Artificial Hypothalamus for Electrical Organizations. Electricity & Natural Gas Advanced Supply Chain & Market Optimization

Webinar. Analítica Avanzada & Optimización Aplicadas al Sector Eléctrico

Fecha: 01/20/2021

10:00 México, 11:00 Bogotá, 16:00 Greenwich, 17:00 Madrid

https://www.dhirubhai.net/pulse/webinar-anal%C3%ADtica-avanzada-optimizaci%C3%B3n-aplicadas-al-sector-jesus/

Last PDF version of Electricity & Natural Gas Advanced Supply Chain & Market Optimization: https://goo.gl/bMp4hc

https://www.dhirubhai.net/pulse/businesses-artificial-hypothalamus-cloud-athenea-jesus-velasquez/

Electricity & Natural Gas Advanced Supply Chain & Market Optimization 

1. INTRODUCTION

?OPCHAIN-ELE (ELEctricity Supply Chain Optimization) corresponds to a set of mathematical models designed to support the decisions of the various actors involved in the electricity supply chain, in terms of sectoral planning and business generation. According to the structure of modern electricity markets, the support of the business decision-making power generation should be seen from two different points of view.

• Central agents: formed by the regulator, supervisor, planner and market operator
• Generators: agents that operate power plants.

OPCHAIN-GAS corresponds to a mathematical model designed to support the decisions of the various actors involved in the chain of supply of natural gas at the level of sectoral planning. OPCHAIN-ELE and OPCHAIN-GAS together make OPCHAIN-E&G a set of optimization model to dispatch the electricity and gas systems. OPCHAIN-E&G is designed to allow its users to parameterize the model according to the complexity of its supply chain and optimization requirements thereof.

Some benefits of the implementation of mathematical models OPCHAIN-E&G are:

• Explicit cost reduction or profit increase;
• Clarification of the goals of the organization, the decision options and environmental constraints;
• Processes more rational and systematic planning;
• Improvements in the communication process; and
• Better focus of the process of data collection and interpretation

The table presents a resume of the optimization models that integrate OPCHAIN-ELE

The diagram below shows the design of the integrated use of the models described above to support the decision-making of a generator agent.

OPCHAIN-E&G is a system of technical and economic planning tools that exploits the latest computer technologies coupled with the advanced mathematical modeling. The power of algorithms used for optimization (like Nested Benders Decomposition (NBD) or Generalized Stochastic Dual Dynamic Programming (G-SDDP), joint with the ability to represent precisely the relation of cost and volume, provides confidence in optimal results that cannot be provide by simpler approaches; its services for generation of models, coupled with spreadsheets, databases, multidimensional analysis tools, visualization software and Monte-Carlo simulation models to generate probabilistic scenarios; providing an ideal place to develop quickly and comprehensively optimization studies of the of electrical, smart grids and natural gas systems.

OPCHAIN-SGO is a decision support system orient to Smart Grids Optimization as a new decision support system that is included in OPCHAIN-E&G

2. OPCHAIN-E&G: FUNDAMENTS

2.1. CONCEPTUALIZATION

OPCHAIN-E&G provides the solution to a wide range of strategic, tactical and operational problems considering many aspects of the different types of problems and its components. OPCHAIN-E&G  can be used to support consultancy work, end customer studies, or in the "cloud" on an optimization server to directly support decision-making processes.

 OPCHAIN-E&G was implemented using OPTEX Optimization Expert System, it can produce program algorithms in various optimization technologies (GAMS, AMPL, AIMMS, C-GUROBI, … )

2.2. STRUCTURED MATHEMATICAL MODELING

OPCHAIN-E&G integrates a set of mathematical optimization models with its corresponding information system; the models are aggregate for strategic and tactical planning and detailed for scheduling operations.

OPCHAIN-E&G is built based on the concepts of Structured Mathematical Modeling in which the constraints, and all algebraic elements (indexes, sets, parameters, variables, objective functions), are stored in a Mathematical Modeling Information System (MMIS); subsequently the mathematical models are built as a set of optimization problems and the problems, in turn, are defined as a set of constraints. OPCHAIN-E&G has a set of basic equations (core) are those that represent the physical system, these equations are added the specific equations of each problem.   

2.2. NON-LINEAR MODELING

Traditionally electrical systems planning models are based on stochastic optimization and are solved using Nested Benders Decomposition (NBD), this is the case of SDDP model (Stochastic Dual Dynamic Programming). Due to limitation of Benders Theory, NBD only can solve linear problems, which becomes an important constraint to multiple cases of real-life that require discrete and/or non-linear models; then linearized solutions do not correspond to the optimal solutions real-life system. The G-SDDP methodology (Generalized Stochastic Dual Dynamic Programming) used by OPCHAIN-E&G can solve real-life (discrete and/or non-linear) problems providing optimal solutions.

2..3. STOCHASTIC OPTIMIZATION

The power of the optimization solvers (GUROBI, IBM CPLEX, XPRESS) and the power of current computers, allows the analysis of problems based on stochastic optimization models, leaving aside the traditional deterministic models. The modeling of random events in optimization models is supported in:

• We don’t know what will happen
• We know what can happen

Random events are modeled based on scenarios, which are assigned to probabilities of occurrence.

