Power grid partition parallel recovery two-stage optimization method considering multi-source cooperation

Abstract

The invention discloses a power grid partition parallel recovery two-stage optimization method considering multi-source cooperation, and relates to the technical field of power system recovery. The method comprises the following steps: providing basic conditions for the new energy power generation system to participate in black start, and determining the number and type of black start power supplies; constructing a power grid partition optimization model based on a network flow theory in a first stage; and establishing a power grid partition parallel recovery optimization model considering multi-source cooperation in a second stage, and realizing rapid recovery of the power system taking the wind-light-water-storage multi-source cooperation as the black-start power supply. According to the invention, complete recovery of each generator set, power transmission line and power load in a power-off power grid can be realized, and the problems of long recovery process and important load recovery failure possibly caused by a serial recovery strategy are effectively solved. Meanwhile, the invention provides a power grid partition parallel recovery optimization model taking wind-light-water-storage multi-source cooperation as a black-start power supply, and the problem of insufficient black-start resources possibly existing in a local power grid is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of power system restoration technology, and in particular to a two-stage optimization method for parallel restoration of power grid zones considering multi-source collaboration. Background Technology

[0002] Power system restoration strategies are mainly divided into two types: sequential restoration strategies and parallel restoration strategies. Sequential restoration strategies are suitable for power grids with only one black-start power source, typically using hydropower units with good self-starting capabilities. However, this approach suffers from the disadvantages of relying on a single black-start power source and a lengthy and complex restoration process. Parallel restoration strategies are suitable for power grids with multiple black-start power sources. This involves decomposing the original network into several independent sub-regions with black-starting capabilities and then restoring them in parallel, effectively shortening the system restoration time. However, in regions like Northwest my country, there are few black-start power sources with self-starting capabilities, low starting power, and continuous stable output, such as hydropower units. Furthermore, this strategy is highly dependent on the availability and efficiency of the black-start power sources in each sub-region, which poses a significant obstacle to the application of parallel restoration strategies. Summary of the Invention

[0003] To address the problem that existing serial recovery strategies using a single black-start power source cannot fully utilize the black-start capability of new energy power generation systems, support the rapid recovery of non-black-start thermal power units, and accelerate the recovery process of power outage grids, this invention provides a two-stage optimization method for parallel recovery of grid zones considering multi-source collaboration. This method can solve problems such as lengthy system recovery processes and failures to restore critical loads that may result from the scarcity of black-start resources in power outage grids. The specific technical solution is as follows:

[0004] A two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration includes the following steps:

[0005] S1: Based on the power requirements of non-black-start thermal power units, propose the basic conditions for new energy power generation systems to participate in black start, and determine the number and type of black-start power sources;

[0006] S2: For the case where multiple types of power sources act as black-start power sources simultaneously, a first-stage power grid partition optimization model based on network flow theory is constructed. The optimization objective is to minimize the number of sub-region tie lines. The constraints include black-start power source constraints, sub-region connectivity constraints, sub-region power balance constraints, and special line interruption constraints within the sub-region.

[0007] S3: Building upon S2, a second-stage grid partition parallel recovery optimization model considering multi-source collaboration is established, incorporating the selection logic of the startup characteristic curve of the new energy power generation system into the model. This model aims to minimize the total recovery time and load recovery loss of all thermal power units, with constraints including node power balance constraints, line power flow constraints, unit startup characteristic constraints, and network recovery status constraints.

[0008] S4: Solve the first stage of the power grid partition optimization model based on network flow theory and the second stage of the power grid partition parallel recovery optimization model considering multi-source collaboration to obtain the recovery sequence and recovery time of each generator set, transmission line and power load in the power outage power grid.

[0009] The basic conditions for the new energy power generation system to participate in black start include:

[0010] Preferably, the new energy power generation system includes a wind-storage power generation system and a solar-storage power generation system. The basic conditions that the wind-storage power generation system must meet as a black-start power source are:

[0011]

[0012]

[0013] Where: G NBS The set of non-black-start thermal power units within the network; The minimum capacity requirement for wind-storage power generation systems (WS) to participate in black start; The starting power of non-black start thermal power unit g; The time for a non-black start thermal power unit (g) to absorb power; The minimum power requirement for the wind-storage power generation system ws to participate in black start; the coefficient ΔP% is the line loss rate; P ws_load This is for the self-consumption of the wind-storage power generation system.

[0014] Equation (1) represents the minimum total energy requirement for the wind-storage power generation system to participate in black start, that is, the total energy of the wind-storage power generation system must meet the recovery needs of the unit with the largest start-up energy in the network; Equation (2) ensures that the wind-storage power generation system can continuously and stably output power during the black start process, that is, the minimum output power must meet the recovery needs of the unit with the largest start-up power in the network and the power consumption needs of the power generation system itself.

[0015] (1) Operational constraints of wind-storage power generation system

[0016]

[0017]

[0018] In the formula: These represent the upper and lower limits of the active power output of the wind-storage power generation system (WS). These represent the upper and lower limits of reactive power output from the wind-storage power generation system (WS). ωs represents the predicted active and reactive power output of the wind-storage power generation system at time t; T represents the total recovery period.

[0019] Equation (3) represents the upper and lower limits of the active power output of the wind-storage power generation system ws at time t; Equation (4) represents the upper and lower limits of the reactive power output of the wind-storage power generation system ws at time t.

[0020] Preferably, the basic conditions that the photovoltaic-storage power generation system needs to meet as a black-start power source are:

[0021]

[0022]

[0023] Where: G NBS The set of non-black-start thermal power units within the network; The minimum capacity requirement for photovoltaic-storage power generation systems (PS) to participate in black start; The starting power of non-black start thermal power unit g; The time for a non-black start thermal power unit (g) to absorb power; The minimum power requirement for a photovoltaic-storage power generation system (PS) to participate in black start; the coefficient ΔP% is the line loss rate; P ps_load This is for the self-consumption of the photovoltaic-storage power generation system.

[0024] Equation (5) represents the minimum total energy requirement for the photovoltaic-storage power generation system to participate in black start, that is, the total energy of the photovoltaic-storage power generation system ps must meet the recovery needs of the unit with the largest start-up energy in the network; Equation (6) ensures that the photovoltaic-storage power generation system can continuously and stably output power during the black start process, that is, the minimum output power must meet the recovery needs of the unit with the largest start-up power in the network and the power consumption needs of the power generation system itself.

[0025] (1) Operational constraints of photovoltaic and energy storage power generation systems

[0026]

[0027]

[0028] In the formula: These are the upper and lower limits of the active power output of the photovoltaic-storage power generation system (PS). These are the upper and lower limits of reactive power output from the photovoltaic-storage power generation system (PS). , representing the predicted active and reactive power outputs of the photovoltaic-storage power generation system at time t; T represents the total recovery period.

[0029] Equation (7) represents the upper and lower limits of the active power output of the photovoltaic-storage power generation system ps at time t; Equation (8) represents the upper and lower limits of the reactive power output of the photovoltaic-storage power generation system ps at time t.

[0030] The first stage of the power grid zoning optimization model based on network flow theory includes:

[0031] (1) Objective function

[0032]

[0033] In the formula: L is the set of all lines in the network; α is the α-th sub-region in the network, α = 1, 2, ..., m; z iα Let z be an integer variable between 0 and 1, representing the subregion α to which node i belongs. iα =1, then node i belongs to subregion α, if z iα If = 0, then node i does not belong to subregion α.

[0034] Clearly, equation (9) is a nonlinear expression, achieved by introducing a 0-1 integer variable e. ijα Linearizing the above equation yields equation (11).

[0035]

[0036]

[0037] In the formula: e ijα The auxiliary decision variable introduced is an integer variable of 0-1, representing the situation of sub-region α to which line (i,j) belongs, which is equivalent to e ijα =z iα z jα If e ijα =1, then line (i,j) belongs to sub-region α; if e ijα =0, then line (i,j) does not belong to sub-region α.

[0038] Equation (10) indicates that if the nodes (i,j) at both ends of the line belong to the same sub-region α, then the line must belong to that sub-region α.

[0039] (2) Black-start power supply constraints within sub-regions

[0040]

[0041]

[0042] In the formula: N is the set of all nodes in the network; N αBS Let i be the set of black-start power nodes for subregion α; α This is the black-start power node for sub-region α.

[0043] Equation (12) indicates that each sub-region contains only one black-start power source; Equation (13) indicates that each node in the network belongs to one and only one sub-region.

