Power transmission and distribution network two-stage robust optimization operation method considering frequency security constraint

Abstract

The invention discloses a power transmission and distribution network two-stage robust optimization operation method considering a frequency security constraint, and the method comprises the steps: analyzing a dynamic frequency response process of a system, and building a power transmission and distribution network dynamic frequency security constraint around a frequency change rate, a frequency lowest point and a quasi-steady-state frequency; according to the method, wind and light output uncertainty is considered, a wind and light output uncertainty set is constructed, and a power transmission and distribution network two-stage robust optimization model considering frequency safety constraints is constructed by taking minimization of thermal power generating unit start-stop cost, thermal power generating unit and conventional distributed generator set power generation cost and frequency modulation standby cost of each unit in a system as targets; and converting, iterating and solving the two-stage robust optimization model of the power transmission and distribution network by adopting a column sum constraint generation algorithm and a strong duality theory until the upper bound and lower bound results of the target function are converged, thereby obtaining an optimal scheduling scheme. According to the invention, the cooperative operation of the power transmission and distribution network is realized, and the safety and economy of the system can still be considered when the system is faced with uncertainty.

Description

Technical Field

[0001] The present invention relates to the technical field of power system transmission and distribution separation scheduling, and in particular to a two-stage robust optimization operation method for a transmission and distribution network considering frequency safety constraints. Background Art

[0002] The penetration rate of new energy sources such as wind power and photovoltaic power is increasing, and they are gradually replacing conventional units to become an important part of the power grid. At the same time, the access of a high proportion of distributed energy resources (DER) has gradually transformed the "passive" traditional distribution network into an active distribution network (ADN). DER has the ability to participate in the real-time regulation and management of electricity to a certain extent, and the coupling relationship between the transmission and distribution networks is constantly strengthening. Unlike conventional synchronous generators, new energy power generation devices such as wind power and photovoltaic power basically do not have inertial support capabilities, and with the shutdown of a large number of coal-fired power units in recent years, the system's rotational inertia has decreased sharply.

[0003] At present, in the traditional dispatching and operation mode of power system with separation of transmission and distribution, more and more power systems are gradually evolving into low-inertia power systems with high penetration of new energy. The reduction of system rotational inertia will affect the frequency response capability of the system, which may easily lead to unnecessary grid congestion, make it difficult to give full play to the complementary capacity between transmission and distribution networks, and ensure the overall optimal operation of transmission and distribution networks. When they are disturbed by active power, the frequency may drop sharply, and the frequency safety issue is becoming increasingly prominent.

[0004] To this end, we designed a two-stage robust optimization operation method for transmission and distribution networks considering frequency security constraints to solve the above problems. Summary of the invention

[0005] The purpose of the present invention is to solve the shortcomings of the prior art that the reduction of the rotational inertia of the power system affects the frequency response capability of the system, easily leads to unnecessary grid congestion, makes it difficult to give full play to the complementary capabilities between the transmission and distribution networks, and cannot ensure the overall optimal operation of the transmission and distribution networks. A two-stage robust optimization operation method of the transmission and distribution network considering frequency safety constraints is proposed to explore flexible and reliable frequency regulation means, give full play to the frequency regulation capability of new energy units, improve the stability of the power system, and effectively cope with frequency fluctuations.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: A two-stage robust optimization operation method for a transmission and distribution network considering frequency security constraints, the method mainly comprises the following steps: Step S1: Analyze the dynamic frequency response process of the system, and establish dynamic frequency security constraints for the transmission and distribution network based on the frequency change rate, the lowest frequency point and the quasi-steady-state frequency; In step S2, considering the uncertainties of wind and light output, the uncertainty sets of wind and light output are respectively constructed in the form of intervals. By minimizing the start-stop cost of thermal power units, the power generation costs of thermal power units and conventional distributed generation units, and the frequency regulation reserve costs of each unit in the system, a two-stage robust optimization model of the transmission and distribution network considering frequency security constraints is constructed. In step S3, the column-and-constraint generation algorithm and the strong duality theory are used to transform, iterate, and solve the two-stage robust optimization model of the transmission and distribution network until the upper and lower bounds of the objective function converge, and the optimal scheduling plan is obtained.

[0007] Further preferably, in step S1, the analysis of the system's dynamic frequency response process is as follows: When there is a power deficit after the system is disturbed by unit switching and load increase or decrease, the frequency shows a downward trend. t 0 At this moment, the system starts inertial response, and the kinetic energy provided by the inertia in the system is used to regulate the frequency. The generator sets are not working, and the rate of change of frequency reaches the maximum value. t 1 At this moment, the units in the system start to change their mechanical power. The inertial response and primary frequency regulation jointly regulate the power deficit. The thermal power units in the transmission network adjust their output by unit start-stop to meet the frequency regulation requirements. The wind turbines and the conventional distributed generation units and photovoltaic units in the active distribution network do not consider unit start-stop and directly allocate output and frequency regulation resources. When the unit output is equal to the disturbance, the system frequency drops to the lowest point, and the primary frequency regulation ends at the quasi-steady state frequency. t 2 At this moment, secondary frequency regulation continues to achieve the zero-error regulation of the frequency.

