Use of Residual Load Duration Curves to study the high penetration of renewables in TIMES-Greece

G. Giannakidis

K. Tigas

J. Mantzaris

Centre for Renewable Energy Sources and Saving (CRES), Athens, Greece

Introduction

Questions from the Policy makers:

• Achievement of RES targets, optimal mix of RES

• Analysis on possible CO2 reduction levels scenarios

• Feasibility of new power plants

• Impact of RES in the electricity system

• Storage requirements and reserve capacity requirements

Introduction

A number of issues arise in long term energy planning under environmental constraints and large scale RES utilization requirements:

• strong stochastic nature of RES and the limitations in their dispatching need to be taken into account, given the curtailment that might be necessary when load is low and RES generation high.

• addressing this through the construction of storage plants and fast reserve capacity to balance the load variation.

Approach

Multi-Regional TIMES model

In-house tool Probabilistic simulation for electricity (PropSim)

PSS/E grid impact studies

WASP

Approach

Application:

A multi-regional TIMES model (14 regions)

16 timeslices

Seasons hours

(R S F W) (D N P L)

Electricity grid modelling

1) Standard TIMES trading processes

between regions

2) Include a simplified electricity grid

with 73 nodes and 99 corridors

(to be used in the DC load flow).

Approach

The TIMES solution should incorporate:

• costs related to transmission grid expansions necessary for penetration of geographical areas with a high potential of renewables and

• costs related to balancing units required due to variations of renewable generation (storage plants and fast response power plants (gas turbines)).

Approach

To handle the stochastic aspects introduced by the large scale penetration of RES, the TIMES model was combined (soft linked) with a model for Probabilistic Production Simulation (ProPSim):

• Calculate Residual Load Duration Curves (RLDC) from hourly values of customer load and hourly values of non-dispatchable generation (wind, PV, small hydro and CHP) which are provided as input.

• For a given time interval (hourly simulation) ProPSim then simulates the operation of the generation system and it calculates the peak load capacity required, the balancing units capacity required to cover the residual load hourly variations and the storage capacity required to restrict energy curtailment.

• These ancillary services parameters together with corrected utilization factors of Renewables are then fed back to the TIMES model (include the cost which entails balancing units costs, storage costs, grid expansion and connection costs together with utilization factors of RES in specific areas).

Approach

Methodology

The methodology to derive RLDCs is based on the determination of the load (residual load) that remains to be covered by dispatchable units (thermal, reservoir hydro). 1) Results from TIMES for the electricity demand and electricity production per RES technology for the future years. 2) Time series are developed based on historical data for RES generation combined with concurrent customer load which are extrapolated into the future to forecast the variables of production from RES units (with one hour time resolution). 3) The probability density function (PDF) and the cumulative distribution function (CDF) of the different forms of non-dispatchable generation as well as the customer load are formulated and are input into ProPSim to calculate a Residual Load Duration Curve on a monthly basis through the convolution of the customer load with the non-dispatchable energy generation (hourly zones are used to assure small correlation between load and RES energy).

Methodology

The derived residual load duration curve used in PropSim is obtained from the convolution of the customer load with the generation from non dispatchable sources j which is expressed by the following equation

where Lres = IL−j x is the CDF (cumulative distribution function) of residual load

(Residual Load Duration Curve), L is the customer load, Cj is the generating capacity from non-dispatchable source j and FL−j x is the CDF (cumulative distribution

function) of the convolution of the customer load with the non dispatchable generation source j .

PDF of generation from source j

PDF of Load

Methodology

Based on the formulation of the Residual Load Duration Curve it is possible to define an optimum combination of thermal plants and reservoir-type hydro plants to cover the load that remains to be covered by dispatchable plants. At the same time, the level of penetration of non-dispatchable energy is considered in the light of the required level of additional costs related to non-dispatchable electricity curtailment or balancing units required.

