Evaluation method of a new power system construction based on improved LSTM neural network

Abstract

The evaluation of new power system construction is the research foundation for improving the flexible regulation ability and comprehensive operational efficiency of new power systems, and achieve the comprehensive goals of safe power supply, green consumption, and economic efficiency. However, the existing research on the evaluation index system of new power system construction can not fully reflect the main objectives of new power system construction. Therefore, this paper first develops a source-load and green-intelligence multi-level and multi-dimensional evaluation system for new power system construction from source-load side equipment, green power, reliable power supply, and intelligent power consumption. Secondly, a hybrid optimization algorithm is proposed based on fluid search algorithm (FSO) for improving the Long Short-Term Memory (LSTM) neural network parameter updating method. Then, the improved LSTM neural network is applied to the construction evaluation of the new power system. Finally, the simulation results show that the evaluation error of the new power system construction evaluation method is 0.0063, which has a high evaluation.

Keywords

New power system construction evaluation system LSTM neural networks fluid search algorithms

1. Introduction

The proportion of renewable energy in the power system’s energy supply is gradually increasing due to the ongoing promotion of green and low-carbon energy transformation. Furthermore, the traditional power system structure and market mechanism cannot support a high proportion of new energy consumption, so it is critical to construct a new power system with new energy as the main body [1, 2]. The new power system is based on the premise of ensuring power supply security, with clean energy as the primary supply body and green power consumption as the primary goal. It has such outstanding features as being safe and controllable, intelligent and flexible, open and interactive. Based on digital technology, it’s able to polymerize source, network, load, and storage resources, and the flexible regulation capacity, safety, security level and comprehensive operation efficiency of the system should be enhanced in multiple dimensions, so as to achieve the comprehensive goals of safe power supply, green consumption and economic efficiency [3].

Building the new power system is a complex system engineering, and it still faces many problems. On the one hand, due to the strong correlation between the output of new energy and complex random meteorological factors, and the characteristics of massive distributed interconnection of new energy and new loads, the analysis of safe operation of power grid is further complicated [4, 5]. On the other hand, the current power market construction lacks the market mechanism to support the interaction between source, grid, load, and storage, and it is difficult to support the flexible participation of market participants in all aspects of power generation, transmission and distribution in the new power system, and the optimization depth of power resources is insufficient [6, 7]. However, the above problems can’t give the corresponding decision-making basis when making the power system planning and operation plan, so it is necessary to evaluate the system state capability. At present, the research on evaluation of power system planning and construction focuses on reliability evaluation and stochastic production simulation etc. [8]. The system response capability can be quantified by combining evaluation index system with evaluation methods.

Scholars both at home and abroad have conducted extensive research on the evaluation index system of new power systems. The evaluation index system of multi-energy system is formed by considering the influencing factors of economy, energy utilization and reliability [9]. Based on the light gradient boosting machine, Zhao et al. [10] established a prediction model for the frequency index, and the frequency stability of the system is comprehensively judged by the prediction index. Zeng et al. [11] constructs the design and model of renewable energy policy evaluation system for power grid companies based on ubiquitous power Internet of Things platform. Yuan et al. [12] considers the technical and economic quantification and evaluation analysis of power system operation plan in complex environment, and puts forward the panoramic operation simulation method and evaluation index system of new energy power system considering multi-cycle coordination. Based on the theory of segmented multi-objective risk analysis, a multi-level index and weak link identification system for new energy systems with different risk types is established [13]. Han et al. [14] sorts out the internal and external factors of new power system, and puts forward a new multi-dimensional evaluation system of power system. However, when constructing the system evaluation index system, not only multi-level evaluation indexes but also multi-dimensional evaluation indexes should be considered.

Scholars at home and abroad have also done a lot of research on new power system evaluation methods. Wang et al. [15] proposed a comprehensive evaluation method of power system transient frequency security based on deep residual contraction network. The influence weight of indicators is obtained by grey correlation theory, and the comprehensive possibility index of branch faults is obtained by fuzzy comprehensive evaluation, so as to evaluate the possibility of pre-misoperation concentrated branch faults [16]. An online identification algorithm of characteristic parameters of small signal stability is proposed to evaluate the small signal stability of power system online [17]. The data-driven power system transient stability evaluation method can realize real-time and accurate transient stability evaluation only by using the dynamic response time series data after system failure [18]. The conventional one-dimensional convolutional neural network is improved by using multi-size convolutional kernel and block convolution, and an evaluation method of power system transient stability based on the improved one-dimensional convolutional neural network is proposed, which improves the model’s ability to extract time series information and reduces the redundant parameters of the model [19]. Zhou et al. [20] puts forward an intelligent evaluation model of transient stability of power system based on neural network, and proposes a sample generation method for the process of transfer learning sample generation. However, there are some problems in the above research, such as low accuracy and large error in the results of power system evaluation and analysis. Therefore, this paper proposes a construction evaluation method based on improved LSTM neural network.

