diff --git a/dev/ch1_sec1_install/index.html b/dev/ch1_sec1_install/index.html index 8423ae7..69523e1 100644 --- a/dev/ch1_sec1_install/index.html +++ b/dev/ch1_sec1_install/index.html @@ -1,3 +1,3 @@ Installation · EGRIP.jl
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Installation

For now since EGRIP.jl has not been registered, we need to load the package locally by putting the following code at the beginning of your test script:

cd(@__DIR__)
-push!(LOAD_PATH,"../src/")
+push!(LOAD_PATH,"../src/") diff --git a/dev/ch1_sec2_tutorials/index.html b/dev/ch1_sec2_tutorials/index.html index 07a4b36..59c43e5 100644 --- a/dev/ch1_sec2_tutorials/index.html +++ b/dev/ch1_sec2_tutorials/index.html @@ -25,4 +25,4 @@ t_final = parse(Int64, ARGS[4]) t_step = parse(Int64, ARGS[5]) gap = parse(Float64, ARGS[6]) -solve_restoration(dir_case_network, dir_case_blackstart, dir_case_result, t_final, t_step, gap)

Open Terminal and navigate to the directory containing solve_bs.jl.

$ cd /path to solve_bs/

Execute the following command:

$ julia solve_bs.jl 'case39.m' 'BS_generator.csv' 'results/' 300 100 0.15

Restoration Plan Verification

Restoration Plan File Generation

This process consists of two steps. The first step is to generate restoration plan file (an event list) using the function generateRestorationPlanFromOpt. We need the following inputs:

The function will output exitflag, which 1 means success and fail otherwise. The function can be called using the following command:

generateRestorationPlanFromOpt('D:\Box Sync\Blackstart_data\Blackstart_data\','restoration_plan_test_039.m','d_datane_39_mod_PQ_3')

Simulation

Once the event list is generated, we can run the simulation using the function runDynamicSimulation. We need the following inputs:

There will be two outpus:

The function can be called using the following command:

[flag,msg]=runDynamicSimulation('d_datane_39_mod_PQ_3','restoration_plan_test_039')

Plots

Once the simulation is completed, we could load the simulation data:

Load the *_simp.mat result file (located in ./restoration/)

and plot the results:

plotCurves(1,t,stateCurve,SysDataBase,’variableName’)

The results of the IEEE 39-bus system are shown below. Enhanced Extended-Term Simulation Enhanced Extended-Term Simulation

+solve_restoration(dir_case_network, dir_case_blackstart, dir_case_result, t_final, t_step, gap)

Open Terminal and navigate to the directory containing solve_bs.jl.

$ cd /path to solve_bs/

Execute the following command:

$ julia solve_bs.jl 'case39.m' 'BS_generator.csv' 'results/' 300 100 0.15

Restoration Plan Verification

Restoration Plan File Generation

This process consists of two steps. The first step is to generate restoration plan file (an event list) using the function generateRestorationPlanFromOpt. We need the following inputs:

The function will output exitflag, which 1 means success and fail otherwise. The function can be called using the following command:

generateRestorationPlanFromOpt('D:\Box Sync\Blackstart_data\Blackstart_data\','restoration_plan_test_039.m','d_datane_39_mod_PQ_3')

Simulation

Once the event list is generated, we can run the simulation using the function runDynamicSimulation. We need the following inputs:

There will be two outpus:

The function can be called using the following command:

[flag,msg]=runDynamicSimulation('d_datane_39_mod_PQ_3','restoration_plan_test_039')

Plots

Once the simulation is completed, we could load the simulation data:

Load the *_simp.mat result file (located in ./restoration/)

and plot the results:

plotCurves(1,t,stateCurve,SysDataBase,’variableName’)

The results of the IEEE 39-bus system are shown below. Enhanced Extended-Term Simulation Enhanced Extended-Term Simulation

diff --git a/dev/ch1_sec3_formulations/index.html b/dev/ch1_sec3_formulations/index.html index a578e11..dd48123 100644 --- a/dev/ch1_sec3_formulations/index.html +++ b/dev/ch1_sec3_formulations/index.html @@ -195,4 +195,4 @@ \end{aligned} \end{align*}\]

Objective

\[\begin{align*} \min \sum_{g \in G}x_{g}+\sum_{d \in D}x_{d} - \end{align*}\]

+ \end{align*}\]

diff --git a/dev/ch1_sec4_advanced_algorithm/index.html b/dev/ch1_sec4_advanced_algorithm/index.html index cc198fd..9c8b542 100644 --- a/dev/ch1_sec4_advanced_algorithm/index.html +++ b/dev/ch1_sec4_advanced_algorithm/index.html @@ -1,2 +1,2 @@ -Advanced Algorithms · EGRIP.jl
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Advanced Algorithms

Multi-Resolution Approach

We developed a multi-resolution restoration algorithm to accelerate the overall solution time and prepare the software package for large-scale systems. The approach is based on the fact that better solutions can be found with smaller time steps, that is, higher resolution, which results in more complex optimization model. In addition, it is often difficult for the solver to obtain a feasible solution when the time step is small. Therefore, the essence of the algorithm is to hierarchically increase the resolution (that is, decrease the time steps) and guide the search of higher-resolution problem using solutions from lower-resolution solutions. Specifically, generator decision variables at certain time interval will be fixed to either zero or one depending on the result from the previous step. The algorithm is illustrated in Figure 1, where Figure 1 (a) shows the step of the approach and Figure 1 (b) illustrate the fixing rules. Multi-resolution method

We verify the method on the black start problem for the IEEE 39-bus system. The computation results are shown in Table 1 with total time equal to 300 minutes. In Scenario 2, the solver cannot reach to convergence after 71 hours. On the other hand, the proposed method can save eight times of the computation time with slightly compromised optimality. This preliminary computation experiments verify the effectiveness of our proposed approach.

Scenario IndexGapResolution (min)Solving Time (sec)With Fixed ConstraintAll generator dispatchable (min)
11%50728No251
21%20255854 (71h) without convergenceNo\
310%208709No201
45%20327Generator sequence fixed based on S1221

Enhanced Extended-Term Event-Driven Simulation

We enhanced the extended-term simulation approach based on semi-analytical simulation (SAS) for restoration studies. And we implemented hybrid simulation switching between the full-dynamic simulation and quasi-steady-state (QSS) simulation. The switch from full-dynamic simulation to QSS simulation is realized directly from SAS coefficients, which is much more efficient than the traditional method that needs extra period of simulation. Enhanced Extended-Term Simulation

We further use SAS to simulate a restoration process of IEEE 39-bus system. The whole process lasts 12,065s and includes 396 events, including bus energization, line energization, line switching, generator cut-in, generator ramping, load cut-in, load ramping events. The QSS simulation covers about 39% of the whole process, and the time saving compared with full-dynamic simulation is about 36%. This verifies that QSS simulation is much faster than the full-dynamic simulation, and the hybrid simulation can significantly enhance efficiency without losing accuracy. Enhanced Extended-Term Simulation

+Advanced Algorithms · EGRIP.jl
Edit on GitHub

Advanced Algorithms

Multi-Resolution Approach

We developed a multi-resolution restoration algorithm to accelerate the overall solution time and prepare the software package for large-scale systems. The approach is based on the fact that better solutions can be found with smaller time steps, that is, higher resolution, which results in more complex optimization model. In addition, it is often difficult for the solver to obtain a feasible solution when the time step is small. Therefore, the essence of the algorithm is to hierarchically increase the resolution (that is, decrease the time steps) and guide the search of higher-resolution problem using solutions from lower-resolution solutions. Specifically, generator decision variables at certain time interval will be fixed to either zero or one depending on the result from the previous step. The algorithm is illustrated in Figure 1, where Figure 1 (a) shows the step of the approach and Figure 1 (b) illustrate the fixing rules. Multi-resolution method

We verify the method on the black start problem for the IEEE 39-bus system. The computation results are shown in Table 1 with total time equal to 300 minutes. In Scenario 2, the solver cannot reach to convergence after 71 hours. On the other hand, the proposed method can save eight times of the computation time with slightly compromised optimality. This preliminary computation experiments verify the effectiveness of our proposed approach.

