An optimization method for inter-regional DC transmission plan based on master-slave game

Abstract

The present invention discloses a method for optimizing inter-regional direct current (DC) transmission plans based on a master-slave game, which belongs to the technical field of power system operation and dispatching. The method comprises step 1: obtaining expressions for the adequacy margin and flexibility margin of the DC transmitting and receiving systems based on a supply and demand model of adequacy and flexibility resources of the DC transmitting and receiving systems; step 2: constructing a leader model based on the master-slave game theory, and formulating a DC transmission plan according to the leader model; step 3: constructing a follower model based on the master-slave game theory, and performing unit combination and economic dispatch according to the follower model; and step 4: obtaining a Stackelberg equilibrium solution of the master-slave game. The model of the present invention can reflect the differences in the supply and demand of adequacy and flexibility resources of the DC transmitting and receiving systems, thereby providing an effective optimization method for balancing adequacy and flexibility between the DC regulating transmitting and receiving systems.

Description

Technical Field

[0001] The present invention relates to the technical field of power system operation and dispatching, and in particular to a method for optimizing an inter-regional direct current transmission plan based on a master-slave game. Background Art

[0002] Since my country's large-scale renewable energy bases and load centers are inversely distributed, promoting cross-regional renewable energy consumption through HVDC transmission will become a key feature of the development of the new power system. When formulating day-ahead transmission plans for cross-regional HVDC transmission channels, it is first necessary to optimize the HVDC transmission power based on the daily decomposition of medium- and long-term transaction volumes to arrive at a pre-planned day-ahead plan. This is then followed by day-ahead cross-regional spot market transactions. Power system abundance refers to the ability of available generating power from online units to meet real-time, fluctuating load demands; flexibility refers to the ability of a power system to adapt to random changes in power generation, grid conditions, and load by optimizing the allocation of available resources. The balance between supply and demand for abundance and flexibility resources can vary significantly across different regions of the power system, reducing the system's ability to accommodate renewable energy and even leading to load shedding. Therefore, HVDC transmission is necessary to optimize the scheduling of abundance and flexibility resources within the power system to promote balanced abundance and flexibility across different regions.

[0003] However, current research on the optimization of inter-regional DC transmission plans focuses on exploring the flexibility of DC interconnection lines, economic scheduling of DC interconnected systems, and day-ahead and intra-day coordination optimization of DC planned transmission power. However, there are problems such as failing to fully reflect the game characteristics between DC interconnection lines and the sending and receiving AC systems, failing to fully consider the differences in the supply and demand of flexibility and abundance resources between the sending and receiving systems, and failing to fully utilize the flexibility and abundance resources in the power system optimized by DC interconnection lines in the optimization process.

[0004] Therefore, there is an urgent need to establish a cross-regional DC transmission plan optimization model that can improve the balance between the abundance and flexibility of the DC transmitting and receiving systems, fully reflect the game characteristics between the AC systems at the transmitting and receiving ends, and make full use of DC interconnection lines to optimize the allocation of abundance and flexibility resources in the power system. Summary of the Invention

[0005] The present invention aims to propose a method for optimizing inter-regional direct current transmission plans based on a master-slave game, which is characterized by comprising the following steps:

[0006] Step 1: Based on the resource supply and demand model of the DC transmission and receiving end system, obtain the expressions of the DC transmission and receiving end system's ...

[0007] Step 2: Construct a leader model based on the master-slave game theory and formulate a DC transmission plan based on this leader model;

[0008] Step 3: Construct a follower model based on the master-slave game theory, and perform unit commitment and economic dispatch according to this follower model;

[0009] Step 4: Obtain the Stackelberg equilibrium solution of the master-slave game.

[0010] The adequacy margin of the DC transmitting and receiving end systems in step 1 is specifically:

[0011]

[0012] in, are the adequacy margins of the transmitting and receiving ends in the wind power scenario s during the dispatch period t; are the available power generation capacity at the sending and receiving ends respectively; are the load requirements of the sending and receiving ends respectively; For DC transmission power; are the sets of controllable loads of the sending and receiving systems respectively; I represents the set of areas connected to area a through DC tie lines.

[0013] The flexibility margin of the DC transmitting and receiving end systems in step 1 is specifically:

[0014]

[0015]

[0016] in, They represent the upward and downward flexibility margins of the DC sending-end system respectively; They represent the upward and downward flexibility margins of the DC receiving system respectively; They represent the upward and downward flexibility requirements of the sending-end system respectively; They represent the upward and downward flexibility requirements of the receiving system respectively; They are the flexible power adjustment that the DC in the area can provide, up and down; They are respectively the flexible adjustment power supply can provide up and down adjustment of the power; They are the flexible power adjustment that energy storage can provide, up and down; are the flexibly adjustable power that can be provided by the controllable load; I represents the set of areas connected to area a through DC tie lines; Respectively represent the collection of energy storage of the sending and receiving end systems; Respectively represent the set of controllable loads of the sending and receiving end systems; They represent the collection of conventional units at the sending and receiving ends respectively.

