Flexible load control of new energy based on improved genetic algorithm

Abstract

In the medium and low voltage distribution network, the load form of users is complex and changeable. There are a large number of single-phase and two-phase loads connected to the distribution network, resulting in a three-phase unbalanced operation of the distribution network. With the development of the new energy, the high proportion of distributed new energy will further aggravate the three-phase imbalance of the distribution network. Therefore, this paper proposes a coordinated optimization framework of droop parameters based on the multi-converter droop control, which takes the minimum loss of the distribution network as the optimization objective, and optimizes the reference point and the slope of the VSC droop hierarchically. A small-signal stability optimization dispatching method for the VSC droop slope in the DC distribution network is proposed. By adding small-signal stability constraints to the slope optimization model, the optimal slope command and slope stability region which can ensure the small-signal stable operation of the system are obtained. Experiments show that the optimization model of the VSC small-signal stability slope can make the droop control instruction significantly improve the small-signal stability of the system to adapt to the intra-day source load power fluctuations with a small economic cost. The slope stability region pre-optimization model can provide a reliable stability slope upper limit for the slope optimization problem based on ensuring the system operation economy. The research in this paper can make full use of the flexible control ability of power electronic equipment, and then suppress the three-phase imbalance, which is of great significance to improve the security and economy of the distribution system operation.

Keywords

New energy flexible load distribution network regulation genetic algorithm slope stability region model

Introduction

The increasing penetration rate of new energy in distribution networks brings new challenges to the operation and dispatch of distribution networks while saving energy and protecting the environment. The key issues of the distribution network with a high proportion of distributed new energy at the operation and dispatching level mainly include the safe and stable consumption of the source load fluctuation power of the distribution network, the suppression of the three-phase imbalance in the distribution network, and the coordination of multi-agents in the distribution system under the market mechanism. The three aspects are as follows:

(1) The safe and stable consumption of the source load fluctuation power in the distribution system: first, the output of new energy is uncertain. A high proportion of the distributed new energy is connected to the distribution network, which aggravates the power fluctuation in the actual operation of the system.

(2) The suppression of the three-phase imbalance in the distribution network: the distribution network usually contains various types of single-phase, two-phase, and three-phase asymmetric loads.

(3) The multi-agent coordination of distribution network under market mechanism: with the advancement of power system reform, the participants and participation modes of the distribution network operation regulation with a high proportion of distributed new energy are increasingly diversified, and some distributed new energy and loads can participate in the distribution network operation as independent stakeholders through microgrid integration (Mohammadi et al., 2019).

With the increasing penetration of distributed new energy, the distribution network is facing severe challenges such as the safe and stable absorption of source load fluctuation power, the suppression of three-phase imbalance, and the coordination of multi-agents under the market mechanism (Guo et al., 2020). At the same time, the large-scale application of power electronic devices represented by converters in the distribution network can significantly improve the flexible control ability of power flow in the distribution network. By replacing the traditional interconnection switch with the flexible power electronic converter at the key node of the distribution network and giving full play to its advantages of two-way flexible power regulation, the distribution network is transformed from the traditional rigid distribution network to the flexible distribution network, which can provide a new solution to the problems caused by the high proportion of the distributed new energy access (Qiu et al., 2018).

To solve the problem of large deviation of long-term prediction of new energy output, Ye and Li (2016) studies the multi-time-scale coordinated energy management method based on different system topologies. It pre-dispatches in the day-ahead dispatching stage based on the long-term prediction data and determines the values of system discrete control variables such as energy storage charging and discharging state, transformer tap position, and so on. In the intra-day dispatching stage, real-time dispatching is carried out based on short-time-scale prediction data. The day-ahead dispatching scheme is corrected according to the deviation of the new energy output. The values of continuous control variables such as distributed generation output, energy storage charging and discharging power, and the like are determined, and the system operation economy on a long time scale and the system operation security on a short time scale are considered. Li et al. (2018) further studies the power system energy management method based on model predictive control on the basis of hierarchical scheduling with a refined time scale, considering that the prediction data of a short time scale is more accurate but less forward-looking. Model predictive control refers to the idea of rolling optimization and feedback correction of the control model in the industrial control field. In the process of real-time scheduling in a day, the scheduling is carried out step by step according to the time interval of short time scale prediction data. The optimization model is solved once in each scheduling step, and the optimal scheduling scheme for several steps in the future can be obtained each time. However, only the scheduling instruction of the first step is executed, and the subsequent scheduling instructions will be gradually optimized and corrected with the rolling of the prediction data (Zhao et al., 2018).