Scenario IndexGapResolution (min)Solving Time (sec)With Fixed ConstraintAll generator dispatchable (min)
11%50728No251
21%20255854 (71h) without convergenceNo\
310%208709No201
45%20327Generator sequence fixed based on S1221

Enhanced Extended-Term Event-Driven Simulation

We enhanced the extended-term simulation approach based on semi-analytical simulation (SAS) for restoration studies. And we implemented hybrid simulation switching between the full-dynamic simulation and quasi-steady-state (QSS) simulation. The switch from full-dynamic simulation to QSS simulation is realized directly from SAS coefficients, which is much more efficient than the traditional method that needs extra period of simulation. Enhanced Extended-Term Simulation

We further use SAS to simulate a restoration process of IEEE 39-bus system. The whole process lasts 12,065s and includes 396 events, including bus energization, line energization, line switching, generator cut-in, generator ramping, load cut-in, load ramping events. The QSS simulation covers about 39% of the whole process, and the time saving compared with full-dynamic simulation is about 36%. This verifies that QSS simulation is much faster than the full-dynamic simulation, and the hybrid simulation can significantly enhance efficiency without losing accuracy. Enhanced Extended-Term Simulation

diff --git a/dev/ch2_sec1_library_public/index.html b/dev/ch2_sec1_library_public/index.html index 60192fb..c566fd4 100644 --- a/dev/ch2_sec1_library_public/index.html +++ b/dev/ch2_sec1_library_public/index.html @@ -1,2 +1,2 @@ -Public Library · EGRIP.jl
Edit on GitHub

Public Library

Formulation Function

EGRIP.solve_restoration_full — Function

Solve full restoration problem (The restoration problem could be partial or full restorations)

  • Full restoration problem assumes that the entire network is broken down.
  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
  • Output: Restoration plans
  • Constraints:
    • linearized AC power flow constraint
    • steady-state voltage variation constraint
    • generator cranking constraint
    • generator status and output constraint
    • load pick-up constraint
source
Missing docstring.

Missing docstring for solve_restoration_part. Check Documenter's build log for details.

EGRIP.solve_section — Function

Solve sectionalization problem for restoration preparedness

  • Problem type: The sectionalization problem could assign all buses to certain sections or only critical buses.
  • Inputs:
    • network data directory
    • restoration data directory
    • result storage directory
    • gap
  • Output:
    • JSON file of network data of each section
  • Constraints:
source
EGRIP.solve_startup — Function

Solve generator start-up problem

  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
    • formulation types
    • specifications of wind power
      • wind activation 0 denotes no wind will support the restoration
      • wind activation 1 denotes wind will support the restoration with its distribution as normal
      • wind activation 2 denotes wind will support the restoration with time seires wind data
      • wind activation 3 denotes wind will support the restoration with real quantile and interpolation (linear, cubic, or spline)
    • if wind activation = 3, then real wind power density will be specified in wind_data
    • The followings are the keyword arguments
      • wind_data: time series wind data
      • saa_mode: different chance constraints enforcement in sample average approximations
  • Output: Generator start-up sequence
  • Constraints:
    • generato cranking
    • load pickup
    • power balance
source
+Public Library · EGRIP.jl
Edit on GitHub

Public Library

Formulation Function

EGRIP.solve_restoration_full — Function

Solve full restoration problem (The restoration problem could be partial or full restorations)

  • Full restoration problem assumes that the entire network is broken down.
  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
  • Output: Restoration plans
  • Constraints:
    • linearized AC power flow constraint
    • steady-state voltage variation constraint
    • generator cranking constraint
    • generator status and output constraint
    • load pick-up constraint
source
Missing docstring.

Missing docstring for solve_restoration_part. Check Documenter's build log for details.

EGRIP.solve_section — Function

Solve sectionalization problem for restoration preparedness

  • Problem type: The sectionalization problem could assign all buses to certain sections or only critical buses.
  • Inputs:
    • network data directory
    • restoration data directory
    • result storage directory
    • gap
  • Output:
    • JSON file of network data of each section
  • Constraints:
source
EGRIP.solve_startup — Function

Solve generator start-up problem

  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
    • formulation types
    • specifications of wind power
      • wind activation 0 denotes no wind will support the restoration
      • wind activation 1 denotes wind will support the restoration with its distribution as normal
      • wind activation 2 denotes wind will support the restoration with time seires wind data
      • wind activation 3 denotes wind will support the restoration with real quantile and interpolation (linear, cubic, or spline)
    • if wind activation = 3, then real wind power density will be specified in wind_data
    • The followings are the keyword arguments
      • wind_data: time series wind data
      • saa_mode: different chance constraints enforcement in sample average approximations
  • Output: Generator start-up sequence
  • Constraints:
    • generato cranking
    • load pickup
    • power balance
source
diff --git a/dev/ch2_sec2_library_internal/index.html b/dev/ch2_sec2_library_internal/index.html index ce27943..0096313 100644 --- a/dev/ch2_sec2_library_internal/index.html +++ b/dev/ch2_sec2_library_internal/index.html @@ -1,5 +1,5 @@ -Internal Library · EGRIP.jl
Edit on GitHub

Internal Library

Integrated Restoration

EGRIP.solve_restoration_full — Method

Solve full restoration problem (The restoration problem could be partial or full restorations)

  • Full restoration problem assumes that the entire network is broken down.
  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
  • Output: Restoration plans
  • Constraints:
    • linearized AC power flow constraint
    • steady-state voltage variation constraint
    • generator cranking constraint
    • generator status and output constraint
    • load pick-up constraint
source
EGRIP.solve_restoration_part — Method

Solve partial restoration problem given generator startup plan

  • Here the generator startup plan is given from the Parallel Power System Restoration (PPSR) module.
  • Inputs:
    • network data directory where data format could be json, matpower and psse
    • restoration plan
    • result directory
    • gap
  • Output: Rest part of the restoration plans
  • Constraints:
    • linearized AC power flow constraint
    • steady-state voltage variation constraint
    • generator startup and load pickup should be consistent with the given plan
source

Sectionalization Models

EGRIP.solve_section — Method

Solve sectionalization problem for restoration preparedness

  • Problem type: The sectionalization problem could assign all buses to certain sections or only critical buses.
  • Inputs:
    • network data directory
    • restoration data directory
    • result storage directory
    • gap
  • Output:
    • JSON file of network data of each section
  • Constraints:
source

Generator Startup Models

EGRIP.solve_startup — Function

Solve generator start-up problem

  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
    • formulation types
    • specifications of wind power
      • wind activation 0 denotes no wind will support the restoration
      • wind activation 1 denotes wind will support the restoration with its distribution as normal
      • wind activation 2 denotes wind will support the restoration with time seires wind data
      • wind activation 3 denotes wind will support the restoration with real quantile and interpolation (linear, cubic, or spline)
    • if wind activation = 3, then real wind power density will be specified in wind_data
    • The followings are the keyword arguments
      • wind_data: time series wind data
      • saa_mode: different chance constraints enforcement in sample average approximations
  • Output: Generator start-up sequence
  • Constraints:
    • generato cranking
    • load pickup
    • power balance
source
EGRIP.verify_startup_ppsr — Method

