STOCHASTIC OPTIMAL POWER FLOW (SOPF) FORREAL-TIME MANAGEMENT OF DISTRIBUTEDRENEWABLE GENERATION AND DEMAND RESPONSE

Junshan Zhang, ASU

Network Optimized Distributed Energy Systems (NODES)Annual Review Meeting

February 12 and 13, 2019

Project Summary‣ Challenges being addressed:

– Increasing uncertainty and variability due to a large number of distributed DER assets and DR products

– High penetration of wind and solar renewables and DR leads to increase in costs (e.g., increase in reserve requirements) and detriment to reliability in the operation of the power grid

‣ Key deliverables:• Algorithms and prototype software product for stochastic security

constrained economic dispatch (SCED or SOPF)• Enhanced computational performance using parallel processing• Scalable to large system with high percentage of renewable (stochastic

resources) penetration• A suite of forecast algorithms for bulk and distributed wind and solar

generation • Aggregation and disaggregation algorithms of demand response products

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Project Summary

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• Key outcomes and impacts:

• Demonstrate that this prototype can be used as an advisory tool within market/operational environment

• Show that it will provide system operators with operational guidance for uncertainty management (i.e., increase reliability) and result in reduced operating cost (e.g., through markets)

‣ Technical approach: Holistic approach to real-time coordination of DERs, DR, and DS.

• The SCED tool is a standalone parallel advisory tool and it is not intended to replace a market tool. SCED will provide the necessary real-time policy functions (or inputs) to be implemented within the existing market model.

• Enhanced modeling, control, and management of these resources (DER, DR, and storage) at the bulk level is needed to realize potential benefits.

• Also contemplating the development of a stochastic Look-ahead Commitment (SLAC) tool; partnering with MISO is in progress

• Used in the intra-day time frame so allow operators more time to make changes or corrections

Key Deliverable: Integration of the Stochastic SCED and SLAC Advisory Tool

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DeterministicLook-Ahead Commitment

Hour-Ahead Start of Operating Hour

TimeCurrent Industry Practice

Proposed Approach

DeterministicReal-Time

SCED / EMS

Hours-Ahead

System Operator

SLAC

Advisory Tool

Stochastic Optimization

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SCED

Advisory Tool

Stochastic Optimization

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SCED and SLAC Advisory Tool’s Benefits ‣ Increased operator confidence in the ability of stochastic resources to provide grid

services;‣ Enable stochastic resources (e.g., bulk renewable resources, distributed energy

resources, and demand response) to provide services not currently allowed within ISO and utility operations;

‣ Enable more efficient integration of stochastic resources through advanced uncertainty management;

‣ Lower operational costs and increases in market surplus;‣ Increased operational security;‣ Decreased instances of out-of-market instructions to manage stochastic resources;‣ Optimized out-of-market corrections (reserve disqualification, managing stranded

capacity) in replace of operator discretionary changes to market solutions;‣ Ability to provide transparency to market participants and oversight commissions for

making operational decisions, which is critical for stochastic resources to achieve a much larger market share;

‣ Improved ancillary service requirements that could lower costs to end-users while also enabling the utilization of stochastic resources; and

‣ Better understanding of operational issues and their corresponding solution due to analyzing the SCED and SLAC results.

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Team

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‣ Organizations and expertise:– ASU:

• Junshan Zhang (stochastic modeling and network optimization/control)• Vijay Vittal (power system stability and real-time control)• Kory Hedman (electricity market and energy system optimization)• Anna Scaglione (distributed learning and signal processing, demand

response management)– Sandia Lab: Jean-Paul Watson (algorithmic development and

implementation for stochastic optimization) – Nexant Inc: A company that specializes in software products for power

system network analysis and optimization, represented by Narsi Vempati– PJM: Jianzhong Tong (operation in power systems)

‣ Stochastic LAC: stochastic modeling of DERs and DR, coordination of the DERs and DR control, and necessary upgrades and novel functionalities for the decision support systems used today.

– MISO: Jessica Harrison and Yonghong Chen (Market Services Division)

Main Tasks

‣ Task 1: A suite of short-term forecast algorithms of DER

(particularly wind/solar) generation by spatio-temporal analysis.

‣ Task 2: Stochastic security constrained economic dispatch for

management of stochastic and distributed resources.

‣ Task 3: Adaptive flexible load management for demand response.

‣ Task 4: Integration and software development of proposed

stochastic look-ahead commitment.

‣ Task 5: Technology to market.

