Optimal unit combination method and device considering spatial distribution characteristics of inertia-frequency change rate

Abstract

The optimal unit combination method and device considering the spatial distribution characteristics of inertia-frequency change rate include: extending the traditional DC power flow model to the nodes after the internal reactance of the generator, constructing the inertial response process model of different nodes and analyzing the injected power and phase angle change coupling relationship of the generator node and the load node at the moment after the disturbance; establishing the inertia-frequency change rate spatial distribution model according to the characteristics of different nodes; combining the inertia-frequency change rate spatial distribution model established in the previous step, comprehensively considering the spatial characteristics and inertia distribution of the power grid topology, and constructing the optimal unit combination scheduling model based on satisfying the frequency safety constraints and steady-state constraints of the power grid nodes. The present invention improves the frequency stability of the system after a major disturbance.

Description

Technical Field

[0001] The invention relates to an optimal unit combination method and device taking into account the spatial distribution characteristics of inertia-frequency change rate. Background Art

[0002] In order to characterize the frequency transient change process after a fault occurs, the center of inertia (COI) model is widely used to simplify the frequency response analysis of complex power systems. The COI model approximates the overall frequency response behavior of the power grid after a large disturbance by weighted averaging the rotor speed of the synchronous generator of the entire system. The application of this model not only greatly reduces the computational difficulty of complex power system analysis, but also provides a theoretical basis for frequency control and optimal scheduling. However, with the large-scale access of renewable energy, the distribution of inertia in the system has become increasingly uneven, resulting in significant differences in the frequency transient behavior of different nodes. This difference makes the traditional scheduling method based on the center of inertia face many challenges in the frequency control of modern power systems, and it is gradually difficult to meet the needs of practical applications. In this context, it is urgent to explore more refined models and methods to deal with the problem of frequency control in complex systems with low inertia and uneven inertia distribution.

[0003] At the moment of fault occurrence, the frequency change rate at different nodes of the power grid is not the same. Its distribution depends not only on the location of the fault, but also on the distribution of inertia in the entire system and the topology and parameters of the transmission line. Therefore, even if the frequency change rate after the fault of the system inertia center is within the safe range, there may still be some nodes where the frequency change rate exceeds the safety threshold and induces secondary accidents such as new energy disconnection and unit tripping. Summary of the invention

[0004] In order to overcome the above-mentioned shortcomings of the prior art, the present invention proposes an optimal unit combination method and device that includes safety constraints on the frequency change rates of all system nodes, aiming to optimize the distribution of inertia in the entire system by reasonably scheduling the start and stop states of the units, thereby ensuring that the frequency change rates of all system nodes after a fault are always within a safe range.

[0005] To this end, the present invention first establishes an inertia-frequency change rate spatial distribution model to analyze the changes in the injected power and voltage phase angle of each node in the power grid immediately after the fault. On this basis, a safety constraint on the frequency change rate of the power grid node considering the start and stop state of the unit is derived and constructed, and the constraint is linearized and applied to the unit combination optimization problem. The proposed unit combination method can ensure the stability of the frequency change rate of all system nodes in the event of a power grid fault.

[0006] In order to achieve the above object, the technical solution of the present invention is:

[0007] The optimal unit combination method and device considering the spatial distribution characteristics of inertia-frequency change rate include the following steps:

[0008] S1: Extend the traditional DC power flow model to the nodes behind the internal reactance of the generator, build the inertial response process model of different nodes and analyze the coupling relationship between the injected power and phase angle change of the generator node and the load node immediately after the disturbance; establish the inertia-frequency change rate spatial distribution model according to the characteristics of different nodes;

[0009] S2: Combined with the inertia-frequency change rate spatial distribution model established in the previous step, the spatial characteristics of the power grid topology and the inertia distribution are comprehensively considered to construct an optimal unit combination scheduling model based on satisfying the power grid node frequency safety constraints and steady-state constraints.

[0010] Furthermore, in step S1, the inertia-frequency change rate spatial distribution model constructed is specifically as follows:

[0011] S1-1: Expand the DC power flow equation, extend the traditional DC power flow model to the nodes behind the internal reactance of the generator, and then analyze the changes in the injected power and voltage phase angle of each node in the power grid after the fault. The specific expansion steps are as follows:

[0012] Assume that the system is At the same time, the traditional DC power flow model is extended to the nodes behind the internal reactance of the generator, and the coupling relationship between the power injection and phase angle changes of each node in the power grid can be obtained immediately after the disturbance. Generator For a node power grid, the coupling relationship between the power and phase angle changes of each node can be expressed as:

[0013] (1)

[0014] (2)

[0015] (3)

[0016] Where: and They represent the injected power and electromotive force phase angle of the virtual node after the internal reactance of the generator. dimensional column vector; and They represent the injected power and voltage phase angle of the load node respectively. dimensional column vector; and Respectively represent the moments before and after the fault occurs; , and is the susceptance matrix obtained after considering the internal reactance of the generator; represents the network node susceptance matrix, whose diagonal elements augment the internal reactance of the synchronous motor on the generator bus. It is worth noting that Each system node is a load node. The generators were expanded to The virtual node after the internal reactance of the generator is referred to as the generator node hereinafter.

