Fundamentals of Energy Systems: Definitions and Structure
1. System Definition and Differentiation
What is a system? A system is a set of distinguished and active elements (objects, operations, processes) with existing relations between those elements. It is separated from its surroundings, yet it is under the impact of the surroundings and has an impact on the surroundings. It is organized and intentionally arranged for the realization of a defined purpose within its surrounding environment.
System vs. Set: A system implies active elements, defined relations, and interaction with surroundings for a purpose, whereas a set is a collection of objects without these specific functional constraints.
2. Energy Systems and Surroundings
What is an energy system? An energy system is a sequence of energy processes isolated from, yet interacting with, its surroundings. It includes plants and devices realizing these processes, possessing determined properties and parameters, mutually related by streams of mass and energy. It is intentionally arranged to cover the demand for useful energy in the surroundings at a defined place and time, with required power, amount, and parameters.
Surrounding of an Energy System
The Surrounding is the set of all elements which do not belong to the system but have an impact on the system or are affected by the system due to their features or operation.
Interactions
Interactions involve the exchange of mass, energy, and information streams between the energy system and its surroundings.
3. Reasons for Creating Energy Systems and Examples
An energy system is primarily designed to supply energy services to end-users, aiming to minimize energy losses to a negligible level and ensure efficient energy use.
Examples of System Elements (Receivers)
- Isolated or complex devices, including energy receivers: boiler, pump, electric motor, pipeline, lamp, heater, wind turbine, PV panel, heat accumulator, battery…
Examples of Plants/Facilities
- Power Stations: Thermal PS (nuclear, coal-fired, CCGT units), wind farm, PV farm, heating plant (HOB), CHP plants, hydrogen generation plant, briquette plant.
- Internal Systems: Internal building heating system, district heating network (as a sub-system of a municipal heating system), factory internal power grid, ice water system.
- Multi-Carrier Systems: Combined heat and power plant (CHP plant), refinery.
- National Economy Systems: National (country-wide) power system, national gas system, hard coal sector, domestic system of liquid fuels.
- Future Systems: Generation and storage of “derivative fuels” (produced based on excess power generated at RES).
4. Impacts of Energy Systems on Surroundings
Positive Influence
- The surroundings development due to energy supply: quality of life, increase of goods and services value, culture and information development.
Negative Influence
Resulting from Energy Acquiring:
- Non-renewable primary energy (fossil fuels) deposits depleting.
- Change of properties and parameters of fossil fuels deposits during exploitation, and changes at the surroundings.
- Pressure reduction at deposits of natural gas and crude oil.
- Surface damages above deep mines; areas of open mines excluded from other use.
- Drop of the underground water level around open mines.
- Removal of salted waters; mining wastes disposal (mine heaps).
Resulting from Energy Conversion and Transmission:
- Emission of atmospheric pollutants from combustion products (dust, SO₂, NOₓ), negatively impacting human health.
- Emission of greenhouse gases (climate change).
- Thermal pollution of waters and land.
- Mechanical pollutants, electromagnetic pollution.
5. System Autonomy
A system is autonomous if, during its operation, it does not receive from the surroundings nor transmit to the surroundings:
- Any streams of mass (substances).
- Any streams of energy.
- Any information which could influence its action.
Technical System Autonomy
There are no fully autonomous systems in industry, as technical systems are intentionally created to supply required services. Some systems can be temporarily autonomous (e.g., a closed chemical reactor, thermally isolated from the surroundings).
The term “autonomous system” is also applied to systems with the ability to control themselves and react if there is a risk that control can be lost.
A system can be described as more-autonomous or less-autonomous. A more-autonomous system’s operation is less dependent on changes in the surroundings and is able to fulfill its target even if those changes are adverse.
Examples of more-autonomous systems: Photovoltaic system with a battery supplying luminous road signs, security monitoring systems.
6. System Coherence
A system is COHERENT if all elements of the system are mutually related such that any change at any element results in changes at all other elements of the system. Particularly, in a coherent system:
- All elements are active.
- There are no passive elements.
- All elements are interactive (mutually related).
Features of highly coherent systems: Strong interdependence between components.
Advantage or Disadvantage? High coherence can be an advantage for predictable, tightly controlled processes, but a disadvantage if a failure in one element cascades throughout the entire system.
Examples of highly coherent energy systems: Power plant based on the simple gas-cycle, power turbojet, chiller.
7. System Independence
A system is INDEPENDENT (not-coherent) if its active elements are not related to each other. A change at any element results in no change at any other element of the system.
Independence and Coherence are reverse properties. Energy systems are neither fully internally independent nor fully coherent.