[0017] The leader model in step 2 includes:

[0018] Benefit function:

[0019]

[0020] Among them, ρ s is the probability of scenario s; I is the set of regions connected to region a through DC; K1, K2, and K3 are the weight coefficients of the three parts of the balance of abundance between the sending and receiving ends, the balance of flexibility, and the economy of the day-ahead scheduling strategy; C(P g (t)) is the power generation cost of conventional units; are the penalty costs for wind curtailment and load curtailment respectively; ΔP wt ,ΔP lt are wind curtailment and load curtailment respectively; are the collections of thermal power, wind power and load respectively; T, S are the collections of scheduling period and scenario respectively;

[0021] Constraints:

[0022]

[0023]

[0024] Among them, P d (t) is the DC transmission power; P dmax (t),P dmin (t) are the upper and lower limits of DC power respectively; δ dmax ,δ dmin are the upper and lower limits of the DC power regulation within the unit dispatching period respectively; They are the DC power increase and decrease flags, respectively. If adjusted, the value is 1, otherwise 0; is an auxiliary large number; N W N is the maximum number of DC regulation times; T is the minimum holding period after DC regulation; E d is the daily transaction power of DC;

[0025]

[0026] Among them, U d (t),I d (t) are DC voltage and current respectively; P d (t),Q d (t) are the active and reactive power of the converter station respectively; K is the AC voltage amplitude of the commutation bus obtained by the follower model; d (t) is the transformation ratio of the converter transformer; is the power factor angle of the converter station; X d ,k γare commutation reactance and safety factor respectively; are the identifiers and sets of converter stations connected to converter station d; G dm is the DC network conductivity matrix; λ is the rectifier and inverter identifier. If λ = 1, it represents the rectifier side, and θ d (t) represents the trigger angle, if λ = -1, it represents the inverter side, and θ d (t) represents the arc extinction angle;

[0027]

[0028] Among them, N C ,N K are the maximum operating times of AC filter and converter transformer respectively; K d (t) is the transformer ratio; K N is the rated transformation ratio of the converter transformer; They are the number of AC filter groups and the capacity of a single AC filter group respectively; They are the converter transformer tap changer gear position and adjustment step length respectively;

[0029]

[0030] Among them, P w (t) is the wind power used by the power grid; is the day-ahead forecast value of wind power;

[0031]

[0032] in, are the upper and lower limits of the equivalent conventional unit output during period t, respectively, and their values ​​are calculated by the follower model; P g (t) is the output of the equivalent conventional unit during period t; RU g ,RD g Respectively represent the upper limits of the ramp-up and ramp-down rates of the equivalent conventional units;

[0033]

[0034] in, are the charging and discharging power of energy storage, respectively; are the upper and lower limits of charging power; is the upper and lower limits of discharge power; E k (t) is the energy stored for period t; is the maximum capacity of energy storage; η ch ,η dis Respectively represent the charge and discharge efficiency; SOC k (t) is the state of charge of the energy storage period t; SOC k,min ,SOCk,max Respectively represent the minimum and maximum value of the state of charge; SOC k (0),SOC k (T) represents the state of charge at the initial and final periods, respectively;

[0035]

[0036] Among them, P a,l (t),P b,l (t) are the load power of the sending and receiving ends respectively; P a,g (t),P b,g (t) are the outputs of equivalent conventional units at the sending and receiving ends respectively; P a,w (t) is wind power; A collection of energy storage.

[0037] The follower model in step 3 includes:

[0038] Demand function:

[0039]

[0040] Among them, v g (t) is the binary state variable of the unit startup, 1 represents startup; w g (t) is the unit shutdown binary state variable, 1 represents shutdown; C(v g (t),w g (t)) is the unit startup and shutdown cost; P g (t) is the output of conventional units in the day-ahead period during the t period; C(P g (t)) is the power generation cost of conventional units; are the cost coefficients for adjusting the reserve capacity up and down for thermal power units respectively; They represent the up and down reserve capacity of conventional units respectively; are the reserve capacity cost of thermal power units for upward and downward adjustment, respectively; ρ s is the probability of scene s; P g,s (t) is the output of the conventional unit in the real-time stage during the t period under scenario s; C(P g,s (t))-C(P g (t)) Cost of re-adjusting unit output; are the penalty coefficients for wind curtailment and load curtailment respectively; ΔP w,s (t) is the amount of wind curtailment under scenario s, ΔP l,s (t) is the load shedding amount under scenario s;

[0041] Day-ahead constraints:

[0042]

[0043] Among them, u g (t), v g (t), w g (t) are the running state variables, startup and shutdown state variables of the thermal power unit, respectively. When they are equal to 1, it means that the unit is running, starting up and shutting down during the t period respectively; P g (t) is the output of the thermal power unit in the day-ahead phase; RU g ,RD g are the upper limits of the ramp-up and ramp-down active power regulation rates of thermal power units respectively; P gmax ,P gmin They are the upper and lower limits of the unit’s active output respectively; Adjust the spare capacity of the unit upward and downward respectively; They are used to increase and decrease the upper limit of the spare capacity of the unit respectively; MU g is the minimum continuous start-up time of thermal power unit g; MD g is the minimum continuous shutdown time of thermal power unit g;

[0044]

[0045]

[0046]

[0047] Where i, j are AC nodes; V j (t),θ j (t) is the voltage amplitude and phase angle of AC node j; G ij is the real part of the node admittance matrix, B i ' j is the imaginary part of the node admittance matrix without considering the ground branch; P g (t),P w (t),P d (t),P l (t) is thermal power, wind power, DC power and load power; are the thermal power plants, wind farms, converter stations and load collections connected to the AC node i; g ij ,b ij are the conductance and susceptance of branch ij respectively; P ijmax is the upper limit of the active transmission power of the branch;

[0048]

[0049] in, Respectively represent the output of conventional units in the sending section and receiving end area; is the wind power at the sending end; is the load power of the sending and receiving ends; represents the planned DC transmission power obtained by optimizing the leader model;

[0050] Real-time phase constraints:

[0051]

[0052] Among them, P g,s (t) is the output of the thermal power unit under scenario s; P g (t) is the output of the thermal power unit in the day-ahead phase; RU g ,RD g They are the upper limits of the ramp-up and ramp-down active power regulation rates of thermal power units respectively; They are the upward and downward adjustment of reserve capacity of thermal power units;

[0053]

