CN111814330B - Flexible power distribution system cascading failure risk assessment method and system - Google Patents
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- G—PHYSICS
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- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/001—Methods to deal with contingencies, e.g. abnormalities, faults or failures
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- G—PHYSICS
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/70—Smart grids as climate change mitigation technology in the energy generation sector
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- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
Abstract
The invention relates to a cascading failure risk assessment method and system for a flexible power distribution system, wherein the method comprises the following steps: (1) Analyzing FMS operation characteristics and a control protection strategy, and establishing a mathematical model of FMS steady-state operation; (2) Aiming at a feeder single-phase grounding fault, analyzing transient operation characteristics of an FMS after the fault; (3) Based on four uncertainty factors influencing cascading failures, modeling is carried out respectively to obtain a load and distributed power output model, an equipment failure moment model and a protection setting and measuring error model; (4) And according to the model, determining the occurrence probability of cascading failures and the DG risk through optimizing load flow calculation. The method and the system can control the occurrence probability of cascading failures, and reduce the risk as well as the failure result. The method can adopt measures such as improving standby capacity, reasonably planning system structures and the like aiming at the region with concentrated sensitive load, and ensures safe and stable operation of the system.
Description
Technical Field
The invention relates to the field of reliability of power distribution networks, in particular to a cascading failure risk assessment method and system caused by various uncertain factors after a flexible multi-state switch is connected into a flexible power distribution network.
Background
Along with the continuous promotion of energy revolution, a large number of distributed power supplies are connected into a power distribution network, so that the power network state and the power quality are deteriorated, higher requirements are also put forward for the power supply reliability due to the economic rapid development, the number of loads requiring uninterrupted power supply is gradually increased, and meanwhile, the utilization efficiency of power distribution network equipment is greatly reduced due to the increase of loads of electric automobiles, electric heating and irrigation. In order to cope with the above problems, a conventional power distribution network generally adopts a divide-and-conquer method, which results in more complex power distribution system and technical limitation of improvement degree. The Flexible Multi-state Switch (FMS) is applied to a power distribution network to replace a traditional interconnection Switch, so that a Flexible interconnection system for closed-loop power supply is formed, an important user can be supplied with power uninterruptedly under a fault, and the continuous power flow regulating function can effectively solve the problems of voltage fluctuation, unbalanced feeder power flow and the like caused by grid connection of a distributed power supply, so that the Flexible Multi-state Switch becomes a comprehensive solution. However, most of power electronic equipment has low overcurrent tolerance, and after the power grid fails, the damage of elements such as IGBT and the like can be possibly caused, so that the power failure range is enlarged; meanwhile, due to the fact that a large number of full-control devices are used, a control system is more and more complex, difficulty in coordinated control of all equipment in the system is increased, and requirements on reliability of communication equipment are also improved due to modulation and protection functions of converter equipment. The introduction of flexible equipment enables all links of the power distribution network to be mutually coupled, the risk of fault outage is possibly increased, and how to ensure safe and stable operation of the system becomes the key of popularization and application of the FMS at present.
Disclosure of Invention
Aiming at the defects, the invention provides a cascading failure risk assessment method and system caused by various uncertain factors after a flexible multi-state switch is connected into a flexible distribution network.
The invention is realized by the following technical scheme:
a method for risk assessment of cascading failures of a flexible power distribution system, the method comprising the steps of:
(1) Analyzing FMS operation characteristics and a control protection strategy, and establishing a mathematical model of FMS steady-state operation;
(2) Aiming at a feeder single-phase grounding fault, analyzing transient operation characteristics of an FMS after the fault;
(3) Based on four uncertainty factors influencing cascading failures, modeling is carried out respectively to obtain a load and distributed power output model, an equipment failure moment model and a protection setting and measuring error model;
(4) And according to the model, determining the occurrence probability of cascading failures and the DG risk through optimizing load flow calculation.
Further, the method for evaluating risk of cascading failures of the flexible power distribution system is characterized in that the mathematical model established in the step (1) is as follows:
wherein ,
u sj j=a, b, c for a network side equivalent ac voltage source; r is R T For equivalent resistance of converter transformer, L T Equivalent reactance of the converter transformer; r is R arm Is MMC bridge arm equivalent resistance, L arm The equivalent reactance of the bridge arm of the MMC is obtained; u (u) a 、u b 、u c Fundamental voltages for each phase; i.e sa For a-phase power supply side current, i sb For b-phase power supply side current, i sc Is the c-phase power supply side current.
Further, in the step (2), after the ac feeder fault is detected, whether the ac fault ride-through is related to the matching of the converter control and protection system is completed; under the condition that the performance of the controller is certain, the fault current inhibition effect is related to a fault initial value, and the performance of the protection system is related to measured and setting errors.
