CN114139761A

CN114139761A - Depth-first search method for power grid black start initial start path

Info

Publication number: CN114139761A
Application number: CN202111166045.2A
Authority: CN
Inventors: 余笑东; 周鲲鹏; 李群山; 吴亚骏; 蔡德福; 曹侃; 王莹; 王涛; 万黎; 陈汝斯
Original assignee: State Grid Corp of China SGCC; Central China Grid Co Ltd; Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
Current assignee: State Grid Corp of China SGCC; Central China Grid Co Ltd; Electric Power Research Institute of State Grid Hubei Electric Power Co Ltd
Priority date: 2021-09-30
Filing date: 2021-09-30
Publication date: 2022-03-04

Abstract

The invention provides a depth-first searching method for a black start initial starting path of a power grid, which comprises the following steps: (1) determining a basic condition which the initial path should have; (2) the method comprises the following steps of providing a corresponding search rule by considering the problems of possible self excitation, overvoltage, stability and the like of a path; (3) based on the rule, a depth search strategy is adopted to carry out rapid search on the initial path; (4) comparing the searched initial paths, and selecting a plurality of better paths for verification; (5) if no feasible solution exists, the black start power supply is searched again or selected again after the rule is relaxed. The method saves a great deal of time for the optimal path decision of starting the large-capacity unit by the black start power supply and the subsequent evaluation of the black start scheme, can greatly improve the black start efficiency, shortens the power failure loss caused by overlong black start process time of the power grid, and plays an important role in stabilizing national economy.

Description

Depth-first search method for power grid black start initial start path

Technical Field

The invention relates to a black start process of a power grid full stop after a serious fault of a power system, in particular to a depth-first search method for a black start initial start path of the power grid.

Background

When a large-area power failure occurs to a regional power system due to an accident, the power grid is in a completely black state, and the power grid needs to be immediately subjected to black start in order to quickly recover load power supply, reduce economic loss and ensure social stability. The black start is the last defense line of the safe operation of the power system, and a reasonable black start scheme is formulated, so that the method has important significance for accelerating the recovery process after the system full black accident and reducing the accident loss.

In the initial stage of black start, the path of starting the large-capacity unit by the black start power supply is an important basic stone in the whole-network black start process, and the black start path search work is required immediately after the power grid is completely black. Therefore, a corresponding rule for searching the black start path is formulated according to relevant regulations and regulations, and factors such as the voltage, the power angle and the frequency stability of the power grid, and all the better paths meeting the conditions are quickly searched by using a depth-first strategy, so that the method has important significance for making the optimal path for starting the large-capacity unit by using the black start power supply and accelerating the whole network recovery process.

At present, the research focus of evaluation of the black start scheme is to give corresponding weights to indexes such as scheme recovery time, operation times and recovery success rate for comprehensive evaluation, and is mainly focused on the superiority and inferiority of the scheme; however, in the actual black-start process of the power grid, the depth-first search of the black-start path can reduce the work of scheme evaluation, reduce the blackout time of the power grid, and has important significance in accelerating the whole-grid recovery process.

Therefore, the invention provides a depth-first search method for the initial starting path of the black start of the power grid, which saves a great deal of time for the decision of the optimal path for starting the large-capacity unit by the black start power supply and the evaluation of the subsequent black start scheme, can greatly improve the black start efficiency, shortens the power failure loss caused by overlong black start process time of the power grid, and plays an important role in national economy and stability.

Disclosure of Invention

In view of the above, the invention provides a depth-first search method for a black start initial start path of a power grid, which makes a corresponding rule for searching the black start path according to relevant regulations and regulations, factors such as power grid voltage, power angle and frequency stability characteristics, and quickly searches all superior paths meeting conditions by using a depth-first strategy.

