CN104600706A - Quadratic constraint quadratic optimization-based offshore wind farm-containing voltage and reactive power optimal control method - Google Patents

Abstract

The invention relates to a quadratic constraint quadratic optimization-based offshore wind farm-containing voltage and reactive power optimal control method. A transformer branch is regarded as that a normal branch is connected in series with an ideal transformer, a voltage phasor eik+jfik of a middle node is introduced, eckTk=ejk, fckTk=fjk, so active and reactive power flows at the two ends of the transformer branch can be described as a quadratic function of eik, fik, eck and fck; for a compensation node I of a parallel compensator, the compensating reactive power is QCi=(ei<2>+fi<2>)Bi, an auxiliary variable Ui=(ei<2>+fi<2>), Ui is square of voltage amplitude of the node I, and Qci=UiBi; through the treatment, voltage reactive power optimization problem in rectangular coordinates can be mathematically described as a quadratic constraint quadratic programming problem. According to the voltage reactive power optimization, the safety of power grid operation is used as a constraint condition, and the improvement of the economy of the power grid operation is used as an optimization target, so whole network reactive power comprehensive optimization is realized.

Description

A kind of based on quadratic constraints double optimization containing marine wind electric field voltage power-less optimized controlling method

Technical field

The present invention relates to wind power generation field, especially a kind of based on quadratic constraints double optimization containing marine wind electric field voltage power-less optimized controlling method.

Background technology

Along with the continuous deterioration of the day by day exhausted of the fossil class non-renewable energy resources such as coal, oil, natural gas and global ecological environment, how to realize social economy and Coordination Development Between Eco-environment becomes countries in the world key subjects urgently to be resolved hurrily.In this context, utilize clear energy sources, regenerative resource to replace fossil class, non-renewable energy resources are just more and more subject to people's attention, and become global focus.To in the flow of research of clear energy sources, the long history due to the spatter property of wind energy, recyclability, abundant reserves and human use's wind energy makes it obtain to first develop.As a kind of form of Wind Power Utilization, be also one of regenerative resource development scheme of the most ripe, the on the largest scale exploitation of technology and commercialized development prospect, wind generating technology is more and more subject to the attention of various countries and obtains development and application widely simultaneously.Current various new technology, new material upgrade day by day, and operational efficiency and the grid-connected characteristic of modern wind generating set are obtained for very large improvement.

Marine wind electric field has the advantages such as wind speed is high, wind-force stable, disturb less, energy output is large, has become the important selection of following Wind Power Development.Especially European in the world, offshore wind farm has obtained very enough attention, and the European countries such as Germany, Denmark, Britain have stepped into the scale development phase of offshore wind farm.EWEA (European Wind EnergyAssociation) predicts, to the year two thousand thirty, sea/offshore wind generating can meet the electricity needs of European Union 17%.And China is also in the starting stage, there is huge development space.On the one hand, China has very abundant coastal waters wind-resources, and for land blower fan, offshore wind turbine has benefited from wind-resources more powerful, more stable on sea, can produce more electric energy.Data show, the wind energy resources of China coastal seas 10 meters of depth of waters about 100,000,000 kilowatts, the wind energy resources of the 20 meters of depth of waters in coastal waters about 300,000,000 kilowatts, the wind energy resources of the 30 meters of depth of waters in coastal waters about 4.9 hundred million kilowatts.On the other hand, Deposits in Eastern Coastal China area offshore wind energy resource is abundant and distance load center is near, possesses resources supplIes and the market demand of extensive development, and exploitation offshore wind farm effectively can improve Tohoku Electric Power's Supply Structure energy supply situation.Offshore wind farm development maybe can become one of key increasing regenerative resource popularity rate, therefore, promote China's offshore wind farm development energetically, to alleviation coastal area shortage of electric power situation, successfully managing climate change etc. all to have a very important role, is an important content of China's energy strategy.

Because wind-powered electricity generation has very strong randomness and fluctuation, land and sea breeze presents anti-peak regulation in the diurnal variation in some areas, after extensive offshore wind farm access electrical network, can bring challenges to the operation of electrical network, scheduling.Therefore, in order to ensure the power grid security after large-scale wind power access, in the urgent need to for the grid-connected key issue of extensive, high concentration degree offshore wind farm, systematically carry out extensive, high concentration degree offshore wind farm grid-connected after and basic theory and the Core Technology Research such as reciprocal effect of electrical network, promote to build electrical network friendly wind energy turbine set and wind-powered electricity generation friendly power grid construction, realize China's offshore wind farm development re-set target.