[0008] Further preferably, in step S1, around the rate of change of frequency, the lowest frequency point, and the quasi-steady state frequency, the following dynamic frequency security constraints of the transmission and distribution network are established: Rate of change of frequency constraint: In the short time interval of inertial response, no unit in the system has taken action. The system inertia time constant is jointly determined by the inertia time constants of each unit in the system and meets the maximum allowable requirement of the rate of change of frequency, that is: ; In the formula, is the system base frequency; H t is t the system inertia time constant at this moment; H i , H w , H j , H pThe inertia time constants of thermal power units, wind power units, conventional distributed generation units, and photovoltaic units, respectively; P i 、 P w 、 P j 、 P p The power generation capacities of thermal power units, wind power units, conventional distributed generation units, and photovoltaic units, respectively, 、 、 and represent the installed capacities of thermal power units, wind power units, conventional distributed generation units, and photovoltaic units, respectively; u i,t is the start / stop state of the thermal power unit at t moment, is t the system power deficit at moment, represents the maximum allowable value of the frequency change rate; Frequency minimum point constraint: The combined action of inertia response and primary frequency regulation causes the system frequency to drop to the frequency minimum point. Each unit needs to reserve frequency regulation capacity to participate in frequency regulation to prevent the frequency deviation from exceeding the given safety threshold, as shown in the following formula: ; In the formula, represents t the frequency deviation at moment, R t is the sum of the frequency regulation reserve capacities of the dispatchable frequency regulation resources in the system at t moment; is the frequency dead zone; D is the load damping rate; is t the system load at moment; T d is the primary frequency regulation response time, represents the given frequency deviation safety threshold; Quasi-steady state frequency constraint: When the primary frequency regulation reserve capacities of all generating units in the system are fully released, the quasi-steady state frequency constraint of the system is as shown in the following formula: ;

[0009] In the formula, represents t the quasi-steady state frequency deviation at moment, represents the maximum allowable quasi-steady state frequency deviation of the system, D t is tMoment load damping coefficient.

[0010] Further preferably, in step S2, considering the uncertainties of wind and light output, the uncertainty sets of wind and light output are respectively constructed in the form of intervals, and are expressed by the following formula: ; ; In the formula, Un W 、Un P are the uncertainty sets of wind and light output respectively; , are respectively t The power of wind and light output after uncertainty processing at the moment; , are respectively t The predicted wind and light output at the moment; , are respectively t The maximum allowable fluctuation range of wind and light output at the moment, and as well as and are respectively t Binary variables for the wind and light output to obtain the interval boundary at the moment; Γ w 、Γ p are the introduced wind and light uncertainties respectively, representing the total number of moments when the wind power and photovoltaic output reach the interval boundary, T is the total number of dispatching time periods; By minimizing the start-stop cost of thermal power units, the power generation costs of thermal power units and conventional distributed generation units, and the frequency regulation reserve costs of each unit in the system, the expression of the two-stage robust optimization model of the transmission and distribution network considering frequency security constraints is as follows: ;

[0011] In the formula, , , represent the start-stop cost of thermal power units, the power generation costs of thermal power units and conventional distributed generation units, and the frequency regulation reserve costs of each unit in the system respectively; , are the start-up and shutdown costs of thermal power units respectively; C i , C j are the power generation costs of thermal power units and conventional distributed generation units respectively; , , , The frequency regulation reserve costs of thermal power units, wind power units, conventional distributed generation units, and photovoltaic generation units, respectively; su i,t 、 sv i,t Are respectively t The start-up and shutdown states of thermal power units at time P i,t 、 P j,t Are respectively t The active power outputs of thermal power units and conventional distributed generation units at time R i,t 、 R w,t 、 R j,t 、 R p,t Are respectively the frequency regulation reserve capacities of thermal power units, wind power units, conventional distributed generation units, and photovoltaic units at t time 、 、 And Represent the installed capacities of thermal power units, wind power units, conventional distributed generation units, and photovoltaic units, respectively.

[0012] The two-stage robust optimization model of the transmission and distribution network is constrained by the following constraints: ;

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] In the above formula, is the transmission capacity of the tie line between the transmission and distribution networks at t time; is the set of start nodes with the end node being ; , are the transmission powers of lines , at t time respectively; P tranl,t is the predicted load of the transmission and distribution network at t time; P w,t is the active power output of the wind turbine at t time; is the upper limit of the transmission power of line ; is the susceptance of line ; , are the phase angles of node and node b at t time respectively; represents the phase angle of the slack node r at t time; T on,i , T off,i are the minimum start-up and shut-down times of the thermal power unit respectively, u i,k is the start-stop state of the thermal power unit at k time, u i,t is the start-stop state of the thermal power unit at t time, u i,t-1 is the start-stop state of the thermal power unit at the previous time t ; su i,t , svi,t respectively t the start-up and shutdown states of the thermal power unit at a certain moment P i,t-1 is the previous moment t the active power output of the thermal power unit R i,t-1 is the frequency regulation reserve capacity of the thermal power unit at the previous moment t ; and are the upward and downward ramp rates of the thermal power unit respectively and are the upper and lower limits of the output of the thermal power unit respectively and respectively t are the upper and lower limits of the output of the wind power unit at a certain moment is the upper limit of the reserve capacity of the thermal power unit is the wind power unit at t the upper limit of the reserve capacity at a certain moment P j,n,t and P p,n,t respectively t at a certain moment, the conventional distributed generator 、 photovoltaic unit injects n the active power of the node Q j,n,t and Q p,n,t respectively t at a certain moment, the conventional distributed generator 、 photovoltaic unit injects n the reactive power of the node and respectively represent t at a certain moment, the power grid injects into node n the active and reactive powers transmitted by the connecting line between the transmission and distribution networks and respectively are the sets of the start node and the end node where the end node and the start node are n ; is the set of start nodes where the end node is d ; P mn,t and Q mn,t respectively t at a certain moment, the active and reactive powers injected by node m into node n ; P nd,t and Q nd,t respectively t at a certain moment, noden Active and reactive power output to the node d ; P distl,n,t and Q distl,n,t are respectively t the active and reactive load predicted by the node at time n ; I mn,t is t the current flowing through line mn at time r mn and x mn are respectively mn the resistance and reactance of line U m,t and U n,t are respectively t the voltages of node m and node n at time ; and n are respectively the upper and lower limits of the voltage of node ; and are respectively t the upper and lower limits of the output of the photovoltaic unit at time ; is the upper limit of the reserve capacity of the conventional distributed generator ;

