A virtual inertia optimization scheduling method and device considering frequency space-time distribution

Abstract

A virtual inertia optimization scheduling method and device considering frequency space-time distribution, the method comprising: based on the "frequency divider" theory, establishing the independent frequency dynamic response model of each node in the whole network; using frequency differential control to establish an equation relationship between virtual inertia and the output power of energy storage, and providing virtual inertia for some nodes; further, considering that the internal reactance of synchronous generators in the extended admittance matrix is inconsistent with the order of magnitude of line reactance, the energy storage device providing virtual inertia needs to be approximately processed, and a virtual impedance is introduced to ensure the feasibility of the model; then, the frequency change rate of each node in the initial inertia response process of the optimization disturbance is scheduled, the virtual inertia is scheduled, and the frequency change rate stability of each node in the power system is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to a virtual inertia optimization scheduling method and device considering frequency space-time distribution. BACKGROUND

[0002] In recent years, traditional energy shortage and increasingly serious environmental problems need to be solved, and the power system gradually transforms from traditional thermal power units to wind, light and other new energy power generation, and coal pollution problems have been effectively controlled. With the introduction of China's carbon peak and carbon neutralization target, the proportion of new energy in primary energy consumption is increasing. Therefore, the power system is about to enter an era of high proportion of new energy, and actively promoting new energy to replace fossil energy is one of the key tasks in the future, and new energy generation is an inevitable trend of future power system development.

[0003] With the gradual replacement of traditional units in the power system by new energy units, the overall inertia of the power system gradually decreases, because new energy represented by wind energy is generally connected to the grid through power electronic converters, resulting in decoupling from the grid and being unable to actively provide inertia support for the grid under active power disturbance. At the same time, new energy units follow the maximum power tracking control to deliver power to the grid, and when a large power disturbance occurs in the system, they cannot increase the output power of the unit to provide active support for the system like traditional units through the prime mover speed regulation system. New energy high proportion system will lead to system inertia degradation, large frequency deviation, and system instability or collapse.

[0004] To cope with the low inertia system caused by high proportion of new energy configuration scheme, scholars have conducted a lot of research on virtual inertia. Including the virtual synchronous machine, synchronous frequency converter, virtual synchronous generator (VSG), all of which are used to enhance the inertia of grid-connected inverters, or virtual inertia control method based on double-fed wind turbine, so that the wind turbine has virtual moment of inertia; virtual energy storage system (VESS) using photovoltaic generators and variable frequency air conditioners to provide virtual inertia and frequency regulation for low inertia microgrid, improve the virtual inertia of microgrid, use frequency differential control method to control the output power of energy storage, and provide virtual inertia for the system. SUMMARY

[0005] In order to overcome the shortcomings of the existing research methods, the present application proposes a virtual inertia scheduling method and device considering frequency space-time dynamic distribution.

[0006] The present application is based on the theory of "frequency divider", and establishes a dynamic frequency response model of each node in the whole network; frequency differential control is used to establish an equation relationship between virtual inertia and output power of energy storage, and virtual inertia is provided for part of nodes. Through the frequency dynamics of each node in the system, the problem of uneven inertia distribution caused by high proportion of new energy grid connection can be more intuitively observed, and on this basis, virtual inertia optimization scheduling is carried out to ensure the frequency safety of each node in the system.

[0007] In order to achieve the above purpose, the technical scheme of the present application is:

[0008] The first aspect of the present application relates to a virtual inertia optimization scheduling method considering frequency space-time distribution, which comprises the following steps:

[0009] S1: Based on the inverter, the energy storage device can simulate the inertia response of the synchronous generator, so as to enhance the frequency transient stability of the power system and avoid the reduction of new energy generation, and the basic control logic in the working process of the inverter is analyzed;

[0010] S2: According to the proposed space-time distribution model, the internal impedance of the generator node is considered

[18] , and the admittance matrix is expanded. From the extended admittance matrix data, it can be seen that the extended internal reactance of the generator and the admittance value of the line parameter differ by an order of magnitude, so the virtual inertia provided by the energy storage connected to the load node in this paper cannot directly inject power at the load node, and needs to be processed similarly to the generator model in this paper, that is, the virtual admittance at the connected energy storage is considered. Considering the above, the extended direct current flow required in this paper is established;

[0011] S3: A space-time dynamic model of inertia response at the moment of disturbance is established, and the working state of the generator node at the initial moment of disturbance is analyzed as a constraint condition of the optimization scheduling model;

[0012] S4: A dynamic output model of the energy storage node and the load node at the moment of disturbance is established, and the working state of the energy storage node and the load node at the initial moment of disturbance is analyzed as a constraint condition of the optimization scheduling model;

[0013] S5: Correctly scheduling distributed virtual inertia devices is an effective method to enhance the frequency stability of all nodes in the power system. An optimal scheduling strategy is established to ensure the stability of space-time frequency and minimize the cost of distributed virtual inertia support;

[0014] S6: There are various nonlinear constraints in the optimization scheduling model, in order to successfully optimize and solve, the nonlinear constraints need to be linearized, and different linearization methods are used to linearize different nonlinear problems in the model;

[0015] In step S1, the basic control logic of the inverter includes the following processes:

[0016] S1-1: Voltage control loop, the output voltage of the device is controlled by the voltage controller to track the reference voltage . In order to simulate the behavior of the synchronous generator in the primary frequency response, the change of the phase angle follows the swing equation. Specifically, the angular velocity is the value obtained by multiplying the integral of the difference between the power reference and the output power by , so is the virtual inertia, which describes the sensitivity of the angular velocity to the integral of the power deviation over a period of time;

