CN106684857A - Linear optimal power flow model containing unified power flow controller - Google Patents

Abstract

The invention discloses a linear optimal power flow (LOPF) model containing a unified power flow controller (UPFC). DC optimal power flow (DCOPF) is the most popular OPF linear method so far, and is fast in solution speed but relatively low in calculation accuracy, and two electrical quantities of a node voltage amplitude value and a circuit reactive power cannot be solved; the UPFC can be used for improving the power supply capability of a regional power grid, the UPFC is introduced into a DCOPF model, thus, the problem complexity is improved, and the linear DCOPF is also converted to a non-linear model; on the basis, the invention proposes a novel LOPF model which is higher in accuracy and is more perfect; by the model, the voltage and the reactive power can be solved, a current source type steady-state model of the UPFC is processed and is equivalently embedded into a circuit, and thus, the novel LOPF model is applicable to the LOPF model proposed by the invention; and an example simulation result shows that the high efficiency of the linear model is maintained, the calculation result has relatively high accuracy, and moreover, power flow information which is more perfect than the DCOPF model can be figured out.

Description

A kind of linearisation optimal load flow model containing THE UPFC

Technical field

Invention is related to a kind of linearisation optimal load flow model containing THE UPFC, belongs to electric power system optimization operation Field.

Background technology

THE UPFC (Unified power flow controller, UPFC) is used as third generation flexible AC Power transmitting device (Flexible AC Transmission System, FACTS), it combines the various flexible control of FACTS elements Means processed, can control node voltage, phase angle and line impedance, can the quick spirit on the basis of existing grid structure is not changed Control livingly, active, the reactive power flow of adjusting circuit, and reasonable distribution is carried out to system load flow, so as to lift area power grid Power supply capacity.Additionally, UPFC also has positive role to aspects such as limiting short-circuit current, reduction system losses.

Optimal Power Flow Problems (optimal power flow, OPF), can meet specific operation of power networks and peace Under the conditions of staff cultivation, the optimum system stable operation shape of predeterminated target is realized by available control device in adjustment system State.OPF can as much as possible improve its economy while power system security is ensured, this is for practical power systems Scheduling, operation and control have great significance.But the raising of the expansion and complexity with power system scale, it is traditional Alternating current optimal power flow (Active current optimal power flow, ACOPF) model is because of the non-linear meter of its complexity Calculate, at the aspect such as real-time and applicability the requirement in power system optimal dispatch field cannot have been met, if research meter and UPFC ACOPF, then its computational efficiency will further decrease.Direct current optimal power flow (direct current optimal power Flow, DCOPF) it is a kind of method that Nonlinear A COPF problem is converted into linear problem, with asking that its linear characteristic is brought The advantages such as solution convenience, misconvergence sex chromosome mosaicism, all many-sides such as overload prevention device preliminary screening are obtained extensively in static security analysis Using, but the result of calculation accuracy of the model is poor, and cannot computing system node voltage amplitude and the idle work(of circuit Two electric parameters of rate, and both are stable significant with control for power system.If additionally, UPFC is introduced DCOPF models, by the linear character of damage model, while increasing computation burden calculation error may be further expanded.Therefore Optimized Operation based on DCOPF models is with its intrinsic deficiency using less in engineering.

Based on this, the present invention proposes a kind of linearisation optimal load flow (Linear optimal power containing UPFC Flow, LOPF) model.

The content of the invention

The technical problem to be solved is in power train for the alternating current optimal power flow containing THE UPFC The poor situation of system Optimized Operation field real-time and applicability, there is provided a kind of linearisation containing THE UPFC is optimum damp Flow model.

The present invention for achieving the above object, is adopted the following technical scheme that：

The present invention is a kind of linearisation optimal load flow model containing THE UPFC, it is characterised in that methods described It is to realize according to the following steps successively in a computer：

(1) electric network data is read, is mainly included：Bus numbering, title, burden with power, load or burden without work, shunt compensation electricity Hold, the branch road number of transmission line of electricity, headend node and endpoint node numbering, series impedance, shunt admittance, transformer voltage ratio and resistance It is anti-, bound that active power supply is exerted oneself, reactive power source is exerted oneself, generator fire coal economic parameters etc..