While several decades ago to solve problems of stochastic optimization of large size using lots of scenarios seemed unattainable, technological advances in all directions (speed of the processor, cache memory capacity and memory RAM, "solvers" speed, networks of high-speed communications,...) made the stochastic optimization a viable methodology to face the problem of handling uncertainty in decision-making process.

Stochastic optimization is necessary when we want to manage financial risks related to the investment and operation of industrial systems; a case known is related to the management of resilient supply chains to face disasters, which cannot be achieved with deterministic models.

Traditionally, Multi-Stage Stochastic Programming (MS-SP) has been part of the mathematical methods used to optimize the dispatch of electricity generation plants; initially, Stochastic Dynamic Programming models were the most used; later, the models based on Nested Benders Stochastic Decomposition (NBD) are the “standard”.

All models of OPCHAIN-E&G can be modeled using MS-SP, this is a decision of the end-user, no a decision of the mathematical modeler.

The use of MS-SP implies the definition by the user of five fundamental aspects:

1.  The “core” deterministic model, all E&G models can be converted in a stochastic optimization model.

2. The dimensions of uncertainty (the number of random parameters, i.e. water inflows, demand, oil prices, …) that define the random environment of decisions (scenarios). The user can select many uncertainty dimensions, according to the situation or to the model.

3. The decision-making process is represented by a multi-stage tree that is configured by the user.

4. The policy of risk management, financial or operational, that the user wants to include in the analysis.

5. The methodology of mathematical problem solution, which can be: i) default or ii) selected the user according to the format of the problem.

2.4. LARGE-SCALE OPTIMIZATION METHODOLOGIES

In the future, the real-life solution based on Mathematical Programing, applied to large physical and social structures/organizations, must be based on multilevel parallelism using the modern computational architectures, then, Large-Scale Optimization Methodologies (LSOM) are the fundamental to atomize an optimization mathematical problem in multiple types of sub-problems that can be solve using the concepts of: i) Asynchronous Parallel Optimization and ii) Real-Time Distributed Optimization.

The table presents a summary of benchmarks made by the researchers to compare Benders Theory (BT) with IBM-CPLEX, one of the best solvers in the optimization market. The conclusions are clear: LSOM speed-up the solution time of large problems.

All models supported by OPTEX may use LSOM like Benders Theory (BT), Lagrangean Relaxation (LR), Dantzig-Wolfe Decomposition (DW-D), Stochastic Optimization (SO), Column Generation (CG), Cross Decomposition (CD), Disjunctive Programming (DP), Parallel and/or Distributed Optimization … and its variations.

 The image shows the control parameters of BT in OPTEX; it allows to the user of OPCHAIN-E&G to select the LSOM more convenient.

All mathematical problems of OPCHAIN-E&G may be resolved using LSOM and stochastic optimization.

2.5. G-SDDP: GENERALIZED STOCHASTIC DUAL DYNAMIC PROGRAMMING

To speed-up the solution time of large-scale problems, DW created the GDDP (Generalized Dual Dynamic Programming) oriented to solve dynamic optimization problems, integrating the Benders Theory (BT) and Dynamic Programming (DP) approaches (Velasquez, 2002, 2018). Based on the DP approach, GDDP makes a distinction between state variables and control variables, this distinction permits a more detailed algorithm in which the sub-problems are smaller than in the NBD. The NBD has been widely used in the economic dispatch of power systems. The main limitation of NB, including Dual Dynamic Programming (DDP), is that they only solve linear models, then GDDP is more robust than NBD.

The next tables present a DW benchmark between standard GDDP and standard NBD using a “little” determinist linear economic electricity dispatch (variables 1057, constraints 337 and no-Ceros 2245). The conclusions are: i) the case complexity doesn’t justify the large-scale methodologies, ii) the experiments show that GDDP is 7.69 times faster than NBD and iii) the integrated coordinator is 3.37 faster that NBD coordinator.

The next tables present a DW benchmark between standard G-SDDP and standard SNBD (Stochastic Nested Benders Decomposition, like SDDP) using a stochastic linear economic electricity dispatch. The conclusions are: i) The complexity of the case does not justify the large-scale methodologies, ii) the experiments show that the best G-SDDP is, approximately, 100 times faster than SNBD and iii) the experiments show that the best G-SDDP with NBD coordinator is, approximately, 15 times faster than SNBD.

The following table and the image resume the study of behavior of G-SDDP for a stochastic mix-linear economic electricity dispatch. The decrease in the solution time per scenario, when increase the number of scenarios, is a measure of the learning capacity of the G-SDDP.

2.5. RISK MANAGEMENT

Risk Management (RM), financial and operational, is the true profit provided by stochastic optimization models. The complexity of this problem lies in its bi-criterion nature: i) the desire to maximize the expected payoff and ii) the desire to minimize the risk assumed in decisions under uncertainty.

The risk management using neutral risk models, that optimize the expected value of the objective function, excluding the risk management methodologies based on risk measures (like CVaR, Conditional Value-At-Risk), lead to system to vulnerable positions (high risk positions).

OPTEX facilitates the inclusion of multiple types of criteria to measure the risks and introduce such measures as part of the decision-making process, the following may be appointed: i) income expected value, ii) mean-variance, iii) minimax, iv) maximum regret, v) down-side risk, vi) minimum risk plus expected income constrains and vii) expected value plus risk constraints. The user can select which criteria must include in the stochastic models.

