A kind of idle work optimization method adapting to bulk power grid automatism voltage control
Technical field
The invention belongs to technical field of electric power automation, and in particular to a kind of to adapt to the idle of bulk power grid automatism voltage control
Optimization method.
Background technology
The core of the automatism voltage control of bulk power grid is that the idle work optimization of electric system calculates.Idle work optimization is optimal load flow
In a typical problem.Traditional bulk power grid automatism voltage control is under given trend section, i.e. the network of system is opened up
It flutters when thinking fixed with parameter, active and idle, the generated power output of load, is meeting system operation putting equipment in service condition
In the case of system status parameters range of operation, to generator terminal voltage, reactive-load compensation equipment throwing is moved back and adjustable transformer
Gear adjust, change the reactive power distribution of system with this, to reduce the network loss of system.
The Reactive Power Optimazation Problem of extensive practical power systems at present, widely used is that nonlinear interior-point method carries out directly
Solve and pass through two kinds of technology paths of district and grade control.The method of degree and zoning stresses the validity to power grid control, in electricity
It is weaker in net analysis.Due to subregion, controlled quentity controlled variable and quantity of state and controlled quentity controlled variable and state outside region between setting area by force
Between amount without directly affect either weak influence but it is interregional in practice be interconnection or the control for adhering to two regions separately of interconnection region
Amount processed and quantity of state are also strong correlation, therefore, do not ensure that its control direction is directed towards optimal direction adjusting sometimes.It is non-thread
Property interior point method stress the direct optimization to power grid analysis, due to directly carry power flow equation constrain, generate control strategy
It is also to meet power flow equation to be.However the data that provide of appearance due to discrete device and state estimation occur deviation it is larger when
The problem of will appear solution difficulty and being difficult to solve, therefore, the prior art also needs to be improved.
Invention content
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provide it is a kind of adapt to bulk power grid automatism voltage control it is idle
Optimization method specifically adopts the following technical scheme that：
The present invention provides a kind of idle work optimization method adapting to bulk power grid automatism voltage control, and the method includes following steps
Suddenly：
Step 1：Determine the voltage stability index of branch；
Step 2：Establish idle work optimization model；
Step 3：Idle work optimization model is solved using interior point method.
The step 1 specifically includes following steps：
Step 1-1：The voltage stability margin L of branch ij between calculate node i and node j_{ij}, as the electricity of branch ij
Press stability index；
Step 1-2：Judge L_{ij}Whether it is more than threshold value T, if more than respective branch is contributed to set of fingers M.
In the step 1-1, the voltage stability margin of branch ij is L between node i and node j_{ij}It is expressed as：
Wherein, R and X indicates resistance and the reactance of branch ij, δ_{ij}Indicate the phase difference of voltage of node i and node j, U_{i}It indicates
The voltage magnitude of node i, P_{j}And Q_{j}The outflow active power and reactive power of node j are indicated respectively；
In the step 2, idle work optimization model includes idle work optimization object function and idle work optimization constraints.
The idle work optimization constraints includes equality constraint and inequality constraints；
The equality constraint includes trend equality constraint, transformer voltage ratio equality constraint and capacitive reactance device equality constraint；
The inequality constraints includes node voltage inequality constraints, the inequality constraints of voltage slack and generator reactive
Output inequality constraints.
The idle work optimization object function is expressed as：
Wherein, f (x) indicates that idle work optimization object function, M indicate set of fingers, U_{i}And U_{j}Node i and node j are indicated respectively
Voltage magnitude, G_{ij}Indicate the conductance of branch ij, δ_{ij}Indicate that the phase difference of voltage of node i and node j, N indicate node set, m
Indicate that voltage stability margin is more than the branch of threshold value；S_{i}Indicate the voltage slack of node i,Indicate that the voltage of branch ij is steady
Determine nargin, ω indicates that variation weight, ψ indicate voltage stability index weight.
