CN115663824A - Novel calculation method for emergency voltage control strategy of high-voltage direct-current power transmission system - Google Patents
Novel calculation method for emergency voltage control strategy of high-voltage direct-current power transmission system Download PDFInfo
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Abstract
The invention relates to a novel calculation method for an emergency voltage control strategy of a high-voltage direct-current power transmission system, and provides a multi-objective nonlinear optimization model aiming at reducing HVDC power transmission energy transmission and improving voltage recovery rate. Because the solving calculation amount of the objective function and the differential equation in the constraint is large and difficult to be applied on line, the invention further converts the objective function and the differential equation in the constraint condition including the direct current model into an algebraic equation based on a global orthogonal configuration method, thereby converting a multi-objective optimization model into a multi-objective nonlinear programming problem, leading the model to be easy to solve, and solving the emergency voltage control strategy by adopting a multi-objective evolutionary algorithm. The invention has the advantages that: on one hand, the transient voltage instability phenomenon which takes the induction motor as a main factor can be avoided to the greatest extent, the transient voltage stability of the direct current receiving end power grid can be recovered quickly, and the reduction of the transmission electric energy of a direct current system can be reduced to the greatest extent; on the other hand, the calculation efficiency is greatly improved.
Description
Technical Field
The invention belongs to the technical field of novel emergency voltage control of a power system, and particularly relates to a calculation method of a novel emergency voltage control strategy of a high-voltage direct-current power transmission system.
Background
It is well known that reliable and marginally reliable power systems are critical to the economy and safety of all countries. However, multiple dc feeds and large scale trans-regional power transmission make it more difficult to control the voltage stability of the system when the grid is subject to large disturbances. When a large-scale new energy station is connected to a receiving end near High Voltage Direct Current (HVDC) and a conventional unit near a Direct Current grid-connected point is replaced by the new energy station, reactive power of the Direct Current near area is in a relatively tense state. When a fault occurs in an alternating current system, particularly when an induction motor is used as a main load of a high-voltage direct-current transmission receiving end system, the load bus voltage can be continuously reduced, and therefore the transient voltage stability problem of a power grid can be caused. In order to solve the problem of transient voltage stability in an HVDC receiving end system, an effective emergency voltage control strategy calculation method needs to be formulated to ensure safe and stable operation of a power grid.
Most of the existing researches focus on adjusting the power angle stability and the frequency stability of a power system by using the active power emergency control function of HVDC, and few researches improve the transient voltage stability by using the reactive power emergency control function of HVDC. For example, research is carried out to prolong the time of a direct current command at a low-level value after a fault, so that voltage instability caused by too fast recovery of active transmission capacity of a direct current system is avoided, but definite theoretical analysis on time delay and the magnitude of a current value is lacked; the method is characterized in that the relation between transmission active power and consumption reactive power of a direct current system is analyzed based on a quasi-steady-state model, the problem of transient voltage drop of a power grid near a converter station when emergency power is supported between direct current lines in a multi-direct-current feed-in area is researched, and the stability of the power grid voltage in the feed-in area is realized in the aspects of standby reactive power input, reactive power compensation capability of reactive power compensation equipment utilizing fault direct current, power coordination between an alternating current system and a direct current system and the like, but the multiple schemes are based on experience judgment and lack of reasonable calculation; the method also researches a principle that a direct current inversion station can be used as a high-capacity dynamic reactive power source of a receiving-end power grid, utilizes a mode of reducing direct current in a step mode to release the reactive power capability of a capacitor of a converter station, effectively improves the voltage level of the receiving-end power grid under the instability condition taking transient voltage instability as a main factor, and adopts a still tentative method to gradually reduce a direct current instruction, so that the control effect on voltage recovery is slow.