3. OPCHAIN-ELE: ELECTRICITY ADVANCED ANALYTICS

The Electricity Economic Dispatch (EDI) the central model of OPCHAIN-ELE, it optimizes the plants dispatch minimizing the operation cost of the interconnected system, it simulates a perfect electricity market. Two models are integrated in OPCHAIN-ELE: the hydraulic and the electrical.

3.1. HYDRAULIC MODEL

For optimum management watershed, the hydraulic model may be use individually (IWRPS, Integrated Water Resources Planning System).

3.1.1. TOPOLOGY

Hydraulic OPCHAIN-ELE model corresponds to a general model that includes all types of hydraulic components: reservoirs, hydroelectric plants, pumping stations, pumping storages, rivers, spillage channels, connection points, demands (irrigation, aqueducts, environmental, industrial, …). The components can be linked to form any topology.

 Hydroelectric power plants are modeled independently of the reservoirs so that connectivity plant-reservoir and reservoir-plant must be set. The regulation capacity of reservoir is simulated in detail, so such consistently represent the dispatch of power plants considering its ability to regulate the water resource multi-year, annual, hourly, .... For special reservoirs, it is possible to establish rules of operation established based on agreements or laws that must be observed when using the water resources

3.1.2. SPILLAGE, MINIMUM FLOW RATES AND MINIMUM LEVELS

It is quite common that the spillage, the minimum flow rates and minimum levels should be managed using soft constraints, which involve subjective penalties in the objective function. This is due to that the format of the problem cannot be solved by the selected solver or by the mathematical methodology. For example, NBD only solves linear problem that ever has feasible solutions. 

The problems arising from the penalties are concentrated on the fact that they are “mathematical tricks” to control the representation of the physical solution of problem which ends up altering the representativeness of the economic solution (dual variables).

 For example, this can lead to wrong decisions, when the economic variables are used to estimate the spot price of an energy market; the marginal cost of the demand equation is considered a "proxy" of the electricity spot price. But due to the penalties the marginal cost may be negative (its value depends on the value of the penalty).

 To be exact the modeling of the spillage of reservoirs must include binary variables. The distortion is greater when shedding moves water from a basin of lower productivity to a basin of higher productivity. OPCHAIN-ELE has no problem to model exactly such situations.

3.1.3. HYDROGENERATION FUNCTION

Two types of power plants are considered: i) fixed head: considered an efficiency factor independent of the state of the reservoirs, and ii) variable head: considered an efficiency factor dependent on the head of the reservoir associated with the central. The first case is modeled using linear models; the second case, the modeling is based on the "convex hull" approach (Diniz and Pi?eiro-Maceira, IEEE Transactions on Power Systems, Vol. 23, No. 3, August 2008); this approach considers the combined effect of the hydraulic head and the turbine flow; therefore, it can be used generically for hydroelectric power stations of fixed head, when it is convenient consider the "exact" modeling of the turbine flow that would be a particular case of the "convex hull' modeling.

3.1.4. RENEWABLE ENERGY SOURCES

For the generation of synthetic scenarios of the variable climatic variables, there are two requirements: i) short term (hours, days) and ii) medium/long term (weeks, months). Short-term specific models for each renewable source, should be built, it is not considered in detail in this part.

For medium/long term, there are two alternatives to generate synthetic scenarios:

1.    Statistical synthetic generation model of climatic variables (type Fiering-Matalas),

2.    Generate synthetic series of climatic variables based on mixing of historical series

3.    Generate synthetic series based on the historical series having the ENSO (El Ni?o Southern Oscillation) series as an instrumental variable, this is the standard method in OPCHAIN-ELE.

ENSO events have proven to be determinants of climatological variables (water inflow, wind speed and solar luminosity) mainly in the Pacific Sea area; therefore; ENSO is a main variable to forecast the cost of the energy (via spot price or via marginal cost).

The importance of ENSO events has led to large amount of investigation by multiple organizations, which have multiple models oriented to forecast ENSO events in the short/medium term. Two types of models are used: i) Dynamic: based on the physical modeling of the dynamics of the process; and ii) Statistics: based on empirical evidence of the process adjusted through statistical models.

The International Research Institute for Climate and Society (IRI, https://iri.columbia.edu/, Columbia University) integrates all the predictions based on a Bayesian Ensemble Model that dynamically modifies the a-posteriori probability to be the correct for each of the models.

DW methodology is based on integrating the ENSO forecast of the IRI with the observed historical series of climatological variables. OPCHAIN-ENOS uses an optimization model of which results are the convex combination of historical series that “best” represent a synthetic scenario generated from the statistical characteristics of the IRI forecast.

3.2. ELECTRIC MODEL

3.1.1. TOPOLOGY

Electrical connectivity is via a network of circuits (links) and bars (nodes) that integrates different types of facilities: power plants (hydro, thermo, coal, eolic, solar, biomass, … ), demand places (industrial, cities), regional interconnections and energy storages. For each type of plant OPCHAIN-ELE includes the exact equations for its simulation.

3.2.12. ELECTRICITY NETWORK FLOWS AND LOSSES

The electricity network flows are modeled based on a linear DC load flow that consider the active power flowing through the transmission lines (the reactive power is neglected) and the difference between the tension’s angles on the bars. DC model is an approximate way to solve load flow nonlinear equations.

The ohmic losses in circuits are calculated using a piecewise linear function of the approximation based on cosine functions.