[0017] S1-2: Current control loop, in order to achieve a controlled output voltage, the inductor current needs to quickly track the reference current given by the voltage controller . At the same time, the current amplitude should always be within to avoid triggering the overcurrent protection of the inverter. If the reference current copy exceeds the limit, the output voltage of the inverter will not be able to track the voltage reference value, at which point the device degenerates into a constant current source, in other words, if the inverter's energy storage device current saturates, it cannot provide virtual inertia;

[0018] In step S2, the extended DC power flow modeling includes the following:

[0019] S2-1: The proposed time-space distribution model takes into account the internal impedance of the generator node, and the admittance matrix is extended. From the extended admittance matrix data, it can be seen that the extended generator internal reactance and the line parameter susceptance values differ by an order of magnitude, so the virtual inertia provided by the load node access energy storage in this paper cannot directly add the injected power at the load node, and needs to be treated similarly to the generator model in this paper, that is, the virtual admittance at the access energy storage is considered. The extended power flow equation is as follows:

[0020] (1)

[0021] In the formula, the subscripts , and represent the set of generators, energy storage and loads in the power system respectively; and are column vectors composed of the injected active power of the generator node, the injected active power of the energy storage node and the injected active power of the load node respectively; , and The column vector composed of the generator rotor angle position, the energy storage node voltage phase angle and the load voltage phase angle, respectively; , and is the admittance matrix obtained by using the internal impedance of the synchronous machine; , and is the admittance matrix obtained by using the virtual impedance; is the node admittance matrix, the diagonal element of which is augmented with the internal reactance of the synchronous machine on the generator bus and the virtual reactance of the energy storage node;

[0022] In step S3, the inertial response space-time dynamic model at the moment of disturbance is analyzed, and the working state of the generator node is analyzed. The modeling steps are as follows:

[0023] S3-1: Inertial response space-time dynamic model modeling at the moment of disturbance, assuming When the power of the load node suddenly changes, the power flow distribution of the power system will immediately change, and the power and phase angle of each node are divided into initial values and sudden changes, as shown in equation (2):

[0024] (2)

[0025] (3)

[0026] In the formula, , , and , , are the disturbance quantities based on , , , , , in equation (1). Substitute equation (2), equation (3) into equation (1), and eliminate the steady-state term to obtain:

[0027] (4)

[0028] S3-1: Analysis of the dynamic process of the generator node at the moment of disturbance. The rotor of the generator has a certain inertia, and the relative position of the phase angle does not change at the moment of disturbance, and has:

[0029] (5)

[0030] The electromagnetic power at the generator node at the moment of disturbance and the mechanical power output by the generator are not balanced, which causes the frequency change rate to change. The response process is as follows:

[0031] (6)

[0032] wherein, represents the rate of change of the frequency of the generator node at the moment of disturbance; represents the amount of change of the electromagnetic power of the generator at the moment of represents the amount of change of the mechanical power output of the generator at the moment of represents the inertia of the generator at the moment of represents the set of nodes of the generator. It is worth noting that the mechanical power of the generator is subject to the dynamic performance of the governor and the steam turbine and cannot be changed suddenly, so there is:

[0033] (7)

[0034] The electromagnetic power of the generator will change at the moment of disturbance, and the change of the electromagnetic power of the generator node can be obtained by solving equation (4);

[0035] The dynamic process analysis of the energy storage node and the load node in step S4 is as follows:

[0036] S4-1: The injection power of the energy storage node in this paper is expanded, i.e., the control energy storage node, in order to achieve the effect of providing additional inertia for the system. The processing process of the node connected to the energy storage providing virtual inertia is similar to that of the generator node. Since the inertia provided by the energy storage is virtual inertia, the inertia is related to the capacity of the energy storage and the capacity of the energy storage has an upper limit. Due to this special property, special processing is required, and the following can be obtained:

[0037] (8)

[0038] The two boundary condition constraints in equation (8) are rewritten as the following complementary relaxation conditions:

[0039] (9)

[0040] (10)

[0041] The above process describes two output situations of the energy storage in the frequency regulation process: 1) when the capacity of the energy storage is sufficient, the processing process is similar to that of the generator node, i.e., the next step of calculation can be performed through the swing equation, and at this time, the phase angle change at the node is controllable; 2) when the capacity of the energy storage is insufficient, another situation occurs, and at this time, the phase angle at the node is uncontrollable, and only the node phase angle change at this time can be calculated through power flow;

[0042] ​​​Since there are two cases of energy storage output, the processing methods of energy storage are different for different cases. In order to distinguish the two different cases, formula (11) is introduced to distinguish the two cases, and formula (12) is introduced to constrain the energy storage not to output "excessively".

[0043] (11)

[0044] (12)

[0045] For the above first case, formula (13) is used at the moment of disturbance, that is, the energy storage is started and the energy storage output has not reached the upper limit. At this time, the phase angle is controllable when the energy storage capacity is sufficient, and the following formula can represent the control process. For the nodes with insufficient energy storage capacity, the process is similar to the load node, and the specific process will be shown below.