In conclusion, the construction of new power system is the key to promote the clean transformation of energy. However, the construction of new power system faces numerous challenges and changes, such as new balance system, complex safely mechanisms and cost diversion mechanisms. At present, domestic and foreign scholars have little research on the evaluation of new power system construction. Therefore, this paper constructs a multi-level and multi-dimensional evaluation system of source-load and green-intelligence for new power system construction from the aspects of source-side equipment, load-side equipment, green power, reliable power supply and intelligent power consumption. An improved fluid search algorithm based on simulated annealing algorithm is proposed, which is applied to LSTM neural network parameter updating and evaluation of new power system construction.

2. Source-load and green-intelligence multi-level and multi-dimensional evaluation system

Internal and external evaluation factors are included in the multi-level and multi-dimensional evaluation index system of source-load and green-intelligence of the new power system constructed in this paper. Internal evaluation factors include source-side, network-side, and load-side equipment characteristics, reflecting real-time source-load interaction and high integration of all aspects of the new power system. External evaluation factors include green power, reliable power supply, and intelligent power consumption, reflecting the essential characteristics of the new power system of green, efficient, flexible, and open, as well as digitally empowered.

2.1 Internal evaluation factors

The difficulty of new energy consumption and the resulting power peaking problem is an important factor affecting power operation as the proportion of new energy installations increases, where the peaking power of thermal power units and the available climbing capacity of thermal power during peak load hours are defined as indicators to assist in the analysis of the contribution of thermal power peaking.

(1) Thermal power units participate in deep peaking-shaving $Q^{T}_{D}$ :

$\displaystyle Q_{D}^{T}=\sum\limits_{t=1}^{N}{\sum\limits_{t=1}^{N^{T}}{\max% \left({P_{i}^{T,a}-P_{i,t}^{T},0}\right)\Delta t}}$ (1)

where $P^{T}_{i,t}$ is the active power of thermal unit $i$ at time $t$ ; $P^{T,a}_{i}$ is the preset peaking threshold of the thermal unit $i$ ; $N^{T}$ is the number of thermal units participating in short-term and medium-term generation dispatch; $N$ is the total number of optimization periods; $\Delta t$ is the time interval of time period $t$ .

(2) Increasing thermal power unit margins during peak load hours $Q^{T}_{A}$ :

$\displaystyle Q_{A}^{T}=\sum\limits_{t=1}^{N^{T}}{\left({P_{i}^{T,\max}-P_{i,t% }^{T}}\right),t\in N^{P}}$ (2)

where $P^{T,\max}_{i}$ is the maximum installed capacity of the thermal power unit.

At the moment, the new power system is distinguished by “double peaks”, “double highs” and “double random”, with the load side playing an increasingly important role. The load side evaluation indicators of the new power system should take into account the demand response effect reflecting the load side’s regulation ability and the load side power substitution effect. As auxiliary analysis indicators, the maximum daily peak-to-valley ratio and daily variation rate of net load are defined using the mathematical expressions below.

(3) Peak-to-valley differential rate on the maximum net load day $P^{N}_{P}$ :

$\displaystyle P_{P}^{N}={\left[{\mathop{\max}\limits_{t\in D}P_{t}^{N}-\mathop% {\max}\limits_{t\in D}P_{t}^{N}}\right]}\mathord{\left/{\vphantom{{\left[{% \mathop{\max}\limits_{t\in D}P_{t}^{N}-\mathop{\max}\limits_{t\in D}P_{t}^{N}}% \right]}{\mathop{\max}\limits_{t\in D}P_{t}^{N}}}}\right.\kern-1.2pt}{\mathop{% \max}\limits_{t\in D}P_{t}^{N}}$ (3)

where $P^{N}_{t}$ is the power of the net load curve at moment $t$ in day $D$ .

(4) Change in net load per day $R^{N}_{D}$ :

$\displaystyle R_{D}^{N}=\left[{\left({1\mathord{\left/{\vphantom{1{N^{D}}}}% \right.\kern-1.2pt}{N^{D}}}\right)\sum\limits_{t=1}^{N^{D}}{\left({{P_{t}^{N}-% E\left({P_{t}^{N}}\right)}\mathord{\left/{\vphantom{{P_{t}^{N}-E\left({P_{t}^{% N}}\right)}{\mathop{\max}\limits_{t\in D}\left({P_{t}^{N}}\right)}}}\right.% \kern-1.2pt}{\mathop{\max}\limits_{t\in D}\left({P_{t}^{N}}\right)}}\right)}^{% 2}}\right]^{1\mathord{\left/{\vphantom{12}}\right.\kern-1.2pt}2}$ (4)

where $E$ ( $P^{N}_{t}$ ) is the average of the net load curve on day $D$ ; $N^{D}$ is the number of hours included on day $D$ .

