Disclosure of Invention
The invention aims to provide an alternate iterative optimization scheduling method based on the non-convex force characteristic of a cogeneration unit, which can be suitable for a non-convex operation characteristic region of the cogeneration unit, realize the rapid and accurate scheduling of power production, and achieve the level of online scheduling application, and the specific technical scheme is as follows:
an alternating iteration optimization scheduling method based on the non-protrusion force characteristic of a cogeneration unit comprises the following steps:
s1, dividing a non-protrusion force area in the output characteristic curve into a plurality of sub-areas according to the output characteristic curve of each cogeneration unit;
s2, converting the segmented constraint of each cogeneration unit in each subregion into continuous linear constraint of the region according to the output characteristic of each cogeneration unit in each subregion;
s3, establishing an active economic dispatching model of the non-protrusion force characteristic of the cogeneration unit based on the converted continuous linear constraint;
wherein,
in order to reduce the operating cost of the thermal power generating unit,
the running cost of the cogeneration unit; p is a radical of
iThe power output is the active power output of the thermal power generating unit i; p is a radical of
j、h
jRespectively the active output and the heat supply output of the cogeneration unit j; n and m respectively represent the total number of the thermal power generating units and the cogeneration units; a is
i,b
i,c
iThe cost coefficient is the cost coefficient of the thermal power generating unit i; a is
j,b
j,c
j,d
j,e
j,f
j,g
jThe cost coefficient of the cogeneration unit j; d is the system load requirement; s is the heat supply requirement of the system;
p
irespectively representing the upper limit and the lower limit of the active output of the thermal power generating unit i;
TL
αrespectively the upper and lower limits of the alpha transmission capacity of the transmission section; l is the total number of the transmission sections; k is a radical of
αiThe sensitivity coefficient of the thermal power generating unit i to the power transmission section alpha is obtained; k is a radical of
αjThe sensitivity coefficient of the cogeneration unit j to the transmission section alpha is shown; the expression (6.1) represents that the active economic dispatching model aims at minimizing the sum of the operating costs of a thermal power unit and a cogeneration unit in the system, and the expression (6.2) represents the system power generation load balance constraint; expression (6.3) represents the system heating balance constraint; an expression (6.4) represents the upper and lower output limit constraints of the generator set; the expression (6.5) represents transmission capacity constraint of a power transmission section; expression (6.6) represents the output characteristic constraint of the cogeneration unit, namely expression (5);
s4, converting the active economic dispatching model into the sum of the single dispatching models of all the cogeneration units by adopting a Lagrange relaxation method;
s5, decomposing each single machine scheduling model into a heat supply optimization scheduling model and an active optimization scheduling model, respectively solving by adopting a mixed integer quadratic programming method and a quadratic programming method, and obtaining an optimal heat supply output value and an optimal active output value through an iteration process;
and S6, controlling each cogeneration unit to perform heating output and active output work by using the optimal heating output value and the optimal active output value, and obtaining an optimal active economic dispatching curve of the cogeneration unit.
Preferably, step S1 specifically includes:
s11, establishing a non-convex non-linear region expression of the cogeneration unit:
wherein,
respectively the upper and lower limits of the active output of the cogeneration unit j;
respectively the upper and lower limits of the heat output of the cogeneration unit j;
s12, dividing the output area of the cogeneration unit j into njA sub-region; wherein each subregion is regarded as a convex region; for the l-th zone, the output characteristics of the cogeneration unit are expressed in the form:
wherein k is,
β、
Are the coefficients of the thermoelectric coupling relationship, respectively;
the upper limit and the lower limit of the heating output of the first area are respectively set;
for all njFor the sub-regions, the output characteristics of the cogeneration unit j are expressed in the form:
preferably, step S2 specifically includes:
the piecewise linear constraint shown in expression (4) is further converted into a continuous linear constraint:
wherein M is a large positive number, and takes the value of
x
j,lIs a binary variable from 0 to 1.
Preferably, the S4 is specifically:
expression (6) is simplified:
wherein inf { } is the infimum boundary of the expression; d
eRepresenting a standalone constraint, including constraint expressions (6.4) and (6.6);
αwv, η are lagrangian relaxation factors; c is a constant;
the right side of the expression (8) is a form of the sum of the optimization objective functions of all the combined heat and power units, and the active economic dispatching model of the combined heat and power units is finally equivalent to the optimal dispatching of a plurality of combined heat and power units.
