CN111027184B - Ship power grid fault reconstruction convex optimization model considering reliability constraint - Google Patents
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Abstract
A ship power grid fault reconstruction convex optimization model considering reliability constraint comprises the following steps: establishing a reliability index calculation model based on the line-distribution board incidence matrix; aiming at reducing the load loss and the network loss of the ship power grid, considering the voltage constraint of the ship power grid, the reliability constraint of a system and an important load, and establishing a ship power grid fault reconstruction model; and converting the original model into a ship power grid fault reconstruction convex optimization model through second-order cone relaxation so as to solve and obtain a reconstruction strategy with the maximum load recovery amount. The invention can minimize the power loss after the important load is recovered, ensure the reliable power supply of the system and the important load and improve the voltage quality. The method has high precision and can quickly obtain the global optimal solution.
Description
Technical Field
The invention relates to the technical field of power system analysis, in particular to a ship power grid fault reconstruction convex optimization model considering reliability constraint.
Background
When a ship executes a navigation task at sea, the electric power system of the ship is completely separated from the land electric power system, and the whole ship electric equipment can be powered only by the power supply system of the ship. In actual operation, due to problems of navigation damage, improper operation or equipment, various faults or abnormal operation states may occur in a ship power system, which affects safe and reliable operation of the whole network, and may even cause equipment damage or power interruption of the whole power grid, which affects fighting performance and navigation safety of the ship. The fault reconstruction strategy is a common power restoration method, but is different from a conventional power system, if a ship power system has a fault, the reliability of a reconstructed power grid needs to be considered when the power grid is reconstructed and the load is restored. In addition, the ship is supplied with power by a power station, so that the load capacity generally has no too much redundancy, and if major faults occur, the problems of line transmission capacity and voltage safety constraint are also a problem which cannot be ignored.
In conclusion, the method has very important significance in rapidly and maximally recovering the power supply of important loads and ensuring the safety of the ship operation mode aiming at the fault state of the ship power grid. The existing method for reconstructing the fault of the ship power system does not consider the reliability and voltage safety of the power grid after recovery, and the existing fault reconstruction model of the ship power system is usually a non-convex model and is usually solved by an intelligent algorithm based on population evolution, but has the problems of low convergence speed, easy falling into local optimization, low search efficiency and the like.
Therefore, it is necessary to provide a ship power grid reconstruction model capable of rapidly obtaining a global optimal solution and considering reliability and voltage safety operation constraints.
Disclosure of Invention
In order to solve the technical problems, the technical scheme adopted by the invention is to provide a ship power grid fault reconstruction convex optimization model considering reliability constraint, and the model is characterized by comprising the following steps of:
dividing the load of the ship power grid into different important levels based on a reliability index concept and a ship power grid fault reconstruction requirement, and defining the important degrees of the different load levels;
selecting I-level loads according to the load classification result obtained in the step 1, and establishing a reliability index calculation model through a line-distribution board incidence matrix;
aiming at reducing the load loss and the network loss of the ship power grid, considering the voltage constraint of the ship power grid, the reliability constraint of a system and an important load, and establishing a ship power grid fault reconstruction model;
converting the ship power grid fault reconstruction model into a convex optimization model through second-order cone relaxation;
and solving to obtain the action switch which meets the constraint and minimizes the loss load quantity.
In the above method, the importance levels of the ship power grid load include:
the ship power grid is divided into a class I load, a class II load and a class III load according to the importance of the load.
I-level load: this load controls the vitality of the ship and the safety of the passengers belonging to the un-unloadable load; in any case a first order load must be provided. The primary loads of the ship system comprise a boiler, a generator, a weapon system, an electronic countermeasure system, a medical operating room and the like, and at least two power supply paths are required for important loads to be connected. If a certain load is certified as a primary load (e.g. a ship propulsion system) in any one of the ship's operational tasks, it has to be connected to the ship's electrical system by Automatic Bus Transfer (ABT). Automatic bus transfer is a device that detects power loss from a normal power supply. When the normal power supply fails, the ABT can automatically and quickly disconnect the load from the normal power supply and connect the load power supply with the standby power supply. Non-critical loads have only one power path.
And II-stage load: this load is important to the proper operation of the vessel but allows it to be offloaded or transferred to other platforms to supply power if necessary to prevent significant loss of load. These loads include: cargo lifts, sea water pumps, some radar loads, etc.
Stage III load: the ship can be unloaded immediately when necessary, and the service life and the safety of the ship cannot be adversely affected; the method mainly comprises the following steps: residential heating systems, kitchen electrical loads, and the like.