3.2.3. UNIT COMMITMENT DISPATCH

The OPCHAIN-ELE dispatch model can be extended to include all the rules that must comply the unit commitment problem. The constraint may be related with: start/stop plants, must run plants, ramps.

4. OPCHAIN-ELE: ADVANCED ANALYTICS EXTENSIONS

4.1. ECONOMIC REGULATED DISPATCH

 The controlled liberalization of energy markets brings traditional economic dispatch models do not allow to simulate the properly functioning of the system and the electricity market. OPCHAIN-E&G considers two approach to modeling the effect of the market regulation: i) Economic Regulated Dispatch (ERD) models, and ii) Economic Equilibrium (NCD) models. In both cases the models must include equations and variables that allow simulate the impact of the regulated market.

The ERD model approximates the real-life problem (market equilibrium) that minimizes the cost of operation of the interconnected system: physical costs plus regulated cost and less incomes.

 Considering that the regulation is typical of each country or region, the equations and variables related to the regulation. For example, in the case of Colombia is required, or has required, modeling regulatory aspects:

• Ideal dispatch
• Scarcity price
• Long term buy/sell electricity contracts
• Long term buy/sell combustible contracts
• Options of firm energy (reliability charge)
• Daily start/stop of plants

4.2. NASH-COURNOT EQUILIBRIUM DISPATCH

The Economic Equilibrium Dispatch (NCD) model is a dynamic, oligopolistic, spatial, Nash-Cournot equilibrium model to determine electricity dispatch, of medium and long term in an open market, based on standardized financial instruments for future risk hedging.

The modeling is based in the concept of Nash-Cournot equilibrium in competitive Game Theory, the generators agents must decide about their offers of (price, quantity). Four approaches may be used to solve NCD:

 Maximum Revenue Optimization Model: based in the ERD model the generator agents are divided in two types: i) price makers (dominant) and ii) price takers (followers). The objective function maximizes the incomes of the generators, it represents a Stackelberg market

 Bi-Level Equilibrium Model: the first level is associated to the Independent System Operators (ISO, representing the buyer) and the second level to the market agents who are simulated individually as Nash players. The ISO problem is like an Economic Dispatch problem (EDI), each agent has a maximum income problem which result is the offer to ISO. The convergence is bases in a Lagrangean coordination scheme.

Computable Equilibrium: the formulation is based on the format of General Computable Equilibrium, used in economics models.

 Mathematical Programming with Equilibrium Constraints (MPEC): This formulation uses an optimization format and includes explicitly the optimality (complementary) constrains of the equilibrium market.

4.3. MODELING SPOT PRICES IN A FREE MARKET

Prediction spot prices of the energy market is essential for decisions to take an agent that participates in the market, either buyer or seller, either generator, marketer or distributor of energy. Then, the decision-maker requires models that produce spot prices to be used in other mathematical models within the decision-making process.

Mathematical models to be used depend on: i) the planification period (“real-time”/short/medium/long term), and ii) type of the market considering the plant dispatch: by a mathematical model or by offers make by the market agents (“free market”).

 Additionally, two types of mathematical methodologies may be used: i) oriented to forecast based on the historical series” (Advanced Probabilistic Methods (APM), Machine Learning (ML) and Artificial Neural Nets (ANN)) and ii) techno techno-economic models like EDI, ERD, or similar models. This section discusses the case of short/medium/long term forecasting of spot prices using techno-economic models

 In markets dispatched by a mathematical model, the plants are dispatched according to the generation marginal costs that are calculated by a mathematical model that uses the ISO for planning and/or for scheduling (unit commitment); then “best” projection of spot prices, perhaps is that the ISO mathematical model produces.

 In the case of a free market the situation is more complex since the price formation "law" not always can be explained based on mathematical rules (explicit, clear and universal) as that integrates a dispatch mathematical model.

Experience indicates that the relationship of the spot price with marginal costs can be very weak as the graph presents. It was prepared with historical spot prices and the marginal costs of the ISO planning model in the Colombian market.

 Then in a free market the situation is more complex since the "law" of price formation not always can be explained based on mathematical rules (explicit, clear and universal) as traditional economic dispatch model.

The relationship between changes in the market regulation and structural changes in the spot price is evident, at least in the Colombian case. The graph presents two dates that occurred changes in the Colombian regulation, which brought changes in the mean and the standard deviation of the spot price.

Considering the history and experience of DW, OPCHAIN-ELE includes a probabilistic model of the spot price that is linked to variables and parameters of the economic dispatch model (EDI or ERD); it is based the Bayesian combination of several statistical models, that represent different regimes, this approach generates a greater capacity to reflect the tails of the distribution probability function.

4.4. OPERATIONAL RISK MANAGEMENT

 In hydraulic systems, it is common to manage operational risks using mathematical tricks aimed at rationalizing the use of resources by imposing logical restrictions; this is the case of the restrictions known as alert, risk aversion or minimum operating curves; they are a concept of certain regulations, and/or mathematical formulations to prevent the reservoirs to operate below a certain level; this because it is considered that without curves the system could produce energy deficit. Conventionally, this approach includes in the model "soft" constraints that penalize the objective function when a reservoir operating below the curve. This approach entails serious distortions since it doesn’t work as the modeler think, incurring cost overruns that can be significant.