[0017] S1-2: Construct an inertial response process model of the generator node at the moment of disturbance: For online generator sets, due to the inertia of the generator rotor itself, its phase angle will not change suddenly at the moment of disturbance. However, if the generator is in a shutdown state, the corresponding generator node will be regarded as a node without inertia. At this time, the phase angle of the node may change in a step at the moment of disturbance. The phase angle change of the generator node considering the start-stop state can be expressed as follows:

[0018] (4)

[0019] (5)

[0020] Where: is a 0-1 variable, indicating the The on / off status of the generator; , the generator is in the start-up state; , the generator is in shutdown state; For the Phase angle change of each generator node; is an auxiliary variable introduced, whose value is only in , that is, it is meaningful only when the generator is shut down. According to formula (5), if , then the generator node The inertia on will prevent the sudden change of phase angle immediately after the disturbance occurs, that is, ;like , the generator is in a stopped state. At this time, the generator node is a node without inertia, and the sudden change of its phase angle at the moment of disturbance is , whose value depends on the system operating state immediately after the disturbance occurs.

[0021] At the same time, the injected power of all generator nodes in the system can be expressed as:

[0022] (6)

[0023] In the formula, Indicates the instant after the disturbance occurs The change in electromagnetic power of the generator, that is, the column vector The It is worth noting that the electromagnetic power injected into the generator node is positive according to the assumed positive direction of the injected power.

[0024] Unlike electromagnetic power, the mechanical power of the generator will not change at the instant of a fault due to the limitations of the governor and the dynamic performance of the turbine, that is:

[0025] (7)

[0026] In the formula, Indicates the instant after the disturbance occurs The change of the mechanical power of a generator relative to its steady-state value before the fault. According to the swing equation, the frequency change rate of the generator node can be further obtained:

[0027] (8)

[0028] In the formula, Indicates the instant after the disturbance occurs Frequency change rate of each generator node; Indicates The inertia constant of the generator; is the set of generator nodes.

[0029] Consider the on / off status of the generator , modify formula (8) as follows:

[0030] (9)

[0031] When the generator is in the on state ( ), equation (9) will degenerate into the swing equation shown in equation (8), and the frequency change rate of the node after the disturbance is constrained by the rotor inertia and mechanical power and electromagnetic power. ), the electromagnetic power of the generator after the disturbance occurs can be obtained from formula (9): is 0, which is consistent with the facts.

[0032] Equations (4) to (7) and (9) together constitute the frequency change rate model of the generator node at the moment the disturbance occurs.

[0033] S1-3: Establish the inertial response process model of the load node at the moment of disturbance: In the transient process of the power grid after the disturbance occurs, the power consumption of the load node can be approximately considered unchanged. Therefore, except for the node where the disturbance occurs, the change in the power consumption of other nodes is 0, and the corresponding node injection power column vector can be expressed as:

[0034] (10)

[0035] (11)

[0036] In the formula, Indicates the disturbance node The power change at the node, that is, the node injection power column vector The elements of size ; is the set of load nodes.

[0037] Substituting equation (10) and equation (11) into equation (1), we can obtain the following simplified formula:

[0038] (12)

[0039] By taking the time derivative of equation (12), we can obtain the coupling relationship between the frequency change rate of the load node and the generator node.

[0040] (13)

[0041] In the formula, and are the frequency change rate column vectors of the load node and the generator node immediately after the disturbance. It can be seen from formula (13) that the frequency change rate of all load nodes immediately after the disturbance can be linearly expressed by the frequency change rate of the generator node.

[0042] Furthermore, in step S2, the optimal unit commitment dispatching model based on steady-state constraints and node frequency change rate safety constraints is established by comprehensively considering the grid node frequency change rate and inertia distribution spatial characteristics as follows:

[0043] S2-1: Objective function setting: As shown in formula (14), the objective function of the unit combination includes the power generation cost, start-up and shutdown cost, and standby cost of the generator. Among them, the power generation cost adopts a quadratic model.

[0044] (14)

[0045] In the formula, is the number of scheduling periods; , and Respectively The various coefficients of power generation cost of each generator; Indicates Generators in Output power during the time period; is a 0-1 variable indicating the start and stop status of the unit. Indicates Generators in The system is in online operation during the period. Indicates Generators in The device is in off-grid shutdown state during the period; and is a 0-1 variable indicating the start and stop operation of the unit. Generators in If the machine is turned on (off) during the time period, the value is 1, otherwise the value is 0; and Respectively The startup and shutdown cost coefficients of a generator. and Respectively Generators in The size of spinning reserve and unit reserve cost factor provided during the period.

[0046] S2-2: Set the optimal unit combination steady-state operation constraints:

[0047] 1) Unit start and stop constraints

[0048] The generator set should not be started and stopped frequently within a day, that is, the generator set must remain in the start or stop state for a certain period of time before changing its current operating state. The following minimum start and stop time constraints are established accordingly:

[0049] (15)

[0050] (16)

[0051] (17)

[0052] Where: and Indicates Minimum start-up and shutdown time of each generator.

[0053] 2) Unit output constraints

[0054] Due to the limitation of boiler technology, the backup capacity and output power that synchronous generator sets can provide are subject to the constraints of maximum and minimum output power:

[0055] (18)

[0056] (19)

[0057] In the formula, and Respectively The upper and lower limits of the output power of the generator.

[0058] 3) Power flow balance constraints

[0059] In any dispatching period, the steady-state system must satisfy the power flow balance condition as shown below.

[0060] (20)

[0061] In the formula, For Column vector of power injected into each generator node during the time period; For Column vector of the power injected into each load node during the time period.

[0062] 4) Post-fault steady-state power balance constraints

[0063] In order to ensure that the generator set can still meet the power requirements of all loads after a sudden failure of the power grid, the following power balance constraints are established.

[0064] (twenty one)

[0065] In the formula, and Respectively Output power and spare capacity of each generator; is the total load demand of the system.