Given the above problems, this paper proposes the corresponding improvement strategy based on the genetic algorithm and the sequential nonlinear programing algorithm. It combines the advantages of the two algorithms and effectively improves the computational efficiency and optimization ability of the algorithm by comparing and optimizing the local optimal solutions of multiple subspaces on the premise of ensuring the reliability of the optimization results. Experiments show that the active power dispatching model can give full play to the multi-terminal power flow control function, realize the mutual support of power among the sub-distribution networks, and improve the ability of the distribution network to absorb new energy in the microgrid. The main innovations of this paper are:

(1) A VSC small-signal stability slope optimization model is established. In the slope optimization model, the distance from the real part of the dominant eigenvalue to the imaginary axis is taken as the index of the distribution network’s small-signal stability margin.

(2) Linearize the small interference stability constraint based on the matrix perturbation theory, and increase the small interference stability constraint under the expected scene and the extreme source load scene.

(3) A slope stability region pre-optimization model is established to quantitatively obtain the upper limit of the slope that can ensure the stable operation of the system. The upper limit of the stable slope constraint is taken as an equivalent substitution for the small interference stability constraint in the main problem model of slope optimization, to reduce the complexity of the slope optimization model and improve the solving efficiency.

Related work

Power consumption of source load fluctuation in the distribution network

Wind and photovoltaic distributed power supplies usually work in the maximum power point tracking mode and operate as uncontrollable power sources. Influenced by natural factors, the inherent uncertainty of wind and solar new energy output brings difficulties to power prediction, which is not conducive to the formulation of a day-ahead dispatching plan of the distribution network. On the one hand, it aggravates the power fluctuation during the actual operation of the distribution network, which is not conducive to the real-time power flow regulation and power balance of the distribution network (Gao et al., 2018).

To further improve the reliability of scheduling instructions, stochastic optimization, and robust optimization techniques have been focused on and studied. The stochastic optimization regards the output of wind and solar new energy as random variables, obtains the probability distribution function of random variables based on the analysis of historical data, generates a large number of typical scenarios through sampling, clusters and reduces them through scenario reduction technology, and finally optimizes and dispatches them to obtain the average optimal control instructions of the expected scenario set (Ding et al., 2017).

In addition, with the increase of new energy penetration, the power grid gradually shows the development trend of power electrification. Power electronic converters do not have the rotating equipment of traditional generators and cannot provide spinning reserve capacity based on the moment of inertia. The characteristics of low inertia and weak damping reduce the stability margin of the system, and the fluctuation of the source-load power further aggravates the stability risk of the system (Qiu et al., 2019). However, the traditional optimal power flow (OPF) dispatching model often takes the steady-state operation performance of the system as the goal. It only considers the steady-state constraints of the system and power equipment and ignores the impact of dispatching instructions on the small-signal stability of the whole system. The SSSC-OPF (Small-Signal Stability Constrained Optimal Power Flow) has attracted wide attention to solve the stability problem of the power system from the dispatching level. By considering the small-signal stability constraints of the system in the upper optimal scheduling model and jointly optimizing and adjusting the system scheduling instructions, the overall operation economy and stability of the system can be taken into account. The small-signal stability margin at the steady-state operation point of the system can be improved (Maulik and Das, 2018).

Optimization model of VSC small-signal stability slopes

(1) Objective function

The objective function of the slope optimization model is shown in formula (1).

min \sum_{t = 1}^{n} \sum_{m = 1}^{x} P_{v s c, m, t}

(1)

Where, n is the number of expected scenarios in the scheduling interval. $P_{v s c, m, t}$ is the power injected into the DC distribution network by the mth VSC in the tth scenario. x is the number of VSCs. It is worth noting that when the source load power of the system is an uncontrollable variable. The minimum network loss of the system is equivalent to the minimum sum of power injected into the distribution network (Wang et al., 2019).