[0054] Among them, P w,s (t) is the wind power called by the grid under scenario s; is the available wind power value under scenario s;

[0055]

[0056] in, are the charging and discharging power of energy storage under scenario s respectively; The upper and lower limits of the charging power; is the upper and lower limits of discharge power; E k,s (t) is the energy stored for period t under scenario s; is the maximum capacity of energy storage; η ch ,η dis Respectively represent the charge and discharge efficiency; SOC k,s (t) is the state of charge of the energy storage during period t under scenario s; SOC k,min ,SOC k,max Respectively represent the minimum and maximum value of the state of charge; SOC k,s (0),SOC k,s (T) are the state of charge of the energy storage at the initial and final periods under scenario s;

[0057]

[0058] in, are the thermal power of the sending and receiving ends under scenario s respectively; is the wind power at the sending end under scenario s; are the total load power of the sending and receiving ends under scenario s respectively; A collection of energy storage.

[0059] The step 4 specifically includes the following sub-steps:

[0060] Step 41: Solve the leader model and send the optimized DC transmission plan to the followers;

[0061] Step 42: Solve the follower model through distributed optimization to obtain the upper and lower limits of the active power output of the planned start-up units; obtain the commutation bus AC voltage data through power flow calculation, and upload the upper and lower limits of the active power output and the commutation bus AC voltage data to the leader;

[0062] Step 43: The leader continuously updates its own strategy based on the follower's strategy, and the follower also continuously updates its own strategy based on the leader's strategy, solving the master-slave problem through continuous iteration;

[0063] Step 44: When the DC transmission plan formulated by the leader no longer changes, the master-slave game reaches a Stackelberg equilibrium, and the corresponding optimal DC transmission plan is taken as the Stackelberg equilibrium solution.

[0064] The beneficial effects of the present invention are:

[0065] 1. The model of the present invention can reflect the differences in the supply and demand of resource adequacy and flexibility between the DC transmitting and receiving systems, thereby providing an effective optimization method for balancing the adequacy and flexibility between the DC regulation transmitting and receiving systems;

[0066] 2. The model of the present invention ensures the reliability of the DC transmission channel while optimizing the allocation of resources in the DC transmitting and receiving end systems, both in terms of system adequacy and flexibility, across time and space.

[0067] 3. The model of the present invention is in line with my country's cross-regional DC transmission plan formulation system and can enhance the overall power system's ability to accept new energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a flow chart of the cross-regional DC transmission plan optimization method based on master-slave game of the present invention;

[0069] Figure 2 Schematic diagram of the overall framework of the inter-regional DC transmission plan optimization method based on master-slave game of the present invention;

[0070] Figure 3 This is a schematic diagram of the DC transmitting and receiving end system provided by the present invention;

[0071] Figure 4 This is a structural diagram of the DC transmitting and receiving end power grid provided by the present invention;

[0072] Figure 5 This is the wind power day-ahead prediction curve provided by the present invention;

[0073] Figure 6The present invention provides a day-ahead forecast curve for the load of the transmitting and receiving end systems;

[0074] Figure 7 This is the wind power real-time scenario curve provided by the present invention;

[0075] Figure 8 The DC day-ahead transmission plan curves obtained by optimization under the three calculation examples provided by the present invention are:

[0076] Figure 9 This is a diagram of the master-slave game process for optimizing the DC transmission plan provided by the present invention;

[0077] Figure 10 It is the difference curve of the redundancy margin and flexibility margin of the sending end system and the receiving end system under the three calculation example modes provided by the present invention. DETAILED DESCRIPTION

[0078] The present invention proposes a method for optimizing inter-regional direct current transmission plans based on a master-slave game, which will be further described below with reference to the accompanying drawings and specific embodiments.

[0079] Figure 1 、 Figure 2 The flowchart and overall framework diagram of the inter-regional DC transmission plan optimization method based on master-slave game of the present invention are respectively shown. The method includes the following steps:

[0080] S101 builds a resource supply and demand model for the DC transmission and receiving end system's adequacy and flexibility, specifically including:

[0081] (1) Generation of wind power scenarios:

[0082] The autoregressive moving average method was used to generate several wind power and load scenarios, which were then reduced using the K-means clustering method, ultimately retaining five groups of wind power scenarios.

[0083] (2) Available generating capacity of the DC transmitting and receiving systems:

[0084] Let area a represent the DC sending system and area b represent the DC receiving system. The available generating capacity of the sending system is equal to the sum of the available generating capacity of the conventional generating units at the sending end and the available generating capacity of wind power:

[0085]

[0086] in, is the available power generation capacity of the sending-end system in the wind power scenario s during the dispatch period t; is the available generating capacity of conventional units at the sending end; is the available generating capacity of wind power at the sending end under wind power scenario s. They represent the collection of conventional units and wind farms at the sending end respectively.

[0087] The available power generation capacity of the receiving system is equal to the sum of the available power generation capacity of the receiving conventional units, the available power generation capacity of wind power and the DC transmission power:

[0088]

[0089] in, is the available power generation capacity of the receiving system in the wind power scenario s during the dispatch period t; The available generating capacity of the conventional units at the receiving end; is the available generating capacity of wind power at the receiving end under wind power scenario s; is the DC transmission power. They represent the sets of conventional units and wind farms at the receiving end respectively; I represents the set of receiving end areas connected to the sending end through DC tie lines.

[0090] (3) Adequacy margin of DC transmission and receiving systems:

[0091] The adequacy of the power system is characterized by the ability of the available generating capacity of the online units to meet the real-time changing load demand. The adequacy margin of the sending and receiving systems is equal to the system's available generating capacity minus the system's load demand:

[0092]

[0093] in, are the adequacy margins of the sending and receiving systems, are the load demands of the sending and receiving systems respectively.