In the above method, the ship grid reliability constraint includes:
first, the average outage frequency (SAIFI) and the expected low battery (EDNS) of the system are defined by equation (1):
in the formula, N I Representing a set of important electrical panels; lambda [ alpha ] j Representing the outage probability of panel j; c j Represents the number of loads to which panel j is connected; p Lj Representing the real load of panel j.
The reliability constraint of the ship power grid is embodied in that SAIFI and EDNS are smaller than given standard values, as shown in formula (2):
in the formula, SAIFI * Representing a given average outage frequency standard value; EDNS * A standard value representing a desired value of a given charge deficit.
And defining a line-panel association matrix by equation (3):
equation (4) represents a reliability index calculation model based on the line-distribution board correlation matrix:
in the formula (I), the compound is shown in the specification,
representing the failure rate of the mth power supply path of the power distribution board j; lambda [ alpha ] ij Representing the failure rate of the line ij; n is a radical of m (j) A set of power supply paths representing a panel j;
the binary variable represents whether the distribution board j selects the mth power supply path or not; x j A binary variable representing whether the distribution board j is put into use; y is ij The input condition of the line ij is represented by a binary variable; n is a radical of L Representing a collection of distribution boards (meaning distribution boards) in a marine power grid(ii) a L denotes the line set in the vessel's power grid.
In the above method, the mathematical model for reconstructing the ship power grid fault comprises:
the objective of the ship power grid fault reconstruction is to recover important loads as much as possible, and meanwhile, the objective of the ship power grid fault reconstruction also comprises the reduction of the operation loss of the power grid because the ship power grid needs to operate in a reconstruction state for a long time.
The constraint conditions of the ship power grid fault reconstruction comprise active power balance constraint, reactive power balance constraint, voltage drop equality constraint, apparent power equality constraint, voltage safety operation constraint, line transmission capacity constraint, radiation network topology constraint and reliability constraint.
Maximizing the recovered load:
where S is a set of load levels including primary, secondary and tertiary loads, ω s Is the weight of each type of load.
And (3) minimizing the network loss:
in the formula i ij Represents the current of line ij; r is ij Representing the resistance of line ij.
Overall objective:
the active power balance constraint is:
where w (j) is the parent panel set for panel jCombining; p ij Is the active power of line ij; p kj Is the active power of line kj; y is kj The input condition of the line kj is represented by a binary variable; v (j) is the sub-panel set of panel j.
The reactive power balance constraint is:
in the formula, Q ij Is the reactive power of line ij; q kj Is the reactive power of line kj; x is the number of ij Is the impedance of line ij; q Lj Is the reactive load of panel j.
The voltage drop equality constraints are:
in the formula u j Is the voltage of panel j.
The apparent power equation constrains:
voltage safety operation constraint:
in the formula u min And u max Is a safe voltage boundary of a ship power system.
Line transmission capacity constraint:
in the formula (I), the compound is shown in the specification,
is the maximum transmission capacity of line ij.
Topological constraint of the radiation network:
in the method, the second-order cone relaxation strategy of the ship power grid fault reconstruction model comprises the following steps:
converting the power flow model of the power distribution network into a second-order conical form:
wherein N is a distribution board set of the ship power grid; i is ij 、U j Is the square of the line current and panel voltage in the power distribution network flow model;
to consider whether a distribution line is switched on, the voltage is associated with the branch to which it is connected by the equation (17):
in the formula (I), the compound is shown in the specification,
is the square of the link voltage of panel j to line ij;
the objective function is converted into:
constraint (8) -formula (12) is transformed into formula (19) -formula (23):
in the formula (I), the compound is shown in the specification,
is the square of the link voltage of panel i to line ij;
in the formula (I), the compound is shown in the specification,
is the maximum current allowed for line ij.
To avoid islanding, the addition (24) serves as a constraint:
in the formula (I), the compound is shown in the specification,
virtual active power of line ij; ξ is the virtual active load of distribution panel j.
And (5) projecting the solution space onto the cone by the equation (25) to realize the relaxation of the power flow equation:
in the method, the ship power grid fault reconstruction convex optimization model comprises the following steps:
after the second-order cone is relaxed, the ship power grid fault reconstruction model is converted into a form of a formula (26) -a formula (27), the target function is a linear expression, the constraint condition comprises the linear expression and the second-order cone expression, a mixed integer second-order cone plan is formed, and the model is a convex optimization model.