[0066] S2-3: Set the optimal unit combination node frequency change rate safety constraint:

[0067] In the inertia response phase after the disturbance occurs, the rotor inertia of all online generator sets will independently support the node frequency stability of the system. The corresponding node frequency change rate constraint is as follows:

[0068] (twenty two)

[0069] (twenty three)

[0070] (twenty four)

[0071] In the formula, Indicates Generators in the dispatch interval The start and stop state variables within; and Respectively in Frequency change rate of generator node and load node immediately after the period disturbance; It is the maximum value of the frequency change rate that can be tolerated for safe operation of the system.

[0072] It is worth noting that the generator start and stop state variables is the decision variable of the established model. The value of the variable can be solved , , In particular, when any scheduling time interval When it is 0, the model introduces an unknown variable , however, through formula (22) we can get Therefore, regardless of the variable For any value, the number of equations in the model established by the present invention is always equal to the number of variables, so the model is solvable.

[0073] S2-4: Setting the optimal unit commitment method model considering the spatial distribution characteristics of inertia-frequency change rate Model linearization process:

[0074] In the constraints of the optimization model established above, there is a situation where continuous variables are multiplied by integer variables, which makes equations (5) and (9) nonlinear. They can be linearized by the big M method.

[0075] Assumptions is a 0-1 variable, is a continuous variable, is the product of the two, and the linearization process is as follows:

[0076] (25)

[0077] (26)

[0078] Where: For comparison A sufficiently large constant.

[0079] The beneficial effects of the present invention are:

[0080] 1. Aiming at the frequency stability problem caused by the high penetration of renewable energy in modern power systems, an optimal unit commitment method considering the inertia-frequency spatial distribution characteristics is proposed. By establishing an inertia-frequency spatial distribution model, and on this basis, a frequency change rate safety constraint is constructed and embedded into the optimal unit commitment problem. This method effectively improves the frequency stability of the system after a major disturbance, especially in power systems with low inertia and uneven inertia distribution. Compared with the traditional system inertia center model, the method of the present invention pays more attention to the frequency response differences of each node, so as to respond to emergencies more accurately.

[0081] 2. Through the verification of multiple simulation scenarios, the model proposed in this invention significantly reduces the risk of large-scale power outages caused by fault disturbances while maintaining the stable operation of the power system. Under the premise of meeting the full-node frequency safety constraints, the optimized dispatching strategy maximizes the balance between the economy and safety of the system, demonstrating the effectiveness and practicality of the model in practical applications.

[0082] 3. With the advancement of power marketization, the practicability of the present invention can also provide support for the frequency safety constraint unit dispatching strategy under the market environment, while ensuring that the system maintains a high level of security, further considering power market factors to reduce costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 This is the improved WSCC 3-machine 9-node system diagram of the present invention.

[0084] Figure 2(a) to Figure 2(d) 2(a) is a schematic diagram of the frequency change rate of each node at different moments of the present invention, wherein, FIG2(b) is a schematic diagram of the frequency change rate of each node at the moment when a power disturbance of 60MW occurs at node 5 at the 2nd hour, FIG2(c) is a schematic diagram of the frequency change rate of each node at the moment when a fault occurs at node 8 at the 4th hour, FIG2(d) is a schematic diagram of the frequency change rate of each node at the moment when a fault occurs at node 6 at the 7th hour, and FIG2(d) is a schematic diagram of the frequency change rate of each node at the moment when a disturbance of 60MW occurs at node 5 at the 10th hour.

[0085] Figure 3 This is a simplified model diagram of the Southeast Australia 14-unit power system.

[0086] Figures 4(a) to 4(b) are schematic diagrams of the frequency change rate of each node under different inertia level systems of the present invention, wherein Figure 4(a) is a schematic diagram of the node frequency change rate of the low inertia system node 402 when a power disturbance of 600MW occurs in region 4 at the 7th hour, and Figure 4(b) is a schematic diagram of the node frequency change rate of the high inertia system node 402 when a power disturbance of 600MW occurs in region 4 at the 7th hour.

[0087] Figure 5 It is a schematic diagram of the unit combination result considering the frequency safety constraint based on the central inertia of the present invention.

[0088] Figure 6 It is a schematic diagram of the unit combination result considering the frequency safety constraints of all nodes of the present invention.

[0089] Figures 7 (a) to 7 (b) are schematic diagrams of the node frequency change rate considering different frequency safety constraints of the present invention, wherein Figure 7 (a) is a schematic diagram of the node frequency change rate of the scheduling method based on central inertia, and Figure 7 (b) is a schematic diagram of the node frequency change rate after scheduling by the method proposed in the present invention.

[0090] Figure 8 It is a schematic diagram of the total output of the primary frequency regulation of the unit under different scenarios of the present invention.

[0091] Fig. 9 It is a schematic diagram of the device of the present invention.

[0092] Fig.10 It is a schematic diagram of the logic construction of the present invention. DETAILED DESCRIPTION

[0093] The present invention will be further described below in conjunction with the accompanying drawings.

[0094] Example 1

[0095] Reference Figures 1 to 10 , an optimal unit combination method and device considering the spatial distribution characteristics of inertia-frequency change rate, comprising the following steps:

[0096] S1: Extend the traditional DC power flow model to the nodes behind the internal reactance of the generator, build the inertial response process model of different nodes and analyze the coupling relationship between the injected power and phase angle change of the generator node and the load node immediately after the disturbance; establish the inertia-frequency change rate spatial distribution model according to the characteristics of different nodes;

[0097] S2: Combined with the inertia-frequency change rate spatial distribution model established in the previous step, the spatial characteristics of the power grid topology and the inertia distribution are comprehensively considered to construct an optimal unit combination scheduling model based on satisfying the power grid node frequency safety constraints and steady-state constraints.

