Data Analytics (ME-803 (A)) - Unit 3 Short Notes

3.0 Analytical Techniques for Energy Data

3.1 Mass and Energy Balances

Core Principle: Application of conservation laws (mass, energy) to quantify flows and transformations in energy systems. Essential for audit calculations.

3.1.1 Mixing Problems (Percentage Solids, Flow Rates)

• Concept: Steady-state material balance where input mass flow rates equal output (no accumulation).

• General Equation:

$$\sum \text{Input} = \sum \text{Output}$$

• For two streams mixed:

$$F_1 \cdot x_1 + F_2 \cdot x_2 = F_3 \cdot x_3$$

where \(F\) = flow rate (kg/s), \(x\) = mass fraction of solids.

• Example (Past Paper):

  Given: Stream 1: 10% solids at \(F_1 = 5\ \mathrm{kg/s}\), Stream 2: 25% solids, Output: 20% solids. Find \(F_2\).

  Solution:

$$5 \times 0.10 + F_2 \times 0.25 = (5 + F_2) \times 0.20$$

$$0.5 + 0.25F_2 = 1 + 0.20F_2$$

$$0.05F_2 = 0.5 \implies F_2 = 10\ \mathrm{kg/s}$$

Output \(F_3 = 15\ \mathrm{kg/s}\).

[!TIP] Always verify units and assume steady-state (no accumulation) unless specified.

3.1.2 Heat Transfer Calculations (Cooling Water Requirements)

• Concept: Energy balance for cooling process: heat lost by hot stream = heat gained by cooling water.

• Formula:

$$Q = m_{\text{shell}} \cdot C_{p,\text{shell}} \cdot \Delta T_{\text{shell}} = m_{\text{water}} \cdot C_{p,\text{water}} \cdot \Delta T_{\text{water}}$$

• Rearranged for water mass:

$$m_{\text{water}} = \frac{m_{\text{shell}} \cdot C_{p,\text{shell}} \cdot \Delta T_{\text{shell}}}{C_{p,\text{water}} \cdot \Delta T_{\text{water}}}$$

• Example (Past Paper):

  Furnace shell: \(m = 2\ \mathrm{tonnes} = 2000\ \mathrm{kg}\), \(C_p = 0.2\ \mathrm{kcal/(kg\,^\circ C)}\), \(\Delta T = 90 - 55 = 35\,^\circ\mathrm{C}\).

  Water: \(C_p = 1\ \mathrm{kcal/(kg\,^\circ C)}\), \(\Delta T = 5\,^\circ\mathrm{C}\).

$$m_{\text{water}} = \frac{2000 \times 0.2 \times 35}{1 \times 5} = \frac{14000}{5} = 2800\ \mathrm{kg}$$

[!TIP] Use consistent units (kcal, kg, °C). Neglect heat loss unless given.

3.2 Sankey Diagrams: Concept and Application

• Definition: Flow diagram where width of arrows is proportional to the quantity (energy, mass, cost) of the flow.

• Purpose: Visualize energy/material losses, identify major consumption areas, and prioritize conservation measures.

• Key Features:

  • Arrows represent inputs, outputs, losses.

  • Direction shows flow path.

  • Scale must be consistent.

• Application Example (Boiler):

  Input: Chemical energy in fuel → Outputs: Steam energy, flue gas loss, radiation loss, incomplete combustion loss.

  Width of steam arrow indicates boiler efficiency.

• Construction Steps:

  1. Identify all inputs and outputs.

  2. Quantify each flow (e.g., in kW or %).

  3. Draw arrows with widths proportional to quantities.

  4. Label each arrow with value and percentage.

• Benefit: Quickly communicates where energy is being wasted.

[!TIP] Sankey diagrams are qualitative but based on quantitative data; always include actual values.

3.3 CUSUM Analysis: Steps and Applications

• Definition: Cumulative Sum (CUSUM) is a sequential analysis technique to detect small shifts in the mean of a process variable (e.g., energy consumption).