[0031] Further preferably, in step S3, the two-stage robust optimization model of the transmission and distribution network is transformed, iterated and solved by using the column sum constraint generation algorithm and the strong duality theory. The two-stage robust optimization model of the transmission and distribution network is decomposed into the master problem MP and the sub-problem SP. The objective function and constraint conditions after transformation and iteration are represented in the following matrix form: 1) Master problem MP: ;

[0032] In the formula, A , B , E , F , G , H , K , are respectively the coefficient matrices corresponding to the variables; d ,f , g , z , p , is the corresponding constraint constant matrix, η is the slack variable; is the th solution of the sub-problem SP after the th iteration; is the worst scenario of wind and photovoltaic power outputs after the represents the main problem cost coefficient matrix, represents the sub-problem cost coefficient matrix, is the first-stage optimization variable set, represents the matrix transpose symbol; 2) Sub-problem SP: ;

[0033] In the formula, is the th solution of the main problem MP after the , γ , μ , ζ , π 1 , π 2 are the dual variables corresponding to each constraint respectively; is the set of wind and photovoltaic uncertain power outputs, represents the set of wind and photovoltaic power output uncertainties, represents the second-stage optimization variable set, represents the determined optimization variable , after feasible region.

[0034] For the max-min two-layer model in the sub-problem SP, the inner min problem is transformed into its dual max problem by using the strong duality theory and the big M method, and combined with the outer max to obtain the following single-layer max model: ; In the formula, α + , α - is the set of binary variables representing the interval boundaries of wind and photovoltaic power outputs; M 2 , M 3 are the variables artificially introduced by the big M method; A + , A - are the introduced continuous auxiliary variables; represents the set of wind and photovoltaic predicted power outputs, Denote the set of maximum allowable fluctuation deviations of wind and light output π 1，m 、 π 2,m Denote the dual variables corresponding to each constraint in branch m of the distribution network The master problem MP makes a preliminary decision without considering uncertainty. The sub-problem SP searches for the worst-case scenario according to the decision result of the master problem MP, enabling the master problem MP to continuously introduce variables and constraints related to the sub-problem SP until the upper and lower bounds of the objective function converge, obtaining the optimal scheduling plan

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows: Based on the dynamic frequency response characteristics of the transmission and distribution network, the present invention embeds the frequency security constraint into the unit commitment. Considering the frequency support capabilities of thermal power units, centralized new energy units, and high-proportion distributed energy sources in the embedding of the frequency security constraint into the unit commitment, taking into account the uncertainty of wind and light output, through the transformation and solution of the two-stage robust optimization model of the transmission and distribution network, the optimal scheduling plan of the system under the worst-case scenario of wind and light output is obtained, realizing the coordinated operation of the transmission and distribution network, ensuring that the system can still balance system security and economy when facing uncertainty, flexibly adjusting the conservatism of the system by changing the number of uncertain moments of wind power and photovoltaic power, enhancing the stability and reliability of the system, improving the ability to cope with the uncertainty of wind and light output and frequency fluctuations, and realizing the optimal operation of the transmission and distribution network BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Is the flowchart of the two-stage robust optimization operation method for the transmission and distribution network considering frequency security constraints in the embodiment of the present invention Figure 2 Is the basic structure diagram of the transmission and distribution network in the embodiment of the present invention Figure 3 Is the schematic diagram of the transmission and distribution network coupling system in the embodiment of the present invention Figure 4 Is the system load prediction diagram in the embodiment of the present invention Figure 5 Is the comparison diagram of the lowest frequency points of Scenario 1, Scenario 2, and Scenario 3 in the embodiment of the present invention Figure 6 Of Scenario 1, Scenario 2, and Scenario 3 in the embodiment of the present invention RoCoF Comparison diagram Figure 7 Is the unit start-stop status diagram of Scenario 1, Scenario 2, and Scenario 3 in the embodiment of the present invention DETAILED DESCRIPTION OF THE INVENTION

[0037] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments.

[0038] Embodiment 1: A two-stage robust optimal operation method for transmission and distribution networks considering frequency security constraints proposed in this embodiment is based on the dynamic frequency response characteristics of transmission and distribution networks. Considering thermal power units with unit start-stop states, centralized new energy units, and high-proportion distributed energy resources (Distributed Energy Resource, DER) for the frequency support ability of the system, it realizes the coordinated operation of transmission and distribution networks, improves the operation economy while ensuring the system frequency security under the worst scenarios of wind and light output. The main steps of this method are as follows: In step S1, establish the basic framework of the transmission and distribution network, analyze the system dynamic frequency response process (analyze the influence of thermal power units considering unit start-stop, centralized new energy units, and DER participating in frequency support on the frequency change rate, the lowest frequency point, and the quasi-steady state frequency), and establish the dynamic frequency security constraints of the transmission and distribution network around the frequency change rate, the lowest frequency point, and the quasi-steady state frequency.

[0039] In step S2, considering the uncertainty of wind and light output, construct the uncertainty sets of wind and light output in the form of intervals respectively. By minimizing the start-stop cost of thermal power units, the generation costs of thermal power units and conventional distributed generation units, and the frequency regulation reserve costs of each unit in the system, construct a two-stage robust optimization model for the transmission and distribution network considering frequency security constraints.

[0040] In step S3, use the Column and Constraint Generation (C&CG) algorithm and the strong duality theory to transform the two-stage robust optimization model of the transmission and distribution network into a Mixed-integer Second-order Cone Programming (MISOCP) model and iterate and solve it until the upper and lower bounds of the objective function converge to obtain the optimal scheduling plan.