Preferably, step S5 specifically includes:
the optimal scheduling models of the thermal power generating unit and the cogeneration unit are respectively expressed as expressions (9) and (10):
and (3) directly solving the optimal solution of the expression (9) by utilizing a quadratic programming method and comparing the target function symmetry axis with the upper limit and the lower limit of the active output of the unit, namely:
f (p) in expression (10)j,hj) The function containing bilinear terms pjhjIt is decomposed into two sub-optimization models of expressions (12) and (13):
the expression (12) is a heat supply optimization scheduling submodel, and the expression (13) is an active optimization scheduling submodel; solving the expressions (12) and (13) by adopting the following alternative iteration method:
in the k iteration process, the active output of the unit j is set as the k-1 suboptimal result
Solving an optimized model expression (12) by adopting a mixed integer quadratic programming method to obtain the optimal heat supply output of the unit j
And variable x
j,lValue of (A)
Then, the optimal heat supply output of the unit and the binary variable x
j,lAre respectively set as
And (3) for the optimization model expression (13), adopting a quadratic programming method, directly solving an optimal solution by comparing the symmetry axis of the objective function with the upper limit and the lower limit of the active output of the unit, and repeatedly carrying out the iterative process of solving the optimal heat supply output and the optimal active output until the optimization objective function is not reduced any more.
Preferably, step S6 specifically includes:
and controlling each cogeneration unit to work according to the final iterative optimization result of the active economic scheduling model, so that the active economic scheduling of the cogeneration units is optimal.
The invention has the beneficial effects that:
the invention applies the alternative iteration method to the active economic dispatching of the cogeneration unit, can be suitable for the non-convex and non-linear coupling characteristics existing between the heat output and the power output of the cogeneration unit, solves the problems of too long calculation time, incapability of obtaining an optimal result and irreproducible calculation process existing in the operation process of the existing method, improves the solving efficiency, can obtain a verifiable optimal result and realizes the aim of online application.
Detailed description of the invention
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the present invention provides an alternating iterative optimization scheduling method based on the non-stick force characteristic of a cogeneration unit, comprising the following steps:
step (1): and dividing a non-convex force area in the output characteristic curve into a plurality of sub-areas according to the output characteristic curve of each cogeneration unit.
In this step, fig. 2 is a typical output characteristic curve of a certain type of 250MW cogeneration unit, where the output characteristic is a non-convex non-linear region, and a non-convex non-linear region expression of the cogeneration unit is established:
wherein p is
j、h
jRespectively the active output and the heating output of the cogeneration unit j.
Respectively the upper and lower limits of the active output of the cogeneration unit j;
respectively the upper and lower limits of the heating output of the cogeneration unit j.
The expressions (1) and (2) show that the active output limit value of the cogeneration unit j is a function of the heating output, and meanwhile, the heating output limit value is also a function of the active output.
Segmenting the output area of the combined heat and power generation unit j into njA sub-region. Wherein each sub-region is considered to be a convex region. For the l-th zone, the output characteristics of the cogeneration unit are expressed in the form:
wherein,
k、
β、
are the coefficients of the thermocouple relationship, respectively.
Respectively the upper limit and the lower limit of the heating output of the first area.
For all njFor the sub-regions, the output characteristics of the cogeneration unit j are expressed in the form:
step (2): and converting the segmented constraint of each cogeneration unit in each subregion into the continuous linear constraint of the region according to the output characteristic of each cogeneration unit in each subregion.
In this step, based on the large M method, the piecewise linear constraint in expression (4) is further converted into a continuous linear constraint:
wherein M is a large positive number, and takes the value of
x
j,lIs a binary variable from 0 to 1.
And (3): and establishing an active economic dispatching model of the non-protrusion force characteristic of the cogeneration unit based on the converted continuous linear constraint.
In the step, considering the power generation load balance constraint, the heat supply load balance constraint, the generator output upper and lower limit constraint, the system section tidal current safety constraint and the cogeneration unit output characteristic constraint described in the expression (5), and meanwhile, taking the minimum system operation cost as a target function, establishing an active economic dispatching model considering the non-salient force characteristic of the cogeneration unit, wherein the model type is a mixed integer nonlinear programming model:
wherein,
in order to reduce the operating cost of the thermal power generating unit,
the running cost of the cogeneration unit; p is a radical of
iThe power output is the active power output of the thermal power generating unit i; p is a radical of
j、h
jRespectively the active output and the heat supply output of the cogeneration unit j; n isM represents the total number of the thermal power generating units and the cogeneration units respectively; a is
i,b
i,c
iThe cost coefficient is the cost coefficient of the thermal power generating unit i; a is
j,b
j,c
j,d
j,e
j,f
j,g
jThe cost coefficient of the cogeneration unit j; d is the system load requirement; s is the heat supply requirement of the system;
p
irespectively representing the upper limit and the lower limit of the active output of the thermal power generating unit i;
TL
αrespectively the upper and lower limits of the alpha transmission capacity of the transmission section; l is the total number of the transmission sections; k is a radical of
αiThe sensitivity coefficient of the thermal power generating unit i to the power transmission section alpha is obtained; k is a radical of
αjThe sensitivity coefficient of the cogeneration unit j to the transmission section alpha is shown; the expression (6.1) represents that the active economic dispatching model aims at minimizing the sum of the operating costs of a thermal power unit and a cogeneration unit in the system, and the expression (6.2) represents the system power generation load balance constraint; expression (6.3) represents the system heating balance constraint; an expression (6.4) represents the upper and lower output limit constraints of the generator set; the expression (6.5) represents transmission capacity constraint of a power transmission section; expression (6.6) represents the constraint of the output characteristics of the cogeneration unit, i.e., expression (5).
