CN109301838B - SVC controller PI parameter optimization method - Google Patents
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Abstract
The invention discloses a method for optimizing PI (proportion integration) parameters of an SVC (static var compensator) controller, which comprises the steps of establishing an electromagnetic transient model containing an optimized SVC and a power grid, and solving an electromagnetic oscillation mode of a system and an output reactive power response of the SVC under the excitation of step signals by adopting a linearization method. The rising time and the stable time of an SVC output reactive power response curve are used as voltage regulation performance indexes, the system electromagnetic oscillation modal damping level is used as an electromagnetic oscillation suppression capability index, and a comprehensive optimization index function is established. The method takes the SVC controller PI parameter as an optimization object, combines the comprehensive optimization index function to establish an optimization mathematical model, adopts an intelligent algorithm to carry out parameter optimization, and provides a technical means for inhibiting electromagnetic oscillation by optimizing the SVC controller PI parameter.
Description
Technical Field
The invention belongs to the technical field of parameter adjustment of Static Var Compensator (SVC) control systems, and particularly relates to a PI parameter optimization method of an SVC controller with both voltage regulation performance and electromagnetic oscillation suppression.
Background
The basic task of the SVC is to automatically adjust the SVC reactive power output according to the change of the bus voltage, so that the bus voltage reaches a set value, and simultaneously, the SVC provides reactive power support for the power grid in the transient process.
Whether the control parameter selection of the SVC is proper or not directly determines the quality of the SVC voltage regulation performance. Unreasonable parameter selection can cause poor SVC voltage control performance, limit the supporting effect of SVC on the grid voltage and cause serious safety problems. Especially, system oscillation is easily caused in weak power grid or weak power grid networking engineering. Unlike general electromechanical oscillation, the oscillation is mainly characterized in that electromechanical transient cannot be simulated and can only be found through electromagnetic transient analysis. The oscillation frequency of the frequency-variable oscillator often exceeds the low-frequency oscillation frequency range, and the frequency of the frequency-variable oscillator is possible at 5-250 Hz or even higher, and is mainly related to LC parameters of a power system and PI controller parameters of SVC.
The existing literature and method mainly aim at parameter optimization of an SVC additional damping controller, and there are few reports on the induction of power system electromagnetic oscillation caused by improper PI control parameters of an SVC voltage control loop. The parameter adjustment of the SVC voltage control loop PI control is mainly carried out by a trial and error method. On one hand, the fast voltage control performance requires a larger PI parameter; on the other hand, the suppression of the electromagnetic oscillation requires a small PI parameter, and these parameters contradict each other. At present, no technical method can give consideration to both SVC electromagnetic oscillation suppression and voltage regulation performance, and great safety risk is brought to SVC and power grid operation.
Disclosure of Invention
Aiming at the blank of the prior art, the invention provides a method for optimizing the PI parameters of the SVC controller which gives consideration to both the voltage regulation performance and the electromagnetic oscillation suppression, and provides a technical means for suppressing the electromagnetic oscillation by optimizing the PI parameters of the SVC controller.
The method comprises the steps of establishing an electromagnetic transient model containing an optimized SVC and a power grid, and solving an electromagnetic oscillation mode of a system and an output reactive power response of the SVC under the excitation of step signals by adopting a linearization method. The rising time and the stable time of an SVC output reactive power response curve are used as voltage regulation performance indexes, the system electromagnetic oscillation modal damping level is used as an electromagnetic oscillation suppression capability index, and a comprehensive optimization index function is established. And (3) taking the PI parameter of the SVC controller as an optimization object, establishing an optimization mathematical model by combining the comprehensive optimization index function, and performing parameter optimization by adopting an intelligent algorithm.
