Unit combination method containing dynamic frequency constraint based on N-1 fault and load side inertia uncertainty

Abstract

A unit combination method containing dynamic frequency constraint based on N-1 fault and load side inertia uncertainty comprises the following steps: deducing a dynamic frequency response model containing load side inertia, and obtaining a frequency lowest point and a frequency change rate expression; constructing an N-1 fault probability uncertainty set model; aiming at wind power, load and load side inertia uncertainty problems, on the basis of dynamic frequency constraint, a two-stage robust unit combination model based on fuzzy opportunity constraint is constructed; in order to solve the problem that a min-max-min structure of two-stage robust optimization cannot be directly solved, a dual theory is combined with Camp; the CG algorithm decomposes the model into a main problem and a sub-problem for iterative solution. According to the method, the inertial response and the primary frequency modulation capability of the system can be improved, the conservative property of a traditional scheme of exiting from operation with a maximum-capacity unit is reduced, the result of the scheduling scheme is more accurate, and the economical efficiency is better.

Description

Technical Field

[0001] The present invention relates to the field of power system optimization dispatching, and in particular to a unit combination method containing dynamic frequency constraints based on N-1 faults and load side inertia uncertainty. Background Art

[0002] In the new power system with new energy as the main body, as the scale of wind power grid connection becomes larger and larger, the system inertia level and primary frequency regulation capability decrease. Under occasional fault disturbances, it is easy to cause a series of frequency safety accidents, bringing new challenges to the frequency safety of the power grid.

[0003] In response to the power disturbance caused by occasional unit failures, on the one hand, the dispatch plan formulated by the unit combination must pass the N-1 safety check before it can be implemented. On the other hand, in the existing research on the unit combination considering dynamic frequency constraints, the maximum capacity generator is taken out of operation according to the extreme expected failure, and the impact of the unit withdrawal on the frequency response is not considered when calculating the dynamic frequency. In actual dispatching operation, all units operating in the system have the possibility of withdrawing from operation. Only considering the withdrawal of the maximum capacity unit is likely to lead to overly conservative optimization results. In reality, the probability distribution information of unit failure is difficult to obtain, and the probability distribution mined through historical data often has errors. The optimization plan obtained based on the deterministic failure probability does not match the actual operation. Because the failure probability of different units is different, the larger the capacity, the higher the reliability. In the process of optimizing scheduling, the impact of the uncertainty of the unit failure probability should be taken into account to reduce the conservatism of the uncertainty set. In addition, in the study of unit combination considering dynamic frequency constraints, only the inertia on the power supply side is mainly considered. According to research, the inertia on the load side accounts for about 20% of the system inertia. Taking into account the inertia on the load side can improve the inertial support capacity of the system, and the impact of the inertia on the frequency characteristics should be taken into account.

[0004] In recent years, global blackouts caused by accidental failures have become more frequent, and the power shortage disturbance caused by failures has posed a serious threat to the frequency safety of the power grid. Generators are easily affected by external factors, and accidental failures of varying degrees occur, causing serious power shortages. It is of great significance to study the impact of power shortage disturbances caused by accidental failures on the stable operation of the system. However, unit failures are often uncertain, and the failure probabilities of different units are inconsistent. Generally, the larger the unit capacity, the more reliable it is. Traditional studies usually analyze the extreme expected failure of the largest unit to exit operation as a disturbance, which often makes the results of optimized scheduling too conservative and poor in practical reference value. In addition, the probability of unit failure is difficult to accurately estimate, and the probability of failure of different units is uncertain. In the process of studying the N-1 safety check of accidental failures of units, the influence of the uncertainty of the probability of unit failure should be taken into account. Establishing the N-1 failure probability uncertainty set can reduce the conservatism of the scheduling plan and provide guidance for dispatchers.

[0005] Based on the above background, considering the influence of load side inertia uncertainty and unit failure probability uncertainty, a unit commitment method with dynamic frequency constraints taking into account wind power, load power, load side inertia and failure probability uncertainty is proposed. Summary of the invention

[0006] The present invention provides a unit combination method with dynamic frequency constraints based on N-1 faults and load-side inertia uncertainty. The method can improve the ability of the power grid to resist sudden faults and improve the frequency response capability of the system. The method seeks the best under the worst scenario of the fault probability uncertainty concentration to determine the unit fault scheduling plan, reduces the conservatism of the traditional plan of withdrawing the unit with the maximum capacity, and makes the scheduling plan more accurate and more economical.

[0007] The technical solution adopted by the present invention is:

[0008] The unit commitment method with dynamic frequency constraints based on N-1 faults and load side inertia uncertainty includes the following steps:

[0009] Step 1: Construct a dynamic frequency response model including load-side inertia and derive the expressions of the lowest frequency point and frequency change rate;

[0010] Step 2: Construct N-1 failure probability uncertainty set model;

[0011] Step 3: Aiming at the uncertainty of wind power, load and load-side inertia, a two-stage robust unit commitment model based on fuzzy chance constraints is constructed on the basis of dynamic frequency constraints;

[0012] Step 4: Use the duality theory combined with the C&CG algorithm to decompose the two-stage robust unit commitment model based on fuzzy chance constraints into main problems and sub-problems for iterative solution to obtain the optimal scheduling solution.

[0013] In step 1, the dynamic frequency response model including the load side inertia is shown in the following equations (1) to (5):

[0014] The rotor motion equations for this model are expressed as follows:

[0015]

[0016] In formula (1): H G is the synchronous inertia time constant; H L is the load side inertia time constant; △ω is the frequency deviation of the system; △P G is the primary frequency regulation active power adjustment of the unit; △P L is the active unbalance amount caused by the disturbance; D is the damping coefficient of the system. The frequency minimum point result derived from the dynamic frequency response model including the load side inertia is as follows:

[0017]

[0018]

[0019] In the above formula: f nadir Indicates the lowest frequency point; t nadir Indicates the time corresponding to the lowest frequency point; f0 is the initial frequency of the system; f B is the base frequency of the system; N is the total number of thermal power units; i is the number of thermal power units;

[0020] Each conventional unit C i The expression is as follows:

[0021]

[0022] In formula (4): U i is the start and stop status of the i-th unit; K i is the unit regulation power coefficient of the i-th generator; T i is the response time constant of the i-th generator, i=1,…,N; where U1 represents the start / stop state of the first unit; U N The start and stop status of the Nth unit; K1 represents the unit adjustment power coefficient of the first generator; K N represents the unit regulation power coefficient of the Nth generator; T1 represents the response time constant of the first generator, T N Represents the response time constant of the Nth generator. The frequency change rate expression is as follows:

[0023]

[0024] Where: RoCoF represents the frequency change rate; △ω represents the frequency deviation of the system; t represents the time of change of the system frequency deviation; t=0 + Indicates the value of the frequency deviation when the frequency deviation is differentiated with respect to time.

