Two-stage robust optimization operation method for transmission and distribution networks considering frequency security constraints

Abstract

The present invention discloses a two-stage robust optimization operation method for a transmission and distribution network that considers frequency security constraints. The method includes: analyzing the system's dynamic frequency response process, establishing 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; considering the uncertainty of wind and solar output, constructing an uncertainty set for wind and solar output; and constructing a two-stage robust optimization model for the transmission and distribution network that considers 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 standby costs of each unit in the system; and using a column sum constraint generation algorithm and strong duality theory to transform, iterate, and solve the two-stage robust optimization model for the transmission and distribution network until the upper and lower bounds of the objective function converge, thereby obtaining an optimal scheduling solution. The present invention achieves coordinated operation of the transmission and distribution network, ensuring that the system can still take into account system security and economy when facing 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 security constraints. Background Art

[0002] The penetration rate of renewable energy sources such as wind power and photovoltaics continues to increase, gradually replacing conventional units and becoming a vital component of the power grid. At the same time, the integration of a high proportion of distributed energy resources (DER) is gradually transforming the "passive" traditional distribution network into an active distribution network (ADN). This enables DERs to participate to a certain extent in the real-time regulation and management of electricity, and the coupling relationship between transmission and distribution networks continues to strengthen. Unlike conventional synchronous generators, renewable energy generation devices such as wind power and photovoltaics have little inertial support capacity. Furthermore, with the closure of a large number of coal-fired power units in recent years, the decline in system rotational inertia has intensified.

[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 affects the frequency response capability of the system, which can easily lead to unnecessary grid congestion, making it difficult to give full play to the complementary capabilities between transmission and distribution networks, and unable to ensure the overall optimal operation of transmission and distribution networks. When they are subjected to active power disturbances, 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. Instead, 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 respond to frequency fluctuations.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] A two-stage robust optimization operation method for a transmission and distribution network considering frequency security constraints is provided. The method mainly comprises the following steps:

[0008] Step S1: Analyze the system's dynamic frequency response process and establish dynamic frequency security constraints for the transmission and distribution network based on the frequency change rate, frequency minimum point, and quasi-steady-state frequency.

[0009] 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. 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, a two-stage robust optimization model of the transmission and distribution network considering frequency security constraints is constructed.

[0010] 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.

[0011] Further preferably, in step S1, the process of analyzing the dynamic frequency response of the system is as follows:

[0012] 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 begins to respond by inertia, using the kinetic energy provided by the inertia within the system to adjust the frequency. The generator set is not working, and the frequency change rate reaches its 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 the same time to achieve zero-error frequency regulation.

[0013] Further preferably, in step S1, the dynamic frequency security constraints of the transmission and distribution network are established around the frequency change rate, the lowest frequency point and the quasi-steady-state frequency as follows:

[0014] Frequency change rate constraint:

[0015] During the short inertia response time interval, 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:

[0016] ;

[0017] Where, is the system reference frequency; H t for tThe inertia time constant of the system at that moment; H i 、 H w 、 H j 、 H p are the inertia time constants of thermal power generation units, wind power generation units, conventional distributed power generation units, 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 Always on and off state, for t The system power shortage at all times, Indicates the maximum allowable value of the frequency change rate;

[0018] Frequency minimum point constraint:

[0019] The inertial response and primary frequency regulation work together to reduce the system frequency to the lowest 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:

[0020] ;

[0021] Where, express t 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;

[0022] Quasi-steady-state frequency constraint:

[0023] When the primary frequency regulation reserve capacity of all generator sets in the system is fully released, the system quasi-steady-state frequency constraint is as follows:

[0024] ;

[0025] Where, 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 coefficient at all times.

[0026] Further preferably, in step S2, the uncertainty of wind and solar output is considered, and the uncertainty sets of wind and solar output are constructed in the form of intervals, respectively, and are expressed by the following formula:

[0027] ;

[0028] ;

[0029] Where, Un W 、Un P are the uncertainty sets of wind and solar output respectively; 、 They are t Power after processing when wind and solar output are uncertain at any moment; 、 They are t Wind and solar power forecast 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 representing 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;

[0030] By minimizing the start-up and shutdown costs of thermal power units, the generation costs of thermal power units and conventional distributed generation units, and the frequency regulation standby 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 as follows:

[0031] ;

[0032] Where, 、 、 They represent 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; 、 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; 、 、 、 The frequency regulation and standby costs are thermal power units, wind power units, conventional distributed power generation units, and photovoltaic power generation units respectively; 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 generators at each 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 generation units and photovoltaic units respectively.

