CN112564084B - Method for rapidly determining voltage stability of large-scale distributed photovoltaic access power distribution network - Google Patents
Method for rapidly determining voltage stability of large-scale distributed photovoltaic access power distribution network Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- H—ELECTRICITY
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
- H02J3/16—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by adjustment of reactive power
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
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- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
- H02J2300/20—The dispersed energy generation being of renewable origin
- H02J2300/22—The renewable source being solar energy
- H02J2300/24—The renewable source being solar energy of photovoltaic origin
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- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
- Y02E10/56—Power conversion systems, e.g. maximum power point trackers
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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- Y02E40/30—Reactive power compensation
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Abstract
The invention discloses a method for rapidly determining voltage stability of a distribution network with large-scale distributed photovoltaic access, which comprises the steps of expressing the relevance between voltage change and node reactive change by using a network tide equation, expressing the relevance between node reactive adjustment quantity and measuring point voltage by using a piecewise linear function equation, and integrating two types of equations based on a function transformation rule to describe the relation between a network state and any node voltage measuring result; in order to describe a state equation of network voltage change, the voltage stability problem of the power distribution network is further expressed as a process for describing reactive power output of two adjacent iterations, the voltage stability problem of the power distribution network is converted into a reactive power change process of an inverter, and differential solution is carried out; the method solves the technical problems that in the prior art, the large-scale cluster distributed photovoltaic grid connection is faced, all nodes or most nodes in a network are connected with a photovoltaic power supply, the calculated amount and the calculated difficulty of the traditional voltage stability calculating method are increased sharply, the parameter setting is very inflexible, and the like.
Description
Technical Field
The invention belongs to the technical field of voltage stability of power distribution networks, and particularly relates to a method for quickly determining the voltage stability of a power distribution network with large-scale distributed photovoltaic access.
Background
Currently, fossil energy still occupies a pillar position in a global energy structure, and power generation still mainly depends on fossil fuels such as coal, natural gas and the like. However, environmental problems are increasingly prominent due to the emission of a large amount of carbon dioxide and toxic and harmful gases, and extreme weather problems frequently occur due to the emission of greenhouse gases, which leads to the rise of global air temperature and the melting of glaciers at both poles; the toxic and harmful substances after the combustion of fossil energy enter air, and gases such as nitrogen oxides, sulfur dioxide and the like cause ecological problems such as photochemical smog, acid rain, ozone layer damage and the like, thus forming serious danger for human bodies and natural ecosystems.
Currently, the duty ratio of the grid-connected capacity of the distribution network of the distributed photovoltaic power generation is rapidly increased, and the trend of large-scale cluster grid-connection is presented in the future. In the early stage, the photovoltaic power generation mainly uses concentrated grid connection, a large amount of photovoltaic power is collected and boosted and then is transmitted through a power transmission line to supply power for remote loads, but the grid connection mode occupies the original power transmission capacity of a power grid and limits the transmission of other types of electric energy. However, the solar energy rejection ratio is still high due to the capacity limitation of a power transmission corridor, and the average utilization hour number is only 1115 hours according to national energy agency (2018 national photovoltaic power generation statistics information) and the national photovoltaic power generation rejection amount is 54.9 hundred million kilowatt-hours. Compared with the centralized photovoltaic power generation, the distributed photovoltaic power generation can realize plug and play, photovoltaic power can be utilized in situ, and meanwhile, the problems of capacity occupation and line loss caused by high-capacity power transmission are avoided. By 2018 years, the centralized power station 12384 kilowatts is increased by 23% compared with 2330 kilowatts newly increased in the last year; the distributed photovoltaic 5061 kilowatts, which is increased by 71% in comparison with 2096 kilowatts in the last year, becomes a necessary trend in large-scale grid-connected power generation of the medium-low voltage distribution network.
The grid connection of a large-scale distributed power supply can cause the risks of voltage out-of-limit and voltage fluctuation of a power distribution network, and the current newly-grid-connected distributed photovoltaic units are generally required to have certain voltage-reactive power regulation capability so as to achieve the aims of inhibiting the voltage fluctuation and the voltage out-of-limit and reducing network loss. However, distributed photovoltaic grid-connection is difficult to uniformly plan through distribution operators (distribution system operator, DSO), so that the grid-connection position and capacity have certain randomness. The grid-connected power factors of the distributed power supplies only meet the relevant requirements, and the shape and the slope of a voltage-reactive droop control curve are not constrained, so that the voltage stability of the power distribution network is greatly risked. According to a power flow equation (Newton Lafson method or forward push back substitution method) of the power distribution network, the reactive power change of a single node can cause voltage linkage change of all nodes, the voltage change can further cause reactive power adjustment of the nodes, the change of the network node voltage presents an iterative fluctuation process, and if the process is iteratively converged, the network voltage presents a stable characteristic; if the process iteration does not converge, the network voltage will be unstable and even cause malfunction of the protection device.
