CN104103023A - Comprehensive optimization modeling method for electricity generation and transmission economy and power grid security - Google Patents

Abstract

Due to lack of whole-journey quantization and monotonous security indexes, security is generally taken as an inequation constraint condition in a traditional optimization model, and an optimization target generally only comprises an economical index, so that power grid security can not be simultaneously optimized. Researches find that the mapping elastic potential energy of a power grid can be used as a quantitative index for the power grid security, and the change of the mapping elastic potential energy of the power grid and the network loss change of a major network are in the same trend. The invention provides a comprehensive optimization modeling method for electricity generation and transmission economy and power grid security. The modeling method is characterized in that the mapping elastic potential energy is brought into a target function of an economical power generation optimization model so as to solve the comprehensive optimization problems of the electricity generation and transmission economy and the power grid security. A line reactive constraint condition is omitted so as to improve the calculation efficiency and the reliability of the optimization. The reasonability of the optimization modeling method is verified through an IEEE39 (Institute of Electrical and Electronic Engineers) node system example. The optimization modeling method exhibits practical significance for the optimizing operation and planning of a power system.

Description

Send out the modeling method of transmission of electricity economy and power grid security complex optimum

Technical field

Electric system (electrical network) safety analysis.

Background technology

Send out, transmission of electricity economy and electric network security be the target that Operation of Electric Systems is pursued simultaneously, the former reduces cost of electricity-generating and Transmission Loss, the latter is mainly merit-angle stability and the voltage stability that improves electrical network.In major network, if reactive-load compensation ability is stronger, security mainly refers to static merit-angle stability.

Before this, because the whole process of electric network security is quantitative and dull On Index fails to solve well, in Optimized model, generally using security as inequality constrain boundary condition, in optimization aim, generally only comprise economic index, cannot be optimized electric network security.

In recent years, for solving the complex optimization problem of economy and security, Optimized model has been carried out constantly improving: first kind thinking is that security constraint is improved, as dwindled restrained boundary to improve security; Or by after border flexibility, laxization, then flexibility index, slack variable are put into objective function, with economic index stack optimizing; Equations of The Second Kind thinking is to keep original security constraint border, builds in addition quantitative security function and puts into objective function, as the line load rate sum of squares of deviations, load factor quadratic sum, operation risk index etc.The essential problem that first kind thinking exists is security could not be carried out to whole process to quantize, thereby cannot carry out full optimization, the main body of optimization or economy; In addition, merely by border flexibility or laxization, probably suddenly change " firmly " border of security of the result of optimization.In Equations of The Second Kind thinking, from the harmonious angle tolerance of load factor network-wide security, realistic experience, but whether the load factor sum of squares of deviations, load factor quadratic sum there is monotonic relationshi with security, lack tight Theoretical Proof; Adopt risk indicator too complicated as safety indexes, and can not quantize the security in safe threshold values border, finally also will choose optimum compromise by load factor harmony and separate.In addition, the security inequality constrain in conventional model, has also added difficulty to the Optimization Solution of objective function, and Optimization Solution calculated amount is large; When random optimization and discrete optimization, solving result is easily absorbed in local optimum.

Aspect network loss optimization, mainly by idle work optimization, reduce network loss before this, but the network loss of major network is in fact mainly caused by meritorious transmission.Network loss and electric network security all with meritorious trend distribution correlation, but relation between the two has no and analyzed.When complex optimum modeling, should analyze the relation between network loss and security, reduce the index component in objective function, to improve optimization efficiency and reliability as far as possible.

Deficiency for traditional Optimized model, for solving electric network security and send out, the complex optimization problem of transmission of electricity economy, based on early-stage Study achievement (Chinese invention patent: CN102227084B, CN103474993A), be the quantitative safety indexes of mapping elastic network(s) model and the electrical network of electrical network---mapping elastic potential energy, analyze the relation of transmission of electricity economy and electric network security, research " is sent out the modeling method of transmission of electricity economy and power grid security complex optimum ", to realize complex optimum.