[0094] If and only if When , it means that the adequacy of the sending end system meets the requirements. When , it indicates that the adequacy of the receiving system meets the requirements.

[0095] (4) Flexibility supply and demand model of DC transmission and reception systems:

[0096] Flexibility refers to the ability of a power system to adapt to random changes in power generation, grid, and load at a certain cost by optimizing the deployment of various available resources in the active power balance on the time scale of interest. This includes both flexibility supply and flexibility demand. The flexibility resources of the sending system include DC, flexibly adjustable power sources, energy storage, and controllable loads. The flexibility resources of the receiving system also include DC, flexibly adjustable power sources, and controllable loads. The flexibility that the sending and receiving systems can provide can be divided into two directions: upward and downward.

[0097] For the sending-end system, DC is equivalent to the load. The flexible power that the sending-end DC can provide is:

[0098]

[0099] in, They represent the upward and downward regulation of the DC power at the sending end, which can flexibly adjust the power; min{} represents the minimum function; δ dmax Indicates the maximum power regulation of DC in a unit scheduling period; P d (t) is the DC transmission power during period t; P dmax (t),P dmin (t) are the maximum and minimum DC transmission powers, respectively.

[0100] For the receiving system, DC is equivalent to the power supply. The DC at the receiving end can provide flexible power adjustment:

[0101]

[0102] in, They respectively indicate that the upward and downward regulation of the receiving end DC can flexibly adjust the power.

[0103] The flexible power supply can provide flexible power adjustment up and down as follows:

[0104]

[0105] in, Respectively represent the flexible adjustment of power supply upward and downward; RU g Indicates the maximum power regulation amount of the flexible adjustable power supply within the unit scheduling period; P g (t) is the output of the flexibly adjustable power supply; P gmax ,P gmin They represent the maximum and minimum technical outputs of the flexibly adjustable power supply.

[0106] The flexibly adjustable power that the controllable load can provide is expressed as:

[0107]

[0108] in, They represent the upward and downward adjustment of controllable loads, which can flexibly adjust the power; P L (t) is the power of the controllable load in period t; P L,max (t),P L,min (t) represent the maximum and minimum power of the controllable load respectively.

[0109] The energy storage in the system can provide flexible power adjustment up and down:

[0110]

[0111] in, Respectively indicate the upward and downward adjustment of energy storage to flexibly adjust power are the charging and discharging powers of the energy storage during period t respectively; are the upper limits of the discharging and charging powers of energy storage j, respectively; is the energy stored in time period j; are the maximum and minimum values ​​of energy storage j respectively; η ch ,η dis are the charging and discharging efficiencies of energy storage j, respectively; Δt is the length of the scheduling period.

[0112] The fluctuation component of the net load of the DC transmitting and receiving systems obtained by HP filtering is used as the flexibility requirement of the system. The fluctuation component of the net load of the transmitting and receiving systems is:

[0113]

[0114] in, Represents the net load of the sending end and the receiving end respectively; P a,l (t),P b,l (t) are the power of the system load at the sending and receiving ends respectively; They represent the trend components of the net load at the sending end and the receiving end respectively; ζ is the decomposition coefficient; H a ,H b They represent the constant coefficient decomposition matrices of the sending end and the receiving end respectively; E is the identity matrix; Represent the fluctuating components of the net load of the sending and receiving systems respectively; They represent the sets of sending and receiving system loads respectively.

[0115] The upward flexibility demand at the sending and receiving ends is equal to the part of the net load fluctuation component that is greater than zero, and the downward flexibility demand is equal to the absolute value of the part of the net load fluctuation component that is less than zero.

[0116] (5) Flexibility margin of DC transmission and receiving systems:

[0117] The flexibility margin is defined as the flexibility supply minus the flexibility demand. The flexibility margin can be adjusted up or down at the sending end under scenario s. This is equivalent to the flexible power adjustment that the DC in the area can provide. Flexible power supply can provide up and down adjustment to flexibly adjust the power Energy storage can provide flexible power adjustment The controllable load can provide flexible power adjustment up and down The sum of the two minus the flexibility requirements for adjustment up and down The definition of flexibility margin at the receiving end in scenario s is the same as that at the sending end.

[0118]

[0119]

[0120] in, They represent the upward and downward flexibility margins of the DC sending-end system respectively; They represent the upward and downward flexibility margins of the DC receiving system respectively; They represent the upward and downward flexibility requirements of the sending-end system respectively; They represent the upward and downward flexibility requirements of the receiving system respectively; I represents the set of areas connected to area a through DC tie lines; Respectively represent the collection of energy storage of the sending and receiving end systems; They represent the sets of controllable loads of the sending and receiving systems respectively.

[0121] like This means that the sending end has ample flexibility in adjusting the amount of money up and down; if This means that the receiving end has ample flexibility to adjust up or down.

[0122] S102 builds a model of the leader in the master-slave game, including:

[0123] (1) Construction of benefit function:

[0124] Taking the National Dispatching Center as the leader, after simplifying the power grids at the transmitting and receiving ends, the profit function is to pursue the balance between the sufficient and flexible ends of the transmitting and receiving ends and minimize the economic cost. It includes the penalty cost of balancing the sufficient and flexible ends of the transmitting and receiving ends and the economic cost. Specifically, it is:

[0125]

[0126] Among them, ρ s is the probability of scenario s; I is the set of regions connected to region a through DC; K1, K2, and K3 are the weight coefficients of the three parts of the balance of abundance between the sending and receiving ends, the balance of flexibility, and the economy of the day-ahead scheduling strategy; C(P g (t)) is the power generation cost of conventional units; are the penalty costs for wind curtailment and load curtailment respectively; ΔP wt ,ΔP lt are wind curtailment and load curtailment respectively; are the collections of thermal power, wind power and load respectively; T, S are the collections of scheduling period and scenario respectively.