In order to recover voltage quickly, reduce the risk of transient voltage instability and reduce investment cost, a high-voltage direct-current converter station can be used as an emergency reactive power supply, the consumption of reactive compensation quantity is reduced by reducing direct-current transmission current for a short time, and reactive support is provided for a system under the condition that the reactive compensation quantity is unchanged, so that the emergency control of the transient voltage stability of a power grid of a high-voltage direct-current receiving end system is realized. Aiming at the quantitative calculation of the short-time reduced direct current magnitude, the invention provides a multi-objective nonlinear optimization model which takes reduction of HVDC transmission energy in a control period and improvement of the fault near-zone busbar voltage recovery rate as targets and takes an asynchronous motor slip recovery path as a constraint condition. Because the solving calculation amount of the objective function and the differential equation in the constraint is large and difficult to be applied on line, the invention further converts the objective function and the differential equation in the constraint condition including the direct current model into an algebraic equation based on a global orthogonal configuration method, thereby converting the optimization model into a multi-objective nonlinear programming problem, leading the optimization model to be easy to solve, and solving the emergency voltage control strategy by adopting a multi-objective evolutionary algorithm. The invention has the advantages that: on one hand, the transient voltage instability phenomenon which takes the induction motor as a main factor can be avoided to the greatest extent, the fault near-zone bus transient voltage stability can be recovered quickly, and the reduction of the transmission electric energy of a direct current system can be reduced as much as possible; on the other hand, the introduction of the global orthogonal configuration method greatly improves the calculation efficiency of the method, and embodies the advantages of the method in the aspect of calculation efficiency and the potential of online application.
Disclosure of Invention
The invention relates to a calculation method for an emergency voltage control strategy of a novel high-voltage direct-current power transmission system. Generally speaking, a converter station consumes 40% -60% of its transmitted real power. During normal operation, the converter station bus bars of the converter station are connected in parallel with a compensation capacitor to compensate for this part of the reactive power consumption. When the compensation capacitance of the converter bus does not change in a short time after the fault occurs, the reactive power consumed by the converter station will also decrease if the active power transmitted by the dc system decreases. The compensation capacitor may provide more reactive power compensation than consumed reactive power, and thus the remaining reactive power may be provided to the grid system, thereby increasing the voltage level of the ac system. Therefore, in order to solve the problem of transient voltage stability, the high-voltage direct current converter station can be used as an emergency reactive power supply, the consumption of reactive compensation quantity is reduced by reducing direct current transmission current for a short time, and reactive support is provided for a system under the condition that the reactive compensation quantity is kept unchanged, so that the emergency control of the transient voltage stability of the power grid of the high-voltage direct current receiving end system is realized. Aiming at the quantitative calculation of the short-time reduced direct current magnitude, the invention provides a multi-objective nonlinear optimization model which takes reduction of HVDC transmission energy in a control period and improvement of the voltage recovery rate of a fault near-zone bus as targets and takes an asynchronous motor slip recovery path as a constraint condition. Because the objective function and the differential equation in the constraint condition are extremely complex and difficult to solve on line, the invention further converts the objective function and the differential equation in the constraint condition comprising the direct current model into an algebraic equation based on a global orthogonal configuration method, thereby converting an optimization model into a multi-objective nonlinear programming problem, enabling the model to be easy to solve, and solving an emergency voltage control strategy by adopting a multi-objective evolutionary algorithm. The technical problem of the invention is mainly solved by the following technical scheme:
a novel calculation method for an emergency voltage control strategy of a high-voltage direct-current power transmission system is characterized by comprising the following steps:
step 1: establishing an emergency voltage control multi-target nonlinear optimization model aiming at reducing HVDC transmission energy in a control period and improving the fault near-zone busbar voltage recovery rate based on a dynamic model of HVDC and other power system elements;
and 2, step: converting the objective function in the step 1 and a differential equation in a constraint condition including a direct current model into an algebraic equation based on a global orthogonal configuration method, so as to convert the multi-objective nonlinear optimization model in the step 1 into a multi-objective nonlinear programming problem;
and step 3: solving a nonlinear programming problem by adopting a multi-objective evolutionary algorithm to obtain an emergency voltage control strategy; the emergency voltage control strategy is issued to a safety control system by a dispatching center for on-line updating, transient voltage instability of a direct-current receiving end power grid is avoided, high calculation efficiency is achieved, and the problem of large real-time calculation amount caused by an on-line rolling optimization process of a model prediction control algorithm is solved.
