# A Coordinated Control Strategy of Multi-Type Flexible Resources and Under-Frequency Load Shedding for Active Power Balance

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Controllable Resources Participating in Frequency Response

#### 2.1.1. Inertia Analysis

_{ESS1}, is expressed by (4):

_{ep}is the proportionality control coefficient set for the energy storage system.

_{ESS2}, can be expressed as (5):

_{ed}is the virtual inertia control coefficient set for the energy storage system.

#### 2.1.2. Comparison of Frequency Regulation Capability

_{1}and T

_{2}are the times used to increase the output of the storage unit and the thermal unit, respectively; T

_{del1}and T

_{del2}are the control delays of the storage unit and the thermal unit, respectively.

#### 2.1.3. Emergency Load Shedding Based on the Differential Evolution Algorithm

_{L}is the number of load-shedding stations; c

_{j}is the load-shedding cost factor for each station; φ is the function representing the variation of the cost factor with the load-shedding ratio, approximating the cost factor as a linear function; k

_{j}is the growth coefficient of the cost factor; b

_{j}is the base cost factor; p

_{j}is the shedding ratio; and P

_{Lj}

_{,0}is the active load of the shedding station at steady state before direct current (DC) blocking.

_{f}, ŋ

_{v}, ŋ

_{I}, and ŋ

_{δ}are transient frequency, voltage security index, line current security index, and rotor angle security index; ξ

_{f}, ξ

_{v}, ξ

_{I}, and ξ

_{δ}are the set limits for transient frequency, voltage, current, and rotor angle constraints; and ρ

_{j}

_{,max}is the maximum load-shedding ratio.

_{1}, r

_{2}, and r

_{3}are distinct random integers within the [1, N] interval; v

_{i}is the generated mutated individual; and K is the mutation factor. Equation (9) is commonly referred to as random mutation, and another faster converging optimal mutation method is expressed by (10):

_{R}is the crossover factor, ranging between [0, 1]; u

_{i}is the individual after crossover; rand

_{j}is a random number within [0, 1]; and rand(j) is a random integer between 1 and L, ensuring that at least one control variable is updated.

#### 2.2. Considering Different Operating States of Energy Storage Control Strategies

#### 2.2.1. Energy Output Control Strategies

_{G}(s) in relation to frequency deviation Δf(s), energy storage system’s active power output ΔP

_{b}(s) in relation to frequency deviation Δf(s), and the disturbance of load ΔP

_{L}(s), ΔP

_{G}(s), ΔP

_{b}(s), Δf(s) are expressed by (13).

_{ref}is the expected grid-connected power of the renewable energy generation system, and P

_{w}and P

_{PV}are the uncontrollable original power of the wind and photovoltaic fields. When P

_{ref}> P

_{w}+ P

_{PV}, the energy storage system releases its stored energy to make up the difference between them. When P

_{ref}< P

_{w}+ P

_{PV}, the energy storage system absorbs excess power. The principle is illustrated in Figure 3.

_{min}) and remaining discharge time (T

_{sy}). The shortest discharge time (T

_{min}) represents the minimum time required for energy storage to provide power support in emergency situations. The remaining discharge time (T

_{sy}) indicates the sustainable time that energy storage can output power at the maximum rate.

_{min}and T

_{sy}. Under this setup, for an energy storage unit corresponding to the shortest discharge time t

_{min}, SOC

_{min}is shown in Equation (16):

_{dis}

_{,t}is the unit output required by the operator and ŋ

_{dus}is the discharge efficiency of energy storage. Similarly, corresponding to the remaining discharge time t

_{sy}, SOC

_{sy}is shown in Equation (17).

_{min}and T

_{sy}may vary.

_{sy}is longer than T

_{min}, it falls into the first category of energy storage. If the T

_{sy}is shorter than T

_{min}, indicating insufficient SOC, and the system is in a charging state, it is categorized as the second type of energy storage. If the system is in a standby or discharge state and the SOC is too low to provide power support, it falls into the fourth category of energy storage, and charging or discharging is stopped. Otherwise, it is categorized as the third type of energy storage, providing power support by reducing output.

_{dis,1}(t) is the output power of the first type of energy storage, SOC(t − 1) is the remaining energy at time t − 1, and S

_{min}is the minimum remaining charge allowed when energy storage outputs at the current power.

_{dis,3}(t) is the output power of the third type of energy storage, SOC

_{high}is the minimum charge corresponding to the allowable power support of energy storage, SOC

_{max}is the maximum charge of energy storage, and λ is the attenuation coefficient.

#### 2.2.2. Adaptive Constraint Handling in Under-Frequency Load Shedding Optimization Strategy

_{i}and x

_{j}be two individuals under consideration, with x

_{i}> x

_{j}indicating that x

_{i}is superior to x

_{j}. Setting ε as the threshold for constraint violation, the specific comparison criteria are as follows:

_{ζ}is the constraint limit value.

_{e}is the truncation algebra, which is transformed to the feasibility law when taking 0.

- (1)
- Generate a large number of load-shedding plans randomly within the [0, ρ
_{max}] space, serving as the initial set S. - (2)
- Filter samples that satisfy frequency constraints. Utilize a uniform removal approach to explore and determine approximate lower (P
_{low}) and upper (P_{up}) limits of load-shedding amounts. Choose plans in S that meet P_{low}< P_{up}to compose the sample set S_{f}. - (3)
- Filter samples that satisfy current or voltage constraints. Calculate the sensitivity of all load-shedding stations and identify the station L
_{s}with the maximum sensitivity. Explore and determine its approximate lower limit with the maximum sensitivity. Explore and determine its approximate lower limit (P_{low,L}). Choose plans in the sample set S_{f}that meet the requirements to form the sample set S_{1}. - (4)
- Randomly select N plans from S
_{1}to form the initial population X_{0}.