[0033] The following constraints are used to constrain the two-stage robust optimization model of the transmission and distribution network:

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] In the above formula, For the interconnection line between transmission and distribution network t Transmission capacity at the time; The end node is The set of starting nodes; 、 Line 、 exist t Transmission power at the moment; P tranl,t for t Forecast load of transmission and distribution network at all times; P w,t for t Active power output of wind turbines at all times; For the line Transmit power upper limit; For the line Susceptance; 、 Node and node b in t Phase angle of moment; Represents a balance node r exist tPhase angle of moment;

[0053] 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 Always on and off state, u i,t For thermal power units t Always on and off state, 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 or 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; 、 are the upward and downward climbing rates of thermal power units respectively;

[0054] 、 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 moment;

[0055] P j,n,t 、 P p,n,t They are t Conventional distributed generator sets at all times 、 Photovoltaic unit injection n Node active power; Q j,n,t 、 Q p,n,t They are t Conventional distributed generator sets at all times 、 Photovoltaic unit injection n Node reactive power; 、 Respectively tTransmission network injection node n The tie lines between the transmission and distribution grids transmit active and reactive power; 、 The end node and the starting node are n The set of start and end nodes; The end node is d The starting node set of 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 Node predicted active load and reactive load; I mn,t for t Time flows through the line mn Current; r mn 、 x mn Line mn resistance and reactance;

[0056] U m,t 、 U n,t They are t Time Node m With node n Voltage; 、 Separate nodes n Voltage upper and lower limits; 、 The upper and lower limits of 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; The upper limit of the standby capacity of the photovoltaic unit; 、 They are the upper and lower limits of the transmission capacity of the tie lines between transmission and distribution networks, respectively.

[0057] Further preferably, 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, and the two-stage robust optimization model of the transmission and distribution network is decomposed into a main problem MP and a sub-problem SP. The objective function and constraints after transformation and iteration are expressed in the following matrix form:

[0058] 1) Main question MP:

[0059] ;

[0060] Where, A 、 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; 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;

[0061] 2) Sub-problem SP:

[0062] ;

[0063] In the formula, is 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 optimized variables in the second stage, Indicates the determination of optimization variables 、 back feasible domain.

[0064] The max-min two-layer model in the SP subproblem uses 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 problem to obtain the following single-layer max model:

[0065] ;

[0066] Where, 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; Represents the wind and solar power forecast set, Indicates 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;

[0067] The main problem MP makes a preliminary decision without considering uncertainty. The subproblem SP looks for adverse 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.

[0068] Compared with the prior art, the beneficial effects of the present invention are: based on the dynamic frequency response characteristics of the transmission and distribution network, the present invention embeds frequency safety constraints into the unit combination, and considers the frequency support capabilities of thermal power units, centralized new energy units and high-proportion distributed energy to the system in the frequency security constraint embedding unit combination, and considers the uncertainty of wind and solar output. By transforming and solving the two-stage robust optimization model of the transmission and distribution network, the optimal scheduling plan for the system under the worst wind and solar output scenarios is obtained, and the coordinated operation of the transmission and distribution network is realized, ensuring that the system can still take into account system safety and economy when facing uncertainty. By changing the number of uncertain moments of wind power and photovoltaic power to flexibly adjust the conservatism of the system, the stability and reliability of the system are enhanced, and the ability to cope with wind and solar output uncertainty and frequency fluctuations is improved, thereby achieving the optimal operation of the transmission and distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of a two-stage robust optimization operation method for a transmission and distribution network considering frequency security constraints in an embodiment of the present invention;

[0070] Figure 2 is a basic structural diagram of a transmission and distribution network in an embodiment of the present invention;

[0071] Figure 3 Schematic diagram of a transmission and distribution network coupling system in an embodiment of the present invention;

