Living Lab Long-Term Sustainability in Hybrid Access Positive Energy Districts—A Prosumager Smart Fog Computing Perspective

Living lab, one of the recent emerging smart city concepts, faces long-term sustainability challenges associated with its complexity and breadth of use. To be efficient, it must rely on comprehensive set of information distributed appropriately among all stakeholders to unleash its full innovation potential. This is especially true in the case of positive energy districts (PEDs), where timely data dissemination is essential for prosumager decisions and their greedy behavior. This article interconnects intelligent information exchange, supported by ultralow latency hybrid access network infrastructure, with the clever use of available fog computing resources to properly disseminate complex energy details to all participating entities. As the optimal task offloading for effective information distribution constitutes the convergence problem, we reintroduced higher order neural units. These units contribute to sustaining both computational and energy efficiency, as well as the balance of the entire system. We have achieved a reliable hourly energy consumption prediction with a computationally very lightweight alternative to commonly used deep neural network approaches that can be deployed on available smart appliances with ease. The application and simulation were performed on the data set provided by one of Europe’s smart city pioneers, where the prosumager PED transition has already started.


I. INTRODUCTION
L IVING lab (LL) represents an emerging self-evolving entity within a smart city concept [1].Sometimes referred to as the "Urban Lab," it allows its stakeholders to develop, operate, and evaluate smart city services with the main mission of innovation to ensure the continuous development and improvement of the "smart" ecosystem [2].This not only assumes efficient sharing of common resources but also requires sustainable partnerships and cooperation strategies between the parties involved [3] bearing in mind that they are the real key players determining the direction of innovation.Technological readiness in LL areas is directly related to quality of life, where several evaluations have also been carried out in the past [4] in these types of urban areas.
In Europe, most LLs are united under the umbrella of the "European Network of LLs" [5] and provide added value services that allow selected parts of the city to be transformed into innovative and partially self-sustaining smart blocks or districts [6].These smart city areas combine the uniqueness of the services offered with added value to the community, as an example of crowd sensing [7], smart water monitoring [8], or complex active control of all devices connected to a grid [9].Efficiency in energy management has always been seen as a typical application and could lead, to some extent, to positive energy [10], or even off-grid urban areas [11].The term positive energy district (PED) is often mentioned [12] as a synonym for the long-term sustainability of a smart grid [13] and is in line with the implementation of the LL concept.Although many "to-PEDs transition" projects are currently running [14], [15] the actual implementation of PED also requires a precise calculation of electricity consumption/demand and production/supply in a certain area, which is not easy to achieve [16].Scaling down to positive energy blocks (PEBs) represented by the interconnection of several buildings in the PED area [17], the role of the prosumager is much more notable.
Another area in which PEBs/PEDs and LLs have in common is their high dependency on fog and cloud resources [18] and for these it is necessary to provide a sufficiently robust and reliable access and computing infrastructure with emphasis on stable jitter and low latency [19], especially for critical c 2023 The Authors.This work is licensed under a Creative Commons Attribution 4.0 License.
For more information, see https://creativecommons.org/licenses/by/4.0/services [20].From the point of view of the local government, every LL area presents valuable information where knowledge and especially its timely possession [21] mean an advantage for effective decision making [22].Several LL technological foundations are considerably dependent on the Internet of Things (IoT) [23] or even the City of Things [24].What these contributions have in common is the assumption that PEB/PED infrastructure must be designed to meet the scalability, information availability, and network latency requirements [25] to address the heterogeneity of a smart city between devices, data collections, and information security [26].However, IoT is only the first step toward optimal behavior of the prosumager on the energy market within PEDs, even though an IOT role in smart energy systems is inevitable [27].By accessing, controlling, and using smart devices, the prosumager can significantly influence the energy balance of the PEB (and figuratively also of the PED) in his favor to maximize his energy benefit.This entity focuses on greedy or selfish behavior, where self-benefit is always prioritized (maximized), it is necessary to connect the available edge/fog computing resources with a smart infrastructure [28] using elements of the tactile Internet (TI) or Tactile IoT [29].
Considering PED as a system that has to be stabilized in order to be sustainable in the long term, a complete information exchange is an essential prerequisite, especially considering the selfish manners of the energy market prosumers.A system that uses the shallow neural network apparatus to help optimally allocate available computing resources with a goal of prosumager efficient decision-making mechanism.The rapid distribution of information on the availability and consumption of energy will utilize the means of fog computing, in other words, moving the real-time data processing toward the edge of the network [30].The possession of correct information on the energy demand response, which is even enhanced with energy supply and storage with complex knowledge of the status of other nodes that are active in the PED trading, is crucial [31].Here, prediction systems play a vital role and are one of the key aspects in smart city infrastructure, taking into account optimal node task offloading in the fog environment [32] as well as its proper scheduling [33].Therefore, prediction techniques shall play an important role not only for the prediction task but also for the system stability monitoring and predictability evaluation, anomaly detection, etc.However, the sufficient amount of training data can be achieved for deep learning techniques [34] and some prediction tasks may even require nondeep techniques, such as for highly nonstationary systems where only contemporary system behavior, can be used for real-time learning predictors.Shallow (nondeep) neural networks and real-time learning regressors can be utilized in such cases.However, the local minima is one of the practical issues with conventional neural networks (e.g., multilayer perceptron (MLP), alternatively with exponential linear unit (ELU)s and rectified ELU (RELU)s types of neurons) that results in performance variation of the same MLP instances when trained from different initial weights, for example, as studied on the prediction of mean power consumption [35].