Conventionally, this approach includes in the model "soft" constraints that penalize the objective function when a reservoir operating below the curve. This approach entails serious distortions since it doesn’t work as the modeler think, incurring cost overruns that can be significant.

However, should be aware that this problem is due to the mathematical formulation and not for the concept itself: penalize the reservoir level is different from penalize the use of water (generation), that requires binary variables. OPCHAIN-ELE includes the formulation the two cases. The graph shows how the generation penalization can interpret the idea of minimum operating levels.

OPCHAIN-ELE allows the risk management including "exact" equations (probabilistic) to control the different types of risk: the financial and the scarcity of natural resources.

5. OPCHAIN-SGO: SMART GRIDS OPTIMIZATION

5.1. FRAMEWORK

OPCHAIN-SGO is integrated by forecast models and optimization models oriented to support the decision making of:

• Electricity Agents Smart Grids: optimization of the economic and technical aspects related to the “smart grids” in electricity companies;
• Buildings/Homes Demand Response: optimization of the management of energy in building assemblies, as: universities, malls, office buildings, homes, urbanizations and/or small towns
• Industrial Energy Efficiency: optimization of the energy management in heavy industries intensive in the consumption of energy.

The forecast models are:  

• FRES - Forecast of Renewable Energy Sources prediction of long (years, months), medium (week, months) and short (days, hours) term availability of renewable energy sources, such as: wind, solar radiation and water inflows.
• FDEM - Forecast of Electricity Demand prediction of long, medium and short term of the of electricity demand.

OPCHAIN-SGO is integrated by the following optimization models: 

• Smart Grid Economic/Regulated Dispatch: optimization of the management of electrical energy in: factories, universities, shopping centers, office buildings, urbanizations.
• Smart Grid Unit Commitment: optimization of the management of the electrical load in real-time.
• Smart Grid Network Reconfiguration: optimization of the topology of the network for: i) voltage control, ii) configuration of feeders, iii) location/activation of electrical assets (transformers, capacitors) and iv) phase balancing.
• Smart Grid Network Design: optimization of design and/or re-design of "smart grids" 
• ETRM - Electricity Trading & Risk Management: decisions to buy/sell electric power one day in advance and on the day of dispatch.

The mathematical models of OPCHAIN-SGO may be integrated with OPCHAIN-E&G models sharing the same data-model information system.

5.2. ECONOMIC/REGULATED DISPATCH

Mathematical model oriented to medium-term planning of the management of electric power in: factories, universities, shopping centers, office buildings, urbanizations, ... . It corresponds to a model of economic dispatch, including constraints associated with the regulation of the electricity market.

 In addition to a planning tool, it is used as a primary information source in other models that are part of the OPCHAIN-SGO and it is based on the concepts of the current OPCHAIN-E&G dispatch model

5.3. SMART GRID UNIT COMMITMENT

 The OPCHAIN-SGO-UC dispatch model includes all the rules that must comply the unit commitment problem. The constraint may be related with: start/stop plants, must run plants, ramps, eolic efficiency, …

5.4. NETWORK DESIGN OPTIMIZATION

Optimal design of radial distribution networks including: power plants with renewable energy, energy storages, sub-stations, transformers, feeders and reliability restrictions. Network Design Optimization is part of the three models required for strategic decision making: 

• NDO - Network Design Optimization: Model of optimization that determines the topology and capabilities of the different types of power technologies that are part of a radial distribution network; 
• ERD – Economic Regulated Dispatch: Model used to determine primary information that is required in the optimal design model, this information may be related to: spot market prices and/or plant clearance. 
• FIN - Financial Evaluation: produces the financial reports required to evaluate the profitability of the financial viability of the projects.

The optimal design of smart grids entails a change in the traditional design modeling approach that assumes that the network topology remains constant once installation has been included in the system.

 New power technologies and the smart metering systems allow on-line, or frequently short (hourly, daily, weekly, monthly), reconfiguration of the system topology, then the optimization model must select the availability of core assets which can be reconfigured over the planning horizon, anticipating the actual operation that will be given in the future.

5.5. NETWORK RECONFIGURATION

Network reconfiguration is the dynamic optimization of the network topology for i) voltage control, ii) feeder configuration, iii) location/activation of electrical assets (transformers, capacitors) and iv) phase balancing.

5.5.1. VOLTAGE CONTROL

 The purpose of voltage control in distribution networks is to change the tap position of transformer regulators in order to achieve the goal of reducing power losses while maintaining satisfactory voltage profiles.

The change of voltage is through several onload tap changers (OLTCs), each capable of regulate the voltage of the secondary side of a transformer at one point in the network.

The purpose of voltage control in distribution networks is to change the tap position of transformer regulators in order to achieve the goal of reducing power losses while maintaining satisfactory voltage profiles.

The change of voltage is through several onload tap changers (OLTCs), each capable of regulate the voltage of the secondary side of a transformer at one point in the network.

 The problem minimizes power losses and switching (tap change) costs; subject to:

• Power flow equations;
• Voltage constraints, both phase to neutral and phase to phase;
• Current constraints, including cables, overhead lines, transformers, neutral and grounding resistance;
• Tap change constraints
• Shunt capacitor change constraints

The voltage control includes the Conservative Voltage Reduction (CVR) that is the concept of lowering the utilization voltage to end-use consumers such that their demands, and energy consumption, decreases. The most prominent benefit of CVR is the peak load reduction, which accordingly reduces the cost of power delivery because it costs more to run peaking generation units; CVR has another benefit of reducing power loss. CVR uses of both capacitors and voltage regulators.