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Refresher and Overview of Main Tasks

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Task 5

Validation Plan

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‣ Wind– One wind farm in Colorado (300 MW), 10 minute resolution data– Four wind farms in the PJM system (100 to 200 MW), 5 minute

resolution data‣ Solar

– Three First Solar solar farms in California (50, 65, 139 MW), 10 second resolution data

– One solar farm in Australia (433 kW), 15 minute resolution data– 532 residential sites in California (few kW each), 15 minute

resolution data- Large scale simulation plan: Market based SCED on large-scale

system with >10K bus network like PJM system data (with DER and DR)

Project Progress

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Task 1 Task 2 and Task 4 Task 3 Task 5Renewable Forecasting

Markov Chain Model Development

Single Site Wind Forecasting Algorithm

Single Site Solar Forecasting Algorithm

Multi-Site Wind and Solar Forecasting

Algorithms

Complete

In Progress

To Come

Deterministic SCED Development

Stochastic SCED Algorithm Development

Demand Resource Integration

SCED Validation and Performance Evaluation

Industry Advisory Board Establishment

In-Person Meetings with Potential Customers

Technology Dissemination and

Demonstration

Technology to Market Final Assessment

Stochastic Look-Ahead Commitment Technology Transition

Load Modeling

Estimation of realistic DR capacity

Evaluation of power dynamics

Incorporation in SCED

Validation

Adaptive DR Management

Tasks 2 and 4: Stochastic SCED Prototype‣ Formulated as a two-stage stochastic optimization problem‣ Uncertainty is captured via renewable scenarios and

contingencies ‣ Recourse variables connect first stage and second stage

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Tasks 2 and 4: Stochastic SCED Prototype

‣ Prototype implemented using progressive hedging (PH)technology – solves very large stochastic problems with needed performance‣ Many important results from the Stochastic SCED

– Generation commitment– Reserve product requirements– Ramp requirements– Reserve sharing protocols– Participation factors / generator loss distribution factors– Critical contingency / renewable scenario list and critical security

criteria‣ Applicable to ISO markets

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Tasks 2 and 4: Stochastic SCED Prototype

‣ Performance Testing on the PJM system with varying wind penetration levels

– 12 sub-problems consisting of 3 generator contingencies and 4 renewable wind scenarios

– 6 time periods of length 5, 5, 10, 10, 15 and 15 minutes‣ Results show that this technology can be used in an

advisory tool role

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Renewable penetrationlevel

# of iterations to convergence

Total PH wall-clock time Optimality gap

20% 3 2.47 minutes 1.2%

24% 8 4.64 minutes 0.8%

51% 6 3.41 minutes 1.4%

Stochastic SCED vs Deterministic SCED

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‣ The stochastic SCED (S-SCED) formulation guarantees optimal procurement and optimal deployment of reserve products (for contingencies, renewable scenarios)

‣ Deterministic SCED (D-SCED) does not provide these guarantees

Stochastic SCED vs Deterministic SCED

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Differentiated Value Proposition Flow Chart

Stochastic SCED vs Deterministic SCED

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Cost Type Deterministic SCED Stochastic SCED

Generation and reserve procurement costs $1,586,968 $1,611,272

Base case penalties [1] Including power balance and flow limit penalties $96,133 $35

T-1 flow limit penalties $30,119 $61

Generator contingency penalties including power balance and flow limit penalties $3,752 $0

Total cost: $1,716,972 $1,611,368 (6.2% saving)

Calculations based on transmission flow penalties of $7,000/MWh, and power balance penalties of $6,500/MWh extracted from [1].

[1] California Independent System Operator, “Revised Update to CAISO Draft Final Proposal on Uneconomic Adjustment Policy andParameter Values,” [Online]. October 2008. Available: https://www.caiso.com/Documents/Update-DraftFinalProposalonUneconomicAdjustments.html

‣ Differentiated Value Proposition results‣ PJM system with 144 sub-problem: 9 generator contingencies, 16

renewable wind scenarios and 6 intra-hour time periods of length 5, 5, 10, 10, 15 and 15 minute

Summary of Our Technology to Market Efforts

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‣ A number of conference and journal papers are submitted/published‣ We have filed a patent application on wind/solar forecast‣ Multiple T2M activities

– PJM: site visit on April 11, 2016

– MISO: site visit on November 21, 2016

– ERCOT: site visit on January 30, 2017

– IAB kickoff meeting on March 31, 2017

– Pacific Gas and Electric: site visit on May 4, 2017

– CAISO: e-mail exchanges in April 2017 – September 2017

– SPP: site visit on May 31, 2017

– Dominion Energy: June 19, 2017

– MISO: Fall 2017 and 2018

– IAB meeting on March 20, 2018

– FERC Technical Conference, June 2018

– MISO Market Symposium, August 2018

– IEEE PES August 2018

– CAISO: September and October 2018

– Industry Wide Webinar: February 2019, over 1,500 invitees

Summary of Our Technology to Market Efforts

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‣ Cost Plus Partnership with MISO– Starting in April 2019 with an 18 month duration– Further development of these technologies

‣ MISO Management (Executive VP, CIO, Line managers) is strongly behind this initiative. Many visited our booth at the MISO symposium and expressed strong support. MISO is the best client for this technology -an entity that experiences problems dealing with uncertainties of renewable resources, DR, DER etc.

