A new energy and heterogeneous converter multi-resource collaborative control method

Abstract

The application discloses a new energy and heterogeneous converter multi-resource collaborative control method, and belongs to the technical field of power system and micro-grid operation and control, which comprises the following steps: constructing a unified differential algebraic model containing heavy-load railway traction load and various heterogeneous resources, defining a multi-dimensional safety boundary in combination with railway dynamic disturbance, and constructing a generalized dynamic safety domain; online identifying a dominant safety boundary closest to a current operation point, establishing a multi-step dynamic support performance matrix of the dominant safety boundary and various control degrees of freedom; constructing a safety-priority lexicographic rolling optimization model based on the matrix, and solving and generating control instructions of various heterogeneous resources. The application breaks the traditional mode of preset fixed allocation ratio, can adaptively identify the weakest risk dimension of the system and efficiently match the optimal resource, and improves the multi-dimensional dynamic safety and stability margin of the heavy-load railway micro-grid without triggering the current limiting of equipment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of power system and microgrid operation and control, in particular to a new energy and heterogeneous converter multi-resource collaborative control method. BACKGROUND

[0002] Heavy haul railway traction load has the characteristics of high power level, fast change speed, significant single-phase imbalance and frequent bidirectional switching between traction and regeneration. With the access of wind power, photovoltaic and electrochemical energy storage along the railway power supply corridor, the traction power supply system gradually evolves from the traditional strong power grid supply mode to the high proportion of power electronic microgrid. Existing research has carried out research on the energy management and uncertain scheduling of flexible traction substation of heavy haul railway, but its focus is mainly on economic operation, plan tracking and power quality compensation. On the other hand, the train-network system has the risk of low-frequency oscillation caused by the impedance characteristics of the converter. Some scholars have proposed a quantitative stability index for train-network low-frequency oscillation based on the improved Nyquist criterion; some scholars further pointed out that different train and traction converter control structures will significantly change the train-network coupling stability condition. Therefore, for heavy haul railway microgrid, only meeting the active power balance cannot guarantee the safety of railway operation.

[0003] Grid-forming converters can establish voltage and frequency references and improve the disturbance tolerance of low-inertia systems through virtual inertia, damping and voltage source characteristics; grid-following converters rely on phase-locked loops for synchronization and have mature power tracking and negative sequence / harmonic compensation capabilities, but their small-signal stability is more sensitive to grid strength and impedance conditions. At the same time, the current limiting link of GFM will change the device dynamics and system stability boundary under large disturbances. The synchronous condenser or static synchronous compensator (STATCOM) can improve the stability margin of weak grids through short-circuit capacity, physical inertia or fast reactive power. Related research has quantified the role of synchronous condenser support from the perspective of impedance stability.

[0004] Existing multi-resource collaborative strategies usually predefine the control sequence of “GFM fast response, GFL subsequent takeover, STATCOM voltage stabilization” according to the time scale, or set fixed / adaptive participation factors according to frequency difference and voltage deviation. This kind of method can improve a certain dynamic index, but it still lacks a unified mechanism to answer two key questions: (1) What is the stability boundary that currently threatens the safety of heavy haul railway first; (2) Which kind of heterogeneous resource and which control degree of freedom is most effective for the recovery of this boundary. Microgrid safety domain research shows that mapping multiple operating constraints to safety regions and boundary distances can provide more comprehensive preventive control information than single out-of-limit criteria, but existing safety domain research has not formed a unified dynamic safety domain and resource matching method for heavy haul railway impact load, heterogeneous converter impedance interaction and GFM current limiting. SUMMARY

[0005] The present application provides a new energy and heterogeneous converter multi-resource collaborative control method to solve the technical problems that the existing control strategy based on fixed control sequence or fixed participation factor cannot accurately identify the current security boundary that threatens the weakest system, and cannot realize adaptive matching of the control freedom of various heterogeneous resources for security boundary recovery, thus easily triggering device protection action or multi-dimensional security overrun, and cannot guarantee the comprehensive stable and safe operation of the heavy load railway microgrid under the multiple complex working conditions of impact load, impedance interaction of heterogeneous converters, and current limiting of network type equipment.

[0006] To solve the above problems, the technical scheme adopted by the present application is as follows:

[0007] A new energy and heterogeneous converter multi-resource collaborative control method, comprising: constructing a unified differential algebraic model of an alternating current microgrid containing heavy load railway traction load, network type energy storage, grid following type energy storage, static synchronous compensator and wind and light resources; based on the unified differential algebraic model, defining multiple dimensions of railway security boundaries, and combining the railway dynamic disturbance of the heavy load railway traction load to construct a generalized dynamic security domain; in the generalized dynamic security domain, identifying the dominant security boundary closest to the operating point in real time, and establishing a multi-step dynamic support performance matrix between the dominant security boundary and the control freedom of each heterogeneous resource; based on the multi-step dynamic support performance matrix, constructing a security priority lexicographic rolling optimization model, and solving to generate control instructions corresponding to each heterogeneous resource, the control instructions including active power, reactive power and converter control parameters.

[0008] Further, the process of constructing the unified differential algebraic model comprises:

[0009] extracting a dynamic state vector, an algebraic state vector, a control vector and a disturbance vector describing the railway dynamic disturbance of the system;

[0010] The dynamic state vector includes internal control states of network type energy storage, internal control states of grid following type energy storage, and state of charge of the two types of energy storage; the control vector includes active reference value, reactive reference value, virtual inertia, virtual damping, virtual resistance and virtual reactance of network type energy storage, active reference value, reactive reference value and negative sequence compensation current reference value of grid following type energy storage, reactive output reference value of static synchronous compensator, and available power reference value of wind and light resources; the disturbance vector includes traction active power, traction reactive power, traction power change rate, railway side imbalance characteristic quantity and equivalent dynamic impedance of train and traction network.

[0011] Based on the extracted vectors, a unified differential algebraic model is generated by solving differential equations describing the converter control, the energy storage and the equivalent electromagnetic dynamics, and algebraic equations describing the AC network power flow and algebraic constraints.

