Two new methods for power flow tracing using bus power balance equations

Two new methods were presented for power flow tracing(PFT).These two methods were compared and the results were discussed in detail.Both methods use the active and reactive power balance equations at each bus in order to solve the tracing problem.The first method considers the proportional sharing assumption while the second one uses the circuit laws to find the relationship between power inflows and outflows through each line,generator and load connected to each bus of the network.Both methods are able to handle loop flow and loss issues in tracing problem.A formulation is also proposed to find the share of each unit in provision of each load.These methods are applied to find the producer and consumer's shares on the cost of transmission for each line in different case studies.As the results of these studies show,both methods can effectively solve the PFT problem.

Power flow forecasts at transmission grid nodes using Graph Neural Networks

The increasing share of renewable energy in the electricity grid and progressing changes in power consumption have led to fluctuating,and weather-dependent power flows.To ensure grid stability,grid operators rely on power forecasts which are crucial for grid calculations and planning.In this paper,a Multi-Task Learning approach is combined with a Graph Neural Network(GNN)to predict vertical power flows at transformers connecting high and extra-high voltage levels.The proposed method accounts for local differences in power flow characteristics by using an Embedding Multi-Task Learning approach.The use of a Bayesian embedding to capture the latent node characteristics allows to share the weights across all transformers in the subsequent node-invariant GNN while still allowing the individual behavioral patterns of the transformers to be distinguished.At the same time,dependencies between transformers are considered by the GNN architecture which can learn relationships between different transformers and thus take into account that power flows in an electricity network are not independent from each other.The effectiveness of the proposed method is demonstrated through evaluation on two real-world data sets provided by two of four German Transmission System Operators,comprising large portions of the operated German transmission grid.The results show that the proposed Multi-Task Graph Neural Network is a suitable representation learner for electricity networks with a clear advantage provided by the preceding embedding layer.It is able to capture interconnections between correlated transformers and indeed improves the performance in power flow prediction compared to standard Neural Networks.A sign test shows that the proposed model reduces the test RMSE on both data sets compared to the benchmark models significantly.

Short-Term Power Load Forecasting with Hybrid TPA-BiLSTM Prediction Model Based on CSSA

Since the existing prediction methods have encountered difficulties in processing themultiple influencing factors in short-term power load forecasting,we propose a bidirectional long short-term memory(BiLSTM)neural network model based on the temporal pattern attention(TPA)mechanism.Firstly,based on the grey relational analysis,datasets similar to forecast day are obtained.Secondly,thebidirectional LSTM layermodels the data of thehistorical load,temperature,humidity,and date-type and extracts complex relationships between data from the hidden row vectors obtained by the BiLSTM network,so that the influencing factors(with different characteristics)can select relevant information from different time steps to reduce the prediction error of the model.Simultaneously,the complex and nonlinear dependencies between time steps and sequences are extracted by the TPA mechanism,so the attention weight vector is constructed for the hidden layer output of BiLSTM and the relevant variables at different time steps are weighted to influence the input.Finally,the chaotic sparrow search algorithm(CSSA)is used to optimize the hyperparameter selection of the model.The short-term power load forecasting on different data sets shows that the average absolute errors of short-termpower load forecasting based on our method are 0.876 and 4.238,respectively,which is lower than other forecastingmethods,demonstrating the accuracy and stability of our model.

Probabilistic Load Flow Considering Correlation between Generation, Loads and Wind Power

In this paper a procedure is established for solving the Probabilistic Load Flow in an electrical power network, considering correlation between power generated by power plants, loads demanded on each bus and power injected by wind farms. The method proposed is based on the generation of correlated series of power values, which can be used in a MonteCarlo simulation, to obtain the probability density function of the power through branches of an electrical network.