‣ From MISO: “The deterministic Look Ahead Commitment (LAC) tool at MISO is estimated to save more than $8 million annually. MISO anticipates that the adoption of Stochastic Look Ahead Commitment technology could yield additional savings. Out of market actions to manage headroom requirements or over-estimated stranded capacity can cause unnecessary commitment of additional generator resources. Under this project, MISO believes tools could be developed to systematically determine the impact form uncertainties and potentially reduce or avoid such actions.”

Task 1: Short-Term Forecasting of Wind and Solar Generation: Online Forecasting

‣ Most recent measurements are used, together with the stochastic model, to generate scenario trees for SLAC

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Induced Markov Chain (IMC) Model

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‣ The induced Markov chain (IMC) model was developed in this project to forecast wind and solar generation

– A Markov Chain model is often built using the time series of power generation

– The Induced Markov Chain (IMC) Forecast Model is built using the difference process S(t) = P(t)-P(t-1)

• The difference process is more stationary

• Much smaller state range (~25x); leads to high resolution

– State definitions also consider time and generation levels

Example Induced Markov Chain model using data from a

300 MW wind farm

From IMC to Polynomial Regression

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‣ Advantages of this model:– Non-parametric

• Able to capture any non-linear input to output relationship• Creates detailed distributional forecasts• Very low computational complexity

‣ In the past, it is widely believed that 5-15 minute ahead conditional distribution, for both wind and solar, is irregular in shape

– The data would not fit any standard distribution– A non-parametric method would be required to correctly capture the

uncertainty‣ Upon further investigation, the ‘local’ distributions created by the model are

very close to Gaussian, for both wind and solar‣ The IMC model was used as a means of visualizing the relationships between

input variables and the output forecast‣ This relationship was then modeled using polynomial regression‣ The distributional forecast is assumed to be Gaussian

Point Forecast Example

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‣ Let X(t)=P(t)-P(t-1)‣ The relationship, X(t) to X(t+1), using

the IMC model is plotted to the right using wind data

‣ The relationship is non-linear but not very complex

‣ This relationship can be modeled by polynomial regression using the formulation:𝑋𝑋 𝑡𝑡 + 1 = 𝜃𝜃1 + 𝜃𝜃2𝑋𝑋 𝑡𝑡 + 𝜃𝜃3𝑋𝑋 𝑡𝑡 2 + 𝜃𝜃4𝑋𝑋 𝑡𝑡 3

‣ Where, 𝜃𝜃 represents a regression coefficient, 𝑋𝑋 𝑡𝑡 is the linear term, 𝑋𝑋 𝑡𝑡 2 is the quadratic term, and 𝑋𝑋 𝑡𝑡 3

is the cubic term

The point forecast input-to-output relationship using an induced Markov chain model for a 300 MW wind farm

Distributional Forecast Example

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‣ Let 𝑟𝑟 𝑡𝑡 = �𝑋𝑋 𝑡𝑡 − 𝑋𝑋(𝑡𝑡) , where �𝑋𝑋 is the forecasted value and 𝑋𝑋 is the actual value

‣ The relationships are approximately linear, with the slope abruptly changing near the origin

‣ The effect of P(t) is approximately quadratic

The estimated residual when using different portions of the farm output range

‣ The relationship can be represented by the formulation:

r 𝑡𝑡 + 1 = �𝜃𝜃1 + 𝜃𝜃2𝑋𝑋 𝑡𝑡 + 𝜃𝜃3𝑃𝑃 𝑡𝑡 + 𝜃𝜃4𝑋𝑋 𝑡𝑡 𝑃𝑃 𝑡𝑡 + 𝜃𝜃5𝑃𝑃(𝑡𝑡)2 + 𝜃𝜃6𝑋𝑋 𝑡𝑡 𝑃𝑃(𝑡𝑡)2 if 𝑋𝑋 𝑡𝑡 ≥ 0𝜃𝜃7+𝜃𝜃8𝑋𝑋 𝑡𝑡 + 𝜃𝜃9𝑃𝑃 𝑡𝑡 + 𝜃𝜃10𝑋𝑋 𝑡𝑡 𝑃𝑃 𝑡𝑡 + 𝜃𝜃11𝑃𝑃(𝑡𝑡)2 + 𝜃𝜃12𝑋𝑋 𝑡𝑡 𝑃𝑃(𝑡𝑡)2 if 𝑋𝑋 𝑡𝑡 < 0

