Resource Planning with Uncertainty for NorthWestern Energy Selection of Optimal Resource Plan for 213 Resource Procurement Plan August 28, 213 Gary Dorris, Ph.D. Ascend Analytics, LLC gdorris@ascendanalytics.com 33.415.311 www.ascendanalytics.com
Outline Resource Planning Paradigms and Choices Resource Selection Best in Breed Resource Selection Best in Show Resource Selection Risk Reduction Value (RRV) for Renewables 2
Activity Plan 3
Planning Steps 1. Develop Model Inputs (August) 1. Market prices 2. Load forecasts 3. Resource options 2. Validate Model (August) 1. Consistency of model 1. Historic values 2. Expectations 3. Resource Selection (September) 1. Deterministic Models 2. Stochastic Models 4. Automatic Resource Selection (October) 1. Deterministic Models 2. Stochastic Models 5. Project Finalization (November) 1. Full Resource Plan(s) 2. Technical Write-up 4
Resource Planning Paradigms and Choices 5
Planning in Transition Portfolio perspective Fuel diversity Reliability and intermittent resources Uncertainty in fuel, emissions, and power Use of market for fuel and power Analyze generation resource options with respect to market dynamics Capture new dynamics Weather o Load o Wind generation Market conditions o Forward markets for fuel and power o Spot price dynamics Resource adequacy Reliable service at cost effective rates Market interactions 6
Best-In-Breed Objective: Find the cheapest capacity expansion plan that satisfies the constraints Cheapest is often defined as the net present value of the revenue requirements Constraints : Renewables, RECs, limits on market sales and purchases, Result Optimal capacity expansion of generation resources and conservation options to minimize revenue requirements subject constraints. Breed is a dog show analogy referring to the best expansion plan from a deterministic run (single forecast) of simulated weather, load, and prices. ICU Wind Aero CT CC 7
Components of Uncertainty: Integrating Physical and Financial Financial Fuel Prices Gas (Monthly, Daily) Coal Emission Allowances o CO2, SO2, Nox RECs Electric Prices Supply Stack Transmission Hydro Levels Load Fuel and Emission Prices Interest Rates Construction Costs Physical Load Weather Growth o Customer Mix o Energy Efficiency Wind Weather Load Hydro Weather Unit Contingencies Construction risk Performance risk Transmission Unified simulation framework reflecting joint financial and physical uncertainty Rigorous validation Capture of critical covariate relationships Frequency and magnitude of price spikes 8
Tools of Supply Planning Model Attributes Uncertainty Factor Production Cost Models Integrated Risk Based Planning Models Load Growth Fixed Simulated Uncertainty Load Patterns Typical profile Uncertainty in Profile and Usage Pattern Conservation Fixed Weather Based Demand Response Weather Fixed Weather Based Demand Response Hydro Fixed Simulated Annual Daily Operations Wind Fixed Simulated with Weather Env. Hg, CO2, SO2, NOx Fixed Simulated Based on Uncertainty in Costs Gas Prices Fixed Simulated Monthly and Daily Prices Transmission Fixed Input/Output Variable Flow Contingent Factors Financial Instruments Modeled as Fixed Assets Simulated Values Reserve Margins Fixed, Small Effect Simulated and Key Driver of Prices Integration of Elements Cost Based Linked Equations and Casual Effects Capital Cost Fixed Simulated Interest Rates and Capital 9
Best-In-Breed & Best-In-Show Simulation 1 Simulation 2 Simulation 3 Simulation 4 Simulation 5 Best-In-Breed Simulation engine creates a number of possible simulated scenarios and finds the optimal plan for each iteration The Best-In-Breed plans have the bestachieved value of the objective function under the specified inputs for a particular simulated scenario Simulations Capacity planning finds the optimal expansion plan using dynamic programming in a simulation-based framework Optimal plan defined by: Portfolio of generation assets Constraints on portfolio Objective function Best-In-Breed 1 Best-In-Breed 2 Best-In-Breed 3 Best-In-Breed 4 Best-In-Breed 5 Best-In-Show PowerSimm subjects each of the Best-in-Breed plans to all the scenarios and calculates the value of the objective function in each of those scenarios Best-in-Show is the plan with the lowest mean of the objective function across all the scenarios This plan performed the best across a variety of scenarios 1
Total Ave Revenue Requirements ($Millions) Best In Show Total Ave Rev Requirements vs Cost at Risk $8 $7 $7 $6 $6 $5 $ $4 $4 $3 Case Rank 5 Case Rank 3 Case Rank 1 Case Rank 2 Case Rank 4 How do environment controls on coal impact risks? What resources are more highly valued with growing percentage of renewables? How do I tie Best in Breed back to specific scenarios? Cost @ Risk ($Millions) PowerSimm Result 11