[0012] Further, seven types of non-dimensionalized railway safety boundaries are defined, including a traction voltage boundary, a system frequency boundary, a frequency rate of change impact boundary, a negative sequence boundary, a heterogeneous converter impedance stability boundary, a network type energy storage current limiting boundary, and a continuous energy support boundary. The seven types of non-dimensionalized railway safety boundaries are integrated into a generalized dynamic safety domain in combination with the railway dynamic disturbance. In the generalized dynamic safety domain, the values of each of the railway safety boundaries are set to be greater than or equal to zero, indicating an out-of-limit state.

[0013] Further, the railway safety boundary is defined in the following manner:

[0014] The traction voltage boundary is obtained by taking the minimum value between a first voltage ratio term and a second voltage ratio term. The first voltage ratio term is a difference between an actual traction bus voltage and a minimum allowable voltage, divided by a difference between a rated traction bus voltage and the minimum allowable voltage. The second voltage ratio term is a difference between a maximum allowable voltage and the actual traction bus voltage, divided by a difference between the maximum allowable voltage and the rated traction bus voltage.

[0015] The system frequency boundary is obtained by taking the minimum value between a first frequency ratio term and a second frequency ratio term. The first frequency ratio term is a difference between an actual frequency and a lower limit of an allowable frequency, divided by a difference between a rated frequency and the lower limit of the allowable frequency. The second frequency ratio term is a difference between an upper limit of the allowable frequency and the actual frequency, divided by a difference between the upper limit of the allowable frequency and the rated frequency.

[0016] The frequency rate of change impact boundary is obtained by subtracting a ratio between an actual frequency rate of change absolute value and a maximum allowable frequency rate of change from a constant 1.

[0017] The negative sequence boundary is obtained by subtracting a ratio between an actual negative sequence voltage ratio and an upper limit of an allowable negative sequence voltage ratio from a constant 1.

[0018] Further, the railway safety boundary is defined in the following manner:

[0019] The heterogeneous converter impedance stability boundary is obtained by calculating a generalized impedance loop matrix based on an equivalent impedance matrix of the heterogeneous converter and the AC network and a railway side equivalent impedance matrix, extracting a minimum distance of the generalized impedance loop matrix relative to a Nyquist critical point as an impedance stability margin, and dividing a difference between a current impedance stability margin and a minimum allowable stability margin by a difference between a reference operation reference margin and the minimum allowable stability margin.

[0020] The networked energy storage current limiting boundary: the difference between the maximum allowable current and the actual output current, divided by the difference between the maximum allowable current and the reference operation reference current;

[0021] The continuous energy support boundary: based on the difference between the railway traction power prediction value within the prediction window and the sustainable power provided by the external resource, the required net support energy is calculated by integral calculation; the difference between the energy that can be released by the energy storage and the required net support energy, divided by the reference energy.

[0022] Further, the method of identifying the dominant safety boundary online and establishing the multi-step dynamic support efficiency matrix includes:

[0023] Calculate the current normalized value of each of the railway safety boundaries, and select the safety boundary with the smallest current normalized value as the dominant safety boundary;

[0024] Nonlinearly map the current normalized values of all the railway safety boundaries by a smoothing coefficient to calculate a continuous and differentiable comprehensive safety margin as an optimized micro-safety target;

[0025] Obtain the state transition matrix of the unified differential algebraic model after discretization at the current working point;

[0026] Combine the first-order expansion partial derivative matrix of the railway safety boundary near the current working point with the state transition matrix to calculate the incremental influence of changing the control freedom of the heterogeneous resource on the dominant safety boundary in the future prediction steps at the current time, forming the multi-step dynamic support efficiency matrix.

[0027] After establishing the multi-step dynamic support efficiency matrix, further calculate the effective safety support efficiency of each heterogeneous resource, specifically including:

[0028] From the multi-step dynamic support efficiency matrix, extract the dominant boundary support sensitivity of the target resource to the dominant safety boundary in the future prediction steps;

[0029] According to the difference between the maximum output capacity upper limit of the target resource and the current output absolute value, calculate the remaining capacity; combine the device health state and current limiting state parameters to obtain the corresponding availability coefficient;

[0030] Multiply the dominant boundary support sensitivity, the remaining capacity and the availability coefficient to obtain the effective safety support efficiency of the target resource.

[0031] Further, the lexicographic rolling optimization model includes a first-level optimization model and a second-level optimization model in a hierarchical progression:

[0032] The first-level optimization model aims to maximize the uniform minimum safety margin within the prediction time domain, thereby obtaining the optimal minimum safety margin.

[0033] The second-level optimization model: Under the premise that the railway safety boundary of each prediction step is greater than or equal to the optimal minimum safety margin minus the allowable slack, economic optimization is performed with the goal of minimizing the system operating cost to generate the control command; the system operating cost includes the control increment cost, energy storage loss cost, and new energy curtailment cost.

[0034] In the second-level optimization model, the control increment cost generated by each control command is adjusted by the control increment weight matrix. The dynamic update method of the control increment weight matrix includes: dynamically adjusting the control increment weight of each heterogeneous resource according to the effective security support performance of each resource. When the absolute value of the effective security support performance of the target resource is larger, it is given a smaller control increment weight, so as to drive the heterogeneous resource with higher support performance to participate in the recovery of the current dominant security boundary first.

[0035] Furthermore, the method of the present invention also introduces a robust safety region shrinkage mechanism that takes into account errors, specifically including:

[0036] The railway dynamic disturbance is decomposed into a set of predicted disturbances and bounded errors;

[0037] Calculate the local sensitivity of each of the railway safety boundaries to the dynamic disturbance of the railway, and combine the bounded error set to solve for the robust contraction of each of the railway safety boundaries;

[0038] The robust contraction amount is subtracted from the generalized dynamic safety domain to generate a contracted safety boundary, which serves as a constraint condition for the lexicographical rolling optimization model, ensuring that the actual closed-loop control state always remains within the generalized dynamic safety domain.