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FIG. 1 is a flow chart provided by the present invention.
FIG. 2 is a schematic diagram of a statistical marine power system configuration according to the present invention;
Detailed Description
The invention is described in detail below with reference to specific embodiments and the accompanying drawings.
As shown in FIG. 1, the invention provides a ship power grid fault reconstruction convex optimization model considering reliability constraint, which comprises the following steps:
s1, dividing the load of a ship power grid into different important levels based on a reliability index concept and a ship power grid fault reconstruction requirement, and defining the important degrees of the different load levels;
and S11, dividing the ship power grid into a class I load, a class II load and a class III load according to the importance of the load.
I-level load: this load controls the vitality of the ship and the safety of the passengers belonging to the un-unloadable load; in any case a first order load must be provided. The primary loads of the ship system comprise a boiler, a generator, a weapon system, an electronic countermeasure system, a medical operating room and the like, and at least two power supply paths are required for connecting important loads. If a certain load is certified as a primary load (e.g. a ship propulsion system) in any one of the ship's operational tasks, it has to be connected to the ship's electrical system by Automatic Bus Transfer (ABT). Automatic bus transfer is a device that detects power loss from a normal power supply. When the normal power supply fails, the ABT can automatically and quickly disconnect the load from the normal power supply and connect the load power supply with the standby power supply. Non-critical loads have only one power supply path.
And II-stage load: this load is important to the proper operation of the vessel, but allows it to be offloaded or transferred to other platforms for power if necessary, in case of substantial loss of load. These loads include: cargo lifts, sea water pumps, some radar loads, etc.
Stage III load: the ship can be unloaded immediately when necessary, and the service life and the safety of the ship cannot be adversely affected; the method mainly comprises the following steps: residential heating systems, kitchen electrical loads, and the like.
And S12, establishing importance degrees of loads with different importance degrees.
In the present invention, the level of importance of the level I load is defined as 20, the level of importance of the level II load is defined as 5, and the level of importance of the level III load is defined as 1.
S2, establishing a reliability index calculation model through a line-distribution board incidence matrix;
and S21, defining the reliability constraint of the ship power grid.
First, the average outage frequency (SAIFI) and the expected low battery (EDNS) of the system are defined by equation (1):
in the formula, N I Representing a set of important distribution boards; lambda [ alpha ] j Representing the outage probability of panel j; c j Represents the number of loads to which panel j is connected; p Lj Representing the real load of panel j.
The reliability constraint of the ship power grid is embodied in that SAIFI and EDNS are smaller than given standard values, as shown in formula (2):
in the formula, SAIFI * Representing a given average outage frequency standard value; EDNS * A standard value representing a desired value of a given charge deficit.
And S22, obtaining a reliability index calculation model based on the line-distribution board incidence matrix.
First, a line-panel association matrix is defined by equation (3):
equation (4) represents a reliability index calculation model based on the line-distribution board correlation matrix:
in the formula (I), the compound is shown in the specification,
representing the failure rate of the mth power supply path of the power distribution board j; lambda ij Represents the failure rate of line ij; n is a radical of m (j) A set of power supply paths representing a panel j;
the binary variable represents whether the distribution board j selects the mth power supply path or not; x j A binary variable representing whether the distribution board j is put into use; y is ij The input condition of the line ij is represented by a binary variable; n is a radical of L Represents a collection of distribution boards (meaning distribution boards) in a marine power grid; l denotes the line set in the vessel's power grid.
S3, establishing a ship power grid fault reconstruction model by taking the voltage constraint of a ship power grid, the system and the reliability constraint of important loads into consideration with the aim of reducing the load loss and the network loss of the ship power grid;
and S31, establishing an objective function of the ship power grid fault reconstruction model.
The goal of ship grid fault reconstruction is to recover as important loads as possible, and also to reduce the operating losses of the grid, since the ship grid needs to operate in a reconstructed state for a longer time.
Maximizing the recovered load:
where S is a set of load levels including primary, secondary and tertiary loads, ω s Is a weight for each type of load.
And (3) minimizing the network loss:
in the formula i ij Represents the current of line ij; r is ij Representing the resistance of line ij.
Overall objective:
and S32, establishing a constraint condition of the ship power grid fault reconstruction model.
The constraint conditions of the ship power grid fault reconstruction comprise active power balance constraint, reactive power balance constraint, voltage drop equality constraint, apparent power equality constraint, voltage safety operation constraint, line transmission capacity constraint, radiation network topology constraint and reliability constraint.