[0098] In step S1, the inertia-frequency change rate spatial distribution model constructed is specifically as follows:

[0099] S1-1: Expand the DC power flow equation, extend the traditional DC power flow model to the nodes behind the internal reactance of the generator, and then analyze the changes in the injected power and voltage phase angle of each node in the power grid after the fault. The specific expansion steps are as follows:

[0100] Assume that the system is At the same time, the traditional DC power flow model is extended to the nodes behind the internal reactance of the generator, and the coupling relationship between the power injection and phase angle changes of each node in the power grid can be obtained immediately after the disturbance. Generator For a node power grid, the coupling relationship between the power and phase angle changes of each node can be expressed as:

[0101] (1)

[0102] (2)

[0103] (3)

[0104] Where: and They represent the injected power and electromotive force phase angle (variation) of the virtual node after the internal reactance of the generator. dimensional column vector; and They represent the injected power and voltage phase angle (variation) of the load node respectively. dimensional column vector; and Respectively represent the moments before and after the fault occurs; , and is the susceptance matrix obtained after considering the internal reactance of the generator; represents the network node susceptance matrix, whose diagonal elements augment the internal reactance of the synchronous motor on the generator bus. It is worth noting that Each system node is a load node. The generators were expanded to The virtual node after the internal reactance of the generator is referred to as the generator node hereinafter.

[0105] S1-2: Construct an inertial response process model of the generator node at the moment of disturbance: For online generator sets, due to the inertia of the generator rotor itself, its phase angle will not change suddenly at the moment of disturbance. However, if the generator is in a shutdown state, the corresponding generator node will be regarded as a node without inertia. At this time, the phase angle of the node may change in a step at the moment of disturbance. The phase angle change of the generator node considering the start-stop state can be expressed as follows:

[0106] (4)

[0107] (5)

[0108] Where: is a 0-1 variable, indicating the The on / off status of the generator; , the generator is in the start-up state; , the generator is in shutdown state; For the Phase angle change of each generator node; is an auxiliary variable introduced, whose value is only in , that is, it is meaningful only when the generator is shut down. According to formula (5), if , then the generator node The inertia on will prevent the sudden change of phase angle immediately after the disturbance occurs, that is, ;like , the generator is in a stopped state. At this time, the generator node is a node without inertia, and the sudden change of its phase angle at the moment of disturbance is , whose value depends on the system operating state immediately after the disturbance occurs.

[0109] At the same time, the injected power of all generator nodes in the system can be expressed as:

[0110] (6)

[0111] In the formula, Indicates the instant after the disturbance occurs The change in electromagnetic power of the generator, that is, the column vector The It is worth noting that the electromagnetic power injected into the generator node is positive according to the assumed positive direction of the injected power.

[0112] Unlike electromagnetic power, the mechanical power of the generator will not change at the instant of a fault due to the limitations of the governor and the dynamic performance of the turbine, that is:

[0113] (7)

[0114] In the formula, Indicates the instant after the disturbance occurs The change of the mechanical power of a generator relative to its steady-state value before the fault. According to the swing equation, the frequency change rate of the generator node can be further obtained:

[0115] (8)

[0116] In the formula, Indicates the instant after the disturbance occurs Frequency change rate of each generator node; Indicates The inertia constant of the generator; A collection of generator nodes.

[0117] Consider the on / off status of the generator , modify formula (8) as follows:

[0118] (9)

[0119] When the generator is on ( ), equation (9) will degenerate into the swing equation shown in equation (8), and the frequency change rate of the node after the disturbance is constrained by the rotor inertia and mechanical power and electromagnetic power. ), the electromagnetic power of the generator after the disturbance occurs can be obtained from formula (9): is 0, which is consistent with the facts.

[0120] Equations (4) to (7) and (9) together constitute the frequency change rate model of the generator node at the moment the disturbance occurs.

[0121] S1-3: Establish the inertial response process model of the load node at the moment of disturbance: In the transient process of the power grid after the disturbance occurs, the power consumption of the load node can be approximately considered unchanged. Therefore, except for the node where the disturbance occurs, the change in the power consumption of other nodes is 0, and the corresponding node injection power column vector can be expressed as:

[0122] (10)

[0123] (11)

[0124] In the formula, Indicates the disturbance node The power change at the node, that is, the node injection power column vector The elements of size ; is the set of load nodes.

[0125] Substituting equation (10) and equation (11) into equation (1), we can obtain the following simplified formula:

[0126] (12)

[0127] By taking the time derivative of equation (12), we can obtain the coupling relationship between the frequency change rate of the load node and the generator node.

[0128] (13)

[0129] In the formula, and are the frequency change rate column vectors of the load node and the generator node immediately after the disturbance. It can be seen from formula (13) that the frequency change rate of all load nodes immediately after the disturbance can be linearly expressed by the frequency change rate of the generator node.

[0130] Furthermore, in step S2, the optimal unit commitment dispatching model based on steady-state constraints and node frequency change rate safety constraints is established by comprehensively considering the grid node frequency change rate and inertia distribution spatial characteristics as follows:

[0131] S2-1: Objective function setting: As shown in formula (14), the objective function of the unit combination includes the power generation cost, start-up and shutdown cost, and standby cost of the generator. Among them, the power generation cost adopts a quadratic model.