[0025] In step 2, an N-1 failure probability uncertainty set model is constructed, and the model is as follows:

[0026] The N-1 uncertainty set is used to describe the uncertainty factors of unit failure, which can be described as:

[0027]

[0028] Where: Z is the N-1 fault probability uncertainty set; N is the number of equipment or lines in the power system; A it Is the fault of unit i at time t, 0 for fault and 1 for normal;

[0029] The calculation formula for the probability of unit outage accident is:

[0030]

[0031] Where: P it is the failure probability of the i-th unit; MTTR i is the average repair time of the i-th unit; MTTF i is the average failure time of the i-th unit.

[0032] For the unit repair time T involved in the unit failure probability MTTR and unit failure time T MTTF It is difficult to estimate accurately. Generally, it obeys exponential distribution and can be generated by Monte Carlo simulation sampling. The expression is as follows:

[0033] T MTTR =-MTTR·lnγ MTTR (8);

[0034] T MTTF =-MTTF·lnγ MTTF (9);

[0035] Where: γ MTTR and γ MTTF They are all random numbers uniformly distributed in the interval (0,1); MTTR is the mean repair time of the unit; MTTF is the mean failure time of the unit.

[0036] By adopting α cut The criterion is used to add the probability information of unit outage emergencies to the uncertain set to reduce the conservatism of the robust optimization method. cut The worst case generated by the criterion only includes probability greater than a given α cut Threshold case, constrained α cut The criterion can be expressed as:

[0037]

[0038] Where: α cut is the fault probability threshold, which is set to 10 in the present invention. -2 ; Since formula (10) is a nonlinear expression, it cannot be directly used to solve the two-stage robust unit commitment. The logarithms on both sides of formula (10) are converted into linear expressions:

[0039]

[0040] Further arrangement can get the following formula:

[0041]

[0042] In step 3, a two-stage robust unit commitment model based on fuzzy chance constraints is constructed, as follows:

[0043] When the confidence level of the fuzzy chance constraint α>1 / 2, the clear equivalence class form of the form Cr{g(x,ξ)≤0}≥α can be expressed as:

[0044]

[0045] Where: α is the confidence level of the fuzzy chance constraint; g(x,ξ) represents the constraint function; x represents the trapezoidal fuzzy variable; ξ represents the trapezoidal fuzzy parameter; Indicates the definition function; r k1 ~r k4 represents the trapezoidal membership parameter; k = 1, 2,…, t, t∈R; R represents a real number; t represents the number of value sets; h0(x) represents a part of the function g(x,ξ).

[0046] The objective function of the two-stage robust unit commitment is as follows:

[0047]

[0048] f(P Git )=a i +b i P Git +c i P Git 2 (16);

[0049] Where: U it is the start / stop status of the i-th unit in time period t, 1 indicates start, 0 indicates stop; U i,t-1 is the start / stop status of the i-th unit in time period t-1; S U,it , S D,it are the start-up and shutdown costs of the i-th unit in period t; Q is the total cost of the second stage; z is the probability of failure; Z is the N-1 failure probability uncertainty set; y i,t is the operating state variable of thermal power unit i at time t, which is a 0-1 variable; is the predicted value of wind power in period t; q w P is the wind abandonment penalty coefficient; wt is the output power of the wind turbine in period t; T is the scheduling period of the study; f(P Git ) is the power generation cost of thermal power units; a i 、b i 、c i is the coefficient of the quadratic cost function of the i-th thermal power unit.

[0050] In step 4, since the min-max-min structure of the two-stage robust optimization cannot be solved directly, the duality theory combined with the C&CG algorithm is used to decompose the model into main and sub-problems for iterative solution to obtain the optimal scheduling solution;

[0051] The general form of the two-stage robust optimization is as follows:

[0052]

[0053] Where: y is the matrix of decision variables of the C&CG algorithm in the first stage; c T is the cost coefficient corresponding to the start and stop in the first stage; x is the matrix composed of decision variables in the second stage of the C&CG algorithm; b T is the cost coefficient corresponding to the output of the second stage; is the matrix corresponding to the start and stop of the first stage; the optimization constraint condition F(y,u) is a linear function of the parameter u of the second stage; d is the constant coefficient matrix corresponding to the start and stop constraints of the first stage; matrices A2, A3, A4 and h are the constant coefficient matrices corresponding to the constraints of the second stage.

[0054] The two-stage robust optimization model established above is a nonlinear model with a min-max-min structure. It cannot be solved directly. It is necessary to decompose the original problem into a main problem and sub-problems, and use the duality theory to transform and process the sub-problems. The two-stage robust unit commitment model can be expressed as:

[0055] minc T y+Q(x,z)(18);

[0056]

[0057] Where: λ is the dual variable; Formula (21) is the constraint condition after dualization, and in Formula (22), is the constraint matrix corresponding to the output of the second stage.

[0058] By replacing the original equation of Q(x,z) with its dual, the subproblem Q(x,z) in the original problem can be transformed into the constraint condition after the dualization of equation (21). This problem is equivalent to the following equation:

[0059]

[0060] After the above-mentioned dual transformation, the second-stage max-min model of the objective function can be transformed into a max model, and the original two-stage robust model min-max-min structure is finally transformed into a min-max model, which can be solved with the help of the C&CG algorithm and calling the Gurobi solver.

[0061] The present invention provides a unit combination method with dynamic frequency constraints based on N-1 faults and load side inertia uncertainty, and the technical effects are as follows:

[0062] 1) In step 1 of the present invention, load-side inertia is further introduced into the traditional study of unit combination considering dynamic frequency constraints, which can improve the system inertial response and primary frequency regulation capability under the premise of ensuring the frequency safety of the power grid, increase the system's ability to resist sudden failures, absorb more wind power, and improve the economy of the system scheduling plan.