[0046] (13)

[0047] In the formula, represents the virtual inertia provided by the first energy storage; represents the start and stop of the first energy storage; is a binary variable, 0 / 1 respectively represents whether the energy storage reaches the upper limit when it is working; represents the maximum capacity of the first energy storage; represents the node set of the energy storage. By solving the simultaneous equations, the frequency change rate of the generator node at the moment of disturbance can be obtained, which can realize the control of the frequency change and the phase angle change of the generator node at the next moment;

[0048] S4-2: In this paper, all loads are considered to be inertialess by themselves. Therefore, their phase angles can experience to step changes. And assuming that the power of the nodes other than the one where the power surge occurs does not change, then:

[0049] (14)

[0050] Since the power of the load node does not change over time, the second order derivative of formula (4) is taken, then:

[0051] (15)

[0052] For the case where the energy storage output reaches the capacity upper limit mentioned above, the node can be handled as a load node. Since the energy storage output power reaches the maximum value at the moment of disturbance, the right derivative of the power at this time must be 0, so for this part of the node, it satisfies:

[0053] (16)

[0054] In step S5, the virtual inertia optimization scheduling model is established, including the following steps:

[0055] S5-1: Establish a target function to minimize the cost of distributed virtual inertia support while ensuring the stability of space-time frequency. In the above, two operating modes of energy storage in response to sudden failures are distinguished, and the cost calculation method is different according to different modes. When the output of the energy storage does not reach the upper limit, the energy storage can fully provide the corresponding virtual inertia, and the cost is the inertia cost; when the output of the energy storage reaches the upper limit, the virtual inertia provided by the energy storage is invalid, and the operating cost at this time is calculated through power. In order to minimize the total operating cost of distributed virtual inertia devices, a cost function is built:

[0056] (17)

[0057] wherein, is the price coefficient of the virtual inertia provided by the node , in this example, the inertia service adopts ; represents the power cost provided by the node , according to the maximum virtual inertia provided by the maximum capacity, the power cost coefficient is estimated, and is taken. The virtual inertia devices on different nodes need to declare the unit price of the virtual inertia they want to provide and the maximum output power of the inverter, and the system operator will decide who wins the bid;

[0058] S5-2: Establish constraint conditions, consider the frequency space-time distribution model, and perform transient stability constraint on each variable in the frequency modulation process. Instantaneous constraints include equations (4) to (16). In addition, frequency safety constraints and virtual inertia constraints are added:

[0059] (18)

[0060] (19)

[0061] (20)

[0062] wherein, , respectively represent the initial maximum frequency change rate and the maximum allowed frequency change rate on each node; , represent the upper and lower limits of the virtual inertia provided by the virtual inertia device.

[0063] In step S6, the nonlinear constraint linearization process includes the following steps:

[0064] S6-1: There are many nonlinear equations in the above established optimization model, and linearization is needed in the optimization solving process. The nonlinear constraints include equations (9), (10), (11), (13), (17), and the linearization process is described in detail as follows.

[0065] The above-mentioned five groups of nonlinear constraints contain three types of nonlinearities, 1) multiplication of binary variables and continuous variables; 2) multiplication of two continuous variables; 3) multiplication of two binary variables.

[0066] 1) Take equation (9) as an example, linearize it using the big M method, the process is as follows, first, let:

[0067] (21)

[0068] (22)

[0069] (23)

[0070] 2) The nonlinear term in equation (13) is the multiplication of two continuous variables, we choose to perform binary expansion as:

[0071] (24)

[0072] In the equation, and respectively represent the binary expansion bit and the corresponding binary variable, let: , then:

[0073] (25)

[0074] Let , then:

[0075] (26)

[0076] Through the standard big M method of linearization, we can get:

[0077] (27)

[0078] (28)

[0079] 3) There are two binary variables multiplied in equation (17), a new binary variable can be introduced, and the logical AND operation is performed, that is:​

[0080] (29)

[0081] (30)

[0082] All the variables mentioned in the formula are a large enough quantity, the newly added variables in the above linearization process include , , etc., which have no practical significance and are intermediate variables in the linearization process.

[0083] The second aspect of the application relates to a virtual inertia optimization scheduling device considering the spatial and temporal distribution of frequency, characterized by comprising a memory and one or more processors, the memory stores executable code, and the one or more processors execute the executable code to implement the virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency.

[0084] The third aspect of the application relates to a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency.

[0085] The application is based on the "frequency divider" theory, establishes a dynamic response model of independent frequency of each node in the whole network, uses frequency differential control to establish an equation relationship between virtual inertia and output power of energy storage, provides virtual inertia for part of the nodes, further, considering that the internal reactance of the synchronous generator in the extended admittance matrix is inconsistent with the order of magnitude of the line reactance, the energy storage device providing virtual inertia needs to be approximately processed, a virtual impedance is introduced to ensure the feasibility of the model, then, the frequency change rate of each node in the initial inertia response process of the optimization disturbance is optimized, the virtual inertia is scheduled, and the frequency change rate stability of each node of the power system is improved.

[0086] The beneficial effects of the application are:

[0087] 1. For a high new energy ratio system, with the grid connection of a high proportion of power electronic equipment, the problem of uneven inertia distribution of each node in the system network is becoming increasingly serious, the error of the traditional frequency analysis method based on the center inertia estimation system is gradually increasing, and the application considers the frequency index of each node in the whole network, which can more accurately determine whether the system is stable.

[0088] 2. By calling virtual inertia to increase inertia at the position of weak inertia in the system network, compared with the traditional method of cutting wind and light, the application has obvious economic superiority.

[0089] 3. Considering that virtual inertia is essentially obtained by providing system inertia support through the rapid response characteristics of energy storage devices, this invention fully considers the relationship between virtual inertia and power, and explains the impact of the upper limit of energy storage capacity on frequency regulation effect. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the virtual inertial device of the present invention.

[0091] Figures 2(a1)-2(b2) Figure 2a1 shows the scheduling operation of the central inertia method under different schemes in the three-machine nine-node model of the present invention under different fault conditions. Figure 2a2 shows the scheduling operation of the distributed optimization method under the fault condition (a). Figure 2b1 shows the scheduling operation of the central inertia method under the fault condition (b). Figure 2b2 shows the scheduling operation of the distributed optimization method under the fault condition (b).