[0127] (2) Constraints of the leader model:

[0128] The DC regulation characteristic constraints include DC power upper and lower limit constraints, DC regulation amount constraints within a unit dispatch period, DC daily regulation times constraints, minimum number of holding periods after DC regulation constraints, and DC daily transaction power constraints. Specifically:

[0129]

[0130]

[0131] Among them, P d (t) is the DC transmission power; P dmax (t),P dmin (t) are the upper and lower limits of DC power respectively; δ dmax ,δ dmin are the upper and lower limits of the DC power regulation within the unit dispatching period respectively; They are the DC power increase and decrease flags, respectively. If adjusted, the value is 1, otherwise 0; is an auxiliary large number; N W N is the maximum number of DC regulation times; T is the minimum holding period after DC regulation; E d is the daily transaction amount of DC.

[0132] Converter station steady-state operation constraints:

[0133]

[0134] Among them, U d (t),I d (t) are DC voltage and current respectively; P d (t),Q d (t) are the active and reactive power of the converter station respectively; K is the AC voltage amplitude of the commutation bus obtained by the follower model; d (t) is the transformation ratio of the converter transformer; is the power factor angle of the converter station; X d ,k γ are commutation reactance and safety factor respectively; are the identifiers and sets of converter stations connected to converter station d; G dm is the DC network conductivity matrix; λ is the rectifier and inverter identifier. If λ = 1, it represents the rectifier side, and θ d (t) represents the trigger angle, if λ = -1, it represents the inverter side, and θ d (t) represents the arc extinction angle.

[0135] Due to the nonlinearity of the steady-state operation model of the converter station, it can be linearized through first-order Taylor expansion.

[0136] DC reactive equipment operation constraints are mainly used to limit the number of operations of AC filters and converter transformers. These constraints include the range of reactive power exchanged between AC and DC systems, discretization constraints on converter transformer ratios, and the maximum daily operation times of AC filters and converter transformers.

[0137]

[0138] Among them, N C ,N K are the maximum operating times of AC filter and converter transformer respectively; K d (t) is the transformer ratio; K N is the rated transformation ratio of the converter transformer; They are the number of AC filter groups and the capacity of a single AC filter group respectively; They are the tap changer position and adjustment step of the converter transformer respectively.

[0139] Wind power constraints:

[0140]

[0141] Among them, P w (t) is the wind power used by the power grid; is the day-ahead forecast value of wind power.

[0142] The relevant constraints of the equivalent conventional units include output upper and lower limit constraints and ramp rate constraints:

[0143]

[0144] are the upper and lower limits of the equivalent conventional unit output during period t, respectively, and their values ​​are calculated by the follower model; P g (t) is the output of the equivalent conventional unit during period t; RU g ,RD g They represent the upper limits of the ramp-up and ramp-down rates of the equivalent conventional units respectively.

[0145] Energy storage-related constraints include energy storage charging and discharging power constraints, energy continuity constraints, and state of charge constraints. Specifically:

[0146]

[0147] in, are the charging and discharging power of energy storage, respectively; are the upper and lower limits of charging power; is the upper and lower limits of discharge power; E k (t) is the energy stored for period t; is the maximum capacity of energy storage; η ch,η dis Respectively represent the charge and discharge efficiency; SOC k (t) is the state of charge of the energy storage period t; SOC k,min ,SOC k,max Respectively represent the minimum and maximum value of the state of charge; SOC k (0),SOC k (T) represents the state of charge at the initial and final time periods, respectively.

[0148] Power balance constraints of the sending and receiving systems:

[0149] Delivery system:

[0150]

[0151] Receiving system:

[0152]

[0153] Among them, P a,l (t),P b,l (t) are the load power of the sending and receiving ends respectively; P a,g (t),P b,g (t) are the outputs of equivalent conventional units at the sending and receiving ends respectively; P a,w (t) is wind power; A collection of energy storage.

[0154] The leader model obtains the DC day-ahead transmission plan through optimization

[0155] S103 builds a follower model in the master-slave game, specifically including:

[0156] (1) Construction of demand function:

[0157] The transmitting and receiving systems perform unit combination and economic dispatch within the region using a two-stage stochastic programming model. This model uses the DC transmission plan obtained by the leader optimization as the boundary and considers the uncertainty of wind power for stochastic optimization. The first stage of the two-stage stochastic programming model is the day-ahead stage, where the optimization objectives of the demand function include the unit combination cost, the conventional unit power generation cost, and the cost of adjusting reserve capacity up and down. The second stage is the real-time stage, where the optimization objectives of the demand function include the re-adjustment cost of conventional unit output, and the penalty costs for wind and load curtailment. Specifically, the following are the optimization objectives:

[0158]

[0159] Among them, v g (t) is the binary state variable of the unit startup, 1 represents startup; w g(t) is the unit shutdown binary state variable, 1 represents shutdown; C(v g (t),w g (t)) is the unit startup and shutdown cost; P g (t) is the output of conventional units in the day-ahead period during the t period; C(P g (t)) is the power generation cost of conventional units; are the cost coefficients for adjusting the reserve capacity up and down for thermal power units respectively; They represent the up and down reserve capacity of conventional units respectively; are the reserve capacity cost of thermal power units for upward and downward adjustment, respectively; ρ s is the probability of scene s; P g,s (t) is the output of the conventional unit in the real-time stage during the t period under scenario s; C(P g,s (t))-C(P g (t)) Cost of re-adjusting unit output; are the penalty coefficients for wind curtailment and load curtailment respectively; ΔP w,s (t) is the amount of wind curtailment under scenario s, ΔP l,s (t) is the load shedding amount under scenario s.