Therefore, the method is very significant for maintaining safe and stable operation of the power distribution network in the face of large numbers of distributed photovoltaic power grid connection, rapid judgment of network voltage stability and measurement and calculation of stability boundaries. According to the traditional power distribution network voltage stability evaluation method, when the grid-connected scale of a distributed power supply of a network is low, the power distribution network can be equivalent to a voltage source or a synchronous machine, the influence of reactive power regulation on a system after single photovoltaic grid connection is researched, and the voltage-reactive power sagging slope is adjusted through a disturbance-observation method; if a small amount of photovoltaic grid connection is realized, the network voltage stability can be evaluated through CPU parallel kernel-dividing calculation, and the voltage-reactive parameter is determined through multi-core joint debugging. However, in the face of grid connection of large-scale clustered distributed photovoltaic (all nodes or most nodes in a network are connected with a photovoltaic power supply), the calculated amount and the calculated difficulty of the traditional voltage stability calculation method are increased sharply, and the parameter setting is very inflexible.
Disclosure of Invention
The invention aims to solve the technical problems: the method for quickly determining the voltage stability of the distribution network with the large-scale distributed photovoltaic access is provided, so that the technical problems that the prior art faces to the grid connection of the large-scale cluster distributed photovoltaic, all nodes or most nodes in the network are connected with a photovoltaic power supply, the calculated amount and the calculated difficulty of the traditional voltage stability calculating method are increased sharply, the parameter setting is very lack of flexibility and the like are solved.
The technical scheme of the invention is as follows:
a method for quickly determining voltage stability of a distribution network with large-scale distributed photovoltaic access includes the steps that a network tide equation is utilized to express the relevance between voltage change and node reactive change, a piecewise linear function equation is utilized to express the relevance between node reactive adjustment quantity and measuring point voltage, and two equations are integrated based on a function transformation rule to describe the relation between network state and any node voltage measurement result; in order to describe a state equation of network voltage change, the problem of power distribution network voltage stability is further expressed as a process of describing two adjacent iterative reactive outputs, and the problem of power distribution network voltage stability is converted into a change process of reactive power of an inverter and is subjected to differential solving.
The method for converting the voltage stability problem of the power distribution network into the reactive change process of the inverter and performing differential solving comprises the following steps: simplifying the problem of the voltage stability of the power distribution network into linear operation of a voltage-reactive sensitivity matrix and an inverter voltage-reactive droop control parameter matrix, and judging the voltage stability of the power distribution network based on a spectrum radius upper limit theory; calculating voltage-reactive inverter parameter adjustable range sets of different photovoltaic grid-connected points based on the proposed power distribution network voltage stability analysis solving algorithm; if all the photovoltaic grid-connected unit voltage-reactive inverter parameters in the network are set in the adjustable range, the voltage stability of the power distribution network can be ensured even if the position capacity of the grid-connected photovoltaic is always in the dynamic change process.
The method for quickly determining the voltage stability of the distribution network with large-scale distributed photovoltaic access comprises the following steps:
step 1, establishing a voltage sensitivity solving model based on a ox-Law tide algorithm;
step 2, establishing a voltage-reactive power control network description model based on a voltage sensitivity matrix;
step 3, establishing a power distribution network voltage stability judgment model based on a voltage sensitivity matrix and a spectrum radius upper limit theory;
and 4, establishing a network voltage stability critical parameter set based on the power distribution network voltage stability judgment model.
The method for establishing the voltage sensitivity solving model based on the ox-Law tide algorithm comprises the following steps:
an initial solution of nonlinear equation f (x) =0 is set to x 0 ，x 0 Phase difference Deltax from true solution x (0) The essence of the solution is to iterate to make deltax (k) 0, wherein k represents the number of iterations, and finally the true solution of the equation is found;
let N total nodes, the set of network nodes be n= {1,2 … N }, according to kirchhoff's law, the voltage versus current relationship of the nodes is as follows:
wherein: y is the node admittance matrix, Z is the node impedance matrix,is the node voltage vector, ">Is the injection current vector of the node; after the formula (1) is unfolded, the following steps are carried out:
the injected active power and reactive power of the node i are respectively marked as P i And Q i The voltage conjugate value of node i is denoted as V i * The method comprises the steps of carrying out a first treatment on the surface of the The injection current of node i can be further expressed as:
substituting formula (3) into formula (2) includes:
voltage at node iPolar form is +.>Wherein V is i Is the voltage amplitude, delta, of node i i Is the voltage phase angle of node i; in addition Y ij ＝G ij +jB ij The polar form of the power equation is:
assuming that n nodes exist in the system, wherein one balance node exists, the n nodes are balance nodes, m PQ nodes exist, 1-m are PQ nodes, n-m-1 PV nodes, and m+1-n-1 are PV nodes, the power balance equation is:
the corresponding correction equation is as follows:
wherein: the non-diagonal elements i not equal j of the submatrix are as in formula (8), and the diagonal elements i not equal j are as in formula (9)
The iterative form of the formula (7) is shown as the formula (10), and the convergence criterion is
Wherein: deltaV '(k) The expression of (2) is shown as (11)
Correction vector after each iteration of (8)And V i (k+1) The method comprises the following steps:
if it is assumed that there are no PV nodes in the network, only PQ nodes and one balance node, then the jacobian matrix in equation (7) becomes 2× (n-1) in size, and the iterative equation (10) is modified as:
the result after iteration convergence is recorded as
Gaussian elimination of equation (13) is performed, assuming H 1 、N 1 、M 1 And L 1 All have an inverse matrix
The relation between the node voltage change DeltaV, the node active change DeltaP and the node reactive change is DeltaQ
ΔV＝S V-P ΔP+S V-Q ΔQ (16)
Wherein: s is S V-P ＝(M 1 H 1 -1 N 1 -L 1 ) -1 M 1 H 1 -1 As a voltage-active sensitivity matrix,
S V-Q ＝(L 1 -M 1 H 1 -1 N 1 ) -1 is a voltage-reactive sensitivity matrix;
after the expansion of (16)
For any node i (i e N), its voltage changes DeltaV i The relation between the active and reactive power changes of other nodes is that
Wherein:and->Voltage-active and voltage-reactive sensitivities, i, j e N, respectively, i.e. the voltage change of node i caused by the active and reactive changes of node j; ΔP i And DeltaQ i The amount of change in the activity and the reactive power of node j, respectively.
The method for establishing the voltage-reactive power control network description model based on the voltage sensitivity matrix comprises the following steps: expressing node active and reactive as correlation equation with network voltage and phase angle
Wherein: f (f) PF_P Is the correlation equation of node active power and network voltage, phase angle; f (f) PF_Q The correlation equation of the node reactive power and the network voltage and phase angle; p (P) load 、Q load Active and reactive power of node load respectively; p (P) PV 、Q PV The active and reactive power of the node photovoltaic are respectively; v, δ are the voltage and phase angle of the node, respectively.
According to the voltage reactive droop control curve, the photovoltaic inverter absorbs reactive power when the voltage is higher, injects reactive power when the voltage is lower, and keeps reactive power zero when the voltage is close to a target value; q (Q) PVmax,i And Q PVmin,i The maximum injection power and the maximum absorption power of the photovoltaic inverter are respectively obtained when the node i is connected with the grid; v (V) i,max And V i,min The corresponding voltage values when the maximum reactive power is absorbed and the maximum reactive power is injected are respectively corresponding; v (V) ref,i Is the target voltage; the target voltage is d/2 from the initial reactive injection voltage and d/2 from the initial reactive absorption voltage; m is m i Is the sagging control parameter of the photovoltaic inverter when the node i is connected with the grid, m i ≥0。
The equation for the voltage reactive output of the photovoltaic grid-connected node and the node voltage can be expressed as
The equation for reactive power regulation can be further expressed as
Q PV,i,t+1 ＝f(V i,t )＝f(u(Q PV,i,t ))＝ψ(Q PV,i,t ) (22)
Wherein: v (V) i,t Is the voltage amplitude of node i at time tA value; u (·) is an equation for the influence of the reactive power node reactive power change on the node voltage change; f (u (·)) is denoted ψ (·) and represents the relation between the reactive output at time t+1 and the reactive output at time t.
Step 3, establishing the voltage stability of the power distribution network based on the voltage sensitivity matrix and the spectrum radius upper limit theory
The method for judging the model comprises the following steps:
to describe the correlation of reactive changes at two adjacent moments, one can determine the partial derivative of ψ (, i.e.)
In the aboveThe voltage-reactive sensitivity matrix parameters are solved; can see +.>I.e. electricity
The voltage-reactive control slope parameter is expressed as follows by a diagonal matrix:
wherein M is a slope matrix of the clustered distributed photovoltaic power supply;
the stability determination condition is
ρ(MS V-Q )＜1 (25)
Based on equation (25), once the distribution network voltage-reactive sensitivity matrix and the photovoltaic slope matrix are constructed, the stability for each node can be expressed in the form of an analytical expression
Wherein: n (N) - Is the set of network nodes excluding the head node, namely nodes {2,3, … n };
as can be seen from formula (26), the voltage stability problem of the distribution network containing clustered distributed photovoltaic units is mainly affected by the position of the photovoltaic grid-connected nodes and the voltage-reactive sag slope parameter, and the position of the photovoltaic grid-connected nodes mainly affects the voltage stability problem in formula (26)The parameters related to the line resistance, reactance parameters, line length and topology of the line of the network are not related to the reactive adjustable capacity of the photovoltaic inverter; voltage-reactive sag slope, i.e. m i Parameters, p (MS) V -Q ) The easier the voltage fluctuation approaches 1 or exceeds 1, the non-convergence condition of the voltage fluctuation in the voltage regulating process can be caused; the condition for stabilizing the voltage of the distribution network is that any node in the network should meet the judgment condition of the formula (26).