The invention is realized by adopting the following technical scheme:

a depth-first search method for a black start initial starting path of a power grid comprises the following steps:

(1) determining the basic conditions which the initial path should have according to the relevant regulations and regulations related to the current black start;

(2) on the basis of the basic conditions, the problems of self-excitation, overvoltage and stability possibly existing in the path are considered, and in order to enable the searched path to be more effective, a corresponding search rule is formulated during path depth search to eliminate bad paths;

(3) based on the search rule, a depth search strategy is adopted to carry out rapid search on the initial path;

(4) comparing all the searched initial paths, and selecting a plurality of better paths for verification;

(5) and (4) if no feasible path exists, selecting the relaxation constraint and the depth limit for searching again, and if no limit still exists after relaxation, reselecting the black start power supply and executing the steps (1) to (4) again.

Further, in step (1), the basic conditions to be possessed by the initial path are determined according to the current relevant regulations and regulations related to black start, and specifically: according to the guidance rules of the black start scheme compilation and implementation technical specifications (trial) of the power system in the file of the debugging technology [2005]8 in China, the black start scheme path should meet the following conditions:

1) the number of voltage conversion in the starting path does not exceed 3, i.e. the number of transformers N passed_T≤3；

2) The number N of the black start power supplies (system side buses) and the number N of the transformer substations passed by the started power plant (between the system side buses) in each black start scheme_S≤5；

3) The path electrical distance of each scheme is as short as possible, namely the total path impedance is required to be minimum value Z when the scheme is decided_Smin；

4) The capacity of the started unit selected under the premise of starting capacity allowance in each scheme is required to be as large as possible, namely the target unit should search the maximum value S_max。

Further, the search rule formulated in step (2) is:

1) if multiple paths exist in the same node during searching, the path without voltage conversion is preferentially selected;

2) when the number of stations passed by the path exceeds 5, immediately stopping searching;

3) the shortest path electrical distance principle;

4) when the capacity of the started unit is sought to be as large as possible, the important auxiliary machine capacity of the started unit must be considered to be not larger than the black-start power supply capacity.

Further, the depth-first search strategy adopted in the step (3) is a traversal search strategy, all feasible black start paths in the topological relation of the power grid are searched out under the limitation of the rule, and bad paths which do not meet the rule are eliminated.

Further, the searching process in the step (3) is divided into two processes of forward progress and backtracking: the forward search is carried out according to the depth priority principle, and the backward search is carried out according to the backtracking principle;

in the advancing process, counting the number of passed stations, the voltage conversion times and the path length, and determining which branch to search along, wherein the branch needing to be subjected to the voltage conversion is not searched as much as possible;

backtracking is started when the following conditions are met: a terminal that has proceeded to a certain branch cannot search down; a loop was found to be formed; the number of stations passing through is 5; the voltage conversion times reach 3 times;

during backtracking, the number of stations passing through the backtracking, the voltage conversion times and the path length are subtracted.

The invention has the advantages that:

1. on the basis of the existing black start related regulation and regulation in China, the problems of self excitation, overvoltage, stability and the like possibly existing in the path are considered, the characteristics of the current grid structure of the China are combined, corresponding search and center search rules are further formulated during deep search, bad paths are eliminated, a better path can be quickly searched, and a foundation is laid for the decision of a subsequent optimal path and the acceleration of the whole network recovery process;

2. when the depth-first strategy based on the rules is adopted for searching, not only relevant constraints and depth limits are formulated, but also a complete search stopping mechanism and backtracking mechanism are set, so that all better feasible paths can be quickly searched, and the feasible paths and the optimal solution can be prevented from being lost in the searching process.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.

FIG. 1 is a black start partition of a regional grid;

FIG. 2 is a flowchart of an algorithm for rapidly searching all the better paths meeting the conditions by using the depth-first strategy according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the application. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. It is explicitly and implicitly understood by one skilled in the art that the embodiments described herein can be combined with other embodiments.

The embodiment of the invention provides a stability verification method for a black start initial starting path of a power grid, which comprises the following steps:

(1) determining basic conditions which the initial path should have according to the relevant regulations and regulations of the existing black start in China; specifically, according to the guidance rules of the black start scheme compilation and implementation technical specifications (trial) of the power system in the document of the state transfer [2005]8, the black start scheme path should satisfy:

(2) On the basis of the basic conditions, considering the problems of self excitation, overvoltage and stability possibly existing in the path, in order to make the searched path more effective, a corresponding search rule is made during the path depth search to eliminate bad paths which can not meet the following rules at the same time, namely:

1) if multiple paths exist in the same node during searching, the path without voltage conversion is preferentially selected.