2.2 External evaluation factors

“Green power” is not only the power grid company’s social responsibility, but also the power industry’s overall social responsibility. The focus of attention in developing a new power system is on how to increase the proportion of new energy in China’s energy consumption structure. The environmental indicators in this paper are divided into the total utilization rate of primary energy and the proportion of renewable energy.

(1) Rate of total primary energy utilization: The formula shown below calculates the comprehensive primary energy utilization rate $\eta$ . The higher the indicator, the lower the consumption of nonrenewable primary energy and the higher the consumption of renewable energy.

$\displaystyle\eta=\frac{W_{e,t}+W_{h,t}+W_{c,t}}{W_{G,t}}$ (5)

where $W_{e,t},W_{h,t}$ and $W_{c,t}$ are the electricity, heat and cooling supply of the multi-energy system at time $t$ respectively; $W_{G,t}$ is the power generation of thermal power units at time $t$ .

(2) The ratio of renewable energy: The renewable energy ratio is the proportion of electricity supplied by renewable energy sources such as wind and light to total cooling, heating, and electricity demand in a multi-energy system. The renewable energy ratio reflects the use of wind, light, and other renewable energy sources, and the calculation formula is shown in Eq. (6):

$\displaystyle\beta_{\textit{RE}}=\frac{W_{\textit{RE,t}}}{W_{e,t}+W_{h,t}+W_{c% ,t}}$ (6)

where $W_{\textit{RE,t}}$ is the amount of electricity supplied by renewable energy sources such as wind and light from the multi-energy system at time $t$ .

The basic requirement for the new power system is a “reliable power supply”. Power grid companies must ensure adequate resources, a strong grid, safe and stable operation, and increased electricity supply reliability. The reliability index is divided into supply reliability and peak capacity ratio in this paper.

(3) Supply reliability: The ability of a power supply system to supply electricity continuously is referred to as supply reliability. The energy supply deficit $\Delta W_{\textit{LOSS}}$ , defined as a system’s reliability, is expressed as:

$\displaystyle\Delta W_{\textit{Loss}}={\left({\Delta W_{e,t}+\Delta W_{h,t}+% \Delta W_{c,t}}\right)}\mathord{\left/{\vphantom{{\left({\Delta W_{e,t}+\Delta W% _{h,t}+\Delta W_{c,t}}\right)}{\left({W_{e,t}+W_{h,t}+W_{c,t}}\right)}}}\right% .\kern-1.2pt}{\left({W_{e,t}+W_{h,t}+W_{c,t}}\right)}$ (7)

where $\Delta W_{e,t}$ , $\Delta W_{h,t}$ , $\Delta W_{c,t}$ are the supply deviations of the electrical, thermal and cooling loads respectively for time period $t$ .

(4) Peaking capacity ratio: The peaking capacity ratio $\delta$ is defined as the ratio of the adjustable capacity of the operating units in the system to the total rated capacity of the units, reflecting the system’s reliability, and is calculated as shown in Eq. (8):

$\displaystyle\delta={\sum\limits_{t}{\sum\limits_{r=1}^{R}{P_{f,t,r}}}}% \mathord{\left/{\vphantom{{\sum\limits_{t}{\sum\limits_{r=1}^{R}{P_{f,t,r}}}}{% \sum\limits_{r=1}^{R}{P_{N,r}}}}}\right.\kern-1.2pt}{\sum\limits_{r=1}^{R}{P_{% N,r}}}$ (8)

where $R$ is the number of operating units; $P_{f,t,r}$ is the adjustable capacity of unit $r$ at time $t$ ; $P_{N,r}$ is the rated capacity of unit $r$ .

“Smart electricity” is the main technical approach that reflects the improvement of quality and efficiency of power grid companies. It is a prerequisite for promoting “green power”, “reliable power” and “efficient power”. The intelligence indicators in this paper are divided into intelligent distribution network capacity ratio and intelligent rate of substation primary equipment.

(5) Intelligent distribution network capacity ratio: This indicator reflects the level of promotion and application of intelligent distribution networks, as shown in Eq. (9):

$\displaystyle\eta=\left({{S_{a}}\mathord{\left/{\vphantom{{S_{a}}S}}\right.% \kern-1.2pt}S_{z}}\right)\times 100\%$ (9)

where $\eta$ is the intelligent distribution network capacity ratio; $S_{a}$ , $S_{z}$ are the intelligent distribution network capacity and the full distribution network electrical capacity respectively.