The method for determining the stability judging condition comprises the following steps: the voltage stability judging condition gradually reduces the degree of voltage change along with the rising of the iteration times and finally tends to be stable; the process is equivalent to the process that the reactive power output of the photovoltaic gradually decreases and finally tends to be stable along with the rising of the iteration times; setting ρ (·) to represent the spectrum radius of any matrix, namely the maximum value of the absolute value of the matrix eigenvalue; for the equation described in equation (24), ρ (MS) is based on the upper limit of the spectral radius V-Q ) < 1 represents the most unstable node t+1 moment reactive absolute value output in all photovoltaic power sources in the network compared with the moment tThe photovoltaic reactive power change tends to zero after infinite iteration to obtain a stability judging condition rho (MS) V-Q )＜1。
The method for establishing the network voltage stability critical parameter set based on the power distribution network voltage stability judgment model comprises the following steps:
derived according to formula (25)As a result of (1), if ρ (MS V-Q ) 1, i.e. in formula (23)Representing that the reactive power change degree is not gradually reduced along with the continuous rising of the control iteration times, the iteration times of the voltage-reactive power control system are approaching to infinite times, the stable condition of the control system can not be met, and rho (MS) V-Q ) The set of slopes of the sagging curve at 1 is denoted +.>Wherein->Is the upper bound of the droop slope of each node, i.e., m i The variation range is-> And M is:
the invention has the beneficial effects that:
according to the invention, the dependence of the traditional power distribution network voltage stability solving method on the CPU computing capacity is greatly reduced by the algorithm itself based on the power distribution network voltage stability resolving algorithm based on the voltage sensitivity matrix and the spectrum radius upper limit theory and the network voltage stability boundary measuring technology, and the voltage stability condition after a large-scale distributed photovoltaic grid-connected (thousands of nodes) is accessed into the power distribution network can be calculated too quickly; in addition, the voltage stability boundary of the power distribution network is provided, the voltage-reactive slope of each node is conveniently constrained, all photovoltaic grid-connected nodes in the network only meet the requirement of the voltage-reactive slope change range in the setting of the control strategy, even if the position capacity of the grid-connected photovoltaic is always in the dynamic change process, the voltage stability of the power distribution network can be ensured, and a user can have better flexibility in the formulation of the control strategy.
The method solves the technical problems that in the prior art, the large-scale cluster distributed photovoltaic grid connection is faced, all nodes or most nodes in a network are connected with a photovoltaic power supply, the calculated amount and the calculated difficulty of the traditional voltage stability calculating method are increased sharply, the parameter setting is very inflexible, and the like.
Description of the drawings:
FIG. 1 is a schematic diagram of a voltage-reactive droop control curve (type 1) in an embodiment;
fig. 2 is a schematic diagram of a voltage-reactive droop control curve (type 2) in an embodiment.
Detailed Description
The invention provides a network level mathematical model which simultaneously considers a voltage-reactive sag curve and a tide equation; on one hand, the invention utilizes the network tide equation to express the relevance between the voltage change and the node reactive change, and utilizes the piecewise linear function to express the relevance between the node reactive adjustment quantity and the voltage of the measuring point, and integrates the two equations based on the function transformation rule to describe the relation between the network state and the voltage measuring result of any node; on the other hand, in order to describe a state equation of network voltage change, the power distribution network voltage stability problem is further expressed as a process of describing two adjacent iterative reactive outputs, and the power distribution network voltage stability problem is converted into differential solution of the change process of the reactive of the inverter.
A power distribution network voltage stability analysis solving model and a voltage-reactive power critical parameter calculating method based on voltage sensitivity and a spectral density upper limit theory. And transforming a differential equation of the reactive power change process of the inverter, simplifying the problem of voltage stability of the power distribution network into linear operation of a voltage-reactive power sensitivity matrix and an inverter voltage-reactive power droop control parameter matrix, and judging the voltage stability of the power distribution network based on a spectrum radius upper limit theory. Based on the provided analysis and solving algorithm for the voltage stability of the power distribution network, a calculation method for the parameter adjustable range set of the voltage-reactive power inverter aiming at different photovoltaic grid-connected points is further provided. If all the photovoltaic grid-connected unit voltage-reactive inverter parameters in the network are set in the adjustable range, the voltage stability of the power distribution network can be ensured even if the position capacity of the grid-connected photovoltaic is always in the dynamic change process.
The invention specifically comprises the following contents:
(1) A voltage sensitivity solving model based on a cattle-pull tide algorithm;
(2) A voltage-reactive control network description model based on a voltage sensitivity matrix;
(3) A power distribution network voltage stability judgment model based on a voltage sensitivity matrix and a spectrum radius upper limit theory;
(4) Network voltage stability critical parameter set based on power distribution network voltage stability judgment model.