The increase of the number of voltage conversion directly influences whether an empty charging line in the initial stage of black start causes voltage out-of-limit or not, and also increases voltage loss and the probability of three-phase different-phase closing, which is directly related to whether the black start can be successful or not, so the number of voltage conversion is limited during searching. Thus, if a node has several sub-nodes, the selection of the node that does not undergo over-voltage conversion is preferably expanded, i.e., the search down the branch that does not undergo over-voltage conversion is preferably considered.

2) When the number of stations passed by the path exceeds 5, the search is stopped immediately;

the increase of the number of times of the transformer substation will increase the number of times of operation of the disconnecting link and the breaker when the system is recovered, and will cause adverse effects on the system, such as increasing the possibility of generating operation overvoltage, prolonging black start time and the like. Meanwhile, the number of stations is limited, and the limit of depth-first search is set actually, so that the depth-first search cannot be continued without limitation. Considering the capacity of the black start power supply of the power grid and the length of the outgoing line of the power plant in China at present, the number of the stations should not exceed 5 in order to prevent the self-excitation problem.

3) And the shortest path electrical distance.

If two or more paths from the black start power supply to the started power plant exist, the path with the shortest electrical distance length is selected possibly, so that the probability of self-excitation, overvoltage and stability problems is low, the operation frequency of a dispatcher is less, and the probability of black start failure is low.

When starting along the black start path, the plant load of the started power plant and the important load on the path are carried, so that the sum of the plant load and the important load of the started power plant cannot exceed the capacity of the black start power supply unit. If the factory load capacity of the started unit exceeds the allowable value, the path cannot be started and should be rejected.

(3) And based on the search rule, performing rapid search on the initial path by adopting a depth search strategy.

1) Terms and definitions:

and the current node: searching the nodes which are traversed in the process;

child node of the current node: all other nodes directly connected with the current node by the topological connection relation of the elements;

nodes are not traversed: nodes that have not been traversed;

path node table: storing nodes passed by the black start path;

not traversing the node table: storing nodes which are not traversed;

transformer node: representing a node whose component type is a transformer.

2) Search process

The searching process is divided into two processes of forward progress and backtracking: the search is carried out in sequence by the depth priority principle before the progress, and the search is carried out in reverse direction after the backtracking.

In the process of moving forward, the number of stations passed by, the number of voltage conversion times (the number of transformers passed by), the path length, and which branch to search along needs to be determined, and the branch which needs to be subjected to voltage conversion (i.e. the branch which needs to be subjected to transformer) is not passed by as much as possible.

Backtracking is started when the following conditions are met: a terminal that has proceeded to a certain branch cannot search down; a loop was found to be formed; the number of stations passing through is 5; the number of voltage conversion times reaches 3 times.

During backtracking, the number of stations passing through backtracking, the voltage conversion times and the path length are subtracted.

(4) And comparing all the searched initial paths, and if the number of the paths is excessive, taking a plurality of the superior paths for subsequent verification.

If the number of all the paths searched according to the rule is more than 5, in order to reduce the operation times and the line length during the black start, comprehensive sequencing is carried out according to the electrical distance and the number of the stations passing through, and the first 5 paths are selected.

(5) If there is no feasible path at the specified search depth, the number of stations allowed to pass through and the number of voltage conversion times should be properly relaxed, and the capacity limit of the started unit should be strictly followed.

And (4) if no feasible path exists after the relaxation, reselecting the black start power supply and re-executing the steps (1) to (4).

The above algorithm is embodied in the examples.

Taking a black start partition of a regional power grid as an example, the method is applied to make a corresponding rule of black start path search according to relevant regulations and regulations, factors such as power grid voltage, power angle and frequency stability characteristics, and all better paths meeting the conditions are quickly searched by using a depth-first strategy. By the method, all better paths meeting the conditions can be quickly searched, the method has important significance for making the optimal path for starting the large-capacity unit by the black start power supply and accelerating the whole network recovery process, the power failure loss caused by overlong black start process time of the power grid is reduced, and the method plays an important role in national economy stability.