[0063] 2) In step 2 of the present invention, the power shortage is regarded as the maximum capacity unit being decommissioned, which easily leads to overly conservative optimization results and the difficulty in accurately obtaining the probability of occasional failures. Taking the influence of the uncertainty of unit failure probability into consideration, an N-1 failure probability uncertainty set is established, which can find the best solution from the worst scenario of the uncertainty set and determine the units that may fail. This reduces the conservatism of the traditional scheme of optimizing scheduling by decommissioning the maximum unit, making the scheduling scheme more economical.

[0064] 3) In step 3 of the present invention, fuzzy chance constraints are introduced into the two-stage robust unit combination model to address the uncertainty issues of wind power, load and load-side inertia. The uncertainty variables can be characterized by trapezoidal fuzzy parameters, and clear equivalence class conversion is performed based on the credibility theory in uncertain planning, so that the model can be quickly solved by the solver.

[0065] 4) Step 4 of the present invention cannot directly solve the min-max-min structure of the two-stage robust optimization. The duality theory is combined with the C&CG algorithm to decompose the model into main and sub-problems for iterative solution to obtain the optimal scheduling solution.

[0066] 5) The method of the present invention can improve the ability of the power grid to resist sudden failures, improve the frequency response capability of the system, absorb more wind power, reduce the system's spare capacity, and have a wider optimization range; it can also find the best solution from the worst scenario of the uncertainty concentration of the probability of failure, determine the unit failure scheduling plan, and reduce the conservatism of the traditional plan of withdrawing the unit with the maximum capacity, so that the results of the scheduling plan are more accurate and more economical. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Schematic diagram of the dynamic frequency response model including load side inertia.

[0068] Figure 2 Flowchart for solving the overall optimization problem of the model.

[0069] Figure 3 It is the wind power forecast and load power curve for each period.

[0070] Figure 4 This is a schematic diagram of the start and stop status of the unit in Scheme 1.

[0071] Figure 5 This is a schematic diagram of the start and stop status of the unit in Scheme 2.

[0072] Figure 6 This is a schematic diagram of the start and stop status of the unit in Scheme 3.

[0073] Figure 7 This is the frequency minimum point distribution diagram of different scheduling schemes.

[0074] Figure 8 The frequency change rate distribution diagram of different scheduling schemes.

[0075] Fig. 9 Schematic diagram of system inertia time constant under different schemes.

[0076] Fig.10 This is the frequency minimum point diagram under different schemes.

[0077] Fig.11 It is the frequency change rate diagram under different schemes. DETAILED DESCRIPTION

[0078] The unit commitment method with dynamic frequency constraints based on N-1 faults and load side inertia uncertainty includes the following steps:

[0079] Step 1: Use the improved system equivalent frequency response model to introduce the load side inertia and derive the dynamic frequency response model including the load side inertia. Figure 1 As shown, the expressions of the model's lowest frequency point and frequency change rate are derived.

[0080] The rotor motion equations for this model are expressed as follows:

[0081]

[0082] Where: H G is the synchronous inertia time constant; H L is the load side inertia time constant; △ω is the frequency deviation of the system; △P G is the primary frequency regulation active power adjustment of the unit; △P L is the active unbalance caused by the disturbance; D is the damping coefficient of the system.

[0083] The lowest frequency point derived from the dynamic frequency response model is as follows:

[0084]

[0085] Where: f0 is the initial frequency of the system; f B is the base frequency of the system; each conventional unit C i The expression is as follows:

[0086]

[0087] Where: U i is the start and stop status of the i-th unit; K i is the unit regulation power coefficient of the i-th generator; T i is the response time constant of the i-th generator.

[0088] The frequency change rate expression is as follows:

[0089]

[0090] Step 2: Construct N-1 failure probability uncertainty set model:

[0091] The probability of unit failure is difficult to estimate accurately, and the probability of failure of different units is uncertain. When studying the N-1 safety verification process of unit accidental failures, the impact of unit failure probability uncertainty should be taken into account. Establishing the N-1 failure probability uncertainty set can reduce the conservatism of the scheduling plan and provide guidance for scheduling personnel.

[0092] Robust optimization is usually used to study optimal scheduling problems under uncertain conditions, because it can find the optimal decision under the worst conditions in the uncertainty set and has a good decision description ability for real decision scenarios. Therefore, robust optimization analysis is used to deal with the uncertainty problem of unit occasional failures. The N-1 safety criterion is usually used to check and verify the uncertainty of unit failures. The present invention uses the N-1 uncertainty set to describe the uncertainty factors of unit failures, which can be described as:

[0093]

[0094] Where: A it Indicates whether unit i has a fault at time t, which is 0 for fault and 1 for normal condition.

[0095] In the worst case, the outage probability of all units is the same, which may cause multiple large-capacity units to be out of service at the same time, but in fact, the operation reliability of large-capacity units is very high. At this time, if the uncertainty set is constructed with the same unit failure probability to perform the N-1 safety check of the unit shutdown, the dispatch result is often too conservative. In the actual power system, the probability of outage accidents in units of different capacities or types is different. Generally speaking, the larger the capacity, the higher the operating reliability of the unit, and the unit failure probability is difficult to accurately estimate and often has uncertainty. Therefore, it is necessary to consider the failure probability information in the uncertainty set. The calculation formula for the probability of unit outage accident is:

[0096]

[0097] Where: P it is the failure probability of the i-th unit; MTTR i is the average repair time of the i-th unit; MTTF i is the average failure time of the i-th unit.

[0098] For the unit repair time T involved in the unit failure probability MTTR and unit failure time T MTTF It is difficult to estimate accurately. Generally, it obeys exponential distribution and can be generated by Monte Carlo simulation sampling. The expression is as follows:

[0099] T MTTR =-MTTR·lnγ MTTR (8);

[0100] T MTTF =-MTTF·lnγ MTTF (9);

[0101] Where: γ MTTR and γ MTTF are uniformly distributed random numbers in the interval (0,1).

