Modelling and Simulation Analysis of Power Flow Router in Energy Internet

With a large number of distributed generation (DG) and controllable load connected to the power grid under the background of energy Internet development, the security and stability of the grid are challenged. Power flow control has become a problem of the operation of the power grid. Power flow router (PFR) has become an important element of energy Internet. It is an effective way to realize the power flow control of active distribution network when abundant distributed resources are connected to the grid. In this paper, the steady-state and dynamic operation characteristics of PFR are studied, and the corresponding mathematical model is established. The effect of PFR on optimizing the power flow and improving the dynamic characteristics of distribution network is analysed by the 14-node distribution network case simulating.

network PFR is presented in [7], which has three ports: high-voltage AC port, low-voltage AC port and lowvoltage DC port. In [8] and [9], a Y-type PFR based on three port isolated DC / DC converter is proposed, which uses phase-shifting technology to control the power flow in open-loop, but lacks certain generality. In [10], energy routers are classified, and a hierarchical and partitioned optimization strategy for energy Internet based on PFR is proposed. In the bottom layer, a distributed local optimization strategy is implemented with the lowest generation cost as the goal. In the upper layer, the routing and trading center adopts the transaction optimization strategy based on graph theory, and selects the lowest network loss path without blocking through PFR for power transmission to maximize benefits and congestion management. In [11] and [12], a PFR topology based on power electronic architecture is proposed, and a PFR topology applied to AC-DC hybrid microgrid is proposed in [13]. The relationship between the current effective value and the system on-state loss in the traditional phaseshift modulation mode of DC distribution network is quantitatively analysed, and the system optimal control strategy based on triangular wave current modulation is proposed. A PFR model with virtual inertia is proposed in [14], which makes the PFR not only have the characteristics of inertia and damping, but also can be applied to the constant power load of DC converter, and enhance the stability of power grid. In [15], sensitivity is integrated into optimal power flow (OPF) to increase the correction control of PFR, but the calculation is complex and the reactive power is not considered. In [16], the power flow model of PFR with the characteristics of "branch port voltage" is established, which only involves the branch power flow modelling and does not refer to the local injection power flow modelling.
In the above references, the topological structure and model of PFR are different, but the function description of the PFR in the power system is similar, that is, the network power flow hub integrating multiple system regulation and protection functions. In this paper, based on the above existing research on PFR, the steady-state and dynamic operation characteristics of PFR are studied, and the corresponding mathematical model is established. Then, the effect of PFR on optimizing the power flow and improving the dynamic characteristics of distribution network is analysed by the case simulating.

Modelling of PFR
The architecture of PFR is shown in Figure 1, in which all the incoming and outgoing lines are connected with the common bus through the line power flow controller (PFC), and each PFC automatically controls the corresponding line power flow. In addition, some DC or frequency conversion equipment are connected to the common bus through voltage source converter (VSC). VSC controls the output and terminal voltage of corresponding equipment, and it is also part of PFR. The equivalent circuit of PFC is shown in Figure 2. PFC is installed on the line connecting bus i and j, and has three control parameters: the voltage amplitude V S and phase angle ϕ S at the series side and the current amplitude Iq at the parallel side, which is orthogonal to bus voltage V i . According to the equivalent circuit and vector relationship, the basic mathematical relationship is as follows: The VSC model is shown in Figure 3. The AC-DC-AC conversion is realized by VSC1 and VSC2. If the bus voltage V i is given, the voltage phase and amplitude of V ik can be adjusted in a certain range based on the common DC bus, so as to control the line power flow.
Where, M 1 and M 2 are the modulation ratios of VSC1 and VSC2 respectively, and α 1 and α 2 are the phase shift angles of VSC1 and VSC2 respectively.
From the above equivalent models, in the aspect of power flow control, the PFC and VSC can be regarded as phase-shifting transformers with controllable parameters. In addition, PFR may also include solid-state transformers and various FACTS. Therefore, PFR can be equivalent to a combination of phase-shifting transformers, series voltage sources and parallel reactive power compensation.

Steady-state model of PFR
The steady-state model of PFR is mainly used to solve the optimal power flow (OPF). The OPF is to find the optimal solution (system generator output, voltage amplitude and phase angle) to meet the system constraints (voltage constraints, power flow constraints, output constraints). The objective function can be composed of generation cost, network loss, transmission capacity and other indicators. Taking minimization of network loss as an example, the OPF model is as follows: ( cos sin ) 0 ( 1,..., ) ( 1,..., ) Where, P is the active power, Q is the reactive power, V is the voltage amplitude, θ is the voltage phase angle, G is the line conductance, B is the line susceptance, and t is the non-standard transformation ratio. The subscript i represents the ith node, ij represents the line between node i and node j, s represents the input, d represents the output, and b represents the PCC point where the regional energy system connects to the superior power grid.
If PFR is considered, t is regarded as a complex variable, , the G and B are variables of τ and σ. We can rewrite (3) as the following partial differential equation: Where, ∆f is the difference between the objective function value and the upper limit value.
(5) is introduced into the nonlinear indeterminate equations of augmented constrained power flow as shown in (6). By using Newton Raphson method to solve (6), the optimal power flow with PFR can be obtained.
Where, α, β, δ are the auxiliary decision variables of V, P and Q respectively, and y b is the auxiliary variable that transforms the objective function into the equation form.