II. REQUIREMENTS
The optimal information exchange between the parties involved that has a direct influence on individual decision making depends on and contributes to the stability of the system is based in general on the following.
1) Infrastructure for the information sharing.
3) Available resources.4) Timing of the information delivery.
There are two main topics that our contribution addresses.
1) The long-term sustainability of LL is based on the balanced behavior of the parties involved, which can be problematic in the long run.Our proposed approach addresses the decision process by optimizing the distribution of the computational problem and the timeliness distribution and availability of the resulting information to the end prosumager.2) Optimal infrastructure concept for the given scenario.
This includes a hybrid access infrastructure to minimize latency in communication between individual nodes and with the central workload forwarding coordinator (WFC) node.This will be further elaborated on in the methodology chapter.The conceptual design of the infrastructure is based both on the restrictive conditions of the area and on the feasibility study of the chosen smart city.The assumption is that the infrastructure must be complex and should not limit the decision-making and innovation potential of the LL complex in any way.On the optimal information processing and distribution side, we utilize a class of shallow neural architectures that can be used as suitable learning predictors in the sense of fog computing [36].These neural architectures are polynomial neural architectures, that is, higher-order neural units (HONUs) [37], [38] with customized order of polynomial are a subclass of in-parameter-linear nonlinear architectures (IPLNAs) [38] that have intriguing properties regarding computational efficiency and simultaneous weight convergence assurance [39] and stability monitoring of the underlying system represented by the training data.Recall that HONUs can also be viewed as energy-saving computing machine learning tools due to their properties and abilities to run efficiently on low power consumption devices.

