Abstract: Reactive power optimization and reactive power compensation in power system are effective means to improve system operating voltage, reduce network loss and improve system stability. This paper summarizes the research status of reactive power optimization and reactive power compensation at home and abroad, and discusses and studies the existing problems of reactive power compensation and optimization.

Keywords: reactive power optimization reactive power compensation nonlinear network loss voltage quality?

The preface of 1

With the rapid development of national economy and the increase of electricity consumption, the economic operation of power grid has been paid more and more attention. Reducing network loss, improving transmission efficiency and economy of power system operation are practical problems faced by power system operation departments, and also one of the main directions of power system research. Especially with the implementation of power market, transmission companies (power grid companies) can reduce network losses through effective means, improve the economy of system operation, and bring higher benefits and profits to transmission companies. Reactive power optimization and reactive power compensation in power system are important parts of the research on safe and economic operation of power system. Through the rational allocation of reactive power and the optimal compensation of reactive load in power system, not only can the voltage level be maintained, but also the stability of power system operation can be improved, and the active and reactive network losses can be reduced, so that the power system can operate safely and economically.

Reactive power optimization calculation is to minimize the network loss of the system under various constraints by adjusting the control variables (reactive power output and terminal voltage level of the generator, installation and switching of capacitor banks and adjustment of transformer taps) under a given system network structure and system load. Reactive power optimization can not only make the voltage of the whole network run near the rated value, but also achieve considerable economic benefits, which perfectly combines the power quality, the safety and economy of system operation, so the prospect of reactive power optimization is very broad. Reactive power compensation can be regarded as a sub-part of reactive power optimization, that is, by adjusting the installation position and capacity of capacitors, the network loss under various constraints is minimized.

What are the principles and types of reactive power optimization and compensation?

2. 1 reactive power optimization compensation principle?

In reactive power optimization and reactive power compensation, we must first determine the appropriate compensation point. Reactive load compensation points are generally determined according to the following principles:?

1) According to the characteristics of the network structure, select several center points to control the voltage of other nodes; ?

2) According to the principle of reactive power local balance, select the node with large reactive power load. ?

3) Hierarchical reactive power balance, that is, to avoid the mutual flow of reactive power with different voltage levels, so as to improve the economy of system operation. ?

4) The reactive power compensation degree in the power grid should not be lower than the provisions of the ministerial standard 0.7. ?

2.2 Types of reactive power optimization and compensation?

Reactive power compensation in power system includes not only capacitive reactive power compensation, but also inductive reactive power compensation. In EHV transmission lines (500kV and above), due to the large capacitive charging power, according to statistics, the capacitive charging power per kilometer reaches 1.2 MVAR/km at 500kV. Therefore, it is necessary to compensate the inductive reactive power of the system to offset the capacitive power of the line. In fact, all 500kV substations carry out inductive reactive power compensation, and high-voltage reactance and low-voltage reactance are connected in parallel to balance the reactive power of 500kV power grid. ?

3 reactive power optimization of transmission and distribution network (closed network)?

Reactive power compensation of power system can be optimized from two aspects, namely, transmission and distribution network (closed network) and reactive power optimization compensation of distribution lines and users (open network).

3. 1 reactive power optimization objective function?

The famous law of equal loss and slight increase rate in reference [3] points out that when the total loss and slight increase rate are equal, the loss is the smallest. The reactive power compensation point should be set at the point where the slight increase rate of network loss is small (reactive power compensation is usually carried out when the slight increase rate of network loss is negative), so that the best advantage can be obtained by iterative solution combined with the optimal slight increase rate of network loss. On the one hand, this method does not consider the adjustment function of other control variables, and at the same time, it is impossible to make the slight increase rate of the whole network loss equal through repeated iteration in actual operation, which is too huge and time-consuming. At the same time, scholars at home and abroad have done a lot of research on reactive power optimization and put forward a lot of optimization algorithms for reactive power optimization mathematical models. There are two main mathematical models for reactive power optimization. One is to ignore the cost of reactive power compensation equipment, and the main purpose is to minimize the network loss of the system. That is to say, the objective function of reactive power optimization in the optimized state can be expressed by the following formula:

Secondly, taking the optimal operation of the system as the objective function, the reduced cost of network loss and the increased cost of compensation equipment after compensation are considered, which can be expressed as:

Where β is the electricity price per kWh, τmax is the annual maximum load loss hours, α and γ are the annual depreciation maintenance rate and investment recovery rate of reactive power compensation equipment, KC is the unit price of reactive power compensation equipment, and QC∑ is the total capacity of reactive power compensation. ?

The second model considers the investment problem and can be considered as an ideal model. Especially with the implementation of the electricity market, all departments are pursuing economic benefits, so it is obviously more reasonable to consider the issue of reactive power investment. ?

3.2 Optimization algorithm?

Due to the nonlinearity of power system, the diversity of constraints, the mixture of continuous variables and discrete variables and the large calculation scale, reactive power optimization of power system is very difficult. The linearization of nonlinear reactive power optimization model is the starting point of some algorithms, such as reactive power optimization power flow based on sensitivity analysis, linear programming interior point method for reactive power comprehensive optimization, reactive power optimization power flow with penalty term and interior point method. All of the above are the expansion of nonlinear programming with Taylor series, ignoring the second order and above terms, and establishing a linearization model to get the optimal solution. Because the second order and above terms are ignored in the linearization process, the convergence of these methods cannot be guaranteed. In order to improve the convergence of optimization calculation, the idea of penalty function is introduced into linear programming, and a reactive power optimization power flow model and algorithm with penalty term are proposed to eliminate or reduce the overrun of dependent variables to the minimum. But it can't fundamentally end the problem of non-convergence after linearization. ?

Aiming at the shortcomings of linear algorithms, some nonlinear algorithms, such as mixed integer programming, constrained polyhedron method and nonlinear primal dual algorithm, are proposed. Although these methods can find the optimal solution in theory, due to the characteristics of reactive power optimization itself, the calculation is complicated and time-consuming, and the reliable convergence cannot be guaranteed.

In order to improve the convergence and nonlinear treatment of discrete variables in reactive power optimization (transformer tap adjustment and capacitor bank switching), a genetic algorithm based on a new method of artificial intelligence is proposed. Taboo? Search method, heuristic algorithm, improved genetic algorithm, distributed genetic algorithm and simulated annealing algorithm. These algorithms improve the convergence and calculation speed of reactive power optimization to a certain extent, and some methods have been put into practical application and achieved good results. ?

However, there are still some problems to be solved in reactive power optimization. Solve:

1) Because reactive power optimization is a nonlinear problem, and nonlinear programming often converges to the local optimal solution, how to find its global optimal solution still needs further study and discussion. ?

2) Because the objective function is to minimize network loss, it is itself a function of voltage square. When solving reactive power optimization, many bus voltages may be close to the upper limit of voltage, but the actual operation department does not want the voltage to be close to the upper limit. If the voltage constraint range is narrowed, the reactive power optimization may not converge, or it needs to be revised and iterated repeatedly to get the solution (the local constraint conditions need to be changed artificially). How to unify voltage quality and economic operation index still needs further study. ?

3) The real-time problem of reactive power optimization. With the improvement of power system automation level, the demand for real-time reactive power optimization is getting higher and higher. How to avoid non-convergence and find the optimal solution in a short time needs further study. & lt！ [endif]& gt；

4 distribution line reactive power compensation and user reactive power compensation

4. 1 reactive power compensation for distribution lines?

Because the resistances of 35kV, 10kV and some low-voltage distribution lines are relatively large, and the power loss and voltage loss caused by reactive power flow on the lines are relatively large, the theory of reactive power compensation is based on them. The classical line compensation theory holds that the installation position of capacitor is shown in the table below.