Features of highly internally independent systems: Elements operate largely in isolation from each other’s state changes.
Advantage or Disadvantage? High internal independence increases robustness against localized failures but may reduce overall system optimization potential.
Examples of less coherent energy systems:
- Systems consisting of similar elements in parallel connection (e.g., thermal collector-kind systems, power plants consisting of power units).
- Systems with storage elements (accumulators).
- Systems which can be supplied with different energy carriers (e.g., different fuels: biomass-coal duo-units).
Elements that increase internal independence: Storage elements or parallel connections of similar functional units.
8. System Centralization
A system has the property of CENTRALIZATION if there is an element or sub-system that has a steering role in relation to other elements. The central element (sub-system) receives, converts, and transmits information to other elements. Relations between the central (“nerve-centre”) element and other elements or sub-systems are enforced.
Importance: Centralization is introduced to coordinate complex operations, ensure system stability, and manage overall performance based on centralized information.
Examples of energy systems with centralization:
- Small systems: Control room of a power unit, control room at a chemical plant (e.g., refinery, ammonia plant).
- Bigger systems: National power dispatch center, regional dispatch centers, dispatch center at the national gas transmission system.
9. System Availability
Availability: A ratio of time of operation or readiness to operation and a considered period of time (usually a year).
Time Availability
The fraction of the considered period during which the system is in an operational or standby-ready state, regardless of how much it actually produces. Formula: (uptime or ready time / total time in the period).
Production Availability
The ratio between the actual production and the maximum production that would be expected if the system had operated perfectly whenever the resource was available. It directly reflects how losses of operation reduce the delivered output.
10. Power Capacity Definitions
Reachable Power (Capacity)
The maximum available power of a generation unit or a set of units—what can be obtained under the most favorable conditions.
Available Power
The maximum power of a generation unit or a set of generation units under the present actual conditions.
Nominal Power (Capacity)
The capacity of a generation unit for which the generation effectiveness is the highest. It is the rated maximum output or throughput of a device or system under specified standard conditions, as declared by the manufacturer (e.g., MW for a plant, kWh for a battery).
11. System Stability and Adaptivity
System Stability
A system is stable if values of its characteristic parameters do not exceed accepted limits.
Examples of stable parameters: Power frequency (power systems), steam pressure at a boiler, room temperature (when the internal heating system is equipped with thermostats), a temperature at a cooling chamber (at a chiller).
Stabilizers are elements of stable systems that stabilize values of all parameters important for the proper operation and goal fulfillment of the system at the required level.
System Adaptivity
A system is adaptive if it can adjust its internal state or behavior in response to internal or external changes.
Full Adaptivity
Full adaptivity implies the system can maintain its primary function across the entire range of expected environmental and operational variations.
Examples of adaptive systems: Control systems using feedback loops, systems with integrated storage that buffer external fluctuations.
12. System Changes Over Time
Systems may undergo degressive (regressive) change or progressive development over time, affecting their coherence or independence.
a. Degressive Change (e.g., in boiler systems)
A degressive (regressive) change that reduces installed capacity and usually decreases system coherence (e.g., decommissioning old components without replacement).
b. Progressive Change (e.g., in district heating)
A progressive developmental change, which increases coherence/coupling between the district heating system and the national power system (e.g., integrating heat pumps connected to the grid).
c. Progressive Structural Change (e.g., in power systems)
A progressive structural change that increases decentralization and local independence of subsystems, while making the whole power system more complex (e.g., integrating many distributed energy resources).
13. Reasons for System Modernization or Construction
Modernization or new construction is driven by the need to adapt the system’s goal or performance criteria:
- Goal Change (Productivity/Parameter Increase): Demand increase for energy carriers or a change in required supply parameters (e.g., reliability) that existing systems cannot cover. Goal: Increase productivity (quantitative change) and improve parameters (qualitative change).
- Goal Change (Effectiveness Improvement): Demand reduction or a demand for energy carriers with changed parameters, resulting in existing system effectiveness deterioration. Goal: Improve effectiveness based on economic, technical, or other criteria.
- Competitiveness Recovery: Degradation of technical condition or competitor activity leading to lost competitiveness. Goal: Quality improvement and/or cost reduction to recover competitiveness.
- Effectiveness Improvement via New Solutions: Possibility to apply new technical or managerial solutions. Goal: Productivity and/or quality improvement to enhance competitiveness and economic effectiveness.
- Adaptation to External Requirements: New administrative requirements related to system operation (e.g., environmental limits). Goal: Adaptation of the system to external, formal requirements.