Investigating Periodic Dependencies to Improve Short-Term Load Forecasting

With a further increase in energy flexibility for customers,short-term load forecasting is essential to provide benchmarks for economic dispatch and real-time alerts in power grids.The electrical load series exhibit periodic patterns and share high associations with metrological data.However,current studies have merely focused on point-wise models and failed to sufficiently investigate the periodic patterns of load series,which hinders the further improvement of short-term load forecasting accuracy.Therefore,this paper improved Autoformer to extract the periodic patterns of load series and learn a representative feature from deep decomposition and reconstruction.In addition,a novel multi-factor attention mechanism was proposed to handle multi-source metrological and numerical weather prediction data and thus correct the forecasted electrical load.The paper also compared the proposed model with various competitive models.As the experimental results reveal,the proposed model outperforms the benchmark models and maintains stability on various types of load consumers.

A Feasible Zone Analysis Method with Global Partial Load Scanning for Solving Power Flow Coupling Models of CCHP Systems

Heat exchanger systems(HXSs)or heat recovery steam generators(HRSGs)are commonly used in 100 kW to 50 MW combined cooling,heating,and power(CCHP)systems.Power flow coupling(PFC)is found in HXSs and is complex for researchers to quantify.This could possibly mislead the dispatch schedule and result in the inaccurate dispatch.PFC is caused by the inlet and outlet temperatures of each component,gas flow pressure variation,conductive medium flow rate,and atmosphere condition variation.In this paper,the expression of PFC is built by using quadratic functions to fit the non!inearit>of thermal dynamics.While fitting the model,the environmental condition needs prediction,which is calculated using phase space reconstruction(PSR)Kalman filter.In order to solve the complex quadratic dispatch model,a hybrid following electricity load(FEL)and following thermal load(FTL)mode for reducing the dimension of dispatch model,and a feasible zone analysis(FZA)method are proposed.As a result,the PFC problem of CCHP system is solved,and the dispatch cost,investment cost,and the maximum power requirements are optimized.In this paper,a case in Jinan,China is studied.The PFC model is proven to be more precise and accurate compared with traditional models.

Decoupled Piecewise Linear Power Flow and Its Application to Under Voltage Load Shedding

Various optimizations in power systems based on the AC power flow model are inherently mixed-integer nonlinear programming(MINLP)problems.Piecewise linear power flow models can handle nonlinearities and meanwhile ensure a hi^h accuracy.Then,the MINLP problem can he turned into a tractable mixed-integer linear programming(MILP)problem.However,piecewise linearization also introduces a heavy computational burden because of the incorporation of a large number of binary variables especially for large systems.To achieve a better trade off between approximation accuracy and computational efficiency,this paper proposes a model called decoupled piecewise linear power flow(DPWLPF)for transmission systems.The P-Q decoupling characteristic is used to ease the evaluation of the piecewise cosine functions in the power flow equations.Therefore,in optimizations,the coupling between variables is reduced.Moreover,an under voltage load shedding(UVLS)approach based on DPWLPF is presented.Case studies are conducted for benchmark systems.The results show that the DPWLPF facilitates the solution of optimal power flow(OPF)and UVLS problems much better than conventional piecewise models.And DPWIJM^still enhances the approximation accuracy by usinj»the decoupled piecewise modeling.

Theory Study and Application of the BP-ANN Method for Power Grid Short-Term Load Forecasting

Aiming at the low accuracy problem of power system short-term load forecasting by traditional methods, a back-propagation artificial neural network （BP-ANN） based method for short-term load forecasting is presented in this paper. The forecast points are related to prophase adjacent data as well as the periodical long-term historical load data. Then the short-term load forecasting model of Shanxi Power Grid （China） based on BP-ANN method and correlation analysis is established. The simulation model matches well with practical power system load, indicating the BP-ANN method is simple and with higher precision and practicality.