[0039] Compared with the prior art, the beneficial effects of the present invention are:

[0040] (1) The core control logic of this invention is transformed from the traditional "who bears the power deficit" to "which safety boundary is the most dangerous at present, and which resource can most efficiently restore the boundary". By constructing a generalized dynamic safety domain and identifying the dominant safety boundary online, and relying on the multi-step dynamic support efficiency matrix for lexicographical rolling optimization, this invention breaks the rigid mode of pre-defined control sequence (such as rapid response takeover, voltage stabilization) and realizes the automatic reconfiguration of control weights according to the dominant risk. It can adaptively match the control degree of heterogeneous resources without triggering equipment current limiting, thereby improving the comprehensive stability and safety margin of heavy-haul railway microgrids under composite operating conditions.

[0041] (2) This invention uniformly defines a generalized dynamic safety domain covering seven dimensions: traction voltage, system frequency, rate of change of frequency, negative sequence, impedance stability of heterogeneous converters, current limiting of grid-type energy storage, and continuous energy support. By directly mapping the internal constraints of the converter (such as current limiting of grid-type energy storage) and the grid strength into the safety domain, the system avoids falling into a pseudo-safety state where the frequency and voltage appear normal but have lost their continuous traction bearing capacity, or a blind zone caused by low-frequency oscillation instability due to heterogeneous converter interaction.

[0042] (3) The present invention introduces a soft-min smoothing function to nonlinearly map the discretized, multi-dimensional safety boundary into a continuously differentiable comprehensive safety margin, so that the online rolling optimizer can obtain a smooth and continuous gradient direction, thereby improving the solution efficiency and numerical stability of online optimization.

[0043] (4) When calculating the effective safety support performance, this invention integrates the physical limits (remaining capacity), health status, and current limiting status of the equipment. For example, when a network-type device approaches the current limiting, its performance automatically decreases, and the system smoothly transfers the safety pressure to other resources, naturally forming a multi-timescale relay that conforms to the physical characteristics of the equipment (such as rapid support of network-type devices and continuous takeover of network-type devices), avoiding chain failures caused by the overload of a single device.

[0044] (5) This invention proposes a robust safety domain contraction mechanism based on local sensitivity to address the power prediction error and the reduced-order model error of heavy-haul railways. By performing bounded contraction of the safety boundary before optimization, a rigorous closed-loop safety domain preservation condition is given, ensuring that the actual closed-loop operating trajectory of the system will not cross the safety red line when facing uncertain disturbances, thus endowing the system with robust safety.

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, embodiments of the present invention are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is the overall structure of the coordinated control of the new energy microgrid and heterogeneous converter for heavy-haul railways in the embodiment;

[0048] Figure 2 This is the core theoretical framework of the multi-resource collaborative control method in the embodiments;

[0049] Figure 3 It is a two-dimensional projection of the dynamic safety domain evolution of heavy-haul railways in the embodiment;

[0050] Figure 4 This is the multi-time-scale collaborative control structure for the heterogeneous converter in the embodiment;

[0051] Figure 5 This is a simulation of the heavy-haul railway composite traction-weak network-regeneration working condition in the embodiment;

[0052] Figure 6 The figures shown are the frequency and RoCoF response in the embodiments, where (a) is the system frequency response and (b) is the frequency change rate response.

[0053] Figure 7 The figures show the traction bus voltage and negative sequence response in the embodiments, where (a) shows the dynamic response of the traction bus voltage and (b) shows the negative sequence voltage suppression effect.

[0054] Figure 8 These are the dynamic security boundaries and dominant boundaries in the embodiments, where (a) shows seven types of security boundaries and (b) shows the switching of dominant security boundaries;

[0055] Figure 9 The embodiments show resource support performance and power allocation, where (a) figure shows the security support performance of heterogeneous resources, and (b) figure shows the active power collaborative allocation of multiple resources.

[0056] Figure 10 This is a verification of GFM current limiting and impedance stability in the embodiment, where (a) is the GFM current and (b) is the generalized impedance Nyquist trajectory;

[0057] Figure 11 This is a comparison of the comprehensive dynamic safety margin of railways using the three control methods in the embodiments. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0059] I. System Structure and Unified Dynamic Model

[0060] 1. System Structure

[0061] This invention focuses on an AC microgrid incorporating wind power, solar power, grid-forming energy storage system (GFM-ESS), grid-following energy storage system (GFL-ESS), STATCOM, and heavy-haul railway traction load. Wind and solar resources provide the primary continuous energy supply; GFM-ESS provides voltage / frequency shaping and rapid active power support; GFL-ESS handles continuous power takeover and negative sequence compensation; and STATCOM provides rapid reactive power and traction bus voltage support. An upper-level dynamic security domain coordinator generates online reference values ​​for active power, reactive power, and GFM control parameters based on railway disturbances, grid strength, and the status of various resources. The system structure of this invention is as follows: Figure 1 As shown.

[0062] To ensure consistent notation throughout the text, the dynamic state vector of the system is extracted. Algebraic state vector Control vector and the disturbance vector describing the dynamic disturbance of the railway They are defined as follows:

[0063] (1)

[0064] (2)

[0065] (3)

[0066] (4)

[0067] In the formula, x G and x F These represent the internal control states of GFM and GFL, respectively; u G Depend on , H v D v R v and X v Composition, u F Depend on , and Composition; SOC G SOC F There are two types of energy storage states of charge; The internal control state of wind and solar resources; U and θ represent the bus voltage amplitude and phase angle; U1 and U2 represent the positive and negative sequence voltages; superscript Indicates the control reference value. P T >0 indicates that the train's traction absorbs active power, P T<0 indicates that regenerative braking feeds active power back to the microgrid; ε T Z represents the characteristic quantity of imbalance on the railway side. T The equivalent dynamic impedance of the train-traction network.

[0068] For control vector : From the active reference value of GFM reactive power reference value Virtual inertia Virtual damping Virtual resistance and virtual reactance composition; From GFL's active power reference value reactive power reference value and negative sequence compensation current reference value composition; This is the reference value for STATCOM reactive power output; , This is a reference value for available wind and solar power. (Superscript) This indicates the control reference value.

[0069] For the perturbation vector : and To drive active and reactive power, This indicates that the train's traction has absorbed the active power. This indicates that regenerative braking feeds back active power to the microgrid; The rate of change of traction power; This refers to the characteristic quantity of imbalance on the railway side; The equivalent dynamic impedance of the train-traction network.