Verify generator start-up problem

  • Inputs: A set of restoration data in csv format and original system data
    • network data directory
    • network data format, which could be json, matpower and psse
    • generator black start data directory
    • result storage directory
    • solver
  • Output: Generator start-up sequence and island splitting
source

Generator Models

EGRIP.def_var_gen — Method

Define generator variables

  • The definitation of variables corresponds to different formulations.
  • The default variable definition is the formulation 4, which is used in the resotoration problem
source
EGRIP.form_gen_cranking — Method

Generator cranking constraint (formulation 4 in the generator start-up formulation and also used in the restoration)

  • Once a non-black start generator is on, that is, $y_{g,t}=1$, then it needs to absorb the cranking power for its corresponding cranking time
  • "After" the time step that this unit satisfies its cranking constraint, its power goes to zero; and from the next time step, it becomes a dispatchable generator
    • set non-black start unit generation limits based on "generator cranking constraint"
    • cranking constraint states if generator g has absorb the cranking power for its corresponding cranking time, it can produce power
  • Mathematically if there exist enough 1 for $y_{g,t}=1$, then enable this generator's generating capability
  • There will be the following scenarios
    • (1) generator is off, then $y_{g,t}-y_{g,t-Tcr_{g}} = 0$, then $pg_{g,t} = 0$
    • (2) generator is on but cranking time not satisfied, then $y_{g,t} - y_{g,t-Tcr_g} = 1$, then $pg_{g,t} = -Pcr_g$
    • (3) generator is on and just satisfies the cranking time, then $y_{g,t} - y_{g,t-Tcr_g} = 0$, $y_{g,t-Tcr_g-1}=0$, then $pg_{g,t} = 0$
    • (4) generator is on and bigger than satisfies the cranking time, then $y_{g,t} - y_{g,t-Tcr_g} = 0$, $y_{g,t-Tcr_g-1}=1$, then $0 <= pg_{g,t} <= pg^{\max}_{g}$
  • All scenarios can be formulated as follows:

\[\begin{align*} +Internal Library · EGRIP.jl

Edit on GitHub

Internal Library

Integrated Restoration

EGRIP.solve_restoration_full — Method

Solve full restoration problem (The restoration problem could be partial or full restorations)

  • Full restoration problem assumes that the entire network is broken down.
  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
  • Output: Restoration plans
  • Constraints:
    • linearized AC power flow constraint
    • steady-state voltage variation constraint
    • generator cranking constraint
    • generator status and output constraint
    • load pick-up constraint
source
EGRIP.solve_restoration_part — Method

Solve partial restoration problem given generator startup plan

  • Here the generator startup plan is given from the Parallel Power System Restoration (PPSR) module.
  • Inputs:
    • network data directory where data format could be json, matpower and psse
    • restoration plan
    • result directory
    • gap
  • Output: Rest part of the restoration plans
  • Constraints:
    • linearized AC power flow constraint
    • steady-state voltage variation constraint
    • generator startup and load pickup should be consistent with the given plan
source

Sectionalization Models

EGRIP.solve_section — Method

Solve sectionalization problem for restoration preparedness

  • Problem type: The sectionalization problem could assign all buses to certain sections or only critical buses.
  • Inputs:
    • network data directory
    • restoration data directory
    • result storage directory
    • gap
  • Output:
    • JSON file of network data of each section
  • Constraints:
source

Generator Startup Models

EGRIP.solve_startup — Function

Solve generator start-up problem

  • Inputs: A set of restoration data in csv format and original system data
    • network data directory where data format could be json, matpower and psse
    • restoration data directory
      • restoration_gen: specify initial generator status, cranking specifications and black-start generators
      • restoration_bus: specify initial bus status and its load priority, from where the problem type (partial or full restorations) can be determined
      • restoration_line: specify initial line status, from where the problem type (partial or full restorations) can be determined
    • result storage directory
    • gap
    • formulation types
    • specifications of wind power
      • wind activation 0 denotes no wind will support the restoration
      • wind activation 1 denotes wind will support the restoration with its distribution as normal
      • wind activation 2 denotes wind will support the restoration with time seires wind data
      • wind activation 3 denotes wind will support the restoration with real quantile and interpolation (linear, cubic, or spline)
    • if wind activation = 3, then real wind power density will be specified in wind_data
    • The followings are the keyword arguments
      • wind_data: time series wind data
      • saa_mode: different chance constraints enforcement in sample average approximations
  • Output: Generator start-up sequence
  • Constraints:
    • generato cranking
    • load pickup
    • power balance
source
EGRIP.verify_startup_ppsr — Method

Verify generator start-up problem

  • Inputs: A set of restoration data in csv format and original system data
    • network data directory
    • network data format, which could be json, matpower and psse
    • generator black start data directory
    • result storage directory
    • solver
  • Output: Generator start-up sequence and island splitting
source

Generator Models

EGRIP.def_var_gen — Method

Define generator variables

  • The definitation of variables corresponds to different formulations.
  • The default variable definition is the formulation 4, which is used in the resotoration problem
source
EGRIP.form_gen_cranking — Method

Generator cranking constraint (formulation 4 in the generator start-up formulation and also used in the restoration)

  • Once a non-black start generator is on, that is, $y_{g,t}=1$, then it needs to absorb the cranking power for its corresponding cranking time
  • "After" the time step that this unit satisfies its cranking constraint, its power goes to zero; and from the next time step, it becomes a dispatchable generator
    • set non-black start unit generation limits based on "generator cranking constraint"
    • cranking constraint states if generator g has absorb the cranking power for its corresponding cranking time, it can produce power
  • Mathematically if there exist enough 1 for $y_{g,t}=1$, then enable this generator's generating capability
  • There will be the following scenarios
    • (1) generator is off, then $y_{g,t}-y_{g,t-Tcr_{g}} = 0$, then $pg_{g,t} = 0$
    • (2) generator is on but cranking time not satisfied, then $y_{g,t} - y_{g,t-Tcr_g} = 1$, then $pg_{g,t} = -Pcr_g$
    • (3) generator is on and just satisfies the cranking time, then $y_{g,t} - y_{g,t-Tcr_g} = 0$, $y_{g,t-Tcr_g-1}=0$, then $pg_{g,t} = 0$
    • (4) generator is on and bigger than satisfies the cranking time, then $y_{g,t} - y_{g,t-Tcr_g} = 0$, $y_{g,t-Tcr_g-1}=1$, then $0 <= pg_{g,t} <= pg^{\max}_{g}$
  • All scenarios can be formulated as follows:

\[\begin{align*} & pg^{\min}_{g} \leq pg_{g,t} \leq pg^{\max}_{g}\\ & \text{ if }t > Tcr_{g}+1\\ & \quad\quad -Pcr_{g}(y_{g,t}-y_{g,t-Tcr_{g}}) \leq pg_{g,t} \leq pg^{\max}_{g}y_{g,t-Tcr_{g}-1}-Pcr_{g}(y_{g,t} - y_{g,t-Tcr_{g}}) \\ @@ -7,7 +7,7 @@ & \quad\quad pg_{g,t} = -Pcr_{g}y_{g,t}\\ & \text{else }\\ & \quad\quad pg_{g,t} = -Pcr_{g}(y_{g,t} - y_{g,1}) -\end{align*}\]

source
EGRIP.form_gen_cranking_1 — Method

Generator cranking constraint (formulation 1)