[0160] (2) Constraints of the follower model:

[0161] 1) Day-ahead constraints:

[0162] Safe operation constraints of thermal power units, including unit output constraints, ramp rate constraints, spare capacity constraints, and minimum continuous start-up and shutdown time constraints.

[0163]

[0164] Among them, u g (t), v g (t), w g (t) are the running state variables, startup and shutdown state variables of the thermal power unit, respectively. When they are equal to 1, it means that the unit is running, starting up and shutting down during the t period respectively; P g (t) is the output of the thermal power unit in the day-ahead phase; RU g ,RD g are the upper limits of the ramp-up and ramp-down active power regulation rates of thermal power units respectively; P gmax ,P gmin They are the upper and lower limits of the unit’s active output respectively; Adjust the spare capacity of the unit upward and downward respectively; They are used to increase and decrease the upper limit of the spare capacity of the unit respectively; MU g is the minimum continuous start-up time of thermal power unit g; MD g is the minimum continuous shutdown time of thermal power unit g.

[0165] Wind power constraints:

[0166]

[0167] Energy storage related constraints:

[0168]

[0169] AC node voltage calculation and branch power flow constraints:

[0170]

[0171] Where i, j are AC nodes; V j (t),θ j (t) is the voltage amplitude and phase angle of AC node j; G ij is the real part of the node admittance matrix, B i ' j is the imaginary part of the node admittance matrix without considering the ground branch; P g (t),P w (t),P d (t),P l (t) is thermal power, wind power, DC power and load power; are the thermal power plants, wind farms, converter stations and load collections connected to the AC node i; g ij ,b ij are the conductance and susceptance of branch ij respectively; P ijmax It is the upper limit of the active transmission power of the branch.

[0172] The commutation bus AC voltage obtained by follower model optimization is:

[0173] Power balance constraints within the transmitting and receiving systems:

[0174]

[0175] in, Respectively represent the output of conventional units in the sending section and receiving end area; is the wind power at the sending end; is the load power of the sending and receiving ends; represents the planned DC transmission power obtained by optimizing the leader model.

[0176] 2) Real-time constraints:

[0177] Safe operation constraints of thermal power units in multiple wind power scenarios, including unit output constraints, ramp rate constraints, and reserve capacity constraints.

[0178]

[0179] Among them, P g,s (t) is the output of the thermal power unit under scenario s; P g (t) is the output of the thermal power unit in the day-ahead phase; RU g ,RD g They are the upper limits of the ramp-up and ramp-down active power regulation rates of thermal power units respectively; They are respectively the upward and downward adjustment of the reserve capacity of thermal power units.

[0180] Wind power constraints:

[0181]

[0182] Among them, P w,s (t) is the wind power called by the grid under scenario s; is the available wind power value under scenario s.

[0183] Energy storage related constraints:

[0184]

[0185] in, are the charging and discharging power of energy storage under scenario s; E k,s (t) is the energy stored in the energy storage period t under scenario s; SOC k,s (t) is the state of charge of the energy storage during period t under scenario s; SOC k,s (0),SOC k,s (T) are the charge states of the energy storage at the initial and final periods under scenario s; the definitions of other parameters are the same as those in formula (20).

[0186] Power balance constraints within the sending and receiving systems:

[0187]

[0188] in are the thermal power of the sending and receiving ends under scenario s respectively; is the wind power at the sending end under scenario s; are the total load power of the sending and receiving ends under scenario s respectively; A collection of energy storage.

[0189] Finally, the AC voltage amplitude of the commutation bus obtained by follower model optimization is And the upper and lower limits of the equivalent conventional unit output are as follows:

[0190]

[0191] in, They are the upper and lower limits of the output of the equivalent conventional unit at the sending end; They are the upper and lower limits of the output of the equivalent conventional unit at the receiving end; Respectively represent the collection of conventional units at the sending end and the receiving end; u g The definition of (t) is the same as that of formula (24).

[0192] S104 The solution strategy of the master-slave game problem includes:

[0193] (1) The leader formulates its own optimal strategy and sends it to followers:

[0194] As the leader, the National Coordination Center obtains the optimized DC transmission plan by solving the leader model and sends it to the followers;

[0195] (2) Followers formulate their own optimal strategies based on the leader’s strategy:

[0196] The DC transmitting and receiving system acts as a follower. It solves the follower model through distributed optimization to obtain the upper and lower limits of the active power output of the planned start-up units and the AC voltage data of the commutation bus obtained through power flow calculation, and then uploads it to the leader.

[0197] (3) Leaders and followers constantly update their strategies:

[0198] The leader continuously updates its own strategy based on the follower's strategy, and the follower also continuously updates its own strategy based on the leader's strategy. The master-slave problem is solved through continuous iteration.

[0199] (4) Conditions for obtaining equilibrium solutions:

[0200] When the DC transmission plan formulated by the leader no longer changes, the master-slave game reaches the Stackelberg equilibrium, and the corresponding optimal DC transmission plan This is the Stackelberg equilibrium solution.

[0201] The following comparative analysis uses specific examples to analyze the effects of optimizing resource allocation for resource abundance and flexibility in a DC transmission plan obtained by the method proposed in the present invention, without considering the balance between flexibility and resource abundance. The specific contents include:

[0202] Adopting a wind power DC transmission system in Northwest China, Figure 3 This is a schematic diagram of the DC transmitting and receiving end system. The equivalent system structure of the transmitting and receiving end is as follows: Figure 4 As shown in the figure, the installed thermal power capacity of the sending system is 18.9 GW, the installed thermal power capacity of the receiving system is 41.5 GW, and the wind farm is located at node 9 of the sending system. The case study was programmed using Yalmip in MATLAB R2018b and the GUROBI 9.5.0 solver was used.