(2) by node power equation decoupling into line power stream and loss flow two parts, formula is：

Wherein：P_Gi、P_DiFor active power supply, the burden with power of node i；Q_Gi、Q_DiFor the reactive power source of node i, idle negative Lotus；P_il、Q_ilFor active, the reactive power flow of circuit l head ends；P_l ^loss、For active, the reactive loss of circuit；A_ilFor circuit Power flow incidence matrix, exponent number is N × N_l, N for system nodes, N_lFor the circuit number in system, if node i is that circuit is first Node, then corresponding element is 1, and node i is circuit end-node, then corresponding element is -1, is otherwise 0；A_ilossFor line loss pass Connection matrix, node i is circuit end-node, then corresponding element is 1, is otherwise 0；L ∈ i represent the circuit being connected with node i.

(3) by simplified and equivalent substitution, loss flow is brought into power flow formula, formula is：

Wherein：V_iFor the voltage magnitude of node i；V_jFor the voltage magnitude of node j；g_ij、b_ijFor the conductance of circuit l, susceptance； θ_ij=θ_i-θ_jFor the phase angle difference at circuit two ends.

(4) current scheduling flow data is read, including active, the reactive power of node voltage amplitude and circuit, open in heat Under rotating ring border, by nonlinear node power equation linearization process in OPF problems, formula is：

Wherein：m₁~m₁₆、Coefficient after to carry out conversion process.

(5) UPFC equivalent current source models are set up, equivalent model is processed into embedded model, impacts of the UPFC to system The load of circuit first and last section can be processed into P_i ^E、Be UPFC parallel connection side to section Point i sides (i.e. side in parallel installation place) active, reactive power flow affects, P_i ^B、For UPFC series sides are active to node i side, idle tide Stream affects,For UPFC series sides are active on node j sides, reactive power flow affects.

(6) the new LOPF models of meter and UPFC are set up, model is divided into following three part

Object function：

Or

Equality constraint：

Wherein：N_gFor the generator number in system；a_2i、a_1i、a_0iIt is divided into the consuming characterisitic parameter of i-th unit；For The active power of UPFC series sides,For the active power of UPFC parallel connections side.

Inequality constraints includes active, reactive power source units limits, and node voltage amplitude, phase angle are constrained, and line power is about Beam, UPFC series and parallels side voltage magnitude, phase angle constraint.

(7) above-mentioned model is solved using simplified primal dual interior point method.

(8) optimal solution is exported, draws electrical network optimized operation state.

The present invention first passes around trend decoupling, 3 links of equivalent substitution and thermal starting environment linearization process, is formed new LOPF models；Then the equivalent current source model of UPFC devices is studied, and is processed into embedded steady-state model so as to be suitable for In the new LOPF that the present invention is carried；

Finally establish a kind of new LOPF models containing UPFC based on thermal starting environment.

Description of the drawings

Fig. 1：The inventive method flow chart.

Fig. 2：UPFC equivalent current source illustratons of model.

Fig. 3：The embedded modular concept figures of UPFC.

Fig. 4：Model of the present invention and master pattern voltage magnitude deviation map.

Fig. 5：Model of the present invention and master pattern voltage phase angle deviation map.

Specific embodiment

OPF is typical nonlinear programming problem, and its non-linear node power being mainly reflected in equality constraint is flat Weighing apparatus equation.

Wherein：P_Gi、P_DiFor active power supply, the burden with power of node i；Q_Gi、Q_DiFor the reactive power source of node i, idle negative Lotus；V_iFor the voltage magnitude of node i；G_ij、B_ijFor the row of bus admittance matrix i-th, jth column element；θ_ij=θ_i-θ_jFor circuit two ends Phase angle theta_i、θ_jPhase angle difference；N is the nodes of system.

First, new LOPF models

The present invention is mainly through trend decoupling, 3 links of equivalent substitution and thermal starting environment linearization process by formula (1) Linearisation.