Summary of the invention

Mapping elastic network(s) model based on electrical network and mapping elastic potential energy, research discovery, the mapping elastic potential energy of electrical network not only can be used as the quantitative target of electric network security, and it also changes and changes with becoming with the network loss of major network.The present invention's " modeling method of a transmission of electricity economy and power grid security complex optimum " includes the mapping elastic potential energy of electrical network in the objective function of economic generating Optimized model, to solve a difficult problem for the complex optimum of economics of power generation, transmission of electricity economy and electric network security; Omitted the meritorious constraint condition of circuit, to improve counting yield and the reliability of optimization.IEEE39 node system Example Verification the rationality of this modeling method.The method has realistic meaning to optimization operation and the planning of electric system, and the Optimized model based on the method can obtain sending out transmission of electricity economy and electric network security with excellent generator operation mode, power supply layout scheme and electrical network route planning scheme etc.

Accompanying drawing explanation

Fig. 1 electrical network-mapping elastic network(s) Topological Mapping, (1) electrical network, (2) mapping elastic network(s)

The equivalence mapping elasticity branch road of Fig. 2 electrical network

Fig. 3 transmission line of electricity Equivalent Model

Fig. 4 IEEE39 node system structure

The variation tendency of Fig. 5 cost of electricity-generating, mapping elastic potential energy and network loss

Electrical network-mapping elastic network(s) structure of Fig. 6 generation mode 1

Electrical network-mapping elastic network(s) structure of Fig. 7 generation mode 3

Electrical network-mapping elastic network(s) structure of Fig. 8 generation mode 5

Embodiment

1. the mapping elastic potential energy of electrical network

If L two ends, alternating current circuit node voltage phase differential be θ _l, active power is P _l, reactance is X _l, negligible resistance.Work as U _l1, U _l2change when little, merit-angle characteristic of circuit L and single-degree-of-freedom elasticity branch road l stressed-deformation behavior is similar, sets up L and l quantity of state mapping relations are as follows

$\left\{\begin{array}{c}{P}_L=F_l\\ {\mathrm{\θ}}_L=x_l\\ k_L=k_l\end{array}\right.---\left(1\right)$

In above formula, F _l, x _land k _lbe respectively acting force, elongation and the elasticity coefficient of l; k _lmapping elasticity coefficient for L.Wherein

$\left\{\begin{array}{c}{k}_L={\mathrm{dP}}_L/d{\mathrm{\θ}}_L\\ k_l=d{F}_l/{\mathrm{dx}}_l\end{array}\right.---\left(2\right)$

If the active power of L transmission is expressed as

$P_L=\frac{U_{L1}{U}_{L2}}{X_L}\sin {\mathrm{\θ}}_L---\left(3\right)$

Have

$\left\{\begin{array}{c}{k}_L=C\cos {\mathrm{\θ}}_L\\ k_l=C\cos x_l\end{array}\right.---\left(4\right)$

$\left\{\begin{array}{c}{P}_L=k_L\·\tan {\mathrm{\θ}}_L\\ F_l=k_l\·\tan x_l\end{array}\right.---\left(5\right)$

Wherein, according to physical definition, the elastic potential energy of l is

E _l＝∫F _ldx _l (6)

Can obtain

$E_l=F_l\tan \frac{x_l}{2}=k_l\frac{1-\cos x_l}{\cos x_l}=\frac{\cos x_l}{1+{\cos }_{x}l}\·\frac{F_l^2}{k_l}---\left(7\right)$

According to mapping relations, the mapping elastic potential energy of L is

$E_L=P_L\tan \frac{{\mathrm{\θ}}_L}{2}=k_L\frac{1-\cos {\mathrm{\θ}}_L}{\cos {\mathrm{\θ}}_L}=\frac{\cos {\mathrm{\θ}}_L}{1+\cos {\mathrm{\θ}}_L}\·\frac{{P_L}^2}{k_L}---\left(8\right)$