[0070] Based on the extracted vectors, the system is uniformly represented as a differential-algebraic equation model:

[0071] (5)

[0072] (6)

[0073] Where f(·) describes converter control, energy storage and equivalent electromagnetic dynamics, and g(·) describes AC network power flow and algebraic constraints.

[0074] Table 1. Main Variables and Symbols

[0075]

[0076] 2. Traction / Regenerative Disturbance Model for Heavy-Haul Railways

[0077] Given the train mass, speed, track gradient, and traction / braking commands, the train's longitudinal dynamics are as follows:

[0078] (7)

[0079] In the formula, For wheel-rail traction; The total mass of the train; For train speed; For running resistance; Let be the acceleration due to gravity; α be the gradient angle of the track. When using the Davis resistance model:

[0080] (8)

[0081] in, , , This is the drag coefficient determined by train formation and track testing. Train traction / regenerative power is expressed as:

[0082] (9)

[0083] In the formula, For traction transmission efficiency. This is for regenerative braking feedback efficiency. Therefore, railway disturbances are not only related to power amplitude... Related to, and also with Negative sequence characteristics and equivalent impedance Z T They are mutually related.

[0084] 3. GFM-ESS dynamic model and current limiting constraints

[0085] GFM-ESS uses a virtual synchronous machine equivalent outer loop, and its frequency dynamics are as follows:

[0086] (10)

[0087] (11)

[0088] in, ; This is the actual output angular frequency of the GFM. This is the rated angular frequency; The phase angle of the internal voltage of the GFM; for The first derivative with respect to time. Reactive power-voltage control is written as:

[0089] (12)

[0090] in, The rated internal potential, This is the reactive power-voltage droop factor. A virtual impedance is introduced to adjust the output impedance and suppress heterogeneous converter coupling.

[0091] (13)

[0092] GFM is limited by the overcurrent capability of power devices, and its current constraint is:

[0093] (14)

[0094] Among them, i d,G i q,G I is the dq component of the GFM output current. G max This is the maximum permissible current. Since current limiting alters the voltage source characteristics and transient stability behavior of the GFM, this invention directly incorporates it into the railway dynamic safety domain, rather than merely using it as an equipment protection constraint.

[0095] 4. GFL-ESS, STATCOM and new energy models

[0096] GFL-ESS is synchronized via PLL, and its active and reactive power closed loops adopt a first-order equivalent model:

[0097] (15)

[0098] (16)

[0099] Among them, T P,F T Q,F These are the active and reactive equivalent time constants of the GFL, respectively. , These are the first derivatives of the active and reactive power of the GFL with respect to time, respectively. Negative sequence compensation is achieved through... Adjustment is mainly used for addressing imbalances on the railway side.

[0100] STATCOM reactive power dynamics are:

[0101] (17)

[0102] Among them, T ST The STATCOM equivalent response time constant, Q is the first derivative of the reactive power output of STATCOM with respect to time. ST max This is its upper limit for reactive power capacity. The available power of wind power and photovoltaic power are respectively P w av P pv av Its safety backup is:

[0103] (18)

[0104] In the formula, , These represent the actual active power outputs of wind power and solar power, respectively. >0 indicates that the new energy source actively reserves power for future use.

[0105] II. Generalized Dynamic Safety Domain of Heavy-Haul Railways

[0106] The core theoretical chain of the method of this invention is as follows: Figure 2 As shown: a generalized dynamic safety domain is constructed from railway dynamic disturbances, the current dominant safety boundary is identified, the dynamic support efficiency of heterogeneous resources is calculated, and control commands are generated through safety-priority rolling optimization.

[0107] 1. Seven types of railway safety boundaries

[0108] Define seven types of dimensionless railway safety boundary vectors:

[0109] (19)

[0110] Each component is normalized to a dimensionless quantity that is "larger for greater security, zero corresponds to the boundary, and negative values ​​indicate out-of-bounds." These boundaries are then integrated into a generalized dynamic security domain, taking into account railway dynamic disturbances.

[0111] (1) Traction voltage boundary The voltage ratio is obtained by taking the minimum value between the first voltage ratio term and the second voltage ratio term. The first voltage ratio term is the actual traction bus voltage. With the minimum allowable voltage The difference, divided by the rated traction bus voltage The difference between the voltage and the minimum allowable voltage; the second voltage ratio term is the maximum allowable voltage. The difference between the actual traction bus voltage and the rated traction bus voltage is divided by the difference between the maximum allowable voltage and the rated traction bus voltage. The formula is as follows:

[0112] (20)

[0113] (2) System frequency boundary It is obtained by taking the minimum value between the first frequency ratio term and the second frequency ratio term. The first frequency ratio term is the actual frequency. With the lower limit of the allowed frequency The difference, divided by the rated frequency The difference between the lower and upper allowable frequency limits; the second frequency ratio term is the upper allowable frequency limit. The difference between the actual frequency and the rated frequency is divided by the difference between the allowable upper frequency limit and the rated frequency. The formula is as follows:

[0114] (twenty one)

[0115] (3) RoCoF impact boundary (frequency change rate impact boundary) Subtract the absolute value of the actual rate of change of frequency from a constant 1 With the maximum allowable rate of frequency change The ratio is obtained. This boundary directly characterizes the requirements of sudden power changes in heavy-haul railways on system inertia and rapid support capabilities. The formula is as follows:

[0116] (twenty two)

[0117] (4) Negative order boundary First, calculate the actual negative sequence voltage ratio. Then, subtract the actual negative sequence voltage ratio from the constant 1. The upper limit of the allowable negative sequence voltage ratio The ratio is obtained using the following formula:

[0118] (twenty three)

[0119] in, This represents the upper limit of the permissible negative sequence voltage ratio.

[0120] (5) Impedance stability boundary of heterogeneous converter

[0121] At the current operating point, small-signal impedance linearization is performed on the GFM, GFL, new energy converter, and AC network to obtain the source-side equivalent dq impedance matrix Z. s (jω), the equivalent impedance on the railway side is Z. T (jω). Define the generalized impedance loop matrix:

[0122] (twenty four)

[0123] set up Let q be the eigenvalue, then the minimum distance relative to the Nyquist critical point -1+j0 is defined as:

[0124] (25)

[0125] in, For the frequency band of interest, the impedance safety margin is defined as follows:

[0126] (26)

[0127] In the formula, To minimize the allowable stability margin, This serves as the baseline operating reference margin (normal operating condition reference margin). That is, the impedance stability boundary of the heterogeneous converter. The calculation logic is as follows: based on the current impedance stability margin With minimum allowable stability margin The difference, divided by the baseline operating reference margin With minimum allowable stability margin The difference is obtained. This definition allows the PLL, virtual impedance, and grid strength variations of heterogeneous converters to be directly mapped to the railway safety domain.