Definition of Common Planning Risk Metrics Cost at Risk (CaR) for Rev Req = CaR = 95 th percent costs mean costs How do you decide where to be on the frontier? Avista IRP 211 12
Total Cost Portfolio Selection 13
Forecasted monthly forward prices During delivery to simulations Integrating Physical and Financial Uncertainty Dispatch Detail Hourly chronological dispatch Forced Outages modeled as random events Seasonal and peak period generating characteristics Optimal Resource Selection Unified simulation framework reflecting joint financial and physical uncertainty o o o o Rigorous validation Framework to assess Flexible Resource Adequacy (FRA) Capture of critical covariate relationships Frequency and magnitude of price spikes 14
$/MBtu Scenario Analysis 14. 12. 1. 8. 6. 4. 2.. Year 25 27 Common Scenarios: High, Med, Low Gas Price Scenario Analysis Year 29 211 213 215 217 219 221 223 225 227 229 Scenario 1=$4 Scenario 2= $5 Scenario 3=$6 Scenario 4=$7 Which forecast are the best? Scenarios with prices monotonically increasing over time. Are these prices consistent with observed patterns? What s the probability weight of being in scenario 1 or 4? Why is the max prix in 225 less than historical prices observed 25 years prior? Can we capture probabilistically future states and a more market consistent pattern of gas prices? 15
Validation Tests Simulation Module Statistical Test Purpose Power Spot Daily 5th, mean, 95th Simulation calibration to observed data Autocorrelation within month Time series pattern of movement in prices Correlation between on/off peak Time series pattern of movement in prices Daily option quotes at a strike price for each month Measures fit to market data Spark spread to price fit Consistency of gas to electric price relationship Visual inspection of continuous price paths over a year Heuristic interference of model performance Spot Basis Gas and Elect 5th, mean, 95th by month Simulation calibration to observed data Temp and gas basis structural relationship Maintain relationship where gas price mean and variance are a function of temperature Load and power basis structural relationship Maintain relationship where power price mean and variance are a function of load and gas prices Autocorrelation Time series pattern of movement in prices Spot Hourly 5th, mean, 95th by month Simulation calibration to observed data Autocorrelation Time series pattern of movement in prices Correlation to load Comparison of relationship of hourly simulated prices and load to actual values Spot Basis Hourly 5th, mean, 95th by month Simulation calibration to observed data Autocorrelation Time series pattern of movement in prices 5th, mean, 95th by hour Simulation calibration to observed data 16
Validation Tests (continued) Simulation Module Statistical Test Purpose Weather 5th, mean, 95th actual vs. simulated Simulation calibration to observed data Autocorrelation Time series pattern of weather Correlation between stations Spatial correlation of weather Load 5th, mean, 95 th by monthly summary Simulation calibration to observed data Autocorrelation Time series pattern of load 5th, mean, 95th by month Simulation backtest to observed data 5th, mean, 95th by hour Simulation backtest to observed data equation fit, parameter estimates, p- values, F-test, DW, CP, White, correlation matrix of parameters and residuals Measures of statistical fit, parameter robustness, and assessment of model performance Forward price 5th, mean, 95th Simulation calibration to observed data Volatility consistency Simulated output realizes vols consistent with input values and/or constraints Autocorrelation Time series pattern of movement in prices Correlation between commodities Measures coincident movement of commodities and neighboring months consistent with input correlations and pos definate transformed correlation values Monthly option quotes at multiple strikes prices Measures fit to market data Clean spark spread at 5th, mean, 95th Brown spark spread at 5th, mean, 95th Measures consistency of forward electric and gas price simulations Measures consistency of forward electric and gas price simulations 17
Forward Price Validation History and Simulations: Natural Gas Simulated forward market prices for Henry Hub Large price spikes followed by mean reversion 2 to five year cycle Large volatility in prices followed by quiescent periods Forward Price Validation- Price Paths for Final Evolved Forward Curve Simulation Historic prompt month prices for Henry Hub Large price spikes followed by mean reversion 2 to five year cycle Large volatility in prices followed by relative quiescent periods 18
Fuel Price Simulations AECO Gas PRB Coal 19
Weather Hydro Flows Load Price Simulations Hydro Flows Intermittent Generation Gas Weather Load Electric Price 2