In the generator start-up sequence optimization problem, we consider the following cranking procedure

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_gen_cranking_1 — Method

Generator cranking constraint (formulation 1)

In the generator start-up sequence optimization problem, we consider the following cranking procedure

\[\begin{align*} p_{g}(x_g,t)=\begin{cases} 0 & 0\le t<x_{g}\\ -c_{g} & x_{g}\le t < x_{g}+t_{g}^{c}\\ @@ -42,7 +42,7 @@ \end{align*}\]

  • We can write the generation output of unit $g$ in time period $t$ as

\[\begin{align*} \label{eq_gen_power} p_g(t) = -c_gy_{gt}+ \sum_{i=1}^t{z_{gi}r_g} -\end{align*}\]

source
EGRIP.form_gen_cranking_2 — Method

Generator cranking constraint (formulation 2)

In the generator start-up sequence optimization problem, we consider the following cranking procedure

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_gen_cranking_2 — Method

Generator cranking constraint (formulation 2)

In the generator start-up sequence optimization problem, we consider the following cranking procedure

\[\begin{align*} p_{g}(x_g,t)=\begin{cases} 0 & 0\le t<x_{g}\\ -c_{g} & x_{g}\le t < x_{g}+t_{g}^{c}\\ @@ -55,7 +55,7 @@ \end{aligned} \end{align*}\]

Note that $p_{g}(i,t)$ is constant given $i$ and $t$.

  • The generator can only be started once, so we have

\[\begin{align*} \sum_{t\in T}p_{g,t}=1 -\end{align*}\]

source
EGRIP.form_gen_cranking_3 — Method

Generator cranking constraint (formulation 3)

In the generator start-up sequence optimization problem, we consider the following cranking procedure

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_gen_cranking_3 — Method

Generator cranking constraint (formulation 3)

In the generator start-up sequence optimization problem, we consider the following cranking procedure

\[\begin{align*} p_{g}(x_g,t)=\begin{cases} 0 & 0\le t<x_{g}\\ -c_{g} & x_{g}\le t < x_{g}+t_{g}^{c}\\ @@ -86,19 +86,19 @@ \end{align*}\]

  • For the last stage, we do not need to introduce new variables.

\[\begin{align*} &-M (a_{gt}+ b_{gt} + c_{gt}) \leq p_{gt} - p^{\mbox{max}} \\ & p_{gt} - p^{\mbox{max}} \leq M (a_{gt}+ b_{gt} + c_{gt}) -\end{align*}\]

source
EGRIP.form_gen_logic — Method

generator status and output constraint

  • generator ramping rate constraint

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_gen_logic — Method

generator status and output constraint

  • generator ramping rate constraint

\[\begin{align*} -Krp_{g} \leq pg_{g,t}-pg_{g,t+1} \leq Krp_{g} \end{align*}\]

  • black-start unit is determined by the cranking power

\[\begin{align*} y_{g,t}=1 \text{ if } Pcr_{g}=0 \end{align*}\]

  • on-line generators cannot be shut down

\[\begin{align*} y_{g,t} <= y_{g,t+1} -\end{align*}\]

source

Load Models

EGRIP.form_load_logic — Method

Load pickup constraint used for full restoration problem

  • restored load cannot exceed its maximum values

\[\begin{align*} +\end{align*}\]

source

Load Models

EGRIP.form_load_logic — Method

Load pickup constraint used for full restoration problem

  • restored load cannot exceed its maximum values

\[\begin{align*} & 0 \leq pl_{l,t} \leq pl^{\max}u_{l,t}\\ & 0 \leq ql_{l,t} \leq ql^{\max}u_{l,t}\\ \end{align*}\]

  • restored load cannot be shed

\[\begin{align*} & pl_{l,t-1} \leq pl_{l,t}\\ & ql_{l,t-1} \leq ql_{l,t}\\ -\end{align*}\]

source
EGRIP.form_load_logic_1 — Method

Load pickup constraint (formulation 1)

The load sequential actions are described below:

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_load_logic_1 — Method

Load pickup constraint (formulation 1)

The load sequential actions are described below:

\[\begin{align*} p_{d}(x_d,t)=\begin{cases} 0 & 0\le t < x_{d}\\ -p_{d} & x_{d}\le t\le T, @@ -115,7 +115,7 @@ \end{align*}\]

  • We can write the load $d$ in time period $t$ as

\[\begin{align*} \label{eq_load_power} p_d(t) = - y_{dt}p_d -\end{align*}\]

source
EGRIP.form_load_logic_2 — Method

Load pickup constraint (formulation 2)

The load sequential actions are described below:

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_load_logic_2 — Method

Load pickup constraint (formulation 2)

The load sequential actions are described below:

\[\begin{align*} p_{d}(x_d,t)=\begin{cases} 0 & 0\le t < x_{d}\\ -p_{d} & x_{d}\le t\le T, @@ -124,7 +124,7 @@ p_{dt}=\sum_{i=1}^{t}x_{di}p_{g}(i,t)\quad \forall t\in T \end{align*}\]

  • The load can only be started once

\[\begin{align*} \sum_{t\in T}x_{dt}=1 -\end{align*}\]

source
EGRIP.form_load_logic_3 — Method

Load pickup constraint (formulation 3)

The load sequential actions are described below:

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_load_logic_3 — Method

Load pickup constraint (formulation 3)

The load sequential actions are described below:

\[\begin{align*} p_{d}(x_d,t)=\begin{cases} 0 & 0\le t < x_{d}\\ -p_{d} & x_{d}\le t\le T, @@ -136,10 +136,10 @@ &0 \leq p_{dt} \leq M (1- e_{dt})\\ &-M e_{dt} \leq p_{dt} + p_{d} \leq M e_{dt}\\ \end{aligned} -\end{align*}\]

source

Power Flow Models

EGRIP.form_branch — Method

Branch (power flow) constraints

  • linearized power flow

\[\begin{align*} +\end{align*}\]

source

Power Flow Models

EGRIP.form_branch — Method

Branch (power flow) constraints

  • linearized power flow

\[\begin{align*} p_{bij,t}=G_{ii}(2vl_{ij,t}-x_{ij,t}) + G_{ij}(vl_{ij,t} + vl_{ji,t}-x_{ij,t}) + B_{ij}(al_{ij,t}-al_{ij,t})\\ q_{bij,t}=-B_{ii}(2vl_{ij,t}-x_{ij,t}) - B_{ij}(vl_{ij,t} + vl_{ji,t}-x_{ij,t}) + G_{ij}(al_{ij,t}-al_{ij,t})\\ -\end{align*}\]

source
EGRIP.form_nodal — Method

Form the nodal constraints:

  • voltage constraint
    • voltage deviation should be limited
    • voltage constraints are only activated if the associated line is energized

\[\begin{align*} +\end{align*}\]

source
EGRIP.form_nodal — Method

Form the nodal constraints:

  • voltage constraint
    • voltage deviation should be limited
    • voltage constraints are only activated if the associated line is energized

\[\begin{align*} & v^{\min}_{i} \leq v_{i,t} \leq v^{\max}_{i}\\ & v^{\min}_{i}x_{ij,t} \leq vl_{ij,t} \leq v^{\max}_{i}x_{ij,t}\\ & v^{\min}_{j}x_{ij,t} \leq vl_{ji,t} \leq v^{\max}_{j}x_{ij,t}\\ @@ -161,4 +161,4 @@ \end{align*}\]