Voltage sensitivity solving model based on ox-Law tide algorithm
The Newton-Laportson algorithm is a common nonlinear equation solving method and can be used for solving the power flow of the power grid. The solving thought of the Newton-Laportson algorithm is as follows: an initial solution of nonlinear equation f (x) =0 is set to x 0 ，x 0 Phase difference Deltax from true solution x (0) The essence of the solution is to iterate to make deltax (k) 0, where k represents the number of iterations, the true solution of the equation is eventually found, so the core problem of the newton-raphson algorithm is the correction and solution of the equation.
There are N total nodes, let the set of network nodes be n= {1,2 … N }. According to kirchhoff's law, the voltage and current relationship of a node is as follows:
wherein: y is the node admittance matrix, Z is the node impedance matrix,is the node voltage vector, ">Is the injection current vector of the node. After the formula (1) is unfolded, the following steps are carried out:
the injected active power and reactive power of the node i are respectively marked as P i And Q i The voltage conjugate value of node i is denoted as V i * . The injection current of node i can be further expressed as:
substituting formula (3) into formula (2) includes:
voltage at node iPolar form is +.>Wherein V is i Is the voltage amplitude, delta, of node i i Is the voltage phase angle of node i. In addition Y ij ＝G ij +jB ij The polar form of the power equation is
Let us now assume that there are n nodes in the system, one of which is a balancing node (n nodes are balancing nodes), m PQ nodes (1-m are PQ nodes), n-m-1 PV nodes (m+1-n-1 are PV nodes). The power balance equation is:
the corresponding correction equation is as follows:
wherein: the non-diagonal elements (i. Noteq. J) of the submatrices are as in equation (8), and the diagonal elements (i. Noteq. J) are as in equation (9)
The iterative form of the formula (7) is shown as the formula (10), and the convergence criterion is
Wherein: deltaV '(k) The expression of (2) is shown as (11)
Correction vector after each iteration of (8)And V i (k+1) The method comprises the following steps:
if it is assumed that there is no PV node in the network, only a PQ node and one balance node, the scale of the jacobian matrix in formula (7) becomes 2× (n-1). The iterative equation (10) is modified as:
the result after iteration convergence is recorded as
Gaussian elimination of equation (13) is performed, assuming H 1 、N 1 、M 1 And L 1 All have an inverse matrix
The relation between the node voltage change DeltaV, the node active change DeltaP and the node reactive change is DeltaQ
ΔV＝S V-P ΔP+S V-Q ΔQ (16)
Wherein: s is S V-P ＝(M 1 H 1 -1 N 1 -L 1 ) -1 M 1 H 1 -1 As a voltage-active sensitivity matrix,
S V-Q ＝(L 1 -M 1 H 1 -1 N 1 ) -1 is a voltage-reactive sensitivity matrix.
After the expansion of (16)
/>
For any node i (i e N), its voltage changes DeltaV i The relation between the active and reactive power changes of other nodes is that
Wherein:and->Voltage-active and voltage-reactive sensitivities (i, j e N), respectively, i.e. the voltage change of node i caused by the active (reactive) change of node j; ΔP i And DeltaQ i The amount of change in the activity and the reactive power of node j, respectively.
Network description model based on voltage-reactive power control system
Expressing node active and reactive as correlation equation with network voltage and phase angle
Wherein: f (f) PF_P Is the correlation equation of node active power and network voltage, phase angle; f (f) PF_Q The correlation equation of the node reactive power and the network voltage and phase angle; p (P) load 、Q load Active and reactive power of node load respectively; p (P) PV 、Q PV The active and reactive power of the node photovoltaic are respectively; v, δ are the voltage and phase angle of the node, respectively.
Fig. 1 is a more common voltage reactive droop control curve, where a photovoltaic inverter absorbs reactive power when the voltage is high, injects reactive power when the voltage is low, and maintains reactive power at zero when the voltage approaches a target value. Q (Q) PVmax,i And Q PVmin,i The maximum injection power and the maximum absorption power of the photovoltaic inverter are respectively obtained when the node i is connected with the grid; v (V) i,max And V i,min The corresponding voltage values when the maximum reactive power is absorbed and the maximum reactive power is injected are respectively corresponding; v (V) ref,i Is the target voltage; the target voltage is d/2 from the initial reactive injection voltage and d/2 from the initial reactive absorption voltage; m is m i Is a photovoltaic inverter when node i is connected with gridSag control parameter (m) i 0). Fig. 2 is another, more common voltage reactive droop control curve, i.e., a voltage reactive droop control curve with d/2 of zero.
The equation for the voltage reactive output of the photovoltaic grid-connected node and the node voltage can be expressed as
The equation for reactive power regulation can be further expressed as
Q PV,i,t+1 ＝f(V i,t )＝f(u(Q PV,i,t ))＝ψ(Q PV,i,t ) (22)
Wherein: v (V) i,t Is the voltage amplitude of the node i at the time t; u (·) is an equation for the influence of the reactive power node reactive power change on the node voltage change; f (u (·)) is denoted ψ (·) and represents the relation between the reactive output at time t+1 and the reactive output at time t.