[0072] Figure 4 A system load prediction diagram in an embodiment of the present invention;

[0073] Figure 5 This is a comparison chart of the lowest frequency points of scenario 1, scenario 2, and scenario 3 in an embodiment of the present invention;

[0074] Figure 6 For scenes 1, 2, and 3 in the embodiment of the present invention RoCoF Comparison chart;

[0075] Figure 7 Schematic diagram of the start and stop status of the units in Scenario 1, Scenario 2 and Scenario 3 in the embodiment of the present invention. DETAILED DESCRIPTION

[0076] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0077] Example 1:

[0078] This embodiment proposes a two-stage robust optimization operation method for a transmission and distribution network that considers frequency security constraints. Based on the dynamic frequency response characteristics of the transmission and distribution network, this method takes into account the frequency support capabilities of thermal power units (including the start and stop states of the units), centralized new energy units, and a high proportion of distributed energy resources (DER). This method achieves coordinated operation of the transmission and distribution network, ensuring system frequency security under the worst-case wind and solar output scenarios while improving operational economics. The method mainly includes the following steps:

[0079] In step S1, the basic framework of the transmission and distribution network is established, and the dynamic frequency response process of the system is analyzed (including the impact of thermal power units with unit start-up and shutdown, centralized renewable energy units, and DER participation in frequency support on the frequency change rate, frequency minimum point, and quasi-steady-state frequency). Based on the frequency change rate, frequency minimum point, and quasi-steady-state frequency, dynamic frequency security constraints of the transmission and distribution network are established.

[0080] 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. 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, a two-stage robust optimization model of the transmission and distribution network considering frequency security constraints is constructed.

[0081] In step S3, the column and constraint generation (C&CG) algorithm and strong duality theory are used 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 the model is iterated and solved until the upper and lower bounds of the objective function converge, resulting in the optimal scheduling solution.

[0082] In summary, the embodiment of the present invention improves the ability to cope with wind and solar output uncertainty and frequency fluctuations through the above-mentioned steps S1 to S3, enhances the stability and reliability of the system, and achieves optimal operation of the transmission and distribution network.

[0083] Example 2:

[0084] Reference Figure 1 The solution in the first embodiment is further introduced below with reference to specific calculation formulas and examples.

[0085] S11, the basic structure of the transmission and distribution network is as follows Figure 2 As shown in the figure, the dispatchable frequency regulation resources in the transmission network include thermal power units and wind turbines that take into account the start and stop of units. The dispatchable frequency regulation resources in the active distribution network (ADN) include conventional distributed generators and photovoltaic units. Power between the transmission and distribution networks can be transmitted bidirectionally to balance the overall load of the power grid and meet the system frequency safety requirements, thereby achieving optimal scheduling of unit output and frequency regulation reserves.

[0086] The process of analyzing the dynamic frequency response of the system is as follows:

[0087] 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 to 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 RoCoF (Rate of Change of Frequency, RoCoF) reaches its maximum value; tAt 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 within 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. f nadir , a frequency modulation ends at the quasi-steady-state frequency f qss , t 2. Continue to perform secondary frequency modulation at the same time to achieve zero-error frequency regulation.

[0088] S12, constructs constraints related to the three important indicators that characterize system frequency security, namely, frequency change rate, frequency minimum point, and quasi-steady-state frequency. The dynamic frequency security constraints of the transmission and distribution network are established as follows:

[0089] 1) Frequency change rate constraint:

[0090] During the short inertial response time interval, no unit in the system takes action. RoCoF The size of is proportional to the power shortage and inversely proportional to the system inertia. 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:

[0091] (1)

[0092] Where, 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 Thermal power units , wind turbines w , conventional distributed generator sets j , photovoltaic units p The inertia time constant; P i 、 P w 、 P j 、 P p Thermal power units , wind turbines w , conventional distributed generator sets j , photovoltaic unitsp The power generation capacity, 、 、 and Represent thermal power units , wind turbines w , conventional distributed generator sets j , photovoltaic units p installed capacity; u i,t For thermal power units exist t Start and stop status at all times (1 for running, 0 for stopping), is the system power deficit, Indicates the maximum allowable value of the frequency change rate.