[0041] In summary, the embodiments of the present invention improve the ability to cope with the uncertainty of wind and light output and frequency fluctuations through the above steps S1 - S3, enhance the stability and reliability of the system, and realize the optimal operation of the transmission and distribution network.

[0042] Embodiment 2: Referring to Figure 1 , the solution in Embodiment 1 will be further introduced below in combination with specific calculation formulas and examples. See the following description for details: S11, the basic structure of the transmission and distribution network is asFigure 2 As shown in the figure, the dispatchable frequency regulation resources in the transmission grid include thermal power units and wind turbines considering unit start-stop. The dispatchable frequency regulation resources in the active distribution network (ADN) include conventional distributed generation units and photovoltaic units. The power between the transmission and distribution grids can be balanced through two-way transmission to meet the overall grid load and the system frequency security requirements, thereby realizing the optimal dispatch of unit output and frequency regulation reserve.

[0043] The analysis of the system's dynamic frequency response process is as follows: When the system has a power deficit due to disturbances such as unit switching and load increase or decrease, the frequency shows a downward trend. t 0 At this moment, the system starts inertial response, and the kinetic energy provided by the system inertia regulates the frequency. The generating units are not working, and the rate of change of frequency (RoCoF) reaches the maximum value. RoCoF (Rate of Change of Frequency, RoCoF) reaches the maximum value; t 1 At this moment, the units in the system start to change their mechanical power. The inertial response and primary frequency regulation jointly regulate the power deficit. The thermal power units in the transmission grid adjust their output by unit start-stop to meet the frequency regulation requirements. The wind turbines and the conventional distributed generation units and photovoltaic units in the active distribution network do not consider unit start-stop and directly allocate output and frequency regulation resources. When the unit output is equal to the disturbance, the system frequency drops to the lowest point. f nadir , and the primary frequency regulation ends at the quasi-steady state frequency. f qss , t 2 At this moment, secondary frequency regulation continues to achieve the zero-error regulation of frequency.

[0044] S12. Construct the relevant constraints for three important indicators characterizing the system frequency security, that is, around the rate of change of frequency, the lowest frequency point, and the quasi-steady state frequency, establish the dynamic frequency security constraints of the transmission and distribution grids as follows: 1) Rate of change of frequency constraint: During the short time interval of inertial response, no units in the system have taken action. At this time, RoCoF The magnitude of is proportional to the power deficit and inversely proportional to the system inertia. The system inertia time constant is jointly determined by the inertia time constants of each unit in the system and meets the maximum allowable requirement of the rate of change of frequency, that is: (1) In the formula, is the system base frequency; H t is t the system inertia time constant at this moment;H i , H w , H j , H p are the inertia time constants of thermal power units , wind power units w , conventional distributed generation units j , and photovoltaic units p ; P i , P w , P j , P p are the generating capacities of thermal power units , wind power units w , conventional distributed generation units j , and photovoltaic units p ; , , and represent the installed capacities of thermal power units , wind power units w , conventional distributed generation units j , and photovoltaic units p ; u i,t is the start-stop state (1 for running, 0 for shutdown) of the thermal power unit at t , is the system power deficit, represents the maximum allowable value of the frequency change rate.

[0045] 2) Frequency nadir constraint: The combined action of inertial response and primary frequency regulation causes the system frequency to drop to the frequency nadir f nadir . Each unit needs to reserve frequency regulation capacity to participate in frequency regulation to prevent t the frequency deviation at from exceeding the given safety threshold , as shown in the following equation: (2) In the formula, ,t represents t the frequency deviation at R t is the sum of the frequency regulation reserve capacities of the dispatchable frequency regulation resources in the system at t ; is the frequency dead zone; D is the load damping ratio; is the system load; T d is the primary frequency regulation response time, represents the given frequency deviation safety threshold.

[0046] 3) Quasi-steady state frequency constraint: When the primary frequency regulation reserve capacity of all generating units in the system is fully released, the frequency will remain at a constant level, i.e., the quasi-steady state frequency . At this time, at time t the quasi-steady state frequency deviation must also be controlled within the maximum range allowed by the system. The system quasi-steady state frequency constraint is shown as follows: (3) In the formula, represents t the quasi-steady state frequency deviation at time represents the maximum allowable quasi-steady state frequency deviation of the system, D t is the load damping coefficient.

[0047] S21. This method considers the uncertainty of wind and photovoltaic power outputs, and based on the given fluctuation intervals of wind and photovoltaic power outputs, establishes a two-stage robust optimization model considering frequency security constraints to ensure the economy, security and robustness of the system. Considering the uncertainty of wind and photovoltaic power outputs, the uncertainty sets of wind and photovoltaic power outputs are constructed in interval form respectively, and are expressed by the following formula: (4) (5) In the formula, Un W 、Un P are the uncertainty sets of wind and photovoltaic power outputs respectively; , are the powers of wind and photovoltaic power outputs after uncertainty processing respectively; , are the predicted outputs of wind and photovoltaic power respectively; , are the maximum allowable fluctuation ranges of wind and photovoltaic power outputs respectively, and as well as and are respectively t the binary variables when the wind and photovoltaic power outputs reach the interval boundaries at time Γ w 、Γp They are the introduced uncertainties of wind and light respectively, representing the total number of moments when the output of wind power and photovoltaic power reaches the interval boundaries. T is the total number of dispatching time periods; S22. By taking the minimization of the start-stop cost of thermal power units, the power generation costs of thermal power units and conventional distributed generation units, and the frequency regulation reserve costs of each unit in the system as the objective, the expression of the two-stage robust optimization model of the transmission and distribution network considering frequency security constraints is as follows: (6) In the formula, , , represent the start-stop cost of thermal power units, the power generation costs of thermal power units and conventional distributed generation units, and the frequency regulation reserve costs of each unit in the system respectively; , are the start-up and shutdown costs of thermal power unit respectively; C i , C j are the power generation costs of thermal power unit and conventional distributed generation unit j respectively; , , , are the frequency regulation reserve costs of thermal power unit , wind turbine w , conventional distributed generation unit j and photovoltaic generation unit p respectively; su i,t , sv i,t are the start-up and shutdown states of thermal power unit t at time respectively; P i,t , P j,t are the active power outputs of thermal power unit and conventional distributed generation unit j respectively; R i,t , R w,t , R j,t , R p,t are the active power outputs of thermal power unit , wind turbine w , conventional distributed generation unit j , photovoltaic unit p at tThe frequency modulation reserve capacity at a moment 、 、 and respectively represent the installed capacities of thermal power units ,wind turbine units w ,conventional distributed generation units j ,and photovoltaic units p .