In the equality constraint, have：
(1) trend equality constraint is expressed as：
Wherein, P_{G,i}And Q_{G,i}Generator injection active power and reactive power, P at node i are indicated respectively_{D,i}And Q_{D,i}Respectively
Indicate generated power load and load or burden without work at node i, U_{i}And U_{j}The voltage magnitude of node i and node j, G are indicated respectively_{ij}With
B_{ij}Indicate that the conductance and susceptance of branch ij, N indicate node set, δ respectively_{ij}For the phase difference of voltage of node i and node j, and δ_{ij}
=θ_{i}-θ_{j}, wherein θ_{i}、θ_{j}Respectively node i, j voltage phase angle；
(2) transformer voltage ratio equality constraint is expressed as：
(T_{k}-T_{k,min})(T_{k,max}-T_{k}The k ∈ S of)=0_{T} (4)
Wherein, T_{k}Indicate the no-load voltage ratio of k-th of transformer, T_{k,max}And T_{k,min}Above and below the no-load voltage ratio for indicating k-th of transformer respectively
Limit, S_{T}Indication transformer set；
(3) capacitive reactance device equality constraint is expressed as：
(B_{h}-B_{h,min})(B_{h,max}-B_{h}The h ∈ S of)=0_{B} (5)
Wherein, B_{h}Indicate the susceptance of h-th of capacitive reactance device, B_{h,max}And B_{h,min}Above and below the susceptance for indicating h-th of capacitive reactance device respectively
Limit, S_{B}Indicate capacitive reactance device set.
In the inequality constraints, have：
(1) node voltage inequality constraints is expressed as：
U_{i,min}+S_{i}≤U_{i}≤U_{i,max}-S_{i} i∈N (7)
Wherein, S_{i}Indicate the voltage slack of node i, U_{i}Indicate the voltage magnitude of node i, U_{i,max}And U_{i,min}It indicates respectively
The voltage magnitude bound of node i, N indicate node set；
(2) inequality constraints of voltage slack is expressed as：
S_{i}≥0 i∈N (8)
Wherein, S_{i}Indicate that the voltage slack of node i, N indicate node set；
(3) inequality constraints of generator reactive output is expressed as：
Q_{Gi,min}≤Q_{G,i}≤Q_{Gi,max} i∈N (9)
Wherein, Q_{G,i}Indicate that generator injects reactive power, Q at node i respectively_{Gi,max}And Q_{Gi,min}It indicates at node i respectively
Generator injects reactive power bound, and N indicates node set.
The step 3 specifically includes following steps：
Step 3-1：Idle work optimization model is divided into discrete device equality constraint and continuous quantity Optimized model first；
Step 3-2：Continuous quantity Optimized model is expressed as：
Wherein, f (x) indicates that idle work optimization object function, M indicate set of fingers, U_{i}And U_{j}Node i and node j are indicated respectively
Voltage magnitude, G_{ij}Indicate the conductance of branch ij, δ_{ij}Indicate that the phase difference of voltage of node i and node j, N indicate node set, m
Indicate that voltage stability margin is more than the branch of threshold value；S_{i}Indicate the voltage slack of node i,Indicate that the voltage of branch ij is steady
Determine nargin, ω indicates that variation weight, ψ indicate voltage stability index weight, B_{h,i}Indicate the electricity of h-th of capacitive reactance device at node i
It receives, T_{k,i}Indicate the no-load voltage ratio of k-th of transformer at node i, Δ P_{i}、ΔQ_{i}Active deviation and idle deviation at node i are indicated respectively；
Definition vector x=[Q_{G,1},…,Q_{G,i},…,Q_{G,N},S_{1},…,S_{i},…,S_{N},U_{1},…,U_{i},…,U_{N},θ_{1},…,θ_{i},…,
θ_{N}]^{T}, unconfined majorized function L is formed for continuous quantity Optimized model, is had：
Wherein, S_{G}Indicate that generator node, μ indicate disturbance variable, and μ >=0；l_{i}、u_{i}Under the voltage for indicating node i respectively
Slack variable in slack variable and voltage, y_{pi}、y_{qi}、z_{i}、w_{i}Indicate the lagrange's variable of node i, definition vector l=[l_{1},