Optimization of support vector machine power load forecasting model based on data mining and Lyapunov exponents

According to the chaotic and non-linear characters of power load data,the time series matrix is established with the theory of phase-space reconstruction,and then Lyapunov exponents with chaotic time series are computed to determine the time delay and the embedding dimension.Due to different features of the data,data mining algorithm is conducted to classify the data into different groups.Redundant information is eliminated by the advantage of data mining technology,and the historical loads that have highly similar features with the forecasting day are searched by the system.As a result,the training data can be decreased and the computing speed can also be improved when constructing support vector machine(SVM) model.Then,SVM algorithm is used to predict power load with parameters that get in pretreatment.In order to prove the effectiveness of the new model,the calculation with data mining SVM algorithm is compared with that of single SVM and back propagation network.It can be seen that the new DSVM algorithm effectively improves the forecast accuracy by 0.75%,1.10% and 1.73% compared with SVM for two random dimensions of 11-dimension,14-dimension and BP network,respectively.This indicates that the DSVM gains perfect improvement effect in the short-term power load forecasting.

A novel recurrent neural network forecasting model for power intelligence center

In order to accurately forecast the load of power system and enhance the stability of the power network, a novel unascertained mathematics based recurrent neural network (UMRNN) for power intelligence center (PIC) was created through three steps. First, by combining with the general project uncertain element transmission theory (GPUET), the basic definitions of stochastic, fuzzy, and grey uncertain elements were given based on the principal types of uncertain information. Second, a power dynamic alliance including four sectors: generation sector, transmission sector, distribution sector and customers was established. The key factors were amended according to the four transmission topologies of uncertain elements, thus the new factors entered the power intelligence center as the input elements. Finally, in the intelligence handing background of PIC, by performing uncertain and recursive process to the input values of network, and combining unascertained mathematics, the novel load forecasting model was built. Three different approaches were put forward to forecast an eastern regional power grid load in China. The root mean square error (ERMS) demonstrates that the forecasting accuracy of the proposed model UMRNN is 3% higher than that of BP neural network (BPNN), and 5% higher than that of autoregressive integrated moving average (ARIMA). Besides, an example also shows that the average relative error of the first quarter of 2008 forecasted by UMRNN is only 2.59%, which has high precision.

Scheduling Framework Using Dynamic Optimal Power Flow for Battery Energy Storage Systems

Battery energy storage systems(BESS)are instrumental in the transition to a low carbon electrical network with enhanced flexibility,however,the set objective can be accomplished only through suitable scheduling of their operation.This paper develops a dynamic optimal power flow(DOPF)-based scheduling framework to optimize the day(s)-ahead operation of a grid-scale BESS aiming to mitigate the predicted limits on the renewable energy generation as well as smooth out the network demand to be supplied by conventional generators.In DOPF,all the generating units,including the ones that model the exports and imports of the BESS,across the entire network and the complete time horizon are integrated on to a single network.Subsequently,an AC-OPF is applied to dispatch their power outputs to minimize the total generation cost,while satisfying the power balance equations,and handling the unit and network constraints at each time step coupled with intertemporal constraints associated with the state of charge(SOC).Furthermore,the DOPF developed here entails the frequently applied constant current-constant voltage charging profile,which is represented in the SOC domain.Considering the practical application of a 1 MW BESS on a particular 33 kV network,the scheduling framework is designed to meet the pragmatic requirements of the optimum utilization of the available energy capacity of BESS in each cycle,while completing up to one cycle per day.

Optimal power flow calculation in AC/DC hybrid power system based on adaptive simplified human learning optimization algorithm

This paper employs an efficacious analytical tool,adaptive simplified human learning optimization(ASHLO)algorithm,to solve optimal power flow(OPF)problem in AC/DC hybrid power system,considering valve-point loading effects of generators,carbon tax,and prohibited operating zones of generators,respectively.ASHLO algorithm,involves random learning operator,individual learning operator,social learning operator and adaptive strategies.To compare and analyze the computation performance of the ASHLO method,the proposed ASHLO method and other heuristic intelligent optimization methods are employed to solve OPF problem on the modified IEEE 30-bus and 118-bus AC/DC hybrid test system.Numerical results indicate that the ASHLO method has good convergent property and robustness.Meanwhile,the impacts of wind speeds and locations of HVDC transmission line integrated into the AC network on the OPF results are systematically analyzed.

