CN112182815A - Multi-rate real-time simulation method based on Nonton equivalence - Google Patents

Multi-rate real-time simulation method based on Nonton equivalence Download PDF

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CN112182815A
CN112182815A CN202010975857.0A CN202010975857A CN112182815A CN 112182815 A CN112182815 A CN 112182815A CN 202010975857 A CN202010975857 A CN 202010975857A CN 112182815 A CN112182815 A CN 112182815A
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朱俊杰
张炳达
靳朝
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Abstract

The invention discloses a multi-rate real-time simulation method based on Norton equivalence, which is characterized in that after Norton equivalence is respectively carried out on a small-step sub-network and a large-step sub-network, simultaneous solution is carried out at boundary nodes; the interaction between the small-step-size sub-network and the large-step-size sub-network data interface is realized by applying an extrapolation method; in order to ensure the real-time performance of the simulation, a method for calculating in advance of a small-step sub-network is provided for a large-step sub-network with a large calculation amount. Compared with the traditional multi-rate simulation method, the simulation precision is improved by the method on the premise of not losing the simulation scale, and the method has important theoretical and practical significance for realizing the real-time simulation of the alternating current-direct current hybrid power grid.

Description

Multi-rate real-time simulation method based on Nonton equivalence
Technical Field
The invention belongs to the technical field of electric power automation, and relates to a multi-rate real-time simulation method based on Nonton equivalence.
Background
In the alternating current-direct current hybrid system, high-power electronic equipment with a rapid control characteristic and an alternating current large power grid are mutually interwoven in different time scale processes, so that the operation control characteristic of the alternating current-direct current power grid is more complex. Therefore, in the simulation of the alternating current-direct current hybrid system, various time scale processes in the alternating current-direct current hybrid power grid need to be considered, and the simulation can be used for carrying out simulation on the rapid electromagnetic transient processes (time scales from a few microseconds to tens of microseconds) of power electronic equipment such as a converter and a static synchronous compensator; but also can simulate the switching process of the converter valve of the direct current transmission system and the electromagnetic transient process (time scale from dozens of microseconds to hundreds of microseconds) of the alternating current system. When a single step length is adopted to simulate the alternating current-direct current hybrid system, if the simulation step length is too small, the calculation amount required to be completed in the single step length is large, and the problem that the calculation cannot be completed within a specified time is easy to occur; if the simulation step length is too large, the dynamic characteristics of the power electronic element cannot be reflected, and the simulation accuracy is reduced. In order to take the simulation precision and the simulation scale into consideration, the whole system is decomposed into a plurality of subsystems, and different step lengths are adopted for different subsystems according to the time scale of power equipment in the subsystems to carry out simulation calculation, namely multi-rate simulation.
However, the existing multi-rate real-time simulation method has a big defect: the existing fast priority algorithm and the slow priority algorithm use an extrapolation method to carry out synchronization of different step lengths, thereby reducing the precision and the stability of simulation. The multi-rate simulation of the relaxation variable method strictly meets the voltage and current constraints through iteration, but the simulation efficiency is low and the parallelism cannot be realized. The multi-rate simulation method based on the ideal power source equivalence utilizes the characteristic that state variables on state elements in a network cannot be suddenly changed, an inductance-capacitance element is equivalent to an ideal power source model, the whole system is decoupled by the idea of replacing the theorem, and the equivalent power source of the other network is a predicted value when the sub-networks with large step length and small step length are calculated. The accuracy of these methods is greatly affected.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a multi-rate real-time simulation method which is reasonable in design and can effectively improve the simulation accuracy, and has important theoretical and practical significance for realizing the real-time simulation of an alternating current-direct current hybrid power grid.
The purpose of the invention is realized by the following technical scheme:
a multi-rate real-time simulation method based on Nonton equivalence is used for an alternating current-direct current hybrid power system and comprises the following steps:
(1) dividing the whole system into a plurality of subsystems according to different time scales of power equipment in the system, and performing simulation calculation on different subsystems by adopting different step lengths according to the time scales of the power equipment in the subsystems;
(2) performing norton equivalence on the sub-systems after the sub-networks are separated; firstly, each sub-system after being divided into networks is changed into a Norton equivalent circuit, and then the node voltage of the solving interface of each sub-system is solved;
(3) solving state variables inside each subsystem; according to the superposition principle, the state variables of the dynamic elements can be obtained by linear combination of responses generated by the independent action of each power supply on the dynamic elements in the sub-network, and for each subsystem, the state variables of the state elements at the current moment can be expressed as linear combination of the value of the state variable at the previous moment, the value of the independent current source at the current moment and the value of the interface node voltage at the current moment, so that the state variables of the subsystems are respectively solved according to the solved interface node voltage.
Furthermore, the norton equivalent circuit parameters of the large-step sub-network and the small-step sub-network are needed to be used when the solution of the interface node voltage is carried out; the time for solving the Noton equivalent circuit by the large-step sub-network is advanced so as to ensure that the calculation of the equivalent conductance and the equivalent current source can be completed before the calculation of the interface node voltage, thereby not influencing the solution of the interface node voltage.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