The active power balance constraint is:
where w (j) is the parent panel set of panel j; p ij Is the active power of line ij; p is kj Is the active power of line kj; y is kj The input condition of the line kj is represented by a binary variable; v (j) is the sub-panel set of panel j.
The reactive power balance constraints are:
in the formula, Q ij Is the reactive power of line ij; q kj Is the reactive power of line kj; x is a radical of a fluorine atom ij Is the impedance of line ij; q ij Is the reactive load of the panel.
The voltage drop equation constrains:
in the formula u j Is the voltage of panel j.
The apparent power equation constrains:
voltage safety operation constraint:
in the formula u min And u max Is a safe voltage boundary of a ship power system.
Line transmission capacity constraint:
in the formula (I), the compound is shown in the specification,
is the maximum transmission capacity of line ij.
And (3) topological constraint of the radiation network:
s4, converting the ship power grid fault reconstruction model into a convex optimization model through second-order cone relaxation;
s41, a second-order cone relaxation strategy.
Converting the power flow model of the power distribution network into a second-order conical form:
wherein N is a distribution board set of the ship power grid; i is ij 、U j Is the square of the line current and panel voltage in the power distribution network flow model;
to consider whether a distribution line is dropped, the voltage is related to the branch to which it is connected by equation (17):
in the formula (I), the compound is shown in the specification,
is the square of the contact voltage of panel j to line ij.
The objective function is converted into:
constraint (8) -formula (12) is transformed into formula (19) -formula (23):
in the formula (I), the compound is shown in the specification,
is the square of the link voltage of panel i to line ij;
in the formula (I), the compound is shown in the specification,
is the maximum current allowed for line ij.
To avoid islanding, the addition (24) serves as a constraint:
in the formula (I), the compound is shown in the specification,
virtual active power of line ij; ξ is the virtual active load of distribution panel j.
And (3) projecting the solution space onto the cone by the equation (25) to realize the relaxation of the power flow equation:
and S42, reconstructing the convex optimization model of the ship power grid fault.
After the second-order cone is relaxed, the ship power grid fault reconstruction model is converted into a form of a formula (26) -a formula (27), an objective function of the ship power grid fault reconstruction model is a linear expression, constraint conditions comprise the linear expression and the second-order cone expression, a mixed integer second-order cone plan is formed, and the ship power grid fault reconstruction model is a convex optimization model.
And S5, solving to obtain the action switch which meets the constraint and minimizes the loss load.
The present invention is not limited to the above-mentioned preferred embodiments, and any structural changes made under the teaching of the present invention shall fall within the protection scope of the present invention, which has the same or similar technical solutions as the present invention.
Claims (9)
1. A ship power grid fault reconstruction method based on a convex optimization model is characterized in that the ship power grid fault reconstruction method considers reliability constraint and comprises the following steps:
step 1, dividing the load of a ship power grid into different important levels based on reliability indexes and ship power grid fault reconstruction requirements, and defining the important degrees of the different load levels;
step 2, according to the load classification result obtained in the step 1, establishing a reliability index calculation model through a line-distribution board incidence matrix;
step 3, taking the reliability index calculation model in the step 2 as a constraint condition, taking reduction of the loss load and the network loss of the ship power grid as a target, considering voltage constraint of the ship power grid, reliability constraint of a system and important loads, and establishing a ship power grid fault reconstruction model;
step 4, converting the ship power grid fault reconstruction model into a convex optimization model through second-order cone relaxation;
step 5, solving the convex optimization model to obtain an action switch which meets the constraint and minimizes the load loss of the ship power grid;
and 6, executing the action switch.
2. The method of claim 1, wherein defining a load level of a vessel's power grid comprises:
dividing a ship power grid into a class I load, a class II load and a class III load according to the importance of the load;
the I-level load is a first-level load of a ship system, each first-level load is connected with at least two power supply paths in a distributed mode, and each power supply path is connected to a ship electrical system through automatic bus transmission; the automatic bus transmission can automatically and quickly disconnect the load from the normal power supply and connect the load power supply with the standby power supply;
the II-level load is the second-level load of the ship system and is allowed to be unloaded or transferred to other platforms for power supply, so that the load is prevented from being greatly lost;
the III-class load is a three-class load of a ship system and can be unloaded immediately.