Summary of the invention

The present invention will solve the shortcoming of above-mentioned prior art, provide a kind of based on quadratic constraints double optimization containing marine wind electric field voltage power-less optimized controlling method.

The present invention solves the technical scheme that its technical problem adopts: this based on quadratic constraints double optimization containing marine wind electric field voltage power-less optimized controlling method, transformer branch is regarded as an ordinary branch is connected in series a desirable no-load voltage ratio, introduce the voltage phasor e of intermediate node _ik+ jf _ik, then e _ckt _k=e _jk, f _ckt _k=f _jk, the meritorious of transformer branch two ends and reactive power flow can be described as e thus _ik, f _ik, e _ckand f _ckquadratic function, for the compensation node i of shunt compensator, compensating reactive power is introduce auxiliary variable i.e. U _ifor node i voltage magnitude square, then have Q _ci=U _ib _i, through above-mentioned process, under rectangular coordinate, voltage and reactive power optimization problem mathematically can be described as following quadratically constrained quadratic programming problem:

minObj(e,f,U,B,T,Q _G)

s.t.

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ U_i-e_i^2-{f_i}^2=0& i\&Element;S_N\\ {\underset{\&OverBar;}{Q}}_{\mathrm{Gi}}<Q_{\mathrm{Gi}}<{\stackrel{\&OverBar;}{Q}}_{\mathrm{Gi}}& i\&Element;S_G\\ {\underset{\&OverBar;}{V}}_i^2<U_i<{\stackrel{\&OverBar;}{V}}_i^2& i\&Element;S_N\\ {\underset{\&OverBar;}{B}}_i<B_i<{\stackrel{\&OverBar;}{B}}_i& i\&Element;S_C\\ {\underset{\&OverBar;}{T}}_k<T_k<{\stackrel{\&OverBar;}{T}}_k& k\&Element;S_T\\ e_{\mathrm{ck}}{T}_k=e_{\mathrm{jk}}& k\&Element;S_T\\ f_{\mathrm{ck}}{T}_k=f_{\mathrm{jk}}& k\&Element;S_T\end{array}\right.$

In formula, Obj (e, f, B, T, Q _g) be target function, be generally network loss; U _i, v _i, e _i, f _i, P _gi, Q _gi, P _liand Q _lirepresent respectively the voltage magnitude of node i square, voltage magnitude lower limit, the voltage magnitude upper limit, voltage phasor real part, voltage phasor imaginary part, power supply meritorious inject, power supply is idle injection, burden with power and load or burden without work, B _ifor the shunt susceptance of shunt compensation equipment i, T _kfor the mark no-load voltage ratio of transformer on-load voltage regulating tap k, S _nfor the set of all topology points, S _gby the set of organic end topology point, S _cfor the set of shunt compensation equipment, S _tfor the set of transformer on-load voltage regulating tap.

Introduce artificial variables s _ito reflect the voltage out-of-limit amount of node i, and by introducing in target function to the punishment of voltage out-of-limit amount to embody the requirement to line voltage quality, then voltage and reactive power optimization problem can be described below:

$\min \mathrm{Obj}(e,f,U,B,T{,Q}_G)+w\underset{i\&Element;S_N}{\mathrm{\&Sigma;}}{s}_i$

s.t.

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ U_i-e_i^2-{f_i}^2=0& i\&Element;S_N\\ {\underset{\&OverBar;}{Q}}_{\mathrm{Gi}}<Q_{\mathrm{Gi}}<{\stackrel{\&OverBar;}{Q}}_{\mathrm{Gi}}& i\&Element;S_G\\ {({\underset{\&OverBar;}{V}}_{\mathrm{ci}}-s_i)}^2<U_i<{({\stackrel{\&OverBar;}{V}}_{\mathrm{ci}}+s_i)}^2& i\&Element;S_N\\ {\underset{\&OverBar;}{B}}_i<B_i<{\stackrel{\&OverBar;}{B}}_i& i\&Element;S_C\\ {\underset{\&OverBar;}{T}}_k<T_k<{\stackrel{\&OverBar;}{T}}_k& k\&Element;S_T\\ e_{\mathrm{ck}}{T}_k=e_{\mathrm{jk}}& k\&Element;S_T\\ f_{\mathrm{ck}}{T}_k=f_{\mathrm{jk}}& k\&Element;S_T\end{array}\right.$

In formula, with v _cibe respectively the voltage bound after compression, s _ifor the slack that node i is introduced, characterize the out-of-limit amount of node voltage, w represents in target function the weight that voltage out-of-limit is punished.