If θ _lless, L can be mapped as linear elasticity branch road, has

$\left\{\begin{array}{c}{k}_L=k_l\≈1/X_L\\ P_L\≈k_L{\mathrm{\θ}}_L\\ F_l\≈k_l{x}_l\end{array}\right.---\left(9\right)$

$\left\{\begin{array}{c}{E}_l=\frac{1}{2}{F}_l{x}_l=\frac{1}{2}{k}_l{x_l}^2=\frac{{F_l}^2}{{2k}_l}\\ E_L=\frac{1}{2}{P}_L{\mathrm{\θ}}_{\mathrm{ij}}=\frac{1}{2}{k}_L{{\mathrm{\θ}}_{\mathrm{ij}}}^2=\frac{P_L^2}{2k_L}\end{array}\right.---\left(10\right)$

If elastic network(s) consists of n bar branch road, its total potential energy E _{l Σ}meet linear superposition characteristic; The mapping elastic potential E of electrical network _{l Σ}also be like this.

$E_{\mathrm{l\Σ}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{li}}---\left(11\right)$

$E_{\mathrm{L\Σ}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{Li}}---\left(12\right)$

Wherein: E _lifor the i bar Branch Potential Energy of elastic network(s), E _lii bar branch road mapping elastic potential energy for electrical network.

The mapping relations of potential energy as shown in the formula

E _LΣ＝E _lΣ (13)

2. electrical network merit-angle security and the relation of shining upon elastic potential energy

According to patent of invention " electrical network-elastic mechanics network topology mapping method ", (authorize publication No.: CN 102227084B), electrical network is mapped to vertical stressed elastic network(s), and keeps the incidence relation of node, branch road constant, as shown in Figure 1.Because branch road is all longitudinal stress, thus as long as all equate with total potential energy and total load, available 1 elasticity branch road equivalence, in like manner, electrical network is also used a branch road equivalence, as shown in Figure 2.Quantity of state mapping relations are

$\left\{\begin{array}{c}{k}_{\mathrm{leq}}=k_{\mathrm{Leq}}\\ x_{\mathrm{leq}}={\mathrm{\θ}}_{\mathrm{Leq}}\\ F_{\mathrm{\Σ}}=P_{\mathrm{\Σ}}\\ E_{\mathrm{l\Σ}}=F_{\mathrm{L\Σ}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{li}}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_{\mathrm{Li}}\end{array}\right.---\left(14\right)$

Wherein, k _leq, k _leqbe respectively equivalent elasticity coefficient (rigidity) and mapping elasticity coefficient, x _leq, θ _leqbe respectively equivalent deformation and phase differential, F _Σ, P _Σbe respectively the total load-bearing of elastic network(s) and the total burden with power of electrical network.

According to announce apply for a patent " the electric network active load-bearing capacity quantitative test index based on mapping elastic potential energy " (application publication number: CN 103474993A) known, when total load one regularly, from the whole angle of electrical network, E _{l Σ}be approximated to direct ratio with equivalent deformation, be approximated to inverse ratio with equivalent stiffness; From interior angle, when branch road is meritorious, distribute when the most balanced, E _{l Σ}minimum, when meeting

P _L1:P _l2:…:P _Ln＝k _L1:k _L2:…:k _Ln (15)

E _{l Σ}approximate minimum.

So mapping elastic potential energy is the omnidistance whole merit-angle characteristic that has reflected quantitatively electrical network both, meet again actual conditions harmonious and security, can be used as the quantitative target of electric network security.

The transmission of electricity economy of power transmission network with mapping elastic potential energy relation

Transmission of electricity economy can be measured by network loss, and network loss is less, and the economy of transmitting electricity is better.

If circuit i both end voltage is end power is P _li+ jQ _li, impedance is R _i+ jX _i, susceptance is B _i, to ignore electricity and lead, Π shape Equivalent Model is as shown in Figure 3.