Specifically, the step 1 of establishing a multi-objective nonlinear optimization model of the emergency voltage control strategy based on the dynamic model of each element of the power system specifically includes:
1. the model of the generator is as follows:
wherein x is d Denotes the direct-axis synchronous reactance, x q Represents a quadrature axis synchronous resistance, T' d0 Means for indicating straightTime constant of open circuit of shaft transient state, T ″) d0 Representing the direct axis transient open-circuit time constant, D representing the damping coefficient of the generator, f 0 Indicating the nominal frequency, T, of the system J Representing the time constant of inertia, K, of the generator rotor G Representing the saturation factor.
2. The asynchronous motor employs a mechanical transient model, as follows:
wherein U represents the terminal voltage of the asynchronous motor, R s And X s Respectively representing stator resistance and reactance, R r And X r Representing rotor resistance and electricity, X, respectively m Representing field reactance, s representing slip ratio of asynchronous motor, P E And Q E Representing the active and reactive parts of the electromagnetic power of the asynchronous motor, H representing the rotor time constant of the asynchronous motor, P M Representing the mechanical power of the generator.
Differential equations for a hvdc high voltage direct current transmission system are as follows:
wherein R is ci And R cj Respectively the sum of the commutation resistance, the grounding lead resistance and the grounding resistances at two sides, L si And L sj Respectively the sum of the inductance of the smoothing reactor and the inductance of the grounding wires at two sides.
4. The power grid model is established as follows:
for nodes i other than the direct current converter station node or the asynchronous motor node, the power balance equation is as follows:
wherein, P Li And Q Li Representing load active and reactive power on node i，P Gi And Q Gi Representing the active power generated and the active power of node i, U i And U j Representing the voltages of nodes i and j, θ ij ＝θ i -θ j Representing the phase angle difference, G, of nodes i and j ij And B ij Representing the real and imaginary parts of the corresponding elements of the nodal admittance matrix.
For an HVDC converter node, the power balance equation is as follows:
wherein B represents the number of poles of the DC system, I d Representing direct current, T representing the conversion ratio of the converter transformer, X B Representing leakage reactance, gamma, of converter transformer ref And the command value represents a turn-off angle, and the extra-high voltage direct current specifically refers to the voltage of a bus of the converter.
For a node connected to an asynchronous motor, the power balance equation is as follows:
from the above equation, the grid model can be obtained as follows:
wherein, x = [ theta, U, s]Is a state variable, u = [ I = [) d ]And controlling variable direct current in a nonlinear optimization model.
In order to realize the rapid recovery of the transient voltage stability of the direct current receiving end power grid and simultaneously make the control cost as small as possible, namely the transmission reduction of the direct current active energy quantity as small as possible, a power balance equation of a node i except a direct current converter station node or an asynchronous motor node is used as an equality constraint condition, a variation range of a state variable and a control variable is used as an inequality constraint condition, and a multi-objective optimization model with the multiple targets is further established as follows:
wherein,
wherein the objective function f 1 Represents the reduction of the transmission of the DC active energy during the control period, u l Representing the fault near zone bus voltage, objective function f 2 Representing the inverse of the fault near zone bus recovery rate after the fault.
Meanwhile, in the control process, in order to prevent the voltage and power angle from being unstable, the node voltage constraint and the power angle constraint are as follows:
-180°≤θ i k -θ COI k ≤180°
wherein, P dcn Representing rated transmission power, U, of HVDC HVDC In particular to the unit voltage value, T, of the inverter station converter bus start And T finish Respectively the start and end times of the control duration, i U k and
respectively, a lower limit and an upper limit, i U k set to be 0.80p.u,
set to 1.1p.u, theta i Representing the phase angle, θ, of node i COI Representing the center of inertia of the system.
