CN105356447A - Analysis method for steady-state security region of electric-pneumatic interconnected integrated energy system - Google Patents

Abstract

The invention discloses an analysis method for a steady-state security region of an electric-pneumatic interconnected integrated energy system. The method comprises the following steps: firstly, building a steady-state energy flow model of the electric-pneumatic interconnected integrated energy system; secondly, proposing the concept of the steady-state security region of the electric-pneumatic interconnected integrated energy system by referring to a definition and a model of the steady-state security region of a power system; thirdly, obtaining a group of boundary operation points on the boundary of the security region through repeated energy flow calculation; and finally, obtaining the steady-state security region of the electric-pneumatic interconnected integrated energy system on the basis of linear hyperplane fitting. The security region model disclosed by the invention provides a theoretical basis for real-time operation scheduling and online security evaluation of the electric-pneumatic interconnected integrated energy system.

Description

A kind of electric-gas interconnected integrated energy system Analysis of Steady-state Security Region method

Technical field

The present invention relates to a kind of electric-gas interconnected integrated energy system Analysis of Steady-state Security Region method, belong to the analysis of integrated energy system safety on line, assessment technology field.

Background technology

Compared to fired power generating unit, gas turbine set carbon emission amount is few, dynamic response is quick, the construction period is short, and therefore gas turbine power generation proportion progressively increases in recent years.Correspondingly, electric power system also constantly increases with being coupled of natural gas system.On the other hand, electricity turns the advantage of gas technology in extensive energy storage, is expected to the two-way flow realizing electrical network and gas network energy stream.Electric power system promotes the large-scale grid connection of new forms of energy with interconnected being expected to that be coupled of natural gas system from two aspects: 1) gas turbine set fast dynamic response characteristic can be used for stabilizing the fluctuation that new forms of energy exert oneself; 2) for the new forms of energy that electrical network cannot be dissolved, turning gas technology by this part Conversion of Energy by electricity is natural gas, is stored in natural gas network.Therefore, the interconnected integrated energy system of electric-gas is the only way which must be passed that human society changes to low-carbon (LC), sustainable energy system.

But the degree of depth between electrical network with gas net is coupled and brings potential risks to the safe operation of the two.The such as U.S. in 2011 stops the supple of gas or steam greatly (electricity) event, its Evolution Mechanism as shown in Figure 2, two aspects that have its source in of this event: 1) extreme weather; 2) electrical network is coupled with the degree of depth of gas net.Because interruptible price contract generally signed by gas turbine, when gas net generation gas transmission obstruction or fault, gas turbine set will be first cut; In this case, when gas turbine power generation proportion is larger, the disappearance of a large amount of power supply will cause large-scale power outage, natural gas pressurizing point is made to lose firm power supply, natural gas network gas transmission ability is caused to reduce further, namely accident spreads to electrical network from gas net, spreads to gas net conversely again from electrical network, causes accident to grow in intensity.

In fact, when electrical network is coupled with the gas net degree of depth, the generating proportion of gas turbine not only depends on self installed capacity, more depends on the security constraint of natural gas network, traditional power system static security domain is then difficult to embody this point, and namely power system static security domain result is too optimistic.

Summary of the invention:

Goal of the invention: technical problem to be solved by this invention is the security constraint that the existing power system static security domain of solution is difficult to embody natural gas network, the problem that namely power system static security domain result is too optimistic.

