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Deep Learning for Intelligent Demand Response and Smart Grids: A Comprehensive Survey

Prabadevi B, Quoc-Viet Pham, Madhusanka Liyanage, N Deepa, Mounik VVSS, Shivani Reddy, Praveen Kumar Reddy Maddikunta, Neelu Khare, Thippa Reddy Gadekallu, Won-Joo Hwang

arXiv:2101.08013v1cs.LGcs.SYeess.SY

TL;DR

The paper addresses the lack of a comprehensive survey of deep learning for demand response and smart grids. It reviews application areas and use cases, then discusses challenges and potential directions. Its conclusion presents the survey as a reference for researchers and engineers interested in deep learning and smart grids.

  • Problem

    Existing surveys focus on particular smart-grid topics, leaving a comprehensive review of deep learning for demand response and smart grids missing.

    Source: §I · p. 2

  • Method

    The paper surveys deep-learning applications in load forecasting, state estimation, energy theft detection, energy sharing, and trading, alongside use cases and challenges.

    Source: §IV · p. 14, §VI · p. 22

  • Results

    The survey presents state-of-the-art deep-learning solutions across four themes and discusses use cases, challenges, and potential directions.

    Source: §VI · p. 22

  • Takeaways & Limitations

    The authors offer the survey as a reference for researchers and engineers interested in deep learning and smart-grid systems.

    Source: §VI · p. 22

Abstract

from arXiv · show

Electricity is one of the mandatory commodities for mankind today. To address challenges and issues in the transmission of electricity through the traditional grid, the concepts of smart grids and demand response have been developed. In such systems, a large amount of data is generated daily from various sources such as power generation (e.g., wind turbines), transmission and distribution (microgrids and fault detectors), load management (smart meters and smart electric appliances). Thanks to recent advancements in big data and computing technologies, Deep Learning (DL) can be leveraged to learn the patterns from the generated data and predict the demand for electricity and peak hours. Motivated by the advantages of deep learning in smart grids, this paper sets to provide a comprehensive survey on the application of DL for intelligent smart grids and demand response. Firstly, we present the fundamental of DL, smart grids, demand response, and the motivation behind the use of DL. Secondly, we review the state-of-the-art applications of DL in smart grids and demand response, including electric load forecasting, state estimation, energy theft detection, energy sharing and trading. Furthermore, we illustrate the practicality of DL via various use cases and projects. Finally, we highlight the challenges presented in existing research works and highlight important issues and potential directions in the use of DL for smart grids and demand response.

I. INTRODUCTION

Traditional grids must meet electricity demand as it is produced, while peak-hour demand can strain the system. The paper surveys deep learning for smart grids and demand response, covering applications, use cases, and open challenges.

I. INTRODUCTION

  • Smart grids use sensing and prediction to forecast electricity demand and transmit power accordingly, addressing traditional-grid problems including short circuits and transformer failures.The introduction connects these systems with smart vehicles, buildings, power plants, and cities.Source: §I · p. 1, Figure 1 · p. 2
  • Demand response encourages customers to shift non-essential electricity use away from peak hours, and data-driven prediction can support its automation.The paper identifies ML, IoT, and big-data analytics as technologies that can be integrated with smart grids for this purpose.Source: §I · p. 1
  • The authors identify a gap in comprehensive surveys of deep learning for demand response in smart grids, as existing reviews focus on narrower topics and may omit recent developments.They frame their survey as addressing that gap and educating readers on the state of the art.Source: §I · p. 2

A. Contributions and Paper Organization

  • The survey reviews deep-learning applications in electric load forecasting, state estimation, energy theft detection, energy sharing, and trading.It also presents fundamentals of deep learning, smart grids, and demand response.Source: A. Contributions and Paper Organization · p. 2
  • The paper presents use cases and discusses challenges, open issues, and future directions for deep learning in smart grids and demand response.Its organization assigns these topics to later sections alongside the application review and concluding remarks.Source: A. Contributions and Paper Organization · p. 2

II. BACKGROUND AND MOTIVATIONS

This section introduces machine-learning and deep-learning fundamentals, then illustrates DNN applications to power-loss prediction, machine-tool energy use, aggregated load forecasting, and smart-meter data.