The standard of the transient voltage stability in China is that in the transient process after the disturbance of a power system, the voltage of a load bus can be recovered to be 0.80p.u.or more within 10 seconds after the fault. Therefore, the present invention sets the control duration to 10s.
The nonlinear optimization model is established, but the nonlinear optimization model contains a differential equation, so that the solving difficulty is high, the calculation efficiency is low, and the online application requirement is difficult to meet. Therefore, a global orthogonal configuration method is introduced, and the differential equation in the steps is converted into an algebraic equation, so that the model is easy to solve.
Specifically, the method comprises the following steps: and 2, step: for the non-linear optimization objective f in step 1 1 And converting the global orthogonal configuration method into a nonlinear programming problem.
The orthogonal configuration method is one of the most effective numerical methods for solving the optimal control problem. In order to solve the non-linear optimization objective f in step 1 1 And f 2 The invention is based on a Global Orthogonal Configuration (GOC) method, converts a target function and a differential equation in a constraint condition including a direct current model into an algebraic equation, and takes a function value at a configuration point as a solution target, so that the nonlinear optimization problem is easy to solve.
The GOC adopts a high-order differential polynomial as a basis function to approximate variables, and can obtain higher approximation precision by using fewer configuration points. The basic idea of GOC is to discretize the optimization problem in consecutive sampling intervals into a set of configuration points, transform the integration problem into a weighted algebraic sum of the function values at the configuration points by distributing the configuration points as the roots of some orthogonal polynomial, and thus transform the differential equations into algebraic equations for solution.
The invention adopts the following high-precision Legendre-Gauss matching method:
wherein f (ζ) i ) Is the value of the integral function at the point of integration, W i Is the weight coefficient and K is the number of integration points.
Since the time domain is optimized to be [ T start ，T finish ]But is globally positiveThe cross-configured time domain is defined as [ -1,1]The time interval is transformed from T by the time domain as shown below start ，T finish ]Conversion to [ -1,1]：
Then, the root τ of the Legendre polynomial of order k is used 1 、τ 2 、τ 3 、…、τ k As configuration points, k lagrange interpolation polynomials are constructed to approximate the state variables. Where X and U denote interpolation, and X and U denote actual values.
Wherein,
the derivation of the above formula is:
wherein,
objective function f in step 1 1 Can be expressed as follows:
based on the above formulaObjective function f in step 1 1 Rewritable as follows:
thereby optimizing the objective function f of the model 1 The method can be used for emergency reactive voltage control, and is specifically as follows:
similarly, the objective function f 2 Can be expressed as:
wherein D is k Representation matrix D ij Line k, U of l k Representing the fault near zone bus voltage at the kth configuration point. The differential equation constraints in step 1 can be written as:
x′＝f(x(τ),u(τ),τ)∈[T start ,T finish ]
the differential equation is converted to an algebraic equation as follows:
the dc model is then represented as:
wherein, I D ＝[I d 1 ,I d 2 ...I d k ] T Column vectors of K rows, I d k Indicating the dc current at the kth configuration point.
The equation of motion of the rotor of an asynchronous motor is expressed as:
wherein S = [ S ] 1 ,s 2 ...s k ] T Column vector of K rows, s k Representing the slip at the kth configuration point. P E k And P M k Respectively, the electromagnetic torque and the mechanical torque at the k-th arrangement point, the expression is as follows:
to keep the voltage stable, the final state variable s needs to reach its pre-fault steady-state value s 0 As follows:
wherein s is start Is the slip at the beginning of the control, s 0 Is the pre-fault slip.
Therefore, the multi-objective nonlinear optimization model is converted into a multi-objective nonlinear programming problem by introducing the GOC.