Firstly, based on the step (1), providing basic conditions which should be possessed by an initial path according to the relevant regulations and regulations of the existing black start in China; and then, implementing the step (2) to set a corresponding rule of black start path search in consideration of factors such as self-excitation, overvoltage, grid voltage, power angle and frequency stability characteristics, implementing the step (3) to quickly search all superior paths meeting the conditions by using a depth-first strategy, and finally, if the number of paths meeting the conditions is too large, selecting 5 superior plant stations according to the electrical distance and the number of passed plant stations, so that the workload of subsequent path verification and optimization is reduced.

The implementation process of the method comprises the following steps:

the electrical parameters of the lines and transformers for a black start sub-area of a regional grid as shown in fig. 1 are shown in tables 1 and 2.

TABLE 1 per unit value of parameter for each line

S＝100MVA,U＝525kV

TABLE 2500 kV Transformer substation Transformer parameter

The generator parameters and the step-up parameters of the black start power supply are shown in tables 3 to 5.

TABLE 3 Black Start Power Unit parameters

Index (I)	Parameter(s)
		Type of generator	SAV750/265/24
Rated capacity/rated power	334MVA/300MW
		Rated voltage	15.75kV
Rated current	12244A
		Rated excitation voltage	279V
Rated exciting current	1729A
		Rated power factor (hysteresis)	0.9
Xq (unsaturated value)	0.667
		Rated speed of rotation	250r/min

TABLE 4 black start power unit step-up variable parameters

Index (I)	Parameter(s)
		Model number	SSP10-360000/500
Rated capacity	360MVA
		Rated voltage (high/low voltage)	525±2×2.5％/15.75±2×2.5％kV
Rated current (high voltage/low voltage)	396A/13197A
		Connecting group (three-phase)	Ynd11
Short circuit impedance	14％(+7.5-0％)
		Operating gear	3

The capacities of the started units are shown in table 5:

power plant	Capacity (MW)	Important auxiliary machine capacity (MW)
			Plant 1	660	66
Plant 2	660	66
			Plant 3	330	33
Plant 4	300	30
			Plant 5	300	30
Plant 6	640	64
			Plant 7	150	15

If the method is not adopted, the selection of the black start path is only considered in the distance of the electrical distance, and then the 10 black start paths selected are respectively as follows:

the implementation is carried out according to the step (1), and 10 black starting paths are selected and respectively:

route 1: black start power → 1 → 2 → plant 1;

route 2: black start power → 1 → 2 → 3 → 4 → 5 → plant 2;

route 3: black start power → 1 → 2 → 3 → 16 → factory 5;

path 4: black start power → 1 → 2 → 3 → 4 → 7 → 9 → plant 3;

path 5: black start power → 1 → 2 → 3 → 4 → 8 → plant 3;

path 6: black start power → 1 → 2 → 3 → 4 → 6 → 14 → plant 4;

path 7: black start power → 1 → 2 → 3 → 4 → 6 → 20 → factory 5;

path 8: black start power → 1 → 19 → plant 6;

path 9: black start power → 1 → 2 → 3 → 4 → 10 → 14 → plant 4;

path 10: black start power → 1 → 19 → 18 → plant 7.

The total impedance value X of the above 10 black start paths is shown in table 6.

Table 310 impedance values for the black start path

Route of travel	X	Route of travel	X
					1	0.015295	6	0.071033
2	0.042334	7	0.073866
				3	0.046046	8	0.076343
4	0.055731	9	0.078039
				5	0.057948	10	0.105543

Among the above paths, the

paths

2, 4 and 5 are closer in electrical distance, but the number of stations passing through the factory is larger than 5 required by relevant regulations and regulations, and therefore the paths should not be used as initial paths of black start. And the

paths

8 and 10 pass through a smaller number of stations, but have larger electrical distance and are better black start paths.

Therefore, under the condition of not making constraints, all feasible paths are searched from the topological relation, the calculation time is long, the path searching result is poor, and large workload is brought to the subsequent decision of carrying out the black start initial path.