[0132] (14)

[0133] In the formula, is the number of scheduling periods; , and Respectively The various coefficients of power generation cost of each generator; Indicates Generators in Output power during the time period; is a 0-1 variable indicating the start and stop status of the unit. Indicates Generators in The system is in online operation during the period. Indicates Generators in The device is in off-grid shutdown state during the period; and is a 0-1 variable indicating the start and stop operation of the unit. Generators in If the machine is turned on (off) during the time period, the value is 1, otherwise the value is 0; and Respectively The startup and shutdown cost coefficients of each generator; and Respectively Generators in The size of spinning reserve and unit reserve cost factor provided during the period.

[0134] S2-2: Set the optimal unit combination steady-state operation constraints:

[0135] 3) Unit start and stop constraints

[0136] The generator set should not be started and stopped frequently within a day, that is, the generator set must remain in the start or stop state for a certain period of time before changing its current operating state. The following minimum start and stop time constraints are established accordingly:

[0137] (15)

[0138] (16)

[0139] (17)

[0140] Where: and Indicates Minimum start-up and shutdown time of each generator.

[0141] 4) Unit output constraints

[0142] Due to the limitation of boiler technology, the backup capacity and output power that synchronous generator sets can provide are subject to the constraints of maximum and minimum output power:

[0143] (18)

[0144] (19)

[0145] In the formula, and Respectively The upper and lower limits of the output power of the generator.

[0146] 3) Power flow balance constraints

[0147] In any dispatching period, the steady-state system must satisfy the power flow balance condition as shown below.

[0148] (20)

[0149] In the formula, For Column vector of power injected into each generator node during the time period; For Column vector of the power injected into each load node during the time period.

[0150] 4) Post-fault steady-state power balance constraints

[0151] In order to ensure that the generator set can still meet the power requirements of all loads after a sudden failure of the power grid, the following power balance constraints are established.

[0152] (twenty one)

[0153] In the formula, and Respectively Output power and spare capacity of each generator; is the total load demand of the system.

[0154] S2-3: Set the optimal unit combination node frequency change rate safety constraint:

[0155] In the inertia response phase after the disturbance occurs, the rotor inertia of all online generator sets will independently support the node frequency stability of the system. The corresponding node frequency change rate constraint is as follows:

[0156] (twenty two)

[0157] (twenty three)

[0158] (twenty four)

[0159] In the formula, Indicates Generators in the dispatch interval The start and stop state variables within; and Respectively in Frequency change rate of generator node and load node immediately after the period disturbance; It is the maximum value of the frequency change rate that can be tolerated for safe operation of the system.

[0160] It is worth noting that the generator start and stop state variables is the decision variable of the established model. The value of the variable can be solved , , In particular, when any scheduling time interval When it is 0, the model introduces an unknown variable , however, through formula (22) we can get Therefore, regardless of the variable For any value, the number of equations in the model established by the present invention is always equal to the number of variables, so the model is solvable.

[0161] S2-4: Setting the optimal unit commitment method model considering the spatial distribution characteristics of inertia-frequency change rate Model linearization process:

[0162] In the constraints of the optimization model established above, there is a situation where continuous variables are multiplied by integer variables, which makes equations (5) and (9) nonlinear. They can be linearized by the big M method.

[0163] Assumptions is a 0-1 variable, is a continuous variable, is the product of the two, and the linearization process is as follows:

[0164] (25)

[0165] (26)

[0166] Where: For comparison A sufficiently large constant.

[0167] Example 2

[0168] The present invention adopts Figure 1 and Figure 3 The improved WSCC 3-machine 9-bus system and the Southeast Australia power system shown in the figure are simulated and analyzed. The effectiveness and necessity of the proposed model are verified by improving the 3-machine 9-bus system. The Southeast Australia power system is used to test the effect of the proposed model in a large-scale system. This example sets up scenarios considering different factors for simulation analysis, and the proposed method calls Gurobi for solution in the Matlab-2020b environment.

[0169] The case study includes the following three scenarios:

[0170] Scenario 1: frequency safety constraints are not considered;

[0171] Scenario 2: Consider frequency safety constraints based on central inertia;

[0172] Scenario 3: Consider the safety constraints of the frequency change rate of all nodes;

[0173] Scenario 1 only aims to minimize operating costs and does not consider frequency safety constraints, which is the traditional scheduling method. In Scenario 2, the model introduces frequency safety constraints based on central inertia to ensure that the central frequency of the system can be stabilized within a safe range after a disturbance occurs. Scenario 3 further strengthens the frequency safety constraints and requires that the frequency change rate of all nodes remain within an acceptable range after a disturbance occurs. It is the most stringent scheduling strategy.

[0174] Example 3

[0175] The present invention Figure 1 and Figure 3 The improved WSCC 3-machine 9-bus system and the simplified Southeast Australia 14-machine power system model are simulated as examples, and the data are as follows:

[0176] Table 1 Parameters of the improved WSCC 3-machine 9-node system

[0177]

[0178] Table 2 Simplified model parameters of the Dongnanao 14-machine power system

[0179]

[0180] Simulation Results Description

[0181] Table 3 Optimized scheduling cost of the improved WSCC 3-machine 9-node system in different scenarios

[0182]

[0183] As can be seen from Table 3, in scenario 1 without frequency security constraints, although the operating cost is the lowest, this cost saving comes at the cost of higher system operation risk. In the event of a disturbance or fault, the system may not be able to quickly stabilize the frequency, resulting in a larger power system accident. Scenarios 2 and 3 improve the safety and stability of the system and avoid the potential risk of large-scale power outages by introducing frequency security constraints. Although this safety increases daily operating costs, in the long run, it can reduce direct economic losses caused by accidents, reflecting an effective investment in safety. Comparing scenarios 2 and 3, it can be seen that under stricter frequency security constraints, the scheduling scheme of scenario 3 needs to consider the frequency change rate of all nodes, which usually requires more flexible generator output adjustment. This flexibility is usually achieved by increasing the output of some generators or quickly starting backup generators. Improving scheduling flexibility will also increase the operating cost of the system, with generator costs increasing by 18.65% and backup costs increasing by 13.62%. This part of the backup capacity does not directly generate revenue, but ensures that the system can respond quickly in an emergency and avoid large frequency fluctuations.

