qip course on ‘smart grid...
TRANSCRIPT
QIP course on‘Smart Grid Technology’
Planning of Distribution System with Renewable Energy Resources
Presented by:Dr. Abheejeet Mohapatra
Assistant ProfessorDepartment of Electrical Engineering
Power System Components
May 10, 2019 2
220 kV Power Plant
Generation
ResidentialCustomer
Commercial/IndustrialCustomer
ResidentialCustomer
DistributionPole
UrbanCustomers
Primary Distribution
66 kVTransmission
Distribution Transformer(11/0.415 kV)
Secondary Grid(66/11 kV)
Primary Grid (220/66 kV)
Secondary Distribution
Underground Cable
To Other66Kv
Substations
Primary Transmission(132/220/400/765KV)
Secondary Transmission(66/132KV)
CBX’mer(11/220kV) Bus-bar
Bus-bar Steel Tower
CBFour major components• Generation: source of power• Transmission: transmits power to
load ends• Distribution: local reticulation of
power• Loads: consumersAdditional components
• Control Equipment: coordinate supply with load
Role of Optimization
May 10, 2019 3
Why planning????
System is driven by
loads
Increase in load demands
Generation also must increase to meet loads
Conductor capacity or
number should also increase
Procure additional
resources for reliability and
security
Optimization is attaining optimum/best decision for reliable
and secure operation and planning of the system
Planning phase-> Decision making process
Operation phase-> Having decided, take actions
What is Planning?
May 10, 2019 4
The planning period is for a time horizon – typically 5 - 15 yearsSystem elements may be
• Substation• On load tap changers, voltage regulators• Feeder topology and configuration• Distribution lines• Renewable Energy Resources• Capacitor banks, etc.
Decision making involves• where to allocate the element – Optimal location, siting• what to select for installation – Optimal type and sizing• when to install the element – Optimal time horizon• how to install the element – One at a time or phase wise
Aim is to decide on procurement/ setup of new elements and/ or upgrade existing system elements in order to adequately satisfy loads for foreseeable future
Distribution system planning and operation
May 10, 2019 5
There are generally two paradigms of planning• Strategic Resource planning - deals with optimization of available resources in a very long
planning horizon (typically 5 -15 years)o Optimal siting and sizing of capacitor bankso Optimal siting and sizing of voltage regulatorso Optimal siting and sizing of renewable energy resources such as storage, PVso Substation upgradeo Distribution feeder upgrade
• Operational planning - deals with optimization of system operation for given resources in shorter planning horizon (typically few minutes – 1 day)o Network reconfigurationo Optimal settings of capacitor banks, OLTCs, voltage regulators, etc. in volt – var
optimization and controlo Energy scheduling in the presence of renewable energy resourceso Battery state-of-charge optimization
Static vs Dynamic Optimization
May 10, 2019 6
Static optimization• decision variables pertain to a single time frame• one time investment• implementation is done at the end of time frame• only one set of variables• easy optimization but costly decisions
Dynamic optimization• decision variables pertain to sub-intervals in a time frame• several stage investment• phase wise implementation in sub-intervals of time frame• variables of different sub-intervals are linked together by coupling constraints• complex optimization but low cost decisions
Forecasting for planning and operation
May 10, 2019 7
First crucial step for any planning is to predict the load/ renewable output for the study period
• For long term/ resource planning, long-term load forecast; seasonal load/ solar availability• For short term/ operational planning, short-term load forecast; daily load/ solar output curve
Forecasting is estimation of future loads/ resources output
based on various data and information available and as per
consumer behavior
Forecast average load in kW or total load in kWh for blocks of 15’, 30’, hour, day,
week, month or year for a daily forecast, weekly forecast, monthly forecast or
yearly forecast
There are different tools and techniques for load
forecasting
It is possible to forecast load for unconstraint demand. Load forecasting
of constrained demand is trivial
Why is Forecasting important in India?
