Power system standby configuration method considering operation reliability in freezing weather

Abstract

The invention discloses a power system standby configuration method considering operation reliability in freezing weather. The method comprises the following steps: 1) constructing a wind turbine fault model and a system operation reliability model in freezing weather; 2) respectively calculating the fault rates of a wind motor and a generator and the fault rate of a power transmission line by using the wind motor fault model and the system operation reliability model in the freezing weather; 3) based on the fault rates of the wind generator and the generator and the fault rate of the power transmission line, constructing a system reliability index electric energy insufficiency expectation analytical expression; 4) constructing a standby optimization model of the embedded operation reliability under the freezing weather based on a system reliability index electric energy shortage expectation analytical expression; and 5) solving the standby optimization model of the embedded operation reliability in the freezing weather to obtain a standby configuration scheme of the power system in the freezing weather. According to the method, the reliability analysis formula is embedded into the standby optimization model, so that the calculation efficiency is improved on the premise of not sacrificing the precision.

Description

Technical Field

[0001] The present invention relates to the field of power system configuration, and specifically to a method for configuring power system reserves considering operation reliability under freezing weather conditions. Background Art

[0002] In order to accelerate the transformation of the power system towards sustainable and low-carbon energy, the utilization rate of renewable energy has been significantly enhanced in recent years. However, due to the randomness of renewable energy, load fluctuations, and electrical equipment failures, the reliability of the power system is significantly threatened. As an important measure to ensure the safe and reliable operation of the power system, configuring operation reserves can effectively address the power imbalance problems caused by uncertain factors. In addition, extreme freezing weather poses a major threat to the reliability and economy of the power system. At the same time, the existing reserve principle of the power system mainly adopts the deterministic reserve principle, and the subjective deterministic reserve configuration adaptability is not sufficient to cope with the new power system operation risks under freezing weather. The reserve results are either too aggressive or conservative in multiple operation scenarios: on the one hand, it is difficult to meet the reliability requirements of the complex and changeable system, and even major safety accidents may be triggered; on the other hand, there is an unreasonable utilization of adjustable resources, resulting in economic losses.

[0003] Under this background, proposing a method for configuring power system operation reserves that takes into account both operation reliability and economy is helpful for the safe and reliable operation of a high-proportion new energy power system. Some scholars have studied the method for configuring power system reserves. Some scholars configure reserves using the N-1 principle and a certain wind load ratio principle. The method is simple and easy to implement and is widely used, but it lacks theoretical analysis and is difficult to meet the economy and reliability of the changeable system. Other scholars have proposed methods based on uncertainty optimization, mainly using methods such as typical scenarios, chance-constrained programming, and robust optimization to configure reserves to cope with the uncertainty risks of power sources and loads. However, this type of method still does not balance the economy and reliability of reserves, and has a high computational complexity. Currently, there are also studies considering setting reserves for reliability and economy to improve the system's ability to cope with risks. However, when considering reliability, it is necessary to calculate the massive states brought by the uncertainty of power sources and loads and equipment failures, and the solution is extremely difficult. The above reserve decisions ignore the effective quantification of the grid operation reliability under extreme freezing weather, and the optimization model is high-dimensional and nonlinear and difficult to solve efficiently, and cannot be applied in practice. Summary of the Invention

[0004] The object of the present invention is to provide a method for configuring power system reserves considering operation reliability under freezing weather conditions, including the following steps:

[0005] 1) Construct a wind turbine failure model and a system operation reliability model under freezing weather conditions;

[0006] 2) Calculate the failure rates of wind turbines, generators, and transmission lines respectively using the wind turbine failure model and the system operation reliability model under freezing weather conditions;

[0007] 3) Based on the failure rates of wind turbines, generators, and transmission lines, construct an analytical expression for the expected energy not supplied (EENS), a system reliability index;

[0008] 4) Based on the analytical expression for the expected energy not supplied (EENS), a system reliability index, construct a spare optimization model with embedded operation reliability under freezing weather conditions;

[0009] 5) Solve the spare optimization model with embedded operation reliability under freezing weather conditions to obtain the spare configuration plan for the power system under freezing weather conditions.

[0010] Furthermore, in step 1), the steps for constructing the wind turbine failure model under freezing weather conditions include:

[0011] 1.1) Calculate the flow field distribution on the blade surface, i.e.:

[0012]

[0013] where ρ is the fluid density; is the fluid velocity vector; v x , v y and v z are the components of the velocity vector along the x, y, and z directions; PRESS is the pressure on the fluid element; F x , F y , F z are the body forces along the x, y, and z directions respectively; F x = 0, F y = 0, F z = -ρg, where g is the acceleration due to gravity; μ is the dynamic viscosity of the fluid; ω is the second molecular viscosity of the fluid; t is the time index; Δt is the time step;

[0014] 1.2) Calculate the movement trajectory of the water droplets in the air, i.e.:

[0015]

[0016] where m r is the mass of the freezing rain; V r is the volume of the freezing rain, V r = 4 / 3π(D r / 2) 3 ; A is the frontal area of the freezing rain; D r is the diameter of the freezing rain; ρ a is the air density; ρ r is the density of the freezing rain; is the air velocity vector; is the glaze ice speed vector; c d is the drag coefficient; c l is the buoyancy coefficient;

[0017] 1.3) Calculate the ice accretion amount of the wind turbine, i.e.:

[0018] m ice,t = m ice,t-1 + m im,t + m in,t - m es,t - m out,t (3)

[0019] In the formula, m im is the mass of the water droplets hitting the grid control volume unit; m in is the mass of the water droplets flowing into the control area; m es is the mass of the water droplets evaporating or sublimating in the control area; m out is the mass of the water droplets flowing out of the control area; m ice is the mass of the water droplets frozen into ice in this area;

[0020] 1.4) Construct a fault model of the wind turbine in freezing weather, i.e.:

[0021]

[0022] In the formula, FOR w base is the basic forced outage rate of the wind turbine unit; v fan is the real-time wind speed at the fan blade; T is the real-time temperature; k1, k2 and k3 are the contribution coefficients of wind, icing and temperature to the outage rate of the unit. FOR w,t is the failure rate of the wind turbine unit.

[0023] Furthermore, the system operation reliability model in freezing weather includes a generator fault model and a transmission line fault model in freezing weather.

[0024] Furthermore, the generator fault model in freezing weather is as follows:

[0025]

[0026] In the formula, FIFOR is the forced outage rate in freezing weather; a and b are the parameters of the exponential distribution; i is the generator index; Q i is the load current of generator i; Q i spec is the rated current of generator i; Q i trip is the maximum trip current of generator i; ORR i 0It is the statistical value of the outage probability of generator i.