• Steps:

  1. Collect Data: Obtain periodic measurements (e.g., daily energy use).

  2. Set Target: Define expected/target value (\(\mu_0\)).

  3. Calculate Deviations: \(d_i = x_i - \mu_0\) for each observation \(x_i\).

  4. Compute Cumulative Sum: \(C_i = C_{i-1} + d_i\) (with \(C_0 = 0\)).

  5. Plot CUSUM Chart: \(C_i\) vs. time/sequence.

  6. Interpret: A sustained trend away from zero indicates a shift in performance.

• Applications in Energy Management:

  • Monitor monthly energy consumption against baseline.

  • Detect equipment degradation or operational changes.

  • Validate effectiveness of energy-saving measures.

• Advantage: Sensitive to small, persistent changes that control charts might miss.

[!TIP] CUSUM is not for large one-time spikes; it detects gradual drifts. Use alongside control charts.

3.4 Sensitivity and Risk Analysis

• Sensitivity Analysis:

  • Purpose: Determine how output (e.g., NPV, savings) changes with variations in input parameters (e.g., energy cost, equipment life).

  • Method: Vary one parameter at a time (OAT) while holding others constant. Plot "tornado diagram" to rank parameters by impact.

  • Example: Assess impact of 10% increase in electricity price on project payback.

• Risk Analysis:

  • Purpose: Quantify uncertainty and probability of adverse outcomes.

  • Methods:

    • Scenario Analysis: Best-case, worst-case, most-likely scenarios.

    • Monte Carlo Simulation: Randomly sample input distributions (e.g., uniform, normal) to generate probability distribution of outputs.

  • Output: Probability of achieving target savings, expected value, confidence intervals.

• Integration: Sensitivity identifies critical variables; risk analysis models their uncertainty.

[!TIP] In exams, distinguish: Sensitivity = "what-if" deterministic changes; Risk = probabilistic uncertainty.

3.5 Monitoring, Targeting and Reporting (MTR): Rationale and Benefits

• Definition: Structured process for continuous energy performance improvement.

• Components:

  • Monitoring: Regular collection of energy data (metering, sub-metering).

  • Targeting: Setting realistic, achievable energy reduction goals (e.g., % improvement/year).

  • Reporting: Communicating performance to management/teams (dashboards, monthly reports).

• Rationale:

  • Provides feedback loop for energy management.

  • Creates accountability and awareness.

  • Supports ISO 50001 Energy Management Systems.

• Benefits:

  • Early detection of excess consumption.

  • Quantifies savings from projects.

  • Drives behavioral and operational changes.

  • Facilitates benchmarking against targets.

• Implementation Steps:

  1. Establish baseline energy consumption.

  2. Set SMART targets.

  3. Install metering infrastructure.

  4. Collect and analyze data regularly.

  5. Report deviations and corrective actions.

[!TIP] MTR is cyclical: Monitor → Compare to Target → Report → Act → Re-monitor.

3.6 Energy Benchmarking, Energy Cost, and Energy Performance

• Energy Benchmarking:

  • Definition: Comparing energy performance against peers, industry averages, or best practices.

  • Metrics: Specific Energy Consumption (SEC) = Energy / Output (e.g., kWh/tonne).

  • Use: Identify performance gaps, set improvement targets.

• Energy Cost:

  • Definition: Total expenditure on energy (electricity, fuel) per unit time or per unit production.

  • Calculation:

$$\text{Energy Cost} = \sum (\text{Energy Type}_i \times \text{Unit Cost}_i)$$

• Importance: Key driver for conservation projects.

• Energy Performance:

  • Definition: Measure of efficiency in converting energy inputs to useful outputs.

  • Indicators:

    • Energy Intensity (energy per unit output).

    • Efficiency percentages (e.g., motor efficiency, boiler efficiency).

  • Relation: Better performance → lower energy cost for same output.

[!TIP] Benchmarking requires normalized data (e.g., per production unit, per degree-day) for fair comparison.

