CN107611980B - Alternating current-direct current hybrid power flow optimization method based on double-end generator equivalence - Google Patents
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Abstract
The alternating current-direct current hybrid power flow optimization method based on the double-end generator equivalence realizes the conversion of a direct current transmission line in an alternating current system in an equivalent mode of the double-end generator, integrally synthesizes an optimization model and performs optimization calculation analysis, and has higher flexibility and operability compared with the traditional optimization algorithm.
Description
Technical Field
The invention relates to an alternating current-direct current hybrid network, in particular to an alternating current-direct current hybrid power flow optimization method based on double-end generator equivalence.
Background
The complexity and diversity of the power grid enable the structure and mode of the network to change constantly, and with the development of high-power electronic technology, direct-current power transmission is favored, and at present, direct-current power transmission is popular, and the direct-current power transmission realizes the conversion of current through power electronic devices, so that the direct-current power transmission process is realized. The long-distance high-power transmission promotes the further development of direct-current transmission. The direct current transmission system can improve the fault resistance of the system and reduce the danger of power grid breakdown.
At present, direct current and flexible direct current transmission is widely applied, and hybrid optimization of alternating current and direct current power flow is realized by aiming at different equivalent modes of a direct current line in an alternating current system based on the problems of operation, power flow distribution and optimal power flow of the direct current line in the alternating current system.
Disclosure of Invention
The invention provides an alternating current-direct current hybrid power flow optimization method based on double-end generator equivalence.
The technical solution of the invention is as follows:
the method comprises the following concrete steps:
the method comprises the following steps: respectively arranging the AC system network and parameters and the DC system network and parameters into matrixes of the generator set, the bus group and the line data group, as shown in figures 1-3;
step two: the method comprises the following steps that a double-end generator equivalent method is adopted, and two ends of a direct current circuit are equivalent to a pair of virtual generator sets;
step three: adding the data of the generator set and the direct current line into the parameters of the alternating current system;
step four: and establishing an integral power flow optimization model, and performing optimization calculation solution by using an interior point method.
The optimization method comprises the following specific implementation contents:
1) carrying out double-end equivalent design on a direct current system:
① two ends of DC transmission line are equivalent to two groups of virtual generators, i.e. two ends of DC transmission line are respectively regarded as generator nodes, one end transmits active power, the other end receives active power, the head end from end is equivalent to send out negative power as PfThe end "to" end of the motor is equivalent to receiving PtThe virtual generator set is added into the generator matrix data;
secondly, the loss of the direct current line is a linear function of the power of the head end of the line, the specific situations of the direct current line and the Converter station are neglected in the equivalent form, and the line loss and the Converter loss (Voltage-Source-Converter, referred to as VSC for short) are simply combined into a linear constraint, which is described in the following formula:
Ploss＝l0+l1Pf
further deforming and arranging the power of the head end and the tail end into constraint of power of the head end and the tail end, and writing the constraint into equality constraint of an optimization model;
Pt＝(1-l1)Pf-l0
2) an integral optimization model is established through parameters of an alternating current system and a direct current system, the minimum power generation cost of the system is taken as an objective function, the power generation cost is in a quadratic function form of power, and the total cost can be written into the following form:
wherein, PjThe power generated for each generator set, aj2、aj1、aj0A quadratic term coefficient, a primary term coefficient and a constant term coefficient of the system power generation cost are respectively, j is 1 … … k, and k is the number of the generators;
3) and establishing system constraint conditions associated with the target, wherein the system constraint conditions comprise power flow equation nonlinear constraint, unit operation constraint, direct-current line loss constraint and the like.
PG-PD-Vi∑Vj(Gijcosθij+Bijsinθij)＝0
QG-QD-Vi∑Vj(Bijcosθij-Gijsinθij)＝0
Pi min≤Pi≤Pi max
Qi min≤Qi≤Qi max
Vi min≤Vi≤Vi max
θi min≤θi≤θi max
Pt＝(1-l1)Pf-l0
PG is power sent by a generator, PD is load power, Vi is voltage of a node i, Gij and Bij are active components and reactive components of the ijth element in a system admittance matrix, namely conductance and susceptance between two nodes, sin theta and cos theta are differences of voltage phase angles of the nodes, Pi and Qi are respectively active power and reactive power of the node i, and Vi and theta i are respectively voltage amplitude and phase angle of the node i;
4) after an integral optimization target model is obtained, carrying out load flow optimization calculation through an interior point method;
5) and converting virtual generator data in the generator matrix into direct-current line double-end power data.