Technical scheme: the present invention for achieving the above object, adopts following technical scheme:

A kind of electric-gas interconnected integrated energy system Analysis of Steady-state Security Region method, comprises the following steps:

1) power system mesomeric state energy flow model is set up:

For the branch road l of connected node i, j, its branch power can be expressed as:

$\left\{\begin{array}{c}{P}_l=(g_{ij}+g_{sh,i})V_i^2-g_{ij}{V}_i{V}_j{\mathrm{cos\θ}}_{ij}-b_{ij}{V}_i{V}_j{\mathrm{sin\θ}}_{ij}\\ Q_l=-(b_{ij}+b_{sh,i})V_i^2+b_{ij}{V}_i{V}_j{\mathrm{cos\θ}}_{ij}-g_{ij}{V}_i{V}_j{\mathrm{sin\θ}}_{ij}\end{array}\right.,\∀l\∈B_e;$

In formula: P _lwith Q _lbe respectively branch road active power and reactive power; V and θ is respectively node voltage amplitude and phase angle, θ _ij=θ _i-θ _j; g _ijwith b _ijbe respectively branch road conductance and susceptance; g _{sh, i}with b _{sh, i}be respectively conductance and susceptance over the ground;

Meanwhile, each node inflow power must equal to flow out power:

T _GP _G-T _LP _L＝A _eP _l；

T _GQ _G-T _LQ _L＝A _eQ _l；

In formula: T _gfor grid nodes-generator incidence matrices, T _lfor grid nodes-load incidence matrices, A _efor grid nodes-branch road incidence matrices; P _g, Q _gfor generator injects active power, reactive power, P _l, Q _lfor active power, the reactive power of load absorption;

2) natural gas system steady state energy flow model is set up:

For the pipeline l of connected node m and n, the flow flowing through this pipeline is

$F_l=k_l{s}_{mn}\sqrt{{\mathrm{\π}}_m^2-{\mathrm{\π}}_n^2};$

$s_{mn}=\left\{\begin{array}{cc}+1& {\mathrm{\&pi;}}_m\&GreaterEqual;{\mathrm{\&pi;}}_n\\ -1& {\mathrm{\&pi;}}_m<{\mathrm{\&pi;}}_n\end{array}\right.;$

In formula: F _lfor pipeline l flow; π is node pressure; k _lfor the constant relevant to the pipeline l pressure loss;

Based on the balance of each node flow of natural gas system, can obtain:

T _SF _S-T _DF _D＝A _gF _l；

In formula: T _sfor gas net node-source of the gas incidence matrices, T _dfor gas net node-load incidence matrices, A _gfor gas net node-pipeline incidence matrices; F _sfor source of the gas injects flow, F _dfor gas load flow;

3) gas turbine coupling

The gas quantity that gas turbine consumes and its meritorious output are following non-linear relation:

$F_{G_g,i}={\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_i,i\&Element;G_g;$

In formula: G _gfor gas turbine set; for gas turbine exports meritorious, for the throughput that gas turbine absorbs;

4) power system static security domain

Power system static security domain is that the one group of power meeting direction of energy constraint and network static security constraint injects collection:

${\mathrm{\&Omega;}}_e:=\{y_e:\&Exists;x_e\&Element;R_e\&DoubleRightArrow;f_e\left(x_e\right)=y_e\};$

In formula: y _e=(P _g, P _l, Q _l), x _e=(V _l, θ); R _efor (V under static network constraint _l, θ) and feasible zone in space; f _efor non-linear trend function;

5) the interconnected integrated energy system Steady State Security Region of electric-gas

With reference to the definition of power system static security domain, the interconnected integrated energy system Steady State Security Region of electric-gas may be defined as: meet electrical network and gas network energy stream retrains and one group of energy flow of Static Security Constraints injects and gathers:

$\mathrm{\&Omega;}:=\{y:\&Exists;x\&Element;R\&DoubleRightArrow;f\left(x\right)=y\};$

In formula: y=(P _g, P _l, Q _l, F _s, F _d) be energy flow injection; X=(V _l, θ, π _d); R is the feasible zone in x space under electrical network and gas net Static Security Constraints; F is nonlinear energy flow equation;

6) operating point of security domain boundaries

For keeping the equal of known quantity and unknown quantity quantity, known quantity in certain element (be assumed to ) be set to unknown quantity, correspondingly, electric power system energy flow is equations turned is:

$\left\{\begin{array}{c}{y}_e^{\&prime;}=f_e^{\&prime;}\left(x_e\right)\\ y_e^{\&prime;}=(f_{limit},P_{G_g}^{\&prime;},P_L,Q_L)\end{array}\right.;$