A. Fundamentals of Deep Learning

  • DNNs extend artificial neural networks with more layers, while convolutional and recurrent variants address specialized input structures such as grids and long sequences.The section notes that feed-forward DNNs can map input vectors to outputs, but large inputs may require additional regularization, optimization, or scaling.Source: A. Fundamentals of Deep Learning · pp. 3–4
  • CNNs process grid-structured data through convolutional layers, producing feature maps from inputs and kernels.The section gives time series and image pixels as examples of one- and two-dimensional grids.Source: A. Fundamentals of Deep Learning · p. 4
  • RNNs process variable-length sequences through recurrence, with hidden states mapping task-related inputs over time.The network uses the state at time t to map toward the next state, with the same parameter η used for the transition function.Source: A. Fundamentals of Deep Learning · p. 4
  • A DNN power-loss model for large low-voltage supply zones uses scaled demand and response data, dropout, and k-fold training to predict technical losses.Training stops when the difference between successive errors falls below a threshold.Source: A. Fundamentals of Deep Learning · p. 4
  • A machine-tool energy predictor uses unsupervised deep learning for feature selection during training, then applies the resulting model to recognize current energy usage,.The training process includes data acquisition and transformation, feature subset selection, and model attainment.Source: A. Fundamentals of Deep Learning · p. 4
  • For next-day aggregated load prediction, affinity clustering and sparse-autoencoder feature selection feed a CNN/LSTM fusion model that reconstructs load curves.The CNN and LSTM networks train independently; their high-level features are fused in a new layer.Source: A. Fundamentals of Deep Learning · pp. 4–5
  • A deep CNN and SVM use smart-meter consumption data to extract consumer behavioral patterns and socio-demographic information.The described CNN has eight layers, including convolutional and pooling layers before a fully connected layer and the SVM.Source: A. Fundamentals of Deep Learning · p. 5

B. Demand Response in Smart Grids

The section frames demand response as a way to manage peak demand, then surveys deep-learning approaches for prediction and load control in grid and industrial settings.

B. Demand Response in Smart Grids

  • Demand response lets customers or utilities shed non-essential loads during peak hours, balancing demand and supply and potentially reducing operating and installation costs.Utilities may encourage shifting consumption through lower off-peak prices.Source: B. Demand Response in Smart Grids · p. 5

C. Deep Learning for Demand Response and Smart Grids

  • A five-layer DRNN-GRU model predicts residential-apartment energy supply and demand from hourly load data and is designed to handle time dependencies and missing information.It combines two GRU layers with normalization, backpropagation, regularization, and dropout.Source: C. Deep Learning for Demand Response… · p. 5
  • A DDQN-based system reduced peak electricity demand and operating costs while keeping voltage regulation within limits without compromising safety.It models interruptible loads under time-of-use pricing as a Markov decision process.Source: C. Deep Learning for Demand Response… · p. 5
  • The multiagent DRL system for battery manufacturing produced lower power-consumption costs and production expenditures than the non-DR benchmark in simulation.It formulated the manufacturing system as a POMG and used MADDPG to schedule each machine’s load.Source: C. Deep Learning for Demand Response… · p. 5
  • A short-term load-forecasting framework applies DNN and ResBlock techniques to appliance load series and their correlations, with grid search for DNN hyperparameters.Its modules cover acquisition, preprocessing, learning, and load prediction.Source: C. Deep Learning for Demand Response… · pp. 5–6
  • A deep ensemble framework clusters consumer profiles, learns multiple task-specific features, and combines DNNs for probabilistic prediction; its outputs are polished with LASSO-based quantiles.It was demonstrated on SME consumers and proposed for demand response and home electricity management.Source: C. Deep Learning for Demand Response… · pp. 6–7
  • The review argues that DL’s scalability suits extracting patterns from the large sensor and IoT datasets generated in smart grids, including for theft and meter-tampering detection.It also names fire-accident prediction as a potential application.Source: C. Deep Learning for Demand Response… · p. 7

III. STATE-OF-THE-ART DL APPROACHES FOR DEMAND RESPONSE AND SMART GRIDS

This section surveys deep-learning approaches across four smart-grid and demand-response application areas.