[0092] Figures 3(a) and 3(b) show the virtual inertia and power output (small) provided by energy storage in each region under different fault conditions obtained by the present invention. Figure 3(a) shows the distribution of virtual inertia in the distributed optimization scheduling under fault (a) condition; Figure 3(b) shows the distribution of virtual inertia in the distributed optimization scheduling under fault (b) condition.

[0093] Figure 4(a) and Figure 4(b) show the changes in node RoCoF under different fault conditions of the central inertia method in scenario 1. Figure 4(a) shows the scheduling operation of the central inertia method when the fixed unit is operating as scenario 1 and fault (a) occurs; Figure 4(b) shows the scheduling operation of the central inertia method when the fixed unit is operating as scenario 1 and fault (b) occurs.

[0094] Figure 5(a) and Figure 5(b) are schematic diagrams of the changes in RoCoF of nodes under different fault conditions in the distributed method under scenario 1. Figure 5(a) shows the scheduling operation of the distributed optimization method when the fixed unit is operating under scenario 1 and fault (a) occurs; Figure 5(b) shows the scheduling operation of the distributed optimization method when the fixed unit is operating under scenario 1 and fault (b) occurs.

[0095] Figure 6(a) and Figure 6(b) are large diagrams of the virtual inertia and power output provided by energy storage in each region under different fault conditions. Figure 6(a) shows the distribution of virtual inertia in the distributed optimization scheduling under fault (a), and Figure 6(b) shows the distribution of virtual inertia in the distributed optimization scheduling under fault (b).

[0096] Fig. 7(a) and Fig. 7(b) are diagrams of node RoCoF changes under different fault conditions of scenario 2, wherein Fig. 7(a) is an operation condition of fixed unit operation under fault (a) of scenario 2; and Fig. 7(b) is an operation condition of fixed unit operation under fault (b) of scenario 2.

[0097] Figure 8 It is a flow chart of a virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency. DETAILED DESCRIPTION

[0098] The application will be further described below with reference to the drawings

[0099] Embodiment 1

[0100] Reference Figures 1-8 A virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency, the method comprising the following steps:

[0101] S1: Based on the inverter-based energy storage device, the inertia response of the synchronous generator can be simulated, so as to enhance the frequency transient stability of the power system and avoid the reduction of new energy generation, and the basic control logic in the working process of the inverter is analyzed;

[0102] S2: According to the proposed spatial and temporal distribution model, the internal impedance of the generator node is considered, and the admittance matrix is expanded. From the expanded admittance matrix data, it can be seen that the extended internal reactance of the generator and the susceptance value of the line parameter differ by an order of magnitude, so the virtual inertia provided by the load node connected to the energy storage device in this paper cannot directly inject power at the load node, and needs to be processed similarly to the generator model in this paper, that is, the virtual admittance at the connected energy storage device is considered. Considering the above, the extended direct current flow required in this paper is established;

[0103] S3: A spatial and temporal dynamic model of inertia response at the moment of disturbance is established, and the working state of the generator node at the initial moment of disturbance is analyzed as a constraint condition of the optimization scheduling model;

[0104] S4: A dynamic output model of the energy storage node and the load node at the moment of disturbance is established, and the working state of the energy storage node and the load node at the initial moment of disturbance is analyzed as a constraint condition of the optimization scheduling model;

[0105] S5: Correctly scheduling the distributed virtual inertia device is an effective method to enhance the frequency stability of all nodes in the power system. An optimal scheduling strategy is established to ensure the stability of the spatial and temporal frequency, and at the same time, the cost of the distributed virtual inertia support is minimized;

[0106] S6: There are various nonlinear constraints in the optimization scheduling model. In order to successfully solve the optimization, the nonlinear constraints need to be linearized. Different linearization methods are used to linearize different nonlinear problems in the model;

[0107] In step S1, the basic control logic analysis of the inverter includes the following processes:

[0108] S1-1: Voltage control loop, the output voltage of the device is controlled by the voltage controller to track the reference voltage . In order to simulate the behavior of the synchronous generator in the primary frequency response, the change of the phase angle follows the swing equation. Specifically, the angular velocity is the value obtained by multiplying the integral of the difference between the power reference and the output power by . Therefore is the virtual inertia, which describes the sensitivity of the angular velocity to the integral of the power deviation over a period of time;

[0109] S1-2: Current control loop, in order to achieve a controlled output voltage, the inductor current needs to quickly track the reference current given by the voltage controller. At the same time, the current amplitude should always be within to avoid triggering the overcurrent protection of the inverter. If the reference current copy exceeds the limit, the output voltage of the inverter will not be able to track the voltage reference value, at which point the device degenerates into a constant current source. In other words, if the energy storage device current of the inverter saturates, it cannot provide virtual inertia;

[0110] In step S2, the extended DC power flow modeling includes the following:

[0111] S2-1: The proposed time-space distribution model considers the internal impedance of the generator node, and the admittance matrix is extended. From the extended admittance matrix data, it can be seen that the extended generator internal reactance and the line parameter susceptance values differ by an order of magnitude. Therefore, the proposed virtual inertia for the load node access to energy storage cannot directly add the injected power at the load node, and needs to be treated similarly to the generator model in this paper, that is, the virtual admittance at the access energy storage is considered. The extended power flow equation is as follows:

[0112] (1)