[0184] In order to verify the effectiveness of the model proposed in this paper and the necessity of considering the frequency safety constraint based on the spatial distribution characteristics of inertia, a fault disturbance is set to occur at the load node during the scheduling period, and the frequency change rate of the system node at different times is shown in Figure 2 (a) to Figure 2 (d).

[0185] Obviously, from the frequency change rates at the four moments in Figure 2 (a) to Figure 2 (d), it can be seen that the frequency change rate of some nodes exceeds the limit due to the uneven distribution of system inertia. Figure 2 (a) shows the frequency change rate of each node at the moment when a power disturbance of 60MW occurs at node 5 at the second hour. It is not difficult to see that the frequency change rate based on the central inertia does not exceed the maximum allowable frequency change rate limit, but from the frequency change rate of all nodes, some nodes exceed the allowable safety limit, and the frequency change rate of node 3 is -1.08 Hz / s. Figure 2(d) shows the frequency change rate of each node at the 10th hour when the same power disturbance occurs at node 5. Compared with the frequency change rate in Figure 2(a), the node frequency change rate in Figure 2(d) does not exceed the maximum allowable frequency change rate. It can be seen that the unit combination methods at different scheduling times are different, and the impact of the same size of disturbance at the same location on the frequency of other nodes in the system is different. The optimal unit combination method considering the inertia-frequency spatial distribution characteristics proposed in the present invention is more valuable and reliable than the traditional unit scheduling method based on central inertia.

[0186] Figure 2(b) and Figure 2(c) are schematic diagrams of the node frequency change rate when a fault occurs at node 8 at the 4th hour and the node frequency change rate when a fault occurs at node 6 at the 7th hour, respectively. It can be seen from Figure 2(b) that the system frequency change rate changes significantly at this moment, and the frequency change rate of node 1 is -1.18 Hz / s, which exceeds the maximum allowable limit, indicating that when a major fault disturbance occurs in the system, the frequency change rate of the generator node may exceed the allowable range, which may cause the generator to trip and even cause a more serious power accident. At the same time, from the node frequency change rate in Figure 2(c), it can be seen that after a fault disturbance occurs in the system, the frequency change rate at this node will have a larger value. Through a more reasonable unit combination method, under the inertial support of the generator, the frequency change rate is within the acceptable range.

[0187] From Figure 4 (a) to Figure 4 (b), we can see the frequency change rate of each node after the disturbance in the system with different inertia levels. Figure 4 (a) shows the frequency change rate of the node at the moment of the fault in the low inertia system. It can be seen that the frequency change rate based on the inertia center is -0.6 Hz / s, which does not exceed the specified safety limit. However, from the perspective of the frequency change rate of all nodes in the system, its magnitude has increased significantly, and the frequency change rate of some nodes exceeds the safety limit. The frequency change rate of node 402 is -1.28Hz / s. Due to the low inertia of the system, especially the nodes close to the fault point, the frequency change rate will far exceed the set safety range. From Figure 4 (b), we can see that in the high inertia level system, because the number of generators is large enough and the inertia constant is large, after the fault disturbance occurs, the frequency change rate based on the inertia center and the whole node does not exceed the allowable range. The frequency change rate of node 402 is -0.98 Hz / s. By comparison, it can be seen that the evaluation method based on the inertia center is reliable only when the network inertia distribution is relatively uniform and the inertia level is relatively high. In systems with low inertia or severely uneven inertia distribution, traditional frequency safety assessment methods will no longer be applicable. Therefore, in power systems with a high proportion of renewable energy, the optimal unit combination method proposed in this invention that considers the inertia-frequency distribution characteristics is particularly critical to ensure safe and stable operation of the system when responding to major disturbances.

[0188] Figure 5 and Figure 6 The unit commitment results considering the central inertia frequency safety constraint and the full node frequency safety constraint are compared. Figure 5 It can be seen that, considering the frequency safety constraint based on the central inertia, when a fault occurs, the number of online generators in area 3 increases, and the inertia mainly increases in area 3, satisfying the frequency safety constraint based on the central inertia of the system. However, from the perspective of system safety, there are cases where the frequency change rate of some nodes exceeds the specified range. Figure 6 It can be seen that compared with Figure 5 According to the scheduling results in , in order to meet the frequency safety constraints of all nodes, the number of generators in other areas of the system increases significantly, with 7 more generators scheduled in area 2 and 2 more generators scheduled in area 5. The optimal unit combination method considering the inertia-frequency spatial distribution proposed in the present invention makes the inertia distribution more balanced and improves the system stability by reasonably scheduling the start and stop of generators when dealing with sudden failures, but the cost will also increase accordingly.

[0189] Figure 7(a) and Figure 7(b) show the frequency change rate of nodes after scheduling by the scheduling method based on the central inertia and the method proposed in the present invention, respectively. It can be seen from the figure that when a disturbance occurs, the scheduling method based on the central inertia can ensure that the frequency change rate of the central inertia of the system remains within the safety limit after the disturbance. However, due to the uneven spatial distribution of inertia in the power grid system, when this method is used, the frequency change rate of some nodes exceeds the safety limit, such as the frequency change rate of node 302 reaches -1.17 Hz / s, resulting in potential risks to the system. In contrast, the method proposed in the present invention takes into account the spatial distribution characteristics of the inertia of each node in the system, and can ensure that the frequency change rate of all nodes is within the safe range. The frequency change rate of node 302 is -0.77 Hz / s, which does not exceed the safety limit.