1. respectively carrying out Noton equivalence on a small-step sub-network and a large-step sub-network, and then carrying out simultaneous solution at boundary nodes; in order to ensure the real-time performance of simulation, a method for calculating in advance by using a sub-network with small step size is provided for a sub-network with large calculation amount and large step size. Compared with the traditional multi-rate simulation method, the method provided by the invention improves the simulation precision on the premise of not losing the simulation scale, and has important theoretical and practical significance for realizing the real-time simulation of the alternating current-direct current hybrid power grid.
2. The invention divides the whole power system into networks during real-time simulation, and adopts different step lengths to perform simulation calculation, namely multi-rate simulation, on different subnets according to the time scale of power equipment in the subnets, and considers the simulation precision and the simulation scale.
3. Aiming at the accuracy problem of the traditional multi-rate method, the Noton equivalent circuit is adopted to replace the traditional ideal power supply equivalent circuit, the large-step sub-network and the small-step sub-network are changed into the Noton equivalent circuit, then the node voltage of the interface of the large-step sub-network and the small-step sub-network is solved, and further the state variable inside the sub-network is solved.
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FIG. 1 is a schematic diagram of an AC/DC hybrid power system according to the present invention;
FIG. 2 is a simulation diagram of the present invention based on a Norton equivalent circuit;
FIG. 3 is a timing dependency diagram of the computational tasks of the present invention;
Detailed Description
The invention is described in further detail below with reference to the figures and specific examples. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a component method for a real-time simulation element of a power system, which comprises the following steps:
(1) and (5) carrying out network distribution on the whole system. Firstly, the whole system is decomposed into a plurality of subsystems according to the difference of the time scales of the power equipment in the system, and simulation calculation is carried out on different subsystems by adopting different step lengths according to the time scales of the power equipment in the subsystems.
(2) And performing norton equivalence on the sub-systems after the network division. Firstly, all the subsystems after being separated are changed into a Norton equivalent circuit, and then the node voltage of the solving interface of each subsystem is solved.
(3) And solving state variables inside each subsystem. According to the superposition principle, the state variables of the dynamic elements can be obtained by linearly combining the responses generated by the independent action of the power supplies in the sub-network on the dynamic elements, and for each subsystem, the state variables of the elements at the current moment can be expressed as linear combinations of the value of the state variable at the previous moment, the value of the independent current source at the current moment and the value of the interface node voltage at the current moment, so that the respective state variables can be respectively solved by each subsystem according to the solved interface node voltage.
(4) For hardware-in-the-loop simulation, all the calculation of the step size must be completed within a specified step size, otherwise, the real-time performance of the simulation cannot be guaranteed. For the multi-rate real-time simulation method based on the Norton equivalence, the Norton equivalent circuit parameters of a large-step sub-network and a small-step sub-network are needed when the solution of the interface node voltage is carried out. However, compared with the small-step sub-network, the large-step sub-network has numerous nodes, the calculation amount of the solution process of the Norton equivalent circuit is large, and the solution process is difficult to complete within a small-step time range. Because the large-step sub-network is an alternating-current large power grid, the moment of state change of the dynamic element is not very important, the time for solving the Norton equivalent circuit of the large-step sub-network can be advanced, so that the calculation of the equivalent conductance and the equivalent current source can be completed before the calculation of the interface node voltage, and the solution of the interface node voltage is not influenced.
The function and action of the present invention will be further described below:
there are two linear sourcing subnetworks, one with a smaller time scale, denoted by the subscript f. The other subnet has a larger time scale, denoted by the subscript s. The two subnetworks are connected to each other by k nodes as shown in fig. 1.
In fig. 1, the input vectors of the large-step sub-network and the small-step sub-network are composed of two parts, an independent current source inside the sub-network, and a voltage or a current at a network port. Wherein isAnd ifIs the current vector at the sub-network port; u is the voltage vector at the sub-network port; i.e. isintAnd ifintAre independent power supply vectors inside the sub-network.
Respectively carrying out Norton equivalence on the large-step sub-network and the small-step sub-network to obtain a simulation schematic diagram based on the Norton equivalent circuit shown in figure 2.
Assuming that the simulation step size of the large-step sub-network is Δ T and the simulation step size of the small-step sub-network is Δ T, where Δ T is n Δ T (n is a positive integer), the norton equivalent circuits of the large-step sub-network and the small-step sub-network can be respectively expressed as
is(t)＝Gsu(t)+Iss(t)
if(t)＝Gfu(t)+Isf(t)
Wherein is(t) and if(t) is the current column vector at the norton equivalent circuit port; u (t) is a voltage vector at a port of the Norton equivalent circuit, namely the voltage of an interface node; gsAnd GfIs the admittance matrix of the norton equivalent circuit, which is related to the states of the dynamic elements in the large-step sub-network and the small-step sub-network. Iss(t) and IsfAnd (t) is an equivalent current source of the Norton equivalent circuit. It Is obtained by linear combination of the response of independent current sources and historical current sources, and the historical current source Is in linear relation with the previous value of the state variable of each dynamic element, so that the equivalent current source Iss(t) and Isf(t) may be expressed as a linear combination of the previous time value of each dynamic element state variable and the current time value of the independent current source.
Iss(t)＝Csxs(t-ΔT)+Dsisint(t)
Isf(t)＝Cfxf(t-Δt)+Dfifint(t)
