Traditional thermal power units are continuously replaced by renewable energies, of which fluctuations and intermittence impose pressure on the frequency stability of the power system. Electrolytic aluminum load (EAL) accounts for large amount of the local electric loads in some areas. The participation of EAL in local frequency control has huge application prospects. However, the controller design of EAL is difficult due to the measurement noise of the system frequency and the nonlinear dynamics of the EAL’s electric power consumption. Focusing on this problem, this paper proposes a control strategy for EAL to participate in the frequency control. For the controller design of the EAL system, the system frequency response model is established and the EAL transfer function model is developed based on the equivalent circuit of EAL. For the problem of load-side frequency measurement error, the frequency estimation method based on Kalman-filtering is designed. To improve the performance of EAL in the frequency control, a fuzzy EAL controller is designed. The testing examples show that the designed Kalman-filter has good performance in de-noising the measured frequency, and the designed fuzzy controller has better performance in stabilizing system frequency than traditional methods.

With the increased renewable energy sources such as wind power and photovoltaic connected to the power grid, the active power balance of the power system is facing huge challenges. On the one hand, as renewable energy replaces traditional thermal power units, the proportion of traditional power generation in the total power generation capacity continuously declines, resulting in a decline in the system's active power regulation capability. On the other hand, due to the strong fluctuations of renewable energy sources, it causes disturbances to the system. The problem of active power imbalance caused by the penetration of renewable energy is reflected in the anti-peaking characteristics of power in a longer time scale, and reflected in the frequency stability problem in a short time scale. Since frequency reflects the active power balance, when the power balance is affected, the frequency will increase or decrease.

As a method to stabilize the power fluctuation of renewable energy, demand response (DR) has received more and more attention. DR supports active power balance by adjusting the power consumption on the demand side [

Beside smart home appliances, electrolytic aluminum load (EAL) plays an important role in DR. On the one hand, as a typical high energy-consuming industrial load, electrolytic aluminum occupies a large proportion of the regional electricity loads and has a large regulating capacity [

Focusing on the EAL participating in frequency control, scholars have carried out a lot of researches. To improve frequency stability in an isolated system, the authors in [

Although a large number of theoretical results have been obtained, the above-mentioned literatures do not consider the process of frequency estimation. As a frequency control method on the demand side, the power system frequency is difficult to obtain like the generator side by measuring the speed of the generator rotor. However, measuring the frequency by DR faces the measurement noise problems caused by the electromagnetic transient process. In addition, the above control strategies are mostly PID-based control strategies [

To fill this gap, this paper proposes the Kalman-filtering-based frequency control strategy for the EAL. The system and measurement noise are greatly reduced through Kalman-filtering. By designing the fuzzy control strategy, the performance of frequency control by EAL is improved.

The remainder of this paper is organized as follows. In

In this subsection, the controllable EAL model is developed and the system frequency response model considering EAL is established.

The equivalent circuit of EAL is shown in _{EAL}.

where _{AH} and _{AL} are the high-voltage and low-voltage side of the load bus,

The EAL power consumption _{EAL} can be expressed by

It can be seen that the power consumption _{EAL} can be controlled by the DC-side voltage _{B}. _{EAL} and _{B}. In

Based on the EAL steady flow control system, the EAL can be modelled as a transfer function, which reflects the relationship between the reference control signal and the actual power output, and can be formulated by:

Based on the EAL model represented by

Δ

_{i} Integral gain of the secondary frequency control

_{g} Speed governor time constant

Δ

_{SP} Power set-point of secondary frequency control

Δ_{r} Deviation of the reheated turbines’ thermal power

Δ_{m} Deviation of the generators’ mechanical power

Δ_{d} Disturbance power. Negative indicating load decreasing, while positive indicating load increasing.

Δ_{EAL} Deviation of EAL power

_{HP} Fraction of the high pressure turbine section

_{r} Reheat time constant

_{t} Turbine time constant

The system dynamics can be described by a set of differential equations, which are listed as following:

By some calculation, the above frequency response model can be transformed into the following state-space form:

To utilize Kalman-filtering method to

And the discrete state-space function can be finally obtained:

_{k}, _{k}, _{k}, _{k} and _{k} are discrete form of

In this subsection, the EAL control method is designed. Firstly, the framework of the proposed method is given, and then the components of the method is introduced in detail.

The framework of the control method is shown in _{est}. which is input to the EAL fuzzy controller. After calculating by the EAL fuzzy controller, the control output Δ_{EALref} is obtained, and delivered to the EAL.

The details Kalman-filter and the EAL fuzzy controller are presented as following.