[0113] In the formula, the subscripts , and represent the set of generators, energy storage and loads in the power system, respectively; and P inj, P inj, P inj are column vectors composed of injected active power of generator nodes, injected active power of energy storage nodes and injected active power of load nodes, respectively; , and are column vectors composed of generator rotor angle position, energy storage node voltage phase angle and load voltage phase angle, respectively; , and are admittance matrices obtained by using internal impedance of synchronous machines; , and are admittance matrices obtained by using virtual impedance; is a node admittance matrix, whose diagonal elements are augmented by internal reactance of synchronous machines on generator buses and virtual reactance of energy storage nodes;

[0114] In the step S3, the space-time dynamic model of the transient inertia response is disturbed, and the working state of the generator node is analyzed, and the modeling steps are as follows:

[0115] S3-1: modeling of space-time dynamic model of transient inertia response, assuming When the power of the load node suddenly changes, the power flow distribution of the power system will immediately change, and the power and phase angle of each node are divided into initial value and sudden change value, as shown in equation (2):

[0116] (2)

[0117] (3)

[0118] In the formula, , , and , , are the disturbance quantities based on , , , , , in equation (1). Equation (2), equation (3) is brought into equation (1), and the steady state term is eliminated, to obtain:

[0119] (4)

[0120] S3-1: analysis of dynamic process of generator node at the moment of disturbance, the rotor of the generator has certain inertia, and the phase angle relative position does not change at the moment of disturbance, and has:

[0121] (5)

[0122] The electromagnetic power at the generator node at the moment of disturbance is not balanced with the mechanical power output of the generator, which makes the frequency rate of change start to change, and the response process is as follows:

[0123] (6)

[0124] In the formula, represents the frequency rate of change of the generator node at the moment of disturbance; represents the change in electromagnetic power of the generator at ; represents the change in mechanical power output of the generator at ; represents the inertia of the first generator; represents the set of nodes of the generator. It is worth noting that the mechanical power of the generator is subject to the dynamic performance of the governor and the steam turbine and cannot change suddenly, so there is:

[0125] (7)

[0126] The electromagnetic power of the generator will change at the moment of disturbance, and solving equation (4) can obtain the change in electromagnetic power of the generator node;

[0127] In the step S4, the dynamic process analysis of the energy storage node and the load node, the steps are as follows:

[0128] S4-1: The injection power of the energy storage node in this paper is expanded, that is, the control energy storage node, in order to achieve the effect of providing additional inertia for the system. The process of the node providing virtual inertia to the connected energy storage is similar to that of the generator node. Since the inertia provided by the energy storage is virtual inertia, the inertia is related to the capacity of the energy storage, and the capacity of the energy storage has an upper limit. Due to this special property, special processing is required, and the following can be obtained:

[0129] (8)

[0130] The two boundary conditions of equation (8) are rewritten into the following complementary relaxation conditions:

[0131] (9)

[0132] (10)

[0133] The above process describes two output situations existing in the frequency modulation process of energy storage: 1) when the energy storage capacity is sufficient, its processing process is approximately the same as that of the generator node, that is, the next step of calculation can be carried out through the swing equation, at this time it means that the phase angle change at the node is controllable; 2) when the energy storage capacity is insufficient, another situation occurs, at this time the phase angle at the node is uncontrollable, and only the node phase angle change at this time can be calculated through power flow;

[0134] Since there are two situations of energy storage output, the processing methods of energy storage are different for different situations. In order to distinguish the two different situations, equation (11) is introduced to distinguish the two situations, and equation (12) is introduced to constrain the energy storage not to "excessively" output;

[0135] (11)

[0136] (12)

[0137] For the above first situation, equation (13) is used at the disturbance moment, that is, the energy storage is started and the energy storage output has not reached the upper limit, at this time the phase angle is controllable when the energy storage capacity is sufficient, and the following equation can represent its control process. For the nodes with insufficient energy storage capacity, the processing process is similar to that of the load node, and the specific process will be shown below.

[0138] (13)

[0139] In the formula, represents the virtual inertia provided by the first energy storage; represents the start and stop of the first energy storage; is a binary variable, 0 / 1 respectively represents whether the energy storage reaches the upper limit when it is working; represents the maximum capacity of the first energy storage; represents the node set of the energy storage. By solving the simultaneous equations, the frequency change rate of the generator node at the disturbance moment can be obtained, which can realize the control of the frequency change and the phase angle change of the generator node at the next moment;

[0140] S4-2: In this paper, all loads are considered to be inertialess by themselves. Therefore, their phase angles can experience to a step change. And assuming that the power of the nodes other than the node where the power mutation occurs does not change, then:

[0141] (14)

[0142] Since the power of the load node does not change over time, the second order derivative of equation (4) is taken, and then:

[0143] (15)

[0144] For the case mentioned above that the energy storage output reaches the capacity limit, the node can be approximately treated as a load node. Since the energy storage output power reaches the maximum value at the moment of disturbance, the right derivative of power at this moment must be 0, so for this part of the node, it satisfies:

[0145] (16)

[0146] In the step S5, the virtual inertia optimization scheduling model is established, including the following steps:

[0147] S5-1: Establish the objective function to ensure the stability of space-time frequency while minimizing the cost of distributed virtual inertia support. The two operating modes of energy storage in response to sudden failures are distinguished above, and the cost calculation method is different according to different modes. When the energy storage output does not reach the upper limit, the energy storage can fully provide the corresponding virtual inertia, and the cost is the inertia cost; when the energy storage output reaches the upper limit, the virtual inertia provided by the energy storage is invalid, and the operating cost at this time is calculated through power. In order to minimize the total operating cost of distributed virtual inertia devices, the cost function is built:

[0148] (17)

[0149] In the formula, is the price coefficient of the virtual inertia provided by the node , in this example, the inertia service adopts ; represents the power cost provided by the node , according to the maximum virtual inertia provided by the maximum capacity, the power cost coefficient is estimated, and is taken. The virtual inertia devices on different nodes need to declare the unit price of the virtual inertia they want to provide and the maximum output power of the inverter, and the system operator will decide who wins the bid;

[0150] S5-2: Establish the constraint condition, consider the frequency space-time distribution model, and perform transient stability constraint on each variable in the frequency modulation process. The constraints at the moment of disturbance include equations (4) to (16). In addition, frequency safety constraints and virtual inertia constraints are also added:

[0151] (18)

[0152] (19)

[0153] (20)

[0154] wherein, , respectively represent the initial maximum frequency variation rate and the maximum allowable frequency variation rate on each node; , represent the upper and lower limits of the virtual inertia provided by the virtual inertia device.

[0155] In the step S6, the nonlinear constraint linearization process includes the following steps:

[0156] S6-1: There are many nonlinear equations in the above-mentioned established optimization model, and linearization is needed in the optimization solving process. The nonlinear constraints include equations (9), (10), (11), (13), (17), and the linearization process is described in detail as follows.

[0157] The above-mentioned five groups of nonlinear constraints contain three kinds of nonlinearities, 1) multiplication of binary variables and continuous variables; 2) multiplication of two continuous variables; 3) multiplication of two binary variables.

[0158] 1) Take equation (9) as an example, linearization is performed by using the big M method, and the process is as follows. First, let:

[0159] (21)

[0160] (22)

[0161] (23)

[0162] 2) The nonlinear term in equation (13) is the multiplication of two continuous variables, and we choose to perform binary expansion as:

[0163] (24)

[0164] wherein, and respectively represent the bit of binary expansion and the corresponding binary variable, and let: then:

[0165] (25)

[0166] Let then:

[0167] (26)

[0168] Through the standard big M method of linearization, we can obtain:

[0169] (27)​

[0170] (28)

[0171] 3) There are two binary variables multiplied in equation (17), a new binary variable can be introduced to do logical AND operation, which has:

[0172] (29)

[0173] (30)

[0174] All the variables mentioned in the equation are large enough, and the newly added variables in the above linearization process, including , , etc., have no practical significance and are intermediate variables in the linearization process.

[0175] In order to enable those skilled in the art to better understand the present application, the example analysis includes the following:

[0176] I. Example description

[0177] The method ensures the stability of the disturbance initial system inertia response, introduces virtual inertia, and when the inertia response provided by the existing unit inertia cannot guarantee the stability of the frequency change rate of each node of the system, the virtual inertia is provided by the introduction of energy storage to improve the inertia response of the system and ensure the stable operation of the system.

[0178] This simulation design only considers one time section, that is, a certain time point in the process of stable operation of the system, and observes the frequency change rate of the system at the fault moment after the fault occurs in a certain area of the network (including generator tripping, line fault, load mutation, etc.). Three different schemes are used to compare the possible fault conditions.

[0179] 1) Use the intermediate inertia method, and the frequency change rate based on the inertia center is used as the frequency security constraint for virtual inertia scheduling.

[0180] 2) Consider the frequency spatial distribution characteristics, and use all node frequency change rates in the whole network as frequency security constraints for virtual inertia scheduling.

[0181] 3) Use the traditional scheduling scheme to increase the number of online generators to improve the inertia response level of the system.

[0182] The above-mentioned scheduling schemes are simulated, and the large and small systems are used to verify the frequency modulation effect of each scheme from the aspects of safety and economy.

[0183] II. Simulation example setting

[0184] The simulation example adopts a three-machine nine-node model. The matlab simulation platform is used for verification, and the maximum allowed frequency change rate is set .

[0185] The three-machine nine-node operation scenario is adopted. Three synchronous generators are connected to the system, with a total capacity of 567.5 MW. When the system is balanced, the load is 315 MW, and the unit generates 315 MW. The total inertia of the system is 3305 MWs. This simulation shows two fault conditions: a) assuming that node 6 is disturbed, ; b) assuming that node 8 is disturbed, . The energy storage with a capacity of is connected to nodes 1, 2, and 3 to provide virtual inertia.

[0186] III. Simulation analysis

[0187] For a system with a high proportion of new energy, with the grid connection of a high proportion of power electronic equipment, the problem of uneven inertia distribution at each node in the system network is becoming increasingly serious, and the error of the traditional frequency analysis method based on central inertia estimation of the system as a whole is gradually increasing. From the comparison of Fig. 2 (2a1) and Fig. 2 (2a2), Fig. 2 (b1) and Fig. 2 (b2), it can be seen that the central inertia scheduling method and the distributed scheduling method proposed in the present application can overcome the limitations of the traditional central inertia scheduling scheme and better ensure the frequency safety of the system. Similarly, by comparing the scheduling effects of Fig. 4 (a) and Fig. 5 (a), Fig. 4 (b) and Fig. 5 (b), it can be seen that this method is also applicable to large systems.