In formula: f _limitcorresponding to the key restrain being converted into equality constraint; P' _g=(P _{g, 1}, L, P _{g, i-1}, P _{g, i+1}, L, P _{g, ng}) ^tfor revised power injects vector;

By solving revised energy flow equation, an operating point on security domain boundaries can be obtained; By adjustment P' _gsize, one group of border operating point can be obtained;

7) Hyperplane fit

Assuming that security domain boundaries is hyperplane, then border, power system security territory can be expressed as:

$a\underset{i\&Element;G}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{P}_{G,i}=1,j\&Element;{\mathrm{CB}}_e;$

In formula: CB _efor electric power system key restrain collection; η is CB _ecorresponding hyperplane coefficient;

In like manner, natural gas system security domain boundaries is:

$\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}+\underset{i\&Element;G_g}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{F}_{G_g,i}=1,j\&Element;{\mathrm{CB}}_g;$

In formula: CB _gfor natural gas system key restrain collection; τ is CB _gcorresponding hyperplane coefficient;

Finally, electric-gas interconnected integrated energy system Steady State Security Region Ω can be expressed as:

$\mathrm{\&Omega;}:=\left\{(P_G,F_S)\left|\begin{array}{cc}1)& \begin{array}{cc}\underset{i\&Element;G_e}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{P}_{G,i}\&le;1& j\&Element;{\mathrm{CB}}_e\end{array}\\ 2)& \begin{array}{cc}\underset{i\&Element;G_g}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}({\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_i)+\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}\&le;1& j\&Element;{\mathrm{CB}}_g\end{array}\\ 3)& P_G^{\min }\&le;P_G\&le;P_G^{\max }\\ 4)& F_S^{\min }\&le;F_S\&le;F_S^{\max }\end{array}\right.\right\}.$

As optimization, described step 3) in gas turbine in electrical network, be equivalent to power supply, in gas net, be equivalent to gas load simultaneously; Therefore gas turbine is connected to electrical network and gas net.

As optimization, described step 6) in the border of security domain correspond to certain inequality key restrain and be converted into equality constraint, this equality constraint can join in energy flow equation.

As optimization, described step 7) in hyperplane coefficient η and the τ on electric-gas interconnected integrated energy system Steady State Security Region border least square fitting can be adopted to obtain.

Beneficial effect: the present invention compared with prior art: when electrical network is coupled with the gas net degree of depth, the generating proportion of gas turbine not only depends on self installed capacity, more depend on the security constraint of natural gas network, traditional power system static security domain is then difficult to embody this point, and namely power system static security domain result is too optimistic.The present invention proposes electric-gas interconnected integrated energy system static security domain model, taken into account the Static Security Constraints of electrical network and gas net simultaneously, thus be that the interconnected integrated energy system safety on line of electric-gas is analyzed, the prevention and control before accident and the Corrective control after accident are provided fundamental basis.

Accompanying drawing illustrates:

Fig. 1 is schematic flow sheet of the present invention;

Fig. 2 is that the U.S. in 2011 stops the supple of gas or steam greatly (electricity) event Evolution Mechanism;

Fig. 3 is NGS5 node system schematic diagram;

Fig. 4 is Steady State Security Region border schematic diagram;

Fig. 5 is the visual schematic diagram of Steady State Security Region.

Embodiment:

Be described in detail below in conjunction with the techniqueflow of accompanying drawing 1 ~ 5 to invention:

Set up electric-gas interconnected integrated energy system steady state energy flow model

Set up power system mesomeric state energy flow model:

Assuming that electric power system contains n _e+ 1 node, b _ebar circuit; Defined node 0 is balance node, G={1,2, L, n _egbe PV node, L={n _eg+ 1, n _eg+ 2, L, n _ebe PQ node, B _efor sets of lines.