(6) Transformer primary equipment intelligence rate: Transformer primary equipment refers to all high-voltage equipment, such as transformers, disconnecting switches, circuit breakers, mutual transformers, and so on. The following is the corresponding calculation in Eq. (10):

$\displaystyle\eta_{n}=\left({{N_{a}}\mathord{\left/{\vphantom{{N_{a}}N}}\right% .\kern-1.2pt}N_{z}}\right)\times 100\%$ (10)

where $\eta_{n}$ is the intelligent rate of substation primary equipment; $N_{a}$ , $N_{z}$ are the number of intelligent devices in substation primary equipment and the number of all primary equipment respectively.

3. Based on a hybrid optimization algorithm, the LSTM neural network

3.1 LSTM neural networks

Hochreiter and Schmidhuber proposed the LSTM neural network as a special recurrent neural network that can be used to process long-time sequence data with high accuracy, fast training speed, and strong parallel processing capability [21]. While LSTM shares many characteristics with RNN models, it employs special implicit units to solve the long-term dependence problem and avoid gradient disappearance. The current basic LSTM network structure is shown in Fig. 1.

Figure 1.

LTSM structure diagram.

An oblivion threshold, an input threshold, an output threshold, and a neural unit state comprise the LSTM neural network model. The following mathematical model of an LSTM neural network is constructed in this paper.

The forgetting threshold determines which information needs to be discarded and is expressed as:

$\displaystyle f_{t}=\sigma\left({W_{f}\left[{h_{t-1},x_{t}}\right]+b_{f}}\right)$ (11)

where $f_{t}$ is the activation vector of the forgetting threshold; $\sigma$ is the sigmoid function; $W$ is the weight matrix; $h_{t}$ is the output vector of the LSTM neuron; $x_{t}$ is the LSTM neuron; $b_{f}$ is the bias term, and the subscript $t$ indicates different moments.

The input threshold determines which new information is stored in the cell state and is expressed as:

$\displaystyle i=\sigma\left({W_{i}\left[{h_{t-1},x_{t}}\right]+b_{i}}\right)$ (12) $\displaystyle\tilde{C}=\tanh\left({W_{C}\left[{h_{t-1},x_{t}}\right]+b_{c}}\right)$ (13)

where $i_{t}$ is the activation vector for the input threshold. $\tilde{C}$ is the current state of the input cell.

The unitary state is analogous to a conveyor belt that runs the length of the network. Because there are only minor linear interactions, the expression can easily flow downwards in an invariant manner:

$\displaystyle C_{t}=f_{t}C_{t-1}+i_{t}\tilde{C}_{t}$ (14)

where $C_{t}$ is the neuronal cell state vector.

The expression outputs the current state of the output threshold control unit to the LTMS neural network model.

$\displaystyle o_{t}=\sigma\left({W_{o}\left[{h_{t-1},x_{t}}\right]+b_{0}}\right)$ (15) $\displaystyle C_{t}=f_{t}C_{t-1}+i_{t}\tilde{C}_{t}$ (16)

where $o_{t}$ is the activation vector for the output threshold.

The LSTM neural network’s network parameters are updated using a gradient descent-based error backward transmission method, which consists of the following steps: First, the output values of each neuron are calculated forward according to Eqs (11)–(16), $f_{t},i_{t},C_{t},o_{t},h_{t}$ . Second, the error terms are propagated backward along the time inverse direction, and the previous layer is ignored. Then, the gradient of each weight is calculated based on the error terms to adjust the model parameters so that the predicted output of the model matches the actual output. Finally, the preceding procedure is repeated to train the network model until the training error accuracy or the maximum number of iterations is met, resulting in the construction of the LSTM neural network prediction model.

However, due to the basic LSTM neural network updates the network parameters by using the method of error inverse transmission based on gradient descent, this parameter updating method has two problems. First, it is easy to fall into local extremum, which leads to the calculated network parameters not being the optimal network parameters. Secondly, the optimal network parameters calculated by this method have a great relationship with the initial value of the iterative process of network parameter calculation, which makes the optimal network parameters more uncertain. Therefore, a hybrid optimization algorithm based on fluid search algorithm is proposed to update LSTM neural network parameters, which makes the network parameters trained by the network have higher accuracy.

3.2 Algorithms for fluid search

The fluid search algorithm is an optimization algorithm for fluid search that is inspired by Bernoulli’s principle in fluid mechanics. Bernoulli’s principle states that “for isometric flow, fluid pressure decreases as fluid velocity increases” and is used to describe the relationship between fluid velocity and fluid pressure [22]. The Bernoulli equation is written as follows.

$\displaystyle p+\frac{1}{2}\rho v^{2}=p_{0}$ (17)

where $p$ is the pressure at a point on the flow line; $p$ describes the constant system pressure; $v$ is the fluid velocity at that point, and $\rho$ describes the fluid density at all points in the fluid.