Monthly RLDC

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r (M

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Residual Load Curve

Demand

Tech minimum

Residual Load Curve

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Residual Load Curve

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Methodology

Non dispatchable energy curtailment is related to the technical minimum of thermal power plants of the generation system and can be reduced either by selecting generation technologies with decreased technical minimum, or by using sufficient capacity of storage plants. The storage capacity normally does not balance 100% of the potential curtailment. The probability for curtailment is restricted by a parameter ε (which normally is taken at the level of 1 % or 87 hours annually)

Storage reserve required Rst

Detailed Methodology

Need to calculate the reserve capacity necessary for maintaining a constant index of reliability under variations of the residual load.

In the present approach a load shedding incident can happen in case that the variation of the residual load on an hourly basis (which can be a consequence of load variation, of variation of the production of non-dispatchable units and of the possibility of one or two generator trips) exceeds the spinning reserve.

Some results

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RESM-60%

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EMCM-60%

RESM-60%

CP: Current Policies Scenario. EMCM-60%: Environmental measures 60% emissions reduction in 2050 wrt 2005. RESM-60%: RES-E maximization scenario with 60% emissions reduction in 2050 wrt 2005.

Incorporation of the methodology into TIMES

Residual Load Curve features have been included into the last version of TIMES and could be used for evaluating the impacts of the integration of large amounts of variable renewable generation on the electricity system.

Due to its nature as a long-term energy system modeling framework, TIMES is not very well suitable for stochastic generation expansion planning, but one can try to simulate the impacts of stochasticity on the system by using deterministic variation parameters that are statistically calibrated outside the model.

Implementation in TIMES

The specific residual load modelling features in TIMES include the following components:

• Calculation of residual load curves by region and time period;

• Constraints ensuring that the technically imposed minimum levels of thermal generation are satisfied;

• Constraints for ensuring sufficient storage and peak capacity, taking into account the expected variations in the load and non-dispatchable generation.

Implementation in TIMES

Non - dispatchable power curtailment is related to the technical minimum of thermal power generation in the system.

In TIMES constraints are imposed on the thermal power generation that reflect these technical limits:

for each thermal power technology i and each timeslice j with a duration of dj

Options for declaring this:

Implementation in TIMES

Two capacity constraints are imposed to cope with the variation in the residual load.

1) Define the minimum required storage capacity in each timeslice:

Demanded storage at every residual load level (each timeslice) is defined by the difference of its value from technical minimum of dispatchable plants in the system (thermal minimum)

stg stg th min res

i, j i j j

i

Storage AF CAP P L

Residual Load Curve

Hours

Po

wer

(MW

)

Demand x (-PV-wind)

Tech minimum

res

th min

L(P , t )

res

res

L(L , t )

Variation component

• At every level of residual load (Lres), there is a corresponding probability function describing the possible variations of residual load

• An additional component is added in the equation for storage requirement

stg stg th min res res res

i, j i j j j j

i

Storage AF CAP P L VAR L

-1000 -500 0 500 1000

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1

Load Variation (MW)

Pro

babili

ty(-800, 0.01)

(850, 0.99)res resVAR L

res resVAR L

Implementation in TIMES

In TIMES the following constraint is used for the required storage capacity in each timeslice:

availability factor of storage technology i for timeslice j .

is the expected negative variation in the residual load

Implementation in TIMES

In order to optimize between curtailment and investment in storage:

• if the intermittent variable generation technologies have been modelled with upper bounds for their availability factors, power curtailment cannot actually be easily accounted in the TIMES model.

• suggested to use fixed availability factors for all intermittent power.

Define:

Re-formulate:

Implementation in TIMES

2) Define the minimum dispatchable capacity in each timeslice j:

This equation can be considered supplementary to the peak equation, because its purpose is to ensure sufficient available peak load capacity.

Next Steps

Work in Progress:

• Evaluating the statistical variations of the residual load on a regional level from statistics.

• Compare the solutions of this approach with the solution obtained through the previous approach of the iterative process.

The ATEsT project

http://www.cres.gr/atest/