The invention has the beneficial effects that:
1) the traditional power grid optimization method only considers an alternating current power supply and an alternating current load, the invention considers a direct current line and a loss function thereof in an alternating current system, adopts the principle of optimal economy to plan each power plant to generate power reasonably, and transmits electric energy according to a certain rule.
2) The method is planned aiming at the actual engineering of the alternating current-direct current hybrid network, and the effectiveness and the practicability of the method are proved.
Drawings
FIG. 1 is a flow chart of an alternating current-direct current hybrid power flow optimization method based on double-end generator equivalence.
Fig. 2 is a schematic diagram of a direct current transmission line equivalent to a double-ended generator.
Fig. 3 is a diagram of the transmission loss of a dc link.
Fig. 4 is a network diagram of an embodiment in which (a) is an ac network and (b) is a hybrid ac/dc network.
Detailed Description
The invention is further illustrated with reference to the following figures and examples, which should not be construed as limiting the scope of the invention.
FIG. 1 is a flow chart of an alternating current and direct current hybrid power flow optimization method based on double-end generator equivalence, and the method for performing power flow optimization based on an alternating current and direct current hybrid system is characterized in that firstly, a direct current system is equivalently added into an alternating current system, secondly, a power loss function of a direct current line is added into a constraint of an optimization equation, then, power flow optimization calculation is performed, and data belonging to the direct current line in an obtained result are converted into original data and output to a screen.
The method comprises the following concrete implementation steps:
firstly, carrying out double-end equivalent design on a direct current system:
two ends of the direct current transmission line are equivalent to two groups of virtual generators, namely, two ends of the direct current transmission line are respectively regarded as generator nodes, one end transmits active power, the other end receives active power, as shown in figure 2,the "from" end is equivalent to emitting negative power PfThe "to" end of the motor is equivalent to receiving PtThe active power motor is added into data of a motor matrix through internal conversion, and a power flow network equation is written into a matrix form;
the physical meaning of each row of elements of the system bus data matrix corresponding to the system is as follows:
bus data
bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax Vmin
n1is the number of system buses
Matrix array
bus _ i represents the number of the node; the type is the type of the node, the PQ node code is 1, the PV node code is 2, and the balance node code is 3; pd is active power required by the load; (with a nameplate value), Qd is the reactive power required by the load; (with a name value), Gs represents the conductance in parallel with the node, not the conductance on the line, which is generally the column 0; bs represents susceptance connected in parallel with the node, susceptance on a non-line, the column is generally 0, and area number represents a section number of the bus, and is generally set to 1; vm represents the initial magnitude (per unit value) of the node voltage; va, which represents the initial phase angle of the node voltage; baseKV, representing the reference voltage of the node; zone (with a legend value) represents the loss saving zone of the bus, generally set to 1; maxVm is the maximum voltage that the node can accept; (per unit value) minVm is the minimum voltage (per unit value) that the node can accept.
The physical meaning of each row of elements of the system generator data matrix corresponding to the system is as follows:
generator data
bus Pg Qg Qmax Qmin Vg mBase status Pmax Pmin
n2number of generators of the system
The bus number is the number of the generator node; active power output by the Pg generator node; the Qg generator node outputs reactive power (with a nameplate value), and if the Qg generator node is a balance node Pg, the Qg is set to be 0; qmax (with a nameplate value) the node can accept the maximum reactive power output; qmin (with a data value) the node can accept and output the maximum active power; vg (with a data value) per unit value of the node voltage; the capacity (with the nameplate value) of the generator at mBase; status represents the running state of the generator, 1 represents investment, and 0 represents whether Pmax allows the maximum active power to be output; (with a nameplate value) the maximum reactive power that Pmin is allowed to output; (with Ming value)
The physical meaning of each row element of the system branch data matrix corresponding to the system is as follows
branch data
fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax
n3Is the number of branches of the system
f is the number of the head end of the branch; t is the branch end number; r is the per unit value of the branch circuit resistance; x is the per unit value of the branch reactance; b is the per unit value of branch susceptance; rateA is the allowed capacity (with a nameplate value) of the long-distance transmission branch; rateB is the allowed capacity (with a nameplate value) of the short-distance power transmission branch; rateC is the allowed capacity (with a nameplate value) of the emergency power transmission branch; ratio is the branch transformation ratio, and is set to 0 without a transformer; the transformer transformation ratio is the ratio of the voltage at the head end and the voltage at the tail end of the branch circuit: the angle is a branch phase angle, if the angle is a transformer, the angle is a corner, and otherwise, the parameter is set to be 0; status indicates whether the branch is in operation, and angmin is the minimum phase angle allowed for the branch and angmax is the maximum phase angle allowed for the branch.
