Resilient distribution network infrastructure planning with renewable uncertainty

Abstract

We disclose a decision-dependent, opportunity-constrained optimal model for improving the resilience of a power distribution system under renewable power generation uncertainty by strategically setting up and starting dispatchable diesel generators, renewable distributed power sources, battery energy storage systems, and switchable devices. A moment-based ambiguity set is used to represent the uncertainty arising from renewable distributed power sources by incorporating information on decision variables. By leveraging convex approximations to handle the considered joint opportunity constraints, the disclosed model is transformed into an easy-to-handle mixed-integer quadratic cone programming problem to be solved.

Description

Technical Field

[0001] The present invention generally relates to power distribution systems, and more particularly to resilient distribution network infrastructure planning with renewable uncertainties.

Background Art

[0002] Over the past few decades, the frequency of extreme weather events such as hurricanes, winter storms, and earthquakes has been continuously increasing, significantly affecting the economic and environmental benefits of modern power systems. Power outages caused by these events will bring great difficulties to system operation. Therefore, grid resilience is becoming an extremely important element for protecting against extreme weather events. In particular, since most power outages are likely to occur in the distribution network, more investment needs to be made at the distribution level to improve resilience.

[0003] To achieve this goal, one appealing approach is to plan the integration of power infrastructure such as renewable distributed power sources, energy storage systems, and switchable devices. Generally, equipping them efficiently brings a number of attractive advantages. For example, renewable distributed power sources can maximize the penetration of renewable clean energy and provide the grid with many services (such as reactive power support). However, there are also a number of problems. The biggest one is how to satisfactorily internalize the uncertainties arising from renewable distributed power sources, as the energy generated by renewable distributed power sources is naturally random.

[0004] Several studies have been conducted to address the optimization of power systems with uncertainty. For example, AM Fatehbabard, J. Chen, K. Pan, and F. Chu proposed a two-stage data-driven, distributedly robust optimization model in their paper "Data-driven planning for renewable distributed generation integration," published in IEEE Trans. Power Syst., Vol. 35, No. 6, pp. 4357-4368, 2020. The proposed model determines the optimal placement of renewable distributed power resources, with both load and generation uncertainty explained by using a data-driven set of ambiguities. Another example is presented in the paper "Chance-constrained optimal power flow: Risk-aware network control under uncertainty" by D. Beanstock, M. Chertkov, and S. Harnett, published in SIAM Rev., Vol. 56, No. 3, pp. 461-495, 2014. This paper proposes a chance-constrained optimization method for elucidating optimal power flow with uncertain power generation. Yet another example can be seen in the paper "Distributionally robust chance-constrained optimal power flow with uncertain renewables and uncertain reserve provided by loads" by Y. Chang, S. Shen, and JL Matthew, published in IEEE Trans. Power Syst., Vol. 32, No. 2, pp. 1378-1388, 2017.In this paper, a distributionally robust optimization is used to elucidate the optimal power flow, the opportunity constraints are satisfied for any distribution in the ambiguity set constructed with the first two moments, and two ambiguity sets are used to reformulate the model as a semidefinite programming problem and a quadratic cone programming problem.

[0005] However, most of these approaches focus on modeling and mitigating the impact of uncertainty on power system operation problems under normal operating conditions. They fail to address power system operation requirements arising from emergency operating conditions, such as power outages caused by extreme weather events. Such emergency operating conditions require multiple measures, including operational and planning measures, to ensure that the power system has sufficient capacity to address the uncertainties that persist in normal operation through operational measures and the additional uncertainties caused by power outages through improved resilience.

[0006] Therefore, it is necessary to develop more precise methods for resilient distribution network planning with renewable uncertainty. [Overview of the Initiative]

[0007] Some embodiments of the present invention are based on the recognition that electricity is a vital infrastructure essential to the functioning of modern society. It is important to ensure that power companies are adequately prepared to respond to emergencies that could disrupt the power distribution network, such as natural disasters or fluctuations in renewable power generation.

[0008] An effective emergency response planning system can respond to such emergencies. By developing a comprehensive plan, power companies can ensure that the necessary resources and strategies are in place to respond to emergencies as quickly and efficiently as possible. Emergency response plans include dispatchable power generation resources, such as dispatchable diesel generators and battery energy storage systems, that can be activated for backup power in the event of a blackout. Topological reconfiguration via switchable devices may also be incorporated to facilitate effective coordination between various existing resources during emergencies.

[0009] By strengthening emergency response planning systems, power distribution networks can minimize the collapse caused by power outages, ensure the safety of individuals and communities during emergencies, and enable them to quickly resume normal operation, minimizing the potential impact of future collapses.