[0203] The scheduling cycle for the example is 96 time periods before the day, with each period lasting 15 minutes. Several wind power scenarios were generated using the autoregressive moving average method, and then reduced using the K-means clustering method. Finally, five wind power scenarios were retained to simulate the real-time uncertainty of wind power. The sending system is region a, and the receiving system is region b. The day-ahead forecast curves for wind power and the load of the sending and receiving systems are shown as follows: Figure 5 、 Figure 6 As shown, the wind power real-time scene curves are as follows: Figure 7 The probabilities of the five wind power real-time scenarios are shown in Table 1.

[0204] Table 1 Probability of five groups of wind power real-time scenarios

[0205]

[0206] The LCC-HVDC interconnector connects node 14 on the sending end and node 33 on the receiving end. The maximum number of DC adjustments is six, with a duration of two hours. The daily transaction volume is 165GWh, and the maximum regulation capacity within a DC unit dispatch period is 2.2GW.

[0207] Four case studies were designed for comparative analysis:

[0208] Mode 1: The planned DC transmission power is given according to the traditional two-stage operation mode;

[0209] Mode 2: The DC transmission power is flexibly adjusted, without limiting the number of reactive power device operations, and taking into account the balance between flexibility and redundancy at the transmitting and receiving ends.

[0210] Mode 3: The DC transmission power is flexibly adjusted to limit the number of reactive power device operations; the balance between flexibility and redundancy at the transmitting and receiving ends is not considered.

[0211] Mode 4: The DC transmission power is flexibly adjusted, the number of operations of reactive equipment is limited, and the balance between flexibility and redundancy of the sending and receiving ends is considered.

[0212] Among them, mode 4 is the method provided by the present invention, which obtains the optimized DC transmission plan through the master-slave game. Compared with mode 1, the DC transmission power of modes 2-4 is more flexible and can better allocate multiple types of resources in the power system. Compared with modes 1-2, mode 4 limits the number of actions of DC reactive equipment, and ensures the reliability of the DC transmission channel while flexibly adjusting the DC. Compared with modes 1 and 3, mode 4 takes into account the balance between the flexibility and abundance of the DC sending and receiving ends, and improves the overall system's ability to accept new energy. The DC planned transmission power curves obtained by optimizing the example modes 1, 2, and 4 are shown as follows: Figure 8The number of DC reactive device operations in modes 1, 2, and 4 is shown in Table 2. It can be concluded that limiting the operation of reactive devices can significantly reduce the number of AC filter and converter transformer operations, thereby ensuring DC reliability.

[0213] Table 2 Operation times of DC reactive equipment in calculation modes 1, 2, and 4

[0214]

[0215]

[0216] Case 4 converges after two master-slave games. The specific process of the master-slave game is as follows: changes in the planned DC transmission power will lead to changes in the planned start-up units and the AC voltage of the commutation bus at the sending and receiving ends; however, changes in the planned start-up units and the AC voltage of the commutation bus at the sending and receiving ends will lead to changes in the planned DC transmission power; when the DC transmission plan formulated by the leader no longer changes, the master-slave game reaches the Stackelberg equilibrium, and the corresponding optimal solution is is the Stackelberg equilibrium solution. Figure 9 It shows the changes of HVDC transmission plan during the two master-slave games.

[0217] Figure 10 The following is a comparison of the difference curves between the sufficient margin and flexibility margin of the sending-end system and the receiving-end system after optimization for the case studies 1, 3, and 4. It can be seen that compared to 1, the optimization of Mode 4 improves the balance between sufficient margin and flexibility margin of the sending and receiving systems by 40.14%. Compared to Mode 3, the optimization of Mode 4 improves the balance between sufficient margin and flexibility margin of the sending and receiving systems by 12.33%. Therefore, DC optimization can promote the balance between flexibility and sufficient margin of the sending and receiving systems, which is consistent with my country's cross-regional DC optimized dispatching system and can enhance the system's overall capacity to accommodate new energy.

Claims

1. A method for optimizing inter-regional DC transmission plans based on master-slave game, characterized in that: The following steps are involved: Step 1: Based on the supply and demand model of the DC transmission and receiving end system's adequacy and flexibility resources, derive the expressions for the adequacy margin and flexibility margin of the DC transmission and receiving end system. The adequacy margin of the transmission and receiving end system is equal to the system's available generation capacity minus the system's load demand, and the flexibility margin is defined as the flexibility supply minus the flexibility demand. Step 2: Construct a leader model based on the master-slave game theory and formulate a DC transmission plan based on this leader model; The leader model in step 2 includes a benefit function, which is: Among them, ρ s is the probability of scenario s; I represents the set of regions connected to region a through DC tie lines; K1, K2, and K3 are the weight coefficients of the three parts of the balance of abundance between the sending and receiving ends, the balance of flexibility, and the economy of the day-ahead scheduling strategy; C(P g (t)) is the power generation cost of conventional units; are the penalty costs for wind curtailment and load curtailment respectively; ΔP w (t),ΔP l (t) are the amount of wind curtailment and load curtailment respectively; are the collections of thermal power, wind power and load respectively; T, S are the collections of scheduling period and scenario respectively; are the adequacy margins of the sending and receiving ends in the wind power scenario s during the dispatch period t, They represent the upward and downward flexibility margins of the DC sending-end system respectively; They represent the upward and downward flexibility margins of the DC receiving system respectively; Step 3: Construct a follower model based on the master-slave game theory, and perform unit commitment and economic dispatch according to this follower model; Step 4: Obtain the Stackelberg equilibrium solution of the master-slave game.