14. Methodology for System Analyses and Synthesis
Following the rules of the Methodology for Systems Analyses and Synthesis is essential for:
- Creation of new systems to cover new needs/demands.
- Modernization of existing systems to increase quality: improvement (quantitative and qualitative) to meet changed needs, improvement of energy effectiveness, environmental protection effectiveness, and economic effectiveness.
Creating and changing technical systems requires multi-branch knowledge (thermodynamics, electro-technics, heat transfer, fluid mechanics, combustion, power engineering, materials science, control, system science, micro-economy, etc.) and experience. Energy systems shaping is a creative process, but effective execution requires verified procedures, methods, and rules.
15. Phases of System Creation (Example: Coal Unit to Biomass CHP)
Example: Modernization of a coal-fired unit to a biomass CHP plant supplying district heating.
- Planning of the Undertaking: Define objectives (fuel switch, higher efficiency, CO₂ reduction), required electrical and heat output, and grid/district heating connection concept.
- Supporting Activities: Site and environmental studies, permits, grid and heat-network connection agreements, feasibility and financial analyses.
- Designing: Technical design of boilers, turbines, heat exchangers, fuel and flue-gas systems, and control systems, plus integration with existing networks.
- Realization Phase (Construction): Build or retrofit plant structures, install main equipment and balance-of-plant systems, and construct grid and heat-network connections.
- Commissioning: Perform pre-start checks, cold and hot commissioning, synchronization to the grid, and connection to the district heating network.
- Tests During Initial Operation: Test performance, efficiency, reliability, safety, and compliance with environmental and grid codes under various loads.
- Modifications During Operation: Implement design corrections, optimizations (e.g., control tuning, efficiency upgrades), and adaptations to changing regulations or demand.
16. Physical Models of Systems
A physical model is a simplified, physics-based representation of an energy/technological system that reproduces its key physical processes (flows of mass, energy, momentum) so we can study its behavior.
Purpose of Physical Models
- Understand and explain processes.
- Design or optimize devices.
- Predict performance.
- Support diagnostics and control.
- Verify/validate mathematical or simulation models.
Examples: Scaled physical model of a boiler or turbine flow path, test rig of a wind-turbine blade in a wind tunnel, model of a heat-exchanger or cooling tower, rotating-machine test stand for generators or pumps.
17. Mathematical Models of Technical Systems
A mathematical model of a technical system is an abstract description of that system using variables and equations that represent its key physical/technical behavior (e.g., energy, mass, flows, signals) so we can analyze and predict its performance.
Purpose of Mathematical Models
- Design and optimize systems.
- Simulate behavior in different conditions.
- Support control, diagnostics, and decision-making.
Example: Differential-equation model of a turbine, boiler, or PV inverter.
18. Kinds of Mathematical Models
Categories and Trade-offs
- Black-box vs. Element Models:
- Black-box: + Simple, needs few details; − Weak physical insight, poor extrapolation.
- Element models: + Good insight and design use; − More data and effort required.
- Optimization vs. Simulation:
- Optimization: + Gives “best” (e.g., least-cost) solution; − Strong assumptions, more complex.
- Simulation: + Flexible “what-if” analysis; − No guarantee of optimality.
- Deterministic vs. Probabilistic/Empirical:
- Deterministic: + Simple, clear; − Ignores randomness.
- Probabilistic/empirical: + Captures variability; − Needs a lot of data.
- Linear vs. Nonlinear:
- Linear: + Easy, fast, guaranteed solution; − Often oversimplified.
- Nonlinear: + More realistic; − Harder to solve, risk of many local optima.
- Steady-state vs. Dynamic:
- Steady-state: + Simple, good for long-term averages; − No transients modeled.
- Dynamic: + Captures time behaviour; − More equations and data required.
19. System Structure
A system structure is the network of relations between system elements, identified by their kind and role. It is the basic information needed to build a model that is not a black-box but is based on elements and their connections.
Need for Structure in Modeling
We need the structure when creating physical or element-based mathematical models (e.g., power grid, heating network), because equations and variables must follow how components are connected. It can be described graphically, by graphs, matrices, or alphanumeric descriptions. We do not always need it (e.g., for simple black-box models).
20. Model Comparison
Optimization vs. Simulation Model
Optimization: Model searches for the best solution (minimum cost, etc.) within constraints.
Simulation: Model calculates behavior of a given system/scenario without searching for the best.
Steady State vs. Dynamic Models
Steady-state: Variables do not change with time; time derivatives are zero.
Dynamic: Variables depend on time; transients and time evolution are modeled.
Deterministic, Probabilistic, and Statistical Models
Deterministic: No randomness; same input → same output.
