# A Novel Method for Parameter Identification of Renewable Energy Resources based on Quantum Particle Swarm–Extreme Learning Machine

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Load Model Structure and Parameter Sensitivity Analysis

#### 2.1. Synthesis Load Model with Distributed Photovoltaic Sources

#### 2.2. Identification of Key Parameters

_{response}is recognized as the comprehensive observation. P(k) and U(k) are load power and load voltage at the k-th time step, respectively. P

_{0}and U

_{0}are load power and load voltage at the initial step, respectively.

_{j}can be computed using a mathematical calculation approach, as demonstrated by the following formula.

_{D}), inductive motor active power proportion (P

_{MP}), load ratio (K

_{L}), stator reactance (X

_{s}), and constant reactance load proportion (K

_{Z}).

_{PV}).

## 3. Identification of QPSO-ELM-Based Load Model Parameters

#### 3.1. Machine-Learning-Based Parameter Identification Method for Load Model

#### 3.2. Theorem of QPSO-ELM Algorithm

**Step 1:**Initialization: Randomly initialize the input weights and biases of the ELM network and define the particle swarm for QPSO.

**Step 2:**Particle Swarm Optimization: Employ QPSO to optimize the input weights and biases of the ELM network. Each particle in the swarm represents a specific set of input weights and biases. The fitness function used to assess the performance of each particle is typically the mean square error (MSE) between the predicted outputs and the actual outputs.

**Step 3:**Update Input Weights and Biases: Update the input weights and biases of the ELM network using the optimized values obtained from QPSO.

**Step 4:**Training: Train the ELM network using the updated input weights and biases to learn the nonlinear relationship between the input features and the target outputs.

**Step 5:**Testing: Evaluate the performance of the QPSO-ELM model on a validation or test set.

**Step 6:**Repeat Steps 2 to 5: Repeat Steps 2 to 5 for a predefined number of iterations or until a stopping criterion is met.

#### 3.2.1. Theorem of ELM

_{N}= {(X

_{i},t

_{i})|X

_{i}∈ R

^{n}, t

_{i}∈ R

^{m}}, where

**X**

_{i}= [x

_{i}

_{1}, x

_{i}

_{2}, …, x

_{in}]

^{T}∈ R

^{n}represents the input data consisting of voltage and power measurements of the load before and after perturbations, and t

_{i}= [t

_{i}

_{1}, t

_{i}

_{2}, …, t

_{im}]

^{T}∈ R

^{m}represents the load model parameters to be identified. In this study, the structure depicted in Figure 4 is employed, and the mathematical formulation of the ELM model with L hidden neurons and the activation function g(x) can be expressed as follows.

_{i}. ${w}_{j}$ is the weight matrix between the input nodes and j-th hidden node. ${b}_{j}$ is the bias of the j-th hidden node.

**α**is the output weight matrix. T is the vector consisting of training labels, which are load model parameters in this paper.

**α**is the only parameter to be determined, which becomes a linear calculation problem. It can be solved with the following formula.

^{+}is the Moore–Penrose generalized reverse matrix of output weight matrix H.

#### 3.2.2. Algorithm of QPSO

**Step 1:**Set the number of particles in the population to M and the upper limit of computation steps to T. The ideal particle s in the group consists of input weight values and biases of hidden neurons. It is assumed that the ELM has L hidden neurons.

**Step 2:**The initial population is created by assigning values randomly to the parameters within set S, while ensuring that all elements of a particle fall within the range [0, 1]. This random assignment process is repeated M times to generate the initial population ${S}_{0}=[{s}_{0,1},{s}_{0,2},\mathrm{\dots},{s}_{0,M}]$. For the i-th particle in population S

_{0}, its position vector can be expressed as follows:

**Step 3:**At the k-th iteration of the computation, the fitness of each particle within this population is evaluated. The fitness calculation formula is depicted below

_{train}denotes the number of training samples, t

_{i}represents the output load parameter of the ELM model, and oi represents the actual load model parameter.