2. The inter-regional DC transmission plan optimization method based on master-slave game according to claim 1 is characterized in that: The adequacy margin of the DC transmitting and receiving end systems in step 1 is specifically: in, are the adequacy margins of the sending end and the receiving end under wind power scenario s during dispatch period t; are the available generating capacity at the sending and receiving ends respectively; are the load demands at the sending and receiving ends respectively; For DC transmission power; are the sets of controllable loads of the sending and receiving systems respectively; I represents the set of areas connected to area a through DC tie lines.

3. The inter-regional DC transmission plan optimization method based on master-slave game according to claim 1 is characterized in that: The flexibility margin of the DC transmitting and receiving end systems in step 1 is specifically: in, They represent the upward and downward flexibility margins of the DC sending-end system respectively; They represent the upward and downward flexibility margins of the DC receiving system respectively; They represent the upward and downward flexibility requirements of the sending-end system respectively; They represent the upward and downward flexibility requirements of the receiving system respectively; The DC power in the sending end area can be flexibly adjusted by increasing and decreasing the power; The power can be flexibly adjusted upward and downward for the sending end; These are the upward and downward adjustments that the sending-end energy storage can provide, allowing for flexible power adjustment; They are respectively the upward and downward flexible power adjustments that can be provided by the controllable load at the sending end; The power can be flexibly adjusted by increasing or decreasing the DC power within the receiving area. The receiving end can flexibly adjust the power by increasing and decreasing the power provided by the power supply; The upward and downward adjustments that the receiving-end energy storage can provide can flexibly adjust the power; are the upward and downward flexibly adjustable powers that can be provided by the controllable load at the receiving end; I represents the set of areas connected to area a through DC tie lines; Represent the collection of energy storage at the sending end and receiving end systems respectively; Represent the sets of controllable loads of the sending and receiving systems respectively; Represent the collection of conventional units at the sending end and the receiving end respectively.

4. The method for optimizing inter-regional DC transmission plan based on master-slave game according to claim 1, characterized in that: The leader model in step 2 also includes constraints of the leader model, which include DC regulation characteristic constraints, converter station steady-state operation constraints, DC reactive equipment operation constraints, wind power constraints, related constraints of equivalent conventional units, energy storage related constraints, and power balance constraints of the sending and receiving end systems; The DC regulation characteristic constraints include DC power upper and lower limit constraints, DC regulation amount constraints within the unit dispatch period, DC daily regulation times constraints, minimum holding period number constraints after DC regulation, and DC daily transaction power constraints; The DC reactive equipment action constraints are mainly used to limit the number of actions of the AC filter and converter transformer, including the reactive power range constraints exchanged between the AC and DC systems, the discretization constraints of the converter transformer ratio, and the maximum daily action times constraints of the AC filter and converter transformer; The relevant constraints of the equivalent conventional unit include upper and lower output constraints and ramp rate constraints; The energy storage related constraints include energy storage charging and discharging power constraints, energy continuity constraints and state of charge constraints.

5. The method for optimizing inter-regional DC transmission plan based on master-slave game according to claim 4 is characterized in that: The follower model in step 3 includes the demand function and the constraints of the follower model. The demand function is: Among them, v g (t) is the binary state variable of the unit startup, 1 represents startup; w g (t) is the unit shutdown binary state variable, 1 represents shutdown; C(v g (t),w g (t)) is the unit startup and shutdown cost; P g (t) is the output of conventional units in the day-ahead period during the t period; C(P g (t)) is the power generation cost of conventional units; They are the cost coefficients for adjusting the reserve capacity upward and downward for thermal power units; Respectively represent the upward and downward reserve capacity of conventional units; are the reserve capacity cost of thermal power units for upward and downward adjustment, respectively; ρ s is the probability of scene s; P g,s (t) is the output of the conventional unit in the real-time stage during the t period under scenario s; C(P g,s (t))-C(P g (t)) Cost of re-adjusting unit output; are the penalty coefficients for wind curtailment and load curtailment respectively; ΔP w,s (t) is the amount of wind curtailment under scenario s, ΔP l,s (t) is the load shedding amount under scenario s; The constraints of the follower model include constraints in the day-ahead phase and constraints in the real-time phase; The day-ahead constraints include safe operation constraints for thermal power units, wind power constraints, energy storage-related constraints, AC node voltage calculation and branch power flow constraints, and power balance constraints within the sending and receiving systems. The safe operation constraints for thermal power units include unit output constraints, ramp rate constraints, spare capacity constraints, and minimum continuous on / off time constraints. The constraints in the real-time stage include safe operation constraints of thermal power units in multiple wind power scenarios, wind power constraints, energy storage-related constraints, and power balance constraints within the sending and receiving end systems; among them, the safe operation constraints of thermal power units in multiple wind power scenarios include unit output constraints, ramp rate constraints, and spare capacity constraints.

6. The inter-regional DC transmission plan optimization method based on master-slave game according to claim 1 is characterized in that: The step 4 specifically includes the following sub-steps: Step 41: Solve the leader model and send the optimized DC transmission plan to the followers; Step 42: Solve the follower model through distributed optimization to obtain the upper and lower limits of the active power output of the planned start-up units; obtain the commutation bus AC voltage data through power flow calculation, and upload the upper and lower limits of the active power output and the commutation bus AC voltage data to the leader; Step 43: The leader continuously updates its own strategy based on the follower's strategy, and the follower also continuously updates its own strategy based on the leader's strategy, solving the master-slave problem through continuous iteration; Step 44: When the DC transmission plan formulated by the leader no longer changes, the master-slave game reaches a Stackelberg equilibrium, and the corresponding optimal DC transmission plan is taken as the Stackelberg equilibrium solution.

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