Preserving Relationship and Dependency Weather-Load Validation Simulated vs. Historical Maintaining Correlations Incorporating weather into the load model maintains integrity in the weather load relationship Simulations nicely smooth out bumps of historical weather record Simulations provide for new extreme values to exceed historic record Inter-Commodity Price Relationship External Market Validating Relationship Validate by capturing the weather load relationship in the historical period and simulated backcast The structural state space modeling captures the changes in shape with changes in load 21
Load Evaluating Difference 5 th, Mean, 95 th Load Simulation Validation Results Demonstrate a robust model to simulate future load Capture uncertainty in load growth with extreme weather scenarios validated prior to a load simulation Validated monthly load values Validated hourly load values for hours 1-24 Steeper load change at 95 th Flatter load pattern at 5th Load Simulation Modeling Developed through a structural state-space model integrating weather as a dependant variable Weather effects modeled through a fourth order polynomial that reflects load/temperature relationships Calendar structure in terms of month, weekday and hour Autocorrelation effects where extreme load conditions are measured 22
Long-run Market Price Forecasting 23
Power 22 Years 4-3 Overview of Modeling Market Price Market Data Inputs Electric Spot and Forward Planned Capacity Additions Fuel Spot and Forward Fundamental Analysis Production Cost Analysis Fuel Prices Supply Stack Characteristics NO x, SO 2, CO 2 Load Intertie Transfer New Unit Entry Price Volatility Relationship between reserve margin and price volatility Reserve margin forecast as a function of load growth, new unit entry, and transmission interties following real business cycles of new unit entry investment Long-Run Equilibrium Adjust reserve margin for new unit entry to produce normal returns over twenty years Analytical Parameters for Spot Electricity Prices Forecast Parameters Calibrated for Historical Hedge Instruments Market Data and Forecast Option Prices Forward Prices Spot Prices Monte Carlo Simulation 3 years hourly Dispatch Unit Spot Market Net Revenues Financial Model Heat rate curve Capacity & EFOR Fuel mix Emissions Asset Characteristics VO&M Start costs Ramp rate Min. run & down time Total Revenue Stream 24
Automatic Resource Selection 1. Dynamic Optimization for Resource Selection 2. Structural State Space Modeling to Capture Uncertainty 3. Hedge Instrument Payoffs 4. Ancillary Services 25
Deterministic Optimization Choose values for decision variables to minimize an objective function (e.g., cost), subject to constraints s.t. The values of objective function f and constraints g and h are calculated for decision variables u(resource mix). One realization (i.e., predicted future) 26
Solved using dynamic programming Example: portfolio can build CC, wind, or both Load increases in t = 3 RPS takes force in t = 5 State space including infeasible states shown here t = 1 t = 2 t = 3 Represents a portfolio configuration ( state ) End t = 4 t = 5 Nothing built Gas, no wind Wind, no gas Both wind and gas 27
Solved using dynamic programming Identify and remove infeasible states Infeasible because of need to meet increased load starting from t = 3 End t = 1 t = 2 t = 3 t = 4 t = 5 Nothing built Gas, no wind Wind, no gas Both wind and gas Infeasible because of need to meet RPS starting from t = 5 28
Enumerate costs for states Variable costs shown in green CC makes a profit Wind (contract with independent generator) makes a loss Variable costs sums linearly t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Negative cost indicates operating profit for CC Gas, no wind -1-1 -1 Wind contract makes an operating loss 1 1 1 1 Wind, no gas Both wind and gas Wind + CC combination operating economics sum linearly 29
Enumerate fixed costs for transitions between states Fixed costs sum linearly Building a CC is 2 Wind contract has up-front cost of Allowable transition (e.g., build an asset) feasible action Nothing built Gas, no wind t = 1 2 t = 2 t = 3 t = 4-1 -1-1 t = 5 Transition fixed costs from only a few states shown for diagram simplicity End Wind, no gas 2 1 1 1 1 Both wind and gas 2 3
Backward pass Start from next-to-last time period (t = 4) Begin by enumerating feasible action set for each state t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Gas, no wind Two feasible actions from this state: build CC, or do not build CC. -1-1 -1 One feasible action from this state: build wind. (Need to meet RPS, and cannot un-build CC.) Wind, no gas 1 1 1 2 1 Both wind and gas Only one feasible action from this state: do nothing. (Cannot un-build an asset.)