Power distribution network voltage stability judging model based on voltage sensitivity matrix and spectrum radius upper limit theory
To describe the correlation of reactive changes at two adjacent moments, one can determine the partial derivative of ψ (, i.e.)
From the above descriptionThe voltage-reactive sensitivity matrix parameters are solved; can see +.>I.e. the voltage-reactive control slope parameter, can be expressed in terms of a diagonal matrix (generally specifying the first node as the substation outlet node, which is considered as a balancing node in the flow calculation, which node has no voltage stability problem and is therefore described starting from node No. 2):
wherein: m is the slope matrix of the clustered distributed photovoltaic power supply.
The voltage stability judging condition gradually reduces the degree of voltage change along with the rising of the iteration times and finally tends to be stable; the process is equivalent to the process that the reactive power output gradually reduces and finally stabilizes along with the rising of the iteration times. Let ρ (·) denote the spectral radius of any matrix, i.e. the maximum of the absolute values of the eigenvalues of the matrix. For the equation described in equation (24), ρ (MS) is based on the upper limit of the spectral radius V-Q ) < 1 represents the most unstable node t+1 moment reactive absolute value output in all photovoltaic power sources in the network compared with the moment tAnd the photovoltaic reactive power change tends to zero after infinite iteration. The stability determination condition is
ρ(MS V-Q )＜1 (25)
Based on equation (25), once the distribution network voltage-reactive sensitivity matrix and the photovoltaic slope matrix are constructed, the stability for each node can be expressed in the form of an analytical expression
Wherein: n (N) - Is the set of network nodes excluding the head node, namely nodes 2,3, … n.
As can be seen from formula (26), the voltage stability problem of the distribution network containing clustered distributed photovoltaic units is mainly caused by the grid-connected nodes of the photovoltaic systemPosition and influence of the voltage-reactive droop slope parameter. The location of the photovoltaic grid-tie point affects primarily that in equation (26)The parameters related to the line resistance, reactance parameters, line length and topology of the line of the network are not related to the reactive adjustable capacity of the photovoltaic inverter; voltage-reactive sag slope, i.e. m i Parameters, p (MS) V -Q ) The easier it is to approach 1 or to exceed 1, the more the voltage fluctuation of the voltage regulating process will be caused to be non-converged. In addition, it should be noted that the condition for stabilizing the voltage of the distribution network is that any node in the network should satisfy the determination condition of equation (26).
Network voltage stability critical parameter set based on power distribution network voltage stability judgment model
The rapid judging method for the voltage stability of the power distribution network is deduced, and the condition of the voltage stability of the network can be rapidly analyzed through an analytical expression. However, with continuous grid connection of the photovoltaic, the voltage stability of the power distribution network is in a changed state, and the analysis and judgment result is generally delayed from the setting of the voltage-reactive control law of the photovoltaic inverter. If the set of the upper limit values of the voltage and the reactive power is given in advance, all photovoltaic grid-connected nodes in the network only meet the requirement of the upper limit values of the voltage and the reactive power on the setting of a control strategy, even if the position capacity of the grid-connected photovoltaic is always in a dynamic change process, the voltage stability of the power distribution network can be ensured, and a user can have better flexibility on the establishment of the control strategy.
From the result of the derivation of equation (25), if ρ (MS) V-Q ) 1, i.e. in formula (23)The reactive power change degree is not gradually reduced along with the continuous rising of the control iteration times, and the iteration times of the voltage-reactive power control system are approaching to infinite times, so that the stability condition of the control system cannot be met. Will satisfy ρ (MS) V-Q ) The set of slopes of the sagging curve at 1 is denoted +.>Wherein->Is the upper bound of the droop slope of each node, i.e., m i The variation range is-> And M is: />
According to the invention, in a power distribution network voltage stability analysis solving algorithm based on a voltage sensitivity matrix and a spectrum radius upper limit theory and a network voltage stability boundary measuring technology, the dependence on CPU computing capacity is greatly reduced by the algorithm, the voltage stability condition of large-scale distributed photovoltaic grid connection (thousands of nodes) is rapidly computed, the voltage stability boundary of the network is provided, and the voltage-reactive slope of each node is conveniently constrained.