[0102] By adopting α cut The criterion is used to add the probability information of unit outage emergencies to the uncertain set to reduce the conservatism of the robust optimization method. cut The worst case generated by the criterion only includes probability greater than a given α cut Threshold case, constrained α cut The criterion can be expressed as:

[0103]

[0104] Where: α cut is the fault probability threshold, which is set to 10 in the present invention. -2 ; Since equation (10) is a nonlinear expression, it cannot be directly used to solve the two-stage robust unit commitment. The logarithms of both sides are converted into linear expressions.

[0105]

[0106] Further arrangement can get the following formula:

[0107]

[0108] Step 3: Aiming at the uncertainty of wind power, load and load-side inertia, a two-stage robust unit commitment model based on fuzzy chance constraints is constructed on the basis of dynamic frequency constraints.

[0109] Under the background of high wind power penetration, the system inertia response capability and primary frequency regulation capability are weakened, and the power shortage disturbance caused by the occasional failure of the unit will cause a series of power grid frequency safety accidents. In order to ensure that the frequency does not exceed the limit after the wind power is connected to the grid and can operate reliably and economically, a two-stage robust unit combination model based on fuzzy opportunity constraints is established. In the first stage, the start-stop plan of the unit is formulated with the optimal start-stop cost. In the second stage, based on the start-stop plan of the unit in the first stage, it is proposed to use fuzzy opportunity constraints to deal with the uncertainty of wind power output, load power and load side inertia, and convert its clear equivalence class into deterministic constraints, and perform dynamic frequency constraint N-1 safety verification with the power shortage disturbance caused by the uncertainty of the unit occasional failure, find the best in the worst scenario of the unit occasional failure, optimize the output and inertia response capability of the unit after the occasional failure, and determine the optimal scheduling scheme that meets the dynamic frequency constraints.

[0110] 1) Objective function:

[0111] In order to cope with large-scale wind power grid connection, ensure the safe and stable operation of the system under occasional failures, and improve the level of wind power consumption, the objective function of the unit combination model established by the method of the present invention includes the power generation cost, start-up and shutdown cost of conventional units, and the penalty cost of wind power abandonment. Its expression is as follows:

[0112]

[0113] f(P Git )=a i +b i P Git +c i P Git 2 (16);

[0114] Where: U it is the start / stop status of the i-th unit in time period t, 1 indicates start, 0 indicates stop; a i 、b i 、c i is the coefficient of the quadratic cost function of the i-th thermal power unit; S U,it , S D,it are the start-up and shutdown costs of the i-th unit in period t; q w P is the wind abandonment penalty coefficient; wt is the output power of the wind turbine in period t; is the predicted value of wind power in time period t; T is the scheduling period of the study; y i,t is the operating state variable of thermal power unit i at time t, which is a 0-1 variable.

[0115] 2) Constraints in the first stage

[0116] (1) Unit start-stop operation status constraints:

[0117] y i,t -y i,t-1 -U it ≤0(25);

[0118] y i,t-1 -y i,t -(1-U it )≤0(26);

[0119] (2) Minimum start and stop time constraints:

[0120]

[0121] Where: T i on 、T i off are the minimum continuous start and stop times of the i-th generator, respectively.

[0122] 3) Second stage constraints:

[0123] (1) Power balance constraints:

[0124]

[0125] Where: P Lt is the load power at time t; α is the confidence level.

[0126] (2) Spinning reserve constraints:

[0127]

[0128] Where: It is the upper limit of the maximum output of the thermal power unit at time t.

[0129] (3) Output constraints of thermal power units:

[0130]

[0131] Where: They are the upper and lower limits of thermal power unit output respectively.

[0132] (4) Wind turbine output constraints:

[0133]

[0134] (5) Climbing / slope rate constraints:

[0135]

[0136] Where: △P i upis the maximum climbing capacity of the i-th unit; △P i down is the maximum landslide capacity of the i-th unit.

[0137] (6) Power shortage constraint of faulty units:

[0138]

[0139] (7) Dynamic frequency constraint:

[0140] Use unit to adjust power K t Characterize the primary frequency regulation capability. The faulty unit cannot provide frequency regulation capability and inertia support capability. The regulation capability and inertia time constant expressions of each unit are as follows:

[0141]

[0142] Where: H sys is the system inertia time constant; H Gi is the inherent inertia time constant of the i-th thermal power unit; S Gi is the rated power of the i-th thermal power unit; H L is the load side inertia time constant; S L is the rated capacity on the load side; H k is the inertia time constant of the faulty unit; S k is the rated capacity of the faulty unit; S sys is the total rated capacity of the system.

[0143] (8) Frequency minimum point constraint:

[0144] Cr{f nadir,t ≥f min}≥α (38);

[0145] Where: f nadir,t is the lowest frequency point at time t; f min is the frequency limit.

[0146] (9) Frequency change rate constraint:

[0147] Cr{|RoCoF t |≤RoCoF max}≥α (39);

[0148] Where: RoCoF t is the frequency change rate at time t; RoCoF max is the frequency change rate limit.

[0149] 4) Clear equivalence class transformation of fuzzy chance constraints:

[0150] Since the method of the present invention takes into account the uncertainty of wind power output, load power, and load side inertia and uses fuzzy chance constraints with fuzzy parameters to represent them, it cannot be directly applied to the two-stage robust optimization model for solution. It is necessary to use the clear equivalence class transformation method to transform the uncertainty constraints of the method of the present invention into deterministic constraints for solution. Therefore, when the confidence level of the fuzzy chance constraint α>1 / 2, the clear equivalence class form of Cr{g(x,ξ)≤0}≥α can be expressed as:

[0151]

[0152] Where: g(x,ξ) represents the constraint function; ξ represents the trapezoidal fuzzy parameter; Indicates the definition function; r k1 ~r k4 represents the trapezoidal membership parameter, k=1,2,…,t,t∈R; R represents a real number; t represents the number of value sets; h0(x) represents a part of the function g(x,ξ).

[0153] (1) The clear equivalence class of power balance constraints is transformed into:

[0154]

[0155] Where: P wt1 , P wt2 is the membership parameter of wind power; P Lt3 , P Lt4 is the membership parameter of load power.