Further, in the flexible power distribution system cascading failure risk assessment method, in the step (3), four uncertainty factors are as follows:
the randomness and fluctuation of the load and the distributed power supply, the occurrence probability of equipment faults, the occurrence time of the equipment faults and the errors existing in the setting and transformer measurement.
Further, in the flexible power distribution system cascading failure risk assessment method, in the step (4), the occurrence probability of cascading failure is as follows:
P(A)＝P(D|C)·P(C|B)·P(B)
wherein, the notepad A= { contains FMS flexible distribution network occurrence cascading failure }, B= {1 end MMC connected with alternating current feeder line occurrence single-phase grounding short circuit failure }, C= { failure side MMC blocking or direct current bus protection misoperation }, D= { node voltage out-of-limit }; p (B) is the probability of event B, P (c|b) is the probability of event C under B conditions, and P (d|c) is the probability of event D under C conditions.
Further, in the method for evaluating risk of cascading failures of the flexible power distribution system, in the step (4), the load for cutting off the cascading failures is also calculated, and the calculation formulas of the load for cutting off the cascading failures and the DG risk are as follows:
wherein ,P Li to cut off the minimum capacity of load after each occurrence of cascading failure, P DGi To cut off the minimum capacity of DG after each occurrence of cascading failure, M D For load shedding and DG frequency.
A flexible power distribution system cascading failure risk assessment system, the system comprising:
the FMS steady-state operation module is used for analyzing FMS operation characteristics and controlling protection strategies and establishing a mathematical model of FMS steady-state operation;
the FMS transient operation module is used for analyzing transient operation characteristics of the FMS after the fault aiming at the feeder single-phase grounding fault;
the uncertainty factor modeling module is used for respectively modeling based on four uncertainty factors influencing cascading failures to obtain a load and distributed power output model, an equipment failure moment model and a protection setting and measuring error model; and
and the risk index calculation module is used for determining the occurrence probability of the cascading failure and the DG risk through optimizing load flow calculation according to the model.
Further, the flexible power distribution system cascading failure risk assessment system further comprises an optimized power flow calculation module, wherein the optimized power flow calculation module is used for calculating and obtaining system running state parameters, and the system running state parameters are input into the FMS transient running module.
Further, the flexible power distribution system cascading failure risk assessment system further comprises a protection malfunction module, wherein the protection malfunction module is used for judging the protection malfunction condition and inputting the result to the risk index calculation module.
Further, the flexible power distribution system cascading failure risk assessment system, the uncertainty factor modeling module executes the following sampling steps:
(1) Calculating to obtain system running state parameters by using the optimized power flow calculation module, and recording the voltage of each node;
(2) If the line has single-phase earth fault, executing the step (3), otherwise executing the step (1), and sampling times are +1;
(3) If the protection is false after the fault, executing the step (4), otherwise executing the step (1), and sampling the number of times to be +1;
(4) If the voltage of the node is out of limit due to the protection misoperation, executing the step (5), otherwise executing the step (1), and sampling the number of times to be +1;
(5) Calculating the load of the ith cascading failure and the minimum cut-off capacity of DG, and recording the total sampling number;
(6) And (3) if the total number of samples is a set value, ending the sampling, calculating a risk index, otherwise, executing the step (1).
The invention has the advantages and effects that:
according to the cascading failure risk assessment method and system for the flexible power distribution system, cascading failure risk assessment indexes are established, the probability of occurrence of cascading failures and the risk calculation method are respectively provided, load balancing among different feeder lines can be achieved through optimal scheduling, network loss is reduced, and equipment utilization efficiency and new energy consumption capacity are improved. The method and the system can also control the occurrence probability of cascading failures, and the risk can be reduced as well as the failure result can be reduced. The method can adopt measures such as improving standby capacity, reasonably planning system structures and the like aiming at the region with concentrated sensitive load, and ensures safe and stable operation of the system.
Drawings
FIG. 1 is a typical wiring pattern and physical block diagram of an FMS in a power distribution network;
FIG. 2 is an MMC equivalent circuit diagram;
fig. 3 is a fixed PQ mode control block diagram of the FMS;
FIG. 4 is a fixed PV mode control block diagram of the FMS;
FIG. 5 is a diagram of the protection and control system response time of the FMS;
FIG. 6 is a schematic diagram of a cascading failure reaction;
FIG. 7 is a schematic diagram of a feeder line in a distribution network to which a distributed power source is connected;
FIG. 8 is a schematic diagram of a dual platform joint simulation;
FIG. 9 is a flow chart for lock failure risk indicator evaluation;
FIG. 10 is a diagram of a modified 33 node example;
FIG. 11 is an algorithm convergence analysis chart;
fig. 12 is a schematic diagram of a-way converter leg current after a single phase ground fault;
FIG. 13 is a graph showing the trend of cascading failure probability with failure location;
fig. 14 is a graph showing the trend of the probability of cascade failure with DG permeability.