Claims (6)
1. A method for quickly determining voltage stability of a distribution network with large-scale distributed photovoltaic access is characterized by comprising the following steps of: the method comprises the steps of expressing the relevance between voltage change and node reactive power change by using a network tide equation, constructing a piecewise linear function equation based on a photovoltaic inverter voltage reactive power sagging control curve to express the relevance between node reactive power adjustment quantity and measuring point voltage, and establishing an association equation of active power, reactive power, network voltage and phase angle; in order to describe a state equation of network voltage change, the voltage stability problem of the power distribution network is further expressed as a process for describing reactive power output of two adjacent iterations, the voltage stability problem of the power distribution network is converted into a reactive power change process of an inverter, and differential solution is carried out;
the method for the power distribution network voltage stability judgment model comprises the following steps:
expressing node active and reactive as correlation equation with network voltage and phase angle
Wherein: f (f) PF_P Is the correlation equation of node active power and network voltage, phase angle; f (f) PF_Q The correlation equation of the node reactive power and the network voltage and phase angle; p (P) load 、Q load Active and reactive power of node load respectively; p (P) PV 、Q PV The active and reactive power of the node photovoltaic are respectively; v and delta are the voltage and phase angle of the node respectively;
according to the voltage reactive droop control curve, the photovoltaic inverter absorbs reactive power when the voltage is higher, injects reactive power when the voltage is lower, and keeps reactive power zero when the voltage is close to a target value;
Q PVmax,i and Q PVmin,i The maximum injection power and the maximum absorption power of the photovoltaic inverter are respectively obtained when the node i is connected with the grid; v (V) i,max And V i,min The corresponding voltage values when the maximum reactive power is absorbed and the maximum reactive power is injected are respectively corresponding; v (V) ref,i Is the target voltage; the target voltage is d/2 from the initial reactive injection voltage and d/2 from the initial reactive absorption voltage; m is m i Is the sagging control parameter of the photovoltaic inverter when the node i is connected with the grid, m i ≥0；
The equation for the voltage reactive output of the photovoltaic grid-connected node and the node voltage can be expressed as
The equation for reactive power regulation can be further expressed as
Q PV,i,t+1 ＝f(V i,t )＝f(u(Q PV,i,t ))＝ψ(Q PV,i,t ) (22)
Wherein: v (V) i,t Is the voltage amplitude of the node i at the time t; u (·) is an equation for the influence of the reactive power node reactive power change on the node voltage change; f (u (·)) is denoted as ψ (·) and represents the relation between the reactive output at time t+1 and the reactive output at time t;
to describe the correlation of reactive changes at two adjacent moments, the partial derivative of ψ (, i.e.)
In the aboveThe voltage-reactive sensitivity matrix parameters are solved; can see +.>Namely, the voltage-reactive control slope parameter is expressed as follows by a diagonal matrix:
wherein M is a slope matrix of the clustered distributed photovoltaic power supply;
the stability determination condition is
ρ(MS V-Q )＜1 (25)
ρ (·) represents the spectral radius of any matrix, i.e. the maximum of the absolute value of the matrix eigenvalue;
based on (25), constructBuilding a voltage-reactive sensitivity matrix of a power distribution networkAnd a photovoltaic slope matrix, the stability for each node can be expressed in the form of an analytical expression
Wherein: n (N) - Is the set of network nodes excluding the head node, namely nodes {2,3, … n };is voltage-active sensitivity;
as can be seen from formula (26), the voltage stability problem of the distribution network containing clustered distributed photovoltaic units is mainly affected by the position of the photovoltaic grid-connected nodes and the voltage-reactive sag slope parameter, and the position of the photovoltaic grid-connected nodes mainly affects the voltage stability problem in formula (26)The parameters related to the line resistance, reactance parameters, line length and topology of the line of the network are not related to the reactive adjustable capacity of the photovoltaic inverter; voltage-reactive sag slope, i.e. m i Parameters, p (MS) V-Q ) The easier the voltage fluctuation approaches 1 or exceeds 1, the non-convergence condition of the voltage fluctuation in the voltage regulating process can be caused; the condition for stabilizing the voltage of the distribution network is that any node in the network should meet the judgment condition of the formula (26).
2. The method for rapidly determining the voltage stability of a large-scale distributed photovoltaic access power distribution network according to claim 1, wherein the method comprises the following steps: the method for converting the voltage stability problem of the power distribution network into the reactive change process of the inverter and performing differential solving comprises the following steps: simplifying the problem of the voltage stability of the power distribution network into linear operation of a voltage-reactive sensitivity matrix and an inverter voltage-reactive droop control parameter matrix, and judging the voltage stability of the power distribution network based on a spectrum radius upper limit theory; calculating voltage-reactive inverter parameter adjustable range sets of different photovoltaic grid-connected points based on the proposed power distribution network voltage stability analysis solving algorithm; if all the photovoltaic grid-connected unit voltage-reactive inverter parameters in the network are set in the adjustable range, the voltage stability of the power distribution network can be ensured even if the position capacity of the grid-connected photovoltaic is always in the dynamic change process.
3. The method for rapidly determining the voltage stability of a large-scale distributed photovoltaic access power distribution network according to claim 1, wherein the method comprises the following steps: the determining method specifically comprises the following steps:
step 1, establishing a voltage sensitivity solving model based on a ox-Law tide algorithm;
step 2, establishing a voltage-reactive power control network description model based on a voltage reactive power sagging control curve of the photovoltaic inverter;
step 3, establishing a power distribution network voltage stability judgment model based on a voltage sensitivity matrix and a spectrum radius upper limit theory;
and 4, establishing a network voltage stability critical parameter set based on the power distribution network voltage stability judgment model.