If the method is adopted, basic conditions which the initial path should have are provided based on the step (1) according to the current relevant regulations and regulations about black start in China; then, step (2) is implemented to make a corresponding rule of black start path search in consideration of factors such as self-excitation, overvoltage, grid voltage, power angle and frequency stability characteristics, step (3) is implemented to rapidly search all the better paths meeting the conditions by using a depth-first strategy, and a flow chart is shown in fig. 2.

Considering step (2), when the capacity of the started unit is as large as possible, the important auxiliary machine capacity of the started unit must be considered to be not more than the black-start power supply capacity, and the important auxiliary machine capacity is 10% of the unit capacity.

The specific implementation process is as follows:

acquiring nodes and parameters of a full-network generator, a transformer, a power transmission line, a load and the like, and establishing a node table; each side of the transformer in different grades respectively corresponds to different nodes, and the power transmission line corresponds to the first node and the last node;

and establishing an empty table, taking the black start power supply as an initial point, and setting all the voltage conversion times, the number of stations, the passing electrical distance of the path and the important loads of the path to be 0.

Under the constraint of the rule, a depth-first search method is adopted, the black-start power supply is used as a starting point, all paths close to the power plant are searched, and the voltage conversion times of all the paths, the number of stations experienced, the electrical distance passed by the paths and the important load carried by the paths are recorded.

If more than two paths exist to a certain node, products of the voltage conversion times, the number of stations experienced and the electrical distance passed by the paths are compared, and a smaller value is taken as a better path.

And if any condition that the number of experienced stations is more than 5, the voltage conversion times are more than 3 or the important load carried by the path exceeds the capacity of the black-start power supply exists in the searching process, returning to the black-start power supply for searching again.

If no feasible path exists under the specified depth limit, the depth limit should be relaxed, and the steps should be re-executed, but the limit on the factory load capacity of the started unit should not be relaxed; if the feasible path still can not be searched, the black start power supply is selected again, and the steps are executed again.

As shown in fig. 2, the specific algorithm of the present invention is implemented as follows:

(1) initialization: establishing an empty stack for storing the nodes which are not traversed; establishing an empty table for storing the current path node; the number of stations passing through is counted as 0, the voltage conversion times is counted as 0, the number of stations actually passing through is 0, the path length is 0, and the important load is 0.

(2) According to the selection requirement of the black-start power supply, the black-start power supply is searched out, black-start power supply nodes are stored in a current path node table, the number of the black-start power supply nodes passing through a station is counted to be 1, and then the step (3) is carried out.

(3) And (4) taking the last node in the current path node table as the current node.

(4) And (4) piling child nodes which are not present in the path table and are identified as not-traversed in the current node into the non-traversed node stack. When the node is stacked, if the transformer node exists, the transformer node is placed at the bottom of the stack, and then other nodes are stacked, so that the node which is not subjected to overvoltage conversion is firstly traversed during path search, and then the step (5) is carried out.

(5) And moving the first node in the non-traversed node stack into the tail of the table of the current path node. Judging whether the current path node table (excluding the current node) has the same node as the current node or not:

if yes, forming a loop to indicate that two paths exist from the path root node to the father node of the current node in the current path table, comparing the two paths according to the voltage conversion times, the path length and the number of stations passing through, and selecting the path with the smaller product of the voltage conversion times, the number of stations passing through and the path electrical distance length as the current path; nodes which are not related to the current path in the non-traversed node stack and are related to the other path are removed from the non-traversed node stack and are marked as traversed nodes; taking a father node of the current node as the current node in the current path table; and (6).

If not, go to (6).

(6) Analyzing and judging the current node, and performing the following operations according to different node types:

and the current node is a power plant, the number of the power plant stations is counted and added with 1, if the capacity of the element unit of the power plant does not exceed an allowable value, a path formed by all the nodes in the current path node table in sequence is a black start path, and the current node is the started power plant of the current path. Judging whether the searched (stored) path has a path which takes the current node as the started power plant, if not, storing the current path; if yes, comparing the lengths of the two paths, if the current path is shorter than the saved path, replacing the saved path with the current path, otherwise, not saving the current path.