[0027] Furthermore, the fault model of the transmission line under freezing weather is as follows:

[0028]

[0029] In the formula, l is the transmission line index; Q l is the load current of transmission line l; is the rated current of transmission line l; Q l trip is the maximum tripping current of transmission line l; ORR l 0 is the statistical value of the outage probability of transmission line l; F IW is the ice wind load formed by the combined action of wind force and ice gravity on the transmission line; Th1 and Th2 are the first and second critical values of the ice wind load respectively; is the length of transmission line l; α is the adjustment coefficient of the slope of the exponential function.

[0030] Furthermore, the system operation reliability model under freezing weather is as follows:

[0031]

[0032] In the formula, I is the set of all generating units; L is the set of all transmission line groups;

[0033] p k,t is the failure rate; K G is the set of failed generating units; K L is the set of failed transmission lines.

[0034] Furthermore, the analytical expression of the expected energy not supplied (EENS) of the system reliability index is as follows:

[0035]

[0036] In the formula, is the expected energy not supplied of the system reliability index under the faults of wind turbines and generators; is the expected energy not supplied of the system reliability index under the fault of the transmission line.

[0037] Furthermore, the analytical expression of the expected energy not supplied of the system reliability index under the faults of wind turbines and generators is constructed through the following steps:

[0038] A1) Construct input variables P t , D t are the generator output, wind turbine output, and load; λ tis the failure rate of the wind turbine and the generator;

[0039] A2) Standardize the input variables, i.e.:

[0040]

[0041] where, x n represents the nth element in x; ξ n represents the nth element in the standard random variable ξ; x n has a distribution function F n (x n ); F n -1 (x n ) is the inverse function of F n (x n ); Φ(ξ n ) is the distribution function of ξ n ; N is the total number of input random variables, N = 2(NI + NW) + 1; NI is the number of generators; NW is the number of wind turbines;

[0042] A3) Construct the output response expression, i.e.:

[0043]

[0044] where, a j,t is the coefficient of the chaos polynomial to be solved; Ψ j,k,t (ξ s,t ) is the chaos polynomial basis; NC is the number of undetermined coefficients; NC + 1 = (N + o)! / (N!o!) is the number of expansion terms; o is the maximum order of N and the PCE basis; j is the PCE coefficient index; s is the wind power load scenario index; k is the fault state index; Y s,k,t is the demand reduction;

[0045] where, the multi-dimensional basis function is as follows:

[0046] Ψ(ξ t ) = ψ(ξ 1,t )ψ(ξ 2,t )···ψ(ξ N,t ) (11)

[0047] A4) Select the expansion order of the orthogonal polynomial to be 2, and construct the first two-order expansion expressions of the Legendre basis and the Hermite basis, i.e.:

[0048]

[0049] A5) Substitute equations (12) and (13) into the output response equations (10) and the multi-dimensional basis function (11) to obtain the second-order PCE, i.e.:

[0050]

[0051] Wherein, a j,t is a coefficient; a 0,t is a constant; ξ j-N,s,k,t is the coefficient of the chaos polynomial;

[0052] A6) Calculate the coefficients of the chaos polynomial in formula (10) using the least squares method to obtain:

[0053]

[0054] The coefficients of the chaos polynomial are simplified as follows:

[0055] H t A t = Y t (16)

[0056] Wherein, H t is composed of all the basis elements of PCE; A t is an N CP × 1 order coefficient matrix;

[0057] N CP = (2N + 1); Y t is the output vector set.

[0058] A7) Based on the polynomial chaos expansion basis function and the coefficients of the chaos polynomial, construct an analytical expression for the expected energy not supplied (EENS), a system reliability index under wind turbine and generator failures, that is:

[0059]

[0060] Wherein, is the demand curtailment under N-1 generator failures at time period t and scenario s; EENS t G is the EENS of N-1 generator failures at time period t; p s is the probability of the wind power load scenario; NS is the total number of wind power load scenarios.

[0061] Furthermore, the analytical expression for the expected energy not supplied (EENS), a system reliability index under transmission line failures, is constructed through the following steps:

[0062] B1) Construct the power flow equation of node m when a transmission line fails, that is:

[0063]

[0064] Wherein, P i,t is the output power of generator i at time period t; P Ww,t is the output power of the wind turbine at time t in period w; w is the wind turbine index; f k,l,t is the power flow of the faulty line l at time t in the N-1 transmission line; D m,t is the load at node m within time period t; is the demand reduction at node m of the N-1 transmission line fault at time t; NI m is the number of generators connected to node m; NW m is the number of wind turbines connected to node m.

[0065] B2) Based on the sensitivity method, determine the internal linear relationship of the power flow before and after the transmission line fault, that is:

[0066]

[0067] In the formula, is the line power flow matrix in the fault state k; the fault state k means that the line l:mn with the start and end points being m and n respectively is disconnected; P is the line power flow under normal conditions; x k is the reactance of the line l:mn; Z0 is the node reactance matrix in the normal state; ΔZ k is the incremental matrix of the node reactance matrix; M k =[0,…,1,…,-1…,0] T ; E is the identity matrix;

[0068] B3) Construct an analytical expression for the expected energy not supplied, which is a system reliability index under the transmission line fault, that is:

[0069]

[0070] In the formula, NM is the total number of nodes.

[0071] Furthermore, the objective function of the reserve optimization model for the embedded operation reliability under freezing weather is as follows:

[0072]

[0073] In the formula, NT is the number of optimization periods; NI is the total number of generators; NW is the total number of wind turbines; a i , b i and c i are the fuel cost coefficients of generator set i; u i,t , P i,t are the 0 / 1 variable and the active power output of generator set i at time t respectively; C i SU is the start-up cost of generator set i at time t; C i SD is the shutdown cost of generator set i at time t; C i,t, R i,t are the reserve cost and the reserve capacity provided by unit i during period t, respectively; VOCW is the penalty coefficient for curtailed wind power; VOLL is the value of lost load; is the predicted wind power output of wind farm w during period t.

[0074] Furthermore, the constraint conditions of the reserve optimization model for embedded operation reliability under freezing weather include the power output limits of generators and wind turbines, reserve capacity constraints, power balance constraints, network power flow constraints, and reliability constraints, namely:

[0075]

[0076]

[0077] In the formula, P k,i,t is the output of generator set i during period t in fault state k, is the output of wind turbine w during period t in fault state k; and are the lower and upper limits of the output of generator i during period t; and are the up and down ramp rates of generator set i; t i on and t i off are the start-up and stop times of generator i, respectively, and T i on and T i off are the minimum start-up and stop times of generator i, respectively; r D is the load proportion coefficient that needs to be provided as reserve; τ is the reserve response time; PTDF is the power transfer distribution factor; is the upper limit of EENS. R t is the reserve capacity; D t is the load.