4. The method for rapidly determining the voltage stability of a large-scale distributed photovoltaic access power distribution network according to claim 1, wherein the method comprises the following steps: the method for establishing the voltage sensitivity solving model based on the ox-Law tide algorithm comprises the following steps:
an initial solution of nonlinear equation f (x) =0 is set to x 0 ，x 0 Phase difference Deltax from true solution x (0) The essence of the solution is to iterate to make deltax (k) 0, wherein k represents the number of iterations, and finally the true solution of the equation is found;
let N total nodes, the set of network nodes be n= {1,2 … N }, according to kirchhoff's law, the voltage versus current relationship of the nodes is as follows:
wherein: y is the node admittance matrix and,is the node voltage vector, ">Is the injection current vector of the node; after the formula (1) is unfolded, the following steps are carried out:
the injected active power and reactive power of the node i are respectively marked as P i And Q i The voltage conjugate value of node i is denoted as V i * The method comprises the steps of carrying out a first treatment on the surface of the The injection current of node i can be further expressed as:
substituting formula (3) into formula (2) includes:
voltage at node iPolar form is +.>Wherein V is i Is the voltage amplitude, delta, of node i i Is the voltage phase angle of node i; in addition Y ij ＝G ij +jB ij The polar form of the power equation is:
the system has n nodes, wherein one balance node is arranged, the n nodes are balance nodes, m PQ nodes are arranged, 1-m are PQ nodes, n-m-1 PV nodes, and m+1-n-1 are PV nodes, and then the power balance equation is as follows:
the corresponding correction equation is as follows:
wherein: the non-diagonal element i not equal to j of the submatrix is shown as formula (8), and the diagonal element i=j is shown as formula (9)
The iterative form of the formula (7) is shown as the formula (10), and the convergence criterion is
Wherein: deltaV' (k) The expression of (2) is shown as (11)
Correction vector delta after each iteration of (8) i (k+1) And V i (k+1) The method comprises the following steps:
if it is assumed that there are no PV nodes in the network, only PQ nodes and one balance node, then the jacobian matrix in equation (7) becomes 2× (n-1) in size, and the iterative equation (10) is modified as:
the result after iteration convergence is recorded as
Gaussian elimination of equation (13) is performed, assuming H 1 、N 1 、M 1 And L 1 All have an inverse matrix
The relation between the node voltage change DeltaV, the node active change DeltaP and the node reactive change DeltaQ is as follows:
ΔV＝S V-P ΔP+S V-Q ΔQ (16)
wherein: s is S V-P ＝(M 1 H 1 -1 N 1 -L 1 ) -1 M 1 H 1 -1 As a voltage-active sensitivity matrix,
S V-Q ＝(L 1 -M 1 H 1 -1 N 1 ) -1 is a voltage-reactive sensitivity matrix;
after the expansion of (16)
For any node i (i e N), its voltage changes DeltaV i The relation between the active and reactive power changes of other nodes is that
Wherein:and->Voltage-active and voltage-reactive sensitivities, i, j e N, respectively, i.e. the voltage change of node i caused by the active and reactive changes of node j; ΔP j And DeltaQ j The amount of change in the activity and the reactive power of node j, respectively.
5. The method for rapidly determining the voltage stability of a large-scale distributed photovoltaic access power distribution network according to claim 1, wherein the method comprises the following steps: the method for determining the stability judging condition comprises the following steps: the voltage stability judging condition gradually reduces the degree of voltage change along with the rising of the iteration times and finally tends to be stable; the process is equivalent to the process that the reactive power output of the photovoltaic gradually decreases and finally tends to be stable along with the rising of the iteration times; for the equation described in equation (24), ρ (MS) is based on the upper limit of the spectral radius V-Q ) The < 1 represents that the reactive absolute value output at the time t+1 of the most unstable node in all the photovoltaic power supplies in the network is smaller than that at the time t, and the photovoltaic reactive change tends to zero after infinite iteration to obtain a stability judging condition rho (MS) V-Q )＜1。
6. The method for rapidly determining the voltage stability of a large-scale distributed photovoltaic access power distribution network according to claim 1, wherein the method comprises the following steps: the method for establishing the network voltage stability critical parameter set based on the power distribution network voltage stability judgment model comprises the following steps:
from the result of the derivation of equation (25), if ρ (MS) V-Q ) 1, i.e. in formula (23)Representing that the reactive power change degree is not gradually reduced along with the continuous rising of the control iteration times, the iteration times of the voltage-reactive power control system are approaching to infinite times, the stable condition of the control system can not be met, and rho (MS) V-Q ) The set of sagging curves at 1 is recorded asWherein->Is the upper bound of the droop slope of each node, i.e., m i The variation range is-> And E is:
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