In order to achieve the above object, the present application provides a method for optimizing a PI parameter of an SVC controller, the method comprising:
step 1: reading an SVC regulation system model of parameters to be optimized and all SVC parameters except PI, power grid and other value system parameters;
step 2: initializing a PI parameter of an SVC controller;
and step 3: calculating an electromagnetic oscillation mode of a power system containing SVC, and solving an electromagnetic oscillation mode damping index;
and 4, step 4: establishing an SVC reactive voltage response simulation model, applying certain voltage step disturbance on a voltage reference signal of an SVC control system, starting simulation to obtain SVC output reactive power response, and calculating the rising time and the stabilization time of a reactive power curve;
and 5: obtaining an SVC controller PI parameter optimization comprehensive objective function for inhibiting the electromagnetic oscillation based on an index function reflecting the SVC voltage regulation performance and an index function reflecting the SVC electromagnetic oscillation inhibition capability; optimizing a comprehensive objective function based on the SVC controller PI parameter optimization comprehensive objective function for inhibiting the electromagnetic oscillation, and optimizing the SVC controller PI parameter;
step 6: judging whether the comprehensive optimization objective function is smaller than a certain threshold or reaches the upper limit of the optimization calculation times, if so, ending the SVC parameter optimization process to obtain the optimal PI parameter; if not, returning to the step 3 to continue the calculation.
Further, the parameters read in step 1 specifically include: SVC primary circuit parameters and SVC access point near-region power grid parameters are to be optimized.
Further, step 2 specifically includes: initializing PI parameters of the SVC controller, and determining a weighting coefficient k for measuring SVC reactive voltage regulation performance index1、k2(ii) a Determining SVC reactive voltage regulation performance and electromagnetic oscillation damping level index comprehensive weight coefficient m1、m2(ii) a Determining a weight factor P for each oscillation moden。
Further, the SVC model specifically is:
in the formula (3), ITCR＝[ITCRdITCRq]T，Uldq＝[UldUlq]T，
Wherein ω is0Is a reference frequency, ITCRd、ITCRqD and q-axis current components, U, of the TCR, respectivelyld、UlqD and q-axis current components, U, of the SVC control bus voltagerefIs the reference voltage of SVC, BTCRIs the admittance, k, of the TCRp、kiProportional gain and integral gain, T, of the controller of the SVC, respectivelyvIs the time constant of SVC inertia link, and s is a differential operator.
Further, the calculation of the electromagnetic oscillation mode of the SVC includes:
linearizing a system equation comprising an inductor, a capacitor and an SVC, setting all state variables to form a phasor y, and finally linearizing the equation as follows:
DΔy＝AΔy (4)
in the formula (4), D is a diagonal matrix, and a diagonal element corresponding to an algebraic equation is 0; the system eigenvalue problem can be converted into a generalized eigenvalue problem of (a, D); the electromagnetic oscillation mode after the SVC is accessed into the system can be obtained by calculating the generalized characteristic value;
the characteristic value of the system electromagnetic oscillation mode can be expressed in the form of lambda-sigma +/-j omega, and the corresponding damping ratio is
An oscillation frequency of
Where σ is the attenuation coefficient and ω is the angular frequency.
Further, an index function J reflecting SVC voltage regulation performance1(K) Is defined as:
J1(K)＝k1T0.9+k2Ts(5)
in the formula (5), J1(K) Denotes SVC in PI parameter vector K ═ Kp,ki]Voltage regulation performance index function under value, T0.9Represents the rise time T from the beginning of the voltage difference over-voltage regulation dead zone to the SVC output reactive power reaching the target value of 90%sRepresents the time, k, from the start of the voltage difference over-voltage regulation dead zone to the time when the SVC output reactive power reaches a steady state1Representing a reactive power rise time weight coefficient, k2Representing a reactive power settling time weight coefficient;
index function J reflecting SVC electromagnetic oscillation suppression capability2(K) Is defined as:
in the formula (6), J2(K) Representing the sum of all mode damping ratios within the frequency band of the electromagnetic transient oscillation mode of interest; f. ofnIs the nth electromagnetic oscillation mode frequency; f. ofmaxFor an upper limit of oscillation frequency of interest ξnTo damping ratio at corresponding oscillation frequency；pnIs the weight coefficient of each oscillation mode;
defining the PI parameter optimization comprehensive objective function J (K) of the SVC controller for inhibiting the electromagnetic oscillation as
J(K)＝m1J1(K)+m2J2(K) (7)
In the formula (7), J (K) represents a damping level ξ in the electromagnetic oscillation mode>Under the condition of 0, comprehensively evaluating an index function of the reactive voltage regulation performance and the electromagnetic oscillation suppression capability of the SVC; m is1、m2Respectively representing reactive voltage regulation performance index weight and electromagnetic oscillation suppression capability index weight of the SVC;
determining an optimized objective function as: finding the appropriate PI controller parameter K*So that the integrated objective function is minimal:
K*＝argminJ(K) (8)
further, the method further includes adaptively checking the PI parameters, and specifically includes:
establishing a power grid full-electromagnetic transient simulation model containing SVC;
and (4) checking the electromagnetic oscillation and reactive voltage response performance of the SVC suppression system by considering the large and small operation modes of the power grid, the faults of the lines N-1 and N-2 in each mode and no fault load shedding fault of the generator set.