III. STATE-OF-THE-ART DL APPROACHES FOR DEMAND RESPONSE AND SMART GRIDS

  • The reviewed applications include electric-load forecasting and state estimation in smart grids.Source: §III · p. 7
  • The review also covers deep-learning applications for energy-theft detection in smart grids.Source: §III · p. 7
  • Energy sharing and trading in smart grids are additional application areas covered in the section.Source: §III · p. 7

A. Electric Load Forecasting

The survey reviews short- and long-term load forecasting, covering methods for point and probabilistic prediction, appliance loads, and distributed generation. Reported studies compare these approaches with conventional and alternative models, with some also addressing training costs and load-management outcomes.

A. Electric Load Forecasting

  • [43]’s six ANN, wavelet, and Kalman-filter models and ’s ARIMA–LSTM ensemble outperformed conventional or popular short-term forecasting methods.For, evaluation used 737 weeks of load-consumption data.Source: A. Electric Load Forecasting · p. 7
  • [45]’s rolling-update, attention, and Bi-LSTM method reportedly improved accuracy with less computation time, while ’s joint bagged-boosted ANN reduced bias, variance, and forecasting error against three ANN baselines.The comparisons used actual datasets and real data, respectively.Source: A. Electric Load Forecasting · p. 7
  • [50]’s sequential-grid SVR improved short-term forecasting efficiency and accuracy; ’s PSO-GA-BPNN outperformed PSO-BPNN and GA-BPNN, while and reported advantages over alternative methods.[52] combines clustering, empirical mode decomposition, Bi-RNNs, and DBN; uses Copula-derived peak-load indicators before hourly DBN prediction.Source: A. Electric Load Forecasting · p. 8
  • For appliance loads, found a conditional hidden semi-Markov model effective on one-minute data, and reported better performance from a DCNN framework for non-intrusive load monitoring.[55] addresses energy disaggregation for type II appliances.Source: A. Electric Load Forecasting · p. 8
  • [56] used Bayesian deep LSTM to model residential net-load uncertainty from distributed PV, while and reported effective week- and day-ahead forecasting approaches.[56] identified subprofile clustering and PV visibility as major performance contributors; combines sparse coding with clustered, group-specific DNNs.Source: A. Electric Load Forecasting · p. 8
  • [59]’s LoadCNN achieved prediction accuracy equal to current models with training time and carbon-dioxide emissions around 2% of other state-of-the-art models.It targets day-ahead residential load forecasting while minimizing training costs.Source: A. Electric Load Forecasting · p. 8
  • [60]’s RNN/CNN approach improved accuracy by 22.6% over ARIMAX; [61] found Elmann RNNs less costly than GRU and LSTM for aggregated-load forecasting, and ’s gated RNN outperformed state-of-the-art methods for daily peak-load prediction.[62] combines shape-based dynamic time warping with a three-layer gated RNN.Source: A. Electric Load Forecasting · pp. 8–9
  • Using smart-meter and two-year weather data, ’s Q-learning model selected forecasting models from probabilistic and deterministic pools, reducing PLF and DLF errors by 60% and 50%, respectively, versus traditional models.Source: A. Electric Load Forecasting · p. 9

B. State Estimation in Smart Grids

The section surveys state estimation for batteries and power systems, including methods for limited or unobservable measurements and harmonic states. It also covers cyberattacks on estimation and measurement data, with studies reporting benchmark comparisons and detection results.

