Research on power grid energy saving and loss reduction control methods under the harmonic influence

To reduce energy consumption and power grid operation costs, a control method that considers the influence of harmonics is proposed for power grid energy saving and loss reduction. The zip load model is utilized to build the power grid load model, and voltage characteristic curves are obtained under different parameters to calculate network loss. Furthermore, the voltage RMS and total harmonic distortion of nodes are calculated under varying load levels. Ultimately, a control objective function is established to achieve power grid energy saving and loss reduction. Experimental results indicate that this method outperforms traditional methods in terms of voltage response effect and achieves a more extensive reduction range of network loss, with a maximum reduction exceeding 35%.


Introduction
The use of a variable capacitor is common in supplementing the inductive load within the distribution network.Specifically, when the voltage and current in the power grid are sinusoidal, this capacitor has a compensation effect [1].However, in recent years, some non-linear electrical equipment such as thyristor rectifiers, frequency converters, and energy-saving lighting lamps in the power grid has been used frequently, resulting in the gradual aggravation of harmonic pollution in the power grid.Under the influence of harmonics, it is easy to cause damage to capacitors and aggravation of harmonic pollution [2].
In [3], a control method was proposed for energy conservation and loss reduction in distribution networks that uses on-load voltage regulation and capacity regulation distribution transformers.This method involves calculating the load characteristics of the distribution network and the active power loss through an equivalent circuit.An optimization model is then constructed to minimize network loss, serving as the objective function for power grid energy saving and loss reduction.Finally, a coevolutionary algorithm is utilized to generate the control scheme for energy savings.However, it is worth noting that the loss reduction range of this method is relatively low.In [4], a geographically dispersed control method was proposed for energy conservation and loss reduction in distribution networks.This approach replaces power transfer with grid load transfer and aims to minimize network loss by distributing the operating load of the grid.The working state of the power grid is defined, and the power grid load model is constructed based on the operational data.The particle swarm optimization (PSO) algorithm is utilized to solve the model and achieve power grid energy conservation and loss reduction control.However, effectively controlling voltage response in the presence of harmonic interference still poses a challenge.
In light of the limitations of the previous approaches and the impact of harmonic interference, this paper introduces a new control method for power grid energy conservation and loss reduction.

Voltage sensitivity analysis
The power flow of the power grid is determined by neglecting the impact of voltage on the load power, and the voltage characteristics are calculated using the zip load model under the load power of the grid.The grid load model is expressed as: In Formula (1), 0 P represents the active power under load, U represents the terminal node voltage, 0 Q represents the reactive power under load, N U represents the rated voltage of the power grid, and a , b , and c represent the load proportion of the power grid [5].
The relationship between voltage sensitivity and load power can be obtained through calculation by utilizing the load model expression presented in Formula (1): From Formula (2), it can be seen that the power load of the power grid is not affected by the voltage, and the rated power and current load are the main factors affecting the voltage sensitivity.
The voltage characteristics of the power grid can vary due to changes in different influencing factors during the operation of the distribution network.The voltage characteristic curve shown in Figure 1 demonstrates that the load within the distribution system follows a ZIP load model.Therefore, an expression can be constructed for calculating grid loss: In Formula (3), R jX  represents the line impedance [6].

Control implementation process
To achieve power grid energy conservation and loss reduction in the presence of harmonics, the objective function is to minimize the total amount of electric energy consumption and configuration cost.Therefore, the objective function can be expressed as follows: min ( , ) ( , 0) The constraint conditions of the objective function are the power flow balance equation, point voltage, and grid capacity.The expression of the constraint conditions is: .
In the above formula, z represents the total amount of electric energy consumption, e  represents the configuration cost, t n is the level of load, i t is the action time, c n represents the number of configurable capacitors of the power grid, ( ,0) Based on the above calculation results, the voltage effective value of the node i is calculated considering the capacitance of different load levels: Where, The calculation formula of the voltage total harmonic distortion rate of the node i is: When conducting calculations, it is necessary to consider the impact of harmonic power flow.This involves taking into account the proportion of nonlinear load in the total load during the calculation process.The following formula can be utilized to calculate the harmonic current: * 1 , 1, 2,..., ; 2,..., In Formula (8), i C represents the load ratio and j represents the constant coefficient.The calculated harmonic current is substituted into the harmonic formula to construct the calculation expression of harmonic voltage at node i : Where, n Y represents the harmonic matrix.To achieve power grid energy conservation and loss reduction by minimizing network loss, load power cost, and voltage regulation cost, a control function is established:

Experimental preparation
The capacity benchmark of the power grid used in this experiment is 1110 MVꞏA. the distribution of power grid capacitance is shown in Figure 2.

Figure 2. Distribution diagram of grid capacitance
To ensure comprehensive testing of this method's resistance to harmonic interference, experimental conditions involving harmonic interference are established before testing.Based on the power grid's capacitance distribution outlined in Table 2, a 5-second duration is set for the harmonic interference, allowing for verification of the energy-saving and loss-reduction effects of this method under such conditions.

Comparison of relevant data before and after loss reduction
To confirm the effectiveness of this method in reducing energy loss, a comparison is made between the relevant network loss data before and after the implementation of the loss reduction measures.The results of this comparison are presented in Table 1.
Table 1  In Table 1, after controlling the method in this article, various data of the power grid have changed to a certain extent, to which the maximum value of voltage distortion rate has decreased most significantly except that the net loss has decreased significantly.Therefore, this method can effectively control many parameters of the power grid under the influence of harmonics and improve the operational performance of the power grid.

Voltage response before and after loss reduction
Therefore, the reactive load is added when the power grid is running for 0.4 s, and the reactive load is stopped when the power grid is running for 0.8 s.In this process, the power grid response results under the loss reduction control of this method are verified.The voltage response comparison results before and after loss reduction are shown in Figure 3.By observing the voltage response results before and after loss reduction control as shown in Figure 3, it can be seen that before loss reduction control, the voltage response curve fluctuates greatly, and changes significantly with the addition of reactive load.After the loss reduction control, the reactive load has little effect on the voltage response curve, which shows that the test method can effectively adjust the voltage response curve of the power grid.

Comparison test of network loss reduction
To comprehensively assess the effectiveness of this approach in mitigating energy loss, we compare it with the techniques described in References [3] and [4], utilizing the reduction of network loss as the experimental metric.Figure 4 displays the comparison results of network loss reduction for all three methods.

Figure 4. Comparison results of network loss reduction by different methods
The comparison results of network loss reduction for various methods shown in Figure 4 demonstrate that this method achieves the largest reduction in network loss, exceeding 35%.In contrast, the methods described in References [3] and [4] only achieve a maximum reduction of about 15%.Therefore, this approach is highly effective in reducing network loss.

Conclusion
To enhance the safety and stability of power grids, we proposed a method for energy-saving and loss reduction that accounts for the impact of harmonics.Through theoretical and experimental verification, we demonstrate that this method effectively controls voltage response under harmonic interference, resulting in a significantly reduced power loss.Specifically, compared with the previous control method, our approach maintains a more stable voltage response curve.Moreover, when compared with the methods described in the two literature references, our method achieves the largest reduction in power loss, exceeding 35%.

Figure 1 .
Figure 1.Voltage characteristic curve of network loss under different parameters Load model 1: and configured capacity of the power grid respectively.
10) In the formula, 1 w , 2 w , and 3 w all represent the weight coefficient, loss f represents the loss cost, load f represents the power cost, and M f represents the voltage cost.

Figure 3 .
Figure 3. Voltage response results before and after the method control 1 iV is the fundamental voltage of the power grid, and n i V is the harmonic voltage.
Comparison results of network loss data before and after loss reduction