One or more technical solutions provided by the present application have at least the following technical effects or advantages:
the invention provides a SVC controller PI parameter optimization method considering SVC reactive voltage regulation performance and electromagnetic oscillation suppression, which defines quantitative evaluation indexes for comprehensively measuring SVC reactive voltage regulation performance and electromagnetic oscillation damping level, adopts an optimization algorithm to optimize SVC controller PI parameters, and provides a technical means for optimizing SVC controller PI parameters aiming at considering reactive voltage regulation performance and electromagnetic oscillation suppression.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1a is a detailed wiring diagram of an SVC;
FIG. 1b is a simplified diagram of an SVC;
fig. 2 is a simplified transfer function block diagram of an SVC controller;
fig. 3 is a flow chart of the SVC controller PI parameter optimization.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments and features of the embodiments of the present application may be combined with each other without conflicting with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described and thus the scope of the present invention is not limited by the specific embodiments disclosed below.
Referring to fig. 1 to fig. 3, a method for optimizing PI parameters of an SVC controller with both voltage regulation performance and electromagnetic oscillation suppression provided in the present invention includes:
1) power grid basis data collection
1-1) SVC primary circuit parameters to be optimized comprise filter capacity, capacitance, reactance, resistance parameters, TCR capacity and reactance parameters.
1-2) SVC access point near-zone power grid parameters including power supply, line, main transformer, load, high reactance, low capacitance, low reactance and the like.
2) Electromagnetic transient modeling
2-1) Small electromagnetic oscillation Signal analysis modeling boundary
Preferably, a near-region power grid of the SVC access point to be optimized is modeled in detail, and at least two stages of SVC access points are expanded to the outside. For long-chain networking engineering, a networking channel is subjected to detailed modeling, the long-chain networking engineering expands two stages to a connected power grid, and an external network adopts short-circuit impedance for equivalence.
2-2) SVC Voltage response modeling
When SVC voltage response evaluation is carried out, equivalent modeling can be carried out on a main transformer high-voltage side of an SVC access point, SVC and a connecting transformer thereof are reserved, and an external network adopts short-circuit impedance for equivalence.
2-3) SVC optimization parameter adaptability analysis modeling
Due to the adoption of the simplified power grid model, after SVC parameters are optimized, the actual power grid model is needed to be used for verification. And preferably, a full electromagnetic transient model is established for parameter adaptability verification according to an actual power grid operation mode.
3) Electromagnetic oscillation mode calculation
3-1) SVC small signal model
3-1-1) inductance-capacitance equation under park transformation
The equation for the inductance (reactance X) and capacitance (susceptance B) under the park transformation can be expressed as follows (without considering the zero-axis component):
in the formula idq＝[idiq]T,udq＝[uduq]T
3-1-2) SVC modeling
The primary circuit structure of the SVC is formed by connecting a controllable reactor branch TCR and an ac filter bank in parallel, and the simplified connection is as shown in fig. 1 (FC3 and FC5 represent filter banks of 3 and 5 times, and according to actual conditions, the SVC may be configured with multiple groups of filters, and this is only a schematic diagram here). Since the ac filter bank can be actually decomposed into static inductor and capacitor, the modeling method is the same as 3-1-1, and only the TCR branch of the SVC needs to be modeled here.