And (4): and converting the active economic dispatching model into the sum of the single dispatching models of all the cogeneration units by adopting a Lagrange relaxation method.
In this step, the lagrangian dual expression of expression (6) is established as follows:
wherein inf { } is the infimum boundary of the expression; d
eRepresents stand-alone constraints, including constraints (6.4) and (6.6);
w
αv, η are lagrangian relaxation factors.
Expression (7) is further expressed in the form:
wherein C is a constant. The right side of the expression (8) is a form of the sum of the optimization objective functions of all the combined heat and power units. And finally, decomposing an active economic dispatching model of the non-protrusion force characteristic of the cogeneration unit into optimal dispatching of a plurality of cogeneration units.
And (5): and decomposing each single machine scheduling model into a heat supply optimization scheduling model and an active optimization scheduling model, solving by respectively adopting a mixed integer quadratic programming method and a quadratic programming method, and obtaining an optimal heat supply output value and an optimal active output value through an iteration process.
In this step, the optimal scheduling models of the thermal power generating unit and the cogeneration unit are respectively expressed as expressions (9) and (10):
and (3) directly solving the optimal solution of the expression (9) by utilizing a quadratic programming method and comparing the target function symmetry axis with the upper limit and the lower limit of the active output of the unit, namely:
f (p) of expression (10)j,hj) The function containing bilinear terms pjhjIn the present step, the existing optimization algorithm cannot be directly solved, and is decomposed into two sub-optimization models of expressions (12) and (13):
the expression (12) is a heat supply optimization scheduling submodel, and the expression (13) is an active optimization scheduling submodel; solving the expressions (12) and (13) by adopting the following alternative iteration method:
in the k iteration process, the active output of the unit j is set as the k-1 suboptimal result
The optimization model expression (12) is changed into a mixed integer quadratic optimization model, and the optimal heat output of the unit j is solved and obtained by adopting a mixed integer quadratic programming method
And variable x
j,lValue of (A)
Then, the optimal heat supply output of the unit and the binary variable x
j,lAre respectively set as
The optimization model expression (13) is changed into a quadratic programming model, an optimal solution is directly solved by comparing the symmetry axis of the objective function with the upper limit and the lower limit of the active output of the unit, and the iterative process of solving the optimal heat supply output and the optimal active output is repeatedly carried out until the optimization objective function is not reduced any more.
And (6): and controlling each cogeneration unit to carry out heat supply output and active output work by using the optimal heat supply output value and the optimal active output value to obtain an optimal active economic dispatching curve of the cogeneration units.
In the step, after the solution is completed according to the method provided by the invention, each cogeneration unit is controlled to carry out scheduling work according to the optimization result, and on the premise of meeting the requirements of heat supply output and active output, energy and equipment are reasonably utilized, so that the lowest cost is realized.
The optimization effect of the method provided by the invention is verified as follows:
the verification system comprises a thermal power generating unit, two cogeneration units and a pure heat supply unit. The conditions required to be met in the scheduling process are that the system load requirement is 200MW, the heat supply requirement is 115MWth, and the value of M is 106. The calculation results of the present invention are shown in table 1.
TABLE 1 comparison of the method of the invention with the results of the genetic algorithm
As can be seen from the above table, compared with the genetic algorithm, the method of the invention has lower system operation cost; meanwhile, the method is obviously faster than the genetic algorithm in the aspect of calculation time, the effectiveness of the method is proved, and the method can realize online real-time scheduling.
The foregoing is a preferred embodiment of the present application, and it should be noted that those skilled in the art can make several improvements and modifications without departing from the technical principle, and these improvements and modifications should also be considered as the protection scope of the present application.