1) trend decoupling：First by the Line Flow partly decoupled in formula (1) into line power stream and line loss two Part

Wherein：P_il、Q_ilFor active, the reactive power flow of circuit l head ends；P_l ^loss、For active, the idle damage of circuit Consumption；A_ilFor line power stream incidence matrix, exponent number is N × N_l, N_lFor the circuit number in system, if node i is circuit first node, Then corresponding element is 1, and node i is circuit end-node, then corresponding element is -1, is otherwise 0；A_ilossSquare is associated for line loss Battle array, node i is circuit end-node, then corresponding element is 1, is otherwise 0；L ∈ i represent the circuit being connected with node i.

2) equivalent substitution：Line loss is brought into line power stream formula

Wherein：g_ij、b_ijIt is g with the relation of admittance matrix for the conductance of circuit l, susceptance_ij=-G_ij、b_ij=-B_ij。

But yet suffer from V_i ²And P_l ^loss、These nonlinear terms.P_l ^loss、Computing formula be

Wherein：r_ij、x_ijFor the resistance of circuit l, reactance.

3) thermal starting environment linearization process：Above-mentioned non-linear factor is carried out linearly using known scheduling flow data Change

The present invention define power system optimal dispatch thermal starting environment refer to using power system in a few days dispatch it is previous The flow data of the historical data of section or existing section is used as initial value.

Based on thermal starting environment, the magnitude of voltage V of current system can be obtained_i0With line power flow valuve P_il0、Q_il0.Using Thailand The method for strangling series expansion, then takes its single order item, and ignore truncated error, and then can carry out the nonlinear terms of remaining in 2) Following linearisation.

Wherein：It is by circuit that current flow data is calculated is active, at the beginning of reactive loss according to formula (4) Value.

Finally bring formula (5)-(7) into formula (3) respectively, and equation right side is related into P_il、Q_ilItem move on to left side, Merge, it is then unitization, it is obtained

Wherein：m₁~m₁₆、Coefficient after to carry out conversion process, it is concrete to derive not Repeat.

DCOPF models are compared, the simplification that the model is adopted is less, there is higher computational accuracy in theory, and remains Two important electric parameters of voltage magnitude and reactive power.

2nd, the embedded steady-state models of UPFC

Institute's extracting method of the present invention it is important that the real-time computational problem of the Optimized Operation that solve large-scale power transmission network, transmission line of electricity Line impedance is than often smaller.Additionally, resistance value r in Practical Project analysis in UPFC steady-state models is also to ignore 's.Therefore next the present invention is discussed UPFC equivalent currents source model and linearizing embedded steady-state model, assume that The resistance value of UPFC devices and its place circuit is 0.

1) equivalent current source model

The core concept of equivalent current source model is that the impact by UPFC device series and parallel sides to filled Line Flow is equivalent Into 3 current sources；Then place line admittance is updated, the equivalent susceptance of meter and UPFC impedances is formed, model is as shown in Figure 2.Fig. 2 In each Equivalent admittance meet

Wherein：X_M=X_LX_C+X_BX_C-X_BX_L；X_L、X_CFirst original circuit, the reactance over the ground of respectively UPFC institutes holding position；V_B、V_E、 X_B、X_ERespectively UPFC series and parallels side voltage magnitude and reactance.

2) embedded steady-state model

The embedded steady-state model of UPFC is the load that the effect by current source in upper section to circuit is equivalent to circuit two ends, As shown in Figure 3.The load power at two ends can be tried to achieve by below equation in Fig. 3

Wherein：θ_B、θ_ERespectively UPFC series and parallels side voltage phase angle.

Need to meet active conservation inside UPFC, i.e., neither send power nor absorbed power：

Wherein：The respectively active power of UPFC series and parallels side.

The active power of the series and parallel side of UPFC is represented by：

Here may be assumed that the V in formula (11)-(16)_i≈V_j≈ 1.0, so as to reduce UPFC places routine calculation formula Complexity.Although wherein yet suffering from quadratic term, traditional power injection model is compared, the model has obtained very big letter Change.Most importantly because UPFC apparatus costs are expensive, often it is only installed on important interconnection, negligible amounts, therefore should The quadratic term of remaining brings computation burden can't to the Real time optimal dispatch of big system in model.

3rd, the new LOPF models of meter and UPFC

The Mathematical Modeling of the new LOPF problems of meter and UPFC includes object function, equality constraint and inequality constraints 3 Part.