SVC adopts constant voltage PI control, and the control block diagram is simplified as shown in figure 2. And performing state space modeling on the block diagram, wherein the simplification result is as follows:
in the formula, BTCRIs the admittance of the TCR arms. The SVC model under the simplified model canExpressed as:
in the formula ITCR＝[ITCRdITCRq]T，Uldq＝[UldUlq]T，
3-2) calculation of electromagnetic oscillation modes including SVC
The system equations including the inductors, capacitors and SVC are linearized. Assuming that all state variables constitute phasor y, the equation is finally linearized as:
DΔy＝AΔy (4)
in the formula, D is a diagonal matrix, and the diagonal element corresponding to the algebraic equation is 0. The system eigenvalue problem can be translated into a generalized eigenvalue problem of (a, D). The electromagnetic oscillation mode after the SVC is connected into the system can be calculated through the generalized characteristic value.
The characteristic value of the system electromagnetic oscillation mode can be expressed in the form of lambda-sigma +/-j omega, and the corresponding damping ratio is
An oscillation frequency of
4) SVC step response simulation
4-1) establishing the simulation model described in the step 2-2 in simulation software
And 4-2) applying a step signal with a certain amplitude value on a voltage reference of the SVC control system (preferably without triggering an amplitude limiting link of an SVC controller), and obtaining an SVC output reactive power response curve.
5) Optimizing objective function definition
5-1) index function J reflecting SVC voltage regulation performance1(K) Is defined as
J1(K)＝k1T0.9+k2Ts(5)
In the formula, J1(K) Denotes SVC in PI parameter vector K ═ Kp,ki]Voltage regulation performance index function under value, T0.9Represents the rise time T from the beginning of the voltage difference over-voltage regulation dead zone to the SVC output reactive power reaching the target value of 90%sRepresenting the time elapsed from the onset of the voltage difference exceeding the dead zone of voltage regulation until the SVC output reactive power reaches stability. k is a radical of1Representing a reactive power rise time weight coefficient, k2Representing the reactive power settling time weight coefficient.
5-1) index function J reflecting SVC electromagnetic oscillation suppression capability2(K) Is defined as
In the formula, J2(K) Representing the sum of all mode damping ratios within the frequency band of the electromagnetic transient oscillation mode of interest. f. ofnIs the nth electromagnetic oscillation mode frequency; f. ofmaxFor an upper limit of oscillation frequency of interest ξnIs the damping ratio at the corresponding oscillation frequency; p is a radical ofnAre the weighting coefficients of the respective oscillation modes.
5-2) defining the PI parameter optimization comprehensive objective function J (K) of the SVC controller for inhibiting the electromagnetic oscillation as
J(K)＝m1J1(K)+m2J2(K) (7)
Wherein J (K) represents a damping level ξ in the electromagnetic oscillation mode>And under the condition of 0, comprehensively evaluating the index function of the reactive voltage regulation performance and the electromagnetic oscillation suppression capability of the SVC. m is1、m2And respectively representing the reactive voltage regulation performance index weight and the electromagnetic oscillation suppression capability index weight of the SVC.
5-3) determining an optimized objective function as: finding the appropriate PI controller parameter K*So that the integrated objective function is minimal, namely: the method ensures that unstable electromagnetic oscillation does not occur, and has the minimum reactive voltage response time, namely the fastest response speed.
K*＝argminJ(K) (8)
6) Parameter optimization process
6-1) reading the SVC adjusting system model of the parameter to be optimized and all SVC parameters except PI, power grid and other value system parameters;
6-2) initializing PI parameters of the SVC controller, selecting typical parameters recommended by manufacturers, and determining weighting coefficient k for measuring SVC reactive voltage regulation performance index1、k2(ii) a Determining SVC reactive voltage regulation performance and electromagnetic oscillation damping level index comprehensive weight coefficient m1、m2(ii) a Determining a weight factor P for each oscillation moden。
6-3) calculating the electromagnetic oscillation mode of the system according to the step 3 to obtain the damping index.
6-4) according to the step 4), applying certain voltage step disturbance (such as a step signal with the amplitude of 1%) on the voltage reference signal of the SVC control system, starting simulation to obtain SVC output reactive power response, and calculating the rise time and the stabilization time.