[0048] For S23, the two-stage robust optimization model of the transmission and distribution network is constrained by the following constraint conditions: (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) In Equation (7), is the transmission capacity of the connection line between the transmission and distribution networks at t moment; is the set of start nodes with the end node being ; 、 t are respectively the transmission powers of lines 、 at t moment; P tranl,t is tPredicted load of the power transmission and distribution network at a moment; P w,t For the wind turbine w Active power output.

[0049] In Equation (8), For the line Transmission power upper limit; For the line Susceptance; And Are respectively the phase angles of node And node b at t Moment; Indicates the phase angle of the slack node r At t Moment.

[0050] In Equation (9), T on,i And T off,i Are respectively the minimum start-up and shut-down times of the thermal power unit , u i,k Is the start-stop state of the thermal power unit At k Moment, u i,t Is the start-stop state of the thermal power unit At t Moment, u i,t-1 Is the start-stop state of the thermal power unit At the previous moment t Start-stop state; su i,t And sv i,t Are respectively t Moment start-stop state of the thermal power unit ; In Equation (11), P i,t-1 Is the active power output of the thermal power unit t At the previous moment , R i,t-1 Is the frequency regulation reserve capacity of the thermal power unit At the previous moment t , And Are respectively the upward and downward ramp rates of the thermal power unit .

[0051] In Equation (12), And Are respectively the upper and lower limits of the output of the thermal power unit ; In Equation (13), and are the upper and lower limits of the output of the wind turbine w respectively; In Equation (14), is the upper limit of the reserve capacity of the thermal power unit respectively; In Equation (15), is the upper limit of the reserve capacity of the wind turbine w at t time; In Equation (16), P j,n,t and P p,n,t are respectively t the active power injected into the j、 photovoltaic unit of the conventional distributed generation unit p at n node; Q j,n,t and Q p,n,t are respectively t the reactive power injected into the j、 photovoltaic unit of the conventional distributed generation unit p at n node; and respectively represent t the active and reactive power transmitted through the tie line between the transmission and distribution networks injected into node n at time; and n are respectively the sets of the start node and the end node with the end node being ; d is the set of the start nodes with the end node being P mn,t and Q mn,t are respectively t the active and reactive power injected from node m to node n at P nd,t and Q nd,t are respectively t the active and reactive power output from node n to node d at P distl,n,t and Q distl,n,t are respectively t the predicted active and reactive loads of node n atI mn,t is t the current flowing through the line mn at a certain moment; r mn and x mn are respectively the resistance and reactance of the line mn ; In Equation (17), U m,t and U n,t are respectively t the voltages of node m and node n at a certain moment; In Equation (18), and are respectively the upper and lower limits of the voltage of node n ; In Equation (20), and are the upper and lower limits of the output of the conventional distributed generator j ; In Equation (21), and are respectively the upper and lower limits of the output of the photovoltaic unit p ; In Equation (22), is the upper limit of the reserve capacity of the conventional distributed generator j ; In Equation (23), is the upper limit of the reserve capacity of the photovoltaic unit p ; In Equation (24), and are respectively the upper and lower limits of the transmission capacity of the connection line between the transmission and distribution networks.

[0052] S31. This method uses the column sum constraint generation algorithm and the strong duality theory to transform the two-stage robust optimization model of the transmission and distribution network into a mixed-integer second-order cone programming model (Mixed-integer Second-order Cone Programming, MISOCP), and iterates and solves it. The two-stage robust optimization model of the transmission and distribution network is decomposed into a master problem MP (Master Problem, MP) and a sub-problem SP (Subproblem, SP). The objective function and constraint conditions after transformation and iteration are represented in the following matrix form: 1) Master problem MP:

[0053] In the formula, A and B, E , F , G , H , K , are the corresponding variable coefficient matrices respectively; d , f , g , z , p , is the corresponding constraint constant matrix, η is the slack variable; is the solution of the sub-problem SP after the -th iteration; is the worst-case scenario of wind and photovoltaic power outputs after the -th iteration; represents the main problem cost coefficient matrix, represents the sub-problem cost coefficient matrix, is the first-stage optimization variable set, represents the matrix transpose symbol; 2) Sub-problem SP:

[0054] In the formula, is the solution of the main problem MP after the -th iteration; , γ , μ , ζ , π 1 , π 2 are the dual variables corresponding to each constraint respectively; is the set of wind and photovoltaic uncertain power outputs, represents the set of wind and photovoltaic power output uncertainties, represents the second-stage optimization variable set, represents the determined optimization variable , after the feasible region.