[0188] Fig. 3 (a) (b) and Fig. 6 (a) (b) respectively show the scheduling of the energy storage under the (a) and (b) fault conditions of the two simulation models. From the figure, it can be seen that there is a full-capacity energy storage, which is insufficient to provide the required virtual inertia, so the virtual inertia is invalid at this time. The rest of the energy storage capacity is sufficient to provide the expected virtual inertia, so it is priced based on the virtual inertia cost. At the same time, due to the full-capacity operation of the energy storage, it cannot provide the expected inertia effect, so the remaining energy storage needs to be scheduled to complete its remaining "work". This indirectly verifies that the spatial distribution characteristics of the inertia mentioned in this paper have an impact on frequency regulation, that is, the "most convenient" energy storage is called upon when the "ability" is insufficient. The above simulation results also show that the upper limit of the energy storage capacity has an impact on the virtual inertia scheduling.

[0189] With the gradual increase of new energy in the power system, the traditional frequency regulation resource is scarce, which leads to the decrease of system inertia level and the deterioration of transient frequency characteristics, and there is a risk of large-area load shedding and machine cutting. In order to reduce such fault conditions, wind and light need to be cut significantly, so as to put more units into online use. By comparing the frequency change rate of each node in Figure 4(a) and Figure 7(a), Figure 4(b) and Figure 7(b), it can be seen that the additional online generator reduces the proportion of photovoltaic, which can ensure the stability of the frequency change rate of each node. This not only increases the basic operation cost of the system, but also idles part of the new energy output, resulting in an increase in the overall system operation cost and poor economic benefits. The present application can effectively provide economic benefits by purchasing virtual inertia for inertia-deficient areas to ensure system stability without wind and light cutting. The economic benefit comparison is shown in Table 1.

[0190] Table 1

[0191]

[0192] Embodiment 2

[0193] The present embodiment relates to a virtual inertia optimization scheduling device considering frequency space-time distribution, characterized by comprising a memory and one or more processors, the memory storing executable code, and the one or more processors executing the executable code to implement the virtual inertia optimization scheduling method considering frequency space-time distribution of embodiment 1.

[0194] Embodiment 3

[0195] The present embodiment relates to a computer-readable storage medium, characterized by storing a program thereon, which is executed by a processor to implement the virtual inertia optimization scheduling method considering frequency space-time distribution of embodiment 1.

[0196] The content described in the embodiments of the present specification is only a list of implementation forms of the inventive concept, and the protection scope of the present application should not be considered to be limited to the specific forms stated in the embodiments, and the protection scope of the present application also extends to equivalent technical means that can be thought of by those skilled in the art according to the inventive concept.

Claims

1. A virtual inertia optimization scheduling method considering frequency space-time distribution, characterized in that, Comprise: S1: The inertia response of the synchronous generator is simulated based on the inverter-based energy storage device, and the basic control logic in the operation process of the inverter is analyzed; S1-1: voltage control loop, output voltage of the device controlled by the voltage controller to track the reference voltage ; change of phase angle following the swing equation; angular velocity from the power reference and the difference to the output power of the integral times a factor, is the virtual inertia; S1-2: current control loop, inductor current Fast tracking of reference current ; at the same time, the current amplitude is always within the range of 0.8-1.2; if the reference current copy is out of limits, the energy storage device current of the inverter is saturated, and the virtual inertia cannot be provided; S2: According to the proposed space-time distribution model, considering the internal impedance of the generator node, the admittance matrix is extended, the virtual inertia of the load node connected to the energy storage is provided, and the connection mode needs to consider the virtual admittance at the connection point of the energy storage; The extended direct current flow demand is established; The extended power flow equation is as follows: (1) where the subscripts , and denote the set of generators, energy storage and loads in the power system, respectively; and are the injected active power at the generator nodes, the injected active power at the energy storage nodes and the injected active power at the load nodes, respectively; , and are the generator rotor angle position, the energy storage node voltage phase angle and the load voltage phase angle, respectively; , and are the admittance matrices obtained with the internal impedance of the synchronous machines; , and are the admittance matrices obtained with the virtual impedance; is the node admittance matrix; S3: A space-time dynamic model of the inertia response at the disturbance moment is established, and the working state of the generator node at the initial moment of the disturbance is analyzed as a constraint condition of the optimization scheduling model; S3-1: modeling of the inertia response of the space-time dynamic model at the moment of disturbance, assuming At the moment of power mutation of the load node, the power and phase angle of each node of the power system are divided into initial values and mutation values, as shown in equation (2): (2) (3) 、 、 and 、 、 is the perturbation quantity based on the formula (1) in 、 、 、 、 、 ; formula (2), formula (3) is brought into formula (1), and the steady state term is eliminated, and the following formula is obtained: (4) S3-2: Analysis of dynamic process of generator node at the moment of disturbance, relative position of generator rotor phase angle No sudden change occurs at the moment of disturbance, and there are: (5) The frequency change rate of the generator node starts to change at the disturbance moment, and the response process is as follows: (6) represents the rate of change of the frequency of the generator node at the instant of the disturbance; represents the amount of change in the electromagnetic power of the generator at the instant of the disturbance; represents the amount of change in the mechanical power output of the generator at the instant of the disturbance; represents the amount of change in the mechanical power output of the generator at the instant of the disturbance; represents the amount of change in the mechanical power output of the generator at the instant of the disturbance; represents the amount of change in the mechanical power output of the generator at the instant of the disturbance; represents the amount of change in the mechanical power output of the generator at the instant of the disturbance; represents the set of nodes of the generator; the mechanical power of the generator cannot change abruptly, there is: (7) The electromagnetic power of the generator will change at the disturbance moment, and the change of the electromagnetic power of the generator node is obtained by solving equation (4); S4: A dynamic output model of the energy storage node and the load node at the disturbance moment is established, and the working state of the energy storage node and the load node at the initial moment of the disturbance is analyzed as a constraint condition of the optimization scheduling model; S5: Scheduling distributed virtual inertia devices; Establish an optimal scheduling strategy; S6: Linearize the nonlinear constraints in the optimization scheduling model.