5.5.2.  FEEDER RECONFIGURATION

 Feeder reconfiguration is to alter the topological structures of distribution feeders by changing the open/closed states of the sectionalizing or tie switches. The goal is to minimize the total system power loss while keeping the generation cost of distributed generators at minimum.

Benefits of feeder configuration: i) improve network load balancing, i) reduce power losses and iii) prevent service disruption in case of power outage.

5.5.3.   LOCATION/ACTIVATION OF ELECTRICAL ASSETS

Location or relocation of portable assets in accordance with the characteristics of the market based on the periodic review of the operation of the Smart grid whose design can be adapted to changes in demand, seasonal or permanent. An example, the relocation of transformers.

5.5.4. PHASE BALANCING

The goal of phase balancing is to maximize the feeder capacity utilization, to improve power quality, and to reduce energy losses. It is a “combinatorial optimization” problem. The solution is the assignment of customer load to which of the three phases.

5.6. INDUSTRIAL ENERGY EFFICIENCY

The large-scale industrial production is always tied to heavy use of industrial services (various forms of consumer/producer energy conversion) which make the material conversion process feasible.

The industrial energy efficiency is supported on integration of production processes with energy services oriented to the simultaneous optimization of both industrial production and energy conversion that is related with the contaminant emissions of gas and liquids.

OPCHAIN-SGO can be integrated with models of complex industrial processes, in which is necessary the redesign of the power supply system of in order to optimize it, in accordance with the new power technologies. This type of models includes the handling of polluting processes, i. e. combustion in furnaces, to determine the optimum mix of fuels in accordance with the environmental regulatory taking as a reference the generation of green energy and the sell/buy in the energy markets.

More Information:

• Heavy Industry Energy Efficiency: Optimization, Smart Grids & Process Control

https://www.dhirubhai.net/pulse/heavy-industry-energy-efficiency-optimization-smart-grids-velasquez/ 

6. OPCHAIN-GAS: NATURAL GAS DISPATCH

OPCHAIN-GAS the module of transport and supply of natural gas describes the process of supply and demand for gas; from this point of view its integration with the power system determines the economic balance electricity-gas under the hypothesis assumed about the market; for minimal cost models the economic hypothesis corresponds to "perfect" markets.

The entities of the gas system are:

• Node: place where the installations of the gas system are connected.
• Production fields
• Consumer zones: discriminated by demand sector: refineries, heavy industries, residential, vehicular and commercial.
• Thermoelectric plants
• Ports: may receive and/or send liquefied natural gas (LNG). They are associated with liquefaction and/or regasification plants and have gas storage capacity.
• Transport systems: pipelines and multimodal transport systems, using vehicles.
• Pumping stations: used to compress gas and transport it.

The connectivity between the electricity & gas sectors is given through: the demand for natural gas for use in thermal plants and, it can also occur through substitution of demand can be given between gas and electricity.

 The planning and programming of gas transportation is the result of integrating information and actions on two systems: i) Physical system: associated with physical infrastructure and its operation; and ii) Trading system: associated with business transactions related to the transport of gas, usually through long-term contracts, which are reflected in the nominations made by the agents to arrange the delivery and transport of the products.

7. OPCHAIN-E&G: ADVANCED ANALYTICS EXTENSIONS

7.1. ETRM: ENERGY TRADING & RISK MANAGEMENT

OPCHAIN-ETRM corresponds to a set of mathematical models oriented to support the decisions of the different agents involved in the trade of energy in: i) long-term market, ii) sport market and iii) secondary markets. It is based on a stochastic optimization model that includes equations to risk management. The main input of ETRM is the forecasting of spot prices, two models are available for this:

• E&G-SPOT: Techno-economic (like EDI, ERD, or similar models) that determines spot prices in an energy market economic To be used in medium/large term forecasting. It was presented in a past section.
•  GARCH-SPOT: Spot prices statistical model using S-ARIMAX-GARCH methodologies taking as references historical spot prices series. To be used in real-time or in short-term forecasting. 

The outcome of a risk analysis is the definition of pareto curves risk versus expected income/cost, based on which the decision-maker must define the risk position.

7.2 ENERGY SUPPLY CHAIN DESIGN

 OPCHAIN-E&G-SCD aims to determine optimal strategic decisions regarding investments in energy infrastructure. The investment projects provide the ability to increase capacity of the infrastructure already installed (expansions or modernizations of existing inhalations) or to create new capacity through new facilities. The "optimal" location of the infrastructure and the allocation of resources is related to decisions that minimize costs or maximize benefits, with the overall objective of maximizing social utility

OPCHAIN-E&G-SCD is a multiple-stage stochastic optimization model in which: i) in the first stage are fixed the decisions which must be taken “immediately”, and ii) in the remaining stages, future investment decisions are simulated (these decisions depends on the future of the random environment that affects the system).

This process includes the concept of real options that incorporate the economic value by delaying a decision. SCD includes the management of financial risk.

To make easy modeling and accelerating the process of solution, SCD uses the following concepts: the investment decisions are related to projects, which are composed of multiple alternatives, which can be developed in multiples stages.