[0128] (6) GFM current limiting and sustained energy boundary

[0129] The additional fast-response capability of GFM decreases as the current approaches its limit, therefore it is defined as follows:

[0130] (27)

[0131] In the formula, The reference operating current is used as the baseline. This is the current-limiting boundary for grid-type energy storage. The calculation logic is as follows: based on the maximum allowable current. With actual output current The difference is obtained by dividing the difference between the maximum allowable current and the reference operating current.

[0132] To avoid a pseudo-safe state where the current frequency and voltage are normal but the device is no longer capable of withstanding continuous traction, a prediction window [t, t+T] is defined. p The predicted net power deficit within [ ] is The required net support energy is:

[0133] (28)

[0134] in, To predict the time window length, [x] + =max(x,0), This is the predicted value of railway traction power. Power sustainably supplied to the external power grid, wind, solar, and other resources. Energy storage can release the following energy:

[0135] (29)

[0136] Where the summation subscript j∈{G,F} represents GFM-ESS and GFL-ESS respectively; E j cap For the rated capacity of energy storage, the State of Charge (SOC) is expressed in per-unit values. The energy boundary is defined as follows:

[0137] (30)

[0138] In the formula, This is the normalized reference energy. That is, the sustained energy supports the boundary. The calculation logic is as follows: energy can be released through energy storage. With required net support energy The difference is obtained by dividing by the normalized reference energy.

[0139] (7) Dynamic security domain and dominant security boundary

[0140] Based on the above boundaries, the generalized dynamic safety domain for heavy-haul railways is defined as follows:

[0141] (31)

[0142] in, ={U,f,R,2,Z,I,E} is the set of security boundary indices. Since P T , Z T SCR, SOC, and available wind and solar power are constantly changing, therefore Ω R It is not a fixed set, but a time-varying feasible region that evolves with railway operating conditions and system state. Figure 3 The concept of its two-dimensional projection is given.

[0143] Define the current dominant security boundary:

[0144] (32)

[0145] In the formula, This represents the safety boundary that is currently closest to the operating point and most likely to be touched first. Therefore, =R indicates that RoCoF is the primary risk; =U indicates that traction voltage is the main risk; =Z indicates that impedance coupling stability becomes the dominant risk in heterogeneous converters.

[0146] To obtain a continuously differentiable comprehensive safety margin and avoid non-differentiability issues during the optimization process, a smoothing coefficient is introduced. A soft-min function is constructed to perform nonlinear mapping calculations on the current normalized values ​​of all railway safety boundaries, and this value is used as the micro-safety objective for online optimization.

[0147] (33)

[0148] Among them, the smoothing coefficient and define the actual minimum safety boundary. Soft-min satisfies equation (34), when hour, .therefore It can be used as a continuously differentiable comprehensive safety margin in system control.

[0149] (34)

[0150] III. Coordinated Control of Dynamic Support Efficiency and Safety Priority for Heterogeneous Resources

[0151] 1. Local linearization and multi-step dynamic support performance matrix

[0152] Linearizing equations (5)-(6) near the control time k, we obtain:

[0153] (35)

[0154] And use sampling period T s Discretization. Obtain the state transition matrix of the unified differential algebraic model after discretization at the current operating point (denoted as ). ), and control input matrix and perturbation matrix and with Δx + The state increment at the next sampling time is represented by the equation (36), which is shown in equation (36).

[0155] (36)

[0156] Combining the first-order expansion partial derivative matrix of the railway safety boundary near the current working point ( and ), and the state transition matrix, calculate the control degrees of freedom of each heterogeneous resource at the current moment, and predict the future steps (the th step). The incremental impact of the railway safety boundary (step) constitutes a multi-step dynamic support effectiveness matrix. .

[0157] The first-order expansion of the safety boundary vector near the operating point is:

[0158] (37)

[0159] in:

[0160] (38)

[0161] If a control increment Δu is applied at time k k Its impact on the future safety boundary at step h can be written as:

[0162] (39)

[0163] The heterogeneous resource dynamic support efficiency matrix defined in this invention for:

[0164] (40)

[0165] In the formula, Uses Kronecker notation. Matrix elements:

[0166] (41)

[0167] This represents the incremental impact of changing the j-th control degree of freedom by one unit at time k on the i-th railway safety boundary at the h-th step in the future. Compared with static sensitivity, equation (40) explicitly includes the system state transition matrix A. d h-1 Therefore, it is possible to distinguish the real dynamic effects of GFM, GFL, STATCOM and new energy sources at different time scales.

[0168] 2. Dominant Boundary and Effective Resource Support Capability

[0169] After establishing a multi-step dynamic support performance matrix, the effective security support performance is further calculated for each heterogeneous resource. This is for the current dominant security boundary. Extract target resources from the performance matrix In the future Step-by-step dominant boundary support sensitivity of this boundary :

[0170] (42)

[0171] Based on the maximum output capacity limit of the target resource The absolute value of the current output The difference is used to calculate the remaining capacity. :

[0172] (43)

[0173] The availability coefficient is obtained by combining the equipment health status and current limiting status parameters. :

[0174] (44)

[0175] Finally, by multiplying the dominant boundary support sensitivity, remaining capacity, and availability coefficient, the effective security support performance of the target resource is obtained. :

[0176] (45)

[0177] When GFM approaches its current limit, χ I,G→0, the controller will actively reduce the priority of continuing to increase GFM power; when RoCoF becomes the dominant boundary and GFM still has sufficient current margin, Λ G (1) Typically maximum; when the voltage boundary dominates, Λ ST The reactive power support efficiency of GFM is improved; when the negative sequence boundary dominates, the negative sequence compensation efficiency of GFL is improved. This forms an adaptive matching of "safety boundary - resource" rather than a preset fixed control sequence.