Equation (17) is transformed to express the relationship between fluid pressure and flow rate.

$\displaystyle v=\sqrt{\frac{2(p_{0}-p)}{\rho}}$ (18)

The position update formula is shown in Eq. (19):

$\displaystyle x_{\textit{new}}=x_{\textit{old}}+v$ (19)

This paper defines and builds mathematical models for the pressure, density, and velocity of fluid infinitesimals involved in the FSO algorithm’s optimization process.

Fluid infinitesimal pressure. Assume that the FSO algorithm initially selects n infinitesimal locations at random: $X=[x_{1},x_{2},\ldots,x_{n}]$ and the fitness function is $Y=[y_{1},y_{2},\ldots,y_{n}]$ , where the optimal and worst fitness function values are $y_{\textit{best}}$ and $y_{\textit{worst}}$ respectively. Then the infinitesimal pressure $p_{i}$ is obtained by solving the normalized formula, which is expressed as follows:

$\displaystyle p_{i}=\frac{(y_{\textit{worst}}-y_{i})}{(y_{\textit{worst}}-y_{% \textit{best}})}$ (20)

where $p_{i}$ is a normalized value lying between 0 and 1 to prevent too large a range of objective function values from having an impact on the algorithm’s position update magnitude.

Fluid density is infinitesimal. The total number of adjacent infinitesimals in the current infinitesimal cell is expressed as the density of infinitesimals:

$\displaystyle\rho=\frac{m}{l^{D}}$ (21)

where $l$ is the cell side length of the infinitesimal; $m$ is the number of other infinitesimals in the D-dimensional hypercube with l as the cell side length.

Infinitely small velocity of fluid. Equation (18) can be used to calculate the value of the fluid’s infinitesimal velocity, and Eq. (22) can be used to calculate the direction of the velocity. This vector sum is also normalized to prevent the given weight from being influenced by the distance to other infinitesimals.

$\displaystyle\vec{p}_{i}=\sum\limits_{\begin{subarray}{c}j=1\\ j\neq i\end{subarray}}^{n}{\textit{rand}\otimes p_{j}\frac{(X_{j}-X_{i})}{|(X_% {j}-X_{i})|_{2}}}+\textit{rand}\otimes p_{\textit{best}}\times 2\times\frac{(X% _{\textit{best}}-X_{i})}{|(X_{\textit{best}}-X_{i})|_{2}}$ (22)

Formula for the new direction is expressed as:

$\displaystyle D_{n}=\gamma\times D_{l}+\frac{\overrightarrow{p}_{i}}{|% \overrightarrow{p}_{i}|_{2}}$ (23)

where $D_{n}$ is the new direction; $D_{l}$ is the previous direction; and $\gamma$ is the inertia factor.

However, the basic FSO algorithm performs a local search in the vicinity of $y_{\textit{best}}$ and $y_{\textit{worst}}$ generated during the update of fluid infinitesimals. The values of $y_{\textit{best}}$ and $y_{\textit{worst}}$ directly affect the next update of fluid infinitesimals, while the values of $y_{\textit{best}}$ and $y_{\textit{worst}}$ are determined based on the current position and velocity. This approach causes the fluid infinitesimals in the population to all to converge rapidly towards the optimal position, which in turn causes the FSO algorithm to fall into a local optimum when optimizing the Elman neural network error function, to the detriment of the algorithm’s global search.

Therefore, this topic introduces the simulated annealing algorithm, an algorithm with good global search performance, for improving the process of finding $y_{\textit{best}}$ and $y_{\textit{worst}}$ by the FSO algorithm in order to increase the global optimization potential of the resulting $y_{\textit{best}}$ and $y_{\textit{worst}}$ .

3.3 Improving the fluid search algorithm (IFSO)

In this paper, the simulated annealing formula is introduced as an auxiliary part of the FSO algorithm to find the $y_{\textit{best}}$ and $y_{\textit{worst}}$ for each iteration of the FSO algorithm. The simulated annealing algorithm starts with a certain higher initial temperature and randomly selects the global optimal solution of the objective function in the solution space with a certain probability as the temperature parameter decreases, increasing $y_{\textit{best}}$ and $y_{\textit{worst}}$ to increase the particle diversity and avoid premature particle maturation. IFSO algorithm calculation steps are as follows.

Step1: Initialize the FSO algorithm parameters. Randomly initialize the fluid infinitesimal position $X_{i}$ , the fluid velocity $V_{i}=$ 0, the velocity direction $D=$ 0, the density $\rho=$ 1, and the initial pressure $p=$ 1.

Step2: Calculate the fitness function values. Calculate the fitness function value $y_{i}$ for each infinitesimal based on the location $X_{i}$ of the fluid infinitesimal. Update the best fitness function value $y_{\textit{best}}$ and the worst fitness function value $y_{\textit{worst}}$ and calculate the number of other infinitesimals in the current infinitesimal cell.