6-5) optimizing the PI parameters of the SVC controller by using the comprehensive optimization objective function given in the step 5) and intelligent optimization algorithms such as particle swarm algorithm, genetic algorithm and the like.
6-6) judging whether the target function J is smaller than a certain threshold or reaches the upper limit of the optimization calculation times, if so, ending the SVC parameter optimization process to obtain the optimal PI parameter, otherwise, returning to the step 6-3) to the step 6-5) to continue calculation.
7) Parameter adaptive checking
Reading the PI parameter of the SVC controller obtained in the step 6), wherein the PI parameter is only used for simplifying a system and only represents an optimized parameter in one operation mode, and whether the reactive voltage response and the electromagnetic oscillation suppression effect of the PI parameter in other operation modes meet the requirements or not needs to be checked. The check may be performed as follows:
7-1) establishing a full electromagnetic transient simulation model of a power grid containing SVC
7-2) checking the electromagnetic oscillation and reactive voltage response performance of the SVC suppression system by considering the large and small operation modes of the power grid, the faults of the line N-1 and the line N-2 under each mode, no fault and load shedding of a large-scale generator set and the like.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (5)
1. A method for optimizing proportional-integral parameters of a static var compensation controller, the method comprising:
step 1: reading a static reactive power compensation adjusting system model of a parameter to be optimized and all static reactive power compensation parameters except a proportion-integral and power grid equivalent system parameters;
step 2: initializing a proportion-integral parameter of the static reactive compensation controller;
and step 3: calculating an electromagnetic oscillation mode of the power system with static reactive compensation, and solving an electromagnetic oscillation mode damping index; specifically comprises a step 3-1 and a step 3-2;
3-1) static reactive compensation small signal model
3-1-1) inductance-capacitance equation under park transformation
Under the park transformation, the equations of inductance and capacitance can be expressed as follows:
in the formula idq＝[idiq]T,udq＝[uduq]T，
Wherein X is reactance, B is susceptance, omega0Is a reference frequency(ii) a s is a differential operator;
3-1-2) static var compensation modeling
The static reactive compensation primary circuit structure comprises a controllable reactor branch TCR and an alternating current filter bank which are connected in parallel, wherein the alternating current filter bank comprises a 3-time filter bank FC3 and a 5-time filter bank FC 5; because the alternating current filter bank can be actually decomposed into static inductance and capacitance, the modeling mode is the same as that in the step 3-1-1, and only the TCR branch circuit of the static reactive compensation needs to be modeled;
the static reactive compensation adopts constant voltage proportion-integral control to carry out state space modeling, and the simplification result is as follows:
in the formula, BTCRIs the admittance, k, of the TCR branchpProportional gain of controller, k, for static var compensationiController integral gain, U, for static var compensationrefIs a reference voltage of the static var compensation, TvIs the time constant of the inertia link of the static reactive compensation, and the model of the static reactive compensation can be expressed as:
in the formula ITCR＝[ITCRdITCRq]T，Uldq＝[UldUlq]T，
Wherein ω is0Is a reference frequency, ITCRd、ITCRqD and q-axis current components, U, of the TCR, respectivelyld、UlqD-axis current components and q-axis current components of the static reactive compensation control bus voltage respectively;
3-2) calculation of electromagnetic oscillation mode with static var compensation
Linearizing a system equation containing inductance, capacitance and static reactive compensation, setting all state variables to form phasor y, and finally linearizing the equation as follows:
DΔy＝AΔy (4)；
in the formula, D is a diagonal matrix, and a diagonal element corresponding to an algebraic equation is 0; the system characteristic value problem can be converted into the generalized characteristic value problem of (A, D), and the electromagnetic oscillation mode after the static reactive compensation is accessed into the system can be calculated through the generalized characteristic value;
the characteristic value of the system electromagnetic oscillation mode can be expressed in the form of lambda-sigma +/-j omega, and the corresponding damping ratio is
An oscillation frequency of
Wherein σ is the attenuation coefficient; omega is angular frequency;
and 4, step 4: establishing a static reactive power compensation reactive voltage response simulation model, applying certain voltage step disturbance on a voltage reference signal of a static reactive power compensation control system, starting simulation to obtain a static reactive power compensation output reactive power response, and calculating the rising time and the stabilization time of a reactive power curve;