1) object function

Or

Formula (17) is usually used in power system active optimization, and formula (18) is then used for reactive power optimization of power system.Wherein：N_g For the generator number in system；a_2i、a_1i、a_0iIt is divided into the consuming parameter of i-th unit.

2) equality constraint：

3) inequality constraints:

Wherein：P _Gi 、Q _Gi 、V _i 、θ _i 、Respectively the active power supply of node i is exerted oneself, reactive power source goes out Power, voltage magnitude, the lower limit of voltage phase angle, the upper limit；P _ij 、 Q _ij 、Q _ij For the active of circuit ij, reactive power flow lower limit and on Limit；V _Ei 、V _Bi 、θ _Ei 、θ _Bi 、The series and parallel side voltage magnitude of respectively i-th UPFC device and The lower limit of phase angle, the upper limit；N_NPFCFor the quantity of UPFC in system.

The present invention affects complicated nonlinear problem linearization process, and indivedual quadratic nonlinearity factors of remaining very It is micro-, there is higher efficiency and convergence than traditional ACOPF on the Real-Time Scheduling Domain Theory of big system；Additionally, the model As DCOPF not being approximately 1.0 and ignore reactive power global voltage magnitude affects, and only carries out letter in separate step Change is processed, and has higher precision while improving Power Flow Information in theory.

Two embodiments of the present invention are described below：

Example one：

For the ease of analyzing and showing electric network swim state, the present invention is carried out initially with BPA softwares to certain utility grid etc. Value, obtains the valve systems such as the node of city 78.To mitigate circuit burden, calculate through the optimum addressing of UPFC devices and analyze, and comprehensively After considering many factors such as control effect, difficulty of construction, in No. 8 node sides of 8-26 double loops 2 identical UPFC dresses are set up Put.The parameter of UPFC devices such as table 1.

The UPFC parameters of table 1

The present invention chooses first city winter in 2015 high data, and Load flow calculation is carried out to it using BPA softwares, finds electrical network There is problems with：26-27 and 26-28 two lines road effective power flow is respectively 344.3 and 321.7MW, is in heavy condition； The voltage magnitude of 45 and 46 two nodes is 0.922p.u, and amplitude is low；Grid loss is higher, is 42.96MW.

Therefore, article proposes that following 3 kinds of schemes are analyzed：

Scheme 1：The ACOPF for not installed UPFC is calculated；

Scheme 2：2 UPFC devices of installing, and ACOPF calculating is carried out using traditional UPFC power injection models, it is right UPFC ends trend arrange parameter active 40.0MW, idle 20.0Mvar, No. 8 node voltage amplitudes 1.0p.u；

Scheme 3：OPF calculating is carried out using institute's established model of the present invention, UPFC parameters are with scheme 2.

Table 2 gives above-mentioned 3 kinds of schemes power system active optimization respectively with formula (17), (18) as target and idle The operation result of optimization compares.

The different schemes comparison of computational results of table 2

Either active optimization or idle work optimization are can be seen that from the result of scheme 1, exchange OPF is calculated because it has For voltage and the effect of contraction of power, the voltage magnitude such that it is able to solve 45 and 46 two nodes crosses the border problem, but its Circuit heavy duty and trend skewness cannot be solved the problems, such as.At the same time, OPF can also pass through all adjustable in regulating system Amount so that system optimization target is optimal, and increases economic efficiency.But, exchange OPF processes a large amount of non-linear meters because needing Calculate, computation complexity is high, need more iterations with the time of calculating.

Scheme 2 has added two UPFC devices, therefore computation complexity further to increase, in order to seek on the basis of scheme 1 The calculation cost looked for required for optimal solution becomes much larger.Even with equivalent certain node system of city 78 for processing, scheme 2 The calculating time still close to 3 seconds, this brings greatly challenge to the real time implementation development of power system optimal dispatch.

