power generation and pumping state variables of the unit; and Each represents the start-up variables for the unit's power generation and pumping status; and Variables indicating the shutdown status of power generation and pumping; and This represents the power generation and pumping state variables of the entire power station; (3) Output constraints: ； ； ； ； In the formula: and Each represents the maximum output of unit r under pumping and power generation conditions; and Each represents the ramp limit of the unit under power generation and pumping conditions; (4) Start-stop frequency constraint: ； ； In the formula: and Each represents the maximum number of times unit r can be started in both power generation and pumping modes during the dispatch period.

5. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming photovoltaic power, as described in claim 4, is characterized in that... The specific output constraints of the photovoltaic power station mentioned in step 4 are as follows: ； In the formula: This represents the predicted value of photovoltaic power plant s in time period t.

6. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming photovoltaic power, as described in claim 1, is characterized in that... The DC tie-line power transmission constraints mentioned in step 5 are as follows: ； ； ； ； ； ； In the formula: DC tie lines in typical daily The power transmitted during time period t; and Represents the lower and upper limits of power transmission; 0-1 variables and Indicates whether the power has been adjusted upwards or downwards; and This indicates the power increase and decrease limits for adjacent time periods; This represents the maximum number of times the power can be adjusted.

7. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming photovoltaic power, as described in claim 1, is characterized in that... The specific steps in step 7, including solving the model using the ε-constraint method and selecting a compromise solution using the fuzzy decision method, are as follows: Step 7.1: Solve using the ε-constraint method The uncertainties regarding water inflow and photovoltaic power in the robust model are simplified as follows: ； ； The simplified information gap decision theory model is as follows: ； ； ； ； ； ； The specific steps for solving multi-objective models using the ε-constraint method are as follows: 1) Calculate the optimal value for each single objective and obtain their optimal solutions, which represent the optimal solutions under a single objective; 2) Calculate the payoff matrix: Substitute the optimal solution of a single objective into the payoff matrix for other objectives; 3) Selecting the primary objective: Select the primary objective based on the decision-maker's preferences; 4) Determine the ε constraint: Treat the other objective as a constraint, and the original multi-objective model is transformed into the following model; ； ； ； ； ； ； ； ； In the formula: n represents the number of equal parts; Let be the lower limit value of the objective element included in the constraints during the i-th solution. and To consider the target separately and hour, The value; 5) Solve the nth-degree single-objective model to obtain the Pareto solution set; Step 7.2: Select the Pareto compromise solution using the fuzzy decision-making method. The specific steps are as follows; 1) Determine the satisfaction level of each Pareto solution: ； In the formula: This represents the satisfaction level of the Pareto solution v; This represents the value of the Pareto solution; and Indicates upper and lower limits; 2) Determine the target weight The weight of objectives is determined based on the decision-maker's preferences. ; 3) Determine overall satisfaction ； In the formula: A represents the overall satisfaction level, and V represents the number of Pareto solutions; According to the fuzzy decision-making method, the solution with the highest overall satisfaction is selected as the compromise solution; the total power generation of the system is... and residual load variance If the weights of both objectives are set to 0.5, then the overall satisfaction level is calculated using the following formula: ； In the formula: and These are the upper and lower limits of the system's total power generation; and These are the upper and lower limits of the residual load variance.

8. The multi-objective medium-term scheduling method for cascade hydropower-solar-storage systems considering the uncertainty of incoming photovoltaic power, as described in claim 1, is characterized in that... The equipment parameters of the cascade hydro-solar-storage complementary power generation system mentioned in step 8 include the upper and lower limits of unit output, hydro-electricity conversion coefficient, maximum reservoir capacity, maximum gradient and upper and lower limits of vibration range, as well as load data, inflow water and photovoltaic output prediction data.

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