Colorado 300 MW Wind Farm – Trained 2009/Tested 2010 – 10 Minute Forecast

‣ MAE – Mean Absolute Error – Point forecast error‣ RMSE – Root Mean Square Error – Point forecast error, weights larger errors much larger

than small errors‣ CRPS – Continuous Rank Probability Score – Measure of distributional forecast quality‣ The regression method was tested against an ensemble of 200 artificial neural networks

(ANN)

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Method MAE RMSE CRPSPersistence 6.27 10.67 6.27

Induced Markov chain 4.88 8.66 3.67

Regression 4.76 8.34 3.56

ANNs 4.81 8.35 3.58

‣ The proposed method was able to improve upon ANNs while being able to produce forecasts approximately 1400x faster

‣ The efficiency of the proposed method will provide a significant advantage when generating scenarios for a large system (upcoming work with MISO)

California First Solar 139 MW Solar Farm –Trained 2014/Tested 2015 – 10 Minute Forecast

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Method MAE RMSE CRPSPersistence 3.52 9.17 3.52

Induced Markov Chain 3.29 9.08 2.91

Regression 3.39 8.66 2.60

ANNs 3.42 8.73 2.61

• The proposed algorithm outperforms the ANN ensemble

Task 3: Residential Demand Response

‣ Aggregate models for:– Storage devices– Electric vehicles– Deferrable appliances (washers, dryers)– Thermostatically controlled load (TCL) models

(air conditioners)

‣ Performance analysis:– Various modeling errors and tolerances– Response time and ramping time– Control dynamics– Reserve power capabilities

‣ Integration with Security Constrained OPF– Presents DR products as generators

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Task 3: Aggregator/SCED interaction‣ Aggregator:

– From population state + forecast about future inputs– calculate base-load and pmin/pmax– send to SCED.

‣ Disaggregator:– From a known state, given a dispatch instruction (from

SCED), calculate and issue instructions to population.‣ Individuals:

– React to broadcast instructions.

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Using this component DR can be incorporated in the SCED as, for example, a “negative generator”.

Task 3: Rolling Horizon Interaction

‣ Aggregator and SCED (individually) must solve faster than one period.

– Both depend on past solution.

‣ Disaggregator is fast (much smaller problem than aggregation).‣ Aggregator/Disaggregator

independent for each bus.‣ Scales well to millions of

households.

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Task 3: Implementation remarks

‣ DR can scale to thousands of buses:– Requires a few CPU cores per system bus.– Computational time per bus constant

• Irrespective of population size.‣ SCED complexity increases if we add thousands of

generators.‣ For a UC formulation DR “generators” can be considered to

be always committed.– No additional binary variables.

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Task 3: Simulation‣ We consider 655,440 TCLs and

112,678 batteries on 60 buses.‣ Simulation shows artificial reserve

events:– Purple: Curtailment.– Green: Load increase.

‣ Aggregate load is substantial.‣ Load very responsive to events.

– Fast ramps.– Significant percentage of load.

‣ Errors between estimated load and simulated consumption low, with spikes above 1% for large ramp events.

‣ Rebound peaks evident. – Can be spread over a longer

period – fully controllable.

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Task 3: PJM Rolling Horizon Simulation

‣ Again we consider 655,440 TCLs and 112,678 batteries on 60 buses.‣ This time we place the 60 buses

across the PJM system in Philadelphia, New Jersey, Washington DC, Chicago and Columbus.‣ Solved using an interaction

between the DR aggregator model and the SCED of Task 2.‣ Solved in a rolling horizon fashion

for 12x5 min = 1 hour.

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Task 3: PJM Rolling Horizon Simulation‣ Results:

– Generation costs only go down 0.2% - load shifting insignificant.– Significant reduction of transmission violations during transmission

line outages.– Overall objective savings of 14% - mostly through reduction in N-1

penalties.

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0

50000

100000

150000

200000

250000

1 2 3 4 5 6 7 8 9 10 11 12

Generation Costs

Generation Cost without DR Generation Cost With DR

0

500000

1000000

1500000

2000000

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1 2 3 4 5 6 7 8 9 10 11 12

Penalty Costs

T-1 Penalties Cost Without DR T-1 Penalties Cost With DR

‣ x-axis indicate interval of time

Task 3: Conclusions

‣ DR provides insignificant gain when it comes to load-shifting.‣ DR can provide substantial flexibility:

– Considerable gain for security constrained formulations, acting as a fast reserve.

– Fast response and ramp time.‣ No significant obstacles to adoption:

– Control infrastructure based on off the shelf components.‣ Ideally, SCED/SLAC formulations incorporate flexible

demand as first class citizens:– As residential DR is energy constrained and not ramp

constrained: Generator model a poor fit.– Generator model still able to provide decent benefits.

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