Detailed Description
In order to make the purposes, technical solutions and advantages of the implementation of the present invention more clear, the technical solutions in the embodiments of the present invention are described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are some, but not all, embodiments of the invention. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention. Embodiments of the present invention will be described in detail below with reference to the attached drawings:
it will be apparent to those of ordinary skill in the art after reading this specification that the following are examples and embodiments of the present disclosure and are not limited to operation according to these examples. Other embodiments may be utilized and structural changes may be made without departing from the scope of the exemplary embodiments of the present disclosure.
To clearly illustrate this interchangeability and compatibility of hardware, firmware, and software, various illustrative components, blocks, modules, circuits, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware, firmware, or software depends upon the particular application and design constraints imposed on the overall system. Those familiar with the concepts described herein may implement such functionality in a manner that is appropriate for the particular application, respectively, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
The cascading failure risk assessment method of the flexible power distribution system comprises the following steps:
1. and analyzing FMS operation characteristics and a control protection strategy.
The FMS is a novel power electronic component applied to a power distribution network, and is generally composed of a plurality of voltage source converters with the same structure, and the voltage source converters are connected through direct current lines, and alternating current sides are respectively connected with different feeder lines. Two-level VSC and Modular Multi-level Converter (MMC) are common converters for FMS, wherein MMC based on a half-bridge sub-module structure has wider application scenarios due to lower cost. After the FMS is connected into the power distribution network, the loop closing operation of the system can be realized, the feeder states of all port connections can be monitored in real time, the load balance among different feeders can be realized through optimal scheduling, the network loss is reduced, the equipment utilization efficiency is improved, and the new energy consumption capability is improved. The wiring pattern and physical structure of a MMC-based flexible multi-state switch is shown in fig. 1.
For ease of analysis, the following assumptions are made for the FMS-containing flexible distribution network system:
(1) The MMCs at all ends are three-phase symmetrical, the resistances and the reactance of upper and lower bridge arms of all phases are the same, and R is respectively arm and Larm ；
(2) Three-terminal MMC all adopts the half-bridge submodule structure that is completely unanimous, and the level number is the same.
Because MMC three-phase symmetry under the normal operating condition, and rectification side and contravariant side principle are close, consequently take rectification side as the example to analyze FMS operational characteristic, equivalent circuit is shown in FIG. 2, and under the normal operating condition, the dynamic differential equation of MMC alternating current network side is:
wherein d is a differential calculation sign in mathematics, and dt is the differential of time; i.e s For the current value of the power supply side in FIG. 2, i sa For a-phase power supply side current, i sb For b-phase power supply side current, i sc A c-phase power supply side current; u (u) sj J=a, b, c for a network side equivalent ac voltage source; u (u) cj J=a, b, c for the inverter output voltage; r is R T and LT Equivalent resistance and electricity of the converter transformer respectivelyResistance; r is R arm and Larm The equivalent resistance and reactance of the MMC bridge arm are respectively.
Ignoring harmonic components produced by sub-module switches, i.e. ignoring u ca 、u cb 、u cc The higher harmonic component of (2) is obtained by taking only the fundamental wave voltage u of each phase a 、u b 、u c The MMC low-frequency dynamic mathematical model under the three-phase static coordinate system in normal operation can be obtained:
2. and analyzing transient operation characteristics of the FMS after the fault aiming at the single-phase grounding fault of the feeder line.
From the MMC equivalent circuit, it can be seen that:
in the formula upj and unj Respectively the voltages of upper and lower bridge arms of j phases, u j And inputting voltage for the j-phase bridge arm. Assuming that a feeder line A phase has short circuit ground fault, A phase input voltage u of MMC after fault a Rapidly decreasing, and at the moment of failure, the DC voltage U dc Remains unchanged, so that the fault phase upper line bridge arm submodule voltage u pa and una Both decrease and the B, C phase submodule discharges phase a, which in turn will cause the B, C two phase submodule voltage to drop. When the voltage of the A-phase submodule drops to a certain degree, the submodule is turned off, the voltage output of the submodule is reduced to 0, the A-phase reactor bears the voltage of a fault phase bridge arm, and the bridge arm current is rapidly increased. And (3) neglecting the influence of the zero sequence component by using a symmetrical component method to obtain a positive and negative sequence system of the MMC after the fault:
equations (7) and (8) are positive sequence and negative sequence mathematical models under the MMC three-phase abc static coordinate system. To facilitate analysis of independent control of active and reactive power of MMC systems, park transforms are typically utilized to convert to a d-q rotational coordinate system:
the formula (9) and the formula (10) are positive sequence and negative sequence mathematical models under a d-q rotating coordinate system.
The power of the grid injection converter is as follows:
the active and reactive power of the injection converter during asymmetrical operation can be obtained by utilizing the phase-sequence conversion relation
wherein ：
in the DC component P 0 and Q0 For active and reactive average power, P S2 、P C2 、Q S2 and QC2 And the peak values are the frequency doubling sine and cosine peaks of the input or output active power and reactive power of the converter respectively.