[0156] (2) The clear equivalence class of the spinning reserve constraint is transformed into:

[0157]

[0158] (3) The clear equivalence class conversions of the lowest frequency point and the frequency change rate are shown below:

[0159]

[0160] Where: H L1 , H L2 is the membership parameter of the load side inertia.

[0161] Step 4: Since the min-max-min structure of the two-stage robust optimization cannot be solved directly, the duality theory combined with the C&CG algorithm is used to decompose the model into main and sub-problems for iterative solution to obtain the optimal scheduling solution.

[0162] Solution process:

[0163] The general form of two-stage robust optimization is:

[0164]

[0165] Where y is the matrix of decision variables of the C&CG algorithm in the first stage; x is the matrix of decision variables of the C&CG algorithm in the second stage; the optimization constraint F(y,u) is a linear function of the parameter u in the second stage; matrices A1, b, c and d are constant coefficient matrices corresponding to the constraints in the first stage; matrices A2, A3, A4 and h are constant coefficient matrices corresponding to the constraints in the second stage.

[0166] The two-stage robust optimization model established above is a nonlinear model with a min-max-min structure. It cannot be solved directly. It is necessary to decompose the original problem into a main problem and sub-problems, and use the duality theory to transform and process the sub-problems. The two-stage robust unit commitment model can be expressed as:

[0167] minc T y+Q(x,z)(18);

[0168]

[0169]

[0170] Where: λ is the dual variable; Formula (21) is the constraint condition after dualization.

[0171] By replacing the original equation of Q(x,z) with its dual, the subproblem Q(x,z) in the original problem can be transformed into the constraint condition after the dualization of equation (21). This problem is equivalent to the following equation:

[0172]

[0173] After the above dual transformation, the second-stage max-min model of the objective function can be transformed into a max model, and the original two-stage robust model min-max-min structure is finally transformed into a min-max model. It can be solved by using the C&CG algorithm and calling the Gurobi solver. The solution process is as follows: Figure 2 shown.

[0174] The C&CG algorithm solution steps are as follows:

[0175] Step 1: Data initialization, set LB = -∞, UB = ∞, number of iterations j = 0, set O is an empty set;

[0176] Step 2: Solve the MP main problem

[0177]

[0178] Get the optimal solution Update the Nether

[0179] Step 3: Solve the SP sub-problem

[0180] Substitution It turns out that:

[0181]

[0182] Get the optimal solution And get the upper bound of the original problem

[0183] Step 4: Determine whether the convergence conditions are met

[0184] If UB-LB≤ε, return Termination of proceedings;

[0185] otherwise:

[0186] a: If Add variables And add the following constraints:

[0187] η≥b T x k+1 (46);

[0188]

[0189] Returning to the main problem, the solution to the problem can be obtained by querying the database. j = j + 1, then O = O ∪ j + 1, go to Step 2.

[0190] b: (For some u * ∈U, if the second stage decision If not feasible, Denoted as +∞, add variable x k+1 , and add the following constraints:

[0191]

[0192] Return to the main problem. j=j+1, go to Step 2.

[0193] Dynamic frequency constraint N-1 safety check, due to the nonlinearity of dynamic frequency constraint, the mixed integer programming solver cannot solve it directly. Therefore, the present invention decomposes the optimization problem into two-stage main sub-problems for solving. When the start and stop state of the unit solved in the first stage is used as a known value to check the sub-problem of the frequency minimum point and the frequency change rate exceeding the limit, if the dynamic frequency constraint exceeds the limit, it means that the system frequency regulation capability is insufficient, and the unit regulation power K of the system at time t is tIt can characterize the frequency regulation capability of the system and is related to the start and stop status of the unit. Its expression is as follows:

[0194]

[0195] In order to make the dynamic frequency constraint meet the constraint conditions in each period and avoid excessive wind power grid-connected capacity causing the dynamic frequency to develop in a worse direction, resulting in power grid frequency safety accidents, the following segmentation is returned:

[0196]

[0197] Where: Adjust the power for the units that do not meet the dynamic frequency constraints; when the dynamic frequency constraints are out of limit and When , the optimization cut formula (50) is generated to return to the main problem. By adjusting the number of units started and stopped, the system is made to increase the unit regulation power to improve the system frequency regulation capability, thereby continuously optimizing the number of units started and stopped until all constraints are met to obtain the optimal solution.

[0198] Example:

[0199] In order to verify the feasibility and effectiveness of the model proposed in this invention, the improved IEEE 10-machine 39-node system is used for simulation verification, and the Gurobi solver is called to solve the scheduling model. The MTTR and MTTF of different unit capacities in the example are shown in Table 1, the system parameters of the thermal power unit are shown in Table 2, the trapezoidal fuzzy parameters are shown in Table 3, and the typical daily load curve and wind power prediction curve are shown in Table 4. Figure 3 As shown, the system rated frequency is set to 50 Hz, the minimum frequency limit is set to 49.5 Hz, the frequency change rate limit is set to 0.5 Hz / s, the wind curtailment penalty cost is 100 $ / MW, and the confidence level is set to 0.95.

[0200] Table 1 MTTR and MTTF of different unit capacities

[0201]

[0202] Table 2 System parameters of thermal power units

[0203]

[0204] Table 3 Trapezoid membership parameters

[0205]

[0206] 1) The impact of fuzzy chance constraints on optimal scheduling:

[0207] In order to verify the effectiveness of introducing fuzzy opportunity constraints into the dispatch model of the present invention to deal with the uncertainty of wind power output and load forecast power, two dispatch models are used for simulation comparison. The models are as follows:

[0208] Model 1: Considering the limitation of dynamic frequency constraints, a deterministic model of active power balance is adopted. To cope with the uncertainty of wind power output and load forecast power, the system spinning reserve capacity is set to 20% of the wind power dispatch value and 10% of the load forecast value;

[0209] Model 2: Considering the limitations of dynamic frequency constraints, a fuzzy chance constraint model is used to deal with the uncertainty of wind power output and load forecasting power.

[0210] Without considering the impact of occasional unit failures, the disturbance is set to 0.1P based on the N-1 limit expected failure. L Taking as an example, the scheduling results of two models are obtained through simulation analysis, as shown in Table 4.