Backward pass Calculate cost associated with each feasible action Quantity includes both fixed cost of this action, and future costs t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Gas, no wind Wind, no gas Both wind and gas -1-1 -1 1 1 1 1 1 2 32
Backward pass Select lowest-cost action from each state in t = 4 Retain lowest cost action, and discard suboptimal actions t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built -1-1 -1 Gas, no wind 1 Wind, no gas 1 1 1 1 Both wind and gas 33
Backward pass The reverse partial objective function sum is calculated for each of the states in the t = 4 time period. Nothing built Gas, no wind t = 1 t = 2 t = 3 t = 4 t = 5 End The reverse partial cumulative sum at a state in time represents the cumulative cost going forward from that state in time, for optimal decisions going forward from that state in time. -1-1 Wind, no gas 1 1 3 Both wind and gas 1 34
Backward pass The process is repeated, starting from the previous time period. t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Gas, no wind Wind, no gas Both wind and gas -1-1 1 1 2 3 1 35
Backward pass The process is repeated, starting from the previous time period. t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Gas, no wind Wind, no gas Both wind and gas -1-1 1 1 1 3 3 1 36
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built If there is a tie, either branch can be taken; one branch is shown for visual clarity. -1-1 Gas, no wind Wind, no gas Both wind and gas 1 4 1 37
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built 2 Gas, no wind Wind, no gas Both wind and gas -1-1 1 4 2 2 1 38
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built 1 Gas, no wind Wind, no gas Both wind and gas -1 1-1 2 4 3 4 1 39
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built 1 Gas, no wind -1-1 Wind, no gas Both wind and gas 1 3 1 4
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built 1-2 Gas, no wind Wind, no gas Both wind and gas 2 41
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built 2 1 Gas, no wind -2 Wind, no gas 2 Both wind and gas 2 42
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built 1 Gas, no wind 5 Wind, no gas 4 Both wind and gas 43
Backward pass All time periods are iterated through reverse sequentially (backward in time). t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Gas, no wind Wind, no gas Both wind and gas 44
Backward pass completed t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Gas, no wind Wind, no gas Both wind and gas 45
Forward pass After the backward pass is completed, the optimal path is found by iterating forward through time from the starting state. Starting state t = 1 t = 2 t = 3 t = 4 t = 5 End Nothing built Build CC Gas, no wind Do nothing Do nothing Build wind Wind, no gas Both wind and gas u* The collection of actions is the optimal asset development plan. 46
Relationship Between Deterministic and Stochastic Problems Stochastic problem consists of several parallel deterministic problems Different realizations will have different objective and constraint function values for a given plan u* u* may be non-optimal or infeasible for realizations other than the one optimized for We want to find a plan u** that is good across the whole space of plausible futures Compromise plan that works well in all realizations 47
Mathematical Formulation s.t. Upper case stochastic Lower case deterministic Arithmetic average used for stochastic objective function Some constraints need to satisfied for all realizations, e.g. physical characteristics of asset need to be respected Certain other constraints need only be satisfied % or 95% of the time, e.g., reserve margin 48
Constraints Christy Dunn produced a word document illustrating constraints in deterministic vs. stochastic case For constraints that must be satisfied in all simreps, determining feasibility is simple Major difference between deterministic and stochastic cases is that stochastic case may want to allow a state to violate a constraint in some simreps but still be feasible in the overall stochastic problem Grouped approach each state has an error bar, and each bound has an error bar, and to determine feasibility we can choose which comparisons to make Simrep-by-simrep counting approach evaluate feasibility for each simrep as in deterministic case, and then evaluate feasibility of state in stochastic space by counting e.g., 95% feasible threshhold means that < 5 out of 1 simreps are infeasible 49
Constraints Consider the constraint of the form where Q is a quantity calculated within the optimization and Q max is a bound. Q is the value of some constrained quantity that depends upon the simrep simulated parameters and planning decisions (e.g., total reserve available), and Q max is the bound that may depend on some simrep simulated values (e.g., if the reserve margin is a proportion of load, which differs from simrep to simrep). Then in the equation, both Q and Q max will have a distribution of values. In some cases these are correlated. The grouped way to evaluate constraint satisfaction is to compare some statistical measures of Q and Q max with each other using a feasibility rule that gives the desired feasibility threshold. The simrep-by-simrep way is to compare Q and Q max with each other for each simrep, and then count the number of simreps that are feasible or infeasible. The feasibility threshold is implemented using this count of simreps.
Constraints The group approach is faster, but less rigorous if uncertainty in the constrained quantity and the constraint are correlated. The simrep-by-simrep approach requires a large number of evaluations (one for each simrep), but is mathematically rigorous For some constraints, the error bar on the states will have zero width, that is, all the simreps will have the same quantity (e.g., for reserve margin constraint, a state will have the same capacity in every simrep). These constraints can be evaluated using the group approach without any loss of rigor For other constraints, the error bar on the states will have some width, and the constrained quantity and constraint will be correlated. These constraints should be evaluated, if computationally possible, using the simrep-by-simrep method. 51
Relationship between stochastic and deterministic objective functions 52