According to formulas (12) - (14), after the ac feeder line has an asymmetric fault, the active power and the reactive power of the output of the converter include double frequency ac components, which results in dc voltage fluctuation, thereby causing power and voltage fluctuation of other converters connected with the converter, aggravating the unbalanced condition of the ac system, and blocking the converter from being operated when serious.
The multi-terminal flexible multi-state switch is operated with one terminal of the converter in a constant DC voltage-reactive power control mode (constant V dc Q mode), and the other inverter control system is a constant power control mode (constant PQ mode) in which the function of maintaining the dc bus voltage is performed, and power is output to the other port as a power output terminal. The functional block diagrams of the two control modes are shown in fig. 3 and 4.
The feeder line fault causes the asymmetry of the input current of the FMS, the negative sequence component causes direct-current voltage double frequency fluctuation, if the system is provided with a zero sequence channel, the zero sequence component causes bridge arm overcurrent and direct-current voltage fundamental frequency common mode fluctuation, so that the negative sequence and the zero sequence component of the input current are required to be restrained by a control system during the alternating-current fault crossing period, and the phenomena of direct-current waveform distortion, bridge arm overcurrent and the like are relieved. The control and protection system of the fault side converter is analyzed after feeder faults.
Assuming that one FMS comprises three-terminal MMC, t 0 At moment, the feeder line connected with the 1-end converter has an A-phase ground fault, and the converter protection system is at t 1 Locking at the moment, t 0 -t 1 The time required for the converter to latch. The control system at t 0 -t 2 Time to suppress fault current, t 0 -t 2 The fault current duration is suppressed for the controller. Compared with the protection of the converter, the line protection action time is longer, and the line protection system reaches t 3 And the moment side completes fault removal. The action time sequence relation of the 1-terminal control and protection system after the AC feeder line faults is shown in figure 5.
As can be seen from fig. 5, after ac feeder fault detection, whether ac fault ride-through can be completed is related to the coordination of the control system (inverter) and the protection system; under the condition that the performance of the controller is certain, the fault current inhibition effect is related to a fault initial value, the performance of the protection system is related to measured and setting errors, and therefore misoperation of the protection is possible, namely hidden faults can exist in the protection. The specific relation is as follows:
1) Whether the matching relation between the alternating current fault ride-through and the protection system and the control system can be completed: the control system is used for inhibiting short-circuit current after faults, and the protection system is used for locking and protecting the converter in a short time after the faults occur. If the protection acts in advance, the converter is locked, and the fault ride-through fails; if the control system has suppressed the short-circuit current to a normal level before the protection action, the protection does not act and the fault ride-through is successful.
2) Relationship between fault current suppression effect and fault initial value: since the ac current fluctuates sinusoidally, different fault moments can affect the waveform of the subsequent fault current. For example, in the event of a fault, the sinusoidal current just reaches 0, and then increases from 0 upwards after the fault; when the sinusoidal current reaches the maximum value during the fault, the sinusoidal current decays downwards from the maximum value after the fault.
3) Protection of system performance versus measured and tuning errors: the protection performance is divided into two parts, namely a measurement error and a setting error. In short, the measurement error corresponds to the action of the ammeter, and if the measured value is larger than the actual value, the protection malfunction may be caused, and otherwise, the protection malfunction may be refused. Setting error means that the protection system sets a threshold, and if the measured current is larger than the threshold, the protection will act; if the set current is lower than the calculated value, a protection malfunction may occur, and conversely, a malfunction may be rejected.
3. Four uncertainty factors affecting cascading failures are modeled separately.
(1) And a load and distributed power supply output model.
For randomness and volatility of Load (L) and distributed power supply (distributed generator, DG), it is assumed that the two are in normal distribution, wherein the average value of DG output is the same as the rated capacity, 50.0% of rated power is taken by standard deviation, and the power factors are all 0.9, namely
in the formula ,PDGN Rated active power for distributed power supply, P DG Is the active output of a distributed power supply, f DG As a random variable P DG Probability density function of (2), i.e. P DG ～N[P DGN ,(0.5P DGN ) 2 ]。
The load conforms to a normal distribution with the mean value of rated power and the standard deviation of 5% of rated power, namely
in the formula ,PLN Rated for load active power, P L For the active load, f L As a random variable P L Probability density function of (2), i.e. P DG ～N[P DGN ,(0.05P DGN ) 2 ]。
(2) And (5) an equipment fault model.
The random faults of the alternating current feeder lines are considered to be in accordance with the distribution of 0-1 two states, and the probability of faults of each feeder line is the same. A state of 0 indicates that the line fails, and the random failure probability is lambda, as shown in the following table
TABLE 1 two-state fault model for lines
(3) And (5) a device fault moment model.