[0211] Table 4 Comparison of scheduling results of different models

[0212]

[0213] As shown in Table 4, compared with Model 1, the operating cost, wind abandonment cost and total cost of Model 2 proposed in the present invention are reduced by 8.41%, 79.02% and 18.69% respectively. This is because Model 2 uses fuzzy opportunity constraints to deal with the uncertainty of wind power output and load forecast power. The output power of each unit has reserved spare capacity to deal with the uncertainty of wind power output and load forecast power during the scheduling process. There is no need to set up additional rotating spare capacity, which reduces the total spare capacity of the scheduling model by 37.04% in one scheduling cycle, can better absorb wind power, and the wind power absorption rate is increased by 3.91%. The wind abandonment phenomenon is improved, and a large number of wind abandonment penalties are reduced, so the economy is better. The scheduling model of Model 1 is a deterministic model based on absolute power balance, which is generally only established when the error of wind power and load forecast power is zero. In order to ensure the safe operation of the system and avoid the risk of increasing uncertainty errors in the scheduling process, the required spare capacity is large, which leads to a low wind power absorption rate, a large amount of wind abandonment, and increased power generation costs. Secondly, dynamic frequency constraints are introduced into the model, which can ensure that when large-scale wind power is connected to the system, the system has sufficient inertia support capacity and frequency response capacity, and there will be no risk of frequency over-limit, so as to ensure the safety of the formulated scheduling plan. It can be seen that the present invention uses a fuzzy opportunity constraint model based on dynamic frequency constraints to deal with uncertainty problems. On the one hand, it can ensure that when large-scale wind power is connected to the system during the scheduling process, the system inertia is reduced without causing frequency safety problems, thereby ensuring the safety of the day-ahead scheduling plan; on the other hand, during the scheduling process, the system satisfies the power balance relationship at a preset confidence level, rather than being limited to the absolute power balance equality relationship on both sides of the source and load, so as to meet the expectations of scheduling decision makers, so that the scheduling process optimization range is wider, wind power can be better absorbed, the economy is better, the spare capacity is less, and it is more superior.

[0214] 2) Impact of load-side inertia uncertainty on optimal scheduling

[0215] In addition to the synchronous inertia generated by the synchronous unit, there is also the load side inertia generated by the load (synchronous motor, asynchronous motor, etc.), and the load side inertia is usually uncertain, which can be represented by the fuzzy chance constraint mentioned above. In order to study the impact of load side inertia uncertainty on optimal scheduling, the disturbance is set to 0.1P with the N-1 limit expected fault. L , the following three schemes are established for comparative analysis:

[0216] Scheme 1: Fuzzy chance-constrained optimization scheduling scheme without considering dynamic frequency constraints;

[0217] Scheme 2: Fuzzy chance constrained optimal scheduling scheme taking into account dynamic frequency constraints and ignoring the uncertainty of load side inertia;

[0218] Scheme 3: Fuzzy chance constrained optimization scheduling scheme taking into account dynamic frequency constraints and load side inertia uncertainty.

[0219] Table 5 Comparison of different optimization scheduling schemes

[0220]

[0221] For the dispatching schemes under power disturbance in 24 time periods, it can be seen from Table 5 that compared with the other two schemes, Scheme 1 has the lowest power generation cost, start-stop cost, wind abandonment cost and total cost. This is mainly because Scheme 1 does not take into account the dynamic frequency constraint and only satisfies the dispatching decision from the perspective of power balance. It does not need to consider the risk of frequency over-limit. When large-scale wind power is connected, Figure 4 It can be seen that the number of thermal power units in operation is small, resulting in insufficient system frequency response capability and primary frequency regulation reserve. Once a large power disturbance occurs, it is easy to cause frequency instability, so it is the most economical. Compared with Scheme 1, Scheme 2 takes into account the impact of dynamic frequency constraints. Figure 5 It can be seen that it increases the number of thermal power units in the system, so that the system has sufficient frequency regulation capability to avoid frequency safety accidents when the system is subject to power disturbances, so the cost is increased. In addition, compared with Scheme 2, Scheme 3 takes into account the impact of load side inertia. The system takes into account more inertia, which makes the system have sufficient inertial response capability. Figure 6 It can be seen that it reduces the number of thermal power units that are started and alleviates the frequency regulation pressure of thermal power units, so it is more economical. It can be seen that Scheme 2 is based on the scheduling model of traditional dynamic frequency constraints, and introduces fuzzy opportunity constraints to deal with source-load uncertainty, which can not only ensure the frequency safety of the system, but also reduce the spare capacity, increase the wind power consumption, and make the scheduling scheme better. On the basis of Scheme 2, Scheme 3 proposed by the present invention takes into account the inertia on the load side, and the system takes into account more inertia, so that the system has sufficient inertia support and primary frequency regulation capabilities, which reduces the system operating cost and improves the economy of the system scheduling power generation plan.

[0222] pass Figure 7 and Figure 8It can be seen that scheme 1 does not consider dynamic frequency constraints. Under power disturbance conditions, the lowest frequency point only meets the frequency safety range in periods 5-6 and 23-24, and the frequency exceeds the limit in the remaining periods. The frequency change rate only exceeds the frequency safety range in period 1-2. If the power generation plan is formulated based on this scheduling scheme, the frequency stability is poor due to the insufficient system inertial response capability and primary frequency regulation capability, which is easy to cause frequency safety problems. Scheme 1 shows that the system with a high proportion of new energy should consider the impact of dynamic frequency constraints to ensure the stable operation of the system. Therefore, scheme 2 considers the impact of dynamic frequency constraints on the basis of scheme 1, so that the lowest frequency point and the frequency change rate do not exceed the limit, ensuring the frequency safety of the system. On the basis of scheme 2, scheme 3 takes into account the inertia on the load side, improves the overall inertia level of the system, and enables the system to have sufficient frequency regulation capability. On the premise of meeting the frequency safety requirements, the frequency safety index has been greatly improved, which can absorb more wind power, reduce the frequency regulation pressure of thermal power units, reduce the operating cost of the scheduling process, and make the scheduling scheme more economical.