And secondly, the loss of the direct current line is a linear function of the power of the head end of the line, the specific conditions of the direct current line and the converter station are neglected in the equivalent form, and the line loss and the converter loss are simply combined into a linear constraint:
Pt＝(1-l1)Pf-l0
and thirdly, establishing an optimization target of the system, taking the minimum total power generation cost of the system as a target function, and taking the power generation cost as a quadratic function form of power, wherein the total cost can be written as the following form:
wherein, i is 1, 2 … … n, n is the number of nodes, j is 1 … … k, k is the number of generators.
Fourthly, establishing system constraint conditions related to the optimization target of the system as follows:
PG-PD-Vi∑Vj(Gijcosθij+Bijsinθij)＝0
QG-QD-Vi∑Vj(Bijcosθij-Gijsinθij)＝0
Pi min≤Pi≤Pi max
Qi min≤Qi≤Qi max
Vi min≤Vi≤Vi max
θi min≤θi≤θi max
Pt＝(1-l1)Pf-l0
fifthly, after an integral optimization model is obtained, carrying out load flow optimization calculation through the existing interior point method;
and sixthly, canceling the equivalent form of the optimized calculation result, namely restoring the virtual generator part in the generator matrix into direct-current line data and restoring the virtual generator part into an alternating-current and direct-current data format.
Simulation calculations were performed in an IEEE9 node network, and fig. 4 is a network diagram of a specific implementation. The left side diagram is an original IEEE alternating current network system, and the right side diagram is an alternating current and direct current hybrid connection system after 4 direct current circuits are newly added; after the equivalent load flow optimization calculation of the double-end generator, compared with the original system optimization result, the system power generation cost and the network loss change are shown in the following table
| Name (R) | Active loss (MW) | Reactive loss (MVAR) | Total cost ($/hr) |
| Exchange of electricity | 3.307 | 36.46 | 5396.69 |
| AC/DC | 3.367 | 37.86 | 5221.74 |
TABLE 1 comparison table of simulation data of AC system and AC/DC system
Simulation results prove that the power generation cost of the system can be effectively reduced in an equivalent mode adopted by the alternating current-direct current hybrid power flow method, the operation is simple, the power in the system can be effectively planned, and the algorithm also has good convergence.
Because the method based on the double-end generator equivalence is simple, convenient and novel, the original alternating current and direct current hybrid optimization problem can be greatly simplified based on the direct current line equivalence mode, the calculation speed is improved, and the complexity of combining other optimization algorithms with load flow calculation is avoided; the optimization by adopting an interior point method is also beneficial to improving the calculation speed: the interior point method has certain advantages in the aspects of convergence, calculation speed and the like, and is convenient for planning, designing and analyzing the power system.
Claims (3)
1. An alternating current-direct current hybrid power flow optimization method based on double-end generator equivalence is characterized by comprising the following steps:
1) respectively listing the network data of the alternating current system and the network data of the direct current system into a generator set matrix, a bus group matrix and a line data group matrix;
2) the method comprises the following steps that a double-end generator equivalent method is adopted, the first end and the last end of a direct current line are equivalent to a pair of virtual generator sets, and the virtual generator sets are added into an alternating current system generator set;
3) and the loss function P of the DC linet＝(1-l1)Pf-l0Adding constraints for system optimization, PfFor the head-end power, P, of the DC linetFor the power at the end of the DC line, /)0And l1Is a loss parameter;
4) establishing an integral power flow optimization model, and performing optimization calculation solution by using a primal-dual interior point method;
5) the two-end power data P of the virtual generator in the solution resultf、PtProposed and converted to dc line double ended power.
