With the significant progress of the “coal to electricity” project, the electric kiln equipment began to be connected to the distribution network on a large scale, which caused power quality problems such as low voltage, high harmonic distortion rate, and high reactive power loss. This paper proposes a two-stage power grid comprehensive resource optimization configuration model. A multi-objective optimization solution based on the joint simulation platform of Matlab and OpenDSS is developed. The solution aims to control harmonics and optimize reactive power. In the first stage, a multi-objective optimization model is established to minimize the active network loss, voltage deviation, and equipment cost under the constraint conditions of voltage margin, power factor, and reactive power compensation capacity. Furthermore, the first stage uses a particle swarm optimization (PSO) algorithm to optimize the location and capacity of both series and parallel compensation devices in the distribution network. In the second stage, the optimal configuration model of the active power filter assumes the cost of the APF as the objective function and takes the harmonic voltage content rate, the total voltage distortion rate, and the allowable harmonic current as the constraint conditions. The proposed solution eliminates the harmonics by uniformly configuring active filters in the distribution network and centrally control harmonics at the system level. Finally, taking the IEEE33 distribution network as the object and considering the change of electric furnace permeability in the range of 20%–50%, the simulation results show that the proposed algorithm effectively reduces the distribution network’s loss, its harmonic content and significantly improve its voltage.

Due to the rapid economic development and the consumption of conventional energy, environmental pollution, and energy crisis have become problems that cannot be ignored [

The static var compensator’s installation position and installation capacity are generally optimized in the traditional distribution networks. The total voltage deviation, installation capacity, and reactive power loss weighting are converted into a single objective and solved by a particle swarm algorithm to effectively reduce Power loss and reduce voltage deviation to achieve the distribution network’s economical and safe operation [

In the actual operation process, the scale of alternative loads such as electric furnaces and electric heating significantly impact the power supply capacity of the distribution network. However, the existing literature rarely studies the reactive power optimization problem and the harmonic suppression problem after the electric furnace is connected to the distribution network on a large scale. In this context, it is necessary to make proper application planning for the treatment device to solve the power quality problems such as reactive power, high harmonic distortion rate, and low voltage caused by large-scale access to ensure the safe and stable operation of the system and the voltage quality of the user terminal within the standard range.

Reactive power compensation management devices are divided into parallel compensation and series compensation. Parallel compensation is connected to a compensation capacitor on the feeder, reducing the inductive reactive power flow on the user side, reducing line loss, and reducing voltage drop. However, the reactive power provided by it is proportional to the square of the voltage. When it increases significantly, the line voltage is too low to achieve the control effect [

There are two main aspects of harmonic control. On the one hand, the harmonic source itself is restricted. On the other hand, passive power filters (PPF) or active power filters (APF) are installed in the power grid to achieve harmonic suppression such that the harmonic meet the national standard [

In the context of the large-scale application of electric kilns, this paper proposes a two-stage power grid comprehensive resource optimization model considering reactive power optimization and harmonic control. In the first stage, an optimization model was established from the three aspects of investment, network loss, and voltage deviation to evaluate the impact of the electric furnace on the system after being connected to the distribution network. Moreover, the first stage use particle swarm optimization (PSO) algorithm to optimize the location and capacity of series compensation device and parallel compensation device in the distribution network. In the second stage, through the unified configuration of active filters in the distribution network to eliminate harmonics. Harmonics are managed in a centralized and unified manner at the system level. By establishing the comprehensive resource optimal allocation model of the power grid, the treatment equipment was rationally planned, which solved the power quality problem after the large-scale application of electric kilns and provided a specific theoretical basis for the “coal-to-electricity” supporting power grid renovation project.

The equivalent model of the distribution network includes the electric furnace load, compensation device, and the upper-level grid system. The power quality impact of electric kiln load mainly includes reactive power and voltage drop.