  • nodal power balance constraint

\[\begin{align*} & \sum_{b\in i}p_{b,t}=\sum_{g\in i}pg_{g,t}-\sum_{l\in i}pl_{l,t}-Gs(2vb_{i,t}-u_{i,t})\\ & \sum_{b\in i}q_{b,t}=\sum_{g\in i}qg_{g,t}-\sum_{l\in i}ql_{l,t}+Bs(2vb_{i,t}-u_{i,t}) -\end{align*}\]

source

Renewable Models

EGRIP.form_wind_saa_1 — Method

Form wind power dispatch chance constraints approximated by Sample Averaged Approximation This function is associated with wind activation 1 option: wind data from normal distribution

source
EGRIP.form_wind_saa_2 — Method

Form wind power dispatch chance constraints approximated by Sample Averaged Approximation This function is associated with wind activation 2 option: wind data from real time series in a Dictionary

source
EGRIP.form_wind_saa_3 — Method

Form wind power dispatch chance constraints approximated by Sample Averaged Approximation This function is associated with wind activation 3 option: wind data given by an estimated density The chance constraints in sample-average approximation can be enforced into samples through all periods or individual periods

  • Mode 1: The chance constraints can be enforced into samples through all periods
  • Mode 2: The chance constraints can be enforced into samples through individual periods
source

Util Functions

EGRIP.load_gen — Method

Load restoration plan from parallel power system restoration (PPSR) module

source
+\end{align*}\]

source

Renewable Models

EGRIP.form_wind_saa_1 — Method

Form wind power dispatch chance constraints approximated by Sample Averaged Approximation This function is associated with wind activation 1 option: wind data from normal distribution

source
EGRIP.form_wind_saa_2 — Method

Form wind power dispatch chance constraints approximated by Sample Averaged Approximation This function is associated with wind activation 2 option: wind data from real time series in a Dictionary

source
EGRIP.form_wind_saa_3 — Method

Form wind power dispatch chance constraints approximated by Sample Averaged Approximation This function is associated with wind activation 3 option: wind data given by an estimated density The chance constraints in sample-average approximation can be enforced into samples through all periods or individual periods

  • Mode 1: The chance constraints can be enforced into samples through all periods
  • Mode 2: The chance constraints can be enforced into samples through individual periods
source

Util Functions

EGRIP.load_gen — Method

Load restoration plan from parallel power system restoration (PPSR) module

source
diff --git a/dev/ch3_sec1_development_overview/index.html b/dev/ch3_sec1_development_overview/index.html index faa6cb6..ac95986 100644 --- a/dev/ch3_sec1_development_overview/index.html +++ b/dev/ch3_sec1_development_overview/index.html @@ -1,2 +1,2 @@ -Development Overview · EGRIP.jl
Edit on GitHub
+Development Overview · EGRIP.jl
Edit on GitHub
diff --git a/dev/ch3_sec2_dev_code_loading/index.html b/dev/ch3_sec2_dev_code_loading/index.html index 58a3cbd..bdb6ec2 100644 --- a/dev/ch3_sec2_dev_code_loading/index.html +++ b/dev/ch3_sec2_dev_code_loading/index.html @@ -2,4 +2,4 @@ Code Loading · EGRIP.jl
Edit on GitHub

Code Loading

  • The current confusion is on how Julia load packages and modules that are not registered through Pkg.

Working Directory

  • The working directory, which can be obtained by pwd(), has to be the one containing our packages for things to be loaded correctly.
  • We can add the command cd(@__DIR__) at the beginning of our code to navigate the directory to where our code is running.

Package Loading

Assmue we would like to use our developed but unregistered package EGRIP.jl at a Julia file named testrun.jl. There are two ways to load EGRIP.jl.

Include the package and corresponding modules

We can include the main jl file of the package at the top of testrun.jl:

cd(@__DIR__) # navigate to correct working directory containing `testrun.jl`
 include("path to the source code from current working directory/src/EGRIP.jl")

Then, we can use the package through relative path import of the main module since it cannot be identified by Julia Environment:

using .EGRIP # It tells Julia to find the module around the current working directory instead of Julia Environment

Due to the similar reason, other modules in the package cannot be identified by Julia Environment. When module_a in file_module_a.jl needs to use a function fun_b from module_b in file_module_b.jl, we need to do the following at the beginning of file_module_a.jl (assmue file_module_a.jl and file_module_b.jl are in the same directory):

include("file_module_b.jl")
 using .module_b

Then, if fun_b has been exported, we can directly access it. Otherwise. we need to use module_b.fun_b. This is not very convenient.

Add source code directory into Julia Environment

We can make source directory accessible through Julia's LOAD_PATH. We can add the following line at the top of testrun.jl:

cd(@__DIR__) # navigate to correct working directory `testrun.jl`
-push!(LOAD_PATH,"path to the source code from current working directory/src/")

Then, we can use the package through absolute path import of the main module since it can be identified by Julia Environment:

using EGRIP # It tells Julia to find the module in Julia Environment LOAD_PATH

In addition, all other modules can be used in the same way.

Discussion on include

  • Julia’s include is a function, not a simple input redirector (as in C, Fortran, or Matlab).
  • Evaluate the contents of a source file in the current context. “The current context” means the global scope of the current module when the evaluation takes place.
  • This function is typically used to load source interactively, or to combine files in packages that are broken into multiple source files.
  • Include works in the dynamically-current module, not the lexically-current one.
  • It is really a load-time function, not a run-time one.
+push!(LOAD_PATH,"path to the source code from current working directory/src/")

Then, we can use the package through absolute path import of the main module since it can be identified by Julia Environment:

using EGRIP # It tells Julia to find the module in Julia Environment LOAD_PATH

In addition, all other modules can be used in the same way.

Discussion on include

diff --git a/dev/ch3_sec3_dev_package_org/index.html b/dev/ch3_sec3_dev_package_org/index.html index 729c2df..b92f12c 100644 --- a/dev/ch3_sec3_dev_package_org/index.html +++ b/dev/ch3_sec3_dev_package_org/index.html @@ -52,4 +52,4 @@ end

-power_flow.jl

function func_pf()
 end

-load_restoration.jl

function func_lr()
   func_pf()
-end
+end diff --git a/dev/ch4_sec1_literature/index.html b/dev/ch4_sec1_literature/index.html index 1e8b5ba..60faeb1 100644 --- a/dev/ch4_sec1_literature/index.html +++ b/dev/ch4_sec1_literature/index.html @@ -1,2 +1,2 @@ -Literature Review · EGRIP.jl
Edit on GitHub

Literature Review

There are mainly five steps for power network restoration after a partial or full outage:

  • Restoration time estimation
  • Sectionalization
  • Generator start-up optimization
  • Path search
  • Load pickup

The aforementioned problems have been studied in a separated manner. On the other hand, some researchers are focusing on solving the integrated problems. In addition, many factors such as dynamic security, black-start resource allocation, crew routing and transmission & distribution co-restoration have also been investigated. Here, we will have a brief review of current literature.

It is worth mentioning that there are already review papers on this topic:

  • D. Lindenmeyer, H. W. Dommel, and M. M. Adibi, “Power system restoration - a bibliographical survey,” Int. J. Electr. Power Energy Syst., vol. 23, no. 3, pp. 219–227, 2001.
  • Y. Liu, R. Fan, and V. Terzija, “Power system restoration: a literature review from 2006 to 2016,” J. Mod. Power Syst. Clean Energy, vol. 4, no. 3, pp. 332–341, 2016.