Based on the model of the line fault established in the step (2), the fault occurrence time t is set to be uniformly distributed in 0-0.02s, namely t-U (0,0.02), and the probability density function is
(4) And setting and measuring an error model by the device.
Because the setting and the mutual inductor measurement have errors, the actual protectionThe setting value set by the protection system and the measured value obtained by the transformer fluctuate in a certain interval. Assume a protection setting value I set Measurement value I m Obeying the interval [ - ζ s ,+ζ s] and [-ζm ,+ζ m ]The probability density functions corresponding to the uniform distribution are respectively as follows:
4. the mechanism of occurrence of the fault is linked.
Protection against hidden faults is one of the important reasons for cascading failures of the power system. By cascading failure (Cascading Failure), as defined by the north american power system reliability committee, is meant a situation in which two or more elements of the power system fail in succession, resulting in a wide range of system outages. Although the cascading failure evolution process is extremely complex, the subsequent failures must have a certain correlation with the previous failures.
In fig. 5, it is assumed that at time t0, the feeder 1 has an a-phase ground fault, and at this time, the 1-side converter control mode is switched: v (V) dc Q-PQ, 2 terminal PQ-V dc The terminals Q and PQ are unchanged, and the terminal 2 is used for implementing direct current voltage control. At t 0 -t 1 In the period, the control system of the 1-end converter suppresses overcurrent and voltage fluctuation generated by faults, and because errors exist in setting and measurement of protection, when bridge arm fault current fluctuates near the setting value, the 1-end converter can be locked, and the feeder line 1 loses connection with the FMS. According to the technical regulations of distributed power supply access power grid, the photovoltaic and the fan have fault crossing capability, the feeder line is required to continuously run for 0.625s without off-grid after fault, the feeder lines 2 and 3 lose the regulating source after the 1-end converter is out of operation, the running state of the feeder line has a worsening risk, and according to the standard of the allowable deviation of power quality and power supply voltage, the part DG and the load are required to be cut off to form a cascading failure, and the cascading process is shown in figure 6.
From the above analysis, it can be seen that the distributed power supply and load fluctuation, the moment of failure occurrence, and the errors in the device setting and measuring links are the main uncertainty factors causing the risk of cascading failures, and the model is the basis of risk analysis.
5. And (5) cascading fault risk assessment.
(1) A cascading failure occurrence probability calculation method.
The event A= { contains the flexible distribution network of FMS and takes place the cascading failure }, B= {1 end MMC links to exchange the feeder and takes place single-phase grounding short circuit trouble }, C= { trouble side MMC is blocked or direct current busbar protection is by mistake }, D= { node voltage out of limit }. From the analysis of section 2, the events have the following equivalent relationships:
P(A)＝P(D|C)·P(C|B)·P(B) (20)
the formula (20) shows the probability of cascading failure of the flexible distribution network containing the FMS, namely the probability of node voltage out-of-limit caused by the blocking of the side MMC or the misoperation of the direct current bus under the condition of single-phase grounding short circuit failure of the alternating current feeder.
The method adopts a non-sequential Monte Carlo method to sample uncertain factors, judges event occurrence according to voltage by optimizing load flow calculation, and takes the sampling frequency of random variables as unbiased estimation of probability.
Assuming M samples are taken together, for event B, the line random faults are sampled according to Table 1, if M occurs for feeder 1 faults B The time, event B probability is
At M B In the secondary fault state, sampling the time and the position of the short-circuit fault according to a formula (17) to obtain a fault current initial value, and then sampling the measurement, the setting value and the action time limit of the protection device according to formulas (18) - (19) to judge whether protection misoperation occurs. At M B In the case of secondary failure, if there is M C The probability of the conditional failure of C under the condition B is that
At M C In the secondary protection misoperation state, carrying out power flow calculation on the feeder line 1, and carrying out optimization power flow calculation on the feeder lines 2 and 3 to obtain the voltage of each node in the system. If voltage out-of-limit occurs, DG or power supply needs to be further cut off, resulting in a cascading failure. If D cascading failures occur, the conditional probability of D under the condition C is that
In summary, the probability of occurrence of cascading failure is
(2) And (5) a cascading failure result calculation method.
In order to calculate the cascading failure result, firstly, the influence of DG and FMS connected to the power system on the node voltage needs to be quantitatively analyzed. Taking a certain feeder line in the power distribution network as an example, assume that the feeder line shown in fig. 7 has N loads, and the load size of m nodes is P m +jQ m The equivalent of the power grid is that the output is constant at P G +Q G Is connected with the distributed power supply at the point i, and has the output of P DG +jQ DG The load is L.
1) When DG is not considered, the voltage longitudinal component is ignored, and the voltage drop at the j point due to the power supply voltage is:
2) Under the condition of neglecting the injection power of the power grid, the voltage drop caused by the distributed power supply at the j point is as follows:
then, according to the superposition theorem, after the distributed power supply is accessed, the voltage drop of each node in the power distribution network is as follows:
equation (27) represents the effect on node voltage after DG switch-on.