Among them, the influence of reactive power mainly has the following three aspects: 1) When the reactive power consumed by the electric furnace increases, the power factor of the distribution network will decrease. 2) When the electric furnace load is connected to the power grid on a large scale, it consumes a large amount of reactive power, causing a significant line voltage drop, making the line terminal voltage too low, causing the electric furnace equipment to fail to start. 3) Distribution transformers and power supply lines are designed and operated based on a certain rated current. When electric kilns are connected on a large scale, a large amount of reactive power will be consumed. When the transmitted reactive power is considerable, the distribution transformer will be affected. The ability to transmit active power with the power supply line causes a decrease in power transmission efficiency and decreased capacity utilization rate of power supply equipment. Reactive current is transmitted in distribution transformers and power supply lines, resulting in additional active losses in the equivalent resistance of power distribution and power supply lines, affecting the economic operation of the distribution network.

Permeability index is used to express the large-scale access of electric furnace load. The penetration rate of electric kiln equipment, as expressed in _{ERH} is the total power of the electric kiln equipment in stable operation (kW); _{T} is the total power on the low-voltage side of the distribution transformer (kW); _{LV} is the general load of the low-voltage distribution network Total power (kW).

This paper adopts the method of installing reactive power compensation at the PQ node of the system or between the two branches to compensate the electric kiln large-scale access to the distribution network, considering the smallest investment in reactive power compensation devices, the slightest voltage deviation. The minimum network loss is used as three objective functions to optimize the system with multi-objective reactive power. Considering that the unit resistance value of the line is much greater than the unit reactance value, the calculation of the network loss of the distribution network is to calculate the resistance loss on the line [

where: _{invest} and _{cap} is the total investment of reactive power compensation device and the investment of unit capacity; _{i} is the reactive power connected at the node _{i}, _{ref}, Δ_{b} is the number of branches of the system; _{i} the resistance of branch _{i}, _{i}, _{loss} are the active power, reactive power of branch

The constraint conditions of reactive power optimization control variables need to meet the node active and reactive power balance constraints, as shown in

where: _{Gi} _{Li} are the generator active power and active load of node _{Gi} _{Ci} _{Li} are the generator reactive power, reactive power load and reactive power compensation capacity of node _{i} _{j} are nodes respectively the voltage of _{ij} _{ij} _{ij}—nodes

Inequality constraints are divided into control variable constraints and state variable constraints. This paper selects generator node voltage and reactive power compensation device capacity as control variable constraints. It selects load node voltage and distribution network power factor as state variable constraints, as shown in

where: _{Gi} _{Gimin} _{Gimax} are the breakpoint voltage of generator node _{Ci} _{Cimin} _{Cimax} are the reactive power compensation capacity and its lower limit and upper limit respectively; _{Li} _{Limin} _{Limax} are the voltage of load node _{G} _{C} _{L} are the number of generator nodes in the grid, the number of reactive power compensation nodes, and the number of

Due to the different dimensions and units of voltage deviation, active power loss, and investment cost, it is impossible to connect with weights. It is necessary to normalize the weights first to obtain the minimum value of the objective function (Cost-based quantitative target). The normalization process is shown in _{de},Δ_{loss} and Δ_{invest} are the voltage deviation, active loss, and equipment investment before adding series compensation and parallel compensation, Δ_{max}, Δ_{min}, _{max}, _{min}, _{max}, and _{min} are the maximum and minimum voltage deviation, active loss, and equipment investment, respectively.

The weight is directly given by the expert decision method, namely the Delphi method. Applying the traditional analytic hierarchy process to obtain the weight is shown in

First of all, the voltage quality should be met. Therefore, the voltage deviation is a crucial evaluation standard for the planning of reactive power compensation devices, so it is regarded as the first level; because the network loss cost value is relatively small, as the second level, it meets the voltage requirements and network loss requirements After that, a certain degree of the economy needs to be considered, that is, the fixed investment cost in the power company investment expense, as the third level. According to expert experience to judge the importance of each target, the index judgment matrix J is a 3 * 3 matrix:

According to the expert experience calculated in flow chart 3, the weight W of the first-level index is calculated as:

The essence of APF is a controlled current source with current feedback control [_{ref} and output impedance _{1}, and the grid part is composed of grid voltage _{E}.