III. METHODOLOGY
Smart PED and LL ecosystems that rely on the optimal decision making of the citizen, here represented as a prosumager entity that utilizes fog computing nodes capabilities to support a strict multicriteria analysis and load balancing [40].The computational infrastructure uses intelligent and cooperative fog computing task offloading [41] and taking into account the available computing and energy resources [42] to balance the workload processed and further reduce the service response time, and improve the overall efficiency.Our approach is based on decentralization control systems [43] and enhanced with the cooperative fog computing network [44] and further elaborated in [45].For a particular size of the fog infrastructure [46] we introduce a fog node cooperation strategy, called offload forwarding.In this strategy, each fog node can forward a part or all of its offloaded workload to multiple neighboring fog nodes in the fog and/or help multiple other fog nodes process their workload.Task offloading is based on the distributed alternating-direction method of multipliers by means of the variable splitting (ADMM-VS) algorithm.Here, the WFC is defined as the entity deployed as the part of the fog/edge or cloud infrastructure that coordinates workload among fog nodes through a dual variable for optimization of all nodes workload subproblems, as well as optimal node placement [47].The flowchart of the node optimization problem is depicted in Fig. 1.
The fog computing node optimization problem to be solved is then defined as ( Based on this, ψ as a node updating optimization problem can be defined as where i is the ith fog computing node, N represents the number of individual subproblem, φ represents the vector of workloads (optimization problems) with λi workload value for the ith node, L is Lagrangian form with ρ as the augmented parameter, and is the vector of the dual variables.The IG c (ψ) is indicator function which is defined as The dual variable update subproblem can then be written as follows: The optimization of subproblems is equivalent to the form of the traditional ADMM with two random variables: φ and ψ.In distributed ADMM-VS, each fog node i will calculate the optimal service vector φ * •i by solving the following subproblem: Based on the above mathematical constructions, it is possible to define an optimization algorithm for fog computing task offloading [47].
To ensure ultralow latency and stable jitter, the concept is inspired by selected elements of the TI approach [48].For this work, TI nodes in each residential unit, which represents a prosumager entity in the energy market, are used directly for demand-response and energy supply management in order to optimize greedy behavior in favor of the prosumager.For the purpose of this article each residential unit, where the passive optical network is terminated (see Section V), is considered as IoT network entity with fog resources.

A. Polynomial Neural Architectures for Efficient Fog Computing
The mathematical aspect of convergence, which can be beneficial in fog computing, is also recalled.This concept in the IOT-cloud-fog-edge has recently already been elaborated in greater detail and gives great insight into optimal resource utilization [49], [50].Furthermore, this section recalls HONUs as a subclass of IPLNAs for monitoring the stability of the underlying data-generating process.These exclusive aspects of HONUs can be evaluated for batches of data or even for individual data samples during real-time learning.The demonstration is based on a real example of energy consumption data.We propose that these aspects of HONUs are intriguing for (nondeep) fog computing in IoT applications.
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The mathematical architecture of HONUs for prediction is as follows: where ỹ is the neural output, h is the prediction horizon in samples [hours], x is a columnwise vector of features augmented with unit as its first element, i.e., x 0 = 1, and col r (.) is a columnwise polynomial kernel of polynomial order r, and w is a columnwise vector of neural weights whose length is the same as the length of the columnwise vector col r (.), k is a discrete index of time, and upper T stands for vector transposition (for more details, see [38]).
Let us emphasize that the IPLNA form (6) of HONUs means that each neural weight in w is unique for each polynomial term in col r (x).Additionally, training HONUs represents a linear optimization problem that prevents HONUs from a local minima problem such that it is common for conventional types of neural networks, for example [35].
Moreover, gradient and stochastic incremental learning and its modifications, including ADAM [51] and recursive least squares (RLS, originating from [52] and [53]), allow us to analyze the convergence of neural weights in the sense of bounded-input bounded-state (BIBS) which serves to avoid the divergence of this machine learning tool in real time.Recall briefly the gradient incremental learning rule of HONU, which is in its general form as follows: where μ is the learning rate that can vary over time depending on the applied form of learning, and Q is the error criterion 2 .It is shown in [39] that for IPLNAs, including HONUs, the weight-update system in (7) can be expressed in the linear time-variant state-space representation form where the eigenvalues of the local dynamics matrix A and its relevant state transition matrix A k = k−k 0 j=0 A(k −j) determine the BIBS stability of the weight system (7) during learning (see [39] for further details).The relevant experimental study can be found in [38], where the most strict condition of the spectral radius ρ(A(k)) < 1 is demonstrated when weight convergence is evaluated in every individual data sample (of a time series).
Newly, we highlight the connotation of the weight convergence rule [39] with the famous Levenberg-Marquardt batch learning algorithm (LM, with origins in [53] and [54]) as follows.Recall the fundamental form of the L-M algorithm as follows: where I is the identity matrix, L M is the M × n w matrix (M is the duration of the training batch and n w is a number of neural weights), J is the Jacobian, and the upper "−1" denotes matrix inversion; for the HONU feedforward (and the IPLNA feedforward in general), the Jacobian J is constant because its rows are directly the feature vectors processed by the kernel as follows: where the colX notation for HONUs is from [38], and e in ( 9) is the M × 1 error vector as follows: where y is the vector of all real outputs (targets).Then, the convergence rule of the batch weight updates where is the index of the training epoch, which is as follows.
By substituting ( 9) and ( 11) into ( 12), the batch learning ( 12) yields Thus, the eigenvalues of the resulting local dynamics matrix I − L M • J determine the convergence (stability) of the weightupdate system for the L-M batch algorithm.For feedforward IPLNAs, the weight-update system ( 13) is a linear timeinvariant dynamical system (LTI) because the Jacobian J is constant with respect to the epoch index .For recurrent IPLNAs with the L-M algorithm, system (13) is a dynamical linear time variable (LTV) system, and the BIBS stability paradigm shall be used as in [39].
In addition to ensuring weight convergence, the polynomial architecture of HONUs allows us exclusively to apply the stability of the BIBS concept to HONU as a dynamical system that approximates the dynamics of the underlying data [55], [56].Thus, by learning, HONU approximates (predicts) the dynamics of the underlying system and that naturally reflects the stability of the underlying system.Recall from [55] and [56] that the long-vector form of HONU in (6) can also be expressed in its corresponding time-variant state space forms as follows: where χ is the state vector of HONU, and the hat sign in Â, B, û indicates that the arrays are different from the ones in (3).Then, the eigen values of Â(k) determine the stability of HONU BIBS that reflects the stability of the approximate dynamical system (similarly to the proof in [39]).Notice that for merely time series prediction, the input gain matrix B(k) and input vector û(k) either disappears or represents only the augmenting bias with its weight, i.e., w 0 , w 0,0 , w 0,0,0 , . . ., respectively, as for HONUs of polynomial order r = 1, r = 2, r = 3, . . ., respectively.This section introduces the mathematical architecture of HONUs, their absence of the local minima problem, and their weight update convergence for real-time gradient and stochastic learning.Exclusively for HONUs, the stability monitoring of the underlying data generation system was introduced through HONU, which predicts the data, for example, time series.