Analysis of the Load Flow Problem in Power System Planning Studies

Load flow is an important tool used by power engineers for planning, to determine the best operation for a power system and exchange of power between utility companies. In order to have an efficient operating power system, it is necessary to determine which method is suitable and efficient for the system’s load flow analysis. A power flow analysis method may take a long time and therefore prevent achieving an accurate result to a power flow solution because of continuous changes in power demand and generations. This paper presents analysis of the load flow problem in power system planning studies. The numerical methods: Gauss-Seidel, Newton-Raphson and Fast Decoupled methods were compared for a power flow analysis solution. Simulation is carried out using Matlab for test cases of IEEE 9-Bus, IEEE 30-Bus and IEEE 57-Bus system. The simulation results were compared for number of iteration, computational time, tolerance value and convergence. The compared results show that Newton-Raphson is the most reliable method because it has the least number of iteration and converges faster.

Vertical power flow forecast with LSTMs using regular training updatestrategies

The strong growth of renewable energy sources as well as the increasing amount of volatile energy consumptionis leading to major challenges in the electrical grid. In order to ensure safety and reliability in the electricitygrid, a high quality of power flow forecasts for the next few hours are needed. In this paper we investigateforecasts of the vertical power flow at transformer between the medium and high voltage grid. Forecastingthe vertical power flow is challenging due to constantly changing characteristics of the power flow at thetransformer. We present a novel approach to deal with these challenges. For the multi step time series forecastsa Long-Short Term Memory (LSTM) is used. In our presented approach an update process where the model isretrained regularly is investigated and compared to baseline models. The model is retrained as soon as asufficient amount of new measurements are available. We show that this retraining mostly captures changesin the characteristic of the transformer that the model has not yet seen in the past and therefore cannot bepredicted by the model without an update process. To give more weight to recent data, we examined differentstrategies in terms of the number of epochs and the learning rate. We show that our new approach significantlyoutperforms the investigated baseline models. On average, we achieved an improvement of about 8% with theregular update process compared to the approach without update process.

Day-Ahead Probabilistic Load Flow Analysis Considering Wind Power Forecast Error Correlation

Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.

A Levenberg–Marquardt Based Neural Network for Short-Term Load Forecasting

Short-term load forecasting (STLF) is part and parcel of theefficient working of power grid stations. Accurate forecasts help to detect thefault and enhance grid reliability for organizing sufficient energy transactions.STLF ranges from an hour ahead prediction to a day ahead prediction. Variouselectric load forecasting methods have been used in literature for electricitygeneration planning to meet future load demand. A perfect balance regardinggeneration and utilization is still lacking to avoid extra generation and misusageof electric load. Therefore, this paper utilizes Levenberg–Marquardt(LM) based Artificial Neural Network (ANN) technique to forecast theshort-term electricity load for smart grids in a much better, more precise,and more accurate manner. For proper load forecasting, we take the mostcritical weather parameters along with historical load data in the form of timeseries grouped into seasons, i.e., winter and summer. Further, the presentedmodel deals with each season’s load data by splitting it into weekdays andweekends. The historical load data of three years have been used to forecastweek-ahead and day-ahead load demand after every thirty minutes makingload forecast for a very short period. The proposed model is optimized usingthe Levenberg-Marquardt backpropagation algorithm to achieve results withcomparable statistics. Mean Absolute Percent Error (MAPE), Root MeanSquared Error (RMSE), R2, and R are used to evaluate the model. Comparedwith other recent machine learning-based mechanisms, our model presentsthe best experimental results with MAPE and R2 scores of 1.3 and 0.99,respectively. The results prove that the proposed LM-based ANN modelperforms much better in accuracy and has the lowest error rates as comparedto existing work.