[0178] 3. Safety-first dictionary-order rolling optimization

[0179] Let the number of prediction steps be... Control the number of steps to Construct a hierarchical first-level optimization model and a second-level optimization model.

[0180] First-level optimization model: maximizing the uniform minimum safety margin within the prediction time domain. Solve for the objective:

[0181] (46)

[0182] The constraints are:

[0183] (47)

[0184] Second-level optimization model: The first-level optimization yields the optimal minimum safety margin. Then, the railway safety boundary for each prediction step is constrained to be greater than or equal to the optimal minimum safety margin minus the allowable slack. Under the premise (i.e.) The cost objective function is to perform an economic optimization solution with the goal of minimizing the system operating cost, and then generate control commands.

[0185] (48)

[0186] The system operating cost includes the cost of control increments. Energy storage loss cost and the cost of abandoning renewable energy And satisfy:

[0187] (49)

[0188] Where, ε ρ This represents the minimum permissible safety performance slack. The upper and lower limits of active power, reactive power, and control parameters for each device are uniformly denoted as u. min and u max Then the main control variables and the GFM current constraint can be written as:

[0189] (50)

[0190] Energy storage state simultaneously meets SOC j min ≤ SOC j ≤ SOC j max New energy sources satisfy 0 ≤ P w ≤ P w av and 0≤ P pv ≤ P pv av .

[0191] In this optimization, the control increment cost generated for each control command is influenced by the control increment weight matrix. Adjustment. Based on the effective security support capabilities corresponding to each resource. Dynamically update the incremental weights:

[0192] (51)

[0193] In the formula, Based on weights, To predict step weights, To prevent small positive numbers with a denominator of zero, the dynamic adjustment logic is as follows: when the absolute value of the effective security support performance of the target resource is... The larger the value, the larger the denominator, thus assigning it a smaller control increment weight. The penalty for actions of heterogeneous resources with higher support efficiency is smaller, thus giving them a higher priority in participating in the restoration of the current dominant security boundary.

[0194] 4. Multi-timescale control implementation

[0195] The proposed method adopts a hierarchical structure of "upper-level safety domain rolling coordination + lower-level heterogeneous converter local closed loop", such as Figure 4 As shown. The upper layer updates Ω at a period of approximately 100 ms. R , , and The GFM, GFL, and STATCOM local controllers maintain a millisecond-level inner loop. The combined effect of equipment dynamics and equations (40) to (45) can naturally form a fast GFM support, STATCOM voltage regulation, continuous GFL takeover, and new energy backup recovery. However, this timing is the result of safety boundary and support performance calculations, rather than a fixed rule.

[0196] 5. Robust safety domain contraction and safety maintenance conditions

[0197] To address uncertainty, this method introduces a robust safety region contraction mechanism that considers errors. This addresses the dynamic disturbances to the railway. Decomposed into predicted disturbances and bounded error set :

[0198] (52)

[0199] Calculate the local sensitivity of various railway safety boundaries to dynamic disturbances of the railway. The robust shrinkage amount of each boundary term is obtained by combining the bounded error set. :

[0200] (53)

[0201] Subtracting the robust shrinkage amount from the generalized dynamic safety domain generates the shrunken safety boundary. As constraints for the lexicographical rolling optimization model:

[0202] (54)

[0203] Where z=(x,y), the set constraint applies to all This ensures that the actual closed-loop control state always remains within the generalized dynamic safety domain, achieving robust and secure maintenance.

[0204] IV. Simulation Verification

[0205] 1. Simulation model, parameters, and comparison strategy

[0206] To verify the core theory, a reproducible reduced-order dynamic model was established based on Sections 2-4, with an integration step size of 0.01 s. The model was used to examine three types of control strategies: A) Traditional independent control: GFM with fixed VSG parameters, GFL slowly following according to frequency difference, and STATCOM with independent voltage regulation; B) Conventional GFM / GFL coordination: GFM / GFL allocation with a fixed ratio based on power deficit; C) The method of this invention: based on... The safety domain drives collaborative control. Key parameters are shown in Table 2.

[0207] Table 2. Main Simulation Parameters

[0208]

[0209] Complex working conditions such as Figure 5 As shown: 0-10s is 10MW stable traction; at 10s, the traction power increases to 28MW; during 35-45s, the SCR drops from 4 to 2 to simulate a weak grid; from 45-55s, it enters -8MW regenerative braking; after 55s, it resumes 12MW traction.

[0210] 2. Frequency and RoCoF Response

[0211] Figure 6 The frequency and RoCoF response are given. The lowest frequency for conventional independent control is 49.810 Hz, conventional GFM / GFL coordination improves it to 49.944 Hz, and the method of this invention further improves it to 49.947 Hz. Based on a rated frequency of 50 Hz, the method of this invention reduces the maximum frequency drop from 0.190 Hz to 0.053 Hz compared to conventional independent control, a reduction of approximately 72.3%. The frequency was reduced from 0.441 Hz / s to 0.409 Hz / s and remained within the 0.5 Hz / s boundary. Although conventional coordination can significantly improve the minimum frequency value, its control is still mainly based on power deficit; the method of this invention can maintain a unified safety objective during weak network, regeneration, and other safety boundary switching.

[0212] 3. Traction bus voltage and negative sequence response

[0213] Figure 7 As shown, the minimum traction bus voltage under traditional independent control is 26.113 kV, and under conventional GFM / GFL coordination it is 26.153 kV. The method of this invention increases this to 26.371 kV. Based on a rated voltage of 27.5 kV, the maximum voltage drop decreases from 1.387 kV to 1.129 kV, a reduction of approximately 18.6%. The negative sequence voltage peak value decreases from 2.522% to 1.918%, a reduction of approximately 24.0%, indicating that when φ... U When φ2 becomes the dominant boundary, STATCOM reactive power and GFL negative sequence compensation can obtain higher dynamic support priority.

