In order to minimize the harmonic distortion rate of the current at the common coupling point, this paper proposes a coordinated allocation strategy of harmonic compensation capacity considering the performance of active power filters (APF). On the premise of proportional distribution of harmonic compensation capacity, the harmonic compensation rate of each APF is considered, and the harmonic current value of each APF to be compensated is obtained. At the same time, the communication topology is introduced. Each APF takes into account the compensation ability of other APFs. Finally, three APFs with different capacity and performance are configured at the harmonic source to suppress the same harmonic source, and the harmonic distortion rate is reduced to 1.73%. The simulation results show that the strategy can effectively improve the compensation capability of the multiple APF cascaded system to the power grid without increasing the installed capacity.

With the grid connection of a large number of distributed new energy sources and the development and application of power electronic equipment, the power quality of the power grid has declined, and the harmonic pollution has become increasingly serious [

In order to minimize the harmonic distortion rate, how to control multiple APFs cooperatively and realize the accurate compensation of power grid harmonics is also the key technology. In [

This paper presents a capacity allocation strategy considering the performance of each APF in the system (In this paper, the compensation rate is used to reflect the performance of APF). The command current takes into account the performance of each APF based on the capacity proportion. It realizes that when harmonic compensation is made to the power grid, the APF output with better performance is also more. At the same time, the communication topology is used to introduce the performance weight factor the system can adjust the weight of the performance distribution to occupy the command current, so that the system can get lower harmonic distortion rate after compensation. This method is suitable for networks with various nonlinear loads. Finally, three different APF are used to compensate the PCC. The results of the example verify the effectiveness of the proposed scheme, find out the optimal instruction current distribution, while meeting the requirements of network access, it can also reduce the installation capacity of the combined APF, and make APF have better economic and compensation capability.

The basic topology of modular multi APF is shown in _{s} is power grid voltage, U_{DC} is DC capacitor voltage at DC side of APF, _{s} and _{i} are internal inductance of power supply and equivalent inductance of APF respectively, _{i} is equivalent resistance value of APF, _{ci} and _{L} are actual compensation current of APF and actual current of nonlinear load respectively, _{refi} is the instruction current of the

The upper controller firstly detects and decomposes the _{L}, then gets the magnitude of the harmonic current _{ref} to be compensated. Finally, the harmonic current size to be compensated by each APF is allocated reasonably through the instruction allocation strategy, so as to realize the optimal compensation of the harmonic of the power grid by multiple APF. The optimization strategy also needs to consider the specific parameters of a single APF. The basic structure of the single APF is shown in

According to the relation between Kirchhoff law and the circuit structure in

where,

_{cj}—the output current of

_{cj}—the output voltage of

_{sj}—the

The Laplace transform of a phase is used to obtain the following results:

After _{ca} and (_{sa} − _{ca}) is as follows:

Obviously, the system can be treated as a first-order system. Assuming that the DC side voltage _{dc} of APF is constant during the sampling period, it can be treated as a step signal. In

In addition, it can be obtained from _{ca}

In the communication network, the network topology can be modeled by an undirected weighted graph _{1}, _{2},…, _{n}} is a non-empty finite set used to determine nodes, _{ij}]_{nxn} is a weighted adjacency matrix and matrix composed of non-negative adjacency elements _{ij}. Node index belongs to finite set _{i} represents the _{ij} = (_{i}, _{j}), and the adjacent elements associated with the graph are positive, that is, if and only if _{ij} > 0, _{ij} ∈ _{ij} = 0, if two different nodes of the graph can be connected along the edge of the graph, the graph is called undirected. The Laplacian matrix _{ij}]_{mxm} of a graph is defined by the following

For the cascade operation of multiple APFs, a two-way communication channel is established between the APF and the central controller through centralized control. The central controller first collects the information of the lower controlled object APF, so as to obtain the global information, and uses it to switch the APF and allocate the compensation capacity to realize the optimal coordinated control of the APF. Due to the real-time requirement of APF, the actual output of compensation capacity is realized by the controller of APF.

In order to make good use of the capacity of APF for harmonic current distribution, Yang et al. [_{refp} of each APF can be calculated by

_{Jp} is the capacity proportional distribution coefficient of the

where

From the above analysis, the capacity allocation principle is based on the capacity of each APF participating in the compensation. The compensation capacity is allocated according to the proportion. At the same time, the cut-off current limiting method is used to control the switching and joint operation of APF. The capacity allocation of APF is carried out through

This paper considers the capacity of each APF and the performance of each APF when designing the algorithm. The performance here is mainly reflected in the harmonic compensation rate

where,

_{ref}—the root means square value of ideal command current input to APF.

_{c}—the difference between the actual root means square value of current output from APF and _{ref}.

The allocation of APF cooperative instruction current is to minimize the total harmonic distortion rate when the whole harmonic compensation system is running under a series of operation constraints. Because the algorithm needs to rely on the communication of neighbor nodes when using, the communication topology in this system is assumed to be a connected undirected graph. The capacity compensation allocation considering APF performance is proposed in this paper The basic form of strategy is as follows:

where,

_{refp}, _{Xp} is the performance distribution coefficient of the

where,

Because the communication topology is connected undirected graph introduced in the improved algorithm, the Laplacian matrix ^{T}

Therefore, the sum of the performance compensation part in the formula is ultimately 0, that is, in the process of joint operation of multiple APFs, while improving the performance utilization of each APF, the relationship between the input and output of the whole APF system will not be broken. According to cooperative control theory [

In practice, when the nonlinear load increases, or some types of faults occur in the common coupling point, the strong pulse current caused by these faults will be included in the instruction current, which will lead to the over-current fault of APF. In this paper, the truncated current limiting control strategy is adopted, so the truncated current limiting factor _{p} is introduced:

where,

_{p}—represents the current limiting factor of the

The final allocation strategy of APF capacity compensation can be obtained as follows:

where,

where

In

In order to verify the effectiveness and feasibility of the command power distribution strategy considering APF performance mentioned in this paper, the three-phase two-level active power filter is used for research. The model based on

Parameter | Numerical value |
---|---|

Grid voltage/V, Frequency/Hz | 380 V, 50 Hz |

Harmonic source load R/Ω, L/mH | 15 Ω, 2 mH |

Capacity of the first APF/A | 35 A |

Compensation rate of the first APF/% | 92.1% |

Capacity of the second APF/A | 50 A |

Compensation rate of the second APF/% | 84.3% |

Capacity of the third APF/A | 75 A |

Compensation rate of the third APF/% | 81.7% |

The first APF is used for harmonic compensation at PCC, starting at 0.04 s. The simulation waveform is shown in

It can be seen from

It can be seen from

As can be seen from

Therefore, the capacity allocation strategy of APF is improved by the method proposed in this paper. The communication connection is established for three APFs. The corresponding Laplace matrix

Let

As can be seen from

In order to judge the following situation of the improved strategy, continue to compare the total output compensation harmonic current of the combined APF with the theoretical total output harmonic current, as shown in

The capacity compensation capacity can be expanded by using multiple APF cascades, and the capacity can be allocated to each APF which is involved in harmonic compensation. The capacity coordination allocation compensation scheme considering the performance of APF is proposed in this paper. The performance of each APF is considered while the capacity proportion compensation is considered. The feasibility of the scheme is confirmed by stability analysis and simulation results analysis Sex. The simulation results show that the compensation capacity of cascade APF is improved without changing the installation capacity.