If Δ P _ifor the active loss of circuit i,

$\mathrm{\Δ}{P}_i=\frac{P_i^2+Q_i^2}{U_{i2}^2}{R}_i=\frac{P_{\mathrm{Li}}^2+{(Q_{\mathrm{Li}}-B{U}_{i2}^2/2)}^2}{U_{i2}^2}{R}_i---\left(16\right)$

In trunk power transmission network, if reactive-load compensation is stronger, node voltage amplitude all remains near reference value, Q _li< < P _li; If ignore electricity, lead, circuit transmission losses is approximately again

$\mathrm{\&Delta;}{P}_i\&ap;P_{\mathrm{Li}}^2{R}_i---\left(17\right)$

Therefore network loss is approximately

$\mathrm{\&Delta;}{P}_{\mathrm{\&Sigma;}}\&ap;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}^2{R}_i---\left(18\right)$

If phasing degree, branch road two ends is less, can be mapped as linear elasticity branch road, by formula (9), (18), can be obtained

$\mathrm{\&Delta;}{P}_{\mathrm{\&Sigma;}}\&ap;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}^2\&CenterDot;\frac{1}{k_{\mathrm{Li}}}\&CenterDot;{\frac{R_i}{X_i}}_{}---\left(19\right)$

According to formula (10), (19), can obtain

$\mathrm{\&Delta;}{P}_{\mathrm{\&Sigma;}}\&ap;2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_i\&CenterDot;E_{\mathrm{Li}}---\left(20\right)$

Wherein, a _i=R _i/ X _i.If the R of all branch roads in electrical network _i/ X _i≈ a, a is constant, has

ΔP _Σ≈2a·E _LΣ (21)

Visible, at grid nodes voltage, keep good, and in the less situation in phasing degree, branch road two ends, E _{l Σ}with Δ P _Σapproximate with becoming.

In addition, also analyze and find: if P _Σ=const., when the meritorious distribution of electrical network meets formula (15), Δ P _Σapproximate minimum.Prove as follows:

Build following Lagrange function

$f=\mathrm{\&Delta;}{P}_{\mathrm{\&Sigma;}}-\mathrm{\&lambda;}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}-P_{\mathrm{\&Sigma;}})---\left(22\right)$

Wherein, λ is certain constant.Δ P _Σthe condition that has extreme value is that above formula is to P _lipartial derivative be zero,

$\frac{\&PartialD;f}{\&PartialD;P_{\mathrm{Li}}}=\frac{\&PartialD;\mathrm{\&Delta;}{P}_{\mathrm{\&Sigma;}}}{\&PartialD;P_{\mathrm{Li}}}-\mathrm{\&lambda;}\frac{\&PartialD;}{\&PartialD;P_{\mathrm{Li}}}(\underset{i}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{Li}}-P_{\mathrm{\&Sigma;}})=0---\left(23\right)$

Therefore have

$\frac{\&PartialD;\mathrm{\&Delta;}{P}_{\mathrm{\&Sigma;}}}{\&PartialD;P_{\mathrm{Li}}}-\mathrm{\&lambda;}(1-0)=0---\left(24\right)$

By formula (19) substitution above formula, can obtain

$\frac{2a_i{P}_{\mathrm{Li}}}{K_{\mathrm{Li}}}=\mathrm{\&lambda;}---\left(25\right)$

If R _i/ X _i≈ a, arrives formula (15) can be obtained fom the above equation.While meeting formula (15), Δ P _Σbe approximately extreme value.Unique by the known minimal value of actual conditions, therefore the minimum value of being approximately.Card is finished.

More than analyze known, if the impedance ratio of branch road approaches in major network, Δ P _Σwith E _{l Σ}approximate with becoming, and all when meritorious distribution is the most balanced, be tending towards minimum.So, by the meritorious of reasonable distribution unit, exert oneself, reduce the mapping elastic potential energy of major network, generally can improve the economy of security and the transmission of electricity of electrical network simultaneously.