[0044] (3) Sub-region connectivity constraints

[0045] The basic idea of ​​using network flow to ensure sub-region connectivity is: taking the black-starting power source within sub-region α as the unique source of the network flow, ensuring that all nodes within sub-region α, except for the black-starting power source node, satisfy z iα All nodes with a value of 1 receive traffic and consume one unit of traffic.

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] In the formula: f ijα The auxiliary decision variable introduced represents the size of the network flow from node i to node j in subregion α, and is a non-negative variable; M is a sufficiently large positive number; i α This is the black-start power node for sub-region α.

[0052] Equation (14) indicates that network flow can only occur between nodes i and j when nodes i and j are both within subregion α and there is a path between the two nodes, i.e., when e ijα When f = 1, and node i and node j are both in subregion α, f ijα Only when e can the value be greater than 0, when e ijα When = 0, f ijα The value must be 0; Equation (15) indicates that the black-start power node only acts as the source of the network flow and only provides the network flow; Equation (16) indicates the relationship between the amount of network flow provided and consumed in sub-region α, that is, the size of the network flow provided by the source node is equal to the total number of nodes in sub-region α minus 1; Equation (17) guarantees that except for the black-start power node i α All nodes outside must satisfy Kirchhoff's first law, that is, the total amount of network flow into a node minus the total amount of flow out of the node equals a unit network flow; Equation (18) indicates that nodes in subregion α have at least a unit network flow inflow.

[0053] (4) Power balance constraints within subregions

[0054]

[0055] Where: GNBS This refers to the set of non-black-start thermal power units in the network. ρ represents the maximum output of the thermal power unit located at node i; i A 0-1 integer variable, representing the critical load situation of load node i. If ρ i =1, then node i is a critical load node, if ρ i =0, then node i is a normal load node; P di The active power requirement of critical load i.

[0056] Equation (19) ensures that the sum of the rated capacities of all thermal power units in each sub-zone can meet the power requirements of all critical loads.

[0057] (5) Special line interruption constraints

[0058] Since parallel sub-regions must satisfy the requirement that voltage, frequency, and phase angle are all equal, certain branches in the network (let's call them set L) s For example, transformer branches and transmission lines without synchronous parallel closing devices cannot be used as sub-area tie lines. These can be added to the model in the form of equality constraints.

[0059]

[0060] Equation (20) represents the transformer branch and the transmission line L without a synchronous parallel closing device. s The two endpoints i and j belong to the same sub-region α, and line L s Recovery is performed within subregion α.

[0061] The second stage considers a multi-source collaborative grid partition parallel recovery optimization model, which includes:

[0062] (1) Objective function

[0063]

[0064] Where: G NBS Let N be the set of all non-black-start thermal power units in the network; N is the set of all nodes in the network. The time it takes for a non-black-start thermal power unit (g) to obtain starting power; The time for a non-black-start thermal power unit to absorb power (g); P di Let i be the active power load requirement of node i; Let be the active power of the load that has been restored at node i at time t.

[0065] (2) Node power balance constraints

[0066]

[0067]

[0068]

[0069] In the formula: G(i) is the set of conventional generating units located at node i, including hydropower units and thermal power units; G R L is the set of all new energy power generation systems in the network. Therefore, the wind-storage power generation system, the solar-storage power generation system, and the wind-solar-storage power generation system in the network are collectively referred to as new energy power generation systems; L(i) is the set of lines connected to node i. These represent the active and reactive power of the load that has been restored at node i at time t, respectively. These represent the active and reactive power outputs of unit g at time t, respectively. It is a 0-1 integer variable, representing the energized state of unit g at time t; Let g be the starting power of unit g; These represent the active and reactive power outputs of the new energy generator unit r at time t, respectively. This is a 0-1 integer variable representing the energizing state of the new energy generator unit r at time t; The starting power of the new energy power generation system r; This indicates that the new energy power generation system will not be used as a black start power source; These represent the active and reactive power flowing from node i to node j on line l at time t; P di Let i be the active power load requirement of node i; is a 0-1 integer variable representing the recovery state of node i at time t; T represents the total recovery time period.

[0070] Equation (22) indicates that the active power of the load restored at node i is equal to the active power of the node minus the outflow; Equation (23) indicates that the reactive power of the load restored at node i is equal to the reactive power of the node minus the outflow; Equation (24) indicates that the load at node i can only be restored after node i is energized.

[0071] (3) Line power flow constraints

[0072]

[0073]

[0074] In the formula: T represents the specified recovery period; N is the set of all nodes in the network; L(i) is the set of lines connected to node i; It is a 0-1 integer variable, representing the recovery state of the line at time t; These represent the upper and lower limits of active and reactive power that the line is allowed to flow through; G ij B ij Let be the conductance and susceptance of line (i,j), respectively. Let be the voltage amplitude at node i at time t; Let be the voltage phase angle of node i at time t.

[0075] Equations (25)-(26) represent the upper and lower limits of active and reactive power flowing through the line.

[0076] (4) Constraints on the start-up characteristics of conventional units

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] In the formula: G is the set of conventional units in the network, including hydropower units and thermal power units; These are integer variables ranging from 0 to 1, representing whether unit g is in the power absorption, ramp-up, or maximum output stage, respectively. The startup time of unit g; Let g be the starting power of unit g; R is the power absorption time of unit g; g Let g be the ramp rate of unit g; This represents the maximum output power of unit g. As an auxiliary variable, equations (33)-(34) define it; T is the specified recovery period; Let M be the active power output of unit g at time t; M is a sufficiently large positive number.

[0088] Equation (27) indicates that the unit cannot be in the ramp-up phase and the maximum output phase simultaneously; Equation (28) indicates the time range corresponding to the power absorption phase of the unit; Equation (29) indicates when hour, That is, the unit is in the ramp-up phase or the maximum output phase at this time; Equations (30)-(31) represent the time range corresponding to the ramp-up phase of the unit; Equation (32) represents the time range corresponding to the maximum output phase of the unit; Equations (33)-(34) define auxiliary variables. Equation (35) indicates that all units must be started before the total time period is restored; Equation (36) indicates the power generation capacity of unit g at time t.

[0089] (5) Start-up characteristics constraints of new energy power generation systems

[0090] Preferably, the new energy power generation system has two startup characteristic curves, corresponding to the startup characteristic curves when the new energy power generation system is used as a black start power source and when it is not used as a black start power source, respectively. Integer variables are introduced to linearize the startup characteristic curves of the new energy power generation system piecewise.

[0091] 1) Linearization of the starting characteristic curve when new energy is used as a black start power source

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; These are integer variables (0-1), representing whether the new energy power generation system r is in a high-power output, ramp-up, or stable output phase, respectively. and The starting power and the time required to absorb power for the unit that requires the maximum starting energy in the system are determined by the unit's starting power and the time required for that unit to absorb power. This represents the initial power output of the new energy power generation system during the ramp-up phase. R is the predicted output value of the new energy power generation system. r The ramp rate of the new energy power generation system r; Let r be the power output of the new energy power generation system at time t when it acts as a black-start power source.

[0101] Equation (37) indicates that a new energy power generation system cannot be in the high power output, ramp-up, or maximum output stage simultaneously; Equations (38)-(39) indicate the time range corresponding to the new energy power generation system being in the high power output stage; Equation (40) indicates that when At that time, the new energy power generation system may be in the ramp-up or stable output stage; Equations (41)-(42) represent the time range corresponding to the new energy power generation system being in the ramp-up stage; Equation (43) represents the time range corresponding to the new energy power generation system being in the stable output stage; Equation (44) represents the power output of the new energy power generation system at time t when it is used as a black start power source.

[0102] 2) Linearization of the starting characteristic curve when new energy sources are not used as black start power sources

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; These are integer variables (0-1), representing whether the new energy power generation system r is in the power absorption, ramp-up, or stable output stage, respectively. The start-up time of the new energy power generation system r; The starting power of the new energy power generation system r; The time for the new energy power generation system to absorb power; R r The ramp rate of the new energy power generation system r; The predicted output value of the new energy power generation system r; As an auxiliary variable, equations (51)-(52) define it; T is the specified recovery period; Let r be the power output of the new energy power generation system at time t when it is not used as a black-start power source; M is a sufficiently large positive number.