[0055] S32. Since the max-min two-layer model in the sub-problem SP cannot be directly solved by a solver, the inner min problem can be transformed into its dual max problem using the strong duality theory and the big M method, and combined with the outer max to obtain the following single-layer max model: ; In the formula, α + , α -A set of binary variables characterizing the boundary of the acquisition interval of wind and light output; M 2 and M 3 are variables artificially introduced by the Big M method; A + and A - are introduced continuous auxiliary variables; represents the set of predicted wind and light output, represents the set of maximum allowable fluctuation deviations of wind and light output, π 1，m and π 2,m respectively represent the dual variables corresponding to each constraint in branch m of the distribution network; The master problem MP makes a preliminary decision without considering uncertainty. The sub-problem SP searches for a severe scenario based on the decision result of the master problem MP, enabling the master problem MP to continuously introduce variables and constraints related to the sub-problem SP until the upper and lower bounds of the objective function converge to obtain the optimal scheduling plan.

[0056] Example 3: Next, in combination with a specific example, for a two-stage robust optimal operation method of a transmission and distribution network considering frequency security constraints proposed in the above-mentioned Embodiment 1 and Embodiment 2 of the present invention, the feasibility of this method is verified by coupling the IEEE 24-node transmission system and two IEEE 33-node distribution network systems to form a transmission and distribution network. The transmission and distribution network coupling system is as Figure 3 shown, and the details are described below: Analyze the operation of thermal power units and conventional distributed generation units in each ADN, where units 1-10 are thermal power units and units 11-14 are distributed generation units. The predicted load of the transmission and distribution network is as Figure 4 shown.

[0057] In this embodiment, three sets of comparison scenarios are set to conduct a comparative analysis of the example system: Scenario 1: Do not consider frequency security constraints and add unit auxiliary frequency modulation constraints; Scenario 2: On the basis of Scenario 1, consider frequency security constraints, and only thermal power units and wind turbines provide frequency support; Scenario 3: On the basis of Scenario 2, consider DER participating in system frequency modulation.

[0058] The cost comparisons of Scenario 1, Scenario 2, and Scenario 3 are shown in Table 1 below. In Scenario 1, Scenario 2, and Scenario 3, the frequency drops to the lowest point f nadir and the frequency change rate RoCoF comparisons, as well as the comparison of the frequency modulation reserve capacity of each unit, are as Figure 5 and Figure 6 shown. From Figure 5 andFigure 6 It can be seen that the lowest frequencies at moments 1-2 and 19-22 in Scenario 1 f nadir both exceed the safety range of 49.2 Hz, and the frequency change rate RoCoF is greater than the maximum allowable RoCoF value of 0.125 Hz / s at moments 1-5, 7, 9-24. This is because the frequency safety constraint is not considered in Scenario 1, and only a primary frequency regulation constraint to maintain the basic stability of the system frequency is added on this basis. At this time, the primary frequency regulation reserve capacity of the system cannot guarantee sufficiency, and only a certain degree of frequency adjustment is carried out through the basic reserve capacity of each operating unit, and the stability of the system frequency under large disturbances cannot be ensured. When the frequency safety constraint is considered in Scenarios 2 and 3, the lowest frequencies at each moment f nadir and the frequency change rate RoCoF both remain within the set safety threshold. It can be seen from this that considering the frequency safety constraint has a significant impact on maintaining the safety of the system. At the same time, in Scenario 3, DER replaces a part of the thermal power units and wind turbines to participate in the system frequency regulation, indicating that this method can enable DER to assist the system in frequency support and further realize the coordinated operation of the transmission and distribution networks in terms of frequency regulation.

[0059] Table 1 Costs of Scenarios 1, 2 and 3

[0060] To analyze the impact of the frequency safety constraint and the DER frequency regulation ability on the start-stop decisions of thermal power units and the system cost under three scenarios, the start-stop states of the units under each scenario are as Figure 7 shown. Affected by cost factors, Units 2, 4, and 6 are always in the operating state in the three scenarios. Secondly, the number of operating units in Scenario 1 is the least among the three scenarios. This is because the frequency safety constraint is not considered, and only a certain number of thermal power units and wind turbines in the operating state are required to respond to load changes. At this time, the capacities of Units 1-8 can meet the system load demand, and Units 9 and 10 are always in the shutdown state. When the frequency safety constraint is considered, the number of started thermal power units increases significantly, and as the electricity load increases during the day, the operating thermal power units are mostly concentrated at noon and in the evening. Especially at moments 16 and 17, all 10 units are in operation to cope with the impact of large disturbances on the system frequency at this time. Compared with Scenario 2, some thermal power units are shut down in Scenario 3. At this time, DER replaces a part of the thermal power units to participate in the frequency regulation process, so the number of operating thermal power units decreases.

[0061] As shown in Table 1, since the number of starting units in Scenario 1 is the least, its start-stop cost is the smallest. And because some units in Scenario 3 are shut down, the start-stop cost of Scenario 3 is greater than that of Scenario 2. Secondly, the capacity of low-cost units in Scenario 1 can meet the basic load and frequency regulation requirements of the system. On the contrary, in Scenario 2, considering the frequency security constraint, low-cost units participate in frequency support, while high-cost units start to generate electricity. At the same time, the unit reserve in Scenario 2 is less than that in Scenario 1. Therefore, compared with Scenario 1, the power generation cost in Scenario 2 increases by 5.9×10 4 yuan, while the frequency regulation reserve cost decreases by 3×10 3 yuan. Since low-cost DER is considered to replace some thermal power units to participate in the system frequency regulation process in Scenario 3, the frequency regulation reserve cost in Scenario 3 decreases by 1.4×10 4 yuan compared with Scenario 2. At this time, to balance the load demand of the distribution network and enable low-cost thermal power units to have sufficient capacity to generate electricity again. Therefore, compared with Scenario 2, the power generation cost of the transmission network in Scenario 3 decreases by 1×10 4 yuan, while the power generation cost of the distribution network increases by 9×10 3 yuan. The above analysis proves that the two-stage robust optimal operation method of the transmission and distribution network considering frequency security constraints proposed by the present invention can improve the economy of the transmission and distribution network system.