[0010] According to some embodiments of the present disclosure, a system is provided for automatically generating a network configuration of a resilient power distribution network for recovery from a power outage. The system may include an input interface configured to receive design parameters for a resilient specification for the power distribution network in terms of the minimum power-on period of loads having different priorities under the power outage, and a network configuration of the power distribution network, wherein the network configuration is represented by a digital graph map showing the locations of critical loads, buses, normal loads, branch lines of line segments, main grids, and substations on the power distribution network, wherein the digital graph map of the power distribution network includes renewable distributed power sources, dispatchable diesel generators, battery energy storage systems, and switchable devices and candidate locations to which they can be connected, and the design parameters include a first cost representing the first setup cost and size-based maintenance cost of the renewable distributed power source, a second cost representing the cost of electricity purchased from the main grid via substations under normal conditions, and a third setup cost of the dispatchable diesel generator. The system includes a third cost representing power generation costs and emission costs, a fourth cost representing the setup costs and degradation costs of the battery energy storage system, a fifth cost representing the setup costs and switching costs of the switchable device, a sixth cost representing load limiting costs, and a seventh cost representing the expected adjustment costs of uncertainties inherent in the dispatchable diesel generator, the system further includes a memory for storing the design parameters, the digital graph map of the power distribution network, and a computer-executable program including resilience improvement planning for the power distribution network module, and at least one processor associated with the memory for storing instructions for the computer-executable program, wherein the instructions are provided to the at least one processor by the first cost, the second cost, the third cost, the fourth cost, the fifth cost, the sixth cost,and perform the step of formulating an objective function for determining the network configuration of the power distribution network based on the seventh cost above, the objective function being subject to a set of constraints, the set of constraints being a distributionally robust joint opportunity constraint-based power output limit and renewable uncertainty allocation constraint for dispatchable diesel generator candidates, a charge and discharge dynamics constraint for battery energy storage system candidates, a switching operation constraint for switchable device candidates, a substation power supply constraint for blackouts, a power balance constraint for the bus under normal and blackout conditions, a normal load and critical load constraint under normal and blackout conditions, and the above on apparent power flowing The instruction includes a thermal capacity constraint for the branch wire and a bus voltage constraint in terms of squared voltage amplitude, and further causes the at least one processor to perform the steps of: constructing a decision-dependent moment-based ambiguity set based on a set of observed samples to account for the uncertainty of the reproducible prediction error for the objective function; and placing the candidates for the dispatchable diesel generator, the battery energy storage system, the reproducible distributed power source, and the switchable device at the candidate locations on the digital graph map of the power distribution network by minimizing the objective function under the set of constraints using a mixed-integer quadratic cone programming solver.

[0011] Furthermore, some embodiments of the present disclosure provide a method for automatically generating a network configuration of a resilient power distribution network for recovery from a power outage. In this case, the method may include the step of receiving, via an input interface, design parameters for a resilient specification for the power distribution network in terms of the minimum power-on period of loads having different priorities under the power outage, and a network configuration of the power distribution network, wherein the network configuration is represented by a digital graph map showing the locations of critical loads, buses, normal loads, branch lines of line segments, main grids, and substations on the power distribution network, wherein the digital graph map of the power distribution network includes renewable distributed power sources, dispatchable diesel generators, battery energy storage systems, and switchable devices and candidate locations to be connected, and the design parameters include a first cost representing the first setup cost and size-based maintenance cost of the renewable distributed power source, a second cost representing the cost of electricity purchased from the main grid via substations under normal conditions, and a third setup cost of the dispatchable diesel generator. The method further includes a third cost representing power generation costs and emission costs, a fourth cost representing a fourth setup cost and degradation cost of the battery energy storage system, a fifth cost representing a fifth setup cost and switching cost of the switchable device, a sixth cost representing load limiting costs, and a seventh cost representing expected adjustment costs for uncertainties inherent in the dispatchable diesel generator, wherein the method may further include the steps of storing the design parameters, the digital graph map of the power distribution network, and a computer-executable program including resilience improvement planning for the power distribution network module in memory, and locating at least one processor associated with the memory that stores instructions for the computer-executable program, wherein the instructions are provided to the at least one processor for the first cost, the second cost, the third cost, the fourth cost, the fifth cost, the sixth cost,and perform the step of formulating an objective function for determining the network configuration of the power distribution network based on the seventh cost above, the objective function being subject to a set of constraints, the set of constraints being a distributionally robust joint opportunity constraint-based power output limit and renewable uncertainty allocation constraint for dispatchable diesel generator candidates, a charge and discharge dynamics constraint for battery energy storage system candidates, a switching operation constraint for switchable device candidates, a substation power supply constraint for blackouts, a power balance constraint for the bus under normal and blackout conditions, a normal load and critical load constraint under normal and blackout conditions, and the above on apparent power flowing The instruction includes a thermal capacity constraint for the branch wire and a bus voltage constraint in terms of squared voltage amplitude, and further causes the at least one processor to perform the steps of: constructing a decision-dependent moment-based ambiguity set based on a set of observed samples to account for the uncertainty of the reproducible prediction error for the objective function; and placing the candidates for the dispatchable diesel generator, the battery energy storage system, the reproducible distributed power source, and the switchable device at the candidate locations on the digital graph map of the power distribution network by minimizing the objective function under the set of constraints using a mixed-integer quadratic cone programming solver.