For the branch road l of connected node i, j, its branch power can be expressed as:

$\left\{\begin{array}{c}{P}_l=(g_{ij}+g_{sh,i})V_i^2-g_{ij}{V}_i{V}_j{\mathrm{cos\&theta;}}_{ij}-b_{ij}{V}_i{V}_j{\mathrm{sin\&theta;}}_{ij}\\ Q_l=-(b_{ij}+b_{sh,i})V_i^2+b_{ij}{V}_i{V}_j{\mathrm{cos\&theta;}}_{ij}-g_{ij}{V}_i{V}_j{\mathrm{sin\&theta;}}_{ij}\end{array}\right.,\&ForAll;l\&Element;B_e;$

In formula: P _lwith Q _lbe respectively branch road active power and reactive power; V and θ is respectively node voltage amplitude and phase angle, θ _ij=θ _i-θ _j; g _ijwith b _ijbe respectively branch road conductance and susceptance; g _{sh, i}with b _{sh, i}be respectively conductance and susceptance over the ground.

Meanwhile, each node inflow power must equal to flow out power:

T _GP _G-T _LP _L＝A _eP _l；

T _GQ _G-T _LQ _L＝A _eQ _l；

In formula: T _gfor grid nodes-generator incidence matrices, T _lfor grid nodes-load incidence matrices, A _efor grid nodes-branch road incidence matrices.P _g, Q _gfor generator injects active power, reactive power, P _l, Q _lfor active power, the reactive power of load absorption.

Set up natural gas system steady state energy flow model

First it should be noted that, natural gas system can be stated by transient Model and steady-state model.Wherein transient Model is specifically, but by distributed constant and time become state-variable description, computation complexity is quite large; Comparatively speaking, steady-state model complexity is low, and precision is in tolerance interval.Therefore steady state energy flow model is selected to the modeling of natural gas system herein.

Assuming that natural gas system contains n _gindividual node and b _gbar circuit; Definition W={1,2, L, n _gsbe pressure known node collection, H={n _gs+ 1, n _gs+ 2, L, n _git is flow injection known node collection; For set H, definition S={n _gs+ 1, n _gs+ 2, L, n _gs1be source of the gas set of node, D={n _gs1+ 1, n _gs1+ 2, L, n _gsbe load bus collection, H=S ∪ D.

For the pipeline l of connected node m and n, the flow flowing through this pipeline is

$F_l=k_l{s}_{mn}\sqrt{{\mathrm{\&pi;}}_m^2-{\mathrm{\&pi;}}_n^2};$

$s_{mn}=\left\{\begin{array}{cc}+1& {\mathrm{\&pi;}}_m\&GreaterEqual;{\mathrm{\&pi;}}_n\\ -1& {\mathrm{\&pi;}}_m<{\mathrm{\&pi;}}_n\end{array}\right.;$

In formula: F _lfor pipeline l flow; π is node pressure; k _lfor the constant relevant to the pipeline l pressure loss.

Based on the balance of each node flow of natural gas system, can obtain:

T _SF _S-T _DF _D＝A _gF _l；

In formula: T _sfor gas net node-source of the gas incidence matrices, T _dfor gas net node-load incidence matrices, A _gfor gas net node-pipeline incidence matrices; F _sfor source of the gas injects flow, F _dfor gas load flow.

Calculating gas turbine is coupled

Gas turbine is equivalent to power supply in electrical network, is equivalent to gas load in gas net simultaneously.Therefore gas turbine is connected to electrical network and gas net.The gas quantity that gas turbine consumes and its meritorious output are following non-linear relation:

$F_{G_g,i}={\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_i,i\&Element;G_g;$

In formula: G _gfor gas turbine set; for gas turbine exports meritorious, for the throughput that gas turbine absorbs.

Calculate the interconnected integrated energy system Steady State Security Region of electric-gas

Calculate power system static security domain:

Power system static security domain is defined as the one group of power meeting direction of energy constraint and network static security constraint and injects collection.