Assuming that the three port access points of the FMS are all feeder line ends (i.e., N points of three feeder lines), the three port access points can be equivalent to a power source with continuously adjustable output or an energy storage device with adjustable load, and the voltage drop at the node j is:
by varying FMS output (input) power P FMS and QFMS The node voltage can be changed, the feeder 1 loses the FMS voltage regulating function along with the locking of the 1-end converter, and after the feeders 2 and 3 lose the power injected by the feeder 1, the FMS voltage regulating capability is weakened, and the running state of the system is deteriorated.
Constraint on voltage deviation less than 10% and objective function of cut-off distributed power capacity and load minimization, as shown in equation (29):
in the formula ,Ubias For distribution line voltage deviation, u max 、u min Maximum and minimum node voltages, respectively, objective function f 1 、f 2 Respectively aim at the minimum load loss of DG [18，6] ，P DG 、P L The active power of the distributed power supply and the active power of the load which are cut off due to voltage out-of-limit after the fault are respectively.
3) A risk index calculation method.
The minimum capacities of the cut load and DG after each occurrence of the cascading failure can be obtained according to the formula (29) to be P Li and PDGi Chain cuttingThe result of DG and load removal is M D Secondary ablation volume mean:
according to the risk theory, the calculation formulas of the DG removal and the load risk of the cascading failure can be obtained are as follows:
the invention provides a cascading failure risk assessment system of a flexible power distribution system, which comprises an FMS steady-state operation module, an FMS transient operation module, an uncertainty factor modeling module and a risk index calculation module. The FMS steady-state operation module is used for analyzing FMS operation characteristics and controlling protection strategies and establishing a mathematical model of FMS steady-state operation. The FMS transient operation module is used for analyzing transient operation characteristics of the FMS after the fault aiming at the feeder single-phase grounding fault. The uncertainty factor modeling module is used for respectively modeling based on four uncertainty factors influencing cascading failures to obtain a load and distributed power output model, an equipment failure moment model and a protection setting and measuring error model. And the risk index calculation module is used for determining the occurrence probability of the cascading failure and the DG risk through optimizing load flow calculation according to the model.
Further, the system also comprises an optimized power flow calculation module, wherein the optimized power flow calculation module is used for calculating a system running state parameter and inputting the system running state parameter into the FMS transient running module. The system also comprises a protection misoperation module, wherein the protection misoperation module is used for judging the protection misoperation condition and inputting the result into the risk index calculation module.
In an embodiment of the invention, as shown in fig. 8, a cascading failure risk assessment example analysis is performed, a flexible interconnection power distribution system cascading failure assessment system is built by utilizing a Matlab platform based on Matlab and PSCAD platform joint simulation, system running state parameters are obtained through calculation of an optimized power flow calculation module (model), the system running state parameters are input into an FMS transient running module built by the PSCAD platform, protection misoperation conditions are judged, and a result is returned to a risk assessment module in the Matlab for risk assessment.
As shown in fig. 9, to evaluate the risk of cascading failures, the modeling module performs the following sampling steps for the uncertainty factors in the system:
1) Calculating to obtain the running state of the system by using the optimized power flow model, and recording the voltage of each node;
2) If the line has single-phase earth fault, executing the step (3), otherwise executing the step (1), and sampling times are +1;
3) If the protection is false after the fault, executing the step (4), otherwise executing the step (1), and sampling the number of times to be +1;
4) If the voltage of the node is out of limit due to the protection misoperation, executing the step (5), otherwise executing the step (1), and sampling the number of times to be +1;
5) Calculating the minimum cut-off capacity P of the ith cascading failure Li and PSi Record the total number of samples, where P Li For load shedding capacity in the ith sample, P Si Cutting off the capacity of the distributed power supply for the ith sample;
6) And (3) if the total number of samples is the set value M, ending the sampling, calculating a risk index, and otherwise, executing the step (1).
The system uses three improved IEEE33 node power distribution systems as a cascading failure test system of the distribution network with the FMS, and the FMS is connected to 33 nodes at the tail ends of three feeder lines to connect the three systems together, as shown in figure 10.
The whole power distribution system comprises 100 nodes and 99 branches including an FMS, the FMS adopts a half-bridge MMC topological structure with identical three-terminal parameters, and relevant parameters are shown in table 2. The fans and loads in the power distribution system obey the normal distribution shown in the formulas (15) and (16), the three fans are respectively connected with the 15, 17 and 11 nodes of the 1-end network, and the rated capacities are respectively 400kVA, 450kVA and 500kVA.
Table 2 basic parameters
(1) Algorithm convergence analysis
In order to make the sampling result not lose generality, firstly, analyzing the algorithm convergence, and calculating different sampling times according to the probability of occurrence of the cascading failure, so as to obtain the variation trend of the probability along with the sampling number as shown in fig. 11. As can be seen from fig. 11, the probability of occurrence of the cascading failure finally stabilizes around 0.03, and when the sampling number is greater than 4000, the algorithm shows good convergence.