The current node is a transformer substation, and the number of stations is counted and added by 1.

The current node is the transmission line and the length of the line is added to the path length.

The current node is a transformer and the voltage conversion count is incremented by 1.

And then go to (7).

(7) And calculating the number of the stations actually passing through, wherein the value is the number of the stations minus the voltage conversion times. The reason is that the two elements (buses) at the front and the back of the transformer actually belong to the same transformer substation, and the elements are counted according to different transformer substations when the number of the transformer substations passes through the counting, so that the elements are subtracted. And (8) turning.

(8) Judging whether the number of the stations actually passing through the factory exceeds a limit value, if so, if the non-traversed node stack is not empty, backtracking and turning to (12); if not, turn to (9).

(9) Judging whether the voltage conversion times exceed a limit value, if so, if the non-traversed node stack is not empty, backtracking and turning (12); if not, turn to (10).

(10) Judging whether the load with the important load exceeds a limit value, if so, if the node stack which is not traversed is not empty, backtracking and turning to (12); if not, turn to (11).

(11) Judging whether the current node has a child node which is not in the current path table, if so, turning to (4); if not, if the non-traversed node stack is not empty, backtracking is needed, and the step (12) is carried out.

(12) Judging whether the non-traversed node stack is empty or not, if so, exiting, and finishing the search; if not, go to (13).

(13) Backtracking process

a) Judging whether the current node has a connection relation with a first node in the node stack which is not traversed, if so, finishing backtracking, and turning to the step (3); if not, turning to b);

b) analyzing and judging the current node, and performing the following corresponding operations according to different node types:

the current node is a power plant, and the number of the power plants is counted and subtracted by 1 to turn to c).

And the current node is a transformer substation, the number count of the transformer substation is reduced by 1, and the current node is converted into c).

And c) when the current node is the power transmission line, subtracting the length of the section of the power transmission line from the path length, and turning to c).

The current node is the transformer and the voltage conversion count is decremented by 1, to c).

c) And deleting the last node in the current path node table, and turning to a).

By applying the method, the finally screened black start path is as follows:

route 1: black start power → 1 → 2 → plant 1;

route 2: black start power → 1 → 19 → plant 6;

route 3: black start power → 1 → 2 → 3 → 16 → factory 5;

path 4: black start power → 1 → 19 → 18 → plant 7;

the black start path searched by the method has the station number not exceeding 5, the voltage conversion not exceeding 3 times, and simultaneously satisfies the principle that the capacity of the black start power supply is larger than the capacity of all the important auxiliary machines of the started unit and the limit of the path with large capacity of the started unit. Therefore, the path searched by the method is better than the path searched by only the electrical distance, a large amount of work is saved when the optimal decision of the black start path is subsequently carried out, and the black start process is shortened.

The above description is only an embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention.

Claims

1. A depth-first search method for a black-start initial starting path of a power grid is characterized by comprising the following steps of: the method comprises the following steps:

2. The fast search method for the black start initial start path of the power grid according to claim 1, wherein: in the step (1), the basic conditions which the initial path should have are determined according to the current relevant regulations and regulations related to black start, and specifically: according to the guidance rules of the black start scheme compilation and implementation technical specifications (trial) of the power system in the file of the debugging technology [2005]8 in China, the black start scheme path should meet the following conditions:

2) The number N of black start power supplies and the number N of substations passed by the started power plant in each black start scheme_S≤5；

3. The fast search method for the black start initial start path of the power grid according to claim 1, wherein: the search rule formulated in the step (2) is as follows:

3) the shortest path electrical distance principle;

4. The fast search method for the black start initial start path of the power grid according to claim 1, wherein: and (4) the depth-first search strategy adopted in the step (3) is a traversal search strategy, all feasible black start paths in the topological relation of the power grid are searched out under the limitation of the rule, and bad paths which do not meet the rule are eliminated.

5. The fast search method for the black start initial start path of the power grid according to claim 1, wherein: the searching process in the step (3) is divided into two processes of forward progress and backtracking: the forward search is carried out according to the depth priority principle, and the backward search is carried out according to the backtracking principle;