IV. SMART BEHAVIOR SIMULATION
Simulation of the real use case scenario of all relevant stakeholders in the PED has been carried out using the Smart Grid Typhoon HIL simulator,1 the HIL 602 + appliance type.This simulator allows us to analyze the behavior of the part of the grid [57] in real time based on the collected data or by realtime inputs from distributed sensors.It also enables validation of the performance and control of the grid in virtual environment [58] before deploying new distributed energy resources (DERs).
This simulation contains 51 housing units clustered into 14 load groups, two schools, two shopping centers, a garage parking lot and a car dealership.It also contains two smart public light connection points (with 130 public light passive optical network endpoints as distribution nodes for each residential house), two photovoltaic power plants and one high capacity battery with EV charger.3-phase 400V/50Hz distribution network is used with assumed 10% nominal voltage drop of 10% over underground powerlines.This scenario inspired by the real use case is depicted in Fig. 2 above.The smart appliances behavior is simulated within a Python environment of Typhoon HIL, where the main operation criterion is the current dynamic energy price.
Smart appliances (Fig. 3) connected to a fog environment will optimize their energy consumption.Not all appliances can be adjusted accordingly to energy prices without causing discomfort for home users.However, some tasks could be postponed or prestock (for example, preheating/precooling). Prosumagers can apply various models to optimize their power consumption based on the available energy price and the variable power demand of their appliances [31].Data on long-term measured consumption characteristics of the chest freezer have been used as input for the simulation.Using a smart freezer it is possible to store energy directly (Fig. 4), which allows for the further use of excess power and, at the same time, reduces overall cost.
The simulation setup and the simulated behavior of all elements are based on the greed/selfish strategy due to absence Fig. 3. Overview of the prosumager's home loads (smart appliances) and resources (grid, photovoltaic, battery, and EV).Designed in Typhoon HIL real-time simulator.Fig. 4. Energy consumption comparison between a regular chest freezer at −18 • C and a smart freezer (blue lines) that over freezes to −32 • C during cheap energy periods (see red line), using accumulated cold later.The smart freezer consumed 0.16 KWh, while the regular one used 0.14 KWh, however, saving 10% in costs (due to energy price difference).The smart freezer can also draw energy from wall batteries (green fill) or EV batteries (orange fill) when available and price is above selected threshold.In the first spike during the day, only the wall battery was used; in the second, 65% wall battery and 35% EV battery energy were utilized, further decreasing operating costs. of any central management system.Households or even appliances are seen as individual rational energy users who want to reduce their electricity costs [59].The entire behavior of the system is then influenced only by the billing rules and the price of energy in the spot market in a given network.Because saving money is one of the most important reasons for the transition of prosumagers [60], it is natural to expect that prosumers and their households will selfishly share energy with their neighbors and also schedule their energy storage systems to maximize profits.
The district simulation (Fig. 5) allows us to monitor and analyze the behavior of each component with the 1-s time step and 100 steps-per-second in real time or 15-min time step in virtual simulation.DER can be individually controlled and optimized based on the grid demands.Data from all smart meters (mainly nominal active power and nominal apparent power) and IoT sensors (grid state) are stored separately and loaded within SCADA initialization.Using component scripting, the data are normalized to correspond Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Fig. 6.Energy consumption of the district power grid in one day with dynamic hourly prices.On graph A, we can see normalized energy consumption of the grid without its DER.On graph B, we see the consumption of the power grid (blue) with its DER (orange).As we can see, the energy consumption on this sample winter day is nearly covered by DER around noon, which is more than satisfactory result for its winter behavior.
to the timings.When running the long-term virtual simulation (with various DERs), the input and output values have to be adapted accordingly.
The graphs depicted in Fig. 6 illustrates the total power consumption of the district for 1 day in winter with low utilization of renewable energy resources and higher consumption related to the heating of the building.Graph A shows the total power consumption of the district without DER.Graph B shows the total district power with DER (photovoltaic power plants, battery).An average of four days from consecutive four weeks is used.