Assuming that the active filter only absorbs part of the harmonic current of this node in a particular proportion [_{h} represent the coefficient of the active filter absorbing the _{Ah} and the harmonic current injected by the harmonic source _{h} is shown below:

The optimized configuration of the filter means that after the filter is installed, the harmonic content rate (_{THD}), and allowable value of each harmonic current of each node of the network meet the requirements of the national standard. The optimization result minimizes the initial investment of the filter and achieves the maximum economic benefit while ensuring the safe operation of the filter.

The optimal configuration model takes the cost of the active power filter installed on the low-voltage side of the transformer in the distribution network as the objective function and takes the allowable value of the harmonic current injected into the common connection point, the distortion rate, and the content rate of the harmonic voltage as constraints.

The objective function is as follows:

where: _{0} and _{1} are the base price of the active filter of 400,000 yuan and the coefficient between the capacity and the cost of 450,000/MVA.

where: _{h} is the _{h} is the effective value of the _{1} is the effective value of the fundamental voltage, _{THD} is the total distortion rate of the harmonic voltage, _{Bh} and _{h0} are the harmonic current injected into the common connection point and the allowable value of the harmonic current.

According to the national standard [

3 | 5 | 7 | 9 | 11 | 13 | |
---|---|---|---|---|---|---|

_{h}/A |
20 | 20 | 15 | 6.8 | 9.3 | 7.9 |

To optimize the overall resource configuration of the power grid after the large-scale electric furnace is connected to the distribution network, it is necessary to effectively solve the multi-objective reactive power optimization model and the filter optimization configuration model. This paper builds a computing platform shown in

The entire calculation platform mainly includes three calculation modules: (1) the three-phase power flow calculation module of the distribution network, (2) distribution network harmonic calculation module, (3) comprehensive resource optimization configuration module. OpenDSS is used for three-phase power flow calculation and harmonic calculation of distribution network [

Set up the OpenDSS/MATLAB joint simulation platform: Firstly, build a district distribution network model on the OpenDSS software and perform fast power flow calculations and harmonic calculations. Secondly, complete the establishment of the governance device model and parameter settings in MATLAB and the above-established improved particle swarm optimization algorithm. The two software exchange information through the COM interface [

In this paper, the overall flow chart of the establishment and solution of the comprehensive resource optimal allocation model of the distribution network after the large-scale application of electric kilns is shown in

(1) Build the IEEE33-node distribution network model after the large-scale access of electric kilns in OpenDSS and set network operating parameters and harmonic source spectrum parameters for fast power flow calculation. Realize data transmission between node voltage, power factor, and active power in OpenDSS and MATLAB through a COM interface.

(2) In the first stage of optimization, a multi-objective reactive power optimization model is constructed in MATLAB. Use particle swarm algorithm to find the optimal installation position and compensation capacity of parallel and series reactive power compensation devices.

(3) Analyze the harmonics of the distribution network and realize the data transmission of each node’s harmonic components in OpenDSS and MATLAB through the COM interface.

(4) In the second stage of optimization, the active filter optimal configuration model is constructed in MATLAB. The particle swarm algorithm is used to find the optimal compensation capacity of APF.

(5) Output the optimization results of the first stage and the second stage.

The installation location and capacity of the optimized management device after the electric kiln scale is connected with the IEEE33 node network as the prototype, the IEEE33 distribution network node diagram is shown in

Start the penetration rate of the electric furnace from 20% and gradually increase to 30%, 40%, and 50%. When the distribution network is connected to electric kiln loads with different penetration rates, the distribution network is optimized for reactive power optimization and harmonic control in a two-stage grid comprehensive resource optimization configuration.