2. The virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency according to claim 1, wherein, In the dynamic process analysis of the energy storage node and the load node in step S4, the steps are as follows: S4-1: The injection power of the extended energy storage node, i.e. the control energy storage node, is controlled to provide additional inertia to the system; The process of the node connected to the energy storage to provide virtual inertia is similar to that of the generator node. Since the inertia provided by the energy storage is virtual, the inertia is related to the capacity of the energy storage, and the capacity of the energy storage has an upper limit. Due to this special property, special treatment is required, and the following complementary relaxation conditions can be obtained by rewriting the two boundary conditions in equation (8): (8) The above process describes two output situations of the energy storage in the frequency regulation process: 1) When the energy storage capacity is sufficient, the process is similar to that of the generator node, i.e. the swing equation can be used for further calculation, and the phase angle change at this node is controllable; 2) When the energy storage capacity is insufficient, another situation occurs, and the phase angle at this node is uncontrollable, and only the node phase angle change at this time can be calculated through power flow calculation; (9) (10) Since there are two situations of energy storage output, the treatment of energy storage is different for different situations. In order to distinguish between the two situations, equation (11) is introduced to distinguish between the two situations, and equation (12) is introduced to constrain the energy storage from "over outputting"; For the above first situation, equation (13) is used at the disturbance moment, i.e. the energy storage is turned on and the energy storage output has not reached the upper limit. When the energy storage capacity is sufficient, the phase angle is controllable, and the control process can be represented by the following equation: (11) (12) Since the load node power does not change with time, the second derivative of equation (4) is: (13) In the formula, represents the first virtual inertia provided by the energy storage device; represents the first start and stop of the energy storage device; is a binary variable, 0 / 1 respectively represents whether the upper limit is reached when the energy storage device works. represents the maximum capacity of the energy storage device; represents the set of nodes of the energy storage device; represents the set of nodes of the energy storage device; the frequency change rate of the generator node at the moment of disturbance is solved by solving the simultaneous equations (6) and (7), so that the frequency change and the phase angle change of the generator node at the next moment can be controlled. S4-2: The loads themselves are inertialess, their phase angles will undergo a step change from ; and assuming that the power at the other nodes does not change except at the node where the power surge occurs, then we have: (14) For the case where the energy storage output reaches the capacity upper limit, the node can be handled as a load node; Since the energy storage output power reaches the maximum value at the disturbance moment, the right derivative of the power at this time must be 0, so for this part of the node, it satisfies: (15) In step S5, the virtual inertia optimization scheduling model is established, which includes the following steps: (16)。 3. The virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency according to claim 2, wherein, ​ S5-1: Establish the objective function to ensure the stability of space-time frequency while minimizing the cost of distributed virtual inertia support; when the energy storage output does not reach the upper limit, the energy storage can fully provide the corresponding virtual inertia, at which time the cost is the inertia cost; when the energy storage output reaches the upper limit, the virtual inertia provided by the energy storage fails, and the operating cost at this time is calculated through power; in order to minimize the total operating cost of the distributed virtual inertia device, build the cost function: (17) In the formula, is the node The price coefficient of virtual inertia is provided, and the inertia service adopts ; The power cost provided by the node , according to the maximum virtual inertia provided by the maximum capacity, estimate the power cost coefficient, take The virtual inertia device on different nodes needs to declare the unit price of the virtual inertia it wants to provide and the maximum output power of the inverter, and the system operator will decide who wins the bid; S5-2: Establish the constraint condition, consider the frequency space-time distribution model, and perform transient stability constraint on each variable in the frequency modulation process; instantaneous constraint after disturbance, including equations (4)-(16); in addition, frequency safety constraints and virtual inertia constraints are also added: (18) (19) (20) wherein , respectively represent the initial maximum frequency variation rate and the maximum allowed frequency variation rate on each node; , represent the upper and lower limits of the virtual inertia provided by the virtual inertia device.

4. The virtual inertia optimization scheduling method considering the spatial and temporal distribution of frequency according to claim 3, wherein, In the step S6, the nonlinear constraint linearization process includes the following steps: S6-1: There are many nonlinear equations in the optimization model established above, and linearization is needed during the optimization solving process; the nonlinear constraints include equations (9), (10), (11), (13), (17); The five groups of nonlinear constraints contain three kinds of nonlinear situations, 1) binary variables and continuous variables are multiplied; 2) two continuous variables are multiplied; 3) two binary variables are multiplied; 1) Take the example of formula (9) in which M is large, the process is as follows, first note: (21) (22) (23) 2) The nonlinear term in equation (13) is the multiplication of two continuous variables, we choose The binary expansion is (24) wherein denotes the binary expansion of the binary variable denotes the binary expansion of the binary variable then we have: (25) Recall Then: (26) Through the standard large M method linearization method, the following can be obtained: (27) (28) 3) There are two binary variable multiplications in Equation (17), a new binary variable can be introduced , do logical AND operation, there are: (29) (30) All of the variables mentioned in the formulae above are intermediate variables in the linearization process and have no practical meaning. , , are intermediate variables in the linearization process and have no practical meaning.

5. A virtual inertia optimization scheduling device considering frequency space-time distribution, characterized in that, A memory and one or more processors, the memory stores executable code, and the one or more processors execute the executable code to implement the virtual inertia optimization scheduling method considering frequency space-time distribution in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, A program is stored thereon, which is executed by a processor to implement the virtual inertia optimization scheduling method considering frequency space-time distribution in any one of claims 1-4.

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