[0078] The technical effects of the present invention are beyond doubt. The method for power system reserve configuration considering operation reliability under freezing weather proposed by the method of the present invention is more accurate for reserve configuration of a high-proportion new energy power system under extreme weather. Linking the equipment failure rate with variable operating conditions, a series of equipment operation reliability models established are helpful for allocating more accurate reserves. To reduce the computational burden, considering multiple uncertainties such as renewable energy, load, and equipment failures, a general analytical method for operation reliability based on polynomial chaos expansion and sensitivity method is proposed. By embedding the reliability analysis formula into the reserve optimization model, the computational efficiency is improved without sacrificing accuracy. The results show that the proposed method can obtain a reasonable reserve capacity configuration at a relatively fast computational speed, achieving a balance between system reliability and economy under variable operating conditions. Description of the Drawings

[0079] Figure 1 is the topology diagram of the IEEE-30 bus system;

[0080] Figure 2 is the reserve capacity for 24 time periods of M1-M4;

[0081] Figure 3 is the EENS for 24 time periods of M1-M4. Detailed Embodiment

[0082] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject scope of the present invention is limited to the following embodiments. Without departing from the above technical idea of the present invention, various substitutions and changes made according to ordinary technical knowledge and customary means in the art should be included within the protection scope of the present invention.

[0083] Embodiment 1:

[0084] Refer to Figures 1 to 3 , the method for power system reserve configuration considering operation reliability under freezing weather includes the following steps:

[0085] 1) Construct a wind turbine fault model and a system operation reliability model under freezing weather;

[0086] 2) Calculate the failure rates of wind turbines, generators, and transmission line failure rates respectively by using the wind turbine fault model and the system operation reliability model under freezing weather;

[0087] 3) Based on the failure rates of wind turbines, generators, and transmission lines, construct an analytical expression for the expected energy not supplied (EENS) of the system reliability index;

[0088] 4) Based on the analytical expression for the expected energy not supplied (EENS) of the system reliability index, construct a reserve optimization model with embedded operation reliability under freezing weather;

[0089] 5) Solve the standby optimization model for the embedded operation reliability under freezing weather to obtain the standby configuration plan of the power system under freezing weather.

[0090] Embodiment 2:

[0091] A power system standby configuration method considering operation reliability under freezing weather, the technical content is the same as that of Embodiment 1. Further, in step 1), the steps of constructing a wind turbine fault model under freezing weather include:

[0092] 1.1) Calculate the flow field distribution on the blade surface, that is:

[0093]

[0094] In the formula, ρ is the fluid density; is the fluid velocity vector; v x 、v y and v z are the components of the velocity vector along the x, y, and z directions; PRESS is the pressure on the fluid element; F x 、F y 、F z are the body forces along the x, y, and z directions respectively; F x = 0, F y = 0, F z = -ρg, g is the acceleration due to gravity; μ is the dynamic viscosity of the fluid; ω is the second molecular viscosity of the fluid; t is the time index; Δt is the time step;

[0095] 1.2) Calculate the movement trajectory of the water droplet in the air, that is:

[0096]

[0097] In the formula, m r is the mass of the freezing rain; V r is the volume of the freezing rain, V r = 4 / 3π(D r / 2) 3 ; A is the windward area of the freezing rain; D r is the diameter of the freezing rain; ρ a is the air density; ρ r is the density of the freezing rain;

[0098] is the air velocity vector; is the velocity vector of the freezing rain; c d is the drag coefficient; c l is the buoyancy coefficient;

[0099] 1.3) Calculate the ice accretion amount of the wind turbine, that is:

[0100] mice,t = m ice,t-1 + m im,t + m in,t - m es,t - m out,t (3)

[0101] Wherein, m im is the mass of the water droplets hitting the grid control volume element; m in is the mass of the water droplets flowing into the control area; m es is the mass of the water droplets that evaporate or sublimate in the control area;

[0102] m out is the mass of the water droplets flowing out of the control area; m ice is the mass frozen into ice in this area;

[0103] 1.4) Construct a wind turbine fault model under freezing weather, that is:

[0104]

[0105] Wherein, FOR w base is the basic forced outage rate of the wind turbine; v fan is the real-time wind speed at the wind turbine blade; T is the real-time temperature; k1, k2, and k3 are the contribution coefficients of wind, icing, and temperature to the unit outage rate respectively. FOR w,t is the failure rate of the wind turbine.

[0106] Example 3:

[0107] A method for configuring power system reserves considering operation reliability under freezing weather, the technical content is the same as any one of Examples 1-2. Further, the system operation reliability model under freezing weather includes a generator fault model under freezing weather and a transmission line fault model under freezing weather.

[0108] Example 4:

[0109] A method for configuring power system reserves considering operation reliability under freezing weather, the technical content is the same as any one of Examples 1-3. Further, the generator fault model under freezing weather is as follows:

[0110]

[0111] Wherein, FIFOR is the forced outage rate under freezing weather; a and b are the parameters of the exponential distribution respectively; i is the generator index; Q i is the load current of generator i; Q i spec is the rated current of generator i; Q i tripIs the maximum tripping current of generator i; ORR i 0 Is the statistical value of the outage probability of generator i.

[0112] Embodiment 5:

[0113] A power system reserve configuration method considering operation reliability under freezing weather, the technical content is the same as any one of Embodiments 1-4. Further, the fault model of the transmission line under freezing weather is as follows:

[0114]

[0115] In the formula, l is the transmission line index; Q l Is the load current of transmission line l; Is the rated current of transmission line l; Q l trip Is the maximum tripping current of transmission line l; ORR l 0 Is the statistical value of the outage probability of transmission line l; F IW Is the ice wind load formed by the combined action of wind force and ice gravity on the transmission line; Th1 and Th2 are the first and second critical values of the ice wind load respectively; Is the length of transmission line l; α is the adjustment coefficient of the slope of the exponential function.

[0116] Embodiment 6:

[0117] A power system reserve configuration method considering operation reliability under freezing weather, the technical content is the same as any one of Embodiments 1-5. Further, the system operation reliability model under freezing weather is as follows:

[0118]

[0119] In the formula, I is the set of all generating units; L is the set of all transmission line groups; p k,t Is the failure rate; K G Is the set of failed generating units; K L Is the set of failed transmission lines.

[0120] Embodiment 7:

[0121] A power system reserve configuration method considering operation reliability under freezing weather, the technical content is the same as any one of Embodiments 1-6. Further, the analytical expression of the expected energy shortage of the system reliability index is as follows:

[0122]

[0123] In the formula, Is the expected energy shortage of the system reliability index under the faults of wind turbines and generators; Expected energy not supplied (EENS), which is a system reliability index under transmission line faults.

[0124] Example 8:

[0125] A method for power system reserve configuration considering operation reliability under freezing weather conditions, with the technical content being the same as any one of Examples 1 - 7. Further, the analytical expression for the expected energy not supplied (EENS), which is a system reliability index under wind turbine and generator failures, is constructed through the following steps:

[0126] A1) Construct input variables P t , D t represent the generator output, wind turbine output, and load respectively; λ t represents the failure rates of wind turbines and generators.