Step3: Choose whether to perform oscillation annealing on $y_{\textit{best}}$ and $y_{\textit{worst}}$ according to the probability function of individual diversity, where individual diversity can be used in the FSO algorithm with fluid infinitesimal density. The density function is mapped by the sigmoid function to a probability value $p_{1}$ between 0 and 1, and then the particle velocity position is updated after the annealing shock is chosen by a random number.

$\displaystyle p_{1}=\frac{2}{1+\exp\left({-10\cdot\rho}\right)}-1$ (24) $\displaystyle\left\{{{\begin{array}[]{ll}{\text{Step4}}&{\textit{rand}<p_{1}}% \\ {\text{Step5}}&{\textit{rand}\geqslant p_{1}}\\ \end{array}}}\right.$ (25)

Step4: Shock anneal $y_{\textit{best}}$ and $y_{\textit{worst}}$ . After this step, perform Step6. First, set the initial annealing temperature to:

$\displaystyle T_{0}=-\frac{f(y_{\textit{best}}^{1})}{\ln 0.2}$ (26)

A new individual $x^{\prime}=x+\Delta x$ is then generated in the vicinity of each individual’s cell and the increment of the objective function value $\Delta f(x)=f(x^{\prime})-f(x)$ is calculated.

Calculate $p_{2}$ by the following equation, choose whether to retain the original individuals.

$\displaystyle p_{2}=\left\{{{\begin{array}[]{ll}1,&\Delta f>0\\ \exp\left({-\frac{f\left(x\right)-f\left({x}^{\prime}\right)}{T}}\right),&% \Delta f\leqslant 0\\ \end{array}}}\right.$ (27) $\displaystyle\left\{{{\begin{array}[]{ll}{x=x}&{\textit{rand}<p_{\textit{% reserve}}}\\ {x=x^{\prime}}&{\textit{rand}\geqslant p_{\textit{reserve}}}\\ \end{array}}}\right.$ (28)

The above-simulated annealing operation is performed $l_{k}$ times, after each execution the temperature is reduced according to the temperature decay update formula.

$\displaystyle T\left(k\right)=\delta^{k}T_{0}$ (29)

where $\delta$ is the annealing factor.

Step5: Normalise the fitness function values, i.e. calculate the fluid infinitesimal pressure corresponding to each fitness function.

Step6: Calculate the direction and velocity of the fluid infinitesimals and multiply them together to obtain the fluid infinitesimal velocity vector for the next iteration.

Step7: Update the position of each fluid infinitesimal.

Step8: Determine whether the current iteration count reaches the maximum iteration count, if not then go to Step 2, otherwise the iteration terminates.

3.4 LSTM neural network model based on IFSO algorithm

The proposed IFSO algorithm is implemented in the LSTM neural network in this paper, and the IFSO algorithm is used to solve the LSTM neural network error function in order to solve the optimal network parameters of the LSTM neural network. The improved LSTM neural network based on the IFSO algorithm is shown in Fig. 2.

Figure 2.

Depicts the structure of an improved LSTM neural network based on the IFSO algorithm.

The cost function of the equation is used to train the improved LSTM neural network parameters Eq. (30). The IFSO algorithm optimizes the following error function to allow the LSTM neural network to accurately identify the PEMFC system.

$\displaystyle\textit{Error}=\min\left\{{\sum\limits_{i=1}^{M}{\left({y-\hat{y}% }\right)^{2}}}\right\}$ (30)

where $M$ is the number of training samples; $y$ and $\hat{y}$ . are the predicted and actual values of the output of the improved LSTM neural network, respectively.

4. Case presentation

To validate the effectiveness of the proposed new evaluation method for power system construction, provincial power systems in various regions are selected to conduct multi-level and multi-dimensional cluster analysis, and the basic data of corresponding evaluation indexes are collected. Table 1 shows the basic data of four selected power grid evaluation indices [14].

Table 1
Assessment data for the construction of new power systems

Evaluation index	System1	System2	System3	System4
Utilization of new energy within and outside the region	Good	Commonly	Excellent	Excellent
Comprehensive utilization rate of new energy	78.41%	82.21%	95.97%	93.48%
New energy installed capacity ratio	18.47%	25.26%	35.21%	22.65%
Proportion of new energy electricity	9.67%	15.32%	16.52%	13.07%
System frequency support capability	Commonly	Good	Excellent	Excellent
System reserve rate	5.92%	10.23%	13.15%	11.90%
Transmission line heavy load level	Good	Excellent	Excellent	Excellent
Probability of insufficient power	1.39%	1.23%	0.89%	1.01%
Contribution rate of new energy peak shaving	65.15%	77.35%	79.31%	69.47%
Renewable energy utilization rate	13.84%	11.02%	14.98%	12.62%
Distributed wind and solar penetration rate	Relatively high	Commonly	Commonly	Commonly
Wind and light abandonment rate	Relatively high	Commonly	Commonly	Relatively high
Plant network coordination device application scale	Commonly	Good	Good	Good
Proportion of new power transmission technology applications	Relatively high	Commonly	Relatively high	Commonly
Intelligent substation capacity ratio	30.46%	40.02%	45.13%	38.67%
Electricity information system collection rate	91.45%	97.39%	99.19%	98.09%