Wherein x iss(T-. DELTA.T) and xf(t- Δ t) is the value of the state variable of the dynamic element in the large-step sub-network and the small-step sub-network at the previous moment; i.e. isint(t) and ifint(t) is the current time value of the independent current source in the large-step sub-network and the small-step sub-network; cs、 Ds、CfAnd DfIs a parameter matrix.
On the interface of large-step sub-network and small-step sub-network
is(t)＝-if(t)
Can be obtained by simultaneous
(Gs+Gf)u(t)＝-[Iss(t)+Isf(t)]
The above equation is called the interface node voltage equation. After the voltage vectors u of the ports of the large-step sub-network and the small-step sub-network are obtained, the state variables x of each dynamic element in the large-step sub-network and the small-step sub-network can be calculatedsAnd xf。
When T is m Δ T, i.e. T is at a large-step simulation node, the states of the dynamic elements in the two sub-networks and the state variable x at the previous moment of the sub-network are knowns((m-1) Δ T) and xf(m Δ T- Δ T), norton equivalence can be performed on the two sub-networks to obtain Gs、 Iss(t)、GfAnd IsfAnd (t), the node voltage of the interface can be solved according to the interface node voltage equation, and then the whole network is solved.
When T is m Δ T + k Δ T (k is 1,2, …, n-1), i.e. T is on a small step simulation node, G in both sub-networkssAnd GfAnd the state variable x of the small-step subnetwork at the previous momentf(m Δ T + (k-1) Δ T) is a known quantity, and the state variable x of the large-step sub-networks((m-1) Δ T + k Δ T) can be estimated by means of linear interpolation, i.e.
Figure BDA0002685763600000041
For large step sub-networks, the parameter matrix GsThe state of each dynamic element corresponding to the time of (m-1) delta T + k delta T-m delta T + k delta T spans two sections of (m-1) delta T-m delta T and m delta T-m +1) delta T. For the sake of simplicity of calculation, the norton equivalence is performed on the large-step sub-network by using the states of each dynamic element at the moment of m Δ T, namely G is considereds(mΔT+kΔt)＝Gs(m.DELTA.T). Solving for the Nonton equivalent current source IssIn the case of (t), i is not directly used in order to reduce the amount of calculationsint(m Δ T + k Δ T) to calculate Iss(m Δ T + k Δ T), but using a pass-through isint(m.DELTA.T) and isint(m +1) Δ T) Linear interpolation to get is′int(m Δ T + k Δ T) to calculate Iss(m.DELTA.T + k.DELTA.t), i.e.
Figure BDA0002685763600000051
Thus, the equivalent current source in the norton equivalent circuit can be represented as
Iss(mΔT+kΔt)＝Iss(mΔT)+kΔIss(mΔT)
Wherein the equivalent current source increment is
Figure BDA0002685763600000052
Obviously, by incrementally calculating the equivalent current source in the norton equivalent circuit, the Is only required to be solved once at each Δ Ts(m.DELTA.T) and Δ Iss(m delta T) without the need to solve Is by using a parameter matrix frequentlys(m Δ T + k Δ T) such that Is solvedsThe calculation amount of (m Δ T + k Δ T) is greatly reduced.
Let T be m Δ T (m is a positive integer), i.e., T is on the simulation node of the large-step sub-network. Summarizing and summarizing the solving process, the multi-rate simulation method based on the Norton equivalent has the following process:
(1) calculating a kth (k is 0,1, a., n-1) time period norton equivalent circuit of a large-step sub-network and a small-step sub-network
Figure BDA0002685763600000053
Isf(t+kΔt)＝Cfxf(t+(k-1)Δt)+Dfifint(t+kΔt)
(2) According to Gs、GfIs obtained from the previous steps(t+kΔt)、Isf(t + k Δ t), column write interface node voltage equation
(Gs+Gf)u(t+kΔt)＝-[Iss(t+kΔt)+Isf(t+kΔt)]
(3) And solving a voltage vector u (t + k delta t) of the ports of the large-step sub-network and the small-step sub-network according to the formula.
(4) Calculating a state variable x on the small-step simulation node by the small-step sub-network according to the obtained u (t + k delta t)f(t + k Δ t); on the large-step simulation node, solving the state variable x of the large-step sub-networks(t)。
For hardware-in-the-loop simulation, all the calculation of the step size must be completed within a specified step size, otherwise, the real-time performance of the simulation cannot be guaranteed. For the multi-rate simulation method based on the Norton equivalence, the Norton equivalent circuit parameters of the large-step sub-network and the small-step sub-network are needed when the solution of the interface node voltage is carried out. However, compared with the small-step sub-network, the large-step sub-network has numerous nodes, the calculation amount of the solution process of the Norton equivalent circuit is large, and the solution process is difficult to complete within a small-step delta t time range. Because the large-step sub-network is an alternating-current large power grid and does not pay much attention to the state change moment of the dynamic element, the large-step sub-network can be used for solving the time of the Norton equivalent circuit by delta S in advance so as to ensure the equivalent conductance GsAnd an equivalent current source IssThe calculation of (t) can be done before the calculation of the interface node voltage u (t) so as not to affect the solution of the interface node voltage. For a large-step subnet solution earlier by Δ S, it may be assumed that Δ S is 0.5 Δ T. If G issAnd Iss(t) cannot be completed before the calculation of u (t), Δ S is gradually increased, otherwise Δ S is gradually decreased until an optimal Δ S is found.
FIG. 3 shows the logical relationship between the input and output timing and the calculation task of the multi-rate simulation method based on the Norton equivalent circuit. As can be seen from fig. 3, in a small step Δ t time range, the solution of the norton equivalent circuit of the small-step sub-network, the solution of the interface node voltage, and the solution of the state quantity and the output quantity of the small-step network are completed. The solution of the norton equivalent circuit and the solution of the state quantity and the output quantity of the large-step network are required to be completed within a large-step delta T time range. In each small step Δ t (except for the large step simulation node), the parameters of the norton equivalent circuit of the large step network need to be predicted for solving the interface node voltage.
The present invention is not limited to the above-described embodiments. The foregoing description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention, and the above specific embodiments are merely illustrative and not restrictive. Those skilled in the art can make many changes and modifications to the invention without departing from the spirit and scope of the invention as defined in the appended claims.
(the patent is supported by a 'cultivation plan of scientific research innovation project of Tianjin university research institute' in 2019, the project number is 2019YJSB192, and the project name is flexible direct-current transmission system real-time simulation research based on frequency shift analysis and FRTDS).