7.3. MAINTENANCE OF ENERGY ASSETS

 Any of the previous dispatch models may be used to analyze the problem of preventive maintenance of energy assets, so OPCHAIN-E&G-MAN includes the set of equations that are required to optimize preventive maintenance of industrial plants; it is a two-stage stochastic optimization model in which, in the first stage, are fixed the maintenance decisions.

OPCHAIN-E&G-MAN optimize use of resources of the maintenance by minimizing the expected cost of the operation. The results are decisions on dates for carrying out maintenance (months, weeks, days). The useful life of the asset is consumed in multiple dimensions life such as time (days) and production (MWh).

7.4. ENERGY SYSTEMS OPTIMIZATION AND FINANCIAL ANALYSIS

OPCHAIN-E&G-FIN corresponds to a model that integrates energy planning models with the modeling of financial aspects of the agents, using the ALM approach (Assets & Liabilities Management).

The connection of the financial models with operations models gives, as minimum gain, the automatic generation of financial statements since they reduce the time and effort of the planners to make financial reports and the subsequent risk analysis.

The financial statements are: i) income statement, ii) cash flow and balance sheets (assets and liabilities) and equity.

 The main applications of OPCHAIN-E&G-ALM are:

•  The assessment of income and expenses of: i) investment projects, ii) facilities energy and iii) valuation of companies.
•  Integrated optimization of investments by global energy companies (maximization of the value of the company), having as reference the regulatory laws of the different regions/countries where operating or intended to operate.

8. OPCHAIN-E&G - FORECASTING METHODOLOGIES

The forecast models of OPCHAIN-E&G are required for shaping the future of the following variables: i) energy demand, ii) spot prices, iii) climatological variables and iv) other parameters that may be considered as random variables. These models should support the decision-making processes in: i) real-time/ short and (minutes, hours, days) ii) medium/long term (days, weeks, months,…) 

8.1. MATHEMATICAL METHODOLOGIES 

The methodologies available to deal with the characterization of demand are: i) Advanced Probabilistic Models (APM), ii) Machine Learning (ML), and iii) Artificial Neural Nets (ANN). Any of these methods (or mixes of them) may be the "best"; however, should be considered the integration between forecast models and decision-making optimization models based on Mathematical Programming (MP). In these cases, APM and ML are the simplest way to integrate since they are based on algebraic formulas that can be incorporated in MP optimization models. For the case of APM, the algebraic formulas can be incorporated into the models MP; in the case of ML, the Support Vector Machines (SVM) can be integrated into the MP. 

8.2. SHORT/MEDIUM/LONG TERM FORECASTING 

OPCHAIN-E&G approach is oriented to characterize the forecast using models APM and/or ML that can be formulated as MP optimization models. OPCHAIN-E&G forecast models are based on a simultaneous equations model (linear or non-linear) that is solved with an optimization technology; the objective function may be: i) minimization of the squares of errors (APM), ii) maximization of likelihood function and iii) and minimization of classification errors (ML). This approach facilitates to include restrictions on the parameters to bring coherence to the estimation process. 

More information:

• Stochastic Advanced Analytics Modeling - OPCHAIN-SAAM

https://www.dhirubhai.net/pulse/stochastic-advanced-analytics-modeling-opchain-saam-jesus-velasquez/

8.3. REAL-TIME/SHORT-TERM FORECASTING (STATE ESTIMATION)

 For real-time & short-term forecasting, OPCHAIN-E&G approach is based the concept of State Estimation (SE), specifically the mathematical methodology proposal Kalman (Kalman Filter, KF). 

 SE is supported on a conception of the stochastic processes where the random variable is differentiated of its measures, meaning that the modeler has historic measurements of the random variable and has not the “true” value of the variable; this is the fundamental difference with Classic Statistical approach.

 Therefore, all available observations are considered as random variables, generated by a metering system that is subject of precision errors; moreover, there might be more than one measure, obtained by multiples metering systems. Then two types of noise (errors) are considered in SE modeling:

• e(t), errors due to the modeling of the system, reflecting the uncertainty of knowledge of functions (equations and/or parameters) that determine the behavior of the system that is modeling
• q(t), measurement errors that come from the precision of the metering system.

The classic statistical models only considered a type error, m(t), which integrates modeling errors and measurement errors, m(t) = e(t) + q(t), whereas the SE modeling differs clearly the two types of errors.

KF defines a sequential process of estimation based on the Bayesian combination of a-priori information up to time t-1 with the information obtained at time t.

One of the problems facing in the SE modeling is the definition of the transition state function, Ft[x(t),u(t)], which may be based on: i) the physical process that occurs in the industrial system or ii) statistical parameters identification models. In general terms based on the prediction requires the problem of determining the "true" value of: i) state variables process (i.e precipitation, water inflows, demand, win speed, … ), ii) parameters of the physical models; and iii) parameters of statistical models. Then, SE advantage is possibility of representing the parameters dynamics with equations. This has resulted in creation Dual Kalman Filter () that simultaneously estimates: i) state variables and ii) parameters of the model.

The KF theory can be extended to consider the modeling of systems whose dynamic representation depends on the state system, or regime, in which the system is. The regime/state should be considered as an additional state variable which must be estimated "on line"; it may be associated with Markovian Process that includes a probability of transition between states in each period. The version of KF is called Multi-State Kalman Filter (MS-KF, Velasquez, 1978)

The following table presents the results of the use of the MS-KF in the basin of the Caroni River in Venezuela.