Serial number | Permeability/% | Load/kW |
---|---|---|

1 | 20 | 926 |

2 | 30 | 1592 |

3 | 40 | 2476 |

4 | 50 | 3715 |

To study the reactive power optimization configuration of the distribution network after the large-scale connection of electric kilns, several electric kiln equipment with a power factor of 0.8 and a load capacity of 25 + j20kVA were connected in the station area. The penetration rate of the electric furnace load of the distribution network is 20%, 30%, 40%, and 50%, respectively. After being connected in the four scenarios, the operation of the electric furnace is studied. The reactive power compensation optimization calculation is carried out using a series and parallel reactive power compensation devices. The reactive power compensation response strategy under the large-scale application of electric kilns is proposed. The installation position and capacity of the optimized reactive power compensation device and the comparison of the distribution network situation before and after optimization are shown in

(1) With the gradual increase in the penetration rate of electric kilns, due to insufficient reactive power in the system, to further increase the distribution network’s voltage level and reduce network losses, it is necessary to allocate reactive resources and optimize reactive power rationally. Simple parallel compensation can solve the reactive power problem in the low-permeability scenario. However, as the penetration rate increases, the simple parallel reactive power optimization is not enough to solve the reactive power problem. The combination of series compensation and parallel compensation is used to install two fixed series reactive power compensation devices and three parallel reactive power compensation devices in the distribution network, which can quickly and improve the distribution. The voltage level of the grid.

(2) The reactive power compensation device is optimized in four scenarios where the electric furnace load penetration rate is 20%, 30%, 40%, and 50%. Due to the relatively abundant reactive power resources of the system, the minimum node voltage of each node before and after optimization increased from 0.8739 p.u., 0.8159 p.u., 0.7366 p.u. and 0.5497 p.u. to 0.9552 p.u., 0.9857 p.u., 0.9853 p.u. and 0.9346 p.u. The minimum node voltage is greater than 0.93 pu. The voltage qualification rate is significantly improved, and the power factor can reach 0.95 or more after compensation, which significantly improves the quality of power supply for users.

(3) After optimized calculation, the reactive power compensation capacity and supplementary points of the network line are increased, which reduces the active power loss of the entire line, saves economic expenditures, and increases the economic benefits of the enterprise.

Permeability | Method | Position | Capacity |
---|---|---|---|

20% | Parallel | 15 | 1090kVar |

Parallel | 17 | 1083kVar | |

Parallel | 23 | 479kVar | |

Parallel | 30 | 265kVar | |

Parallel | 32 | 835kVar | |

30% | Tandem | 1-2 | 0.0501Ω |

Tandem | 9-10 | 0.0208Ω | |

Parallel | 2 | 1200kVar | |

Parallel | 16 | 720kVar | |

Parallel | 5 | 1200kVar | |

40% | Tandem | 4-5 | 0.0500Ω |

Tandem | 27-28 | 0.0201Ω | |

Parallel | 1 | 1500kVar | |

Parallel | 4 | 300kVar | |

Parallel | 30 | 1400kVar | |

50% | Tandem | 6–7 | 0.0503Ω |

Tandem | 25-26 | 0.0500Ω | |

Parallel | 15 | 300kVar | |

Parallel | 19 | 1500kVar | |

Parallel | 3 | 1500kVar |

Permeability | Optimization | Minimum voltage/p.u. | Power factor | Active loss/kW |
---|---|---|---|---|