[0190] Table 4 Generation costs of the simplified Southeast Australia 14-unit power system model under different frequency security constraints

[0191]

[0192] As can be seen from Table 4, considering the scenario based on full-node frequency safety constraints, the operating cost increased by 12.86%. Although the cost increased slightly, under this scheme, the frequency change rate after the disturbance was reduced based on the inertia center, which improved the system frequency response.

[0193] Figure 8 The frequency regulation output of each generator node in these two scenarios is shown. In scenario 2, the frequency regulation output of the system is mainly concentrated in high-inertia nodes (such as nodes 2, 5, 6, and 7). By comparison, it is found that the frequency regulation output of scenario 2 mainly depends on the generators in the high-inertia area, and the low-inertia nodes (such as nodes 9, 12, and 13) have almost no contribution in the frequency regulation response, resulting in insufficient flexibility in the overall frequency control. In contrast, the frequency regulation output of scenario 3 shows a more balanced characteristic. All nodes, whether in high-inertia or low-inertia areas, participate in the frequency regulation response when responding to faults, especially the generators in the low-inertia area. This balanced frequency regulation output distribution ensures that the frequency change rate of the system at each node remains within a safe range, effectively alleviating the risk of frequency instability that may be caused by overloading some nodes.

[0194] Fig. 9 The operating components of the present invention are shown, including a memory and one or more processors, wherein the memory stores executable codes, and when the one or more processors execute the executable codes, they are used to implement any component of the present invention.

[0195] Depend on Fig.10 The construction process of the unit combination model based on inertia-frequency safety proposed in the present invention is described.

[0196] By analyzing the spatial distribution characteristics of inertia, inertia response model, and single-point disturbance, the node frequency change rate model is constructed using the extended DC power flow method and the analytical load node and generator node and node frequency change rate model. Combined with frequency safety constraints and steady-state operation constraints, the optimal unit commitment method and model linearization are used to calculate the optimal scheduling plan for multiple periods.

[0197] The contents described in the embodiments of this specification are merely examples of implementation forms of the inventive concept.

[0198] The protection scope should not be considered as being limited to the specific forms described in the embodiments, and the protection scope of the present invention also includes equivalent technical means that can be conceived by those skilled in the art based on the concept of the present invention.

Claims

1. An optimal unit commitment method considering the spatial distribution characteristics of inertia-frequency change rate, comprising the following steps: S1: Extend the traditional DC power flow model to the nodes behind the internal reactance of the generator, build the inertial response process model of different nodes and analyze the coupling relationship between the injected power and phase angle change of the generator node and the load node immediately after the disturbance; establish the inertia-frequency change rate spatial distribution model according to the characteristics of different nodes; S2: Combined with the inertia-frequency change rate spatial distribution model established in the previous step, the spatial characteristics of the power grid topology and the inertia distribution are comprehensively considered to construct an optimal unit combination dispatching model based on satisfying the power grid node frequency safety constraints and steady-state constraints; In step S1, the constructed inertia-frequency change rate spatial distribution model specifically includes: S1-1: Expand the DC power flow equation, extend the traditional DC power flow model to the nodes behind the internal reactance of the generator, and then analyze the changes in the injected power and voltage phase angle of each node in the power grid after the fault; S1-2: Construct an inertial response process model of the generator node at the moment of disturbance. Based on the start-stop state of the generator, the step change of the node phase angle at the moment after the disturbance, and the physical characteristics that the generator inertia cannot change suddenly, analyze the frequency change rate of the generator node at the moment after the disturbance occurs; S1-3: Establish the inertial response process model of the load node at the moment of disturbance, consider the transient process of the power grid after the disturbance occurs, and analyze the frequency change rate fluctuation process of the load node at the moment of disturbance; Step S1-1 specifically includes: Assume that the system is At the same time, the traditional DC power flow model is extended to the nodes behind the internal reactance of the generator, and the coupling relationship between the injected power and phase angle changes of each node in the power grid can be obtained immediately after the disturbance. Generator For a node power grid, the coupling relationship between the power and phase angle changes of each node can be expressed as: ， Where: They represent the injected power and electromotive force phase angle of the virtual node after the internal reactance of the generator. dimensional column vector; They represent the injected power and voltage phase angle of the load node respectively. dimensional column vector; and Respectively represent the moments before and after the fault occurs; and is the susceptance matrix obtained after considering the internal reactance of the generator; represents the network node susceptance matrix, whose diagonal elements augment the internal reactance of the synchronous machines on the generator bus; Each system node is a load node; The generators were expanded to A virtual node after the internal reactance of a generator, hereinafter referred to as a generator node; Step S1-2 specifically includes: The phase angle change of the generator node considering the start-stop state can be expressed as follows: ， Where: is a 0-1 variable, indicating the The on / off status of the generator; , the generator is in the start-up state; , the generator is in shutdown state; For the Phase angle change of each generator node; is an auxiliary variable introduced, whose value is only , that is, it is meaningful only when the generator is shut down; according to formula (5), if , then the generator node The inertia on will prevent the sudden change of phase angle immediately after the disturbance occurs, that is, ;like , the generator is in a stopped state. At this time, the generator node is a node without inertia, and the sudden change of its phase angle at the moment of disturbance is , whose value depends on the system operating state immediately after the disturbance occurs; At the same time, the injected power of all generator nodes in the system can be expressed as: ， In the formula, Indicates the instant after the disturbance occurs The change in electromagnetic power of the generator, that is, the column vector The elements; according to the positive direction assumed by the injected power, the electromagnetic power injected into the generator node is positive; In addition, the mechanical power of the generator will not change immediately after the fault occurs, i.e.: ， In the formula, Indicates the instant after the disturbance occurs The change of the mechanical power of a generator relative to its steady-state value before the fault; the frequency change rate of the generator node can be further obtained according to the swing equation: ， In the formula, Indicates the instant after the disturbance occurs Frequency change rate of each generator node; Indicates The inertia constant of the generator; is the set of generator nodes; Consider the on / off status of the generator , modify formula (8) as follows: ， Equations (4) to (7) and (9) together constitute the frequency change rate model of the generator node at the moment the disturbance occurs; Step S1-3 specifically includes: It is assumed that the changes in power consumption of other nodes except the node where the disturbance occurs are all 0, and the corresponding node injection power column vector can be expressed as: ， In the formula, Indicates the disturbance node The power change at the node, that is, the node injection power column vector The elements of size ; is the set of load nodes; Substituting equation (10) and equation (11) into equation (1), we get: ， By taking the derivative of equation (12) with respect to time, we can obtain the coupling relationship between the frequency change rate of the load node and the generator node; ， In the formula, and are the frequency change rate column vectors of the load node and the generator node at the moment after the disturbance respectively; according to formula (13), the frequency change rate of all load nodes at the moment after the disturbance can be linearly expressed by the frequency change rate of the generator node.