and 5: obtaining a proportional-integral parameter optimization comprehensive objective function of the static reactive compensation controller for inhibiting the electromagnetic oscillation based on an index function reflecting the static reactive compensation voltage regulation performance and an index function reflecting the static reactive compensation electromagnetic oscillation inhibition capacity; optimizing a comprehensive objective function based on proportional-integral parameters of the static reactive power compensation controller for inhibiting electromagnetic oscillation, and optimizing the proportional-integral parameters of the static reactive power compensation controller; wherein
Index function J reflecting static reactive compensation voltage regulation performance1(K) Is defined as
J1(K)＝k1T0.9+k2Ts(5)
In the formula, J1(K) Expressing static reactive compensation in PI proportional-integral parameter vector K ═ Kp,ki]Voltage regulation under valuePerformance index function, T0.9The rising time T from the beginning of the voltage difference over-voltage regulation dead zone to the time when the static reactive compensation output reactive power reaches the target value of 90 percentsRepresents the time k from the beginning of the voltage difference over-voltage regulation dead zone to the stabilization of the reactive power output by the static reactive compensation1Representing a reactive power rise time weight coefficient, k2Representing a reactive power settling time weight coefficient;
index function J reflecting static reactive compensation electromagnetic oscillation suppression capability2(K) Is defined as
In the formula, J2(K) Representing the sum of all mode damping ratios within the frequency band of the electromagnetic transient oscillation mode of interest; f. ofnIs the nth electromagnetic oscillation mode frequency; f. ofmaxFor an upper limit of oscillation frequency of interest ξnIs the damping ratio at the corresponding oscillation frequency; p is a radical ofnIs the weight coefficient of each oscillation mode; step 6: judging whether the comprehensive optimization objective function is smaller than a certain threshold or reaches the upper limit of the optimization calculation times, if so, ending the optimization process of the static reactive compensation parameters, and obtaining the optimal proportion-integral parameters; if not, returning to the step 3 to continue the calculation.
2. The method for optimizing the proportional-integral parameter of the SVC controller according to claim 1, wherein the parameter read in step 1 specifically comprises: and (4) the parameters of the static reactive power compensation primary circuit to be optimized and the parameters of a power grid in the vicinity of the static reactive power compensation access point.
3. The method for optimizing the proportional-integral parameter of the SVC controller according to claim 1, wherein the step 2 specifically comprises: initializing the proportional-integral parameter of the static reactive compensation controller, and determining the weight coefficient k for measuring the reactive voltage regulation performance index of the static reactive compensation1、k2(ii) a Determining static reactive compensation reactive voltage regulation performance and electricityMagnetic oscillation damping level index comprehensive weight coefficient m1、m2(ii) a Determining a weight factor P for each oscillation moden。
4. The SVC controller PID optimization method of claim 1, wherein,
defining the proportion-integral parameter optimization comprehensive objective function J (K) of the static var compensation controller for inhibiting the electromagnetic oscillation into
J(K)＝m1J1(K)+m2J2(K) (7)
In the formula (5), J (K) represents a damping level ξ in the electromagnetic oscillation mode>Under the condition of 0, comprehensively evaluating an index function of the reactive voltage regulation performance and the electromagnetic oscillation suppression capability of the static reactive compensation; m is1、m2Respectively representing reactive voltage regulation performance index weight and electromagnetic oscillation suppression capability index weight of static reactive compensation;
determining an optimized objective function as: finding the appropriate proportional-integral controller parameter K*So that the integrated objective function is minimal:
K*＝argminJ(K) (8)。
5. the method for optimizing the proportional-integral parameter of the SVC controller according to claim 1, wherein said method further comprises adaptively checking the proportional-integral parameter, specifically comprising:
establishing a power grid full-electromagnetic transient simulation model containing static reactive compensation;
and (4) checking the electromagnetic oscillation and reactive voltage response performance of the static reactive power compensation suppression system by considering the large and small operation modes of the power grid, the faults of the lines N-1 and N-2 in each mode and the fault-free load shedding fault of the generator set.
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