[0127] A2) Standardize the input variables, i.e.,

[0128]

[0129] where x n represents the nth element in x; ξ n represents the nth element in the standard random variable ξ; the distribution function of x n is F n (x n ); F n -1 (x n ) is the inverse function of F n (x n ); Φ(ξ n ) is the distribution function of ξ n ; N is the total number of input random variables, N = 2(NI + NW) + 1; NI is the number of generators; NW is the number of wind turbines;

[0130] A3) Construct the output response expression, i.e.,

[0131]

[0132] where a j,t is the coefficient of the chaos polynomial to be determined; Ψ j,k,t (ξ s,t ) is the chaos polynomial basis; NC is the number of undetermined coefficients; NC + 1 = (N + o)! / (N!o!) is the number of expansion terms; o is the maximum order of N and the PCE basis; j is the PCE coefficient index; s is the wind power load scenario index; k is the failure state index; Y s,k,t is the amount of demand reduction;

[0133] Among them, the multi - dimensional basis function is as follows:

[0134] Ψ(ξ t ) = ψ(ξ 1,t )ψ(ξ 2,t )···ψ(ξ N,t ) (11)

[0135] A4) Select the expansion order of the orthogonal polynomial to be 2, and construct the first two-order expansion expressions of the Legendre basis and the Hermite basis, that is:

[0136]

[0137] A5) Substitute equations (12) and (13) into the output response equation (10) and the multi-dimensional basis function (11) to obtain the second-order PCE, that is:

[0138]

[0139] where a j,t is the coefficient; a 0,t is the constant; ξ j-N,s,k,t is the chaos polynomial coefficient;

[0140] A6) Use the least squares method to calculate the chaos polynomial coefficients in formula (10) to obtain:

[0141]

[0142] The chaos polynomial coefficients are simplified as follows:

[0143] H t A t = Y t (16)

[0144] where H t is composed of all basis elements of PCE; A t is an N CP ×1 order coefficient matrix;

[0145] N CP = (2N + 1); Y t is the output vector set.

[0146] A7) Based on the polynomial chaos expansion basis function and the chaos polynomial coefficients, construct an analytical expression for the expected energy not supplied, which is a system reliability index under the faults of the wind turbine and the generator, that is:

[0147]

[0148] where is the demand curtailment under N-1 generator faults at time t and scenario s; EENS tG EENS for N-1 generator failures at time period t; p s is the probability of the wind power load scenario; NS is the total number of wind power load scenarios.

[0149] Example 9:

[0150] A method for configuring power system reserves considering operation reliability under freezing weather conditions, the technical content is the same as any one of Examples 1-8. Further, an analytical expression for the expected energy not supplied, a system reliability index under transmission line failures, is constructed through the following steps:

[0151] B1) Construct the power flow equation at node m when a transmission line fails, that is:

[0152]

[0153] In the formula, P i,t is the output power of generator i at time period t; P W w,t is the output power of wind turbine w at time period t; w is the wind turbine index; f k,l,t is the power flow of the failed transmission line l at time period t in the N-1 transmission line failure; D m,t is the load at node m within time period t; is the demand reduction at node m for N-1 transmission line failures at time period t; NI m is the number of generators connected to node m; NW m is the number of wind turbines connected to node m.

[0154] B2) Based on the sensitivity method, determine the internal linear relationship of the power flow before and after the transmission line failure, that is:

[0155]

[0156] In the formula, is the line power flow matrix in the fault state k; the fault state k means that the line l:mn with the start and end points m and n respectively is disconnected; P is the line power flow under normal conditions; x k is the reactance of line l:mn; Z0 is the node reactance matrix in the normal state; ΔZ k is the incremental matrix of the node reactance matrix; M k =[0,…,1,…,-1…,0] T ; E is the identity matrix;

[0157] B3) Construct an analytical expression for the expected energy not supplied, a system reliability index under transmission line failures, that is:

[0158]

[0159] Wherein, NM is the total number of nodes.

[0160] Embodiment 10:

[0161] A method for configuring power system reserves considering operation reliability under freezing weather, the technical content is the same as any one of Embodiments 1-9. Further, the objective function of the reserve optimization model with embedded operation reliability under freezing weather is as follows:

[0162]

[0163] Wherein, NT is the number of optimization time periods; NI is the total number of generators; NW is the total number of wind turbines; a i , b i and c i are the fuel cost coefficients of generator set i; u i,t , P i,t are the 0 / 1 variable and the active power output of unit i at time period t respectively; C i SU is the start-up cost of unit i at time period t; C i SD is the shutdown cost of unit i at time period t; C i,t , R i,t are the reserve cost and the reserve capacity provided by unit i at time period t respectively; VOCW is the penalty coefficient for wind curtailment; VOLL is the value of lost load; is the predicted wind power output of wind farm w at time period t.

[0164] Embodiment 11:

[0165] A method for configuring power system reserves considering operation reliability under freezing weather, the technical content is the same as any one of Embodiments 1-10. Further, the constraint conditions of the reserve optimization model with embedded operation reliability under freezing weather include power output limits of generators and wind turbines, reserve capacity constraints, power balance constraints, network power flow constraints, and reliability constraints, that is:

[0166]

[0167]

[0168] Wherein, P k,i,t is the output of generator set i at time period t in failure state k, is the output of wind turbine w at time period t in failure state k; and are the lower and upper limits of the output of generator i at time period t; and are the up and down ramp rates of generator set i; t i on and ti off are the start and stop times of generator i, T i on and T i off are the minimum start and stop times of generator i; r D is the load proportion coefficient to be provided as standby; τ is the standby response time; PTDF is the power transfer distribution factor; is the upper limit of EENS. R t is the standby capacity; D t is the load.

[0169] Embodiment 12:

[0170] A method for standby configuration of a power system considering operation reliability under freezing weather conditions, the technical content is the same as any one of Embodiments 1-11. Further, the standby configuration model is constructed based on a security-constrained unit commitment model. By jointly optimizing the start-stop state, output, and standby provided by the units, the sum of the system operation cost, standby cost, curtailment cost, and expected unserved load cost is minimized, thereby obtaining a standby configuration plan. The solution can be obtained using a solution tool such as CPLEX.

[0171] Embodiment 13:

[0172] A method for standby configuration of a power system considering operation reliability under freezing weather conditions, the technical content is the same as any one of Embodiments 1-12. Further, if the transmission line does not fail, in this scenario, ENS in formula (18) is 0, then EENS = 0, and the same applies to the rest of the power system equipment.