May 10, 2019 8
Energy Deficit Market
Nascent Market Mechanism
Significant Growth
Technical and Commercial Losses
Distribution Infrastructure
Regulatory Policies
Integration of Renewable Energy Resources
Benefits of good forecast
May 10, 2019 9
Efficient power procurement/ bidding
Resource planning
Selling of excess power
Optimum supply schedule
Network planning
Good demand side management strategies
Optimum renewable placement and sizing plan
Load driving parameters
May 10, 2019 10
Forecasting accuracy
May 10, 2019 11
Nature of Load and Renewable Energy Sources
May 10, 2019 12
Load has daily variation (load curve) and is also uncertain due to forecast errors Renewable Energy Sources – solar PV, biomass generation, small wind farms, etc. Along with battery/ storage, above are together known as Renewable Energy
Resources The power output of renewable energy sources is uncertain!!
• Solar PV output depends on solar irradiation, shading, clouds, etc.• Biomass generation depends on input availability which has seasonal
dependency• Wind farm output depends on wind speed, weather, etc.
Renewable energy sources are thus non – schedulable/ uncontrollable Battery/ storage power highly depends on state-of-charge
Uncertainty vs Variability
May 10, 2019 13
Uncertainty – the value (or outcome) of a quantity is unknown, e.g. the true or exact demand of IITK or solar power output from IITK cannot be known for sure
Variability – a quantity can takes multiple values at different locations, times or instances, e.g. daily load variation, solar irradiance variation, etc.
Uncertainty can be quantified by a probability distribution which depends upon the state of information about the likelihood of what the single, true value of the uncertain quantity is
Variability can be quantified by frequency distribution of multiple instances of the quantity, derived from the observed data
Both are represented by ‘distributions’ is a major source of confusion This can lead to uncritical adoption of frequency distributions to represent
uncertainty, and thus to erroneous risk assessments and bad decisions Vice – versa is true for variability representation
Models of Uncertainty representation
May 10, 2019 14
Time scale of Uncertainty
May 10, 2019 15
Uncertainties in Distribution System Operation and Planning
May 10, 2019 16
Some typical sources of uncertainty (list is not at all inclusive)• Load and expected price forecast• Availability of distribution system components• Imperfect system parameter, model and simulation• Information confidentiality in markets (futuristic scenario)• Resource availability and cost• Renewable Energy Sources (RES) – wind and solar forecast• Error in system operational constraint limits
Planning is a long range problem while operation is a short term problem Uncertainties have to be considered in these
Consequences of Uncertainties
May 10, 2019 17
RES
What to do?
May 10, 2019 18
Traditional, deterministic planning and operational problems of distribution system are generally difficult optimization exercises
• Integer/ binary variables – 0/1 variables such as location variable, tap setting, capacitor setting, etc.
• Multiple time scale solution has to be obtained instead of single time scale
Considering uncertainties (and variations) is going to further complicate the exercise Further, since system scenario is uncertain, deterministic study is of no use!!Even if it were to be used, then at what value of uncertain parameter?The expectation is that distribution system planning and operation should be good
enough (from economics, security, stability, reliability, etc. perspective) for all best case and worst case unforeseeable situations
Generally, if something works well for worst case situation, it should work well for best case situation – Robust optimization
Possible approaches
May 10, 2019 19
Stochastic optimization• Random probabilistic uncertainties with PDFs• Two typical methods – Monte Carlo Simulation (MCS) and Chance-Constrained
Programming (CCP)• Final solution also has a probability of occurrence• The most probable solution is chosen as best
Fuzzy/ Boundary/ Interval analysis• Possibilistic uncertainties with membership functions• Typical methods – Affine Arithmetic, Boundary analysis• Solution has a possibility of occurrence• Most possible solution is by defuzzification
Solution is not crisp; implementation needs one solution!!Robust optimization
• Focuses on the worst-case scenario analysis• System feasibility is always ensured in terms of constraints• Economics of solution is generally more than deterministic case
Distribution system planning and operation problems can be stated as
Coefficients in the objective function may represent cost, loss coefficients, etc. Same is true for other constraints For worst case realization, the (minimized) objective is to be maximized with respect to
uncertain variables for known specified range of uncertainty (depending on experience)
Mathematical formulation
May 10, 2019 20
where: x is the first stage/ integer variable vector
y is the second stage/ continuous variable vector
u is the uncertain parameter vector
Generally, this cannot be solved directly due to• Different nature of optimization variables – integer variables are complicating variables as
compared to continuous variables• Objective has to be maximized as well as minimized
Mathematical formulation Contd.