Probabilistic: Inputs/parameters are random variables; results are distributions.
Statistical (Empirical): Based on observed data/time series; often uses regression, time functions, neural nets.
Continuous vs. Discrete Domains
Continuous domain: Variables can take any real value in an interval (e.g., power output 0–100 MW).
Discrete (or digital) domain: Variables take separated values (e.g., 0 or 1 for unit on/off, integer number of generators).
21. Empirical and Neuron Models
Empirical Models
- Advantages: Simple to build from data; often good accuracy inside the data range; few physical details needed.
- Disadvantages (Limitations in Use): Weak physical insight; poor extrapolation outside observed data; need enough good data; can break down if conditions change.
Neuron (Neural Network) Models
- Advantages: Can capture very complex nonlinear relations; good for large, noisy datasets.
- Disadvantages (Limitations in Use): “Black box” with low interpretability; need lots of data and tuning; risk of overfitting; unreliable outside training range.
22. Describing Thermodynamic Functions in Models
Thermodynamic functions are described by equations of state and property relations that link state variables (e.g., p, T, v, h, s) so they can be computed in the model. This is done via:
- Analytical formulas (e.g., ideal gas law, polynomials for h(T), c₁(T)).
- Tables with interpolation (steam tables, REFPROP, etc.).
- Empirical correlations fitted to experimental data.
26-29. National Power System Analysis (Example: Spain)
Description: Spain’s 50 Hz power system, operated by REE, has approximately 125 GW capacity with over 50% renewables (wind, solar PV, hydro).
Main Sub-systems and Features
- Generation: Wind/solar/hydro/nuclear/CCGT; renewables account for >56% of production.
- Transmission: 45,000 km of 400/220 kV lines, meshed, interconnected (France/Portugal).
- Distribution: MV/LV networks with smart metering and distributed PV.
- Operation: REE balances real-time, runs markets and ancillary services.
Expected Changes with Decarbonization
- New Elements: More RES/storage (batteries), smart grids, demand response mechanisms, prosumers.
- Elements Disappearing: Coal plants (phased out).
- Changed Elements: Grids reinforced and digitalized; operation focuses on flexibility and inverter control; markets value storage and flexibility.
30. National Gas System Sub-systems
A national gas system transports natural gas at high pressure from entry points to distribution networks, power stations, industries, and storage via interconnected pipelines and facilities.
Main Components and Functions
- Transmission Pipelines: Form the backbone, moving large gas volumes over long distances (e.g., 5,000 miles in the UK NTS) at high pressures while minimizing friction losses.
- Compressor Stations: Typically every 80-100 km with 20-60 turbines, they boost pressure (ratios around 1:1.4) and control flow direction to counteract drops and ensure steady supply.
- Valve and Pressure Reduction Stations: Isolate sections, reduce pressure for exits, odorize gas, and handle blowdowns for safety.
- Storage Facilities: Buffer supply/demand variations.
Operating Parameters
Systems operate at high pressures of 500-1,400 psi (34-94 bar), with gas speeds up to 25 mph (40 km/h). Flow capacities support billions of cubic meters annually, requiring real-time telemetry balancing supply/demand. Pipelines use steel construction for durability.
31. District Heating System Analysis
A district heating system centrally produces heat (via CHP, boilers, or renewables) and distributes hot water/steam through insulated pipes to buildings for heating and hot water.
Sub-systems and Features
- Production: CHP plants or heat pumps generate water at 70-130°C (lower in modern systems: 50-70°C).
- Pipes: Pre-insulated steel networks (primary/secondary) with pumps operating at 6-25 bar, aiming for <10% losses.
- Substations: Heat exchangers, valves, and meters per building regulate flow.
Typical Parameters
Supply temperature 70-130°C, return 40-70°C, resulting in a ΔT of 30-50°C.
Decarbonization Changes
- District Systems: Adopt low-temp 4th/5th generation systems using heat pumps, biomass, geothermal; phase out fossil fuels.
- Individual Systems: Shift towards electric heat pumps (COP 3-4) and general electrification.
32. Functionality of Smart Grids
Smart grids enable advanced functionality through digital communication and control:
- Remote Monitoring and Control: Remote maintenance of power stations and lines in transmission and distribution systems, minimizing losses and maximizing supply reliability.
- Data Transmission and Fault Detection: On-line transmission of measurement data and remote fault detection (including short circuit detection).
- Voltage Control: Regulation of voltage in distribution networks.
- RES Management: Remote management of the collection of excess energy generated in RES, including by prosumers.