Dynamic model of PFR
PFR is mainly used in power flow and voltage control, and stability control is its auxiliary function. In order to give full play to the role of PFR in enhancing system damping, stabilizing system oscillation and enhancing system reliability, it is necessary to study the impact of adding PFR device on system transient performance. Based on the steady-state power flow control, the control strategy of PFR in the transient process is formulated by using the characteristics of PFR to quickly adjust the active and reactive power of the transmission line.
According to the structure and working principle of PFR, the transient stability model of PFR is shown in Figure 4. This model includes power control, fault crossing control and line interface. Among them, the power control link controls the transmissing active and reactive power of the line when the system is in normal operation. The fault crossing control link is the control logic when the system is subject to fault or large disturbance. The line interface takes PFR as the controlled current source and injects the calculated current into the line. The power control model and the fault crossing control model are shown in Figure 5 and Figure 6 respectively.  Where, T m is the measuring time constant. I max , I min are maximum and minimum output current of converter respectively. K p , T p are the scale factor and the integral time constant of active power control under normal working conditions. K q , T q are the scale factor and the integral time constant of reactive power control under normal working conditions. U n is the rated voltage of PFR. K q_h and K q_l are high voltage and low voltage forced reactive compensation coefficient respectively. K pp is the change rate of active current recovery.

Case study
In order to verify the above models, the IEEE standard 5 machine 14 node calculation example system is used, and the model structure is shown in Figure 7. The example system has 5 generator nodes, among which G1 is the balance node, G2, G3, G4 and G5 are PV nodes, and the other 9 nodes are PQ nodes. The system consists of 20 branches, including 3 transformer branches. The node parameters and branch parameters of the example system are shown in Table 1 and Table 2.

Steady state simulation analysis
In the example system, PFR is installed on the central node B2 of 220kV grid and the central node B13 of 110kV grid. The optimal power flow of the whole grid is solved, and the optimization objective is to minimize the network loss of the whole grid, that is, to minimize the output of the balance node G1. The comparison of calculation results is shown in Table 3.   The results show that the network loss of the optimal power flow can be reduced by 3.2% compared with that of the conventional power flow. When PFR is installed in the system, the network loss can be further reduced, which is 9.21% lower than the optimal power flow without PFR, i.e., the installed PFR has an obvious effect on the optimal power flow of the system.

Transient simulation analysis
Transient simulation analysis focuses on the influence of PFR on the transient stability limit of power system. In the calculation, the dynamic model parameters of the generator, load and other equipment are selected from the dynamic model parameters of the same capacity equipment in the actual system, and the electromechanical transient simulation is used. The simulation step length is 0.01s, and the calculation time is 20s. The triggering fault of transient stability limit calculation is the N-1 fault of interconnection line of the section between the external grid and the regional system, and the time of fault occurrence is 1s.
The comparison of transient stability limit calculation results is shown in Table 4. Compared with the system without PFR, when PFR is installed in B2, the system load can be increased by 17.6MW, and the transient stability limit of section power can be increased by 20.2MW. When PFR is installed in B2 and B13, the system load can be increased by 39.5MW, and the transient stability limit of section power can be increased by 46.4MW. It can be seen that the installation of PFR has a significant effect on improving the load capacity and transient stability limit of the system. Based on the limit power flow mode of the system without PFR, the transient stability of the system before and after PFR installation is compared, and the simulation results are shown in Figure 8. It can be seen from the simulation results that when the system is installed with PFR, the power angle stability and voltage stability of the system are significantly improved when N-1 fault occurs in the section connecting line, which is the dual effect that PFR can adjust the active and reactive power injection of the line at the same time. The transmission power deviation of the section connecting line is significantly reduced compared with that without PFR, so the stability of the system operation is improved.

Conclusions
Power flow router (PFR) has become an important element of energy Internet. It can solve the problem of power flow control when a large number of distributed generations and controllable loads are connected into the grid. In this paper, the structure and operation principle of PFR including the line power flow controller and the voltage source converter are studied, the steady-state model of PFR based on the generalized inverse matrix method for solving OPF is established, and the transient characteristics of PFR are studied. Based on the idea of modular modelling, the general transient model of PFR is established, including power control part, fault crossing control part and line interface part.
The PFR model proposed in this paper provides an effective method for power system simulation analysis with PFR. Next, further research work will be carried out in the aspects of model improvement and actual power grid analysis, and the development of the PFR prototype will be guided.