Its principle can be briefly described as follows:

When the reactive power Q transmitted by the line, the line length L and the compensation distance of each group are X, the compensation capacity of each group is Qx?

Qx=Qx/L？

When the capacitor is installed in the center of the compensation interval, the reduced line loss is the largest. Reactive power flow diagram is as shown in figure 1:

When the distance from the installation position of group I capacitor to the end is:

For any group of capacitors, the installation location is:?

xi=L(2i- 1)/(2n+ 1)？

Its best compensation ability is:?

nQx=2nQ/(2n+ 1)？

So you can get the data of table 1 ?

Reactive power compensation of distribution lines can effectively reduce network losses, but the effect is not as good as that of low-voltage side compensation. This conclusion assumes that the reactive power flow is evenly distributed, and if the reactive power flow on the line is unevenly distributed, the conclusion is different; At the same time, when installing the capacitor bank on the line, it is inconvenient to maintain and operate, and the input of compensation equipment is not considered. Therefore, the following methods are recommended. ?

4.2 User's reactive power compensation?

According to the types of reactive power compensation, enterprises and large-load power users can be divided into high-voltage centralized compensation, low-voltage centralized compensation and low-voltage local compensation. Literature [8] points out that under the condition of equal compensation capacity, the line loss reduced by low voltage on-site compensation is the largest, so the economic benefit is the best. That's understandable. Because the low voltage partially compensates the inductive part of the load, the reactive current flowing through the line and transformer is greatly reduced. Obviously, this method has the best economic benefits. However, the above does not indicate what the optimal compensation capacity should be. At the same time, the input of reactive power equipment is not considered. Reference [6] points out the optimal compensation capacity of open networks, and three common open networks are shown in Figure 2. ?

4.2. 1 Optimal reactive power compensation for radial grid opening?

For users with distribution transformers or open networks, reference [6] gives a detailed derivation of the optimal reactive power compensation capacity of open network wiring. Its objective function adopts the second objective function. In order to facilitate analysis, the following is a simple derivation process:

For radial networks, the relationship between annual calculation cost and reactive power compensation can be expressed as:

Because the main research is the influence of reactive power on active power loss, and the influence of active power on network loss can be ignored, Equation (4) can be simplified as the following equation:

Compensation qcn and op of other nodes are the same as the above formula.

4.2.2 Optimal reactive power compensation for trunk lines and chained open networks

For trunk and chain-connected open networks, reactive power compensation is set at i= 1 point, and its QC 1 and OP are the same as those of radial open networks. If the reactive power compensation is set at point i= 1 2, see Figure 2(b) and (c).

At this point, the annual expenditure can be expressed as follows:

Similarly, qc2 can be obtained, and the expression of op is (for simplicity, it can be considered that the voltage of node 2 is approximately equal to the voltage of node 1):

Where is r? ∑ is the sum of line resistances of trunk or chain connected open networks, where r? ∑=R？ 1+R？ 2?

When the number of network nodes is I and the number of trunk or chain open network lines is m, the optimal reactive power compensation capacity QCI and OP can be obtained synthetically. The general formula for calculation is:

The above formula is simple and clear, which combines the well-known equal loss slight increase rate with the optimal loss slight increase rate, and obtains the optimal compensation capacity by calculating the one-time performance of the formula, thus avoiding the iterative process of calculation. See Example 6-2 in Reference [3] for specific examples. In Example 6-2, the optimal compensation capacity is obtained by solving five groups of equations and six iterations, which can be calculated at one time with the formula derived above.

5 conclusion?

Reactive power optimization and compensation of power system need more accurate load data, generator data, transformer parameters and so on. At the same time, in the actual operation of the power system, the state of the power system is constantly changing, so reactive power optimization and reactive power compensation should be flexibly applied according to the actual situation. With the further realization of dispatching automation, distribution automation and unattended substation, an algorithm with fast calculation speed and good convergence is needed. At the same time, with the implementation of power market and the gradual maturity of reactive power pricing theory, reactive power optimization theory will also be changed and further improved. Baidu Maps