Inventing useful effect is: voltage and reactive power optimization, using the fail safe of operation of power networks as constraints, to improve the economy of operation of power networks as optimization aim, realizes the complex optimum that the whole network is idle.

Accompanying drawing explanation

Fig. 1 is transformer equivalent circuit diagram;

Fig. 2 is laxization voltage and reactive power optimization specification of a model figure;

Embodiment

Embodiment:

Adopt rectangular coordinate, trend equilibrium equation can be described as quadratic equation group.When considering shunt compensator and transformer on-load voltage regulating tap-c hange control, then need to introduce additional variable and trend equilibrium equation could be treated to quadratic equation.

For transformer branch, can be regarded as an ordinary branch and be connected in series a desirable no-load voltage ratio, as shown in Figure 1.

Introduce the voltage phasor e of intermediate node _ik+ jf _ik, then

e _ckT _k＝e _jk

f _ckT _k＝f _jk

The meritorious of transformer branch two ends and reactive power flow can be described as e thus _ik, f _ik, e _ckand f _ckquadratic function.

For the compensation node i of shunt compensator, compensating reactive power is

$Q_{\mathrm{ci}}=(e_i^2+{f_i}^2)B_i$

Introduce auxiliary variable

$U_i=(e_i^2+{f_i}^2)$

I.e. U _ifor node i voltage magnitude square.Then have

Q _ci＝U _iB _i

Through above-mentioned process, under rectangular coordinate, voltage and reactive power optimization problem mathematically can be described as following quadratically constrained quadratic programming problem:

minObj(e,f,U,B,T,Q _G)

s.t.

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ U_i-e_i^2-{f_i}^2=0& i\&Element;S_N\\ {\underset{\&OverBar;}{Q}}_{\mathrm{Gi}}<Q_{\mathrm{Gi}}<{\stackrel{\&OverBar;}{Q}}_{\mathrm{Gi}}& i\&Element;S_G\\ {\underset{\&OverBar;}{V}}_i^2<U_i<{\stackrel{\&OverBar;}{V}}_i^2& i\&Element;S_N\\ {\underset{\&OverBar;}{B}}_i<B_i<{\stackrel{\&OverBar;}{B}}_i& i\&Element;S_C\\ {\underset{\&OverBar;}{T}}_k<T_k<{\stackrel{\&OverBar;}{T}}_k& k\&Element;S_T\\ e_{\mathrm{ck}}{T}_k=e_{\mathrm{jk}}& k\&Element;S_T\\ f_{\mathrm{ck}}{T}_k=f_{\mathrm{jk}}& k\&Element;S_T\end{array}\right.---\left(1\right)$

In formula, Obj (e, f, B, T, Q _g) be target function, be generally network loss; U _i, v _i, e _i, f _i, P _gi, Q _gi, P _liand Q _lirepresent respectively the voltage magnitude of node i square, voltage magnitude lower limit, the voltage magnitude upper limit, voltage phasor real part, voltage phasor imaginary part, power supply meritorious inject, power supply is idle injection, burden with power and load or burden without work; B _ifor the shunt susceptance of shunt compensation equipment i; T _kfor the mark no-load voltage ratio of transformer on-load voltage regulating tap k; S _nfor the set of all topology points; S _gby the set of organic end topology point; S _cfor the set of shunt compensation equipment; S _tfor the set of transformer on-load voltage regulating tap.

In the actual motion of electrical network, because load is moment change, correspondingly also will there is corresponding fluctuation in busbar voltage amplitude, if working voltage is near examination border, then may cause voltage out-of-limit because of the normal fluctuation of load, therefore voltage feasible region space should suitably be compressed when carrying out voltage control, to improve rate of qualified voltage.In fact, the voltage order one control device of power plant also needs the regular hour in tracking high voltage bus voltage definite value, and there is certain controlling dead error, also certain deviation can be there is between virtual voltage controlling value and definite value, therefore should allow interval boundary that pre-police region is set at voltage, avoid voltage boundary of keeping to the side to run as far as possible.

In load climbing (or landslide) period, due to growth (decline) speed of load, load side voltage has (rising) trend that declines faster, more easily occur that voltage gets over the situation of lower limit (upper limit), suitably should improve the reduced width of relevant voltage lower limit (upper limit), to ensure the quality of voltage of electrical network, improve rate of qualified voltage.For the load variations period relatively stably, the pace of change of voltage magnitude is comparatively slow, and change amplitude is less, and the decrement of voltage limits can suitably reduce, and increases feasible zone space, to reduce the active loss of electrical network, improves the economy of operation of power networks.