Optimal location of interline power flow controller for controlling multi transmission line： A new integrated technique

In this paper, an interline power flow controller （IPFC） is used for controlling multi transmission lines. However, the optimal placement of IPFC in the transmis-sion line is a major problem. Thus, we use a combination of tabu search （TS） algorithm and artificial neural network （ANN） in the proposed method to find out the best placement locations for IPFC in a given multi transmission line system. TS algorithm is an optimization algorithm and we use it in the proposed method to determine the optimum bus combination using line data. Then, using the optimum bus combination, the neural network is trained to find out the best placement locations for IPFC. Finally, IPFC is connected at the best locations indicated by the neural network. Furthermore, using Newton-Raphson load flow algorithm, the transmission line loss of the IPFC connected bus is analyzed. The proposed methodology is implemen- ted in MATLAB working platform and tested on the IEEE-14 bus system. The output is compared with the genetic algorithm （GA） and general load flow analysis. The results are validated with Levenberg-Marquardt back propagation and gradient descent with momentum network training algorithm.

A Weighted Combination Forecasting Model for Power Load Based on Forecasting Model Selection and Fuzzy Scale Joint Evaluation

To solve the medium and long term power load forecasting problem,the combination forecasting method is further expanded and a weighted combination forecasting model for power load is put forward.This model is divided into two stages which are forecasting model selection and weighted combination forecasting.Based on Markov chain conversion and cloud model,the forecasting model selection is implanted and several outstanding models are selected for the combination forecasting.For the weighted combination forecasting,a fuzzy scale joint evaluation method is proposed to determine the weight of selected forecasting model.The percentage error and mean absolute percentage error of weighted combination forecasting result of the power consumption in a certain area of China are 0.7439%and 0.3198%,respectively,while the maximum values of these two indexes of single forecasting models are 5.2278%and 1.9497%.It shows that the forecasting indexes of proposed model are improved significantly compared with the single forecasting models.

Grid Power Optimization Based on Adapting Load Forecasting and Weather Forecasting for System Which Involves Wind Power Systems

This paper describes the performance, generated power flow distribution and redistribution for each power plant on the grid based on adapting load and weather forecasting data. Both load forecasting and weather forecasting are used for collecting predicting data which are required for optimizing the performance of the grid. The stability of each power systems on the grid highly affected by load varying, and with the presence of the wind power systems on the grid, the grid will be more exposed to lowering its performance and increase the instability to other power systems on the gird. This is because of the intermittence behavior of the generated power from wind turbines as they depend on the wind speed which is varying all the time. However, with a good prediction of the wind speed, a close to the actual power of the wind can be determined. Furthermore, with knowing the load characteristics in advance, the new load curve can be determined after being subtracted from the wind power. Thus, with having the knowledge of the new load curve, and data that collected from SACADA system of the status of all power plants, the power optimization, load distribution and redistribution of the power flows between power plants can be successfully achieved. That is, the improvement of performance, more reliable, and more stable power grid.

Probabilistic Load Flow Algorithm with the Power Performance of Double-Fed Induction Generators

Probabilistic load flow(PLF)algorithm has been regained attention,because the large-scale wind power integration into the grid has increased the uncertainty of the stable and safe operation of the power system.The PLF algorithm is improved with introducing the power performance of double-fed induction generators(DFIGs)for wind turbines(WTs)under the constant power factor control and the constant voltage control in this paper.Firstly,the conventional Jacobian matrix of the alternating current(AC)load flow model is modified,and the probability distributions of the active and reactive powers of the DFIGs are derived by combining the power performance of the DFIGs and the Weibull distribution of wind speed.Then,the cumulants of the state variables in power grid are obtained by improved PLF model and more accurate power probability distributions.In order to generate the probability density function(PDF)of the nodal voltage,Gram-Charlier,Edgeworth and Cornish-Fisher expansions based on the cumulants are applied.Finally,the effectiveness and accuracy of the improved PLF algorithm is demonstrated in the IEEE 14-RTS system with wind power integration,compared with the results of Monte Carlo(MC)simulation using deterministic load flow calculation.