4. the traditional Analysis of Optimal Model based on security constraint

Before this, owing to lacking quantitative safety indexes, traditional Optimized model, is generally all the Optimized model based on security constraint, as economy generating Optimized model is:

Objective function:

$\min f_G=\underset{i=1}{\overset{n_g}{\mathrm{\&Sigma;}}}(a_i{P}_{\mathrm{Gi}}^2+b_i{P}_{\mathrm{Gi}}+c_i)---\left(26\right)$

Constraint condition:

1) trend equality constraint

$B_{\mathrm{ii}}{\mathrm{\&theta;}}_i\underset{j\&NotEqual;s}{\underset{\mathrm{jwi}}{\mathrm{\&Sigma;}}}{B}_{\mathrm{ij}}{\mathrm{\&theta;}}_j-P_{\mathrm{Gi}}+P_{\mathrm{Di}}=0,i\&Element;S_B---\left(27\right)$

2) unit output bound constraint

P _Gimin≤P _Gi≤P _Gimax i∈S _G (28)

3) the meritorious trend bound constraint of circuit.

P _ijmin≤P _ij≤P _ijmax i,j∈S _L (29)

Wherein: f _gfor total power production cost; a _i, b _i, c _ieconomic parameters for unit i; P _girepresent meritorious the exerting oneself of unit i; Jwi represents that node i, j are directly connected but i ≠ j; B _iiand B _ijbe respectively self-admittance and transadmittance; P _diload for node i; P _giminand P _gimaxbe respectively minimum and the maximum output limit of unit; P _ijminand P _ijmaxbe respectively minimum and the maximum meritorious limit of circuit ij; S _b, S _land S _gthe node, circuit and the unit set that comprise for system.

The subject matter of this model has: 1) cannot be optimized electric network security; 2) cannot be to network loss optimization; 3) due to the existence of intermediate variable inequality constrain condition, Optimization Solution calculated amount is large, and especially random optimization, and solving result is easily absorbed in local minimum.

5. the structure of transmission of electricity economy and safety comprehensive Optimized model

For objective function, except traditional generator economic index, the mapping elastic potential energy index of stack major network, and weighting.

Minf=α f _g+ β μ E _{l Σ}(30) wherein: the weight factor that α, β are the two, can be according to the actual conditions setting of different electrical networks, and meet alpha+beta=1,0≤α≤1,0≤β≤1.Due to f _g, E _{l Σ}there is different dimensions and the order of magnitude, so E _{l Σ}be multiplied by coefficient μ, make the two or variation range there is comparability.

Because the mapping elastic potential energy in objective function is less, branch road is meritorious more balanced, is more not easy out-of-limit.Therefore constraint condition can be omitted formula (29), be reduced to formula (27) and (28).

If the circuit out-of-limit situation of gaining merit appears in optimum results, show that the initial value of α in model, β does not meet the actual needs of electric network security.Should suitably increase β value the corresponding α of reducing value, until the α that obtains tallying with the actual situation, β value.

Relatively traditional generating economical optimum model, this model also has the optimizational function of electric network security and transmission of electricity economy, and only has 2 target index components.In addition, also omit the meritorious inequality constrain of circuit, reduced optimization calculated amount, improved the reliability of optimum results.

6. sample calculation analysis

As shown in Figure 4, its median generatrix 31 is balance node to IEEE39 node system structure, and generator operation economic parameters is as shown in table 1.