May 10, 2019 21
where: x is the first stage/ integer variable vector
y is the second stage/ continuous variable vector
u is the uncertain parameter vector
An alternative to the first issue of different nature of variables can be to solve the problem for a fixed ‘x’
For some feasible x = x*, the actual problem can be rewritten as
Mathematical formulation Contd.
May 10, 2019 22
The first issue is resolved as variables ‘y’ and ‘u’ are continuous in nature in primal slaveHowever, the second issue still persists
• Uncertain parameters ‘u’ affect objective and appears in constraints• This needs to be solved for worst case realization of ‘u’• Worst case is realizable only when ‘u’ is at its bounds, which entirely depends on the
optimization problem and its solution• This formulation cannot be enforced for all realizations of ‘u’
Mathematical formulation Contd.
May 10, 2019 23
Primal Slave
It is to be noted that if ‘u’ were to appear only in the objective function, then there would not have been any second issue
To resolve the second issue, primal slave needs to be rewritten so that ‘u’ appears only in the objective function (which will be maximized and/ or minimized)
This reformulation model is dual slave In order to have the dual slave formulation, the following, if ensured in the primal slave,
makes the process very easy• Linearity• Convexity
By this, it is also ensured that primal and dual slave give the same solution
Mathematical formulation Contd.
May 10, 2019 24
A function or variation is considered to be linear when the following is true
)1,0())1(()()1()(
,
2121
21
∈∀−+=−+
∈∀
λλλλλ xxfxfxf
Xxx
Linearity
May 10, 2019 25
A function or variation is considered to be convex when the following is true
Convex set
]1,0[))1(()()1()(
,
2121
21
∈∀−+≤−+
∈∀
txttxfxftxtf
Xxx
Convexity
May 10, 2019 26
]1,0[)1(
,
21
21
∈∀∈−+
∈∀
tXxttx
Xxx
Non convex set
The primal slave formulation is linear as well as convexThe steps to convert primal slave to dual slave are as follows
• Objective function should be in the minimization form (while ignoring ‘u’)
• Inequality constraints are to be rewritten so that they are all in ‘less than equal to’ form (the equality constraints are left as they are)
Mathematical formulation Contd.
May 10, 2019 27
• For each equality constraint, a free dual multiplier (similar to Locational Marginal Price) is associated
• For each inequality constraint, a non – negative dual multiplier (similar to Line Shadow Price) is associated
• Motivation – change in equality constraint may increase or decrease the objective while any change in inequality constraint should always penalize the objective
Mathematical formulation Contd.
May 10, 2019 28
• The augmented objective function can be written as
• The augmented objective is to be minimum with respect to ‘y’• Is the same true with respect to dual multipliers?• A BIG NO!!• As per duality theory, if an objective is to be minimized with respect to ‘y’, then the same
should be maximized with respect to dual multipliers ‘λ’, ‘z1’, ‘z2’, ‘z3’ and ‘z4’
Mathematical formulation Contd.
May 10, 2019 29
• On rearranging ‘L’ (with ‘y’ taken common from all terms), the term independent of ‘y’ is
• This serves as the objective function in the dual slave• The term in ‘L’ which is function of ‘y’ is
Mathematical formulation Contd.
May 10, 2019 30
• The term in ‘L’ which is function of ‘y’ serves as the equality constraint in dual slave
• Motivation is that ‘y’ (which can be positive or negative) serves as dual multiplier vector of the dual constraint (as is the case of actual dual multipliers)
• Thus, the overall dual slave formulation is
Mathematical formulation Contd.
May 10, 2019 31
• The effect of uncertain parameter ‘u’ was to maximize the objective• With this considered, the robust dual slave formulation is
• Benefit of this is that this can be easily solved now as ‘u’ appears only in the objective
Mathematical formulation Contd.
May 10, 2019 32
• For ‘x’, the following master problem is solved
Mathematical formulation Contd.
May 10, 2019 33
Optimality constraint
Overall algorithm
May 10, 2019 34
Initialization of master variable (x)
Solve slave dual
Dual feasible?
Add optimality constraint to the master
Solve Master Problem;Update x
YesNo
Infeasibility Indication
Add feasibility constraint to the master
Optimality Indication
Convergence?
No
Yes
Declare robust ‘x’
THANK YOU