In addition, the following paper describes a holistic toolkit with different modules solving aforementioned restoration perspectives:

  • Y. Hou, C. C. Liu, K. Sun, P. Zhang, S. Liu, and D. Mizumura, “Computation of milestones for decision support during system restoration,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1399–1409, 2011.

1. Restoration time estimation

PaperTechnical FeaturesTest Systems
A. Assis Mota, L. T. M. Mota, and A. Morelato, “Visualization of power system restoration plans using CPM/PERT graphs,” IEEE Trans. Power Syst., vol. 22, no. 3, pp. 1322–1329, 2007.––––––-––-
R. B. Duffey and T. Ha, “The probability and timing of power system restoration,” IEEE Trans. Power Syst., vol. 28, no. 1, pp. 3–9, 2013.––––––-––-

2. Sectionalization

PaperTechnical FeaturesTest Systems
J. J. Joglekar and Y. P. Nerkar, “A different approach in system restoration with special consideration of Islanding schemes,” Int. J. Electr. Power Energy Syst., vol. 30, no. 9, pp. 519–524, 2008.––––––-––-
S. Nourizadeh, S. A. Nezam Sarmadi, M. J. Karimi, and A. M. Ranjbar, “Power system restoration planning based on Wide Area Measurement System,” Int. J. Electr. Power Energy Syst., vol. 43, no. 1, pp. 526–530, 2012.––––––-––-
J. Quirós-Tortós, P. Wall, L. Ding, and V. Terzija, “Determination of sectionalising strategies for parallel power system restoration: A spectral clustering-based methodology,” Electr. Power Syst. Res., vol. 116, pp. 381–390, 2014.––––––-––-
J. Quirós-Tortós, M. Panteli, P. Wall, and V. Terzija, “Sectionalising methodology for parallel system restoration based on graph theory,” IET Gener. Transm. Distrib., vol. 9, no. 11, pp. 1216–1225, 2015.––––––-––-
L. Sun et al., “Network partitioning strategy for parallel power system restoration,” IET Gener. Transm. Distrib., vol. 10, no. 8, pp. 1883–1892, 2016.––––––-––-
N. Ganganath, J. V. Wang, X. Xu, C. T. Cheng, and C. K. Tse, “Agglomerative clustering-based network partitioning for parallel power system restoration,” IEEE Trans. Ind. Informatics, vol. 14, no. 8, pp. 3325–3333, 2018.––––––-––-
P. Demetriou, M. Asprou, and E. Kyriakides, “A real-time controlled islanding and restoration scheme based on estimated states,” IEEE Trans. Power Syst., vol. 34, no. 1, pp. 606–615, 2019.––––––-––-
G. Patsakis, D. Rajan, I. Aravena, and S. Oren, “Strong Mixed-Integer Formulations for Power System Islanding and Restoration,” IEEE Trans. Power Syst., vol. 34, no. 6, pp. 4880–4888, 2019.––––––-––-
J. Zhao et al., “Robust Distributed Coordination of Parallel Restored Subsystems in Wind Power Penetrated Transmission System,” IEEE Trans. Power Syst., vol. 8950, no. c, pp. 1–1, 2020.––––––-––-

3. Generator start-up optimization

PaperTechnical FeaturesTest Systems
W. Sun, C. C. Liu, and L. Zhang, “Optimal generator start-up strategy for bulk power system restoration,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1357–1366, 2011.––––––-––-
X. Gu, W. Liu, and C. Sun, “Optimisation for unit restarting sequence considering decreasing trend of unit start-up efficiency after a power system blackout,” IET Gener. Transm. Distrib., vol. 10, no. 16, pp. 4187–4196, 2016.––––––-––-
Y. Zhao, Z. Lin, Y. Ding, Y. Liu, L. Sun, and Y. Yan, “A model predictive control based generator start-up optimization strategy for restoration with microgrids as black-start resources,” IEEE Trans. Power Syst., vol. 33, no. 6, pp. 7189–7203, 2018.Motivation: microgrids as black-start resources and address uncertainty; Methood: MPC + scenario reduction using mass transportation problem; no power flow models––-
R. Sun, Y. Liu, and L. Wang, “An online generator start-up algorithm for transmission system self-healing based on mcts and sparse autoencoder,” IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2061–2070, 2019.Motivation: the shortcomings of offline restoration plan; Method: Expert system based online generator start-up system ==> Monte Carlo tree search and sparse autoencoderWestern Shandong Power Grid of China
X. Gu, G. Zhou, S. Li, and T. Liu, “Global optimisation model and algorithm for unit restarting sequence considering black-start zone partitioning,” IET Gener. Transm. Distrib., vol. 13, no. 13, pp. 2652–2663, 2019.––––––-––-
L. Sun, W. Liu, C. Y. Chung, M. Ding, R. Bi, and L. Wang, “Improving the restorability of bulk power systems with the implementation of a wf-bess system,” IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2366–2377, 2019.Motivation: adtively dispatch wind and energy storage; Method: define restorability index ==> consider uncertainty and scenario reduction ==> optimal dispatch of wind and energy storage ==> Benders decomposition with restoration as master and dispatch as slaveGuangdong power system in China
L. Sun, Z. Lin, Y. Xu, F. Wen, C. Zhang, and Y. Xue, “Optimal Skeleton-Network Restoration Considering Generator Start-Up Sequence and Load Pickup,” IEEE Trans. Smart Grid, vol. 10, no. 3, pp. 3174–3185, 2019.Motivation: integrate startup and transmission line selection; Method: sequentially solve three problems: generator startup, network building and load pickupIEEE 39-bus; Guangdong power system in China
PaperTechnical FeaturesTest Systems
Y. Liu and X. Gu, “Skeleton-network reconfiguration based on topological characteristics of scale-free networks and discrete particle swarm optimization,” IEEE Trans. Power Syst., vol. 22, no. 3, pp. 1267–1274, 2007.––––––-––-
C. Wang, V. Vittal, V. S. Kolluri, and S. Mandal, “PTDF-based automatic restoration path selection,” IEEE Trans. Power Syst., vol. 25, no. 3, pp. 1686–1695, 2010.––––––-––-
F. Edström and L. Söder, “On spectral graph theory in power system restoration,” IEEE PES Innov. Smart Grid Technol. Conf. Eur., 2011.––––––-––-
W. Sun and C. C. Liu, “Optimal transmission path search in power system restoration,” Proc. IREP Symp. Bulk Power Syst. Dyn. Control - IX Optim. Secur. Control Emerg. Power Grid, IREP 2013, pp. 0–4, 2013.––––––-––-
Y. Xie, K. Song, Q. Wu, and Q. Zhou, “Orthogonal genetic algorithm based power system restoration path optimization,” Int. Trans. Electr. Energy Syst., vol. 28, no. 12, pp. 1–17, 2018.––––––-––-
S. Liao et al., “An improved two-stage optimization for network and load recovery during power system restoration,” Appl. Energy, vol. 249, no. January, pp. 265–275, 2019.––––––-––-
S. Li, X. Gu, G. Zhou, and Y. Li, “Optimisation and comprehensive evaluation of alternative energising paths for power system restoration,” IET Gener. Transm. Distrib., vol. 13, no. 10, pp. 1923–1932, 2019.––––––-––-