- Demand Side Management (DSM/DSR): Remote switching on/off of power supply to consumers and individual receivers, including automation of DSM/DSR services, powering selected devices based on dynamic energy price changes (e.g., EV charging), supported by price forecasting.
- Dynamic Tariffs: Remote meter readings and the possibility of billing energy consumption according to constantly changing energy prices (dynamic tariffs).
I. System Reliability Calculation
Given: Reliability of element A ($R_A$) = 0.95; Reliability of element B ($R_B$) = 0.90. A system requires one A supplying one B.
a) Two A elements in parallel supplying a single B element
Reliability of parallel A ($R_{A,par}$): $1 – (1 – R_A)^2 = 1 – (1 – 0.95)^2 = 1 – 0.0025 = 0.9975$.
System reliability ($R_{sys}$): $R_{A,par} imes R_B = 0.9975 imes 0.90 = 0.89775$ (or 89.775%).
b) Two A elements in parallel and two B elements in parallel, connected in series
Reliability of parallel A ($R_{A,par}$): $0.9975$ (as above).
Reliability of parallel B ($R_{B,par}$): $1 – (1 – R_B)^2 = 1 – (1 – 0.90)^2 = 1 – 0.01 = 0.99$.
System reliability ($R_{sys}$): $R_{A,par} imes R_{B,par} = 0.9975 imes 0.99 = 0.987525$ (or 98.7525%).
c) Two independent A-B pairs in parallel
Reliability of one A-B pair ($R_{pair}$): $R_A imes R_B = 0.95 imes 0.90 = 0.855$.
System reliability ($R_{sys}$): $1 – (1 – R_{pair})^2 = 1 – (1 – 0.855)^2 = 1 – (0.145)^2 = 1 – 0.021025 = 0.978975$ (or 97.8975%).
II. Pressure Distribution in District Heating Pipelines
Consider pipelines connecting two heat sources S1 and S2, with a Pump Station (PS) located between them. Pressure profiles depend on which pumps are active and the flow direction.
Case a) Heat source S1 operating, pump at the supplying pipeline at PS operating
Flow direction: Supply: S1 → PS → S2 | Return: S2 → PS → S1 (Assuming S1 is the primary driver and PS pump boosts flow towards S2).
Supply pipeline pressure:
- Pressure at S1 is relatively low (due to pressure drop through S1’s heat exchanger).
- It decreases linearly from S1 to PS due to friction.
- At PS, the pump provides a significant pressure boost (jump).
- After PS, pressure decreases linearly again until S2.
Return pipeline pressure:
- Pressure at S2 is nearly equal to the supply pressure at S2 (S2 is off, acting as a pass-through).
- It decreases linearly from S2 to PS and continues decreasing linearly from PS to S1.
- At S1, return pressure is higher than supply pressure to drive flow through S1’s heat exchanger.
Typical profile: Supply: Shows a dip before PS, a jump at PS, and then a decrease. Return: Monotonically decreasing from S2 to S1.
Case b) Heat source S1 and S2 operating with their own pump stations, PS is not operating
Assumption: Both sources supply heat to a common load near PS, so flow converges at PS on supply and diverges from PS on return.
Flow direction: Supply: S1 → PS and S2 → PS (converging) | Return: PS → S1 and PS → S2 (diverging)
Supply pipeline pressure:
- Pressure is highest at S1 and S2 (boosted by local pumps).
- Pressure decreases linearly toward PS due to friction, reaching a minimum at PS.
Return pipeline pressure:
- Pressure is highest at PS (from the load return).
- Pressure decreases linearly toward both S1 and S2.
- At each source, return pressure is lower than supply pressure to allow flow through the heat exchangers.
Typical profile: Supply: Two sloping lines from each source down to PS. Return: Two sloping lines from PS down to each source.
Case c) Heat source S2 operating, pump at the returning pipeline at PS operating
Flow direction: Supply: S2 → PS → S1 | Return: S1 → PS → S2 (Assuming S2 is the primary driver and PS pump boosts flow on the return line towards S1).
Supply pipeline pressure:
- Pressure at S2 is relatively low (due to pressure drop through S2’s heat exchanger).
- It decreases linearly from S2 to PS and continues decreasing linearly from PS to S1 (no pump on supply).
Return pipeline pressure:
- Pressure at S1 is nearly equal to the supply pressure at S1 (S1 is off, acting as a pass-through).
- It decreases linearly from S1 to PS due to friction.
- At PS, the pump on the return pipeline provides a significant pressure boost (jump).
- After PS, pressure decreases linearly until S2.
Typical profile: Supply: Monotonically decreasing from S2 to S1. Return: Shows a dip before PS, a jump at PS, and then a decrease towards S2.