[0062] Table 2 Comparison of costs between deterministic optimization and two-stage robust optimization

[0063] The above Table 2 compares the costs of deterministic optimization and two-stage robust optimization. It can be seen from Table 2 that the total cost of the deterministic optimization method is the lowest. At this time, the deterministic optimization method is equivalent to the two-stage robust optimization method when Γ w = Γ p =0. As Γ w 、 Γ p increase gradually, the system needs to consider more uncertainties, and the moments when wind power and photovoltaic reach the lower limit of the uncertainty set increase. At this time, the optimization method is more conservative to ensure that the final solution is effective in all possible uncertain situations, and the additional planning and resource investment make the total cost show an upward trend. From the above analysis, it can be seen that the two-stage robust optimal operation method of the transmission and distribution network considering frequency security constraints proposed by the present invention can flexibly adjust the conservatism of the system by changing the uncertainty degree, making the power system have stronger robustness.

[0064] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes should be covered within the protection scope of the present invention.

Claims

1. A two-stage robust optimization operation method for transmission and distribution networks considering frequency security constraints, characterized in that: The following steps are involved: Step S1: Analyze the dynamic frequency response process of the system, and establish dynamic frequency security constraints for the transmission and distribution network based on the frequency change rate, the lowest frequency point and the quasi-steady-state frequency; Step S2, considering the uncertainty of wind and solar output, construct the uncertainty sets of wind and solar output in interval form respectively, and construct a two-stage robust optimization model of the transmission and distribution network considering frequency security constraints by minimizing the start-up and shutdown costs of thermal power units, the power generation costs of thermal power units and conventional distributed generators, and the frequency regulation and standby costs of each unit in the system; In step S3, the column and constraint generation algorithm and strong duality theory are used to transform, iterate and solve the two-stage robust optimization model of the transmission and distribution network until the upper and lower bounds of the objective function converge and the optimal scheduling plan is obtained.

2. The two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints according to claim 1 is characterized in that: In step S1, the process of analyzing the dynamic frequency response of the system is as follows: When the system is disturbed by the switching of units and the increase or decrease of load and a power shortage occurs, the frequency shows a downward trend. t At time 0, the system starts to respond inertia, and the inertia in the system provides kinetic energy to adjust the frequency. The generator set is not working, and the frequency change rate reaches the maximum value; t At time 1, the units in the system begin to change their mechanical power. The inertia response and primary frequency regulation jointly adjust the power shortage. The thermal power units in the transmission network adjust their own output by starting and stopping the units to meet the frequency regulation requirements. The wind turbines and conventional distributed generators and photovoltaic units in the active distribution network do not take into account the start and stop of the units, and directly allocate output and frequency regulation resources. When the unit output is equal to the disturbance, the system frequency drops to the lowest point, and the primary frequency regulation ends at the quasi-steady-state frequency. t 2. Continue to perform secondary frequency modulation at all times to achieve zero-difference frequency regulation.

3. The two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints according to claim 1 is characterized in that: In step S1, the dynamic frequency security constraints of the transmission and distribution network are established based on the frequency change rate, the lowest frequency point and the quasi-steady-state frequency as follows: Frequency change rate constraint: In the short time interval of inertial response, no unit in the system takes action. The system inertia time constant is determined by the inertia time constants of each unit in the system and meets the maximum allowable frequency change rate requirement, that is: ； In the formula, is the system reference frequency; H t for t The inertia time constant of the system at that moment; H i , H w , H j , H p They are the inertia time constants of thermal power units, wind power units, conventional distributed generators, and photovoltaic units respectively; P i , P w , P j , P p They are the power generation capacity of thermal power units, wind power units, conventional distributed power generation units, and photovoltaic units. , , and Respectively represent the installed capacity of thermal power units, wind power units, conventional distributed power generation units, and photovoltaic units; u i,t For thermal power units t Start and stop status at all times, for t The system power shortage at all times, Indicates the maximum allowable value of the frequency change rate; Frequency minimum point constraint: The inertial response and primary frequency regulation work together to reduce the system frequency to the lowest frequency point. Each unit needs to reserve frequency regulation to participate in frequency regulation to prevent the frequency deviation from exceeding the given safety threshold, as shown in the following formula: ； In the formula, express t The frequency deviation at the moment, R t The frequency modulation resources that can be scheduled in the system t The sum of the frequency regulation reserve capacity at all times; is the frequency dead zone; D is the load damping rate; for t System load at all times; T d is the frequency modulation response time, Indicates a given frequency deviation safety threshold; Quasi-steady-state frequency constraint: When the primary frequency regulation reserve capacity of all generators in the system is fully released, the quasi-steady-state frequency constraint of the system is as follows: ； In the formula, express t The quasi-steady-state frequency deviation at time , Indicates the maximum quasi-steady-state frequency deviation allowed by the system, D t for t Load damping factor at each moment.