2. The alternating current-direct current hybrid power flow optimization method based on the double-ended generator equivalence of claim 1, wherein the double-ended generator equivalence method comprises the following steps:
1) an integral optimization model is established through parameters of an alternating current system and a direct current system, the minimum total cost of power generation of the following systems is taken as a target function, and the power generation cost is in a quadratic function form of the generated power:
wherein, PjFor the power generated by each generator set, the cost of generating power for each motor is a quadratic function of the generated power, aj2、aj1、aj0Coefficients of a quadratic term, a primary term and a constant term of the system power generation cost are respectively, j is 1 … … k, and k is the number of the generators;
2) the optimization constraints associated with the objectives are established as follows:
PG-PD-Vi∑Vj(Gijcosθij+Bijsinθij)＝0
QG-QD-Vi∑Vj(Bijcosθij-Gijsinθij)＝0
Pimin≤Pi≤Pimax
Qimin≤Qi≤Qimax
Vimin≤Vi≤Vimax
θimin≤θi≤θimax
wherein, PGPower generated for the generator, PDFor load power, ViIs the voltage of node i, Gij、BijIs the active and reactive components of the ijth element in the admittance matrix of the system, i.e. the conductance, susceptance, theta between two nodesijIs the difference of the phase angle of the node voltage, PiQi are respectively the active power and reactive power of the node i, Vi、θiRespectively, the voltage amplitude and the phase angle of the node i;
3) carrying out double-end equivalent design on a direct current system:
① the two ends of the DC transmission line are equivalent to a pair of virtual generator sets, namely, the two ends of the DC line are respectively regarded as a generator node, and the head end of the DC line is equivalent to the point that the negative power is PfThe terminal of the DC line is equivalent to receiving PtThe active power of the motor, and adding the data of the virtual generator into the data of the generator set matrix;
secondly, the loss of the direct current line is a linear function of the power of the head end of the line, the specific conditions of the direct current line and the converter station are neglected in the equivalent form, and the line loss and the loss of the flexible direct current converter are simply combined into a linear constraint:
Ploss＝l0+l1Pf
wherein, PfIs the power of the head end of the DC line, P1ossFor the power lost during transmission in the DC line,/0And l1The loss parameters are further transformed and arranged into the constraint of head and tail end power, and the constraint is written into the equality constraint of the optimization model;
Pt＝(1-l1)Pf-l0
Ptthe power at the end of the direct current line;
4) after an integral optimization target model is obtained, carrying out load flow optimization calculation through a primal-dual interior point method;
5) and (4) in the generated power obtained by optimization, the equivalent mode of the optimized power result belonging to the direct current part is cancelled, namely, a newly added virtual generator part in the generator matrix is converted into the original direct current line double-end power.
3. The alternating current-direct current hybrid power flow optimization method based on the double-ended generator equivalence of claim 1, wherein in the step 4, the original dual interior point method optimization method comprises the following steps:
1) simplifying and expressing a system model into a standard form, arranging power flow equality constraint and direct current line loss equality constraint as equality constraint g (x), arranging node power and voltage inequality constraint as inequality constraint h (x), and writing the standard form of the whole system into:
min f(x)
s.t. g(x)＝0
hmin≤h(x)≤hmax
2) introducing non-negative relaxation variables to convert inequality constraint conditions in the original dual interior point method mathematical model into equality constraint conditions, wherein s and z are non-negative relaxation variables, and the result is as follows:
min f(x)
s.t. g(x)＝0
hmax-s-z-hmin＝0
hmax-h(x)-z＝0
s≥0
z≥0
3) introducing a logarithmic barrier function, eliminating non-negative constraints of relaxation variables in the system, introducing an equality constraint condition in the formula into a target function, and establishing a Lagrangian function, wherein the overall result is as follows:
in the formula, lambda ∈ Rm，π∈Rp，v∈RpThe vector of the Lagrange multiplier is also called dual variable; mu is barrier factor, p inequality constraint condition number; x is a state variable, ziAnd siThe relaxation variables are the upper limit and the lower limit of the inequality constraint condition, and the three are also called original variables; the original variables x and zi、siAnd the vectors λ, pi, v of the lagrange multipliers are unified into the variable y, i.e. y ═ si，zi，πi，vi，x，λi)；
After an overall optimization equation is listed, the primal-dual interior point method is adopted for calculation:
the first step is as follows: setting iteration number K0Setting the initial value as an intermediate variable between the maximum value and the minimum value as 0;
the second step is that: according to a correction equation meeting the KKT condition, the optimal search direction of each variable is obtained by applying the steepest descent principle;
the third step: solving iteration step length of the original variable and the dual variable as large as possible, and correcting the original dual variable within a range of [0, 1 ];
the fourth step: judging whether the iteration condition is met, namely whether the barrier parameter is smaller than a given value, if so, finishing the operation and outputting a load flow optimization calculation result, namely meeting the sending power with the lowest power generation cost; if not, determining the barrier parameter mu according to the iteration number K being K +1kAnd then returns to the first step.
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