5. Load pickup

PaperTechnical FeaturesTest Systems
Z. Qin, Y. Hou, C. C. Liu, S. Liu, and W. Sun, “Coordinating generation and load pickup during load restoration with discrete load increments and reserve constraints,” IET Gener. Transm. Distrib., vol. 9, no. 15, pp. 2437–2446, 2015.––––––-––-
A. Gholami and F. Aminifar, “A Hierarchical Response-Based Approach to the Load Restoration Problem,” IEEE Trans. Smart Grid, vol. 8, no. 4, pp. 1700–1709, 2017.––––––-––-
A. Golshani, W. Sun, and K. Sun, “Real-Time Optimized Load Recovery Considering Frequency Constraints,” IEEE Trans. Power Syst., vol. 34, no. 6, pp. 4204–4215, 2019.––––––-––-
J. Zhao, H. Wang, Y. Liu, R. Azizipanah-Abarghooee, and V. Terzija, “Utility-oriented online load restoration considering wind power penetration,” IEEE Trans. Sustain. Energy, vol. 10, no. 2, pp. 706–717, 2019.–––––––––––––––––
J. Zhao, Y. Liu, H. Wang, and Q. Wu, “Receding horizon load restoration for coupled transmission and distribution system considering load-source uncertainty,” Int. J. Electr. Power Energy Syst., vol. 116, no. July 2019, p. 105517, 2020.–––––––––––––––––
J. Zhao, H. Wang, Q. Wu, N. D. Hatziargyriou, and F. Shen, “Distributed Risk-limiting Load Restoration for Wind Power Penetrated Bulk System,” IEEE Trans. Power Syst., vol. 8950, no. c, pp. 1–1, 2020.–––––––––––––––––

Integrated Methods

PaperTechnical FeaturesTest Systems
Qiu, Feng, and Peijie Li. "An integrated approach for power system restoration planning." Proceedings of the IEEE 105, no. 7 (2017): 1234-1252.sequentially integrated method: sectionalization==>optimize generator start-up==>path search==>solution refinementIEEE 30-bus, IEEE 118-bus
A. Golshani, W. Sun, Q. Zhou, Q. P. Zheng, and J. Tong, “Two-Stage Adaptive Restoration Decision Support System for a Self-Healing Power Grid,” IEEE Trans. Ind. Informatics, vol. 13, no. 6, pp. 2802–2812, 2017.–––––––––––––––––
Y. Jiang et al., “Blackstart capability planning for power system restoration,” Int. J. Electr. Power Energy Syst., vol. 86, pp. 127–137, 2017.–––––––––––––––––
A. Golshani, W. Sun, Q. Zhou, Q. P. Zheng, J. Wang, and F. Qiu, “Coordination of Wind Farm and Pumped-Storage Hydro for a Self-Healing Power Grid,” IEEE Trans. Sustain. Energy, vol. 9, no. 4, pp. 1910–1920, 2018.–––––––––––––––––
A. Golshani, W. Sun, Q. Zhou, Q. P. Zheng, and Y. Hou, “Incorporating Wind Energy in Power System Restoration Planning,” IEEE Trans. Smart Grid, vol. 10, no. 1, pp. 16–28, 2019.–––––––––––––––––
W. Liu, J. Zhan, C. Y. Chung, and L. Sun, “Availability Assessment Based Case-Sensitive Power System Restoration Strategy,” IEEE Trans. Power Syst., vol. 35, no. 2, pp. 1432–1445, 2020.–––––––––––––––––
+Literature Review · EGRIP.jl
Edit on GitHub

Literature Review

There are mainly five steps for power network restoration after a partial or full outage:

  • Restoration time estimation
  • Sectionalization
  • Generator start-up optimization
  • Path search
  • Load pickup

The aforementioned problems have been studied in a separated manner. On the other hand, some researchers are focusing on solving the integrated problems. In addition, many factors such as dynamic security, black-start resource allocation, crew routing and transmission & distribution co-restoration have also been investigated. Here, we will have a brief review of current literature.

It is worth mentioning that there are already review papers on this topic:

  • D. Lindenmeyer, H. W. Dommel, and M. M. Adibi, “Power system restoration - a bibliographical survey,” Int. J. Electr. Power Energy Syst., vol. 23, no. 3, pp. 219–227, 2001.
  • Y. Liu, R. Fan, and V. Terzija, “Power system restoration: a literature review from 2006 to 2016,” J. Mod. Power Syst. Clean Energy, vol. 4, no. 3, pp. 332–341, 2016.

In addition, the following paper describes a holistic toolkit with different modules solving aforementioned restoration perspectives:

  • Y. Hou, C. C. Liu, K. Sun, P. Zhang, S. Liu, and D. Mizumura, “Computation of milestones for decision support during system restoration,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1399–1409, 2011.

1. Restoration time estimation

PaperTechnical FeaturesTest Systems
A. Assis Mota, L. T. M. Mota, and A. Morelato, “Visualization of power system restoration plans using CPM/PERT graphs,” IEEE Trans. Power Syst., vol. 22, no. 3, pp. 1322–1329, 2007.––––––-––-
R. B. Duffey and T. Ha, “The probability and timing of power system restoration,” IEEE Trans. Power Syst., vol. 28, no. 1, pp. 3–9, 2013.––––––-––-

2. Sectionalization

PaperTechnical FeaturesTest Systems
J. J. Joglekar and Y. P. Nerkar, “A different approach in system restoration with special consideration of Islanding schemes,” Int. J. Electr. Power Energy Syst., vol. 30, no. 9, pp. 519–524, 2008.––––––-––-
S. Nourizadeh, S. A. Nezam Sarmadi, M. J. Karimi, and A. M. Ranjbar, “Power system restoration planning based on Wide Area Measurement System,” Int. J. Electr. Power Energy Syst., vol. 43, no. 1, pp. 526–530, 2012.––––––-––-
J. Quirós-Tortós, P. Wall, L. Ding, and V. Terzija, “Determination of sectionalising strategies for parallel power system restoration: A spectral clustering-based methodology,” Electr. Power Syst. Res., vol. 116, pp. 381–390, 2014.––––––-––-
J. Quirós-Tortós, M. Panteli, P. Wall, and V. Terzija, “Sectionalising methodology for parallel system restoration based on graph theory,” IET Gener. Transm. Distrib., vol. 9, no. 11, pp. 1216–1225, 2015.––––––-––-
L. Sun et al., “Network partitioning strategy for parallel power system restoration,” IET Gener. Transm. Distrib., vol. 10, no. 8, pp. 1883–1892, 2016.––––––-––-
N. Ganganath, J. V. Wang, X. Xu, C. T. Cheng, and C. K. Tse, “Agglomerative clustering-based network partitioning for parallel power system restoration,” IEEE Trans. Ind. Informatics, vol. 14, no. 8, pp. 3325–3333, 2018.––––––-––-
P. Demetriou, M. Asprou, and E. Kyriakides, “A real-time controlled islanding and restoration scheme based on estimated states,” IEEE Trans. Power Syst., vol. 34, no. 1, pp. 606–615, 2019.––––––-––-
G. Patsakis, D. Rajan, I. Aravena, and S. Oren, “Strong Mixed-Integer Formulations for Power System Islanding and Restoration,” IEEE Trans. Power Syst., vol. 34, no. 6, pp. 4880–4888, 2019.––––––-––-
J. Zhao et al., “Robust Distributed Coordination of Parallel Restored Subsystems in Wind Power Penetrated Transmission System,” IEEE Trans. Power Syst., vol. 8950, no. c, pp. 1–1, 2020.––––––-––-