[0223] In summary, the scheme 2 of the present invention, which takes into account dynamic frequency constraints and introduces fuzzy opportunity constraints, has an increased power generation cost compared to the traditional scheme 1, but it can avoid system frequency instability and prevent cascading failures in the system when power shortages are caused by accidental faults, causing extremely serious power outages. Obviously, with the increasing penetration rate of wind power today, in order to meet the power generation plan of the system with a high proportion of wind power, to ensure that the system meets the frequency safety requirements under occasional fault power disturbances, and to ensure that the frequency does not exceed the limit at any time in the scheduling scheme, scheme 2 is more superior. On the basis of scheme 2, scheme 3 proposed in the present invention takes into account the inertia of the load side, increases the system inertia, and enables the system to have sufficient inertia support and frequency response capabilities. It can reduce the number of startups of some units on the premise of ensuring the stable operation of the system frequency, so as to reduce the scheduling operation cost, improve the economy of the scheduling scheme of the present invention, and better meet the scheduling plan requirements of the new power system, and can provide certain ideas and references for dispatchers.

[0224] 3) Analysis of uncertainty results of N-1 unit failure:

[0225] In order to verify the effectiveness of the N-1 fault probability uncertainty set model established in the present invention, the power shortage caused by the unit failure is taken as the disturbance quantity, and two comparison schemes are set up for simulation analysis. The schemes are as follows:

[0226] Scheme 1: Taking the traditional limit anticipated fault disturbance setting as an example, the maximum rated power unit is set to be out of operation, and the fuzzy opportunity constrained optimization scheduling scheme taking into account the dynamic frequency constraint and the uncertainty of the load side inertia is proposed;

[0227] Scheme 2: Considering the uncertainty of unit failure probability, taking the power shortage of N-1 unit failure as the disturbance, and taking into account the fuzzy chance constrained optimization scheduling scheme of dynamic frequency constraints and load side inertia uncertainty.

[0228] Table 6 Comparison of optimization scheduling results under different schemes

[0229]

[0230] Based on the uncertainty of unit failure probability, the uncertainty of power shortage caused by accidental unit failure is studied. cut Under the fault probability threshold, N-1 safety checks are performed on units with possible faults, and the optimization results are shown in Table 6. Traditional solution 1 uses the maximum capacity unit to exit operation. Its sudden exit from operation causes serious power disturbances. Since the maximum capacity unit has strong inertial response capability and primary frequency regulation capability, when the unit exits operation, it cannot provide inertial support and primary frequency regulation capability, nor can it provide electrical energy to meet the power balance requirements. Figures 9 to 11 It can be seen that under the high power disturbance caused by the withdrawal of the unit, the system inertia time constant and the lowest frequency point of Scheme 1 in most periods are smaller than those of Scheme 2, while the frequency change rate is only related to the power disturbance and inertia. The power shortage of Scheme 1 is much greater than that of Scheme 2, resulting in greater fluctuations. Therefore, the overall frequency response capability of the system decreases, causing the system to abandon wind operation and increase the cost of wind abandonment. In order to meet the requirements of system inertia and frequency regulation and ensure that the system can operate safely and stably, it is necessary to increase the number of thermal power units to be started to make up for the power shortage and insufficient frequency response capability caused by the withdrawal of the unit, so as to meet the power balance requirements and frequency safety requirements. This also leads to an increase of 10.71%, 31.80% and 15.16% in the power generation cost, start-up and shutdown cost and total cost of Scheme 1 compared with Scheme 2, respectively. In actual operation, the failure probabilities of different units are inconsistent. The unit with the largest capacity has high operating reliability and low failure probability. Obviously, Scheme 1 withdraws the largest unit from operation, and the scheduling scheme is too conservative and has poor economy. However, Scheme 2 of the present invention takes into account the uncertainty of the unit failure probability, so it can be used in α cut Under the fault probability threshold limit, based on the distribution of fault probability information of different units, the best is sought from the worst scenario of the uncertainty set to determine the units that may fail, reducing the conservatism of the plan of directly withdrawing the units with the largest capacity from operation, so that the costs of Plan 2 are lower than those of Plan 1, the system frequency response capability and inertia support capability are better, and the wind power consumption is better, which is more in line with the actual application scenario. In addition, because the present invention uses fuzzy opportunity constraints to deal with the influence of multiple uncertainties of wind power output, load power prediction and load side inertia, it reduces the dependence on the number of samples, reduces the conservatism of robust optimization, makes the results of the scheduling plan more accurate, and can provide a basis for scheduling operators.

[0231] The unit combination model proposed in the present invention, which uses joint fuzzy chance-constrained programming to deal with uncertainty problems and considers the uncertainty of load-side inertia, takes into account more inertia, has sufficient inertia support and primary frequency regulation capabilities, has a wider optimization range, can better absorb wind power, has better economy, and has less spare capacity. In addition, the model of uncertainty in the probability of failure of N-1 units proposed in the present invention can optimize the worst scenario of the uncertainty concentration of the probability of failure under the premise of ensuring the frequency safety of the system, determine the unit failure scheduling plan, reduce the conservatism of the traditional plan of withdrawing the unit with the maximum capacity, make the results of the scheduling plan more accurate, more economical, and more in line with the actual application scenario, and provide guidance and ideas for optimizing scheduling personnel.

Claims

1. A unit commitment method with dynamic frequency constraints based on N-1 faults and load side inertia uncertainty, characterized by The following steps are involved: Step 1: Construct a dynamic frequency response model including load-side inertia and derive the expressions of the lowest frequency point and frequency change rate; Step 2: Construct N-1 failure probability uncertainty set model; Step 3: Aiming at the uncertainty of wind power, load and load-side inertia, a two-stage robust unit commitment model based on fuzzy chance constraints is constructed on the basis of dynamic frequency constraints; Step 4: Use the duality theory combined with the C&CG algorithm to decompose the two-stage robust unit commitment model based on fuzzy chance constraints into main problems and sub-problems for iterative solution to obtain the optimal scheduling solution.