According to cost of electricity-generating index factor, α successively decreases, the rule that mapping elastic potential energy index factor β increases progressively, 5 groups of weights of target setting function, μ=25.Adopt quadratic programming optimized algorithm, obtain the meritorious of each unit under 5 kinds of generation modes and exert oneself, as table 2.The cost of electricity-generating of every kind of generation mode, mapping elastic potential energy E _{l Σ}with network loss Δ P _Σ, equivalence mapping elasticity coefficient k _leqwith Rate of average load T _aas shown in table 3.Cost of electricity-generating, E _{l Σ}with Δ P _Σvariation tendency as shown in Figure 5.Mapping elastic potential energy is calculated with MW and radian value, disregards dimension.The corresponding mapping elastic network(s) structure of generation mode 1,3,5 is as shown in Fig. 6-8.

Table 1 unit operation economic parameters

The table 2 unit output distribution of gaining merit

Table 3 total power production cost, Δ P _Σ, E _{l Σ}, k _leq, T _a

Table 3 and Fig. 5 are visible, and in the objective function of Integrated Optimization Model, if α is larger, economics of power generation is better; If β is larger, electric network security and branch road load equilibrium are better, and network loss is also lower.

If simple, adopt generating economical optimum model, mode 1, and security and network loss are the poorest in 5 kinds of modes; If simple, adopt safety and transmission of electricity economy Optimized model, mode 5, and economics of power generation is the poorest; If adopt this Integrated Optimization Model, as mode 3, can reduce cost of electricity-generating and network loss, can improve again the security of major network.

Fig. 6-8 are visible, and along with the increase of β value, the whole deformation of mapping elastic network(s) diminishes, and branch road load equilibrium improves, and the security of electrical network increases.Show that this Integrated Optimization Model can play the effect that security is optimized really.

7. conclusion

In service in major network optimization, owing to lacking omnidistance quantitatively safety indexes, traditional Optimized model, is generally all the generating economical optimum model based on security constraint.The subject matter of this model is: cannot be optimized electric network security and network loss; Due to the existence of Line Flow inequality constrain condition, Optimization Solution calculated amount is large, and solving result is easily absorbed in local extremum.

Research is found, shines upon the quantitative target that elastic potential energy not only can be used as electric network security, and its size variation also changes with becoming with network loss.So, mapping elastic potential energy is included in to the objective function of economic generating Optimized model, can solve the complex optimization problem of generating, the economy of transmitting electricity and electric network security; Omit the meritorious constraint condition of circuit, can improve counting yield and the reliability of optimization.

This Optimization Modeling method has realistic meaning to optimization operation and the planning of electric system, and the Optimized model based on the method can obtain sending out transmission of electricity economy and electric network security with excellent generator operation mode, power supply layout scheme and electrical network route planning scheme etc.

Claims (1)

1. a modeling method of sending out transmission of electricity economy and power grid security complex optimum, the method is characterised in that, comprises the steps:

1) in the objective function of Optimized model, by the mapping elastic potential energy E of major network _{l Σ}with generator economic index (being total power production cost) f _gweighted stacking, i.e. minf=α f _g+ β μ E _{l Σ}, wherein α, β are weight factor, meet alpha+beta=1,0≤α≤1, and 0≤β≤1, according to the actual conditions setting of different electrical networks, coefficient μ makes f _g, μ E _{l Σ}there is rom;

2) step 1), p _gi, a _i, b _i, c _ibe respectively the meritorious of unit i and exert oneself and economic parameters, E _libe the mapping elastic potential energy of i bar circuit, n _g, n is respectively the quantity of generator and circuit;

3), step 2), the mapping elastic potential energy of circuit is p wherein _l, θ _land k _lfor phase differential and the mapping elasticity coefficient of meritorious, the both end voltage of circuit,

4) step 3), if θ _lless, x _lfor line reactance;

5) constraint condition of Optimized model only includes trend equality constraint and the constraint of unit output bound, omits the meritorious trend bound constraint of circuit;

6) if when optimum results occurs that the meritorious trend of circuit is out-of-limit, show step 1) in the initial value of α, β do not meet the actual needs of electric network security, should suitably increase the also corresponding α of reducing value of β value, until the α that obtains tallying with the actual situation, β value.