[0114] Equation (45) indicates that the new energy power generation system cannot be in the ramp-up or maximum output stage at the same time; Equation (46) indicates the time range corresponding to the new energy power generation system being in the power absorption stage; Equation (47) indicates that when At that time, the new energy power generation system may be in the ramp-up or stable output stage; Equations (48)-(49) represent the time range corresponding to the new energy power generation system being in the ramp-up stage; Equation (50) represents the time range corresponding to the new energy power generation system being in the stable output stage; Equations (51)-(52) define auxiliary variables. Equation (53) indicates that all new energy power generation systems must be started before the total recovery period; Equation (54) indicates the power output of the new energy power generation system at time t when it is not used as a black start power source.

[0115] Preferably, the selection logic for the startup characteristic curve of the new energy power generation system includes:

[0116] Introducing integer variables (0-1) to represent the selection of the startup characteristic curve:

[0117]

[0118]

[0119]

[0120]

[0121] Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; The options are as follows: using a new energy power generation system as a black start power source and not using it as a black start power source. This indicates the selection of a new energy power generation system as the black start power source. This indicates that the new energy power generation system will not be used as a black start power source; These are integer variables ranging from 0 to 1, representing the three stages of the two startup characteristic curves, respectively; The actual output power of the new energy power generation system r at time t; This represents the actual output power of the new energy power generation system at time t when it is used as a black-start power source; This represents the actual output power of the new energy power generation system at time t when it is not used as a black-start power source.

[0122] Equation (55) indicates that any new energy power generation system can only select one startup characteristic; Equations (56)-(57) indicate that the startup characteristics of the new energy power generation system that are not selected are all 0, and the actual output corresponding to the startup characteristic is 0; Equation (58) indicates the actual output power of the new energy power generation system.

[0123] (6) Output constraints of conventional units

[0124]

[0125]

[0126] In the formula: T is the total recovery period; G is the set of conventional units in the network, including hydropower units and thermal power units; It is a 0-1 integer variable, representing the energized state of unit g at time t; These represent the active and reactive power outputs of unit g at time t, respectively. These are the upper and lower limits of the active power output of unit g, respectively; These represent the upper and lower limits of the unit's reactive power output g, respectively.

[0127] Equation (59) represents the upper and lower limits of the active power output of the unit at time t; Equation (60) represents the upper and lower limits of the reactive power output of the unit at time t.

[0128] (7) Output constraints of new energy power generation systems

[0129]

[0130]

[0131] In the formula: T is the total recovery period; G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; Let be the active and reactive power outputs of the new energy power generation system r at time t, respectively, and equal to the sum of the output of the new energy generator units and the charging and discharging power of the energy storage devices in system r. This is a 0-1 integer variable representing the energization state of the new energy power generation system r; These represent the upper and lower limits of the active power output of the new energy power generation system. These represent the upper and lower limits of reactive power output of the new energy power generation system, respectively.

[0132] Equation (61) represents the upper and lower limits of the active power output of the new energy power generation system at time t; Equation (62) represents the upper and lower limits of the reactive power output of the new energy power generation system at time t.

[0133] Preferably, the wind turbine, photovoltaic generator and energy storage device in the new energy power generation system must meet the following conditions.

[0134] 1) Wind turbine output constraints

[0135]

[0136]

[0137] In the formula: T is the total recovery period; R is the set of all new energy generator units in the network, including wind turbines and photovoltaic generator units; These are the predicted active and reactive power outputs of the wind turbine w at time t, respectively. This is a 0-1 integer variable representing the energized state of the wind turbine w. These represent the upper and lower limits of the active power output of the wind turbine unit (w); These represent the upper and lower limits of the reactive power output of the wind turbine generator (w).

[0138] Equation (63) represents the upper and lower limits of the active power output of the wind turbine at time t; Equation (64) represents the upper and lower limits of the reactive power output of the wind turbine at time t.

[0139] 2) Output constraints of photovoltaic generator sets

[0140]

[0141]

[0142] In the formula: T is the total recovery period; R is the set of all new energy generator units in the network, including wind turbines and photovoltaic generator units; These are the predicted active and reactive power outputs of photovoltaic generator unit p at time t, respectively. This is a 0-1 integer variable representing the energization state of the photovoltaic generator set p; These represent the upper and lower limits of the active power output p of the photovoltaic generator set; These represent the upper and lower limits of the reactive power output p of the photovoltaic generator set.

[0143] Equation (65) represents the upper and lower limits of the active power output of the photovoltaic generator set at time t; Equation (66) represents the upper and lower limits of the reactive power output of the photovoltaic generator set at time t.

[0144] 3) Constraints of energy storage devices

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] Where: S is the set of all energy storage devices in the network; These are the charging power and discharging power of the energy storage device s at time t, respectively. These are the upper limit thresholds for the charging power and discharging power of the energy storage device s, respectively. These represent the charging and discharging states of the energy storage device s at time t, respectively. Let be the charging and discharging power of the energy storage device s at time t; Let be the energy of energy storage device s at time t; These are the charging and discharging efficiencies of the energy storage device s, respectively. These are the upper and lower energy thresholds for the energy storage device s, respectively.

[0152] Equations (67)-(72) represent the power, charge / discharge state and energy constraint of the energy storage device.

[0153] (8) Single load constraint

[0154]

[0155] Where: T is the total recovery period; N is the set of all nodes in the network; G is the set of conventional units in the network, including hydropower units and thermal power units; Let Δf be the active power of the load that has been restored at node i at time t; max This represents the maximum allowable frequency deviation for normal system operation. The rated active power of unit g; f is a 0-1 integer variable representing the energization state of unit g at time t; g Let g be the frequency response value of unit g.

[0156] Equation (73) represents the maximum load fluctuation that the unit can withstand when the single load input is less than or equal to the maximum frequency deviation.

[0157] (9) Network recovery status constraints

[0158]

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] In the formula: N is the set of all nodes in the network; L is the set of all lines in the network; G is the set of conventional generating units in the network, including hydroelectric generating units and thermal generating units; G R G is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; RNBS This refers to the collection of non-blacklisted new energy power generation systems in the network. and These represent the recovery states of node i, generator g, renewable energy generation system r, and line l within sub-region α at time t, respectively; T l The time taken to restore a line; M is a sufficiently large positive number.

[0169] Equations (74)-(79) represent the recovery conditions of lines, nodes, generators and new energy power generation systems in the network, respectively; Equations (80)-(83) represent that nodes, generators, new energy power generation systems and lines will not be disconnected after recovery.

[0170] (10) Sub-area link restoration constraints

[0171]

[0172]

[0173] Where: N NBS N represents the set of nodes for all non-black-start generator units within the network; including thermal power unit nodes and non-black-start renewable energy power generation system nodes; D N represents the set of all critical load nodes within the network. NBS_D N is the set of all non-black-start units and critical load nodes within the network; V L is the set of nodes at both ends of all sub-area link lines within the network; v It is the set of all sub-area contact lines within the network; It is a 0-1 integer variable, representing the state variable of whether all non-black start unit nodes in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the state variable of whether all critical load nodes i in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the state variable of whether all non-black start unit nodes and critical load nodes in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the endpoint recovery state of all sub-region connection lines within sub-region α at time t; T is a 0-1 integer variable representing the recovery state of sub-region α connection line l at time t; l The time taken to restore a line.

[0174] Equation (84) indicates that at the initial moment of system recovery, all sub-area tie lines are in a disconnected state; Equations (85)-(86) indicate the conditions that need to be met for the sub-area tie line to be restored, namely, all non-black start unit nodes, critical load nodes, and nodes at both ends of the sub-area tie line in the sub-area have been restored, and then after T l Only then can the sub-area connection line be restored.

[0175] (11) System operation constraints

[0176]

[0177]

[0178] In the formula: N is the set of all nodes in the network; θ max θ min These are the upper and lower limits of the voltage phase angle at node i, respectively; Let be the voltage phase angle of node i at time t; These are the upper and lower limits of the phase angle of line l, respectively; U max U min These are the upper and lower limits of the voltage amplitude at node i, respectively; Let be the voltage amplitude at node i at time t; These are the upper and lower limits of the voltage amplitude deviation for line l, respectively.

[0179] Equation (87) represents the upper and lower limits of voltage phase angle for nodes and lines; Equation (88) represents the upper and lower limits of voltage amplitude for nodes and lines.

[0180] (12) System power constraints

[0181]

[0182]

[0183] In the formula: These represent the active and reactive power outputs of unit g at time t, respectively. These represent the active and reactive power outputs of the new energy power generation system r at time t, respectively. B is a 0-1 integer variable representing the recovery state of line l at time t; lV represents the susceptance of line l; V represents the voltage level of the line.