From power system operation knowledge: in the inequality constraints of formula (1), generator reactive is exerted oneself, the inequality constraints such as the shunt susceptance of shunt compensation equipment and main transformer tap leader no-load voltage ratio is hard constraint, can not be out-of-limit in the actual motion of electrical network, in optimizing process, answer its feasibility of strict guarantee; The bound limit value of voltage is then soft-constraint, may be out-of-limit in the actual motion of electrical network, just does not wish to occur out-of-limit situation.When the local Reactive-power control scarce capacity of electrical network, the situation that some node voltage is out-of-limit may be there is completely, the voltage and reactive power optimization problem that this up-to-date style (1) is formed without solution, will will show as when adopting most optimized algorithm to solve and do not restrain or can not find feasible solution.Obviously, this can not meet the reliability requirement of closed loop real-time control system to algorithm.

In fact, when local Reactive-power control scarce capacity appears in electrical network, should provide voltage control strategy in the same old way and implement closed-loop control, to make out-of-limit point few as much as possible, out-of-limit amount is little as much as possible.

The possible traffic coverage of voltage can be divided into place of safety, pre-police region and security area according to above-mentioned analysis, place of safety is the voltage Operational Zone expected, therefore need not apply any punishment, and pre-police region then should give certain punishment, and security area then gives larger punishment.

Introduce artificial variables s _ito reflect the voltage out-of-limit amount of node i, and by introducing in target function to the punishment of voltage out-of-limit amount to embody the requirement to line voltage quality, then voltage and reactive power optimization problem can be described below:

$\min \mathrm{Obj}(e,f,U,B,T{,Q}_G)+w\underset{i\&Element;S_N}{\mathrm{\&Sigma;}}{s}_i$

s.t.

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ U_i-e_i^2-{f_i}^2=0& i\&Element;S_N\\ {\underset{\&OverBar;}{Q}}_{\mathrm{Gi}}<Q_{\mathrm{Gi}}<{\stackrel{\&OverBar;}{Q}}_{\mathrm{Gi}}& i\&Element;S_G\\ {({\underset{\&OverBar;}{V}}_{\mathrm{ci}}-s_i)}^2<U_i<{({\stackrel{\&OverBar;}{V}}_{\mathrm{ci}}+s_i)}^2& i\&Element;S_N\\ {\underset{\&OverBar;}{B}}_i<B_i<{\stackrel{\&OverBar;}{B}}_i& i\&Element;S_C\\ {\underset{\&OverBar;}{T}}_k<T_k<{\stackrel{\&OverBar;}{T}}_k& k\&Element;S_T\\ e_{\mathrm{ck}}{T}_k=e_{\mathrm{jk}}& k\&Element;S_T\\ f_{\mathrm{ck}}{T}_k=f_{\mathrm{jk}}& k\&Element;S_T\end{array}\right.---\left(2\right)$

In formula, with v _cibe respectively the voltage bound after compression; s _ifor the slack that node i is introduced, characterize the out-of-limit amount of node voltage; W represents in target function the weight that voltage out-of-limit is punished.

Above-mentioned process be in fact according to compression after voltage limits voltage violation amount is punished, due to the existence of compression bandwidth, by arranging suitable penalty factor, can effectively avoid unnecessary voltage to keep to the side boundary or out-of-limit operation.For one-dimensional case, the target function constructed as shown in Figure 2.

For the actual motion state of electric power system, when there being the state estimation result of convergence, trend equilibrium equation, unit are idle units limits, the constraint of compensation equipment shunt susceptance bound and main transformer no-load voltage ratio constraint etc. all can be met.When Reactive-power control scarce capacity, as long as slack variable S value is enough large, the bound constraint of voltage also can be met, namely the equation of formula (2) and inequality constraints all will be met, this just means that the optimization problem be made up of formula (2) exists feasible solution certainly, can meet voltage control needs during Reactive-power control ability relative deficiency.

In addition to the implementation, the present invention can also have other execution modes.All employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop on the protection range of application claims.