Kalman-filtering can be used to cope with control problem such as the measurement errors, when the discrete form of the system state space equation is known [

Kalman-filtering method can be divided into two process including prediction process and correction process. The prediction is to estimate the current state based on the state at the previous moment, while correction is to integrate the estimated state and the observed state at the current moment to estimate the optimal state. The whole process can be summarized as following:

The EAL Fuzzy controller is adopted herein to control the power consumption of the EAL. The estimated frequency deviation Δ_{est} and the integral of the estimated frequency deviation _{integ} are selected as the input of the fuzzy controller, and Δ_{EALref} is defined as the output of the fuzzy controller. The diagram of the fuzzy controller is shown in

The input variables Δ_{est}, _{integ} and the output variable Δ_{EALref} are divided into 7 fuzzy subsets, including Negative Big (NB), Negative Middle (NM), Negative Small (NS), Zero (Z), Positive Small (PS), Positive Middle (PM), Positive Big (PB). The membership functions for Δ_{est}, _{integ} and Δ_{EALref} are shown in _{est} and _{integ} are listed in _{EALref} can be calculated.

Δ_{est} |
_{integ} |
||||||
---|---|---|---|---|---|---|---|

NB | NM | NL | Z | PS | PM | PB | |

NB | NB | NB | NM | NM | NL | NL | Z |

NM | NB | NM | NM | NL | NL | Z | PS |

NL | NM | NM | NL | NL | Z | PS | PS |

Z | NM | NL | NL | Z | PS | PS | PM |

PS | NL | NL | Z | PS | PS | PM | PM |

PM | NL | Z | PS | PS | PM | PM | PB |

PB | Z | PS | PS | PM | PM | PB | PB |

The system frequency response model is developed based on

Parameters | Value |
---|---|

0.05 | |

_{g} |
0.2 s |

_{r} |
7 s |

5 s | |

_{t} |
0.3 s |

_{HP} |
0.3 |

1 | |

_{i} |
1.9 |

In this subsection, the performance of EAL in the frequency control is examined. The system is supposed to be imposed by step disturbances, of which magnitude denoted by _{dmax}. The frequency control performance with EAL is compared with that without EAL. The simulation results with _{dmax} varying from 0.02 p.u. to 0.08 p.u. are shown in

In this subsection, the performance of the Kalman-filtering is examined. To verify the effectiveness of the Kalman-filtering method, the following 3 cases are compared:

Case 1: the frequency deviation Δ

Case 2: the frequency deviation Δ

Case 3: the frequency deviation Δ

The EAL with fuzzy controller is considered in each case. The system responses of the above three cases under the continuously varying load disturbances are shown in

The reason for the proposed Kalman-filtering (Case 3) better than LPF method (Case 2) lies in that the proposed method can utilize the system frequency response model, and predict the system states. Compared with traditional LPF method, the frequency measured by the Kalman filter does not introduce response delay. It is of significant importance for the controller to quickly receive the signal, and make response in time. The control performance is therefore improved.

This subsection is to compare the frequency control performances under different EAL control methods, in order to verify the effectiveness of the fuzzy EAL controller. The following methods are compared.

Method 1: Only thermal generation units is considered in the frequency control. The EAL does not participate in the frequency control.

Method 2: EAL participates in the frequency control with traditional PID control method.

Method 3: EAL participates in the frequency control with the proposed fuzzy controller.

The simulation results of the above 3 methods are shown in

The reason for the proposed method (Method 3) better than the traditional PID control method (Method 2) lies in that the proposed method (Method 3) can better adapt to the nonlinear dynamic characteristics of EAL through fuzzy rules. The controller established by fuzzy rules can imitate the process and method of manual control, enhancing the adaptability and intelligence of the control system.

In this paper, Kalman-filtering based fuzzy control method is proposed for the EAL participating in the system frequency control. The main contributions of this paper can be summarized as following:

1. Kalman-filtering based method is designed for EAL participating in the frequency control of the power system. Kalman-filtering can precisely estimate system frequency suffered from measurement noise.

2. Fuzzy control method is adopted for EAL in the system frequency control. Fuzzy controller can better adapt to the nonlinear dynamic characteristics of EAL through fuzzy rules.

The simulation results show that Kalman-filtering performs well in lowering the measurement noise, and exhibits more effectiveness than traditional LPF method. The method with Kalman-filtering can reduce the frequency drop by 0.02 Hz than that without Kalman-filtering. The Fuzzy controller takes into account the nonlinear dynamic characteristics of EAL, and therefore performs better than traditional PID methods by lowing the frequency drop by 0.09 Hz. Future work may be investigating the feasibility proposed method on the other industrial loads, and developing corresponding controllers.