And step 3: the multi-objective optimization problem is solved by adopting a multi-objective evolutionary algorithm to obtain an emergency voltage control strategy, the emergency voltage control strategy in a control time domain can be obtained through one-time solving, the transient voltage instability phenomenon which takes an induction motor as a main factor can be avoided, the transient voltage stability of a receiving end power grid can be quickly recovered, and meanwhile, the reduction of the transmission electric energy of a direct current system can be reduced as much as possible. The emergency voltage control strategy is sent to the safety control main station by the dispatching center every five minutes for on-line refreshing, if the power grid fails, the safety control main station matches the corresponding emergency voltage control strategy according to the running mode of the power grid and the failure, and if the matching is successful, the matched emergency control scheme is sent to the direct current protection system for execution, so that the problem of large real-time calculation amount caused by the online rolling optimization process of the model prediction control algorithm is solved, and the calculation efficiency is greatly improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of an improved IEEE-14 node algorithm system topology;
FIG. 3 is a graph showing the voltage change of each node before and after a fault;
FIG. 4 is a DC current profile after applying an emergency voltage control strategy;
FIG. 5 is a graph of simulation and calculation results of slip s based on GOC;
FIG. 6 is a 14-node voltage graph based on GOC and ode15 s;
FIG. 7 is a 9-node voltage graph based on GOC and ode15 s;
FIG. 8 is a comparison graph of calculated error curves based on GOC and ode15 s;
FIG. 9 is a graph comparing 14 node voltage curves with and without emergency control action applied.
Detailed Description
In the present invention, the calculation method of the emergency voltage control is explained by an improved IEEE-14 node system.
The HVDC receiving end power grid topology of the improved IEEE-14 node system is shown in figure 2. In this system, 10 induction motors based on the IEEE-6 type are provided at node 14. The parameters of the individual motors are shown in table 1. The node 9 is connected to the HVDC converter station. The parameters of the converter station are shown in table 2. Node 1 is an infinite system, and other generators adopt a third-order model. The reference capacity of the system is 440MW, and the reference voltage is 220kV. The improved IEEE-14 node system load information is shown in table 3.
TABLE 1 Induction Motor parameters
TABLE 2 DC System parameters
TABLE 3 improved IEEE-14 node system load information
When t =1.0s, a three-phase short-to-ground fault occurs at the 9-14 signal line end near the node 14. When the emergency voltage control strategy is not applied, the voltages of the nodes near the fault before and after the fault are shown in fig. 3, and the voltages of the node 9 and the node 14 continue to drop and finally drop below 0.8p.u, which finally causes transient voltage instability.
The starting time of the emergency control strategy is set to 0.3s after the fault occurs, that is, when t =1.3s, the emergency voltage control strategy solved by the optimization model based on the GOC in the present invention is implemented, that is, the dc current control amount is as shown in fig. 4. The transmission energy under the scheme is reduced by 0.3624p.u. Slip s and node voltage curves obtained from the model solution based on the emergency voltage control strategy are represented by solid lines in fig. 5, 6 and 7, respectively. As can be seen, the slip s of the equivalent induction motor can be restored to the level before the fault, and the voltages of the nodes 9 and 14 can also be restored to the normal operation state, thus proving the effectiveness of the strategy.
To verify the accuracy of the proposed emergency voltage control strategy, it is introduced into the differential algebraic equations of the power system and solved with the solver ode15s provided by MATLAB. The obtained slip and node voltage curves are shown in fig. 5, 6 and 7, respectively, with dashed lines. FIG. 7 shows the relative error between the results of the calculation of the ode15s and the GOC-based method. According to fig. 3-7, the results calculated based on GOCs and ode15s are substantially consistent. As can be seen from fig. 8, the relative voltage error of the node 9 and the node 14 and the slip ratio of the induction motor are 10 -2 The accuracy requirement can be met by the aid of the number of orders.