Claims (2)

1. A multi-rate real-time simulation method based on Nonton equivalence is used for an alternating current-direct current hybrid power system and is characterized by comprising the following steps:
(1) dividing the whole system into a plurality of subsystems according to different time scales of power equipment in the system, and performing simulation calculation on different subsystems by adopting different step lengths according to the time scales of the power equipment in the subsystems;
(2) performing norton equivalence on the sub-systems after the sub-networks are separated; firstly, each sub-system after being divided into networks is changed into a Norton equivalent circuit, and then the node voltage of the solving interface of each sub-system is solved;
(3) solving state variables inside each subsystem; according to the superposition principle, the state variables of the dynamic elements can be obtained by linear combination of responses generated by the independent action of each power supply on the dynamic elements in the sub-network, and for each subsystem, the state variables of the state elements at the current moment can be expressed as linear combination of the value of the state variable at the previous moment, the value of the independent current source at the current moment and the value of the interface node voltage at the current moment, so that the state variables of the subsystems are respectively solved according to the solved interface node voltage.
2. The multi-rate real-time simulation method based on the norton equivalence of claim 1, wherein norton equivalent circuit parameters of a large-step sub-network and a small-step sub-network are required when solving the interface node voltage; the time for solving the Noton equivalent circuit by the large-step sub-network is advanced so as to ensure that the calculation of the equivalent conductance and the equivalent current source can be completed before the calculation of the interface node voltage, thereby not influencing the solution of the interface node voltage.
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