In this paper, the normalization operation is used to preprocess the data in Table 1 to avoid data loss caused by numerical differences in important data, and all data can be kept in the same order of magnitude, which is convenient for the convergence of the neural network algorithm and parameter model training process. The data normalization processing method is demonstrated in Eqs (31) and (32); Eq. (31) applies to data with a positive correlation between parameter values and targets, while Eq. (32) applies to data with a negative correlation between parameter values and targets.

$\displaystyle{x}^{\prime}_{i}=x_{\min}^{\lim}+\frac{\left({x_{\max}^{\lim}-x_{% \min}^{\lim}}\right)\left({x_{i}-x_{\min}}\right)}{x_{\max}-x_{\min}}$ (31) $\displaystyle{x}^{\prime}_{i}=x_{\max}^{\lim}-\frac{\left({x_{\max}^{\lim}-x_{% \min}^{\lim}}\right)\left({x_{i}-x_{\min}}\right)}{x_{\max}-x_{\min}}$ (32)

where $x^{\lim}_{\max}$ and $x^{\lim}_{\min}$ are the upper and lower bounds of data $x$ , respectively. $x^{\lim}_{\max}$ is set to 1 and $x^{\lim}_{\min}$ to 0. Table 2 shows the processed data.

Table 2

Evaluation data of new power system construction after data preprocessing

Evaluation index	System1	System2	System3	System4
Utilization of new energy within and outside the region	0.5000	0.0000	1.0000	1.0000
Comprehensive utilization rate of new energy	0.0000	0.2164	1.0000	0.8582
New energy installed capacity ratio	0.0000	0.4056	1.0000	0.2497
Proportion of new energy electricity	0.0000	0.8248	1.0000	0.4964
System frequency support capability	0.0000	0.5000	1.0000	1.0000
System reserve rate	0.0000	0.5961	1.0000	0.8271
Transmission line heavy load level	0.0000	1.0000	1.0000	1.0000
Probability of insufficient power	0.0000	0.3200	1.0000	0.7600
Contribution rate of new energy peak shaving	0.0000	0.8616	1.0000	0.3051
Renewable energy utilization rate	0.7121	0.0000	1.0000	0.4040
Distributed wind and solar penetration rate	1.0000	0.0000	0.0000	0.0000
Wind and light abandonment rate	1.0000	0.0000	0.0000	0.0000
Plant network coordination device application scale	0.0000	1.0000	1.0000	1.0000
Proportion of new power transmission technology applications	0.0000	0.5000	1.0000	0.5000
Intelligent substation capacity ratio	0.0000	0.6517	1.0000	0.5596
Electricity information system collection rate	0.5000	0.0000	1.0000	1.0000

5. Simulation results

5.1 Validation of the IFSO algorithm’s performance

To validate the performance of the proposed IFSO algorithm for solving non-linear problems, it is compared to the Genetic Algorithm (GA) algorithm, Particle Swarm Optimization (PSO) algorithm, Ant Colony Optimization (ACO), and Whale optimization algorithm (WOA) for each of the four typical non-linear mathematical functions. The typical non-linear mathematical formulations used for algorithm performance validation are shown in Table 3.

Table 3
Typical non-linear mathematical formulations for algorithm performance verification

Functions	Formula	Restrictions	Dimensionality
Rastrigin	$f_{1}(x)=10D+\sum\limits_{i=1}^{D}{\left({x_{i}^{2}-10\cos\left({2\pi x_{i}}% \right)}\right)}$	[ $-$ 512,512]	50
Rosenbrock	$f_{2}(x)=\sum\limits_{i=1}^{D-1}{\left({100\left({x_{i}^{2}-x_{i+1}}\right)+% \left({x_{i}-1}\right)^{2}}\right)}$	[ $-$ 2.045,2.045]	50
Ackley	$\begin{array}[]{c}f_{3}(x)=-20\exp\left({-0.2\sqrt{\frac{1}{D}\sum\limits_{i=1% }^{D}{x_{i}^{2}}}}\right)\\ -\exp\left({\frac{1}{D}\sum\limits_{i=1}^{D}{\cos\left({2\pi x_{i}}\right)}}% \right)+20+e\\ \end{array}$	[ $-$ 10,10]	50
Sphere	$f_{4}(x)=\sum\limits_{i=1}^{D}{x_{i}^{2}}$	[512,512]	50

For each of the four typical non-linear mathematical formulas in Table 3, each algorithm was solved 50 times, and the mean squared error (MSE) and absolute error (MAE) of the calculated results were recorded. The MSE and MAE of the IFSO, GA, PSO, ACO, and WOA algorithms for the four typical non-linear mathematical formulas are shown in Table 4.