[0093] 2) Frequency minimum point constraint:

[0094] The inertial response and primary frequency modulation work together to reduce the system frequency to the lowest point. f nadir Each unit needs to reserve frequency modulation to participate in frequency modulation to prevent t Time frequency deviation Exceeding a given safety threshold , as shown below:

[0095] (2)

[0096] Where, ,t express t 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; is the system load; T d is the frequency modulation response time, Indicates a given frequency deviation safety threshold.

[0097] 3) Quasi-steady-state frequency constraint:

[0098] When the primary frequency regulation reserve capacity of all generator sets in the system is fully released, the frequency will remain at a constant level, that is, the quasi-steady-state frequency At this moment, t Quasi-steady-state frequency deviation It must also be controlled within the maximum range allowed by the system The quasi-steady-state frequency constraint of the system is as follows:

[0099] (3)

[0100] Where, express t The quasi-steady-state frequency deviation at time , Indicates the maximum quasi-steady-state frequency deviation allowed by the system, D t is the load damping coefficient.

[0101] S21, this method considers the uncertainty of wind and solar output, and establishes a two-stage robust optimization model with frequency security constraints based on the given wind and solar output fluctuation range to ensure the economy, safety and robustness of the system. Considering the uncertainty of wind and solar output, the uncertainty sets of wind and solar output are constructed in the form of intervals, respectively, and expressed as follows:

[0102] (4)

[0103] (5)

[0104] Where, Un W 、Un P are the uncertainty sets of wind and solar output respectively; 、 are the power after uncertainty processing of wind and solar output respectively; 、 They are wind and solar predicted output respectively; 、 are the maximum fluctuation ranges allowed for wind and solar output, and as well as and They are t Binary variables representing 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;

[0105] S22, by minimizing the start-up and shutdown costs of thermal power units, the power generation costs of thermal power units and conventional distributed generation units, and the frequency regulation standby 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 as follows:

[0106] (6)

[0107] Where, 、 、 They represent 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; 、 Thermal power units Startup and shutdown costs; C i 、 C j Thermal power units , conventional distributed generator sets j the cost of electricity generation; 、 、 、 Thermal power units , wind turbines w , conventional distributed generator sets j , photovoltaic generator sets p Frequency regulation reserve cost; su i,t 、 sv i,t They are t Thermal power units On and off status; P i,t 、 P j,t Thermal power units , conventional distributed generator sets j The meritorious contribution; R i,t 、 R w,t 、 R j,t 、 R p,t Thermal power units , wind turbines w , conventional distributed generator sets j , photovoltaic units p exist t Frequency regulation reserve capacity at all times, 、 、 and Represents thermal power , wind turbines w , conventional distributed generator sets j , photovoltaic units p installed capacity.

[0108] S23, the following constraints are used to constrain the two-stage robust optimization model of the transmission and distribution network:

[0109] (7)

[0110] (8)

[0111] (9)

[0112] (10)

[0113] (11)

[0114] (12)

[0115] (13)

[0116] (14)

[0117] (15)

[0118] (16)

[0119] (17)

[0120] (18)

[0121] (19)

[0122] (20)

[0123] (twenty one)

[0124] (twenty two)

[0125] (twenty three)

[0126] (twenty four)

[0127] In formula (7), For the interconnection line between transmission and distribution network t Transmission capacity at the time; The end node is The set of starting nodes; 、 t Line 、 exist t Transmission power at the moment; Ptranl,t for t Forecast load of transmission and distribution network at all times; P w,t For wind turbines w The meritorious contribution.

[0128] In formula (8), For the line Transmit power upper limit; For the line Susceptance; 、 Node and node b in t Phase angle of moment; Represents a balance node r exist t The phase angle of time.

[0129] In formula (9), T on,i 、 T off,i Thermal power units Minimum start and stop time, u i,k For thermal power units exist k Always on and off state, u i,t For thermal power units exist t Always on and off state, u i,t-1 For thermal power units At the last moment t Start-stop status; su i,t 、 sv i,t They are t Thermal power units On and off status;

[0130] In formula (11), P i,t-1 For the previous moment t thermal power units The meritorious contribution, R i,t-1 For thermal power units At the last moment t Frequency regulation reserve capacity, 、 Thermal power units Up and down climbing rate.