(2) Power flow constraint of DC distribution network

P_{i n j, i, t} - u_{n, i, t} \sum_{j = 1}^{N} (G_{d c, i j} u_{n, j, t}) = 0, \forall i \in B, \forall t

(2)

(3) System safety constraints

u_{min} \leq u_{n, i, t} \leq u_{max}, \forall i \in B, \forall t

(3)

- i_{max} \leq i_{l, i j, t} \leq i_{max}, \forall i j \in E, \forall t

(4)

(4) VSC power constraints

0 \leq P_{v s c, m, t} \leq {\bar{P}}_{v s c, m}, \forall m, \forall t

(5)

(5) V-P droop constraint

u_{ref, m} - u_{n, i, t} = k_{m} (P_{v s c, m, t} - P_{ref, m}), \forall m, \forall t

(6)

Where, $u_{ref, m}$ and $P_{ref, m}$ are the droop voltage and power reference points, which are solved by the reference point optimization model and are known parameters in the slope optimization model; $k_{m}$ is the droop slope of the mth VSC and is the optimization variable (Zhang et al., 2019).

(6) Small-signal stability constraint

To ensure that the distribution network can operate stably under all the source load power expectation scenarios, the small-signal stability constraint of the expectation scenario as shown in (7) is added to the slope optimization model.

r e a l (λ_{i, t})_{max} < η_{max}, \forall t

(7)

Where $η_{max}$ is the maximum spectral abscissa, that is, the maximum allowable value of the real part of the eigenvalue, which is used to measure the stability margin of the system. $r e a l (λ_{i, t})_{max}$ represents the maximum real part of the eigenvalue of the small-signal state matrix at the steady-state operating point of the system under each desired scenario (Li et al., 2019).

Small disturbance stability constraints in extreme scenarios as shown in equation (8) are added to the slope optimization model to further improve the stability of the system when the source charge power fluctuates (Zafar et al., 2020).

r e a l (λ_{i, lim})_{max} < η_{max}

(8)

Where $r e a l (λ_{i, lim})_{max}$ represents the maximum real part of the eigenvalue of the small-signal state matrix at the steady-state operating point of the system in the extreme scenario.

Finally, based on the matrix perturbation theory, the VSC small-signal stability slope optimization model can be transformed into a sequential nonlinear optimization problem for iterative solution (Liu et al., 2019a).

Pre-optimization model of slope stability region

The VSC small-signal stability slope optimization model is further decomposed into a slope stability region pre-optimization model and a slope optimization master problem model. Firstly, based on the extreme scenario of the source load power, the slope stability domain pre-optimization considering the small-signal stability constraint is carried out. The slope upper limit $k_{max}$ that can ensure the stable operation of the system within the fluctuation range of source load power is quantitatively obtained (Sun et al., 2021). Furthermore, in the solution of the master problem model of slope optimization, the small-signal stability constraint is equivalently replaced by the upper limit of stability slope constraint. Since $k_{max}$ is mainly determined by the extreme source load scenario, when the extreme source load scenario remains unchanged, it is not necessary to repeatedly solve $k_{max}$ for different expected scenario sets. Thus, based on ensuring the small-signal stability of the system, it can greatly improve the solving efficiency of the slope optimization main problem model and effectively expand the applicable scenarios and scope of small-signal stability constraints (Liu et al., 2019b). The slope stability region pre-optimization model can be expressed as:

max k_{max}, \forall k_{m} = k_{max}

(9)

Where $k_{max}$ is the upper limit of the stable slope and $\forall k_{m}$ is the optimization variable. The slope-optimized master problem model can be expressed as:

min \sum_{t = 1}^{n} \sum_{m = 1}^{x} P_{v s c, m, t}

(10)

s . t . (2.49) - (2.53)

(11)

0 \leq k_{m} \leq k_{max}, \forall m

(12)

In the formula, $k_{max}$ is obtained by solving the pre-optimization model of the slope stability domain, and $\forall m$ is a known parameter.

An improved algorithm based on the sequential nonlinear programing and genetic algorithm

Taking the VSC small-signal stability slope optimization model as an example, the overall solution process of the improved algorithm is shown in Figure 1.

Figure 1.

Overall flow chart of the algorithm.