B. State Estimation in Smart Grids

  • [72]’s hybrid battery-estimation procedure jointly estimated state of charge and state of health, with maximum state-of-charge life-cycle error no more than 2% and state-of-health RMSE no more than 4%.The procedure combines data-driven least-square SVM with a model-based unscented-particle filter.Source: B. State Estimation in Smart Grids · p. 9
  • [73]’s method targets imperfect data-injection attacks on Kalman-filter state variables; [74] found DE more effective than SLSQP for creating adversarial false-data-injection vectors across its simulation scenarios.[74] reports that DE-generated attacks declined ANN state-estimation accuracy with notable probability.Source: B. State Estimation in Smart Grids · pp. 10–11
  • [75] estimated harmonic states and located harmonic sources in unbalanced three-phase systems using DPMU and smart-meter measurements, requiring fewer DPMUs than nodes.Simulations also examined the estimator under increased distributed-energy-resource penetration.Source: B. State Estimation in Smart Grids · p. 11
  • [76]’s Bayesian DL estimation outperformed pseudo-measurement techniques for unobservable systems, while ’s CNN filter showed notable accuracy for detecting false-data-injection attacks in PMU data.[77] evaluated IEEE 118-bus and IEEE 30-bus systems.Source: B. State Estimation in Smart Grids · p. 11
  • [78]’s model-specific DNN for real-time PSSE required reduced tuning and offline training, and outperformed conventional methods, including Gauss–Newton, on the IEEE 118-bus system.The approach was built around an iterative solver using an exact AC model.Source: B. State Estimation in Smart Grids · p. 11
  • [79]’s algebraic method assumes all power-flow and voltage-magnitude measurements are available, converting power flows into rank-one measurements for recovery under specified l1-loss conditions.Simulations on IEEE benchmark systems supported the theoretical developments and method effectiveness.Source: B. State Estimation in Smart Grids · p. 11
  • [80] addressed limited smart-meter and SCADA measurements with a Bayesian estimator that learns load-injection distributions using a GAN, then trains a regression network for MMSE state estimates.Simulations reported notable accuracy and online computation cost relative to existing methods.Source: B. State Estimation in Smart Grids · p. 11
  • [81] compared meter-placement schemes on a German distribution grid for estimation accuracy and computational efficiency, with near-optimal placement framed as important for cost-effective operation.The study seeks to reduce investment while improving estimation accuracy.Source: B. State Estimation in Smart Grids · p. 11

C. Energy Theft Detection

The section surveys energy-theft detection, from theft modes such as meter tampering to data-driven and deep-learning approaches. It describes methods using customer consumption patterns, meter data, and network measurements.

C. Energy Theft Detection

  • Theft includes erased logged events, altered stored demand, tampered meters, and meter disconnection.Fig. 5 depicts these techniques.Source: C. Energy Theft Detection · p. 11, Figure 5 · p. 13
  • Feature-based detection uses customer segmentation and household comparisons, while intermediate monitor meters divide networks to identify non-technical losses,.The intermediate-monitor approach solves an energy-balance system and reports at least 95% accuracy.Source: C. Energy Theft Detection · p. 12
  • ETD-DBRNN models consumption records, while time-series correlation and privacy-preserving CNN methods target abnormal usage,,.The CNN approach combines anomalous-pattern detection with Paillier-based privacy protection and reports accuracy up to 92.67%.Source: C. Energy Theft Detection · pp. 12–13
  • Other approaches include a hidden-theft attack exploiting multiple pricing and countermeasures, plus fuzzy cognitive maps paired with swarm optimization,.The countermeasures include limiting attack cycles, selective meter protection, and billing updates; the approach was tested with expert judgments and simulations.Source: C. Energy Theft Detection · pp. 13–14
  • A hybrid DNN combining multilayer perceptrons and LSTM was evaluated on real Endesa meter data, while PPETD targets privacy-preserving theft detection,.The PPETD evaluation reports detection of fake consumers with privacy preservation and acceptable computation and communication overhead.Source: C. Energy Theft Detection · p. 13
  • Studies also examine socio-economic predictors, partial smart-grid deployments, and multi-household time-series comparisons for theft detection,,.The random-forest study explained 87% of loss-rate variability, and the multidimensional detection approach reported rates above 90%,.Source: C. Energy Theft Detection · p. 14

D. Energy Sharing and Trading

The section reviews energy sharing and trading approaches alongside their efficiency, security, and reliability concerns. The examples span blockchain-based intrusion detection, local trading, and reinforcement-learning-based microgrid trading.

D. Energy Sharing and Trading

  • Energy trading is presented as an energy-management technique for improving power-system efficiency as activity shifts from centralized to distributed arrangements.The section also notes security and reliability concerns associated with sharing and trading.Source: D. Energy Sharing and Trading · p. 14
  • A blockchain-based energy framework combines DeepCoin with an RNN intrusion-detection system and Byzantine fault tolerance; evaluation on three datasets found high throughput.Short signatures and hash functions are used for energy access and attack prevention.Source: D. Energy Sharing and Trading · p. 14
  • In simulated local and microgrid trading, shiftable users showed greater flexibility and higher provider and aggregator profits, while an RL scheme raised three-microgrid utility by 22.3% over its benchmark,.The RL policy uses predicted renewable generation, estimated demand, and battery level.Source: D. Energy Sharing and Trading · p. 14

IV. DL USE CASES FOR DEMAND RESPONSE AND SMART GRIDS

The section presents DL use cases and projects for demand response and smart grids. It identifies application areas and points to figures organizing DL roles and AI use cases.