V. POSITIVE ENERGY DISTRICT LOCAL GOVERNMENT INFRASTRUCTURE
The area is represented by a pilot smart city in the Czech Republic, Pisek, which was one of the partners of the Horizon 2020 project entitled Positive City ExChange (+CityxChange). 2Here, based on the feasibility study, an optimal public hybrid access infrastructure is proposed to support the long-term sustainability of a PED concept.Beyond the scope of this study, infrastructure is designed with respect to the methodology chapter, where energy-efficient infrastructure design is based on a hybrid model of an optical access network with fog computing nodes.It is based on the application of gradient learning cleverly distributed among the computational nodes available in a given residential unit, as well as other unused parts of the network, using the efficient TI traffic flow algorithm [61].This results in intelligent leverage of the fog computing nodes offloading with a real smart city application.The situation is depicted in Fig. 7.
Based on the penetration of commercial optical links that already exist in the area and the feasibility study recommendations, a subset of nodes is eligible for the LL infrastructure.The technology used will be the gigabit-capable passive optical network (GPON) which represents an energy-efficient solution [62] with low power consumption in optical distribution networks (ODNs).The architecture is based on [62] and allows edge-to-edge connections between fog computing nodes.The fiber distribution will be in HDPE microtubes of diameter 40/33 mm containing 19 microtubes, always in pairs, one active, another backup.The installed fiber will be SM 9/125, G.652 D type and/or SM 9/125, G.657 family should be considered for in-house deployments due to higher band tolerance.