(2) Typical cascading failure process analysis
In order to analyze the occurrence mechanism of the cascading failure, a simulation result of a typical cascading failure is selected for analysis, and the sampling result aiming at each uncertain factor is shown in a table.
TABLE 3 sampling results
The a-phase upper and lower arm currents of the MMC at the 1-terminal after the fault are shown in fig. 12.
Since the bridge arm current reaches the set value at 0.510s, the second cycle of the fault current also partially exceeds the set upper limit. Comprehensively considering measurement and setting errors, protecting action, blocking MMC at the 1 end, leading the feeder line 1 to run in island, carrying out load flow calculation on the feeder line 1, carrying out optimized load flow calculation on a system formed by the feeder lines 2 and 3, and obtaining fault results as shown in table 4.
TABLE 4 Single-pass cascading failure results
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The direct cause of the system cascading failure is the false operation of the converter protection, and the fault occurrence position directly influences the fault current characteristic so as to influence the protection system, and the fault position and the false operation probability are analyzed.
(3) Influence of fault location on cascading failure probability
For the feeder line connected with the 1 end, the condition of each calculation of other uncertain factors is guaranteed to be the same, and cascading failure probability calculation is respectively carried out for 33 line failures, so that probability distribution shown in fig. 13 is obtained.
As is evident from fig. 13, the cascading failure increases with the approach of the failure location and the growth rate gradually decreases, because the line impedance has a dominant effect on the protection action when the failure point is far from the converter, and the performance of the protection system itself is dominant when the failure point is near.
(4) Impact of DG permeability on probability of cascading failures
DG permeability levels in distribution networks affect the probability of cascading failures due to the volatility and randomness of DGs. Under the condition that other uncertain factors are the same, sampling is carried out on cascading failures for different DG permeabilities, and the results are shown in the table 5:
TABLE 5 trend of probability of cascading failures with DG permeability
The failure probability was plotted as a function of DG permeability as shown in fig. 14.
As can be seen from fig. 14, the probability of cascading failure increases with increasing DG permeability, and the rate of increase gradually decreases, since the DG output level is smoother overall when the permeability level is higher; when the distribution network is not connected with the DG, even if the FMS port is blocked, the feeder line can still meet the normal operation condition, the node voltage out-of-limit condition does not occur, and the normal operation is resumed after the line fault is removed.
(5) Cascading failure risk calculation
According to the analysis result of the convergence of the section 3.1, the section adopts the Monte Carlo method to sample 5000 times, and calculates risks by using a formula (31), so as to obtain the result shown in the following table:
table 6 number and probability of occurrence of each event of cascading failure
From the probabilities of events in the table, the following conclusions can be drawn:
V dc after single-phase grounding faults occur on alternating current feeder lines connected with the current converter in the Q control mode, the current converter is locked in advance by taking 0.2563 as probability, and voltage out-of-limit conditions occur on the feeder lines with high probability, so that the probability of protection misoperation is reduced, and the occurrence times of cascading faults can be greatly reduced. The method has the advantages that the setting precision is improved, the setting and measuring errors are reduced by selecting the transformer with excellent performance, the fault ride-through capability is enhanced by selecting the power electronic device with high reliability, and meanwhile, the setting value and the action time limit which are reasonably set by considering the cooperation with a control system are also needed.
The average capacity of 189 consecutive fault systems to cut off DG and load was calculated using equations (29) - (30), and the consecutive fault risk was calculated using equation (31), and the results are shown in table 7.
Table 7 capacity cut-off and cascading failure risk
In addition to controlling the probability of occurrence of cascading failures, mitigating the consequences of a failure can also reduce risk. For the region with concentrated sensitive load, measures such as improving standby capacity, reasonably planning system structure and the like can be adopted.
The above embodiments are only for illustrating the technical solution of the present invention, and are not intended to limit the implementation scope of the present invention. All equivalent changes and modifications within the scope of the present invention should be considered as falling within the scope of the present invention.