Scheme 3 is model proposed by the present invention, for the active optimization and idle work optimization of power system is all with stronger Applicability.Model iterations is few, and calculating speed is fast, and efficiency compares the AC model of scheme 2, and to improve twice more, basic to retain The high efficiency of inearized model；In precision aspect, if the result of Scenario 2 is accurate, then this paper models are active excellent The error of change is 0.70%, and the error of idle work optimization is 2.97%.It can be seen that either computational efficiency or precision, the present invention is built Model can meet engineering requirements.Although model has done certain simplification, do not weaken the work of UPFC and OPF With, can not only solve node voltage and Line Flow crosses the border problem, circuit heavy duty hidden danger can also be eliminated, improve the peace of system Quan Xing.It is noted that the inearized model has certain sensitiveness, the meter under thermal starting environment for the selection of initial value Calculate result and be better than flat startup, and for electric power system dispatching department, Optimized Operation decision-making is substantially based on current trend State and make, therefore the inearized model under present invention research thermal starting environment is feasible, and excellent for power system The real time implementation for changing scheduling is significant.

Example two：

The voltage results of the AC model of Scenario 2 are accurate.Fig. 4 gives and carry out respectively active optimization and idle During optimization, the node voltage amplitude and phase angular displacement of scheme 2 and scheme 3.Figure 4, it is seen that because the constraint of OPF is made With voltage magnitude, the phase angle of two schemes is all within voltage restriction range, it is ensured that the quality of power supply of power system.It is most important Be that the change curve of the standard trend value between each node of voltage magnitude, phase angle and scheme 2 of context of methods substantially coincide , and deviation is less.Two scheme voltage magnitudes, the average of phase angular displacement and extreme value are as shown in table 3.Either for active optimization Or idle work optimization, the average of the voltage magnitude deviation of two schemes ensure that within 0.02p.u, and maximum deviation is only 0.033p.u；Phase angular displacement average is less than 1 degree, and maximum deviation is only 1.495 degree.

Impact of the changing load of table 3 to ACOPF, MDCOPF Algorithm Convergence is compared

Claims (6)

1. a kind of linearisation optimal load flow model containing THE UPFC, it is characterised in that set up model according to the following steps：

(1) electric network data is read；

(2) by node power equation decoupling into line power stream and loss flow two parts, formula is：

$\left\{\begin{array}{c}{\mathrm{\ΔP}}_i=P_{Gi}-P_{Di}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{il}{P}_{il}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{iloss}{P}_l^{\mathrm{lo}ss}\\ {\mathrm{\ΔQ}}_i=Q_{Gi}-Q_{Di}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{il}{Q}_{il}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{i\mathrm{lo}ss}{Q}_l^{\mathrm{lo}ss}\end{array}\right.$

Wherein：P_Gi、P_DiFor active power supply, the burden with power of node i；Q_Gi、Q_DiFor the reactive power source of node i, load or burden without work；P_il、 Q_ilFor active, the reactive power flow of circuit l head ends； For active, the reactive loss of circuit；A_ilFor line power stream Incidence matrix, exponent number is N × N_l, N for system nodes, N_lFor the circuit number in system, if node i is circuit first node, Corresponding element is 1, and node i is circuit end-node, then corresponding element is -1, is otherwise 0；A_ilossFor line loss incidence matrix, Node i is circuit end-node, then corresponding element is 1, is otherwise 0；L ∈ i represent the circuit being connected with node i；

(3) by simplified and equivalent substitution, loss flow is brought into line power stream formula, is obtained：

$\left\{\begin{array}{c}{P}_{il}=\frac{1}{2}{g}_{ij}(V_i^2-V_j^2)+\frac{1}{2}{P}_l^{\mathrm{lo}ss}-b_{ij}{\mathrm{\θ}}_{ij}\\ Q_{il}=-\frac{1}{2}{b}_{ij}(V_i^2-V_j^2)+\frac{1}{2}{Q}_l^{loss}-g_{ij}{\mathrm{\θ}}_{ij}\end{array}\right.$

Wherein：V_iFor the voltage magnitude of node i；V_jFor the voltage magnitude of node j；g_ij、b_ijFor the conductance of circuit l, susceptance；θ_ij= θ_i-θ_jFor the phase angle theta at circuit two ends_i、θ_jPhase angle difference；