3. The method of claim 1, wherein considering the vessel grid reliability constraints comprises:
first, the average outage frequency SAIFI and the expected low battery value EDNS of the system are defined by equation (1):
in the formula, N I Representing a set of important distribution boards; lambda [ alpha ] j Representing the outage probability of the distribution board j; c j Represents the number of loads to which panel j is connected; p Lj Represents the active load of panel j;
the reliability constraint of the ship power grid is embodied in that SAIFI and EDNS are less than or equal to given standard values, as shown in formula (2):
in the formula, SAIFI * Representing a given average outage frequency standard value; EDNS * A standard value representing a desired value of a given charge deficit.
4. The method according to claim 3, wherein the establishing of the reliability indicator calculation model specifically comprises the steps of:
first, a line-panel association matrix is defined by equation (3):
equation (4) represents a reliability index calculation model based on the line-distribution board correlation matrix:
in the formula (I), the compound is shown in the specification,
representing the failure rate of the mth power supply path of the power distribution board j; lambda ij Represents the failure rate of line ij; n is a radical of m (j) A set of power supply paths representing a panel j;
the binary variable represents whether the distribution board j selects the mth power supply path or not; x j A binary variable representing whether the distribution board j is put into use; y is ij The input condition of the line ij is represented by a binary variable; n is a radical of L Representing a set of distribution boards in a marine power grid; l denotes the line set in the vessel's power grid.
5. The method of claim 1, wherein the objective of reconstructing the ship grid fault reconstruction model further comprises reducing operating losses of the grid;
the reliability constraint conditions of the ship power grid fault reconstruction model comprise active power balance constraint, reactive power balance constraint, voltage drop equality constraint, apparent power equality constraint, voltage safety operation constraint, line transmission capacity constraint, radiation network topology constraint and reliability constraint.
6. The method according to claim 4, wherein the objective function of the ship grid fault reconstruction model is specifically:
maximizing the recovered load:
where S is a set of load levels including primary, secondary and tertiary loads, ω s Is the weight of each type of load;
and (3) minimizing the network loss:
in the formula i ij Represents the current of line ij; r is ij Represents the resistance of line ij;
overall objective:
7. the method of claim 4, wherein the vessel fault reconfiguration constraints are as follows:
the active power balance constraint is:
wherein w (j) is a parent panel set of panel j; p ij Is the active power of line ij; p kj Is the active power of line kj; y is kj The input condition of the line kj is represented by a binary variable; v (j) is a sub-panel set of panel j;
the reactive power balance constraint is:
in the formula, Q ij Is the reactive power of line ij; q kj Is the reactive power of line kj; x is the number of ij Is the impedance of line ij; q Lj Is the reactive load of the panel;
the voltage drop equation constrains:
in the formula u j Is the voltage of the panel j, u i Is the voltage of panel i;
the apparent power equation constrains:
voltage safety operation constraints:
in the formula u min And u max Is a ship power system safe voltage boundary;
line transmission capacity constraint:
in the formula (I), the compound is shown in the specification,
is the maximum transmission capacity of line ij;
and (3) topological constraint of the radiation network:
8. the method of claim 7, wherein converting the power distribution network reconstruction model shown in the formulas (1) to (14) into a second-order cone planning model through second-order cone relaxation specifically comprises the steps of:
converting the power flow model of the power distribution network into a second-order conical form:
wherein N is a distribution board set of the ship power grid; i is ij 、U j Is line current and distribution board in power distribution network power flow modelThe square of the voltage;
to consider whether a distribution line is switched on, the voltage is associated with the branch to which it is connected by the equation (17):
in the formula (I), the compound is shown in the specification,
is the square of the link voltage of panel j to line ij;
the objective function is converted into:
constraining the transformation of (8) -formula (12) to formula (19) -formula (23):
in the formula (I), the compound is shown in the specification,
is the square of the link voltage of panel i to line ij;
in the formula (I), the compound is shown in the specification,
is the maximum current allowed for line ij;
to avoid islanding, the addition (24) serves as a constraint:
in the formula (I), the compound is shown in the specification,
virtual active power of line ij; ξ is the virtual active load of distribution panel j.
And (3) projecting the solution space onto the cone by the equation (25) to realize the relaxation of the power flow equation:
9. the method of claim 8, wherein the ship power grid fault reconstruction convex optimization model after the second-order cone relaxation is constructed by the following steps:
after the second-order cone is relaxed, the ship power grid fault reconstruction model is converted into a form of a formula (26) -a formula (27), an objective function of the ship power grid fault reconstruction model is a linear expression, constraint conditions comprise the linear expression and the second-order cone expression, a mixed integer second-order cone plan is formed, and the ship power grid fault reconstruction model is a convex optimization model;
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