[0131] In formula (12), 、 Thermal power units Upper and lower limits of output;

[0132] In formula (13), 、 Wind turbines w Upper and lower limits of output;

[0133] In formula (14), For thermal power units upper limit of spare capacity;

[0134] In formula (15), For wind turbines w exist t The upper limit of spare capacity at any moment;

[0135] In formula (16), P j,n,t 、 P p,n,t They are t Conventional distributed generator sets at all times j、 Photovoltaic units p injection n Node active power; Q j,n,t 、 Q p,n,t They are t Conventional distributed generator sets at all times j、 Photovoltaic units p injection n Node reactive power; 、 Respectively t Transmission network injection node n The tie lines between the transmission and distribution grids transmit active and reactive power; 、 The end node and the starting node are n The set of start and end nodes; The end node is d The starting node set of 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; Pdistl,n,t 、 Q distl,n,t They are t time n Node predicted active load and reactive load; I mn,t for t Time flows through the line mn Current; r mn 、 x mn Line mn resistance and reactance;

[0136] In formula (17), U m,t 、 U n,t They are t Time Node m With node n Voltage;

[0137] In formula (18), 、 Separate nodes n Voltage upper and lower limits;

[0138] In formula (20), 、 For conventional distributed generator sets j Upper and lower limits of output;

[0139] In formula (21), 、 Photovoltaic units p Upper and lower limits of output;

[0140] In formula (22), For conventional distributed generators j upper limit of spare capacity;

[0141] In formula (23), For photovoltaic units p upper limit of spare capacity;

[0142] In formula (24), 、 They are the upper and lower limits of the transmission capacity of the tie lines between transmission and distribution networks, respectively.

[0143] S31, this method uses the column and constraint generation algorithm and 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 (MISOCP) and iterates and solves it. The two-stage robust optimization model of the transmission and distribution network is decomposed into the master problem MP (MasterProblem, MP) and subproblem SP (Subproblem, SP). The objective function and constraints after transformation and iteration are expressed in the following matrix form:

[0144] 1) Main question MP:

[0145]

[0146] Where, A 、 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; 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 set of variables for the first stage, Represents the matrix transpose symbol;

[0147] 2) Sub-problem SP:

[0148]

[0149] Where, 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 optimized variables in the second stage, Indicates the determination of optimization variables 、 back feasible domain.

[0150] S32, since the max-min double-layer model in the subproblem SP cannot be solved directly by the solver, the strong duality theory and the big M method can be used to transform the inner min problem into its dual max problem, and combine it with the outer max problem to obtain the following single-layer max model:

[0151] ;

[0152] Where, 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; Represents the wind and solar power forecast set, Indicates the maximum fluctuation deviation allowed for wind and solar output, π 1，m 、 π 2,m They represent the dual variables corresponding to each constraint in the m branch of the distribution network;

[0153] The main problem MP makes a preliminary decision without considering uncertainty. The subproblem SP looks for adverse 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.

[0154] Example 3:

[0155] In the following, with reference to a specific example, the feasibility of the two-stage robust optimization operation method for a transmission and distribution network considering frequency security constraints proposed in the above-mentioned embodiments 1 and 2 of the present invention is verified by coupling an IEEE 24-node transmission system with two IEEE 33-node distribution network systems to form a transmission and distribution network. The transmission and distribution network coupling system is as follows: Figure 3 As shown, see the following description:

[0156] Analyze the operation of thermal power units and conventional distributed generators in each ADN, where units 1-10 are thermal power units and units 11-14 are distributed generators. Figure 4 shown.

[0157] In this embodiment, three sets of comparison scenarios are set up to conduct comparative analysis on the example system:

[0158] Scenario 1: Ignoring frequency safety constraints, adding unit auxiliary frequency regulation constraints;

[0159] Scenario 2: Based on Scenario 1, frequency security constraints are taken into account, and only thermal power units and wind turbines are used for frequency support;

[0160] Scenario 3: Based on Scenario 2, consider DER participation in system frequency regulation.