**Step 4:**For particle i within the population S

_{t}, the historical best position ${p}_{best,i}^{k}$ is updated along with the population’s overall best position ${g}_{best}^{k}$. Additionally, the local attractor of each particle ${P}_{ij}^{k}$ as well as the average best position, ${m}_{best,j}^{k}$, are computed utilizing the following formula:

**Step 5:**Iterate through steps 3 and 4 until the maximum computation step T is reached. At this point, the optimization result ${g}_{best}^{T}$ is obtained, which ultimately determines the input weights and biases of the hidden neurons in the ELM model.

## 4. Case Study

#### 4.1. Sample Generation

#### 4.2. Performance Comparison between PSO and Common ELM Method

#### 4.3. Performance Comparison between Common ELM Method and QPSO-ELM Method

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Structure of the construction and application of the machine-learning-based load model parameter identification method.

**Figure 5.**Performance comparison between ELM and QPSO-ELM: (

**a**) Relative error comparison for parameter XD between ELM and QPSO−ELM. (

**b**) Relative error comparison for parameter PMP between ELM and QPSO−ELM. (

**c**) Relative error comparison for parameter KL between ELM and QPSO−ELM.

Parameter Name | Parameter Symbols |
---|---|

Distributed Network Reactance | X_{D} |

Inductive Motor Active Power Proportion | P_{MP} |

Load Ratio | K_{L} |

Stator Reactance | X_{s} |

Constant Reactance Load Proportion | K_{Z} |

Direct-Current Side Capacitor | C |

Photovoltaic Output Equivalent Reactance | X_{PV} |

Parameter Symbols | X_{D} | P_{MP} | K_{L} | X_{s} |
---|---|---|---|---|

Ranging Region | [0.05, 0.15] | [0, 80] | [0.2, 0.8] | [0.06, 0.18] |

Parameter Symbols | K_{Z} | C | X_{PV} | |

Ranging Region | [0.2, 0.6] | [0, 100] | [0.01, 0.06] |

Parameter Symbols | Set Value | PSO Method | Common ELM Method |
---|---|---|---|

X_{D} | 0.075 | 0.079 | 0.080 |

P_{MP} | 48.0 | 48.621 | 49.134 |

K_{L} | 0.5 | 0.465 | 0.445 |

X_{s} | 0.09 | 0.085 | 0.094 |

K_{z} | 0.35 | 0.367 | 0.355 |

C | 28.0 | 27.251 | 27.089 |

X_{PV} | 0.03 | 0.028 | 0.028 |

Parameter Symbols | Common ELM Method | QPSO-ELM Method |
---|---|---|

X_{s} | 6.13% | 4.32% |

K_{z} | 4.77% | 4.10% |

C | 3.15% | 2.23% |

X_{PV} | 4.62% | 3.66% |

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**MDPI and ACS Style**

Xu, B.; Yin, Y.; Yu, J.; Li, G.; Li, Z.; Yang, D.
A Novel Method for Parameter Identification of Renewable Energy Resources based on Quantum Particle Swarm–Extreme Learning Machine. *World Electr. Veh. J.* **2023**, *14*, 225.
https://doi.org/10.3390/wevj14080225

**AMA Style**

Xu B, Yin Y, Yu J, Li G, Li Z, Yang D.
A Novel Method for Parameter Identification of Renewable Energy Resources based on Quantum Particle Swarm–Extreme Learning Machine. *World Electric Vehicle Journal*. 2023; 14(8):225.
https://doi.org/10.3390/wevj14080225

**Chicago/Turabian Style**

Xu, Baojun, Yanhe Yin, Junjie Yu, Guohao Li, Zhuohuan Li, and Duotong Yang.
2023. "A Novel Method for Parameter Identification of Renewable Energy Resources based on Quantum Particle Swarm–Extreme Learning Machine" *World Electric Vehicle Journal* 14, no. 8: 225.
https://doi.org/10.3390/wevj14080225