[0173] Embodiment 14:

[0174] A method for standby configuration of a power system considering operation reliability under freezing weather conditions, the steps are as follows:

[0175] First, using weather data such as rainfall, temperature, and wind speed, establish a wind turbine fault model based on the Navier-Stokes equation and the Messinger model, establish a generator fault model based on homogeneous Markov and real-time operating conditions, and establish a transmission line fault model in combination with the metal deformation theory; then for the uncertainties of renewable energy, load fluctuations, and N-1 generator faults, based on chaotic polynomials to approximate the reliability assessment process, for N-1 transmission line faults, use the sensitivity method to derive the linear expressions of the power flow before and after the fault, and analytically derive the system reliability index Expected Energy Not Served (EENS); finally, introduce the analytical expression of EENS into the proposed standby capacity optimization model to achieve the joint optimization of reliability and economy.

[0176] The specific steps of the method are as follows:

[0177] 1. Reliability model of system equipment operation under freezing weather

[0178] (1) Establish a fault model of wind turbines under freezing weather

[0179] Considering weather factors such as freezing rain volume, temperature, and wind speed, based on the Navier-Stokes equation, Lagrangian method, and Messinger model, the ice accretion on the blade surface of the wind turbine affected by freezing weather is calculated, and then the failure rate of the wind turbine is determined.

[0180] 1) Calculate the flow field distribution on the blade surface

[0181] Using the Navier-Stokes equation ensures the conservation of momentum of water droplets during movement, which can be expressed as follows.

[0182]

[0183] In the formula, ρ is the fluid density; is the fluid velocity vector; v x , v y and v z are the components of the velocity vector along the x, y, and z directions; PRESS is the pressure on the fluid element; F x , F y , F z are the body forces along the x, y, and z directions respectively. Since gravity only exists in the z direction, F x and F y are zero, and F z =-ρg, where g is the acceleration due to gravity; μ is the dynamic viscosity of the fluid; ω is the second molecular viscosity of the fluid; t is the time index; Δt = 1h.

[0184] 2) Calculate the movement trajectory of water droplets in the air

[0185] Using the Lagrangian method, analyze the forces acting on the water droplets, such as gravity, buoyancy, and air resistance, and establish the motion equation of water droplets in the air flow field as follows.

[0186]

[0187] In the formula, m r is the mass of freezing rain; V is the volume of freezing rain, V = 4 / 3π(D r / 2) 3 ; A is the frontal area of freezing rain; D r is the diameter of freezing rain; ρ a is the air density; ρ r is the density of freezing rain; is the air velocity vector; is the freezing rain speed vector; c d is the drag coefficient; c l is the buoyancy coefficient.

[0188] 3) Calculate the ice accretion

[0189] Use the Messinger model to divide the blade surface into multiple grid control volumes. In each control volume, establish a mass conservation equation for water droplets to calculate the ice accretion on the wind turbine blade.

[0190] m ice,t = m ice,t-1 + m im,t + m in,t - m es,t - m out,t (3)

[0191] In the formula, m im is the mass of the water droplets hitting the grid control volume unit; m in is the mass of the water droplets flowing into the control area; m es is the mass of the water droplets evaporated or sublimated in the control area;

[0192] m out is the mass of the water droplets flowing out of the control area; m ice is the mass frozen into ice in this area.

[0193] 4) Calculate the failure rate of the wind turbine

[0194] The outage rate of the wind turbine is strongly correlated with the changing weather environmental conditions. In addition to being related to icing, wind speed and temperature exceeding the safety limits will also cause the turbine to shut down.

[0195] The failure rate of the wind turbine is as follows:

[0196]

[0197] In the formula, FOR w base is the basic forced outage rate of the wind turbine; v fan is the real-time wind speed at the wind turbine blade; T is the real-time temperature; k1, k2, and k3 are the contribution coefficients of wind, icing, and temperature to the outage rate of the unit respectively.

[0198] (2) Establish a generator failure model under freezing weather

[0199] The generator outage rate mainly depends on the current value and is in the form of a piecewise exponential function. The generator failure rate is as follows:

[0200]

[0201] Wherein, FIFOR is the forced outage rate under freezing weather; a and b are the parameters of the exponential distribution; i is the generator index; Q i is the load current of generator i; Q i spec is the rated current of generator i; Q i trip is the maximum tripping current of generator i; ORR i 0 is the statistical value of the outage probability of generator i.

[0202] (3) Establish a fault model of transmission lines under freezing weather

[0203] For the faults of transmission lines, it is necessary to consider the overload caused by the internal current exceeding the limit and the ice breakage caused by the external freezing weather. The FIFOR of transmission lines is as follows:

[0204]

[0205] Wherein, l is the transmission line index; Q l is the load current of transmission line l; is the rated current of transmission line l; Q l trip is the maximum tripping current of transmission line l; ORR l 0 is the statistical value of the outage probability of transmission line l; F IW is the ice wind load formed by the combined action of wind force and ice gravity on the transmission line; Th1 and Th2 are the first and second critical values of the ice wind load respectively; is the length of transmission line l; α is the adjustment coefficient of the slope of the exponential function.

[0206] (4) Establish a system operation reliability model under freezing weather

[0207] Combining equations (5) and (6), the system operation reliability model under freezing weather is as follows:

[0208]

[0209] Wherein, I is the set of all generating units; L is the set of all transmission line groups; p k,t is the failure rate; K G is the set of failed generating units; K L is the set of failed transmission lines.

[0210] 2. Analytical formula of system operation reliability index

[0211] (1) Analytical formula of EENS based on polynomial chaos expansion

[0212] For the uncertainties of wind power, load, and N-1 generator faults, the polynomial chaos expansion (PCE) is used to analytically solve the EENS expression. First, the input variables, namely generator output, wind turbine output, load, and the normalized failure rates of wind turbines and generators, are standardized. Secondly, based on the types of input random variables, the polynomial basis is determined, and the polynomial chaos expansion formula is constructed. Then, the least squares method is used to calculate the undetermined coefficients of the chaotic polynomials. Finally, the reliability index is calculated.

[0213] 1) Standardization of input variables

[0214] Input random variables of the analytical formula Consist of the generator output P t , the wind turbine output the load D t , and the failure rates of wind turbines and generators λ t . The random variable x n is standardized according to Equation (8).

[0215]

[0216] where x n represents the nth element in x; ξ n represents the nth element in the standard random variable ξ; the distribution function of x n is F n (x n ); F n -1 (x n ) is the inverse function of F n (x n ); Φ(ξ n ) is the distribution function of ξ n ; N is the total number of input random variables, N = 2(NI + NW) + 1; NI is the number of generators; NW is the number of wind turbines.

[0217] 2) Construction of the chaotic polynomial expansion function

[0218] The output response is the demand reduction amount Y s,k,t as follows:

[0219]

[0220] where a j,t is the undetermined coefficient of the chaotic polynomial; Ψ j,k,t (ξ s,t ) is the chaotic polynomial basis; NC is the number of undetermined coefficients; the number of expansion terms is NC + 1 = (N + o)! / (N!o!), which is determined by N and the maximum order o of the PCE basis; j is the PCE coefficient index; s is the wind power load scenario index; k is the fault state index.