TABLE I TABLE OF NUMBER OF ENDPOINT NODES
The proposed scheme of the GPON network was simulated in the VPIphotonics Design Suite (see Fig. 8).Due to the many buildings and end units, the cascade connection of the splitters is necessary, and the class C attenuation of the GPON was selected.This allowed us to ensure an attenuation range in the ODN of 15 to 30 dB.Fig. 8 shows the simulation topology consisting of the OLT, ODN, and ONU.The OLT launches with a power of 6.5 dBm (class C defines a power of 5 to 9 dBm).Data transmission was performed with 2.488 Gbit/s.The ODN contains 20 km of single mode fiber (G.652D) and one splitter, which is the worst case of ODN length.The type of splitter was changed from 1:2 to 1:128.The customer's part had an ONU network with bit error rate (BER) evaluation.
On the customer side (public lightning lamp), the optical network unit (ONU) will be used.To ensure power efficiency on the customer side, the ONU is equipped with power management.The ONUs should move to cyclic sleep mode, where the transmitting and receiving sides are turned off for a specific period, and then the ONU just checks the status of the link.Periodic link status is necessary due to loss of frame LoF and loss of signal LoS timer expiration, which will lead to deactivation of the ONU.The PON-based solution also offers the minimum latency for data transmission [63].The fiber infrastructure footprint will have two separate central distribution units A and B, (see Table I).
The smart district of the city of Pisek consists of six areas with two central office points.Point A controls four branches of the smart district and point B controls two branches.There will be four distribution branches (depicted as green, brown, blue, and purple) originating at optical network termination (OLT) A (see Fig. 9) and two branches (gray and pink) originating at OLT B. OLT will be located at both points.OLT at point A manages four branches of the district via 4 GPON ports with a split ratio up to 1:64 physical reach.Note that the transmission convergence layer supports up to 1:128.The splitters may be connected in cascade, or the operator may use one splitter with a higher split ratio (up to 1:64) in the first distribution box of anchorage.In our case, cascade connection of splitters is a better solution, and the first splitter (with a lower split ratio) should be located at the base of the first house on the street.

TABLE II SIMULATION RESULTS OF GPON SYSTEM WITH VARIOUS SPLIT RATIO
Table II shows the simulation results of the proposed GPON topology.The proposed topology supports a split ratio up to 1:128 without reaching the threshold value of BER (1×10 −10 ).On the other hand, the scheme did not consider the forward error correction (FEC) algorithm, which can move the threshold below (1 × 10 −4 ).The simulation included that split ratio for demonstration usage or future expansion in a real scenario with selected attenuation classes.

VI. APPLICATION OF HONUS TO ENERGY CONSUMPTION PREDICTION
Here, the application of real-time gradient learning of HONUs is demonstrated in the short-term (hour) real-time prediction of building energy consumption for one year recordings [64].We limit the data set to contain hourly measurements of one predicted variable y, which is energy consumption [kWh], and two external input variables u 1 and u 2 representing outside temperature [C • ] and wind speed [m/s], respectively.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.The first-order HONU with real-time retraining was used.Two learning algorithms were applied.First, the incremental learning rule of gradient descent with normalized learning rate was used, also known as the normalized least mean square (NLMS, [65], [66]).Second, the batch L-M algorithm was applied, where the sliding window of the last measured data samples M was used for retraining as in the real-time application.The characteristic vector x of HONU contained current and past energy consumption values, as well as future values of the predicted outside temperature and wind speed.The configuration of applied HONUs and the learning algorithms is in Table III.

TABLE III CONFIGURATION OF APPLIED HONU AND LEARNING ALGORITHMS
The min-max normalized plots for real-time predictions of a residential unit energy consumption with measured and (accurately) predicted both outside temperature and wind speed are shown in Figs. 10 and 11 with full views of the figures in the appendix.The incremental NLMS preserves the constant spectral radius (estimated using the Frobenius norm |A|| 2 ) of the matrix dynamics due to the normalization of the normalization of the learning rate Table III, while the L-M batch retraining maintains a constant learning rate and |A|| 2 is well below 1.The full view of Fig. 10, illustrates the prediction with NLMS incremental learning for the entire year of data samples.The full view of Fig. 13, is showcasing the prediction with batch L-M retraining for all the year's data samples.