2. The unit commitment method with dynamic frequency constraints based on N-1 faults and load-side inertia uncertainty according to claim 1, characterized in that: In step 1, the dynamic frequency response model including the load side inertia is shown in the following equations (1) to (5): The rotor motion equations for this model are expressed as follows: In formula (1): H G is the synchronous inertia time constant; H L is the load side inertia time constant; △ω is the frequency deviation of the system; △P G is the primary frequency regulation active power adjustment of the unit; △P L is the active unbalance amount caused by the disturbance; D is the damping coefficient of the system; the lowest frequency point derived from the dynamic frequency response model including the load side inertia is as follows: In the above formula: f nadir Indicates the lowest frequency point; t nadir Indicates the time corresponding to the lowest frequency point; f0 is the initial frequency of the system; f B is the base frequency of the system; N is the total number of thermal power units; i is the number of thermal power units; Each conventional unit C i The expression is as follows: In formula (4): U i is the start and stop status of the i-th unit; K i is the unit regulation power coefficient of the i-th generator; T i is the response time constant of the i-th generator, i=1,…,N; where U1 represents the start / stop state of the first unit; U N The start and stop status of the Nth unit; K1 represents the unit adjustment power coefficient of the first generator; K N represents the unit regulation power coefficient of the Nth generator; T1 represents the response time constant of the first generator, T N represents the response time constant of the Nth generator; the frequency change rate expression is as follows: Where: RoCoF represents the frequency change rate; △ω represents the frequency deviation of the system; t represents the time of change of the system frequency deviation; t=0 + Indicates the value of the frequency deviation when the frequency deviation is differentiated with respect to time.

3. The unit commitment method with dynamic frequency constraints based on N-1 faults and load-side inertia uncertainty according to claim 1, characterized in that: In step 2, an N-1 failure probability uncertainty set model is constructed, and the model is as follows: The N-1 uncertainty set is used to describe the uncertainty factors of unit failure, which is described as: Where: Z is the N-1 fault probability uncertainty set; N is the number of equipment or lines in the power system; A it Is the fault of unit i at time t, 0 for fault and 1 for normal; The calculation formula for the probability of unit outage accident is: Where: P it is the failure probability of the i-th unit; MTTR i is the average repair time of the i-th unit; MTTF i is the average failure time of the i-th unit; For the unit repair time T involved in the unit failure probability MTTR and unit failure time T MTTF It is difficult to estimate accurately. It obeys exponential distribution and is generated by Monte Carlo simulation sampling. The expression is as follows: T MTTR =-MTTR·lnγ MTTR (8); T MTTF =-MTTF·lnγ MTTF (9); Where: γ MTTR and γ MTTF are all random numbers uniformly distributed in the interval (0,1); MTTR is the mean repair time of the unit; MTTF is the mean failure time of the unit; By adopting α cut The criterion is used to add the probability information of unit outage emergencies to the uncertain set to reduce the conservatism of the robust optimization method; α cut The worst case generated by the criterion only includes probability greater than a given α cut Threshold case, constrained α cut The criteria are expressed as: Where: α cut is the fault probability threshold, and the logarithms on both sides of equation (10) are converted into linear expressions: Further arrangement gives the following formula:

4. The unit commitment method with dynamic frequency constraints based on N-1 faults and load side inertia uncertainty according to claim 1, characterized in that: In step 3, a two-stage robust unit commitment model based on fuzzy chance constraints is constructed, as follows: When the confidence level α of the fuzzy chance constraint is > 1 / 2, the clear equivalence class form of Cr{g(x,ξ)≤0}≥α can be expressed as: Where: α is the confidence level of the fuzzy chance constraint; g(x,ξ) represents the constraint function; x represents the trapezoidal fuzzy variable; ξ represents the trapezoidal fuzzy parameter; Indicates the definition function; r k1 ~r k4 represents the trapezoidal membership parameter; k=1,2,…,t,t∈R; R represents a real number; t represents the number of value sets; h0(x) represents a part of the function g(x,ξ); The objective function of the two-stage robust unit commitment is as follows: f(P Git )=a i +b i P Git +c i P Git 2 (16); Where: U it is the start / stop status of the i-th unit in time period t, 1 indicates start, 0 indicates stop; U i,t-1 is the start / stop status of the i-th unit in time period t-1; S U,it , S D,it are the start-up and shutdown costs of the i-th unit in period t; Q is the total cost of the second stage; z is the probability of failure; Z is the N-1 failure probability uncertainty set; y i,t is the operating state variable of thermal power unit i at time t, which is a 0-1 variable; is the predicted value of wind power in period t; q w P is the wind abandonment penalty coefficient; wt is the output power of the wind turbine in period t; T is the dispatching period of the study; f(P Git ) is the power generation cost of thermal power units; a i 、b i 、c i is the coefficient of the quadratic cost function of the i-th thermal power unit.

5. The unit commitment method with dynamic frequency constraints based on N-1 faults and load-side inertia uncertainty according to claim 1, characterized in that: In step 4, since the min-max-min structure of the two-stage robust optimization cannot be solved directly, the duality theory combined with the C&CG algorithm is used to decompose the model into main and sub-problems for iterative solution to obtain the optimal scheduling solution; The two-stage robust optimization takes the following form: Where: y is the matrix of decision variables of the C&CG algorithm in the first stage; c T is the cost coefficient corresponding to the start and stop in the first stage; x is the matrix composed of decision variables in the second stage of the C&CG algorithm; b T is the cost coefficient corresponding to the output of the second stage; is the matrix corresponding to the start and stop of the first stage; the optimization constraint condition F(y,u) is the linear function of the parameter u of the second stage; d is the constant coefficient matrix corresponding to the start and stop constraints of the first stage; matrices A2, A3, A4 and h are the constant coefficient matrices corresponding to the constraints of the second stage; The two-stage robust optimization model established above is a nonlinear model with a min-max-min structure. The original problem is decomposed into a main problem and sub-problems, and the sub-problems are transformed and processed using the duality theory. The two-stage robust unit commitment model is expressed as: minc T y+Q(x,z)(18)? Where: λ is the dual variable; Formula (21) is the constraint condition after dualization, and in Formula (22), is the constraint matrix corresponding to the output of the second stage; By replacing the original equation of Q(x,z) with its dual, the subproblem Q(x,z) in the original problem can be transformed into the constraint condition after the dualization of equation (21); this problem is equivalent to the following equation: After the above-mentioned dual transformation, the second-stage max-min model of the objective function can be transformed into a max model, and the original two-stage robust model min-max-min structure is finally transformed into a min-max model, which can be solved with the help of the C&CG algorithm and calling the Gurobi solver.

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