l_{2},……,l_{r}], u=[u_{1},u_{2},……,u_{r}], vectorial y={ y_{p1},…y_{pi},…,y_{pN},y_{q1},…,y_{qi},…,y_{qN}, vectorial z=
[z_{1},z_{2},……,z_{r}], vectorial w=[w_{1},w_{2},……,w_{r}], r expression inequality numbers；
Then meet：
Wherein, L_{x}Indicate majorized function L to the local derviation of vector x, L_{y}Indicate majorized function L to the local derviation of vectorial y, L_{z}It indicates
Majorized function L is to the local derviation of vectorial z, L_{w}Indicate majorized function L to the local derviation of vectorial w, L_{l}Indicate majorized function L to the inclined of vectorial l
It leads, L_{u}Indicate majorized function L to the local derviation of vectorial u, ▽_{x}Indicate idle work optimization object function f (x) to the local derviation of vector x, trend
Equality constraint vector h (x)={ Δ P_{1},…,ΔP_{i},…,ΔP_{N}, Δ Q_{1},…,ΔQ_{i},…,ΔQ_{N}, g (x) indicates inequality about
Shu Xiangliang,Indicate the inequality constraints upper limit,gIndicate inequality constraints lower limit, L, Z, U, W are respectively l_{i}、z_{i}、u_{i}、w_{i}The r of composition
Diagonal matrix is tieed up, the r that E is ties up unit matrix；
Step 3-3：The discrete device equality constraint includes transformer voltage ratio equality constraint and capacitive reactance device equality constraint；
Increase duality gapThen have：
Wherein, T_{k}Indicate the no-load voltage ratio of k-th of transformer, T_{k,max}And T_{k,min}Above and below the no-load voltage ratio for indicating k-th of transformer respectively
Limit, S_{T}Indication transformer set；B_{h}Indicate the susceptance of h-th of capacitive reactance device, B_{h,max}And B_{h,min}The electricity of h-th of capacitive reactance device is indicated respectively
Receive bound, S_{B}Indicate capacitive reactance device set；
Step 3-4：Idle work optimization model is solved, is specifically included：
Step 1)：Initialization vector l, z, u, w, y, each vector kind of element is respectively 0.5, -0.2,0.5,0.2, -0.01,
It is 0.99 to initialize centripetal parameter Sigma；
Step 2)：Calculate C_{gap}、L_{x}、L_{y}、L_{z}、L_{w}、L_{l}、L_{u}If calculated C_{gap}、L_{x}、L_{y}、L_{z}、L_{w}、L_{l}、L_{u}Respectively less than count
Precision ε is calculated, then stops calculating；
Step 3)：According to obtained C_{gap}Calculation perturbation variable
Step 4)：Material calculation coefficient step_{P}And step_{D}, have：
Step 5)：According to step_{P}And step_{D}X, l, u, y, z, w are corrected, is had：
Wherein, Δ x, Δ l, Δ u, Δ y, Δ z, Δ w indicate respectively vector x, l, u, y, z, w iteration step length；
Step 6)：T is corrected by solving equation (13)_{k}And B_{h}, have：
T_{k}=T_{k}+ΔT_{k} (18)
B_{h}=B_{h}+ΔB_{h} (19)
Wherein, Δ T_{k}With Δ B_{h}To correct step-length；
Step 7)：By revised T_{k}、B_{h}, after x, l, u, y, z, w bring equation (12) and (13) into, return to step 2).
Compared with prior art, the beneficial effects of the present invention are：
1) according to voltage in actual motion be soft-constraint the characteristics of, idle work optimization is improved using the method for voltage relaxationization
The convergence of computational methods；
2) it is converted into equality constraint by the way that discrete device is adjusted constraint, improves the efficiency of single optimization, can adapt to
The optimization analysis of a large amount of discrete devices control in bulk power grid, and propose corresponding optimization method for equality constraint；
3) by by L_{ij}Index converts P_{j}(R+X)+Q_{j}(X-R) form has needle under conditions of to increase model nonconvex property
The low voltage stability of voltage stability margin is improved to property, to achieve the purpose that improve system voltage stability.