9. OPCHAIN-E&G - TECHNOLOGY PLATFORM

OPCHAIN-E&G is developed using OPTEX Optimization Expert System, that implies that it inherits all the characteristics of OPTEX. For more information: https://goo.gl/S2TV8T.

9.1. ALGORITHMS

 OPTEX separates completely the mathematical models of optimization technologies storing the models in normalized database, allows the user to interact with OPCHAIN-E&G models to update the equations according to the changes in its supply chain. OPCHAIN-E&G may include services to design, to implement, to support and to solve quickly optimization models in multiples optimization technologies like GAMS, IBM ILOG CPLEX OPTIMIZATION STUDIO, MOSEL, C, AMPL, GMPL … .

Next images present a GAMS and a C computer programs generated by OPTEX.

Next image presents a G-SDDP-GAMS programs generated by OPTEX.

9.2. INFORMATION SYSTEMS

 As a complement to other computer systems that require organizations, OPCHAIN-E&G architecture is open (the user knows the data-model) to facilitate their integration with other solutions and/or existing technological tools in organizations (ERP, TMS, WMS, GIS).

OPCHAIN-E&G and OPCHAIN-SGO integrate input-output data models around a common data-model, it permits to connect models automatically through the database.

The data base may be installed any SQL (Standard Query Language) database, including DBF, EXCEL and .csv text files.

OPCHAIN-E&G takes advantage of the facilities of visual environments found in personal computers, the ever-greater speed offered by the new family of servers and technological advances in mathematical optimization. The basic user interface (generate by OPTEX) provides an easy environment and the ability to integrate OPCHAIN-E&G with the requirements of each client.

The OPCHAIN-E&G utilities provide automatic generation of prototype for shell, data and dialog windows to capturing and maintaining the input data required by models.

 The results of the models are stored in SQL tables, generated automatically by OPTEX, the structured if know by the user. The scenario comparison reports allow users to view the results from multiple viewpoints, and net differences between scenarios.

OPCHAIN-E&G includes a tools system that allows easily detect the differences, and possibly the causes, of the actual decisions and the decisions proposed by the models; it includes a feasibility analyzer to detect problems in the models or in the input data.

Finally, the user can connect the results of the models to its Business Intelligence (BI) system. DW can help the user in this process.

9.3. CLIENT-SERVER ARCHITECTURE

OPCHAIN-E&G can operate in a single computer or in a Wide Area Network (WAN) using reference standards intranet/internet. complies with the coordination of tasks and communication between operational modules of OPCHAIN-E&G on different computers on the network. The optimization server facilitates the use of the licenses of the optimization technologies.

10. ABOUT DECISIONWARE

DecisionWaRe maintains permanent lines of research methodologies large scale optimization and modeling decision problems. Its "know how", through its professionals, has more than forty years working on solving real problems using mathematical programming methodologies.

 The following topics may be complementing the information about DW and the energy sector:

 1.    The course ADVANCED ANALYTICS & OPTIMIZATION APPLIED TO ELECTRIC SECTOR is related with all topics including in this document (https://goo.gl/n6mNbS)

 2.    The course OPTEX Optimization Expert System includes lessons related with large-scale optimization technologies and included a license of OPTEX: https://goo.gl/sAai9T

 3.    More information about:

• OPTEX Optimization Expert System: https://goo.gl/S2TV8T.
• GDDP (Generalized Stochastic Dual Dynamic Programming): https://goo.gl/xVjHCn 

 4.    DW has developed the OPCHAIN-OIL oriented to the oil sector. 

 5.    For more information on OPCHAIN the reader is invited to consult the following documents:

https://www.doanalytics.net/documents/DW-PPT-OPCHAIN-E&G-IND.pdf

https://www.doanalytics.net/documents/DW-PPT-OPCHAIN-ESO-Resumen.pdf

https://www.doanalytics.net/documents/DW-PPT-OPCHAIN-ESO-Full.pdf

 6.    The catalogue of OPCHAIN Mathematical Models presents the models made by DW using OPTEX. (https://goo.gl/3EP9j9)

 7.    Customers can access the OPCHAIN-E&G mathematical models in the following forms:

• On premise, in this case the software OPCHAIN-E&G is installed and runs on the servers indicated by the customer. The software can be sold or leased to the customer.
•  On demand, in this case the customer has access to OPCHAIN-E&G software on a server of DW in the cloud (cloud). The software may also be rented by periods (years, months, semesters, weeks). The databases of the customer may be in a customer server.
•  As a service, through a professional services contract in which DW assumes the responsibility to carry out the agreed work.
•  Software Factory, the customer delivers to DW the formulation of the mathematical model and test data and DW delivers to the customer a decision-making support system composed of: i) source of the mathematical model in the selected optimization technology (GAMS, IBM CPLEX, MOSSEL, AMPL, AIMMS,...), ii) data model of information system and iii) test run to probe the correct functioning of the model.

8. DecisionWare Experience (https://goo.gl/RkwdeY). It contains a brief description of the main projects that DW has done.

9. DW is interested in supporting R+D (Research and Development) in universities, facilitating the know-how accumulated in OPCHAIN-E&G for thesis or for research projects.

 10.    DW is looking for business partners, strategic partners and/or technological partners to expand its business around the world.

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