[0161] The cost comparison of scenario 1, scenario 2 and scenario 3 is shown in Table 1 below. The frequency drops to the lowest point in scenario 1, scenario 2 and scenario 3. f nadir Frequency Change Rate RoCoF Comparison and comparison of frequency regulation reserve capacity of each unit Figure 5 and Figure 6 As shown. Figure 5 and Figure 6 It can be seen that the frequency of scene 1 is lowest at 1-2 and 19-22. f nadir Both exceeded the safety range of 49.2Hz, and the frequency change rate RoCoF At 1-5, 7, and 9-24, the time is greater than the maximum allowable RoCoF The value is 0.125Hz / s. This is because the frequency safety constraint is not considered in scenario 1. Only the primary frequency regulation constraint to maintain the basic stability of the system frequency is added on this basis. At this time, the system's primary frequency regulation reserve capacity cannot be guaranteed to be sufficient. Only the basic reserve capacity of each starting unit is used to adjust the frequency to a certain extent, which cannot ensure the stability of the system frequency under large interference conditions. When the frequency safety constraint is considered in scenarios 2 and 3, the lowest frequency at each moment f nadir Frequency Change Rate RoCoF All remain within the set safety thresholds, demonstrating the significant impact of considering frequency safety constraints on maintaining system safety. Furthermore, in Scenario 3, DERs replace some thermal and wind turbines in system frequency regulation, demonstrating that this approach can enable DER-assisted systems to provide frequency support, further enabling coordinated frequency regulation across the transmission and distribution grid.

[0162] Table 1 Cost comparisons for scenario 1, scenario 2, and scenario 3

[0163]

[0164] In order to analyze the impact of frequency security constraints and DER frequency regulation capabilities on the start-up and shutdown decisions and system costs of thermal power units in three scenarios, the start-up and shutdown states of the units in each scenario are as follows: Figure 7 As shown, due to cost factors, units 2, 4, and 6 remain operational in all three scenarios. Secondly, Scenario 1 has the lowest number of operational units of the three scenarios. This is because frequency safety constraints are not considered, requiring only a certain number of operational thermal and wind turbines to respond to load fluctuations. In this scenario, the capacity of units 1-8 can meet system load requirements, while units 9 and 10 remain operational. When frequency safety constraints are considered, the number of thermal unit startups increases significantly. As electricity load increases throughout the day, the number of thermal unit startups is concentrated in the afternoon and evening hours, particularly around 4 p.m. and 5 p.m., when all ten units are operational to mitigate the impact of large disturbances on system frequency. Compared to Scenario 2, some thermal units are shut down in Scenario 3. DERs replace some thermal units in the frequency regulation process, reducing the number of operational thermal units.

[0165] As shown in Table 1, since scenario 1 has the least number of units in operation, its startup and shutdown costs are the lowest. Moreover, since some units in scenario 3 are shut down, the startup and shutdown costs in scenario 3 are greater than those in scenario 2. Secondly, the capacity of low-cost units in scenario 1 can meet the system's base load and frequency regulation requirements. In contrast, scenario 2 considers frequency security constraints and allows low-cost units to participate in frequency support, while high-cost units begin to be put into power generation. 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 standby cost is reduced by 3×10 3 Since low-cost DER is used to replace some thermal power units in Scenario 3 to participate in the system frequency regulation process, the frequency regulation reserve cost in Scenario 3 is reduced by 1.4×10 compared with Scenario 2. 4 At this time, in order to balance the load demand of the distribution network and the low-cost thermal power units once again obtain sufficient capacity for power generation, the power generation cost of the transmission network in scenario 3 is reduced by 1×10 compared with scenario 2. 4 Yuan, while the power generation cost of the distribution network increased by 9×10 3 The above analysis proves that the two-stage robust optimization operation method of the transmission and distribution network considering frequency security constraints proposed in this invention can improve the economic efficiency of the transmission and distribution network system.