Description of the drawings
Fig. 1 is the idle work optimization method flow chart that bulk power grid automatism voltage control is adapted in the embodiment of the present invention.
Specific implementation mode
Invention is further described in detail below in conjunction with the accompanying drawings.
Traditional nonlinear interior-point method calculates idle work optimization and is susceptible to due to not restrained caused by data reasons, for from
It is casually arranged with for needing regular nearby or being caused to calculate inaccurately using intelligent algorithm, for this three classes of the voltage stability of consideration system
Situation.The present invention is by mathematical distortions and considers voltage operation characteristic, compares traditional nonlinear interior-point method idle work optimization, this Shen
The characteristics of being please soft-constraint according to voltage in actual motion, idle work optimization computational methods are improved using the method for voltage relaxationization
Convergence；It is converted into equality constraint by the way that discrete device is adjusted constraint, improves the efficiency of single optimization, can adapt to big
The optimization analysis of a large amount of discrete devices control in power grid, and propose corresponding optimization method for equality constraint；Passing through will
L_{ij}Index converts P_{j}(R+X)+Q_{j}(X-R) it is steady targetedly to improve voltage under conditions of to increase model nonconvex property for form
The low voltage stability of nargin is determined, to achieve the purpose that improve system voltage stability.
Such as Fig. 1, the present invention provides a kind of idle work optimization method adapting to bulk power grid automatism voltage control, the method includes
Following steps：
Step 1：Determine the voltage stability index of branch；
Step 2：Establish idle work optimization model；
Step 3：Idle work optimization model is solved using interior point method.
The step 1 specifically includes following steps：
Step 1-1：The voltage stability margin L of branch ij between calculate node i and node j_{ij}, as the electricity of branch ij
Press stability index；
Step 1-2：Judge L_{ij}Whether it is more than threshold value T, if more than respective branch is contributed to set of fingers M.
In the step 1-1, the voltage stability margin of branch ij is L between node i and node j_{ij}It is expressed as：
Wherein, R and X indicates resistance and the reactance of branch ij, δ_{ij}Indicate the phase difference of voltage of node i and node j, U_{i}It indicates
The voltage magnitude of node i, P_{j}And Q_{j}The outflow active power and reactive power of node j are indicated respectively；
Certain actual electric network result of calculation such as table 1：
Table 1
Circuit name |
Voltage stability index (threshold value is set as 0.6) |
Mountain yellow line |
0.650653 |
Other white line |
0.469824 |
Platform tower line |
0.397849 |
Black multi-color cord |
0.396 |
Xu Lu lines |
0.380926 |
In the step 2, idle work optimization model includes idle work optimization object function and idle work optimization constraints.
The idle work optimization constraints includes equality constraint and inequality constraints；
The equality constraint includes trend equality constraint, transformer voltage ratio equality constraint and capacitive reactance device equality constraint；
The inequality constraints includes node voltage inequality constraints, the inequality constraints of voltage slack and generator reactive
Output inequality constraints.
The idle work optimization object function is expressed as：
Wherein, f (x) indicates that idle work optimization object function, M indicate set of fingers, U_{i}And U_{j}Node i and node j are indicated respectively
Voltage magnitude, G_{ij}Indicate the conductance of branch ij, δ_{ij}Indicate that the phase difference of voltage of node i and node j, N indicate node set, m
Indicate that voltage stability margin is more than the branch of threshold value；S_{i}Indicate the voltage slack of node i,Indicate that the voltage of branch ij is steady
Determine nargin, ω indicates that variation weight, ψ indicate voltage stability index weight.