Under power system static security constraint, (V _l, θ) and the feasible zone in space is:

$R_l:=\left\{\begin{array}{cc}(V_L,\mathrm{\&theta;}):\left|S_l\right(V_L,\mathrm{\&theta;}\left)\right|\&le;S_l^{\max }& \&ForAll;l\&Element;B_e\end{array}\right\};$

$R_{P_G}=\{(V_L,\mathrm{\&theta;}):P_G^{min}\&le;P_G\&le;P_G^{max},P_0^{min}\&le;P_0(V_L,\mathrm{\&theta;})\&le;P_0^{max}\};$

$R_{Q_G}=\{(V_L,\mathrm{\&theta;}):Q_G^{\min }\&le;Q_G(V_L,\mathrm{\&theta;})\&le;Q_G^{\max },Q_0^{\min }\&le;Q_0(V_L,\mathrm{\&theta;})\&le;Q_0^{\max }\};$

$R_e=R_V\&cap;R_l\&cap;R_{P_G}\&cap;R_{Q_G};$

In formula: R _v, R _l, and be respectively (V under voltage magnitude constraint, tributary capacity constraint, generated power and idle constraint _l, θ) and the feasible zone in space; R _efor (V under all power system static security constraints _l, θ) and the feasible zone in space; S _lfor branch road complex power,

Then, power system static security domain can be expressed as:

${\mathrm{\&Omega;}}_e:=\{y_e:\&Exists;x_e\&Element;R_e\&DoubleRightArrow;f_e\left(x_e\right)=y_e\};$

In formula: y _e=(P _g, P _l, Q _l), x _e=(V _l, θ); f _efor non-linear trend function.

Calculate the interconnected integrated energy system Steady State Security Region of electric-gas

With reference to the definition of power system static security domain, the interconnected integrated energy system Steady State Security Region of electric-gas may be defined as: meet electrical network and gas network energy stream retrains and one group of energy flow of Static Security Constraints injects and gathers.

Under natural gas system Static Security Constraints, π _dthe feasible zone in space is

$R_F:=\{{\mathrm{\&pi;}}_D:F_S^{\min }\&le;F_S\&le;F_S^{max},F_W^{min}\&le;F_W\left({\mathrm{\&pi;}}_D\right)\&le;F_W^{max}\};$

$R_{\mathrm{\&pi;}}=\{{\mathrm{\&pi;}}_D:{\mathrm{\&pi;}}_D^{\min }\&le;{\mathrm{\&pi;}}_D\&le;{\mathrm{\&pi;}}_D^{\max }\};$

R _g＝R _F∩R _π；

In formula: R _fwith R _πbe respectively the π under source of the gas capacity-constrained, node pressure constraint _dthe feasible zone in space; R _gfor the lower π of all natural gas system constraints _dthe feasible zone in space.

With reference to power system static security domain models, the interconnected integrated energy system Steady State Security Region of electric-gas can be expressed as:

$\mathrm{\&Omega;}:=\{y:\&Exists;x\&Element;R\&DoubleRightArrow;f\left(x\right)=y\};$

In formula: y=(P _g, P _l, Q _l, F _s, F _d) be energy flow injection; X=(V _l, θ, π _d); R=R _e× R _g, be the feasible zone in x space under electrical network and gas net Static Security Constraints; F is nonlinear energy flow equation.

Calculate the security domain of decision space

The task of system coordinator is under given system configuration and load, by adjusting the object reaching and guarantee system safety, Effec-tive Function of exerting oneself of generator and source of the gas.Under this application background, by the energy of the absorption of fixing electric loading and gas load, the security domain of the interconnected integrated energy system of electric-gas can be reduced to the security domain in decision space:

$\mathrm{\&Omega;}:=\{(P_G,F_G):\&Exists;x\&Element;R\&DoubleRightArrow;f\left(x\right)=y\};$