VII. FUTURE WORK
The involvement of prosumager in the innovative smart city concepts is relatively new and not well mapped, even in the literature currently available.The challenge of electricity storage, as a commodity used to maximize the utility function, is the key to the long-term sustainability of all innovative (electricityusing) efforts within LLs.Although energy-positive districts already have the tools to incorporate prosumagers' greedy behaviors, LLs, which may be constrained by lack of available electricity in advancing their innovative potential are not nearly as far.The question for future work, then, is to focus on holding electricity beyond own need and the resulting maximization of profit at the cost of slowing the pace of innovation creation within LLs or even stagnating it.

VIII. CONCLUSION
Two directly interconnected topics have been merged to uniformly contribute to the long-term sustainability of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.special smart city use case-an LL as a potential complementary innovation linkage to a PED.We contributed to the stability of such districts by leveraging smart energy components and available fog computing resources to support optimal prosumager decision making and proper energy information dissemination.The decision model is based on the distribution of computational complexity using smart fog computing resource allocation.The clever application of shallow neural networks help prosumagers to predict electricity prices and apply greedy/selfish techniques to maximize their utility.For this purpose, distributed workload allocation vectors among individual compute nodes were used exploiting a central WFC controller.This approach is further supported by a hybrid access architecture, which, by adopting elements known from the tactile IoT concept, guarantees very low latency and stable jitter.The foundation of this architecture is an energy-efficient public optical access network that runs up to each residential unit.Design and simulation were performed based on a data set provided by a pilot PED smart city environment that was part of the Horizon 2020 Positive City ExChange project.

Fig. 2 .
Fig. 2. Schematic representation of the model of the energy district of the city of Pisek.Each node represents a different home complex, business, school, public lighting, or cumulative positive energy sources.Each of these node's appliances' behavior is controlled individually on lower level of the simulation.

Fig. 5 .
Fig. 5. Simulation of the overall consumption in a PED running in the Typhoon HIL environment.Overview map in the HIL SCADA environment is shown (bottom) with the available controls allowing access to the details of the power consumption and setup of individual parts (top).

Fig. 7 .
Fig. 7. Real situation of a energy positive block in the city of Pisek, where the black lines represent the chart skeleton of the LL infrastructure and black circles represent the nodes.

Fig. 8 .
Fig. 8. Simulation scheme of the proposed topology in the smart city Pisek.

Fig. 9 .
Fig. 9. Proposed GPON setup for the public lightning infrastructure of the OLT A.

FOR 3 -Fig. 10 .
Fig. 10.Adaptive prediction with NLMS incremental learning (top, y is the real energy consumption), where prediction error (second top), the weight behavior (third top), normalized learning rate (second bottom), and spectral radius of the matrix of dynamics (bottom) is shown for a selected interval of a year, all values are min-max normalized (see Fig. 12 for full view).

Fig. 11 .
Fig. 11.Adaptive prediction with L-M (mini) batch retraining (top, y is the real energy consumption), prediction error (second top), weight behavior (third top), normalized learning rate (second bottom), and spectral radius of the matrix of dynamics (bottom) are shown for a selected interval of a year, all values are min-max normalized (see Fig. 13 for full view).

Fig. 12 .
Fig. 12. Full view for Fig. 10 of prediction with NLMS incremental learning, where prediction error (second top), the weight behavior (third top), normalized learning rate bottom), and spectral of the matrix of dynamics (bottom) is shown for all the year data samples.

Fig. 13 .
Fig. 13.Full view for Fig. 11 of prediction with batch L-M retraining, where prediction error (second top), the weight behavior (third top), normalized learning rate (second bottom), and spectral radius of the matrix of dynamics (bottom) is shown for all the year data samples.