In the equality constraint, have：
(1) trend equality constraint is expressed as：
Wherein, P_{G,i}And Q_{G,i}Generator injection active power and reactive power, P at node i are indicated respectively_{D,i}And Q_{D,i}Respectively
Indicate generated power load and load or burden without work at node i, U_{i}And U_{j}The voltage magnitude of node i and node j, G are indicated respectively_{ij}With
B_{ij}Indicate that the conductance and susceptance of branch ij, N indicate node set, δ respectively_{ij}For the phase difference of voltage of node i and node j, and δ_{ij}
=θ_{i}-θ_{j}, wherein θ_{i}、θ_{j}Respectively node i, j voltage phase angle；
(2) transformer voltage ratio equality constraint is expressed as：
(T_{k}-T_{k,min})(T_{k,max}-T_{k}The k ∈ S of)=0_{T} (4)
Wherein, T_{k}Indicate the no-load voltage ratio of k-th of transformer, T_{k,max}And T_{k,min}Above and below the no-load voltage ratio for indicating k-th of transformer respectively
Limit, S_{T}Indication transformer set；
(3) capacitive reactance device equality constraint is expressed as：
(B_{h}-B_{h,min})(B_{h,max}-B_{h}The h ∈ S of)=0_{B} (5)
Wherein, B_{h}Indicate the susceptance of h-th of capacitive reactance device, B_{h,max}And B_{h,min}Above and below the susceptance for indicating h-th of capacitive reactance device respectively
Limit, S_{B}Indicate capacitive reactance device set.
In the inequality constraints, have：
(1) node voltage inequality constraints is expressed as：
U_{i,min}+S_{i}≤U_{i}≤U_{i,max}-S_{i} i∈N (7)
Wherein, S_{i}Indicate the voltage slack of node i, U_{i}Indicate the voltage magnitude of node i, U_{i,max}And U_{i,min}It indicates respectively
The voltage magnitude bound of node i, N indicate node set；
(2) inequality constraints of voltage slack is expressed as：
S_{i}≥0 i∈N (8)
Wherein, S_{i}Indicate that the voltage slack of node i, N indicate node set；
(3) inequality constraints of generator reactive output is expressed as：
Q_{Gi,min}≤Q_{G,i}≤Q_{Gi,max} i∈N (9)
Wherein, Q_{G,i}Indicate that generator injects reactive power, Q at node i respectively_{Gi,max}And Q_{Gi,min}It indicates at node i respectively
Generator injects reactive power bound, and N indicates node set.
The step 3 specifically includes following steps：
Step 3-1：Idle work optimization model is divided into discrete device equality constraint and continuous quantity Optimized model first；
Step 3-2：Continuous quantity Optimized model is expressed as：
Wherein, f (x) indicates that idle work optimization object function, M indicate set of fingers, U_{i}And U_{j}Node i and node j are indicated respectively
Voltage magnitude, G_{ij}Indicate the conductance of branch ij, δ_{ij}Indicate that the phase difference of voltage of node i and node j, N indicate node set, m
Indicate that voltage stability margin is more than the branch of threshold value；S_{i}Indicate the voltage slack of node i,Indicate that the voltage of branch ij is steady
Determine nargin, ω indicates that variation weight, ψ indicate voltage stability index weight, B_{h,i}Indicate the electricity of h-th of capacitive reactance device at node i
It receives, T_{k,i}Indicate the no-load voltage ratio of k-th of transformer at node i, Δ P_{i}、ΔQ_{i}Active deviation and idle deviation at node i are indicated respectively；
Definition vector x=[Q_{G,1},…,Q_{G,i},…,Q_{G,N},S_{1},…,S_{i},…,S_{N},U_{1},…,U_{i},…,U_{N},θ_{1},…,θ_{i},…,
θ_{N}]^{T}, unconfined majorized function L is formed for continuous quantity Optimized model, is had：
Wherein, S_{G}Indicate that generator node, μ indicate disturbance variable, and μ >=0；l_{i}、u_{i}Under the voltage for indicating node i respectively
Slack variable in slack variable and voltage, y_{pi}、y_{qi}、z_{i}、w_{i}Indicate the lagrange's variable of node i, definition vector l=[l_{1},
l_{2},……,l_{r}], u=[u_{1},u_{2},……,u_{r}], vectorial y={ y_{p1},…y_{pi},…,y_{pN},y_{q1},…,y_{qi},…,y_{qN}, vectorial z=
[z_{1},z_{2},……,z_{r}], vectorial w=[w_{1},w_{2},……,w_{r}], r expression inequality numbers；
Then meet：