4. The two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints according to claim 1 is characterized in that: In step S2, the uncertainty of wind and solar output is considered, and the uncertainty sets of wind and solar output are constructed in interval form, which are expressed as follows: ； ； In the formula, Un W 、Un P are the uncertainty sets of wind and solar output respectively; , They are t The power after the wind and solar output are uncertain at all times; , They are t Wind and light forecast output at all times; , They are t The maximum fluctuation range allowed for wind and solar output at any given moment, and as well as and They are t Binary variables that represent the boundaries of the wind and solar output intervals at each moment; Γ w , Γ p are the introduced wind and light uncertainties, representing the total number of moments when wind power and photovoltaic outputs reach the boundaries of the intervals. T is the total number of scheduling time periods; By minimizing the start-up and shutdown costs of thermal power units, the power generation costs of thermal power units and conventional distributed power generation units, and the frequency regulation and standby costs of each unit in the system, the expression of the two-stage robust optimization model of the transmission and distribution network considering frequency security constraints is constructed as follows: ； In the formula, , , They represent the start-up and shutdown costs of thermal power units, the power generation costs of thermal power units and conventional distributed power generation units, and the frequency regulation and standby costs of each unit in the system; , are the start-up and shutdown costs of thermal power units respectively; C i , C j are the power generation costs of thermal power units and conventional distributed power generation units respectively; , , , They are the frequency regulation and standby costs of thermal power units, wind power units, conventional distributed power generation units, and photovoltaic power generation units; su i,t , sv i,t They are t The start and stop status of thermal power units at all times; P i,t , P j,t They are t Active power output of thermal power units and conventional distributed power generating units at every moment; R i,t , R w,t , R j,t , R p,t They are thermal power units, wind power units, conventional distributed generators, and photovoltaic units. t Frequency regulation reserve capacity at all times, , , and They represent the installed capacity of thermal power units, wind power units, conventional distributed power generating units and photovoltaic units respectively.

5. The two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints according to claim 4 is characterized in that: The following constraints are used to constrain the two-stage robust optimization model of the transmission and distribution network: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； In the above formula, For the interconnection line between the transmission and distribution network t The transmission capacity at the time; The end node is The set of starting nodes; , Line , exist t The transmission power at the moment; P tranl,t for t Forecast load of transmission and distribution grid at every moment; P w,t for t Active power output of wind turbines at all times; For line Transmit power upper limit; For line Susceptance; , Node and node b in t The phase angle of the moment; Represents a balanced node r exist t The phase angle of the moment; T on,i , T off,i are the minimum start and stop time of thermal power units, u i,k For thermal power units k Start and stop status at all times, u i,t For thermal power units t Start and stop status at all times, u i,t-1 The thermal power unit at the last moment t Start-stop status; su i,t , sv i,t They are t The thermal power unit is on and off at all times. P i,t-1 For the previous moment t The active power output of thermal power units, R i,t-1 The thermal power unit at the last moment t Frequency regulation reserve capacity; , They are the upward and downward climbing rates of thermal power units respectively; , They are the upper and lower limits of thermal power unit output respectively; , They are t The upper and lower limits of wind turbine output at all times; The upper limit of the reserve capacity of thermal power units; For wind turbines t The upper limit of spare capacity at any time; P j,n,t , P p,n,t They are t Conventional distributed generator sets 、 Photovoltaic unit injection n Node active power; Q j,n,t , Q p,n,t They are t Conventional distributed generator sets 、 Photovoltaic unit injection n Node reactive power; , Respectively t Transmission network injection node n The interconnection lines between the transmission and distribution networks transmit active and reactive power; , The end node and the start node are n The set of start and end nodes; The end node is d The set of starting nodes, P mn,t , Q mn,t They are t Time Node m To Node n Injected active and reactive power; P nd,t , Q nd,t They are t Time Node n To Node d Output active and reactive power; P distl,n,t , Q distl,n,t They are t time n The active load and reactive load predicted by the node; I mn,t for t Time flows through the line mn The current; r mn , x mn Line mn resistance and reactance; U m,t , U n,t They are t Time Node m With Node n Voltage; , Separate nodes n Voltage upper and lower limits; , It is the upper and lower limits of the output of conventional distributed generator sets; , They are t The upper and lower limits of photovoltaic unit output at all times; It is the upper limit of the standby capacity of conventional distributed generators; for t The upper limit of the standby capacity of photovoltaic units at all times; , They are the upper and lower limits of the transmission capacity of the interconnection lines between transmission and distribution networks, respectively.

6. The two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints according to claim 1 is characterized in that: In step S3, the column and constraint generation algorithm and strong duality theory are used to transform, iterate and solve the two-stage robust optimization model of the transmission and distribution network. The two-stage robust optimization model of the transmission and distribution network is decomposed into the main problem MP and the sub-problem SP. The objective function and constraint conditions after transformation and iteration are expressed in the following matrix form: 1) Main question MP: ； In the formula, A , B , E , F , G , H , K , are the corresponding variable coefficient matrices respectively; d , f , , z , p , is the corresponding constraint constant matrix, η is the slack variable; For the The solution of the subproblem SP after iterations; For the The worst scenario of wind and solar output after the iteration; represents the main problem cost coefficient matrix, represents the sub-problem cost coefficient matrix, Optimize the variable set for the first stage, Represents the matrix transpose symbol; 2) Sub-problem SP: ； In the formula, For the The solution of the main problem MP after iterations; , γ , μ , ζ , π 1. π 2 are the dual variables corresponding to each constraint; For the uncertain output of wind and light, represents the uncertainty set of wind and solar output, represents the set of optimization variables in the second stage, Indicates the determination of optimization variables , back feasible domain.

7. The two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints according to claim 6 is characterized in that: The max-min two-layer model in the subproblem SP uses the strong duality theory and the big M method to transform the inner min problem into its dual max problem, and combines it with the outer max to obtain the following single-layer max model: ； In the formula, α + , α - A set of binary variables to obtain interval boundaries for representing wind and solar output; M 2. M 3 is the Big M method that artificially introduces variables; A + , A - is the introduced continuous auxiliary variable; It represents the wind and solar power forecast set, It represents the maximum fluctuation deviation allowed for wind and solar output. π 1，m , π 2,m represents the dual variables corresponding to each constraint in the m branch of the distribution network; The main problem MP makes a preliminary decision without considering uncertainty. The subproblem SP looks for severe scenarios based on the decision results of the main problem MP, so that the main problem MP continuously introduces variables and constraints related to the subproblem SP until the upper and lower bounds of the objective function converge and the optimal scheduling solution is obtained.

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