[0184] Equation (89) indicates that the system's power generation capacity is always greater than or equal to 0; Equation (90) indicates that the generator sets in the system can absorb the reactive power generated by the recovery path to alleviate the overvoltage problem during the recovery process.

[0185] As can be seen from the technical solutions provided by the embodiments of the present invention above, the present invention proposes a two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration, which fully leverages the black start capability of wind power generation systems and photovoltaic power generation systems, accelerates the system recovery process, and achieves complete recovery of each generator set, transmission line and power load in the power outage grid.

[0186] Preferably, step S4 specifically involves: based on the given basic conditions of the new energy power generation system as a black start power source, the objective function and constraints of the first-stage grid partition optimization model based on network flow theory and the second-stage grid partition parallel recovery optimization model considering multi-source collaboration, constructing a two-stage optimization model for grid partition parallel recovery considering multi-source collaboration in Matlab using the Yamip toolbox, and using the Cplex solver to obtain the recovery sequence and recovery time of each generator set, transmission line and power load in the power outage grid.

[0187] The present invention has the following advantages:

[0188] 1. Based on the power requirements of non-black-start thermal power units, this invention proposes the basic conditions that wind-storage power generation systems and photovoltaic-storage power generation systems must meet as black-start power sources, thereby promoting the consumption of new energy sources and improving the black-start capability of regional power grids.

[0189] 2. This invention considers the full participation of wind-storage power generation systems and photovoltaic-storage power generation systems in system recovery, and proposes two different start-up characteristic curves, which fully utilize the power generation capacity of wind-storage power generation systems and photovoltaic-storage power generation systems, and improve the overall recovery capability of the power grid during power outages.

[0190] 3. The continuous changes in network topology during system recovery will lead to nonlinearity in the power flow-related constraints in the model. This invention linearizes the relevant constraints and also linearizes the models of conventional generator sets and new energy power generation systems, forming a mixed integer linear programming model, which improves the accuracy and robustness of the model solution.

[0191] 4. This invention considers the synergistic use of wind, solar, hydro, and energy storage as a black start power source, giving full play to the black start capabilities of wind and solar power systems and effectively solving the problem of insufficient black start resources in local power grids.

[0192] 5. This invention adopts a parallel recovery strategy, which involves the entire process of power system recovery. It can realize the complete recovery of each generator set, transmission line and power load in the power outage grid, and effectively solves the problem that the serial recovery strategy may lead to a long recovery process and failure to restore important loads. Attached Figure Description

[0193] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0194] Figure 1 This is an overall framework diagram of the present invention;

[0195] Figure 2 This is a schematic diagram of the conventional unit start-up characteristic curve of the present invention;

[0196] Figure 3 This is a schematic diagram of the startup characteristic curve of the new energy power generation system of the present invention. Detailed Implementation

[0197] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0198] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0199] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0200] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0201] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein is for the purpose of describing embodiments of this disclosure only and is not intended to be limiting of this disclosure.

[0202] This invention provides an embodiment of a two-stage optimization method for parallel recovery of power grid sections considering multi-source collaboration. The modular two-stage optimization method for parallel recovery of power grid sections considering multi-source collaboration specifically includes the following:

[0203] S1: Based on the power requirements of non-black-start thermal power units, propose the basic conditions for new energy power generation systems to participate in black start, and determine the number and type of black-start power sources;

[0204] Among them, new energy power generation systems include wind-storage power generation systems and solar-storage power generation systems.

[0205] S11: The basic conditions that a wind-storage power generation system must meet as a black start power source are:

[0206]

[0207]

[0208] Where: G NBS The set of non-black-start thermal power units within the network; The minimum capacity requirement for wind-storage power generation systems (WS) to participate in black start; The starting power of non-black start thermal power unit g; The time for a non-black start thermal power unit (g) to absorb power; The minimum power requirement for the wind-storage power generation system ws to participate in black start; the coefficient ΔP% is the line loss rate; P ws_load This is for the self-consumption of the wind-storage power generation system.

[0209] Equation (91) represents the minimum total energy requirement for the wind-storage power generation system to participate in black start, that is, the total energy of the wind-storage power generation system must meet the recovery needs of the unit with the largest start-up energy in the network; Equation (92) ensures that the wind-storage power generation system can continuously and stably output power during the black start process, that is, the minimum output power must meet the recovery needs of the unit with the largest start-up power in the network and the power consumption needs of the power generation system itself.

[0210] (1) Operational constraints of wind-storage power generation system

[0211]

[0212]

[0213] In the formula: These represent the upper and lower limits of the active power output of the wind-storage power generation system (WS). These represent the upper and lower limits of reactive power output from the wind-storage power generation system (WS). ωs represents the predicted active and reactive power output of the wind-storage power generation system at time t; T represents the total recovery period.

[0214] Equation (93) represents the upper and lower limits of the active power output of the wind-storage power generation system ws at time t; Equation (94) represents the upper and lower limits of the reactive power output of the wind-storage power generation system ws at time t.

[0215] S12: The basic conditions that a photovoltaic-storage power generation system must meet as a black-start power source are:

[0216]

[0217]

[0218] Where: G NBS The set of non-black-start thermal power units within the network; The minimum capacity requirement for photovoltaic-storage power generation systems (PS) to participate in black start; The starting power of non-black start thermal power unit g; The time for a non-black start thermal power unit (g) to absorb power; The minimum power requirement for a photovoltaic-storage power generation system (PS) to participate in black start; the coefficient ΔP% is the line loss rate; P ps_load This is for the self-consumption of the photovoltaic-storage power generation system.

[0219] Equation (95) represents the minimum total energy requirement for the photovoltaic-storage power generation system to participate in black start, that is, the total energy of the photovoltaic-storage power generation system ps must meet the recovery needs of the unit with the largest start-up energy in the network; Equation (96) ensures that the photovoltaic-storage power generation system can continuously and stably output power during black start, that is, the minimum output power must meet the recovery needs of the unit with the largest start-up power in the network and the power consumption needs of the power generation system itself.

[0220] (1) Operational constraints of photovoltaic and energy storage power generation systems

[0221]

[0222]

[0223] In the formula: These are the upper and lower limits of the active power output of the photovoltaic-storage power generation system (PS). These are the upper and lower limits of reactive power output from the photovoltaic-storage power generation system (PS). , representing the predicted active and reactive power outputs of the photovoltaic-storage power generation system at time t; T represents the total recovery period.

[0224] Equation (97) represents the upper and lower limits of the active power output of the photovoltaic-storage power generation system ps at time t; Equation (98) represents the upper and lower limits of the reactive power output of the photovoltaic-storage power generation system ps at time t.

[0225] S2: For the case where multiple types of power sources are used as black-start power sources at the same time, a first-stage power grid partitioning optimization model based on network flow theory is constructed.

[0226] The first stage of the power grid zoning optimization model based on network flow theory aims to minimize the number of sub-regional tie lines. The constraints include black-start power source constraints, sub-regional connectivity constraints, sub-regional power balance constraints, and special line disconnection constraints.

[0227] S21: The objective function of the power grid zoning optimization model based on network flow theory in the first stage is as follows:

[0228]

[0229] In the formula: L is the set of all lines in the network; α is the α-th sub-region in the network, α = 1, 2, ..., m; z iα Let z be an integer variable between 0 and 1, representing the subregion α to which node i belongs. iα =1, then node i belongs to subregion α, if z iα If = 0, then node i does not belong to subregion α.

[0230] Clearly, equation (99) is a nonlinear expression, achieved by introducing a 0-1 integer variable e. ijα Linearizing the above equation yields equation (101).

[0231]

[0232]

[0233] In the formula: e ijα The auxiliary decision variable introduced is an integer variable of 0-1, representing the situation of sub-region α to which line (i,j) belongs, which is equivalent to e ijα =z iα z jα If e ijα =1, then line (i,j) belongs to sub-region α; if e ijα =0, then line (i,j) does not belong to sub-region α.

[0234] Equation (100) means that if the nodes (i,j) at both ends of the line belong to the same sub-region α, then the line must belong to that sub-region α.

[0235] S22: The constraints of the first-stage power grid zoning optimization model based on network flow theory include:

[0236] (1) Black-start power supply constraints within the sub-region

[0237]

[0238]

[0239] In the formula: N is the set of all nodes in the network; N αBS Let i be the set of black-start power nodes for subregion α; α This is the black-start power node for sub-region α.