[0214] 4. Switching between dynamic security boundary and dominant boundary

[0215] Figure 8 Figure (a) in the figure illustrates the evolution of seven types of security boundaries under the method of this invention. Figure 8 Figure (b) in the diagram illustrates the real-time dominant security boundary. Near the 10s heavy traction surge, the RoCoF and voltage-related boundaries shrink rapidly; after the system enters a weak network at 35s, the importance of the impedance stability boundary increases; at the 45s regenerative braking switch, the voltage, power, and resource availability boundaries are reordered. The results show that the dominant risk is not fixed, and the fixed “GFM-GFL-STATCOM” timing cannot fully reflect the multidimensional risk switching, while Equation (32) can identify the weakest safety dimension online.

[0216] 5. Heterogeneous resource support efficiency and active power synergy allocation

[0217] Figure 9Figure (a) shows the normalized resource support efficiency calculated by equation (45). Λ under different operating conditions G Λ F Λ ST and Λ RES The fact that the control weights are reconfigured as the safety boundary changes indicates that the control weights are not fixed. Figure 9 Figure (b) shows that during the initial stage of traction shock, GFM-ESS rapidly increases active power output, followed by GFL-ESS assuming continuous power, while wind and solar power output is gradually adjusted according to safety reserve requirements; during regenerative braking, the two types of energy storage absorb energy in opposite directions. This result verifies that the "dominant safety boundary - resource support efficiency" mapping can form a multi-timescale relay that conforms to the physical characteristics of the equipment without pre-setting a fixed participation ratio.

[0218] 6. Verification of GFM current limiting and weak network impedance stability

[0219] Figure 10 Figure (a) shows the equivalent current of GFM. The method of this invention always satisfies I during heavy-load traction and regenerative switching. G <1.20 pu. When the GFM current approaches the limit, equation (44) makes χ I,G This decreases the priority of GFM to continue increasing power, thus automatically reducing its priority. Figure 10 Figure (b) shows the generalized impedance Nyquist trajectory under weak network conditions. The minimum Nyquist distance for conventional coordination is approximately 0.125, while it increases to 0.392 after reconfiguration of the control parameters driven by the safety domain. This indicates that when φ Z When it becomes a major risk, impedance stability margin can be significantly increased through GFM virtual impedance, damping, and heterogeneous resource power allocation.

[0220] 7. Comprehensive Railway Dynamic Safety Margin

[0221] Figure 11 The soft-min comprehensive safety margins for three control methods are given. The minimum value for traditional independent control is -0.128, indicating that at least one safety dimension exceeds the limit under combined operating conditions; the minimum value for conventional GFM / GFL coordination is only 0.008, with the system repeatedly approaching the safety boundary; the minimum value of the method in this invention is increased to 0.118, consistently remaining within the dynamic safety domain. This result demonstrates that the advantage of the method in this invention is not merely in improving frequency or voltage, but in improving the weakest safety dimension of the system through dominant boundary identification and resource support performance matching.

[0222] Table 3 Comparison of Key Dynamic Performance

[0223]

[0224] It should be noted that the lower maximum current of the GFM under traditional independent control does not necessarily indicate superior performance. Rather, it is due to insufficient rapid support, causing more safety pressure to shift to frequency, voltage, and overall safety margin. The method of this invention, however, utilizes the available current margin of the GFM to improve rapid support capability without triggering the GFM current limiting.

[0225] VI. Conclusion

[0226] This invention proposes a multi-resource collaborative control method for new energy and heterogeneous converters based on the dynamic safety domain of heavy-haul railways. First, it unifies traction voltage, frequency, RoCoF, negative sequence, impedance stability margin, GFM current limiting, and continuous energy support into a generalized dynamic safety domain, enabling the safety domain to evolve in real time with railway disturbances, grid strength, and resource status. Second, it proposes a dominant safety boundary identification and a multi-step dynamic support efficiency matrix, theoretically establishing a mapping between the weakest safety boundary and the degrees of freedom of GFM / GFL energy storage, STATCOM, and wind and solar control. Furthermore, it achieves joint coordination of active power, reactive power, and converter control parameters through lexicographical rolling optimization prioritizing railway safety, and provides robust safety domain contraction and closed-loop safety maintenance conditions.

[0227] Simulation results under the combined traction-weak grid-regenerative operating conditions show that the proposed method can improve frequency, voltage, and negative sequence response without triggering the GFM current limit, and increase the overall railway safety margin from a negative value under traditional control to 0.118; the Nyquist minimum distance is significantly increased in impedance verification. The essence of this invention shifts from the traditional question of "who bears the power deficit" to "which safety boundary is most dangerous at present, and which resource can most efficiently restore that boundary," providing a unified multi-resource coordination theoretical framework for the stable and safe operation of microgrids in high-proportion new energy heavy-haul railways.

[0228] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-resource collaborative control method for new energy and heterogeneous converters, characterized in that, include: A unified differential algebraic model is constructed for an AC microgrid that includes heavy-haul railway traction load, grid-type energy storage, grid-connected energy storage, static synchronizing compensators, and wind and solar resources. Based on the unified differential algebraic model, a railway safety boundary with multiple dimensions is defined, and a generalized dynamic safety domain is constructed by combining the railway dynamic disturbance of the heavy-haul railway traction load. In the generalized dynamic security domain, the dominant security boundary closest to the current operating point is identified online, and a multi-step dynamic support efficiency matrix is ​​established between the dominant security boundary and the control degrees of freedom of each heterogeneous resource; Based on the multi-step dynamic support efficiency matrix, a lexicographical rolling optimization model prioritizing safety is constructed to solve and generate control instructions corresponding to each heterogeneous resource. The control instructions include active power, reactive power, and converter control parameters.

2. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 1, characterized in that, The process of constructing the unified differential algebraic model includes: Extract the system's dynamic state vector, algebraic state vector, control vector, and disturbance vector describing the dynamic disturbance of the railway. The dynamic state vector includes the internal control state of grid-type energy storage, the internal control state of grid-connected energy storage, and the state of charge of both types of energy storage; the control vector includes the active power reference value, reactive power reference value, virtual inertia, virtual damping, virtual resistance, and virtual reactance of grid-type energy storage, the active power reference value, reactive power reference value, and negative sequence compensation current reference value of grid-connected energy storage, the reactive power output reference value of the static synchronous compensator, and the available power reference value of wind and solar resources; the disturbance vector includes traction active power, reactive power, traction power change rate, railway-side unbalanced characteristic quantity, and the equivalent dynamic impedance of the train and the traction network; Based on the extracted vectors, the unified differential-algebraic model is generated by combining differential equations describing converter control, energy storage, and equivalent electromagnetic dynamics, as well as algebraic equations describing AC network power flow and algebraic constraints.

3. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 1, characterized in that, Seven types of dimensionless railway safety boundaries are defined, namely, traction voltage boundary, system frequency boundary, frequency change rate impulse boundary, negative sequence boundary, heterogeneous converter impedance stability boundary, grid-type energy storage current limiting boundary, and continuous energy support boundary; combined with the railway dynamic disturbance, the seven types of dimensionless railway safety boundaries are integrated into the generalized dynamic safety domain. Within the generalized dynamic safety domain, the values ​​of all railway safety boundaries are set to be greater than or equal to zero, indicating a state where no limit has been exceeded.

4. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 3, characterized in that, The methods for defining the railway safety boundary include: The traction voltage boundary is obtained by taking the minimum value between the first voltage ratio term and the second voltage ratio term; the first voltage ratio term is the difference between the actual traction bus voltage and the minimum allowable voltage, divided by the difference between the rated traction bus voltage and the minimum allowable voltage; the second voltage ratio term is the difference between the maximum allowable voltage and the actual traction bus voltage, divided by the difference between the maximum allowable voltage and the rated traction bus voltage. The system frequency boundary is obtained by taking the minimum value between the first frequency ratio term and the second frequency ratio term; the first frequency ratio term is the difference between the actual frequency and the allowable lower frequency limit, divided by the difference between the rated frequency and the allowable lower frequency limit; the second frequency ratio term is the difference between the allowable upper frequency limit and the actual frequency, divided by the difference between the allowable upper frequency limit and the rated frequency. The frequency change rate impact boundary is obtained by subtracting the ratio of the absolute value of the actual frequency change rate to the maximum allowable frequency change rate from a constant 1. The negative sequence boundary is obtained by subtracting the ratio of the actual negative sequence voltage ratio to the upper limit of the allowable negative sequence voltage ratio from a constant of 1.

5. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 4, characterized in that, The definition of railway safety boundaries also includes: The impedance stability boundary of the heterogeneous converter is calculated based on the equivalent impedance matrix of the heterogeneous converter and AC network and the equivalent impedance matrix on the railway side. The minimum distance of the generalized impedance loop matrix relative to the Nyquist critical point is extracted as the impedance stability margin. The difference between the current impedance stability margin and the minimum allowable stability margin is divided by the difference between the reference margin and the minimum allowable stability margin. The current limiting boundary of the grid-type energy storage is obtained by dividing the difference between the maximum allowable current and the actual output current by the difference between the maximum allowable current and the reference operating current. The sustainable energy support boundary is calculated by integrating the difference between the predicted railway traction power within the prediction window and the power that can be sustainably provided by external resources. The required net support energy is obtained by dividing the difference between the energy that can be released from energy storage and the required net support energy by the baseline energy.

6. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 1, characterized in that, The method for identifying the dominant security boundary and establishing the multi-step dynamic support performance matrix online includes: Calculate the current normalized value of each of the railway safety boundaries, and select the safety boundary with the smallest current normalized value as the dominant safety boundary; By performing nonlinear mapping calculations on the current normalized values ​​of all the railway safety boundaries using a smoothing coefficient, a continuously differentiable comprehensive safety margin is constructed as the optimized micro-safety objective. Obtain the state transition matrix of the unified differential algebraic model after discretization at the current operating point; By combining the first-order expansion partial derivative matrix of the railway safety boundary near the current working point with the state transition matrix, the incremental impact of changing the control degrees of freedom of each heterogeneous resource at the current moment on the dominant safety boundary within the future prediction steps is calculated, thus forming the multi-step dynamic support efficiency matrix.

7. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 6, characterized in that, After establishing the multi-step dynamic support performance matrix, the effective security support performance is further calculated for each heterogeneous resource, specifically including: From the multi-step dynamic support effectiveness matrix, extract the dominant boundary support sensitivity of the target resource to the dominant safety boundary within the future prediction step; The remaining capacity is calculated based on the difference between the maximum output capacity of the target resource and the current absolute value of the output; the corresponding availability coefficient is obtained by combining the device health status and current limiting status parameters. The effective security support performance of the target resource is obtained by multiplying the dominant boundary support sensitivity, the remaining capacity, and the availability coefficient.

8. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 7, characterized in that, The lexicographical rolling optimization model includes a hierarchical first-level optimization model and a second-level optimization model: The first-level optimization model aims to maximize the uniform minimum safety margin within the prediction time domain, thereby obtaining the optimal minimum safety margin. The second-level optimization model: Under the premise that the railway safety boundary of each prediction step is greater than or equal to the optimal minimum safety margin minus the allowable slack, economic optimization is performed with the goal of minimizing the system operating cost to generate the control command; The system operating costs include control increment costs, energy storage loss costs, and renewable energy curtailment costs.

9. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 8, characterized in that, In the second-level optimization model, the control increment cost generated by each control command is adjusted by the control increment weight matrix. The dynamic update method of the control increment weight matrix includes: dynamically adjusting the control increment weight of each heterogeneous resource according to the effective security support performance of each resource. When the absolute value of the effective security support performance of the target resource is larger, it is given a smaller control increment weight, so as to drive the heterogeneous resource with higher support performance to participate in the recovery of the current dominant security boundary first.

10. The multi-resource collaborative control method for new energy and heterogeneous converters according to claim 1, characterized in that, The method also introduces a robust safety region shrinkage mechanism that takes into account errors, specifically including: The railway dynamic disturbance is decomposed into a set of predicted disturbances and bounded errors; Calculate the local sensitivity of each of the railway safety boundaries to the dynamic disturbance of the railway, and combine the bounded error set to solve for the robust contraction of each of the railway safety boundaries; The robust contraction amount is subtracted from the generalized dynamic safety domain to generate a contracted safety boundary, which serves as a constraint condition for the lexicographical rolling optimization model, ensuring that the actual closed-loop control state always remains within the generalized dynamic safety domain.

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