[0221] The multi-dimensional basis functions are constructed by the tensor product of one-dimensional basis functions.

[0222] Ψ(ξ t ) = ψ(ξ 1,t )ψ(ξ 2,t )···ψ(ξ N,t ) (10)

[0223] The PCE basis of uniformly distributed generator output and component reliability parameters can be represented by Legendre basis, while the PCE basis of wind power and load with normal distribution can be represented by Hermite basis.

[0224] The expansion order of the orthogonal polynomial is selected as the second order. The first two-order expansions of Legendre basis and Hermite basis are shown in equations (11) and (12).

[0225]

[0226] Substituting equations (11) and (12) into the output response equations (9) and the multi-dimensional basis functions (10), we obtain the second-order PCE as follows:

[0227]

[0228] 3) Calculate the undetermined coefficients of the polynomial

[0229] The least squares method is used to calculate the coefficients of the chaotic polynomial. Based on the principle of linear independence, N optimal collocation points are selected among the roots of the third-order Legendre polynomial, the roots of the third-order Hermite polynomial, and the zeros, making them as close to the origin as possible and symmetrically distributed around the origin. N CP is usually 2 - 3 times the number of undetermined coefficients. The collocation points are transformed into random variables Z that follow the standard normal distribution and have interdependent relationships; subsequently, the Z variables are transformed into random variables x that conform to the specified distribution and have the specified correlation relationship through equation (8); the output response matrix Y CP and the typical sample ξ CP are brought into equation (14). CP Substitute into equation (14).

[0230]

[0231] Equation (14) can be abbreviated as:

[0232] H t A t = Y t (15)

[0233] In the formula, H t is composed of all basis elements of PCE; A t is NCP ×1 order coefficient matrix;

[0234] N CP =(2N + 1); Y t is the set of output vectors.

[0235] 4) Calculate EENS

[0236] Based on the polynomial chaos expansion basis functions and undetermined coefficients, the analytical formula for the demand reduction under faults can be constructed as follows:

[0237] The analytical formula for the demand reduction under faults is:

[0238]

[0239] Combined with Equation (7), the following EENS expression is obtained:

[0240]

[0241] In the formula, where, is the demand reduction amount for the N - 1 generator fault at time period t and scenario s; EENS t G is the EENS for the N - 1 generator fault at time period t; p s is the probability of the wind power load scenario; NS is the total number of wind power load scenarios.

[0242] (2) Analytical formula of EENS under transmission line faults

[0243] When a transmission line fault occurs, node m satisfies the following equation:

[0244]

[0245] In the formula, P i,t is the output power of generator i at time period t; P W w,t is the output power of wind turbine w at time period t; w is the wind turbine index; f k,l,t is the power flow of the fault line l at time period t for the N - 1 transmission line fault; D m,t is the load at node m within time period t; is the demand reduction amount for the N - 1 transmission line fault node m at time period t; NI m is the number of generators connected to node m; NW m is the number of wind turbines connected to node m.

[0246] Based on the sensitivity method, the internal linear relationship of the power flow before and after the transmission line fault is determined. The power flow of the fault line l:mn after the fault is:

[0247]

[0248] In the formula, P Lk(l:mn) is the line power flow matrix under the fault state k (i.e., the line l:mn with the start and end points being m and n is disconnected); P is the line power flow under normal conditions; x k is the reactance of the line l:mn; Z0 is the node reactance matrix under the normal state; ΔZ k is the increment matrix of the node reactance matrix; M k = [0,…,1,…,-1…,0] T ; E is the identity matrix.

[0249] Combined with equations (19)-(20), f k,l,t is the element constituting the P Lk(l:mn) matrix and can be directly solved from (19). The EENS under the N-1 line fault can be expressed as:

[0250]

[0251] In the formula, NM is the total number of nodes.

[0252] (3) Analytical expression of system operation reliability

[0253] Combining (17) and (21), the analytical expression of the system operation reliability EENS is obtained as follows:

[0254]

[0255] 3. Reserve optimization model with embedded operation reliability under freezing weather

[0256] Introduce the analytical expression (22) of EENS into the reserve capacity optimization model to achieve the joint optimization of reliability and economy.

[0257] (1) Objective function

[0258] The reserve optimization model established in this section aims to minimize the sum of the system operation cost, start-up cost, reserve cost, wind curtailment cost, and expected load shedding cost.

[0259]

[0260] In the formula, NT is the number of optimization time periods; NI is the total number of generators; NW is the total number of wind turbines; a i , b i and c i are the fuel cost coefficients of generator set i; u i,t , P i,t are the 0 / 1 variable and the active power output of unit i at time t respectively; C i SU is the start-up cost of unit i at time t; Ci SD is the shutdown cost of unit i at time period t; C i,t , R i,t are the reserve cost and the reserve capacity provided by unit i at time period t, respectively; VOCW is the penalty coefficient for curtailed wind power; VOLL is the value of lost load; is the predicted wind power output of wind farm w at time period t.

[0261] (2) Constraints

[0262] The constraints include power output limits of generators and wind turbines, reserve capacity constraints, power balance constraints, network power flow constraints, reliability constraints, etc. The specific expressions are as follows:

[0263]

[0264]

[0265] Equations (24)-(25) are the power balance constraints before and after the fault, where P k,i,t is the output of generator set i at time period t in the fault state k, is the output of wind turbine w at time period t in the fault state k; Equations (26)-(29) are the output constraints of generators and wind turbines before and after the fault, where and are the lower and upper limits of the output of generator i at time period t; Equations (30)-(33) are the ramping constraints of available unit i in the normal and fault states at time period t, where and are the upper and lower ramping rates of generator set i; Equations (34)-(35) are the minimum limits of the continuous switching times of unit i in the normal and fault states, where t i on and t i off are the start-up and stop times of generator i, respectively, T i on and T i off are the minimum start-up and stop times of generator i, respectively; Equation (36) is the minimum reserve constraint at time period t, where r D is the load proportion coefficient required to provide reserve; Equation (37) is the reserve ramping constraint of generator set i at time period t, where τ is the reserve response time; Equations (38)-(39) are the line power flow limits at time period t in the normal state and fault state k, respectively, where PTDF is the power transfer distribution factor; Equations (40)-(42) are the reliability constraints, where is the upper limit of EENS.

[0266] Example 15:

[0267] Verification of the reserve configuration method for power systems considering operation reliability under freezing weather is as follows:

[0268] The detailed parameters of the IEEE 30 - bus system (such as generator and line specifications) are as Figure 1 shown. The wind farm is connected to buses 20 and 24, with an installed capacity of 80 MW and a new - energy penetration rate of 30%. Consider the following six cases:

[0269] M1: Deterministic method. Reserves are configured by a certain proportion of load and wind power output.