The operating point on border, computationally secure territory

The border of security domain corresponds to certain inequality key restrain and is converted into equality constraint, and this equality constraint can join in energy flow equation.For electric power system, for keeping the equal of known quantity and unknown quantity quantity, known quantity in certain element (be assumed to ) be set to unknown quantity, correspondingly, electric power system energy flow is equations turned is:

$\left\{\begin{array}{c}{y}_e^{\&prime;}=f_e^{\&prime;}\left(x_e\right)\\ y_e^{\&prime;}=(f_{limit},P_{G_g}^{\&prime;},P_L,Q_L)\end{array}\right.;$

In formula: f _limitcorresponding to the key restrain being converted into equality constraint; P' _g=(P _{g, 1}, L, P _{g, i-1}, P _{g, i+1}, L, P _{g, ng}) ^tfor revised power injects vector.

By solving revised energy flow equation, an operating point on security domain boundaries can be obtained.By adjustment P' _gsize, one group of border operating point can be obtained.

Carry out Hyperplane fit:

Assuming that security domain boundaries is hyperplane, then border, power system security territory can be expressed as:

$\underset{i\&Element;G}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{P}_{G,i}=1,j\&Element;{\mathrm{CB}}_e$

In formula: CB _efor electric power system key restrain collection; η is CB _ecorresponding hyperplane coefficient.

In like manner, natural gas system security domain boundaries is:

$\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}+\underset{i\&Element;G_g}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{F}_{G_g,i}=1,j\&Element;{\mathrm{CB}}_g$

In formula: CB _gfor natural gas system key restrain collection; τ is CB _gcorresponding hyperplane coefficient.

It should be noted that, above-mentioned natural gas security domain boundaries has taken into account the natural gas that gas turbine set consumes further, by the meritorious output of gas turbine set replace its gas consumption then natural gas system Steady State Security Region border is converted into:

$\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}+\underset{i\&Element;G_g}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}({\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_i)=1,j\&Element;{\mathrm{CB}}_g$

Meanwhile, hyperplane coefficient η and the τ on electric-gas interconnected integrated energy system Steady State Security Region border can adopt least square fitting to obtain.

Based on the border of electric power system and natural gas system Steady State Security Region, electric-gas interconnected integrated energy system Steady State Security Region Ω can be expressed as:

$\mathrm{\&Omega;}:=\left\{(P_G,F_S)\left|\begin{array}{cc}1)& \begin{array}{cc}\underset{i\&Element;G_e}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{P}_{G,i}\&le;1& j\&Element;{\mathrm{CB}}_e\end{array}\\ 2)& \begin{array}{cc}\underset{i\&Element;G_g}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}({\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_i)+\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}\&le;1& j\&Element;{\mathrm{CB}}_g\end{array}\\ 3)& P_G^{\min }\&le;P_G\&le;P_G^{\max }\\ 4)& F_S^{\min }\&le;F_S\&le;F_S^{\max }\end{array}\right.\right\}.$

Sample calculation analysis

The example of the present invention's test is for being made up of electric power system example IEEE39 node system and natural gas system example NGS5 node system (as shown in annex Fig. 3).Assuming that IEEE39 node interior joint 39 and the connected generator of node 30 are gas turbine, and be connected with node 5 with the node 2 in NGS5 node respectively.

Based on least square fitting, IEEE39 node system interior joint 37 and 30 running fire motors and NGS5 node system interior joint 4 connect the Steady State Security Region border of air accumulator as shown in annex Fig. 4.Definition least square fitting error ε:

ε＝||(P _G,F _S) _EF－(P _G,F _S) _LS||/||(P _G,F _S) _EF||×100％

In formula: (P _g, F _s) _eFfor the border operating point calculated according to repeated power flow; (P _g, F _s) _lSfor the border operating point that least square fitting obtains.

The maximum of error ε and mean value are respectively 3.83% and 0.82%, and this error precision can meet Practical demand.

Based on the common factor of each Steady State Security Region border (hyperplane), being visualized as shown in annex Fig. 5 of Steady State Security Region.