IV. DL USE CASES FOR DEMAND RESPONSE AND SMART GRIDS

  • DL use cases for demand response and smart grids include planning, multi-agent systems, electricity trading, and virtual power-plant management.The list also includes self-healing, optimized energy consumption, flexible distribution, and complex event processing.Source: §IV · p. 14
  • Fig. 6 depicts DL roles across smart-grid demand-response applications.The text names planning, multi-agent systems, electricity trading, and virtual power plants among those roles.Source: §IV · p. 14
  • Fig. 7 organizes demand-response issues alongside AI-model use cases intended to handle them.Source: §IV · p. 14

A. Incentive based Real-Time DR Algorithm for Smart Grids

The section describes an incentive-based real-time DR algorithm and a residential short-term load forecasting framework. The first combines DNN forecasts with reinforcement learning; the second uses appliance data and spatio-temporal correlations.

A. Incentive based Real-Time DR Algorithm for Smart Grids

  • A DNN forecasts undisclosed energy prices and demand, while reinforcement learning selects customer incentives by examining customer and provider net profit.The repeated online process uses updated rates and energy demands to choose incentive prices.Source: A. Incentive based Real-Time DR… · p. 15
  • The incentive algorithm is reported to increase demand-side participation and improve provider and customer profit while stabilizing energy resources and enhancing system reliability.The authors state it can be extended to a larger-capacity resource-market framework involving grid operators and service providers.Source: A. Incentive based Real-Time DR… · p. 16

B. Load Forecasting Framework for Residential Areas

  • Individual-user short-term load forecasting is described as challenging because residential consumption is stochastic and dynamic, and the framework also provides demand-response recommendations [12].Source: B. Load Forecasting Framework for… · p. 16
  • The residential STLF framework applies iterative ResBlocks to smart-meter data to learn spatio-temporal correlations and forecast individual users’ loads [12].Its workflow comprises data collection, preprocessing, training, and load forecasting; the data cover consumption by devices for each customer.Source: B. Load Forecasting Framework for… · p. 16

C. Optimal Demand Response in Multi-zone Official Building

The section surveys learning-based demand response for HVAC systems and interruptible loads, then outlines smart-grid challenges and demand-response approaches for microgrids.

C. Optimal Demand Response in Multi-zone Official Building

  • SLAMP uses supervised learning to schedule HVAC input power directly for the next 24 hours under building thermal conditions and electricity rates.It aims to reduce computation time and provide a rate-versus-optimal-demand curve for distribution system operators.Source: C. Optimal Demand Response in… · p. 18

D. Demand Response Management of Interruptible Load using DRL

  • A DDQN-based, model-free DRL method maps grid states to interruptible-load management policies under changing consumption patterns.The described goals include voltage regulation and minimizing distribution-system operating cost.Source: D. Demand Response Management of… · p. 18

V. CHALLENGES, OPEN ISSUES, AND FUTURE DIRECTIONS

  • The section frames stakeholder variation, energy-supply-chain synchronization, regulation, and demand-response management as open smart-grid issues.It introduces these challenges as matters for future work using deep learning approaches.Source: §V · p. 18

A. Challenges

  • Smart-grid challenges include renewable-source uncertainty, peak-time forecasting, decision control, load balancing, equipment monitoring, microgrid coordination, EV management, and malicious data injection.The section presents feasible technical solutions alongside these challenges.Source: A. Challenges · p. 18

1) Dynamic pricing for demand response in microgrids:

  • Microgrid dynamic pricing must account for uncertain conditions and incomplete customer profiles that complicate predictions of future behavior.A multi-agent RL model in learns consumer energy use and provider pricing; post-decision state learning is used to improve consumers’ learning rate for minimizing energy costs.Source: 1) Dynamic pricing for demand response… · p. 18
  • Consumer-side load flexibility is difficult to predict because appliance-level consumption is random and only partially observed.The section describes non-intrusive load monitoring and DL methods including RNN classification, device-level RL, Q-learning, and CNNs for partial observability,,,,.Source: 1) Dynamic pricing for demand response… · pp. 18–19

2) Load forecasting in smart grids:

The section reviews DL applications in load forecasting, equipment monitoring, cyberattack detection, and EV scheduling, alongside data-labeling challenges in smart grids.