Table 4

Comparison of calculation accuracy results by algorithm

Function		IFSO	GA	PSO	ACO	WOA
$f_{1}$	MSE	0.00	70.61	74.24	13.45	2.58
	MAE	0.00	1.66	8.96	5.34	2.14
$f_{2}$	MSE	2.24	35.41	200.1	56.70	8.47
	MAE	0.13	27.15	59.00	16.89	1.73
$f_{3}$	MSE	0.00	3.19e-2	8.26	3.26e-3	3.17e-16
	MAE	0.00	2.14e-2	1.19	2.17e-3	0.00
$f_{4}$	MSE	0.00	1.15e-4	8.27e-4	5.23e-5	9.65e-11
	MAE	0.00	3.14e-5	5.12e-4	2.45e-5	9.83e-17

As can be seen from Table 4, the IFSO algorithm solves four typical non-linear mathematical formulas with minimal MSE and MAE and higher search accuracy than the GA, PSO, ACO and WOA algorithms. Therefore, the IFSO algorithm has the advantages of high search efficiency, high optimisation accuracy and less likely to fall into local optimality when solving complex functions with multiple polarisation points, and can be used as an effective method for solving non-linear, high-dimensional functions.

5.2 The effectiveness of a new power system evaluation method based on improved LSTM neural networks

The S-fold cross-validation method is used to improve the evaluation accuracy of the improved LSTM neural network proposed in this paper. The S-fold cross-validation method divides all sample data into S mutually independent data subsets with the same number of samples; one subset is reserved for model testing each time, and the remaining S-1 subsets are used for neural network model parameter training, and this process is repeated S times to select the S-fold cross validation method. As the optimal model, the model with the lowest test error in these S experiments is chosen.

In this paper, the evaluation data of three systems are selected as the training set, the remaining system is used as the test set, and the network training is carried out four times. The training error distribution results of the improved LSTM neural network after training are shown in Fig. 3.

Figure 3.

Improved LSTM neural network test error distribution.

As can be seen from Fig. 3, compared with the training results of other networks, the training error of the improved LSTM neural network in the first training is the smallest, and it has higher evaluation accuracy. Therefore, this paper chooses the improved LSTM neural network trained for the third time as the evaluation model for new power system construction.

The comparison between the predicted evaluation results of the improved LSTM neural network on the test set and the actual evaluation results is shown in Fig. 4.

Figure 4.

Comparison of the fitting effect between the evaluation results of the test set and the actual results.

As can be seen from Fig. 4, the average deviation between the evaluation results of the improved LSTM neural network proposed in this paper on the test set and the actual evaluation results of the test set is 0.0063, which has a good fit. In addition, it can be seen from the evaluation result in Fig. 4 that the evaluation result of system 3 has the highest score and the best system performance. Therefore, the improved LSTM neural network proposed in this paper has good performance in the evaluation of new power system construction.

6. Conclusion

In order to evaluate the new power system comprehensively and accurately, this paper constructs a multi-level and multi-dimensional evaluation system of source and charge-green intelligence for the construction of new power system. An improved LSTM neural network based on hybrid optimization algorithm is proposed for the evaluation of new power system construction. The simulation results show that the IFSO algorithm proposed in this paper has higher calculation accuracy than other meta-heuristic algorithms in solving nonlinear problems. The average error of the improved LSTM model proposed in this paper is 0.0063 when identifying new power systems, which can accurately and comprehensively evaluate new power systems In the future, based on the research results of this paper, research on new power system planning, construction, economic operation and market mechanism can be carried out.

Footnotes

Acknowledgments

Supported by Research on Scientific Evaluation System of New Power System Construction in Urban Area.

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Evaluation method of a new power system construction based on improved LSTM neural network

Abstract

Keywords

1. Introduction

2. Source-load and green-intelligence multi-level and multi-dimensional evaluation system

2.1 Internal evaluation factors

3.1 LSTM neural networks

Table 1 Assessment data for the construction of new power systems

5.1 Validation of the IFSO algorithm’s performance

Table 3 Typical non-linear mathematical formulations for algorithm performance verification

Footnotes

Acknowledgments

References

Table 1
Assessment data for the construction of new power systems

Table 3
Typical non-linear mathematical formulations for algorithm performance verification