(4) current scheduling flow data is read, including active, the reactive power of node voltage amplitude and circuit, in thermal starting ring Under border, by nonlinear node power equation linearization process in Optimal Power Flow Problems OPF problems, formula is：

$\left\{\begin{array}{c}{P}_{il}=m_1{V}_i+m_2{V}_j+m_3{\mathrm{\θ}}_i+m_4{\mathrm{\θ}}_j+m_{P_l}\\ Q_{il}=m_5{V}_i+m_6{V}_j+m_7{\mathrm{\θ}}_i+m_8{\mathrm{\θ}}_j+m_{Q_l}\end{array}\right.$

$\left\{\begin{array}{c}{P}_l^{loss}=m_9{V}_i+m_{10}{V}_j+m_{11}{\mathrm{\θ}}_i+m_{12}{\mathrm{\θ}}_j+m_{P_{loss}}\\ Q_l^{loss}=m_{13}{V}_i+m_{14}{V}_j+m_{15}{\mathrm{\θ}}_i+m_{16}{\mathrm{\θ}}_j+m_{Q_{loss}}\end{array}\right.$

Wherein：m₁~m₁₆、The coefficient obtained after to carry out conversion process；

(5) THE UPFC UPFC equivalent current source model is set up, by equivalent current source model treatment into embedded model, Impacts of the UPFC to system is processed into the load of circuit first and last section For UPFC parallel connections, side is active on node i side, reactive power flow affects,It is active to node i side, idle for UPFC series sides Influence on tidal flow,For UPFC series sides are active on node j sides, reactive power flow affects；

(6) the linearisation optimal load flow LOPF models of meter and UPFC are set up；

(7) above-mentioned LOPF models are solved using simplified primal dual interior point method；

(8) optimal solution is exported, draws electrical network optimized operation state.

2. a kind of linearisation optimal load flow model containing THE UPFC as claimed in claim 1, it is characterised in that institute The electrical network parameter stated in step 1 includes：Bus numbering, title, burden with power, load or burden without work, Shunt compensation capacitor, transmission line of electricity Branch road number, headend node and endpoint node numbering, series impedance, shunt admittance, transformer voltage ratio and impedance, active power supply goes out Power, reactive power source are exerted oneself bound, one or more in generator fire coal economic parameters.

3. a kind of linearisation optimal load flow model containing THE UPFC as claimed in claim 1, it is characterised in that institute State that step 6 is fallen into a trap and the LOPF models of UPFC are divided into object function, equality constraint and the part of inequality constraints three.

4. a kind of linearisation optimal load flow model containing THE UPFC as claimed in claim 3, it is characterised in that mesh Scalar functions：

$min.f\left(x\right)=\underset{i=1}{\overset{N_g}{\Σ}}(a_{2i}{P}_{Gi}^2+a_{1i}{P}_{Gi}+a_{0i})$

Or

$min.f\left(x\right)=\underset{i=1}{\overset{N_g}{\Σ}}{P}_{Gi}-\underset{i=1}{\overset{N}{\Σ}}{P}_{Di}$

Wherein：N_gFor the generator number in system；a_2i、a_1i、a_0iIt is divided into the consuming characterisitic parameter of i-th unit.

5. a kind of linearisation optimal load flow model containing THE UPFC as claimed in claim 3, it is characterised in that etc. Formula is constrained：

${\mathrm{\ΔP}}_i=P_{Gi}-P_i^B-P_i^E-P_{Di}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{il}{P}_{il}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{iloss}{P}_l^{loss}$

${\mathrm{\ΔQ}}_i=Q_{Gi}-Q_i^B-Q_i^E-Q_{Di}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{il}{Q}_{il}-\underset{l\∈i}{\overset{N_l}{\Σ}}{A}_{iloss}{Q}_l^{loss}$

$P_{UPFC}^B-P_{UPFC}^E=0$

Wherein：For the active power of UPFC series sides,For the active power of UPFC parallel connections side.

6. a kind of linearisation optimal load flow model containing THE UPFC as claimed in claim 3, it is characterised in that no Equality constraint includes active, reactive power source units limits, and node voltage amplitude, phase angle constraint, line power is constrained, UPFC strings, Side voltage magnitude in parallel, phase angle constraint.