According to the algorithm flow chart, the specific steps of the algorithm are as follows:

(1) Input the system parameters of a direct current distribution network, initialize a genetic algorithm, and randomly generate a population.

(2) Initialize that perturbation rate, and set $α = α_{0} = 100 %$ .

(3) Carry out power flow calculation on the population individuals to obtain the steady-state operating points under the source load power expectation scene and the extreme scene.

(4) Establish a small-signal state matrix model of that system at each steady-state operation point and the eigenvector. Calculate the first-order perturbation parameter $λ_{i 1, m}$ , and obtain the approximate analytical expression of the eigenvalue (Coffrin et al., 2017).

(5) Solve an optimization model of that small interference stable slope of the VSC by adopting an interior point method.

(6) Take the solution result of the interior point method each time as a reference value, and re-substitute the reference value into the step (3) to carry out iterative calculation until the maximum number of iterations $F_{max}$ is reached or the variation range of the slope in the two solution results is less than a set threshold value.

(7) Recalculate a steady-state operating point by taking the slope output by step (6) as a reference value to form a state matrix, and calculate an accurate value of a dominant characteristic value by using a QR method.

(8) If that actual characteristic value exceeds the limit, the perturbation rate is reduced by one time, and the iterative calculation is carried out by returning to the step (3).

(9) If that actual characteristic value does not exceed the limit, or reach the check time $G_{max}$ of the maximum characteristic value, the individual objective function is calculated. The actual out-of-limit state of the characteristic value is added to the objective function in the form of a penalty function.

(10) Judge whether the result is convergent or reaches the maximum running time, otherwise, perform genetic operations such as selection, replication, crossover, mutation, and the like on the population. Then, retain the optimal individual in the population of the previous generation to generate a sub-generation population, and return to step (2) to perform the iterative calculation. If yes, the optimal droop slope is output, and the solution ends (Robbins and Dominguez-Garcia, 2016).

Example analysis

Example system description

The typical ring DC distribution network as shown in Figure 2 is used in the example.

Figure 2.

Structure diagram of annular DC distribution network.

The optimized model parameters are shown in Table 1.

Table 1.

Optimization model parameters.

Variable	Value
Limit of voltage constraint $u_{n, min}$	760 V
Voltage constraint upper limit $u_{n, max}$	840 V
VSC output power upper limit VSC $P_{\csc, m}$	90 kW
Current constraints $i_{l, max}$	300 A
Abscissa of the maximum spectrum $η_{max}$	−0.1
Target function penalty term $μ_{i, t}$	100,000
Maximum number of iterations of the lower layer $F_{max}$	5
Maximum check times of eigenvalues $G_{max}$	4
Minimum perturbation threshold of droop slope $ω$	0.0001
Convergence threshold of droop slope $ε$	0.00001
Population size	10

The rated voltage class of the system is 800 V and the power reference value is 50 kW. It is assumed that the intra-day droop parameter command scheduling interval is 15 minutes, and the number of expected source load power scenarios in the control interval is $n = 4$ . Take a typical intra-day scheduling interval as an example for analysis. The deterministic source load forecast data in this period is shown in Table 2.

Table 2.

Predicted data of deterministic source load in typical period.

Load 1	Load 2	Load 3	Photovoltaic 1	Photovoltaic 2
30 kW	50 kW	60 kW	30 kW	40 kW

System control reliability analysis

Firstly, based on the deterministic source load prediction data in Table 2, the reference point optimization model is solved to obtain the VSC optimal droop reference point instruction, as shown in Table 3.

Table 3.

Droop reference point instruction.

	VSC1	VSC2	VSC3
Power reference point	49,800.2 W	10,481.2 W	10,410.6 W
Voltage reference point	800 V	800.086 V	800.069 V

Secondly, within the fluctuation range of ±20% of the deterministic source charge prediction data, 500 sets of source charge power expectation scenarios are randomly generated by the Monte Carlo method. Based on each set of desired scenarios, the following three methods are used to optimize the slope.

(1) Consider the slope optimization of stability constraints of the extreme source load scenarios (Wang et al., 2020).

(2) Consider the slope optimization of the desired scenario stability constraints. Ignore the constraints in the slope optimization model (Tan and Wang, 2015).