#### 2.3. Hierarchical Coordinated Control Method for Systems with a High Proportion of Renewable Energy Sources

_{PV}is the actual output power of the photovoltaic panels; k is the power temperature coefficient, commonly set to −0.3%/°C [36]; G

_{C}and T

_{C}denote real-time solar radiation intensity and surface temperature of the photovoltaic modules, respectively; P

_{W}(t) is the actual output power of the wind turbine at time t; v

_{r}is the rated wind speed; v

_{in}and v

_{out}are the cut-in and cut-out wind speeds of the wind turbine, respectively; and P

_{r}is the rated power of the wind turbine.

_{ess}is the power deviation value, P

_{ref}is the expected grid-connected power of the renewable energy unit system, and P

_{w}and P

_{PV}are the uncontrollable original power of the wind and photovoltaic fields. When P

_{ref}> P

_{w}+ P

_{PV}, indicating insufficient output from the renewable energy unit, P

_{BESS}takes a positive value, representing discharging power, releasing stored energy to compensate for the gap between them. When P

_{ref}< P

_{w}+ P

_{PV}, indicating excess output from the renewable energy unit, P

_{BESS}takes a negative value, representing charging power, absorbing the surplus power.

_{L}(t), P

_{G}(t), P

_{p,w}(t), and P

_{BESS}(t) are the power at time t for load, thermal power, renewable energy, and the energy storage system, respectively. The power supported by the energy storage is expressed by (29):

_{dis,1}(t) and P

_{dis,3}(t) are the output of the energy storage units for the first and third categories.

_{max}is the maximum load-shedding capacity, ΔP

_{e}is the power deficit of the entire system excluding energy storage units, and λ is the attenuation coefficient. It can be observed that as the SOC decreases, the value of D increases. When D is negative, the system quickly adjusts output through energy storage to achieve stability control without the need for load shedding, thus maintaining system stability. When D is a positive number less than 1, the system initiates emergency load shedding for coordinated control to achieve stability. When D is greater than 1, indicating that the power deficit exceeds the maximum load-shedding capacity and SOC is too low to support stable control, the system becomes unstable.

## 3. Case Studies

#### 3.1. Introduction to the Algorithm

_{1}and L

_{2}represent active loads, and the distribution network operates at a voltage of 10 kV and a frequency of 50 Hz, consisting of wind, solar, storage, and synchronous generator units.

#### 3.2. Analysis of Different Scenarios

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

SOC | State of charge |

AGC | Automatic generation control |

ES | Energy storage |

BESS | Battery energy storage system |

PV | Photovoltaic system |

DE | Differential evolution |

DC | Direct current |

T_{min} | Shortest discharge time |

T_{sy} | Remaining discharge time |

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**Figure 1.**Comparison of frequency regulation capability between energy storage units and thermal power units.

**Figure 2.**The control scheme diagram of energy storage: (

**a**) Virtual droop control; (

**b**) PQ double-loop control.

**Figure 6.**The diagram of adaptive constraint handling in under-frequency load-shedding optimization strategy.

**Figure 7.**The hierarchical coordinated control system framework for systems with a high proportion of renewable energy sources.

**Figure 9.**The frequency response under different perturbations: (

**a**) Load surge; (

**b**) Illumination perturbation; (

**c**) Wind speed disturbance; (

**d**) Insufficient storage.

**Figure 10.**The change in output of each unit: (

**a**) Illumination perturbation; (

**b**) Insufficient storage.

**Figure 11.**System response under power deficit: (

**a**) The change in output of each unit; (

**b**) The comparison of frequency curve.

Aspect | Synchronous Machine Inertia | Energy Storage Virtual Inertia |
---|---|---|

Inertia Continuity | Fixed and discrete | Continuous and designable |

Inertial Response Time | Instantaneous action | Some inherent delay |

Source of Response Energy | Mechanical energy from synchronous machines | Electrical energy from energy storage |

Aspect | Synchronous Machine Frequency Regulation | Energy Storage Frequency Regulation |
---|---|---|

Response Delay | Not more than 3 s | Not more than 0.5 s |

Complete Response Time | 10~20 s | Not more than 2 s |

Output Power Coupling | Mechanical energy from synchronous machines should not exceed governor response limits | Theoretically full power range adjustment, generally with certain limits |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Wang, J.; Cao, Y.; Li, B.; Li, C.
A Coordinated Control Strategy of Multi-Type Flexible Resources and Under-Frequency Load Shedding for Active Power Balance. *Symmetry* **2024**, *16*, 479.
https://doi.org/10.3390/sym16040479

**AMA Style**

Zhang J, Wang J, Cao Y, Li B, Li C.
A Coordinated Control Strategy of Multi-Type Flexible Resources and Under-Frequency Load Shedding for Active Power Balance. *Symmetry*. 2024; 16(4):479.
https://doi.org/10.3390/sym16040479

**Chicago/Turabian Style**

Zhang, Jian, Jiaying Wang, Yongji Cao, Baoliang Li, and Changgang Li.
2024. "A Coordinated Control Strategy of Multi-Type Flexible Resources and Under-Frequency Load Shedding for Active Power Balance" *Symmetry* 16, no. 4: 479.
https://doi.org/10.3390/sym16040479