[0270] M2: The proposed reserve optimization model. The component failure probability is a fixed statistical value.

[0271] M3: Two - stage reserve optimization model. Reserves are obtained by iterative calculation.

[0272] M4: The proposed reserve optimization model. Considering variable operating conditions, the EENS analytical formula is used to accelerate the solution. The method of the present invention can more accurately configure the reserve that takes into account both system reliability and economy under freezing weather. The test cases M1 - M4 are compared with each other to evaluate the importance of considering weather factors and the effectiveness of the proposed reserve configuration method.

[0273] 1) Effectiveness of the proposed reserve configuration method: Table 1 shows the cost comparison of different methods. The reserve cost of M1 is the lowest, but the demand - curtailment cost is the highest. Even if a certain proportion of load - wind power output is reserved, the reserve allocated by M1 is still insufficient. Although M2 has the lowest demand - curtailment cost and the lowest total cost, it may be too conservative because it does not consider weather conditions. M3 effectively balances economy and reliability, as shown by its lower demand - curtailment cost and total cost compared to M1. For M4 and M3, the total cost and its components are almost the same. Although the total cost of M4 is not the lowest, it is still less than M1, a reduction of 23.78%. Compared with M1, the demand - curtailment cost of M4 is reduced by 41.72%. The proposed method can well balance system reliability and economy.

[0274] Table 1 Cost comparison of M1 - M4

[0275]

[0276] Since the values of M2 in Table 1 do not accurately reflect the actual risk level of the system, Figure 2 and Figure 3 respectively give the actual reserve capacity and EENS of 24 time periods for M1 - M4. M1 can cope with a certain load fluctuation and renewable - energy uncertainty, but it cannot effectively cope with emergencies, resulting in low system reliability. As Figure 3As shown, M4 allocates more reserves during a day than M2, so M4 has higher reliability than M2. The reason for this difference is that M2 does not consider variable operating conditions, resulting in an overly optimistic assessment of EENS in extreme weather scenarios. M4 configures additional reserves to cope with the large-scale disconnection of renewable energy caused by freezing weather and ensure the reliable operation of the system. M4 configures the same reserves as M3 in most periods. The proposed method M4 reserves more reserves during low load periods and peak wind power output periods to ensure the reliability of the system. During peak load periods and low wind power output periods, M4 can appropriately reduce reserves to improve system economy.

[0277] 2) Computational efficiency analysis: Table 2 shows the computational times of the four comparison methods. M1 and M2 have shorter computational times, but the reserve configuration results may bring serious operation risks to the system. M3 can effectively balance reliability and economy, but its calculation is extremely time-consuming. At the same time, the premise of ensuring the accuracy of M3 is to have a sufficient number of samples. In the IEEE 30-node system, M3 takes 23556.62 s to process 5000 samples. In contrast, the computational time of M4 is only 161.37 s. The proposed method greatly reduces the computational time.

[0278] Table 2 Comparison of Computational Times of M1 - M4

[0279]

[0280] It can be seen from the experimental results that:

[0281] The method of the present invention can more accurately configure reserves that balance system reliability and economy under freezing weather to cope with power imbalance problems caused by multiple uncertainties. An analytical formula for the operational reliability EENS of the system under multiple uncertainties such as renewable energy, load fluctuations, and equipment failures is derived based on polynomial chaos expansion and sensitivity method, greatly reducing the computational complexity. The established equipment operation reliability model under freezing weather makes the allocation of reserve capacity closer to reality, reduces the operation risk of the system, and the proposed reserve capacity optimization model realizes the efficient configuration of reserves that balance reliability and economy.

Claims

1. A method for power system reserve configuration considering operation reliability under freezing weather, characterized in that, It includes the following steps: 1) Construct a wind turbine fault model and a system operation reliability model under freezing weather; 2) Use the wind turbine fault model and the system operation reliability model under freezing weather to calculate the failure rates of wind turbines, generators, and transmission lines respectively; 3) Based on the failure rates of wind turbines, generators, and transmission lines, construct an analytical expression for the expected energy not supplied (EENS), a system reliability index; 4) Based on the analytical expression for the expected energy not supplied, construct a reserve optimization model with embedded operation reliability under freezing weather; 5) By jointly optimizing the start-stop status, output, and reserve provided by the units, minimize the sum of the system operation cost, reserve cost, curtailment cost, and expected load shedding cost, so as to solve the reserve optimization model with embedded operation reliability under freezing weather and obtain the reserve configuration plan for the power system under freezing weather.

2. The method for configuring power system reserves considering operation reliability in freezing weather according to claim 1, wherein In step 1), the steps for constructing a wind turbine fault model under freezing weather include: 1.1) Calculate the flow field distribution on the blade surface, i.e.: Where ρ is the fluid density; is the fluid velocity vector; v x 、v y and v z are the components of the velocity vector along the x, y, and z directions; PRESS is the pressure on the fluid element; F x 、F y 、F z are the body forces along the x, y, and z directions respectively; F x = 0, F y = 0, F z = -ρg, where g is the acceleration due to gravity; μ is the dynamic viscosity of the fluid; ω is the second molecular viscosity of the fluid; t is the time index; Δt is the time step; 1.2) Calculate the movement trajectory of water droplets in the air, i.e.: where m r is the mass of glaze ice; V r is the volume of glaze ice, and V r = 4 / 3π(D r / 2) 3 ; A is the windward area of glaze ice; D r is the diameter of glaze ice; ρ a is the air density; ρ r is the density of glaze ice; is the air velocity vector; is the glaze ice velocity vector; c d is the drag coefficient; c l is the buoyancy coefficient; 1.3) Calculate the ice accretion amount of the wind turbine, i.e.: m ice,t = m ice,t-1 + m im,t + m in,t - m es,t - m out,t (3) where m im is the mass of the water droplets impinging on the grid control volume element; m in is the mass of the water droplets flowing into the control region; m es is the mass of the water droplets evaporating or sublimating in the control region; m out is the mass of the water droplets flowing out of the outflow control region; m ice is the mass of the water frozen into ice in this region; 1.4) Construct a wind turbine fault model under freezing weather, i.e.: Wherein, FOR w base is the basic forced outage rate of the wind turbine; v fan is the real-time wind speed at the wind turbine blade; T is the real-time temperature; k1, k2, and k3 are the contribution coefficients of wind, icing, and temperature to the unit outage rate, respectively; FOR w,t is the failure rate of the wind turbine.

3. The method for configuring power system reserve considering operation reliability under freezing weather according to claim 1, characterized in that The system operation reliability model under freezing weather includes a generator fault model and a transmission line fault model under freezing weather.