2) Load forecasting in smart grids:

  • Accurate load forecasting is difficult because consumer behavior is stochastic and small forecast errors can cause substantial economic loss.The section describes neural, Bayesian, and aggregated forecasting approaches, including optimization, and notes that the stochastic building-energy models in outperform existing ANN and DNN models.Source: 2) Load forecasting in smart grids · p. 19

3) Equipment health monitoring:

4) Cyber attacks in bidirectional energy trading:

  • The reviewed DL approaches target smart-grid cyberattacks including false-data injection, electricity theft, and network intrusions,,,,.The examples include conditional DBN detection using historical data and live features, and deep-packet inspection for classifying attack families.Source: 4) Cyber attacks in bidirectional… · p. 19

5) Energy management with EVs: EV scheduling:

  • EV scheduling methods use DNNs, CNNs, queuing models, and machine learning to address charging decisions, load prediction, and station selection,,.The section states that LSTM provides better EV-load forecasting results with less forecasting error.Source: 5) Energy management with EVs: EV… · pp. 19–20

B. Open Issues

  • The section identifies DL’s smart-grid application as comparatively limited and introduces unresolved issues.Source: B. Open Issues · p. 20

1) Procuring Labels from Inconsistent Operational Data:

  • Inconsistent operational data makes it difficult to procure labels for smart-grid DL, while communication tampering can affect supply, pricing, and sensitive information.The discussion identifies smart meters and their timing, communication, metering, indicating, encoding, power, and control modules as part of this setting.Source: 1) Procuring Labels from Inconsistent… · p. 20

2) Security concerns with enormous data accumulations:

The section describes data-security and forecasting challenges in smart grids, then discusses blockchain as a possible component of future energy-data systems.

2) Security concerns with enormous data accumulations:

3) Security Issues with Vulnerable Centralized Controllers:

5) Incomplete Energy Acquisition:

  • Incomplete energy acquisition in microgrids leaves consumers and utilities without prior information about the service provider’s strategy or microgrid dynamics.Source: 5) Incomplete Energy Acquisition · p. 20

6) Inaccuracies in electric load forecast:

  • DL load forecasting remains constrained by handcrafted features, limited learning capacity, nonlinear data, and microgrid load variation; the cited hybrid model was not evaluated on real-time data.The passage calls for forecasting that incorporates feature engineering and optimization, and notes EV scheduling should use historical and real-time data.Source: 6) Inaccuracies in electric load… · p. 20

C. Future Directions

  • The section introduces future directions for addressing smart-grid issues through technology, without specifying a particular direction in this passage.Source: C. Future Directions · p. 20

1) Blockchain for smart grid technology:

  • Blockchain is proposed for structuring heterogeneous energy data and supporting secure, privacy-preserving transactions, but mining consumes resources.The passage suggests combining blockchain with edge computing to offload mining and reduce transaction latency [124],.Source: 1) Blockchain for smart grid technology · p. 21

2) Edge AI for SG technology:

The section discusses edge AI, quantum computing, and advanced mobile networks as smart-grid technologies, and concludes with a survey of DL applications and challenges.

2) Edge AI for SG technology:

  • Edge AI places AI processing at smart-grid edge devices to support real-time prediction, distributed optimization, forecasting, and appliance-level fault diagnosis.The section describes reduced computation and offloading delays, identity authentication for security, and sub-second transaction latency as potential benefits.Source: 2) Edge AI for SG technology · p. 21

3) Quantum Computing for SG:

  • Quantum computing is presented as a technology for optimization across distributed, heterogeneous energy sources, while quantum cryptography is proposed for securing smart-grid data and trading.Source: 3) Quantum Computing for SG · pp. 21–22

4) 5G and above technology for faster energy trading:

  • The section presents 5G as supporting smart-grid connectivity and faster processing, while noting cyberattack, legacy-device, dependency, and spectrum-crowding risks.It suggests 6G with enablers such as edge intelligence, homomorphic encryption, and network slicing as a future option,.Source: 4) 5G and above technology for faster… · p. 22

VI. CONCLUSION

  • The paper surveys DL solutions for smart grids and demand response, presents use cases, and discusses challenges and potential directions.Source: §VI · p. 22
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