[0240] Equation (102) indicates that each sub-region contains only one black-start power source; Equation (103) indicates that each node in the network belongs to one and only one sub-region.

[0241] (2) Sub-region connectivity constraints

[0242] The basic idea of ​​using network flow to ensure sub-region connectivity is: taking the black-starting power source within sub-region α as the unique source of the network flow, ensuring that all nodes within sub-region α, except for the black-starting power source node, satisfy z iα All nodes with a value of 1 receive traffic and consume one unit of traffic.

[0243]

[0244]

[0245]

[0246]

[0247]

[0248] In the formula: f ijα The auxiliary decision variable introduced represents the size of the network flow from node i to node j in subregion α, and is a non-negative variable; M is a sufficiently large positive number; i α This is the black-start power node for sub-region α.

[0249] Equation (104) indicates that network flow can only occur between nodes i and j when nodes i and j are both within subregion α and there is a path between the two nodes, i.e., when e ijα When f = 1, and node i and node j are both in subregion α, f ijα Only when e can the value be greater than 0, when e ijα When = 0, f ijαThe value must be 0; Equation (105) indicates that the black-start power node only acts as the source of the network flow and only provides the network flow; Equation (106) indicates the relationship between the amount of network flow provided and consumed in sub-region α, that is, the size of the network flow provided by the source node is equal to the total number of nodes in sub-region α minus 1; Equation (107) guarantees that except for the black-start power node i α All nodes outside the region must satisfy Kirchhoff's first law, that is, the total amount of network flow into a node minus the total amount of flow out of the node equals a unit network flow; Equation (108) indicates that the nodes in subregion α have at least a unit network flow inflow.

[0250] (3) Power balance constraints within subregions

[0251]

[0252] Where: G NBS This refers to the set of non-black-start thermal power units in the network. ρ represents the maximum output of the thermal power unit located at node i; i A 0-1 integer variable, representing the critical load situation of load node i. If ρ i =1, then node i is a critical load node, if ρ i =0, then node i is a normal load node; P di The active power requirement of critical load i.

[0253] Equation (109) ensures that the sum of the rated capacities of all thermal power units in each sub-zone can meet the power requirements of all critical loads.

[0254] (4) Special line interruption constraints

[0255] Since parallel sub-regions must satisfy the requirement that voltage, frequency, and phase angle are all equal, certain branches in the network (let's call them set L) s For example, transformer branches and transmission lines without synchronous parallel closing devices cannot be used as sub-area tie lines. These can be added to the model in the form of equality constraints.

[0256]

[0257] Equation (110) represents the transformer branch and the transmission line L without a synchronous parallel closing device. s The two endpoints i and j belong to the same sub-region α, and line L s Recovery is performed within subregion α.

[0258] S3: Based on S2, establish a second-stage grid partition parallel recovery optimization model that considers multi-source collaboration, and incorporate the selection logic of the start-up characteristic curve of the new energy power generation system into the model.

[0259] The second phase considers a grid partition parallel recovery optimization model with multi-source collaboration, with the optimization objective of minimizing the total recovery time and load recovery loss of all thermal power units. The constraints include node power balance constraints, line power flow constraints, unit start-up characteristic constraints, and network recovery status constraints.

[0260] S31: The objective function of the second-stage grid partition parallel recovery optimization model considering multi-source collaboration is as follows:

[0261]

[0262] Where: G NBS Let N be the set of all non-black-start thermal power units in the network; N is the set of all nodes in the network. The time it takes for a non-black-start thermal power unit (g) to obtain starting power; The time for a non-black-start thermal power unit to absorb power (g); P di Let i be the active power load requirement of node i; Let be the active power of the load that has been restored at node i at time t.

[0263] S32: The constraints of the second-stage grid partition parallel recovery optimization model considering multi-source collaboration include:

[0264] (1) Node power balance constraints

[0265]

[0266]

[0267]

[0268] In the formula: G(i) is the set of conventional generating units located at node i, including hydropower units and thermal power units; G R L is the set of all new energy power generation systems in the network. Therefore, the wind-storage power generation system, the solar-storage power generation system, and the wind-solar-storage power generation system in the network are collectively referred to as new energy power generation systems; L(i) is the set of lines connected to node i. These represent the active and reactive power of the load that has been restored at node i at time t, respectively. These represent the active and reactive power outputs of unit g at time t, respectively. It is a 0-1 integer variable, representing the energized state of unit g at time t; Let g be the starting power of unit g; These represent the active and reactive power outputs of the new energy generator unit r at time t, respectively. This is a 0-1 integer variable representing the energizing state of the new energy generator unit r at time t; The starting power of the new energy power generation system r; This indicates that the new energy power generation system will not be used as a black start power source; These represent the active and reactive power flowing from node i to node j on line l at time t; P di Let i be the active power load requirement of node i; is a 0-1 integer variable representing the recovery state of node i at time t; T represents the total recovery time period.

[0269] Equation (112) indicates that the active power of the load restored at node i is equal to the active power of the node minus the outflow; Equation (113) indicates that the reactive power of the load restored at node i is equal to the reactive power of the node minus the outflow; Equation (114) indicates that the load at node i can only be restored after node i is energized.

[0270] (2) Line power flow constraints

[0271]

[0272]

[0273] In the formula: T represents the specified recovery period; N is the set of all nodes in the network; L(i) is the set of lines connected to node i; It is a 0-1 integer variable, representing the recovery state of the line at time t; These represent the upper and lower limits of active and reactive power that the line is allowed to flow through; G ij B ij Let be the conductance and susceptance of line (i,j), respectively. Let be the voltage amplitude at node i at time t; Let be the voltage phase angle of node i at time t.

[0274] Equations (115)-(116) represent the upper and lower limits of active and reactive power flowing through the line.

[0275] (3) Constraints on the start-up characteristics of conventional units

[0276]

[0277]

[0278]

[0279]

[0280]

[0281]

[0282]

[0283]

[0284]

[0285]

[0286] In the formula: G is the set of conventional units in the network, including hydropower units and thermal power units; These are integer variables ranging from 0 to 1, representing whether unit g is in the power absorption, ramp-up, or maximum output stage, respectively. The startup time of unit g; Let g be the starting power of unit g; R is the power absorption time of unit g; g Let g be the ramp rate of unit g; This represents the maximum output power of unit g. As an auxiliary variable, equations (123)-(124) define it; T is the specified recovery period; Let M be the active power output of unit g at time t; M is a sufficiently large positive number.

[0287] Equation (117) indicates that the unit cannot be in the ramp-up phase and the maximum output phase simultaneously; Equation (118) indicates the time range corresponding to the power absorption phase of the unit; Equation (119) indicates that when hour, That is, the unit is in the ramp-up phase or the maximum output phase at this time; Equations (120)-(121) represent the time range corresponding to the ramp-up phase of the unit; Equation (122) represents the time range corresponding to the maximum output phase of the unit; Equations (123)-(124) define auxiliary variables. Equation (125) indicates that all units must be started before the total time period is restored; Equation (126) indicates the power generation capacity of unit g at time t.

[0288] (4) Start-up characteristics constraints of new energy power generation systems

[0289] There are two startup characteristic curves for the new energy power generation system, corresponding to the startup characteristic curves when the new energy power generation system is used as a black start power source and when it is not used as a black start power source, respectively. Integer variables are introduced to linearize the startup characteristic curves of the new energy power generation system piecewise.

[0290] 1) Linearization of the starting characteristic curve when new energy is used as a black start power source (e.g.) Figure 3 As shown, the curve at the top is the starting characteristic curve when the new energy source is used as a black start power source.

[0291]

[0292]

[0293]

[0294]

[0295]

[0296]

[0297]

[0298]

[0299] Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; These are integer variables (0-1), representing whether the new energy power generation system r is in a high-power output, ramp-up, or stable output phase, respectively. and The starting power and the time required to absorb power for the unit that requires the maximum starting energy in the system are determined by the unit's starting power and the time required for that unit to absorb power. This represents the initial power output of the new energy power generation system during the ramp-up phase. R is the predicted output value of the new energy power generation system r; r The ramp rate of the new energy power generation system r; Let r be the power output of the new energy power generation system at time t when it acts as a black-start power source.