Claims (7)
1. A flexible power distribution system cascading failure risk assessment method, which is characterized by comprising the following steps:
(1) Analyzing FMS operation characteristics and a control protection strategy, and establishing a mathematical model of FMS steady-state operation;
(2) Aiming at a feeder single-phase grounding fault, analyzing transient operation characteristics of an FMS after the fault;
(3) Based on four uncertainty factors influencing cascading failures, modeling is carried out respectively to obtain a load and distributed power output model, an equipment failure moment model and a protection setting and measuring error model;
the four uncertainty factors are: the randomness and fluctuation of the load and the distributed power supply, the occurrence probability of equipment faults, the occurrence time of the equipment faults and the errors existing in the setting and transformer measurement;
(4) According to the model, determining occurrence probability of cascading failures and DG risk through optimization load flow calculation;
the occurrence probability of the cascading failure is as follows:
P(A)＝P(D|C)·P(C|B)·P(B)
wherein, the notepad A= { contains FMS flexible distribution network occurrence cascading failure }, B= {1 end MMC connected with alternating current feeder line occurrence single-phase grounding short circuit failure }, C= { failure side MMC blocking or direct current bus protection misoperation }, D= { node voltage out-of-limit }; p (B) is the probability of event B, P (C|B) is the probability of event C under B condition, and P (D|C) is the probability of event D under C condition;
and calculating the shedding load of the cascading failure, wherein the shedding load of the cascading failure and the DG risk have the following calculation formulas:
wherein ,P Li to cut off the minimum capacity of load after each occurrence of cascading failure, P DGi To cut off the minimum capacity of DG after each occurrence of cascading failure, M D For load shedding and DG frequency.
2. The method for evaluating the risk of cascading failures of a flexible power distribution system according to claim 1, wherein the mathematical model established in the step (1) is as follows:
wherein ,
u sj j=a, b, c for a network side equivalent ac voltage source; r is R T For equivalent resistance of converter transformer, L T Equivalent reactance of the converter transformer; r is R arm Is MMC bridge arm equivalent resistance, L arm The equivalent reactance of the bridge arm of the MMC is obtained; u (u) a 、u b 、u c Fundamental voltages for each phase; i.e sa For a-phase power supply side current, i sb For b-phase power supply side current, i sc Is the c-phase power supply side current.
3. The method for risk assessment of cascading failures of flexible power distribution system according to claim 1, wherein in step (2), after the ac feeder fault is detected, whether the ac fault ride-through is completed is related to the coordination of the inverter control and protection system; under the condition that the performance of the controller is certain, the fault current inhibition effect is related to a fault initial value, and the performance of the protection system is related to measured and setting errors.
4. A flexible power distribution system cascading failure risk assessment system, the system comprising:
the FMS steady-state operation module is used for analyzing FMS operation characteristics and controlling protection strategies and establishing a mathematical model of FMS steady-state operation;
the FMS transient operation module is used for analyzing transient operation characteristics of the FMS after the fault aiming at the feeder single-phase grounding fault;
the uncertainty factor modeling module is used for respectively modeling based on four uncertainty factors influencing cascading failures to obtain a load and distributed power output model, an equipment failure moment model and a protection setting and measuring error model;
the four uncertainty factors are: the randomness and fluctuation of the load and the distributed power supply, the occurrence probability of equipment faults, the occurrence time of the equipment faults and the errors existing in the setting and transformer measurement; and
the risk index calculation module is used for determining occurrence probability of cascading failures and DG risk through optimizing load flow calculation according to the model;
the occurrence probability of the cascading failure is as follows:
P(A)＝P(D|C)·P(C|B)·P(B)
wherein, the notepad A= { contains FMS flexible distribution network occurrence cascading failure }, B= {1 end MMC connected with alternating current feeder line occurrence single-phase grounding short circuit failure }, C= { failure side MMC blocking or direct current bus protection misoperation }, D= { node voltage out-of-limit }; p (B) is the probability of event B, P (D|B) is the probability of event C under B condition, and P (D|C) is the probability of event D under C condition;
and calculating the shedding load of the cascading failure, wherein the shedding load of the cascading failure and the DG risk have the following calculation formulas:
wherein ,P Li to cut off the minimum capacity of load after each occurrence of cascading failure, P DGi To cut off the minimum capacity of DG after each occurrence of cascading failure, M D For load shedding and DG frequency.
5. The flexible power distribution system cascading failure risk assessment system according to claim 4, further comprising an optimized power flow calculation module, wherein the optimized power flow calculation module is configured to calculate a system operation state parameter, and input the system operation state parameter into the FMS transient operation module.
6. The system for cascade fault risk assessment of a flexible power distribution system according to claim 4 or 5, further comprising a protection malfunction module for determining a protection malfunction situation and inputting a result to the risk indicator calculation module.
7. The flexible power distribution system cascading failure risk assessment system according to claim 4 or 5, wherein the uncertainty factor modeling module performs the sampling steps of:
(1) Calculating to obtain system running state parameters by using the optimized power flow calculation module, and recording the voltage of each node;
(2) If the line has single-phase earth fault, executing the step (3), otherwise executing the step (1), and sampling times are +1;
(3) If the protection is false after the fault, executing the step (4), otherwise executing the step (1), and sampling the number of times to be +1;
(4) If the voltage of the node is out of limit due to the protection misoperation, executing the step (5), otherwise executing the step (1), and sampling the number of times to be +1;
(5) Calculating the load of the ith cascading failure and the minimum cut-off capacity of DG, and recording the total sampling number;
(6) And (3) if the total number of samples is a set value, ending the sampling, calculating a risk index, otherwise, executing the step (1).
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