4. The method for configuring power system reserve under freezing weather considering operation reliability according to claim 3, characterized in that, The generator fault model under freezing weather is as follows: Wherein, FIFOR is the forced outage rate under freezing weather; a and b are the parameters of the exponential distribution; i is the generator index; Q i is the load current of generator i; is the rated current of generator i; is the maximum tripping current of generator i; ORR i 0 is the outage probability statistical value of generator i.

5. The method for configuring power system reserves considering operation reliability under freezing weather according to claim 3, wherein The transmission line fault model under freezing weather is as follows: where l is the transmission line index; Q l is the load current of transmission line l; is the rated current of transmission line l; is the maximum tripping current of transmission line l; is the statistical value of the outage probability of transmission line l; F IW is the ice-wind load formed by the combined action of wind force and ice gravity on the transmission line; Th1 and Th2 are the first and second critical values of the ice wind load respectively; is the length of the transmission line l; α is the adjustment coefficient of the exponential function slope. The system operation reliability model under freezing weather is as follows: Where, I is the set of all generating units; L is the set of all transmission line groups; p k,t is the failure rate; K G is the set of faulty generating units; K L is the set of faulty transmission lines.

6. The method for configuring power system reserve under freezing weather considering operation reliability according to claim 1, characterized in that The analytical expression for the expected energy not supplied, a system reliability index, is as follows: In the formula, is the expected energy not supplied (EENS), which is a system reliability index under the faults of wind turbines and generators; is the expected energy not supplied (EENS), which is a system reliability index under the faults of transmission lines.

7. The method for configuring power system reserves considering operation reliability under freezing weather according to claim 6, characterized in that, The analytical expression for the expected energy not supplied of the system reliability index under wind turbine and generator failures is constructed through the following steps: A1) Construct input variables P t 、 D t are the generator output, wind turbine output, and load; λ t is the failure rate of the wind turbine and the generator; A2) Standardize the input variables, i.e.: where x n represents the n-th element in x; ξ n represents the n-th element in the standard random variable ξ; the distribution function of x n is F n (x n ); F n -1 (x n ) is the inverse function of F n (x n ); Φ(ξ n ) is the distribution function of ξ n ; N is the total number of input random variables, N = 2(NI + NW) + 1; NI is the number of generators; NW is the number of wind turbines; A3) Construct the output response expression, i.e.: where a j,t is the coefficient of the chaos polynomial to be solved; Ψ j,k,t (ξ s,t ) is the chaos polynomial basis; NC is the number of undetermined coefficients; NC + 1 = (N + o)! / (N!o!) is the number of expansion terms; o is the maximum order of N and the PCE basis; j is the PCE coefficient index; s is the wind power load scenario index; k is the fault status index; Y s,k,t is the demand reduction; Among them, the multi-dimensional basis function is as follows: Ψ(ξ t ) = ψ(ξ 1,t )ψ(ξ 2,t ) ··· ψ(ξ N,t ) (11) A4) Select the expansion order of the orthogonal polynomial to be 2, and construct the first two-order expansion expressions of the Legendre basis and the Hermite basis, i.e.: A5) Substitute equations (12) and (13) into the output response equations (10) and the multi-dimensional basis function (11) to obtain the second-order PCE, i.e.: where a j,t is a coefficient; a 0,t is a constant; ξ j-N,s,k,t is the coefficient of the chaotic polynomial; A6) Use the least squares method to calculate the coefficients of the chaos polynomial in equation (10) to obtain: The simplification of the coefficients of the chaos polynomial is as follows: H t A t = Y t (16) where H t is composed of all basis elements of PCE; A t is an N CP ×1 coefficient matrix; N CP = (2N + 1); Y t is the set of output vectors. A7) Based on the polynomial chaos expansion basis function and the coefficients of the chaos polynomial, construct the analytical expression for the expected energy not supplied of the system reliability index under wind turbine and generator failures, i.e.: In the formula, ENS s G ,k,t is the demand reduction amount under the N-1 generator fault in period t and scenario s; EENS t G is the EENS of the N-1 generator fault at time t; p s is the probability of the wind power load scenario; NS is the total number of wind power load scenarios.

8. The method for configuring power system reserve considering operation reliability under freezing weather according to claim 1, wherein The analytical expression for the expected energy not supplied of the system reliability index under transmission line failures is constructed through the following steps: B1) Construct the power flow equation of node m when the transmission line fails, i.e.: Where, P i,t is the output power of the generator at time period t of the i-th generator; P W w,t is the output power of the wind turbine at time period t of the w-th wind turbine; w is the wind turbine index; f k,l,t is the power flow of the faulty line l of the N-1 transmission line at time period t; D m,t is the load at node m within time period t; is the demand reduction amount of the faulty node m of the N-1 transmission line at time t; NI m is the number of generators connected to node m; NW m is the number of wind turbines connected to node m. B2) Based on the sensitivity method, determine the internal linear relationship of the power flow before and after the transmission line failure, i.e.: In the formula, is the line power flow matrix under fault state k; the fault state k means that the line l:mn with the start and end points being m and n respectively is disconnected; P is the line power flow under normal conditions; x k is the reactance of the line l:mn; Z0 is the nodal reactance matrix under normal state; ΔZ k is the incremental matrix of the nodal reactance matrix; M k = [0,…,1,…,-1…,0] T ; E is the identity matrix; B3) Construct the analytical expression for the expected energy not supplied of the system reliability index under transmission line failures, i.e.: In the formula, NM is the total number of nodes.

9. The method for configuring power system reserves considering operation reliability under freezing weather according to claim 1, characterized in that The objective function of the reserve optimization model with embedded operation reliability under freezing weather is as follows: where NT is the number of optimization periods; NI is the total number of generators; NW is the total number of wind turbines; a i , b i and c i are the fuel cost coefficients of generator set i; u i,t ,P i,t are a 0 / 1 variable and the active power output of unit i at time period t, respectively; C i SU is the start-up cost of unit i at time period t; C i SD is the shut-down cost of unit i at time period t; C i,t ,R i,t are the reserve cost and the reserve capacity provided by unit i at time period t, respectively; VOCW is the curtailment penalty coefficient; VOLL is the value of lost load; is the predicted wind power output of wind farm w at time period t.

10. The method for configuring power system reserves considering operation reliability in freezing weather according to claim 1, wherein The constraint conditions of the standby optimization model for the embedded operation reliability under freezing weather include the power output limits of generators and wind turbines, standby capacity constraints, power balance constraints, network power flow constraints, and reliability constraints, that is: where, P k,i,t is the output of generator set i at time t under fault condition k, is the output of wind turbine w at time t under fault condition k; and are the lower and upper limits of the output of generator i at time t; and are the up and down ramp rates of generator set i; and are the start-up and shutdown times of generator i respectively, and are the minimum start-up and shutdown times of generator i respectively; r D is the load proportion coefficient to be provided as reserve; τ is the reserve response time; PTDF is the power transfer distribution factor; EENS is the upper limit of EENS; R t is the spare capacity; D t is the load.

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