[0300] Equation (127) indicates that a new energy power generation system cannot be in the high power output, ramp-up, or maximum output phase simultaneously; Equations (128)-(129) indicate the time range corresponding to the new energy power generation system being in the high power output phase; Equation (130) indicates that when... At that time, the new energy power generation system may be in the ramp-up or stable output stage; Equations (131)-(132) represent the time range corresponding to the new energy power generation system being in the ramp-up stage; Equation (133) represents the time range corresponding to the new energy power generation system being in the stable output stage; Equation (134) represents the power output of the new energy power generation system at time t when it is used as a black start power source.

[0301] 2) Linearization of the starting characteristic curve when new energy sources are not used as black-start power sources (e.g.) Figure 3 As shown, the lower curve is the starting characteristic curve when the new energy source is used as a black start power source.

[0302]

[0303]

[0304]

[0305]

[0306]

[0307]

[0308]

[0309]

[0310]

[0311]

[0312] Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; These are integer variables (0-1), representing whether the new energy power generation system r is in the power absorption, ramp-up, or stable output stage, respectively. The start-up time of the new energy power generation system r; The starting power of the new energy power generation system r; The time for the new energy power generation system to absorb power; R r The ramp rate of the new energy power generation system r; The predicted output value of the new energy power generation system r; As an auxiliary variable, it is defined by equations (141)-(142); T is the specified recovery period; Let r be the power output of the new energy power generation system at time t when it is not used as a black-start power source; M is a sufficiently large positive number.

[0313] Equation (135) indicates that a new energy power generation system cannot be in the ramp-up or maximum output phase simultaneously; Equation (136) indicates the time range corresponding to the new energy power generation system being in the power absorption phase; Equation (137) indicates that when... At that time, the new energy power generation system may be in the ramp-up or stable output stage; Equations (138)-(139) represent the time range corresponding to the new energy power generation system being in the ramp-up stage; Equation (140) represents the time range corresponding to the new energy power generation system being in the stable output stage; Equations (141)-(142) define auxiliary variables. Equation (143) indicates that all new energy power generation systems must be started before the total recovery period; Equation (144) indicates the power output of the new energy power generation system at time t when it is not used as a black start power source.

[0314] To establish logical constraints for selecting the startup characteristic curve of the renewable energy generation system in the event of a power outage, integer 0-1 variables are introduced to represent the selection of the startup characteristic curve:

[0315]

[0316]

[0317]

[0318]

[0319] Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; The options are as follows: using a new energy power generation system as a black start power source and not using it as a black start power source. This indicates the selection of a new energy power generation system as the black start power source. This indicates that the new energy power generation system will not be used as a black start power source; These are integer variables ranging from 0 to 1, representing the three stages of the two startup characteristic curves, respectively; The actual output power of the new energy power generation system r at time t; This represents the actual output power of the new energy power generation system at time t when it is used as a black-start power source; This represents the actual output power of the new energy power generation system at time t when it is not used as a black-start power source.

[0320] Equation (145) indicates that any new energy power generation system can only select one startup characteristic; Equations (146)-(147) indicate that the startup characteristics of the new energy power generation system that are not selected are all 0, and the actual output corresponding to the startup characteristic is 0; Equation (148) indicates the actual output power of the new energy power generation system.

[0321] (5) Output constraints of conventional units

[0322]

[0323]

[0324] In the formula: T is the total recovery period; G is the set of conventional units in the network, including hydropower units and thermal power units; It is a 0-1 integer variable, representing the energized state of unit g at time t; These represent the active and reactive power outputs of unit g at time t, respectively. These are the upper and lower limits of the active power output of unit g, respectively; These represent the upper and lower limits of the unit's reactive power output g, respectively.

[0325] Equation (149) represents the upper and lower limits of the active power output of the unit at time t; Equation (150) represents the upper and lower limits of the reactive power output of the unit at time t.

[0326] (6) Output constraints of new energy power generation systems

[0327]

[0328]

[0329] In the formula: T is the total recovery period; G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; Let be the active and reactive power outputs of the new energy power generation system r at time t, respectively, and equal to the sum of the output of the new energy generator units and the charging and discharging power of the energy storage devices in system r. This is a 0-1 integer variable representing the energization state of the new energy power generation system r; These represent the upper and lower limits of the active power output of the new energy power generation system. These represent the upper and lower limits of reactive power output of the new energy power generation system, respectively.

[0330] Equation (151) represents the upper and lower limits of the active power output of the new energy power generation system at time t; Equation (152) represents the upper and lower limits of the reactive power output of the new energy power generation system at time t.

[0331] Wind turbines, photovoltaic generators, and energy storage devices in new energy power generation systems must meet the following conditions:

[0332] 1) Wind turbine output constraints

[0333]

[0334]

[0335] In the formula: T is the total recovery period; R is the set of all new energy generator units in the network, including wind turbines and photovoltaic generator units; These are the predicted active and reactive power outputs of the wind turbine w at time t, respectively. This is a 0-1 integer variable representing the energized state of the wind turbine w. These represent the upper and lower limits of the active power output of the wind turbine unit (w); These represent the upper and lower limits of the reactive power output of the wind turbine generator (w).

[0336] Equation (153) represents the upper and lower limits of the active power output of the wind turbine at time t; Equation (154) represents the upper and lower limits of the reactive power output of the wind turbine at time t.

[0337] 2) Output constraints of photovoltaic generator sets

[0338]

[0339]

[0340] In the formula: T is the total recovery period; R is the set of all new energy generator units in the network, including wind turbines and photovoltaic generator units; These are the predicted active and reactive power outputs of photovoltaic generator unit p at time t, respectively. This is a 0-1 integer variable representing the energization state of the photovoltaic generator set p; These represent the upper and lower limits of the active power output p of the photovoltaic generator set; These represent the upper and lower limits of the reactive power output p of the photovoltaic generator set.

[0341] Equation (155) represents the upper and lower limits of the active power output of the photovoltaic generator set at time t; Equation (156) represents the upper and lower limits of the reactive power output of the photovoltaic generator set at time t.

[0342] 3) Constraints of energy storage devices

[0343]

[0344]

[0345]

[0346]

[0347]

[0348]

[0349] In the formula: S is the set of all energy storage devices in the network; These are the charging power and discharging power of the energy storage device s at time t, respectively. These are the upper limit thresholds for the charging power and discharging power of the energy storage device s, respectively. These represent the charging and discharging states of the energy storage device s at time t, respectively. Let be the charging and discharging power of the energy storage device s at time t; Let be the energy of energy storage device s at time t; These are the charging and discharging efficiencies of the energy storage device s, respectively. These are the upper and lower energy thresholds for the energy storage device s, respectively.

[0350] Equations (157)-(162) represent the power, charge / discharge state and energy constraint of the energy storage device.

[0351] (7) Single load constraint

[0352]

[0353] Where: T is the total recovery period; N is the set of all nodes in the network; G is the set of conventional units in the network, including hydropower units and thermal power units; Let Δf be the active power of the load that has been restored at node i at time t; max This represents the maximum allowable frequency deviation for normal system operation. The rated active power of unit g; f is a 0-1 integer variable representing the energization state of unit g at time t; g Let g be the frequency response value of unit g.

[0354] Equation (163) represents the maximum load fluctuation that the unit can withstand when the single load input is less than or equal to the maximum frequency deviation.

[0355] (8) Network recovery status constraints

[0356]

[0357]

[0358]

[0359]

[0360]

[0361]

[0362]

[0363]

[0364]

[0365]

[0366] In the formula: N is the set of all nodes in the network; L is the set of all lines in the network; G is the set of conventional generating units in the network, including hydroelectric generating units and thermal generating units; G R G is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; RNBSThis refers to the collection of non-blacklisted new energy power generation systems in the network. and These represent the recovery states of node i, generator g, renewable energy generation system r, and line l within sub-region α at time t, respectively; T l The time taken to restore a line; M is a sufficiently large positive number.

[0367] Equations (164)-(169) represent the recovery conditions of lines, nodes, generators and new energy power generation systems in the network, respectively; Equations (170)-(173) represent the conditions under which nodes, generators, new energy power generation systems and lines will not be disconnected after recovery.