Claims (2)

1. based on quadratic constraints double optimization containing a marine wind electric field voltage power-less optimized controlling method, it is characterized in that:

Transformer branch is regarded as an ordinary branch is connected in series a desirable no-load voltage ratio, introduce the voltage phasor e of intermediate node _ik+ jf _ik, then e _ckt _k=e _jk, f _ckt _k=f _jk, the meritorious of transformer branch two ends and reactive power flow can be described as e thus _ik, f _ik, e _ckand f _ckquadratic function, for the compensation node i of shunt compensator, compensating reactive power is introduce auxiliary variable i.e. U _ifor node i voltage magnitude square, then have Q _ci=U _ib _i, through above-mentioned process, under rectangular coordinate, voltage and reactive power optimization problem mathematically can be described as following quadratically constrained quadratic programming problem:

minObj(e,f,U,B,T,Q _G)

s.t.

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ U_i-e_i^2-{f_i}^2=0& i\&Element;S_N\\ {\underset{\&OverBar;}{Q}}_{\mathrm{Gi}}<Q_{\mathrm{Gi}}<{\stackrel{\&OverBar;}{Q}}_{\mathrm{Gi}}& i\&Element;S_G\\ {\underset{\&OverBar;}{V}}_i^2<U_i<{\stackrel{\&OverBar;}{V}}_i^2& i\&Element;S_N\\ {\underset{\&OverBar;}{B}}_i<B_i<{\stackrel{\&OverBar;}{B}}_i& i\&Element;S_C\\ {\underset{\&OverBar;}{T}}_k<T_k<{\stackrel{\&OverBar;}{T}}_k& k\&Element;S_T\\ e_{\mathrm{ck}}{T}_k=e_{\mathrm{jk}}& k\&Element;S_T\\ f_{\mathrm{ck}}{T}_k=f_{\mathrm{jk}}& k\&Element;S_T\end{array}\right.$

In formula, Obj (e, f, B, T, Q _g) be target function, be generally network loss; U _i, e _i, f _i, P _gi, Q _gi, P _liand Q _lirepresent respectively the voltage magnitude of node i square, voltage magnitude lower limit, the voltage magnitude upper limit, voltage phasor real part, voltage phasor imaginary part, power supply meritorious inject, power supply is idle injection, burden with power and load or burden without work, B _ifor the shunt susceptance of shunt compensation equipment i, T _kfor the mark no-load voltage ratio of transformer on-load voltage regulating tap k, S _nfor the set of all topology points, S _gby the set of organic end topology point, S _cfor the set of shunt compensation equipment, S _tfor the set of transformer on-load voltage regulating tap.

2. according to claim 1 based on quadratic constraints double optimization containing marine wind electric field voltage power-less optimized controlling method, it is characterized in that: introduce artificial variables s _ito reflect the voltage out-of-limit amount of node i, and by introducing in target function to the punishment of voltage out-of-limit amount to embody the requirement to line voltage quality, then voltage and reactive power optimization problem can be described below:

$\min \mathrm{Obj}(e,f,U,B,T,Q_G)+w\underset{i\&Element;S_N}{\mathrm{\&Sigma;}}{s}_i$

$\left\{\begin{array}{cc}{P}_{\mathrm{Gi}}-P_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{P}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ Q_{\mathrm{Gi}}-Q_{\mathrm{Li}}-\underset{j\&Element;S_N}{\mathrm{\&Sigma;}}{Q}_{\mathrm{ij}}(e,f,U,B,T)=0& i\&Element;S_N\\ U_i-e_i^2-{f_i}^2=0& i\&Element;S_N\\ {\underset{\&OverBar;}{Q}}_{\mathrm{Gi}}<Q_{\mathrm{Gi}}<{\stackrel{\&OverBar;}{Q}}_{\mathrm{Gi}}& i\&Element;S_G\\ {({\underset{\&OverBar;}{V}}_{\mathrm{ci}}-<s_i)}^2<U_i<{({\stackrel{\&OverBar;}{V}}_{\mathrm{ci}}+s_i)}^2& i\&Element;S_N\\ {\underset{\&OverBar;}{B}}_i<B_i<{\stackrel{\&OverBar;}{B}}_i& i\&Element;S_C\\ {\underset{\&OverBar;}{T}}_k<T_k<{\stackrel{\&OverBar;}{T}}_k& k\&Element;S_T\\ e_{\mathrm{ck}}{T}_k=e_{\mathrm{jk}}& k\&Element;S_T\\ f_{\mathrm{ck}}{T}_k=f_{\mathrm{jk}}& k\&Element;S_T\end{array}\right.$

In formula, with be respectively the voltage bound after compression, s _ifor the slack that node i is introduced, characterize the out-of-limit amount of node voltage, w represents in target function the weight that voltage out-of-limit is punished.