(3) The slope optimization of the stability constraints is not considered. Ignore the constraints in the slope optimization model (Jia and Tong, 2016).

The verification results show that there are 37 groups of out-of-limit eigenvalues in the 500 groups of scenarios. The small interference instability ratio of the system in the expected scenarios is 7.4%. Figure 3 shows the comparison of the maximum real part of the eigenvalue of each method in the above 37 sets of scenarios.

Figure 3.

Comparison of maximum real parts of eigenvalues of predicted scenarios.

In Figure 3, the maximum real part of the characteristic value of the slope command obtained by the method (2) in the 37 groups of the expected scene sets is equal to the set maximum spectral abscissa −0.1, which can ensure the small disturbance stable operation of the system.

The verification results show that there are 45 groups of slope commands with out-of-limit eigenvalues in the actual source load scenario. The small interference instability ratio of the system in the actual source load scenario is 9%.

Figure 4 shows the comparison of the maximum real part of the characteristic value of 45 groups of slope instructions obtained by the method (1) and the method (2) based on the same expected scene set in the actual source-load scene verification.

Figure 4.

Comparison of the maximum real part of the characteristic value of the actual source load scene.

Therefore, it is very important to consider the small-signal stability constraint in extreme source load scenarios for the stable and reliable operation of the system.

Effectiveness analysis of algorithm improvement strategy

To illustrate the effectiveness of the algorithm improvement strategy proposed in this paper, the following methods are used to optimize the slope of 500 sets of source load power expectation scenarios. The results are compared with those of method (1).

Method (5): The sequential nonlinear programing algorithm is used to optimize the slope considering the stability constraints of extreme scenarios (Lv and Ai, 2016).

Method (6): Genetic algorithm is used to optimize the slope considering the stability constraints of extreme scenarios (Liu et al., 2018).

Table 4 shows the statistical results of solutions under three different algorithm of methods (1), (5), and (6). Where, the eigenvalue out-of-limit rate refers to the proportion of the actual small-signal instability scenario of the system when the slope instruction is checked considering the influence of the eigenvalue iteration error. The calculation timeout rate represents the proportion of scenes that take more than 1 minute to optimize.

Table 4.

Algorithm performance comparison.

Method	Type	Network loss recovery rate	Exceedance rate of eigenvalue	Calculate timeout rate	Average solution time per second
(1)	Improved solution algorithm	1	0	0	10.62
(5)	Sequential nonlinear programing algorithm	0.717	13.8%	0	14.36
(6)	Genetic algorithm	0.943	0	6.2%	24.21

The comparison of the average network loss improvement rate under the same maximum solution time can illustrate the effectiveness of the improved strategy. Since the nonlinear model optimization solution algorithms compared in Table 4 cannot theoretically prove the global optimality of their solution results, the optimization capabilities of the three algorithms are indirectly measured by comparing the network loss improvement rates under the same solution time. The optimization result of method (1) is used as a reference value. The network loss improvement rate is expressed in a per-unit form. Under the same maximum solution time, the average network loss improvement rate of the method (1) is 28.3% higher than that of method (5), and 5.7% higher than that of method (6). This shows that the optimization ability of method (1) is better than that of method (5) and method (6).

Conclusion

In this paper, based on the droop coordinated control of multi-converter, the optimal dispatching method of DC distribution network small-signal stable droop is proposed to solve the problem of power consumption of source load fluctuation in the distribution network. By increasing the small-signal stability constraint in extreme scenarios, the optimal slope command and the slope stability range for the small-signal stability operation of the system are obtained. Through experimental analysis, the improved algorithm can effectively solve the problems existing in the traditional algorithm, such as easy to fall into local optimal solution, iterative error accumulation of eigenvalues, and improve the computational efficiency and optimization ability of the algorithm.

Although the improved genetic algorithm is used to regulate the flexible load of new energy in this study, there is still room for further optimization. By introducing more constraints, adjusting parameter settings or adopting other heuristic algorithms, the efficiency and stability of the algorithm are further improved. At the same time, the research object is expanded and the flexible regulation of various new energy types is considered, so that the regulation of flexible load is more diversified and flexible and can better adapt to different energy supply situations.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Jiyan Liu

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