Fig. 9 depicts a comparison of the voltage at node 14 before and after applying the emergency voltage control strategy. As shown, after applying the emergency voltage control strategy, the voltage can be restored to a normal operation state, proving the effectiveness of the emergency control strategy.
In the aspect of computational efficiency, for a control process of 10 seconds, the solution time is 26.7950s by applying a multi-objective optimization algorithm based on GOC, and the time length for solving a first-order differential equation based on ode15s is 309.611s, so that the method has obvious advantages in the aspect of computational efficiency. This demonstrates the superiority in computational efficiency and potential for online application of the emergency voltage control of a new type of hvdc transmission system according to the present invention.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above-mentioned embodiments are described in some detail, and not intended to limit the scope of the invention, and those skilled in the art will be able to make alterations and modifications without departing from the scope of the invention as defined by the appended claims.
Claims (6)
1. A novel calculation method for an emergency voltage control strategy of a high-voltage direct-current power transmission system is characterized by comprising the following steps:
step 1: establishing an emergency voltage control multi-target nonlinear optimization model aiming at reducing HVDC transmission energy in a control period and improving the voltage recovery rate of a fault near-zone bus based on a dynamic model of an HVDC power system element;
step 2: converting the objective function in the step 1 and a differential equation in a constraint condition including a direct current model into an algebraic equation based on a global orthogonal configuration method;
and 3, step 3: and solving the nonlinear programming problem by adopting a multi-objective evolutionary algorithm to obtain an emergency voltage control strategy.
2. The method for calculating the emergency voltage control strategy of the novel high-voltage direct-current power transmission system according to claim 1, wherein in the step 1, the multi-objective nonlinear optimization model is specifically constructed as follows:
(1) The model of the generator is as follows:
wherein x is d Denotes the direct-axis synchronous reactance, x q Represents a quadrature axis synchronous resistance, T' d0 Represents the direct-axis transient open-circuit time constant, T ″) d0 Representing the direct axis transient open-circuit time constant, D representing the damping coefficient of the generator, f 0 Indicating the nominal frequency, T, of the system J Representing the time constant of inertia, K, of the generator rotor G Represents a saturation coefficient;
(2) The asynchronous motor employs a mechanical transient model, as follows:
wherein U represents the terminal voltage of the asynchronous motor, R s And X s Respectively representing stator resistance and reactance, R r And X r Representing rotor resistance and electricity, X, respectively m Representing field reactance, s representing slip ratio of asynchronous motor, P E And Q E Representing the active and reactive parts of the electromagnetic power of the asynchronous motor, H representing the rotor time constant of the asynchronous motor, P M Representing the mechanical power of the generator;
(3) The differential equation for a HVDC high voltage direct current transmission system is as follows:
wherein R is ci And R cj Respectively the sum of the commutation resistance, the grounding lead resistance and the grounding resistances at two sides, L si And L sj The sum of the inductance of the smoothing reactor and the inductance of the grounding wires at two sides respectively;
(4) The grid model is established as follows:
for nodes i other than the direct current converter station node or the asynchronous motor node, the power balance equation is as follows:
wherein, P Li And Q Li Representing the active and reactive power of the load on node i, P Gi And Q Gi Representing the active power generated and the active power, U, of node i i And U j Representing the voltages of nodes i and j, θ ij ＝θ i -θ j Representing the phase angle difference, G, of nodes i and j ij And B ij Representing the real part and the imaginary part of the corresponding element of the node admittance matrix;
for a node connected to an asynchronous motor, the power balance equation is as follows:
for a HVDC converter node, the power balance equation is as follows:
wherein B represents the number of poles of the DC system, I d Representing direct current, T representing the conversion ratio of the converter transformer, X B Representing leakage reactance, gamma, of converter transformer ref And the command value represents a turn-off angle, and the extra-high voltage direct current specifically refers to the voltage of a bus of the converter.