[0368] (9) Sub-cell connection line restoration constraints

[0369]

[0370]

[0371]

[0372] Where: N NBS N represents the set of nodes for all non-black-start generator units within the network; including thermal power unit nodes and non-black-start renewable energy power generation system nodes; D N represents the set of all critical load nodes within the network. NBS_D N is the set of all non-black-start units and critical load nodes within the network; V L is the set of nodes at both ends of all sub-area link lines within the network. v It is the set of all sub-area contact lines within the network; It is a 0-1 integer variable, representing the state variable of whether all non-black start unit nodes in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the state variable of whether all critical load nodes i in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the state variable of whether all non-black start unit nodes and critical load nodes in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the endpoint recovery state of all sub-region connection lines within sub-region α at time t; T is a 0-1 integer variable representing the recovery state of sub-region α connection line l at time t; l The time taken to restore a line.

[0373] Equation (174) indicates that at the initial moment of system recovery, all sub-area tie lines are in a disconnected state; Equations (175)-(176) indicate the conditions that need to be met for the sub-area tie line to be restored, namely, all non-black start unit nodes, critical load nodes, and nodes at both ends of the sub-area tie line in the sub-area have been restored, and then after Tl Only then can the sub-area connection line be restored.

[0374] (10) System operation constraints

[0375]

[0376]

[0377] In the formula: N is the set of all nodes in the network; θ max θ min These are the upper and lower limits of the voltage phase angle at node i, respectively; Let be the voltage phase angle of node i at time t; These are the upper and lower limits of the phase angle of line l, respectively; U max U min These are the upper and lower limits of the voltage amplitude at node i, respectively; Let be the voltage amplitude at node i at time t; These are the upper and lower limits of the voltage amplitude deviation for line l, respectively.

[0378] Equation (177) represents the upper and lower limits of voltage phase angle for nodes and lines; Equation (178) represents the upper and lower limits of voltage amplitude for nodes and lines.

[0379] (11) System power constraints

[0380]

[0381]

[0382] In the formula: These represent the active and reactive power outputs of unit g at time t, respectively. These represent the active and reactive power outputs of the new energy power generation system r at time t, respectively. B is a 0-1 integer variable representing the recovery state of line l at time t; l V represents the susceptance of line l; V represents the voltage level of the line.

[0383] Equation (179) indicates that the system's power generation capacity is always greater than or equal to 0; Equation (180) indicates that the generator sets in the system can absorb the reactive power generated by the recovery path to alleviate the overvoltage problem during the recovery process.

[0384] S4: Based on the objective function and constraints given in S1, S2 and S3, a two-stage optimization model for parallel recovery of power grid partitions considering multi-source collaboration is constructed in Matlab using the Yamip toolbox. The recovery sequence and recovery time of each generator set, transmission line and power load in the power outage grid are obtained by using the Cplex solver.

[0385] In summary, this invention determines whether wind-storage and solar-storage power generation systems can function as black-start power sources by identifying the basic conditions for new energy power generation systems to participate in black-start power generation, thereby determining the number and type of black-start power sources in a power outage grid. Based on the principle of multi-source synergy of wind, solar, hydro, and storage as black-start power sources, a first-stage grid partition optimization model based on network flow theory and a second-stage grid partition parallel recovery optimization model considering multi-source synergy are established. This fully utilizes the black-start capabilities of wind-storage and solar-storage power generation systems, improving the overall recovery capability of the power outage grid and accelerating the system recovery process. Therefore, the technical solution proposed in this invention solves the problems mentioned in the background art.

[0386] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration, characterized in that, Includes the following steps: S1: Based on the power requirements of non-black-start thermal power units, propose the basic conditions for new energy power generation systems to participate in black start, and determine the number and type of black-start power sources; S2: Construct the first-stage power grid zoning optimization model based on network flow theory. Specifically, the optimization objective is to minimize the number of sub-region tie lines. The constraints include black-start power source constraints, sub-region connectivity constraints, sub-region power balance constraints, and special line disconnection constraints within the sub-region. S3: Based on step S2, establish a second-stage grid partition parallel recovery optimization model that considers multi-source collaboration, and incorporate the selection logic of the start-up characteristic curve of the new energy power generation system into the model. The second-stage grid partition parallel recovery optimization model that considers multi-source collaboration takes minimizing the total recovery time and load recovery loss of all thermal power units as the optimization objective. The constraints of the second-stage grid partition parallel recovery optimization model that considers multi-source collaboration include node power balance constraints, line power flow constraints, and network recovery state constraints. S4: Solve the first stage of the power grid partition optimization model based on network flow theory and the second stage of the power grid partition parallel recovery optimization model considering multi-source collaboration to obtain the recovery sequence and recovery time of each generator set, transmission line and power load in the power outage power grid.

2. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 1, characterized in that, The new energy power generation system includes wind-storage power generation system and photovoltaic-storage power generation system. The basic conditions for the new energy power generation system to participate in black start include the basic conditions that the wind-storage power generation system and the photovoltaic-storage power generation system must meet as black start power sources.

3. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 2, characterized in that, The basic conditions that a wind-storage power generation system must meet as a black start power source are as follows: Where: G NBS The set of non-black-start thermal power units within the network; The minimum capacity requirement for wind-storage power generation systems (WS) to participate in black start; The starting power of non-black start thermal power unit g; The time for a non-black start thermal power unit (g) to absorb power; The minimum power requirement for the wind-storage power generation system ws to participate in black start; the coefficient ΔP% is the line loss rate; P ws_load This is for the self-consumption of the wind-storage power generation system; The operating constraints of the wind-storage power generation system are as follows: In the formula: These represent the upper and lower limits of the active power output of the wind-storage power generation system (WS). These represent the upper and lower limits of reactive power output from the wind-storage power generation system (WS). Let ws be the predicted active and reactive power output of the wind-storage power generation system at time t. T represents the total recovery period.

4. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 2, characterized in that, The basic conditions that the photovoltaic-storage power generation system must meet as a black-start power source are as follows: In the formula: G NBS The set of non-black-start thermal power units within the network; The minimum capacity requirement for photovoltaic-storage power generation systems (PS) to participate in black start; The starting power of non-black start thermal power unit g; The time for a non-black start thermal power unit (g) to absorb power; The minimum power requirement for a photovoltaic-storage power generation system (PS) to participate in black start; the coefficient ΔP% is the line loss rate; P ps_load This is for the self-consumption of the photovoltaic-storage power generation system; The operating constraints of the photovoltaic-energy storage power generation system are as follows: In the formula: These are the upper and lower limits of the active power output of the photovoltaic-storage power generation system (PS). These are the upper and lower limits of reactive power output from the photovoltaic-storage power generation system (PS). These are the predicted active and reactive power outputs of the photovoltaic-storage power generation system at time t, respectively. T represents the total recovery period.

5. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 1, characterized in that, The objective function of the power grid zoning optimization model based on network flow theory in the first stage is as follows: In the formula: L is the set of all lines in the network; α is the α-th sub-region in the network, α = 1, 2, ..., m; z iα z is a 0-1 integer variable representing the subregion α to which node i belongs; jα This is a 0-1 integer variable representing the subregion α to which node j belongs; The specific constraints on the black-start power supply within the sub-region are as follows: In the formula: N is the set of all nodes in the network; N αBS Let i be the set of black-start power nodes for subregion α; α For sub-region α, the black-start power node; The specific sub-region connectivity constraints are as follows: In the formula: f ijα The auxiliary decision variable introduced represents the size of the network flow from node i to node j in subregion α, and is a non-negative variable; M is a sufficiently large positive number; i α N is the black-start power node for sub-region α; αBS Let z be the set of black-starting power nodes for subregion α; iα This is a 0-1 integer variable representing the subregion α to which node i belongs; The power balance constraints within the sub-region are as follows: Where: G NBS This refers to the set of non-black-start thermal power units in the network. This represents the maximum output of the thermal power unit located at node i; ρ i A 0-1 integer variable, representing the critical load situation of load node i. If ρ i =1, then node i is a critical load node, if ρ i =0, then node i is a normal load node; P di The active power requirement for critical load i; The specific constraints for the special line disconnection are as follows: In the formula: α=1,2,...,m; z iα z is a 0-1 integer variable representing the subregion α to which node i belongs; jα e is a 0-1 integer variable representing the subregion α to which node j belongs; ijα This refers to the case of sub-region α to which line (i,j) belongs.

6. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 5, characterized in that, The objective function of the second-stage grid partition parallel recovery optimization model considering multi-source collaboration is as follows: Where: G NBS Let N be the set of all non-black-start thermal power units in the network; N is the set of all nodes in the network. The time it takes for a non-black-start thermal power unit (g) to obtain starting power; The time for a non-black-start thermal power unit to absorb power (g); P di Let i be the active power load requirement of node i; Let be the active power of the load that has been restored at node i at time t; The constraints of the second-stage grid partition parallel recovery optimization model considering multi-source collaboration also include constraints on the start-up characteristics of conventional units, output constraints of conventional units, output constraints of new energy power generation systems, single load input constraints, sub-region tie-line recovery constraints, system operation constraints, and system power constraints. The specific node power balance constraints are as follows: In the formula: G(i) is the set of conventional generating units located at node i, including hydropower units and thermal power units; G R Let L be the set of all new energy power generation systems in the network; L(i) is the set of lines connected to node i. These represent the active and reactive power of the load that has been restored at node i at time t, respectively. These represent the active and reactive power outputs of unit g at time t, respectively. It is a 0-1 integer variable, representing the energized state of unit g at time t; Let g be the starting power of unit g; These represent the active and reactive power outputs of the new energy generator unit r at time t, respectively. This is a 0-1 integer variable representing the energizing state of the new energy generator unit r at time t; The starting power of the new energy power generation system r; This indicates that the selected renewable energy power generation system will not be used as a black start power source; P l t , These represent the active and reactive power flowing from node i to node j on line l at time t; P di Let i be the active power load requirement of node i; is a 0-1 integer variable representing the recovery state of node i at time t; T represents the total recovery time period; The specific power flow constraints for the lines are as follows: In the formula: T represents the specified recovery period; N is the set of all nodes in the network; L(i) is the set of lines connected to node i; It is a 0-1 integer variable, representing the recovery state of the line at time t; These represent the upper and lower limits of active and reactive power that the line is allowed to flow through; G ij B ij Let be the conductance and susceptance of line (i,j), respectively. Let be the voltage amplitude at node i at time t; Let be the voltage phase angle of node i at time t; The specific constraints on the start-up characteristics of conventional generating units are as follows: In the formula: G is the set of conventional units in the network, including hydropower units and thermal power units; Variables are integers between 0 and 1; The startup time of unit g; Let g be the starting power of unit g; R is the power absorption time of unit g; g Let g be the ramp rate of unit g; This represents the maximum output power of unit g. As an auxiliary variable; T represents the specified recovery period; Let M be the active power output of unit g at time t; M is a sufficiently large positive number. The specific output constraints of the conventional generating units are as follows: In the formula: T is the total recovery period; G is the set of conventional units in the network, including hydropower units and thermal power units; It is a 0-1 integer variable, representing the energized state of unit g at time t; These represent the active and reactive power outputs of unit g at time t, respectively. These are the upper and lower limits of the active power output of unit g, respectively; These are the upper and lower limits of the unit's reactive power output (g), respectively. The specific output constraints of the new energy power generation system are as follows: In the formula: T is the total recovery period; G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; Let be the active and reactive power outputs of the new energy power generation system r at time t, respectively, and equal to the sum of the output of the new energy generator units and the charging and discharging power of the energy storage devices in system r. This is a 0-1 integer variable representing the energization state of the new energy power generation system r; These represent the upper and lower limits of the active power output of the new energy power generation system. These represent the upper and lower limits of reactive power output of the new energy power generation system, respectively. The specific constraints on the single load input are as follows: In the formula: T is the total recovery period; N is the set of all nodes in the network; G is the set of conventional units in the network, including hydropower units and thermal power units; Let Δf be the active power of the load that has been restored at node i at time t; max This represents the maximum allowable frequency deviation for normal system operation. The rated active power of unit g; f is a 0-1 integer variable representing the energization state of unit g at time t; g This represents the frequency response value of unit g. The specific network recovery status constraints are as follows: In the formula: N is the set of all nodes in the network; L is the set of all lines in the network; G is the set of conventional generating units in the network, including hydroelectric generating units and thermal generating units; G R G is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; RNBS This refers to the collection of non-blacklisted new energy power generation systems in the network. and The recovery states of node i, generator g, renewable energy generation system r, and line l within sub-region α at time t are respectively; T l The time taken to restore a line; M is a sufficiently large positive number; The specific constraints for restoring the sub-regional connection line are as follows: Where: N NBS N represents the set of nodes for all non-black-start generator units within the network; including thermal power unit nodes and non-black-start renewable energy power generation system nodes; D N represents the set of all critical load nodes within the network. NBS_D N is the set of all non-black-start units and critical load nodes within the network; V L is the set of nodes at both ends of all sub-area link lines within the network; v It is the set of all sub-area contact lines within the network; It is a 0-1 integer variable, representing the state variable of whether all non-black start unit nodes in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the state variable of whether all critical load nodes i in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the state variable of whether all non-black start unit nodes and critical load nodes in sub-region α have recovered at time t; It is a 0-1 integer variable, representing the endpoint recovery state of all sub-region connection lines within sub-region α at time t; T is a 0-1 integer variable representing the recovery state of sub-region α connection line l at time t; l The time taken to restore a line; The specific system operation constraints are as follows: In the formula: N is the set of all nodes in the network; θ max θ min These are the upper and lower limits of the voltage phase angle at node i, respectively; Let be the voltage phase angle of node i at time t; These are the upper and lower limits of the phase angle of line l, respectively; U max U min These are the upper and lower limits of the voltage amplitude at node i, respectively; Let be the voltage amplitude at node i at time t; These are the upper and lower limits of the voltage amplitude deviation of line l, respectively; The specific system power constraints are as follows: In the formula: These represent the active and reactive power outputs of unit g at time t, respectively. These represent the active and reactive power outputs of the new energy power generation system r at time t, respectively. B is a 0-1 integer variable representing the recovery state of line l at time t; l V represents the susceptance of line l; V represents the voltage level of the line.

7. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 6, characterized in that, The second stage of the grid partition parallel recovery optimization model considering multi-source collaboration also includes constraints on the start-up characteristics of the new energy power generation system. The constraints on the start-up characteristics of the new energy power generation system include two cases: linearization of the start-up characteristic curve when new energy is used as a black start power source and linearization of the start-up characteristic curve when new energy is not used as a black start power source. The linearization of the startup characteristic curve when the new energy source is used as a black-start power source is as follows: Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; These are integer variables (0-1), representing whether the new energy power generation system r is in a high-power output, ramp-up, or stable output phase, respectively. and The starting power and the time required to absorb power for the unit that requires the maximum starting energy in the system are determined by the unit's starting power and the time required for that unit to absorb power. This represents the initial power output of the new energy power generation system during the ramp-up phase. R is the predicted output value of the new energy power generation system r; r The ramp rate of the new energy power generation system r; Let r be the power output of the new energy power generation system at time t when it acts as a black-start power source; The linearization of the startup characteristic curve when the new energy source is not used as a black-start power source is as follows: Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; These are integer variables (0-1), representing whether the new energy power generation system r is in the power absorption, ramp-up, or stable output stage, respectively. The start-up time of the new energy power generation system r; The starting power of the new energy power generation system r; The time for the new energy power generation system to absorb power; R r The ramp rate of the new energy power generation system r; The predicted output value of the new energy power generation system r; As auxiliary variables, equations (51)-(52) define them; T represents the specified recovery period; Let r be the power output of the new energy power generation system at time t when it is not used as a black-start power source; M is a sufficiently large positive number.

8. The two-stage optimization method for parallel recovery of power grid zones considering multi-source collaboration as described in claim 7, characterized in that, The selection logic for the startup characteristic curve of the new energy power generation system is as follows: Where: G R It is the collection of all new energy power generation systems in the network, including wind-storage power generation systems and solar-storage power generation systems; The options are as follows: using a new energy power generation system as a black start power source and not using it as a black start power source. This indicates that a new energy power generation system has been selected as the black start power source. This indicates that the new energy power generation system will not be used as a black start power source; These are integer variables ranging from 0 to 1, representing the three stages of the two startup characteristic curves, respectively; The actual output power of the new energy power generation system r at time t; This represents the actual output power of the new energy power generation system at time t when it is used as a black-start power source; This represents the actual output power of the new energy power generation system at time t when it is not used as a black-start power source.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device containing the computer-readable storage medium to perform the two-stage optimization method for parallel recovery of power grid partitions considering multi-source collaboration as described in any one of claims 1 to 8.

10. A processor, characterized in that, The processor is used to run a program, wherein the program executes the two-stage optimization method for parallel recovery of power grid partitions considering multi-source collaboration as described in any one of claims 1 to 8.

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