[0166] Table 2 Comparison of costs between deterministic optimization and two-stage robust optimization

[0167]

[0168] Table 2 above compares the cost of deterministic optimization and two-stage robust optimization. As can be seen from Table 2, the deterministic optimization method has the lowest total cost. Γ w = Γ p = 0 is equivalent to the two-stage robust optimization method. Γ w 、 Γ p As the value gradually increases, the system must consider more uncertainties. Wind power and photovoltaic power generation reach the lower bound of the uncertainty set more frequently, requiring more conservative optimization methods to ensure that the final solution is effective under all possible uncertainties. The resulting additional planning and resource investment increases total costs. The above analysis demonstrates that the proposed two-stage robust optimization method for transmission and distribution networks with frequency security constraints flexibly adjusts the system's conservatism by varying the uncertainty, resulting in a more robust power system.

[0169] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A two-stage robust optimization operation method for transmission and distribution networks considering frequency security constraints, characterized by: The following steps are involved: In step S1, the dynamic frequency response process of the system is analyzed, and 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: During the short inertia response time interval, 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: ； Where, 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 are the inertia time constants of thermal power generation units, wind power generation units, conventional distributed power generation units, 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 Always on and off state, 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 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: ； Where, express t Frequency deviation at the moment, R t The schedulable frequency modulation resources 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 generator sets in the system is fully released, the system quasi-steady-state frequency constraint is as follows: ； Where, 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 Momentary load damping coefficient; 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 respectively, which are expressed as follows: ； ； Where, Un W 、Un P are the uncertainty sets of wind and solar output respectively; 、 They are t Power after processing when wind and solar output are uncertain at any moment; 、 They are t Wind and solar power forecast 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 representing 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 generation costs of thermal power units and conventional distributed generation units, and the frequency regulation standby 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 as follows: ； Where, 、 、 They represent 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; 、 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; 、 、 、 The frequency regulation and standby costs are thermal power units, wind power units, conventional distributed power generation units, and photovoltaic power generation units respectively; 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 generators at each 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 Respectively represent the installed capacity of thermal power units, wind power units, conventional distributed power generation units, and photovoltaic units; 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 for a transmission and distribution network considering frequency security constraints according to claim 1 is characterized in that: In step S1, the process of analyzing the system dynamic frequency response 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 begins to respond by inertia, using the kinetic energy provided by the inertia within the system to adjust the frequency. The generator set is not working, and the frequency change rate reaches its maximum value. t At time 1, the units in the system begin to change their mechanical power. The inertial 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 the same time to achieve zero-error frequency regulation.

3. The two-stage robust optimization operation method for a transmission and distribution network considering frequency security constraints according to claim 1 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 transmission and distribution network t Transmission capacity at the time; The end node is The set of starting nodes; 、 Line 、 exist t Transmission power at the moment; P tranl,t for t Forecast load of transmission and distribution network at all times; P w,t for t Active power output of wind turbines at all times; For the line Transmit power upper limit; For the line Susceptance; 、 Node and node b in t Phase angle of moment; Represents a balance node r exist t Phase angle of 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 Always on and off state, u i,t For thermal power units t Always on and off state, 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 or 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; 、 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 moment; P j,n,t 、 P p,n,t They are t Conventional distributed generator sets at all times 、 Photovoltaic unit injection n Node active power; Q j,n,t 、 Q p,n,t They are t Conventional distributed generator sets at all times 、 Photovoltaic unit injection n Node reactive power; 、 Respectively t Transmission network injection node n The tie lines between the transmission and distribution grids transmit active and reactive power; 、 The end node and the starting node are n The set of start and end nodes; The end node is d The starting node set of 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 Node predicted active load and reactive load; I mn,t for t Time flows through the line mn 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; 、 The upper and lower limits of 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 any moment; 、 They are the upper and lower limits of the transmission capacity of the tie lines between transmission and distribution networks, respectively.

4. The two-stage robust optimization operation method for a 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 constraints after transformation and iteration are expressed in the following matrix form: 1) Main question MP: ； Where, 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: ； Where, 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 optimized variables in the second stage, Indicates the determination of optimization variables 、 back feasible domain.

5. The two-stage robust optimization operation method for a transmission and distribution network considering frequency security constraints according to claim 4 is characterized in that: The max-min two-layer model in the subproblem SP uses strong duality theory and the big M method to transform the inner min problem into its dual max problem. Combined with the outer max problem, the following single-layer max model is obtained: ; Where, 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; Represents the wind and solar power forecast set, Indicates 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 adverse 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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