In addition, hyperplane coefficient η embodies the sensitivity of key restrain to generator output.For natural gas node 5 pressure confines, the hyperplane coefficient of generator 30 is approximately 3 times of generator 37.Therefore, when a large amount of electric energy needs to be supplied at once, from natural gas system safety perspective, should first consider to be powered by generator 37 by generator 30 and 37.

Claims (4)

1. an electric-gas interconnected integrated energy system Analysis of Steady-state Security Region method, is characterized in that: comprise the following steps:

1) power system mesomeric state energy flow model is set up:

For the branch road l of connected node i, j, its branch power can be expressed as:

$\left\{\begin{array}{c}{P}_l=(g_{ij}+g_{sh,i})V_i^2-g_{ij}{V}_i{V}_j{\mathrm{cos\&theta;}}_{ij}-b_{ij}{V}_i{V}_j{\mathrm{sin\&theta;}}_{ij}\\ Q_l=-(b_{ij}+b_{sh,i})V_i^2+b_{ij}{V}_i{V}_j{\mathrm{cos\&theta;}}_{ij}-g_{ij}{V}_i{V}_j{\mathrm{sin\&theta;}}_{ij}\end{array}\right.,\&ForAll;l\&Element;B_e;$

In formula: P _lwith Q _lbe respectively branch road active power and reactive power; V and θ is respectively node voltage amplitude and phase angle, θ _ij=θ _i-θ _j; g _ijwith b _ijbe respectively branch road conductance and susceptance; g _{sh, i}with b _{sh, i}be respectively conductance and susceptance over the ground;

Meanwhile, each node inflow power must equal to flow out power:

T _GP _G-T _LP _L＝A _eP _l；

T _GQ _G-T _LQ _L＝A _eQ _l；

In formula: T _gfor grid nodes-generator incidence matrices, T _lfor grid nodes-load incidence matrices, A _efor grid nodes-branch road incidence matrices; P _g, Q _gfor generator injects active power, reactive power, P _l, Q _lfor active power, the reactive power of load absorption;

2) natural gas system steady state energy flow model is set up:

For the pipeline l of connected node m and n, the flow flowing through this pipeline is

$F_l=k_l{s}_{mm}\sqrt{{\mathrm{\&pi;}}_m^2-{\mathrm{\&pi;}}_n^2};$

$s_{mn}=\left\{\begin{array}{cc}+1& {\mathrm{\&pi;}}_m\&GreaterEqual;{\mathrm{\&pi;}}_n\\ -1& {\mathrm{\&pi;}}_m<{\mathrm{\&pi;}}_n\end{array}\right.;$

In formula: F _lfor pipeline l flow; π is node pressure; k _lfor the constant relevant to the pipeline l pressure loss;

Based on the balance of each node flow of natural gas system, can obtain:

T _SF _S-T _DF _D＝A _gF _l；

In formula: T _sfor gas net node-source of the gas incidence matrices, T _dfor gas net node-load incidence matrices, A _gfor gas net node-pipeline incidence matrices; F _sfor source of the gas injects flow, F _dfor gas load flow;

3) gas turbine coupling

The gas quantity that gas turbine consumes and its meritorious output are following non-linear relation:

$F_{G_g,i}={\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_{i}i\&Element;G_g;$

In formula: G _gfor gas turbine set; for gas turbine exports meritorious, for the throughput that gas turbine absorbs;

4) power system static security domain

Power system static security domain is that the one group of power meeting direction of energy constraint and network static security constraint injects collection:

${\mathrm{\&Omega;}}_e:=\{y_e:\&Exists;x_e\&Element;R_e\&DoubleRightArrow;f_e\left(x_e\right)=y_e\};$

In formula: y _e=(P _g, P _l, Q _l), x _e=(V _l, θ); R _efor (V under static network constraint _l, θ) and feasible zone in space; f _efor non-linear trend function;

5) the interconnected integrated energy system Steady State Security Region of electric-gas