3.7 Data and Information Analysis for Energy Management

• Purpose: Transform raw energy data into actionable insights for decision-making.

• Types of Analysis:

  • Descriptive: Summarize historical data (e.g., monthly consumption trends).

  • Diagnostic: Identify causes of anomalies (e.g., why did consumption spike?).

  • Predictive: Forecast future consumption (e.g., time series models).

  • Prescriptive: Recommend actions (e.g., optimization models).

• Common Techniques:

  • Time Series Analysis: Decompose into trend, seasonality, residuals.

  • Regression Analysis: Relate energy use to driving factors (production volume, temperature).

  • Statistical Process Control: Detect out-of-control conditions.

  • Data Visualization: Dashboards, heat maps, histograms.

• Data Sources: Utility bills, sub-meters, SCADA, BMS, weather data.

• Outcome: Prioritize projects, verify savings, improve operations.

[!TIP] Always clean data (handle missing values, outliers) before analysis. Use EMIS for automation.

3.8 Maximum Demand: Concept and Control Methods

• Concept:

  • Maximum Demand (MD): Highest average power (kVA or kW) drawn over a specified interval (e.g., 30 min) during a billing period.

  • Significance: Often billed separately; high MD increases capacity charges.

• Control Methods:

  1. Load Shifting: Move non-essential loads to off-peak times (e.g., run pumps at night).

  2. Demand Response: Temporarily reduce load during utility peak periods (incentive-based).

  3. Power Factor Correction: Reduces apparent power (kVA) for same real power (kW) → lowers MD in kVA.

  4. Efficient Equipment: Replace high-startup-current motors with efficient ones.

  5. Soft Starters/VFDs: Reduce inrush current during motor startup.

  6. Scheduling: Coordinate startup of multiple large loads.

• Calculation Example (Past Paper Context):

  If contract demand = 5000 kVA, minimum billable = 75% = 3750 kVA.

  Actual MD = 3850 kVA → billed at 3850 kVA (if above minimum).

  Savings from PF correction: reduce kVA demand → lower demand charges.

[!TIP] MD is usually measured in kVA (apparent power), not kW. Correction via capacitors reduces kVA.

3.9 Power Factor: Effects of Low Power Factor and Correction

• Definition:

$$\text{Power Factor (PF)} = \frac{\text{Real Power (P, kW)}}{\text{Apparent Power (S, kVA)}} = \cos \phi$$

where \(\phi\) = phase angle between voltage and current.

• Effects of Low PF (< 0.9 typical):

  • Increased current for same real power → higher \(I^2R\) losses in conductors.

  • Reduced system capacity (transformers, cables must carry extra current).

  • Voltage drop → poor voltage regulation.

  • Higher demand charges (if billed in kVA).

  • Penalties from utilities.

• Correction Methods:

  1. Capacitor Banks: Supply leading VARs to cancel lagging VARs from inductive loads (motors).

     KVAR Required:

$$\text{KVAR} = P \left( \tan \phi_1 - \tan \phi_2 \right)$$

 where \(P\) = real power (kW), \(\phi_1 = \arccos(\text{PF}_1)\), \(\phi_2 = \arccos(\text{PF}_2)\).

2. Synchronous Condensers: Over-excited synchronous motors act as capacitors.

3. Active PF Correction: Using power electronics (e.g., STATCOM).

• Example (Past Paper):

  Improve PF from 0.95 to 1.0 for \(P = 3850 \times 0.95 = 3657.5\ \mathrm{kW}\) (assuming MD at 0.95 PF).

  \(\phi_1 = \arccos(0.95) \approx 18.19^\circ\), \(\tan \phi_1 \approx 0.329\)

  \(\phi_2 = \arccos(1) = 0^\circ\), \(\tan \phi_2 = 0\)

  \(\text{KVAR} = 3657.5 \times (0.329 - 0) \approx 1203\ \mathrm{kVAR}\).

[!TIP] PF correction reduces kVA demand, thus lowering MD charges if billed in kVA. Always check utility tariff structure.