2. The optimal unit commitment method considering the spatial distribution characteristics of inertia-frequency change rate according to claim 1, characterized in that: The step S2 comprehensively considers the spatial characteristics and inertia distribution of the power grid topology, and constructs an optimal unit combination dispatching model based on satisfying the power grid node frequency safety constraints and steady-state constraints, specifically including: S2-1: Set the objective function including the power generation cost, start-up and shutdown cost, and standby cost of the generator, and describe the dispatching cost of the system to ensure that the frequency change rate of each node is always within the safety threshold after the disturbance occurs; S2-2: Set the optimal unit combination steady-state operation constraints and describe the mechanism by which the power system can maintain normal operation and return to a stable state when facing various abnormal conditions and external disturbances; S2-3: Set the optimal unit combination node frequency change rate safety constraint to describe the node frequency change rate fluctuation process of the corresponding node in the inertia response stage after the disturbance occurs; S2-4: Set the linearization process of solving the optimal unit commitment method model considering the spatial distribution characteristics of the inertia-frequency change rate.

3. The optimal unit commitment method considering the spatial distribution characteristics of inertia-frequency change rate according to claim 2, characterized in that: Step S2-1 specifically includes: The objective function including power generation cost, start-up and shutdown cost and standby cost is set; in order to better understand and calculate the relationship between power generation cost and power generation, the quadratic model is adopted for power generation cost; ， In the formula, is the number of scheduling periods; and Respectively The various coefficients of power generation cost of each generator; Indicates Generators in Output power during the time period; is a 0-1 variable indicating the start and stop status of the unit. Indicates Generators in The system is in online operation during the period. Indicates Generators in The device is off-grid and down during the period; and is a 0-1 variable indicating the start and stop operation of the unit. Generators in If the machine is turned on or off during the time period, the value is 1, otherwise the value is 0; and Respectively The startup and shutdown cost coefficients of each generator; and Respectively Generators in The size of spinning reserve provided during the period and the unit reserve cost factor.

4. The optimal unit commitment method considering the spatial distribution characteristics of inertia-frequency change rate as claimed in claim 2, characterized in that: Step S2-2 includes: Establish constraints to maintain the system's steady-state operation under unexpected conditions, including: Unit start and stop constraints ， Where: and Indicates Minimum start-up and shutdown time of each generator; Unit output constraints ， In the formula, and Respectively The upper and lower limits of the output power of each generator; Power flow balance constraints In any dispatch period, the steady-state system needs to meet the power flow balance conditions as shown below; ， In the formula, For Column vector of power injected into each generator node during the time period; For Column vector of power injected into each load node during the time period; Post-fault steady-state power balance constraints In order to ensure that the generator set can still meet the power requirements of all loads after a sudden power grid failure, the following power balance constraints are established; , where and Respectively Output power and spare capacity of each generator; is the total load demand of the system.

5. The optimal unit commitment method considering the spatial distribution characteristics of inertia-frequency change rate as claimed in claim 2, characterized in that: Step S2-3 specifically includes: In the inertia response phase after the disturbance occurs, the corresponding node frequency change rate constraints are as follows: ， In the formula, Indicates Generators in the dispatch interval The start and stop state variables within; and Respectively in Frequency change rate of generator nodes and load nodes immediately after the period disturbance; The maximum value of the permissible frequency change rate for safe operation of the system; Step S2-4 specifically includes: In the constraints of the optimization model, there are cases where continuous variables are multiplied by integer variables, which makes equations (5) and (9) nonlinear. They are linearized by the big M method. Assumptions is a 0-1 variable, is a continuous variable, is the product of the two, and the linearization process is as follows: ， Where: For comparison A sufficiently large constant.

6. An optimal unit combination device considering the spatial distribution characteristics of inertia-frequency change rate, characterized in that: The method comprises a memory and one or more processors, wherein the memory stores executable codes, and when the one or more processors execute the executable codes, the method is used to implement the optimal unit combination method considering the spatial distribution characteristics of the inertia-frequency change rate as described in any one of claims 1 to 5.

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