With reference to the definition of power system static security domain, the interconnected integrated energy system Steady State Security Region of electric-gas may be defined as: meet electrical network and gas network energy stream retrains and one group of energy flow of Static Security Constraints injects and gathers:

$\mathrm{\&Omega;}:=\{y:\&Exists;x\&Element;R\&DoubleRightArrow;f\left(x\right)=y\};$

In formula: y=(P _g, P _l, Q _l, F _s, F _d) be energy flow injection; X=(V _l, θ, π _d); R is the feasible zone in x space under electrical network and gas net Static Security Constraints; F is nonlinear energy flow equation;

6) operating point of security domain boundaries

For keeping the equal of known quantity and unknown quantity quantity, known quantity in certain element (be assumed to ) be set to unknown quantity, correspondingly, electric power system energy flow is equations turned is:

$\left\{\begin{array}{c}{y}_e^{\&prime;}=f_e^{\&prime;}\left(x_e\right)\\ y_e^{\&prime;}=(f_{limit},P_{G_g}^{\&prime;},P_L,Q_L)\end{array}\right.;$

In formula: f _limitcorresponding to the key restrain being converted into equality constraint; P' _g=(P _{g, 1}, L, P _{g, i-1}, P _{g, i+1}, L, P _{g, ng}) ^tfor revised power injects vector;

By solving revised energy flow equation, an operating point on security domain boundaries can be obtained; By adjustment P' _gsize, one group of border operating point can be obtained;

7) Hyperplane fit

Assuming that security domain boundaries is hyperplane, then border, power system security territory can be expressed as:

$\underset{i\&Element;G}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{P}_{G,i}=1,j\&Element;{\mathrm{CB}}_e;$

In formula: CB _efor electric power system key restrain collection; η is CB _ecorresponding hyperplane coefficient;

In like manner, natural gas system security domain boundaries is:

$\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}+\underset{i\&Element;G_g}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{F}_{G_g,i}=1,j\&Element;{\mathrm{CB}}_g;$

In formula: CB _gfor natural gas system key restrain collection; τ is CB _gcorresponding hyperplane coefficient;

Finally, electric-gas interconnected integrated energy system Steady State Security Region Ω can be expressed as:

$\mathrm{\&Omega;}:=\left\{(P_G,F_S)\left|\begin{array}{cc}1)& \underset{i\&Element;G_e}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}{P}_{G,i}\&le;1,j\&Element;{\mathrm{CB}}_e\\ 2)& \underset{i\&Element;G_e}{\&Sigma;}{\mathrm{\&eta;}}_{j,i}({\mathrm{\&alpha;}}_i{P}_{G_g,i}^2+{\mathrm{\&beta;}}_i{P}_{G_g,i}+{\mathrm{\&gamma;}}_i)+\underset{i\&Element;S}{\&Sigma;}{\mathrm{\&tau;}}_{j,i}{F}_{S,i}\&le;1,j\&Element;{\mathrm{CB}}_e\\ 3)& P_G^{\min }\&le;P_G\&le;P_G^{\max }\\ 4)& F_S^{\min }\&le;F_S\&le;F_S^{\max }\end{array}\right.\right\}.$

2. electric-gas according to claim 1 interconnected integrated energy system Analysis of Steady-state Security Region method, is characterized in that: described step 3) in gas turbine in electrical network, be equivalent to power supply, simultaneously in gas net, be equivalent to gas load; Therefore gas turbine is connected to electrical network and gas net.

3. electric-gas according to claim 1 interconnected integrated energy system Analysis of Steady-state Security Region method, it is characterized in that: described step 6) in security domain border correspond to certain inequality key restrain be converted into equality constraint, this equality constraint can join in energy flow equation.

4. electric-gas according to claim 1 interconnected integrated energy system Analysis of Steady-state Security Region method, is characterized in that: described step 7) in hyperplane coefficient η and the τ on electric-gas interconnected integrated energy system Steady State Security Region border least square fitting can be adopted to obtain.