3. The method for calculating the emergency voltage control strategy of a new HVDC transmission system according to claim 1, characterized in that in step 1,
obtaining a power grid model according to the equation in the step 1:
wherein, x = [ theta, U, s]Is a state variable, u = [ I = [) d ]And controlling variable direct current in a nonlinear optimization model.
4. The method for calculating the emergency voltage control strategy of the novel high-voltage direct-current transmission system according to claim 1, wherein in the step 1, a multi-objective optimization model with multiple objectives is established by taking a power balance equation of a node i except a direct-current converter station node or an asynchronous motor node as an equality constraint condition and taking a variation range of a state variable and a control variable as an inequality constraint condition, as follows:
wherein,
wherein the objective function f 1 Represents the decrement, u, of the transmission of the DC active energy during the control period 1 Representing the fault near zone bus voltage, an objective function f 2 Representing the reciprocal of the recovery rate of the fault near-zone bus after the fault;
meanwhile, in the control process, in order to prevent the voltage and power angle from being unstable, the node voltage constraint and the power angle constraint are as follows:
-180°≤θ i k -θ COI k ≤180°
wherein, P dcn Representing rated transmission power, U, of HVDC HVDC In particular to the unit voltage value, T, of the inverter station converter bus start And T finish Respectively the start and end times of the control duration, i U k and
respectively, a lower limit and an upper limit, i U k set to be 0.80p.u,
set to 1.1p.u, theta i Representing the phase angle, θ, of node i COI Representing the center of inertia of the system.
5. The method for calculating the emergency voltage control strategy of the novel high-voltage direct current transmission system according to claim 1, wherein the step 2 is specifically as follows:
based on a Global Orthogonal Configuration (GOC) method, converting a target function and a differential equation in a constraint condition including a direct current model into an algebraic equation, and taking a function value at a configuration point as a solution target;
adopting the following high-precision Legendre-Gauss (LG) Legendre-Gaussian matching method:
wherein f (ζ) i ) Is the value of the integral function at the point of integration, W i Is the weight coefficient, K is the number of integration points;
target function f in step 1 1 The following were used:
thereby optimizing the objective function f of the model 1 The method can be used for emergency reactive voltage control, and is specifically as follows:
similarly, the objective function f 2 Can be expressed as:
wherein D is k Representation matrix D ij Line k, U of t k Representing a fault near zone bus voltage at the kth configuration point;
the differential equation constraint in step 1 can be written as:
x′＝f(x(τ)，u(τ)，τ)∈[T start ，T finish ]
similarly, the differential equation is converted to an algebraic equation as follows:
the dc model is then represented as:
wherein, I D ＝[I d 1 ，I d 2 ...I d k ] T Column vectors of K rows, I d k Represents the direct current at the kth configuration point;
the equation of motion of the rotor of an asynchronous motor is expressed as:
wherein S = [ S ] 1 ，s 2 ...s k ] T Column vector of K rows, s k Representing the slip at the kth configuration point; p E k And P M k Respectively, the electromagnetic torque and the mechanical torque at the k-th configuration point, the expression is as follows:
to keep the voltage stable, the final state variable s needs to reach its pre-fault steady-state value s 0 As follows:
wherein s is start Is the slip at the beginning of the control, s 0 Is the pre-fault slip.
6. The method for calculating the emergency voltage control strategy of the novel high-voltage direct current transmission system according to claim 1, wherein the step 3 is as follows: and solving the multi-target optimization problem by adopting a multi-target evolutionary algorithm to obtain an emergency voltage control strategy, obtaining the emergency voltage control strategy in a control time domain by one-time solving, sending the emergency voltage control strategy to a safety control main station every five minutes by a dispatching center, matching the corresponding emergency voltage control strategy by the safety control main station according to the operation mode of the power grid and the fault if the power grid fails, and sending the matched emergency control scheme to a direct current protection system for execution if the matching is successful.
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