20% | Before | 0.8739 | 0.8388 | 471.1655 |

After | 0.9552 | 0.9924 | 424.8412 | |

30% | Before | 0.8159 | 0.7804 | 846.3367 |

After | 0.9857 | 0.9896 | 508.3264 | |

40% | Before | 0.7366 | 0.7409 | 1464.8382 |

After | 0.9853 | 0.9651 | 808.0419 | |

50% | Before | 0.5497 | 0.6920 | 3367.5429 |

After | 0.9346 | 0.9558 | 1504.2138 |

The calculation example continues to use the IEEE33 node power distribution system, the system reference voltage is 10.5 kV, and the reference capacity is 10MVA. The harmonic control of the large-scale application of the harmonic source electric kiln mainly considers four application scenarios with a penetration rate of 20%–50%. The harmonic currents of the common connection points are shown in

Permeability | Harmonic current/A | ||||||
---|---|---|---|---|---|---|---|

3 | 5 | 7 | 9 | 11 | 13 | ||

20% | Amplitude | 48.14 | 49.78 | 48.12 | 17.78 | 12.75 | 6.48 |

Angle | −121.70 | 113.10 | 40.82 | −8.90 | −116.15 | −167.73 | |

30% | Amplitude | 97.49 | 82.14 | 71.75 | 33.89 | 12.87 | 6.15 |

Angle | −120.40 | 134.42 | 55.76 | −5.27 | −114.79 | 160.33 | |

40% | Amplitude | 145.16 | 117.71 | 96.57 | 49.47 | 12.95 | 7.67 |

Angle | −119.80 | 143.28 | 63.24 | −3.50 | −113.50 | 134.69 | |

50% | Amplitude | 207.85 | 166.42 | 130.33 | 69.94 | 12.98 | 11.14 |

Angle | −119.26 | 149.35 | 69.02 | −1.87 | −111.99 | 116.82 |

The optimized configuration of active filters is carried out on the IEEE33 distribution network connected to electric furnaces on a large scale. The optimal configuration of active filters is shown in

Permeability | The active filter absorption coefficient of harmonic current | S/MVA | |||||
---|---|---|---|---|---|---|---|

20% | 0.6203 | 0.6921 | 0.6142 | 0.6432 | 0.8803 | 0.6879 | 1.0343 |

30% | 0.6782 | 0.6283 | 0.8175 | 0.9356 | 0.8996 | 0.6555 | 1.8733 |

40% | 0.7114 | 0.6630 | 0.6568 | 0.9838 | 0.9736 | 0.7569 | 2.6231 |

50% | 0.6615 | 0.8603 | 0.6014 | 0.8554 | 0.6626 | 0.6305 | 3.8971 |

After optimizing the active filter configuration in the distribution network, the total harmonic voltage distortion rate of the distribution network for each scenario under different penetration rates is 0.42%, 0.64%, 0.89%, and 1.23%, which are all dropped to within 4%. The harmonic currents of the common connection points are all less than the allowable value of the harmonic current specified in the national standard, which improves the operating conditions of the system.

This paper studies a two-stage power grid comprehensive resource optimization model after the large-scale integration of electric kiln equipment, considering reactive power optimization and harmonic control. The paper proposes a multi-objective optimization algorithm based on the joint simulation platform of Matlab and OpenDSS. It solves low voltage, harmonics, and high reactive power loss in the distribution network after the large-scale electric furnace is connected to the distribution network. Details of the algorithm are as follows:

(1) At a penetration rate of 20%, install a parallel capacitive reactive power compensation device. The optimization result is that it is close to the side with a heavier load to better control the effect. However, the voltage deviation phenomenon is caused by the distribution network’s high penetration rate. The improvement is not apparent, and the desired governance effect cannot be achieved well;

(2) For distribution networks with 30%, 40%, and 50% permeability, the combination of series compensation and parallel compensation is adopted. The treatment effect is noticeable, and it can ensure the low voltage problem in the case of the high permeability of electric kilns. Improve, reduce active power loss simultaneously, and improve the economy of distribution network operation.

(3) The optimized configuration of active filters was carried out for the four scenarios after the large-scale application of electric kilns, which suppressed the voltage distortion rate, improved the power supply quality of the distribution network, and achieved good economic results.