Wherein, L_{x}Indicate majorized function L to the local derviation of vector x, L_{y}Indicate majorized function L to the local derviation of vectorial y, L_{z}It indicates
Majorized function L is to the local derviation of vectorial z, L_{w}Indicate majorized function L to the local derviation of vectorial w, L_{l}Indicate majorized function L to the inclined of vectorial l
It leads, L_{u}Indicate majorized function L to the local derviation of vectorial u, ▽_{x}Indicate idle work optimization object function f (x) to the local derviation of vector x, trend
Equality constraint vector h (x)={ Δ P_{1},…,ΔP_{i},…,ΔP_{N}, Δ Q_{1},…,ΔQ_{i},…,ΔQ_{N}, g (x) indicates inequality about
Shu Xiangliang,Indicate the inequality constraints upper limit,gIndicate inequality constraints lower limit, L, Z, U, W are respectively l_{i}、z_{i}、u_{i}、w_{i}The r of composition
Diagonal matrix is tieed up, the r that E is ties up unit matrix；
Step 3-3：The discrete device equality constraint includes transformer voltage ratio equality constraint and capacitive reactance device equality constraint；
Increase duality gapThen have：
Wherein, T_{k}Indicate the no-load voltage ratio of k-th of transformer, T_{k,max}And T_{k,min}Above and below the no-load voltage ratio for indicating k-th of transformer respectively
Limit, S_{T}Indication transformer set；B_{h}Indicate the susceptance of h-th of capacitive reactance device, B_{h,max}And B_{h,min}The electricity of h-th of capacitive reactance device is indicated respectively
Receive bound, S_{B}Indicate capacitive reactance device set；
Step 3-4：Idle work optimization model is solved, is specifically included：
Step 1)：Initialization vector l, z, u, w, y, each vector kind of element is respectively 0.5, -0.2,0.5,0.2, -0.01,
It is 0.99 to initialize centripetal parameter Sigma；
Step 2)：Calculate C_{gap}、L_{x}、L_{y}、L_{z}、L_{w}、L_{l}、L_{u}If calculated C_{gap}、L_{x}、L_{y}、L_{z}、L_{w}、L_{l}、L_{u}Respectively less than count
Precision ε is calculated, then stops calculating；
Step 3)：According to obtained C_{gap}Calculation perturbation variable
Step 4)：Material calculation coefficient step_{P}And step_{D}, have：
Step 5)：According to step_{P}And step_{D}X, l, u, y, z, w are corrected, is had：
Wherein, Δ x, Δ l, Δ u, Δ y, Δ z, Δ w indicate respectively vector x, l, u, y, z, w iteration step length；
Step 6)：T is corrected by solving equation (13)_{k}And B_{h}, have：
T_{k}=T_{k}+ΔT_{k} (18)
B_{h}=B_{h}+ΔB_{h} (19)
Wherein, Δ T_{k}With Δ B_{h}To correct step-length；
Step 7)：By revised T_{k}、B_{h}, after x, l, u, y, z, w bring equation (12) and (13) into, return to step 2).
The present invention, to the control feature of voltage, reactive apparatus, this class is improved using relaxationization method according to electric system
The convergence of technology.Secondly as there are many some regional discrete devices, and it is main adjustment equipment, the present invention is set discrete
Standby Controlling model introduces idle work optimization model by the way of Constraints, although increasing the convergence time of single optimization analysis
Number, but traditional two suboptimization calculating regular nearby can be converted to primary calculating.Again, electric for existing in power grid
Stable problem is pressed, and since the generation of Voltage-stabilizing Problems usually has locality, utilizes analysis branch voltage steady stability
Index is improved by targetedly reducing the branch voltage stability index numerical value in certain region in Optimized model object function
The voltage stability margin in this region.
Finally it should be noted that：The above embodiments are merely illustrative of the technical scheme of the present invention and are not intended to be limiting thereof, institute
The those of ordinary skill in category field with reference to above-described embodiment still can to the present invention specific implementation mode modify or
Equivalent replacement, these are applying for this pending hair without departing from any modification of spirit and scope of the invention or equivalent replacement
Within bright claims.