3. Generator start-up optimization

PaperTechnical FeaturesTest Systems
W. Sun, C. C. Liu, and L. Zhang, “Optimal generator start-up strategy for bulk power system restoration,” IEEE Trans. Power Syst., vol. 26, no. 3, pp. 1357–1366, 2011.––––––-––-
X. Gu, W. Liu, and C. Sun, “Optimisation for unit restarting sequence considering decreasing trend of unit start-up efficiency after a power system blackout,” IET Gener. Transm. Distrib., vol. 10, no. 16, pp. 4187–4196, 2016.––––––-––-
Y. Zhao, Z. Lin, Y. Ding, Y. Liu, L. Sun, and Y. Yan, “A model predictive control based generator start-up optimization strategy for restoration with microgrids as black-start resources,” IEEE Trans. Power Syst., vol. 33, no. 6, pp. 7189–7203, 2018.Motivation: microgrids as black-start resources and address uncertainty; Methood: MPC + scenario reduction using mass transportation problem; no power flow models––-
R. Sun, Y. Liu, and L. Wang, “An online generator start-up algorithm for transmission system self-healing based on mcts and sparse autoencoder,” IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2061–2070, 2019.Motivation: the shortcomings of offline restoration plan; Method: Expert system based online generator start-up system ==> Monte Carlo tree search and sparse autoencoderWestern Shandong Power Grid of China
X. Gu, G. Zhou, S. Li, and T. Liu, “Global optimisation model and algorithm for unit restarting sequence considering black-start zone partitioning,” IET Gener. Transm. Distrib., vol. 13, no. 13, pp. 2652–2663, 2019.––––––-––-
L. Sun, W. Liu, C. Y. Chung, M. Ding, R. Bi, and L. Wang, “Improving the restorability of bulk power systems with the implementation of a wf-bess system,” IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2366–2377, 2019.Motivation: adtively dispatch wind and energy storage; Method: define restorability index ==> consider uncertainty and scenario reduction ==> optimal dispatch of wind and energy storage ==> Benders decomposition with restoration as master and dispatch as slaveGuangdong power system in China
L. Sun, Z. Lin, Y. Xu, F. Wen, C. Zhang, and Y. Xue, “Optimal Skeleton-Network Restoration Considering Generator Start-Up Sequence and Load Pickup,” IEEE Trans. Smart Grid, vol. 10, no. 3, pp. 3174–3185, 2019.Motivation: integrate startup and transmission line selection; Method: sequentially solve three problems: generator startup, network building and load pickupIEEE 39-bus; Guangdong power system in China
PaperTechnical FeaturesTest Systems
Y. Liu and X. Gu, “Skeleton-network reconfiguration based on topological characteristics of scale-free networks and discrete particle swarm optimization,” IEEE Trans. Power Syst., vol. 22, no. 3, pp. 1267–1274, 2007.––––––-––-
C. Wang, V. Vittal, V. S. Kolluri, and S. Mandal, “PTDF-based automatic restoration path selection,” IEEE Trans. Power Syst., vol. 25, no. 3, pp. 1686–1695, 2010.––––––-––-
F. Edström and L. Söder, “On spectral graph theory in power system restoration,” IEEE PES Innov. Smart Grid Technol. Conf. Eur., 2011.––––––-––-
W. Sun and C. C. Liu, “Optimal transmission path search in power system restoration,” Proc. IREP Symp. Bulk Power Syst. Dyn. Control - IX Optim. Secur. Control Emerg. Power Grid, IREP 2013, pp. 0–4, 2013.––––––-––-
Y. Xie, K. Song, Q. Wu, and Q. Zhou, “Orthogonal genetic algorithm based power system restoration path optimization,” Int. Trans. Electr. Energy Syst., vol. 28, no. 12, pp. 1–17, 2018.––––––-––-
S. Liao et al., “An improved two-stage optimization for network and load recovery during power system restoration,” Appl. Energy, vol. 249, no. January, pp. 265–275, 2019.––––––-––-
S. Li, X. Gu, G. Zhou, and Y. Li, “Optimisation and comprehensive evaluation of alternative energising paths for power system restoration,” IET Gener. Transm. Distrib., vol. 13, no. 10, pp. 1923–1932, 2019.––––––-––-

5. Load pickup

PaperTechnical FeaturesTest Systems
Z. Qin, Y. Hou, C. C. Liu, S. Liu, and W. Sun, “Coordinating generation and load pickup during load restoration with discrete load increments and reserve constraints,” IET Gener. Transm. Distrib., vol. 9, no. 15, pp. 2437–2446, 2015.––––––-––-
A. Gholami and F. Aminifar, “A Hierarchical Response-Based Approach to the Load Restoration Problem,” IEEE Trans. Smart Grid, vol. 8, no. 4, pp. 1700–1709, 2017.––––––-––-
A. Golshani, W. Sun, and K. Sun, “Real-Time Optimized Load Recovery Considering Frequency Constraints,” IEEE Trans. Power Syst., vol. 34, no. 6, pp. 4204–4215, 2019.––––––-––-
J. Zhao, H. Wang, Y. Liu, R. Azizipanah-Abarghooee, and V. Terzija, “Utility-oriented online load restoration considering wind power penetration,” IEEE Trans. Sustain. Energy, vol. 10, no. 2, pp. 706–717, 2019.–––––––––––––––––
J. Zhao, Y. Liu, H. Wang, and Q. Wu, “Receding horizon load restoration for coupled transmission and distribution system considering load-source uncertainty,” Int. J. Electr. Power Energy Syst., vol. 116, no. July 2019, p. 105517, 2020.–––––––––––––––––
J. Zhao, H. Wang, Q. Wu, N. D. Hatziargyriou, and F. Shen, “Distributed Risk-limiting Load Restoration for Wind Power Penetrated Bulk System,” IEEE Trans. Power Syst., vol. 8950, no. c, pp. 1–1, 2020.–––––––––––––––––

Integrated Methods

PaperTechnical FeaturesTest Systems
Qiu, Feng, and Peijie Li. "An integrated approach for power system restoration planning." Proceedings of the IEEE 105, no. 7 (2017): 1234-1252.sequentially integrated method: sectionalization==>optimize generator start-up==>path search==>solution refinementIEEE 30-bus, IEEE 118-bus
A. Golshani, W. Sun, Q. Zhou, Q. P. Zheng, and J. Tong, “Two-Stage Adaptive Restoration Decision Support System for a Self-Healing Power Grid,” IEEE Trans. Ind. Informatics, vol. 13, no. 6, pp. 2802–2812, 2017.–––––––––––––––––
Y. Jiang et al., “Blackstart capability planning for power system restoration,” Int. J. Electr. Power Energy Syst., vol. 86, pp. 127–137, 2017.–––––––––––––––––
A. Golshani, W. Sun, Q. Zhou, Q. P. Zheng, J. Wang, and F. Qiu, “Coordination of Wind Farm and Pumped-Storage Hydro for a Self-Healing Power Grid,” IEEE Trans. Sustain. Energy, vol. 9, no. 4, pp. 1910–1920, 2018.–––––––––––––––––
A. Golshani, W. Sun, Q. Zhou, Q. P. Zheng, and Y. Hou, “Incorporating Wind Energy in Power System Restoration Planning,” IEEE Trans. Smart Grid, vol. 10, no. 1, pp. 16–28, 2019.–––––––––––––––––
W. Liu, J. Zhan, C. Y. Chung, and L. Sun, “Availability Assessment Based Case-Sensitive Power System Restoration Strategy,” IEEE Trans. Power Syst., vol. 35, no. 2, pp. 1432–1445, 2020.–––––––––––––––––
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