[0012] This disclosure develops a planning model aimed at designing various power infrastructures using a distributedly robust, co-opportunity-constrained method to improve the resilience of power distribution systems. To address reproducible uncertainty, a novel moment-based set of ambiguities that contains information about the decision variables (i.e., decision-dependent) is used. This set of ambiguities can more accurately describe the uncertainty. By applying a convex approximation, the proposed model is cast as a mixed-integer quadratic cone programming problem to be solved.

[0013] The embodiments disclosed herein will be further described with reference to the attached drawings. The drawings shown are not necessarily drawn to a specific scale, and instead, the emphasis is on illustrating the principles of the embodiments disclosed herein as a whole. [Brief explanation of the drawing]

[0014] [Figure 1A] This block diagram shows a method for optimizing a resilience enhancement scheme for a power distribution system with renewable predictive uncertainty, according to an embodiment of the present disclosure. [Figure 1B] This is a block diagram showing an automatic network configuration generation system for a resilient power distribution system under reproducible predictive error uncertainty, according to some embodiments of the present invention. [Figure 2] This is a schematic diagram showing how a circular constraint is approximated as two square constraints according to an embodiment of the present disclosure. [Figure 3] This is a schematic diagram showing a sample power distribution system according to an embodiment of the present disclosure, which includes a renewable distributed generator, a dispatchable diesel generator, a battery energy storage system, and a switchable device. [Figure 4] This is a schematic diagram showing the hourly active power consumption and reactive power consumption of a sample power distribution system, shown as Figure 3, over a 24-hour period, according to an embodiment of the present disclosure. [Figure 5] This is a schematic diagram showing hourly active and reactive power of a wind power generation system over a 24-hour period, as shown in Figure 3, according to an embodiment of the present disclosure. [Figure 6] Figure 3 is a schematic diagram showing the resistance, reactance, and capacitance of a line segment of a sample power distribution system according to an embodiment of this disclosure. [Figure 7]This is a schematic diagram showing the setup results obtained for a sample power distribution system shown in Figure 3, which includes a dispatchable diesel generator, a battery energy storage system, a wind farm, and a switch, according to some embodiments of the present invention. [Figure 8] This is a schematic diagram showing a comparison of costs and reliability between the three optimization methods. [Modes for carrying out the invention]

[0015] The present invention relates in general to power distribution systems, and more specifically to resilient distribution system infrastructure planning. The following description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments provides a practical description for realizing one or more exemplary embodiments for those skilled in the art. The subject matter to be considered is a variety of modifications that can be made in terms of the function and arrangement of elements without departing from the spirit and scope of the subject matter disclosed as described in the appended claims.

[0016] Specific details are given in the following description to ensure a full understanding of the embodiments. However, those skilled in the art will understand that embodiments can be carried out without these specific details. For example, systems, processes, and other elements in the disclosed subject matter may be shown as components in the form of block diagrams so as not to obscure the embodiments with unnecessary details. In other examples, well-known processes, structures, and technologies may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, similar reference numbers and names in different drawings refer to similar elements.

[0017] Figure 1A is a block diagram showing a method for optimizing a resilience enhancement scheme for a power distribution system with renewable predictive uncertainty, according to an embodiment of the present disclosure.

[0018] Figure 1A is a block diagram showing a method 100B (i.e., a method implemented by a computer) for improving the resilience of a power distribution system to meet normal operation requirements and power outage operation requirements under reproducible uncertainties, using an interface 153, a distribution control system 157, a hardware processor 155, and a memory 158 storing instructions for causing the hardware processor to execute the steps of method 100B.

[0019] Step 125 includes method 100B of using interface 153 to receive, via a communication network, data regarding the minimum power-on periods of loads having different priorities (such as normal loads and critical loads) under a power outage, the sample moments and support of a reproducible prediction error distribution, and the risk factors of diesel power generation limit violations.

[0020] Step 130 includes method 100B of using hardware processor 155 to construct an optimal model for improving the resilience of the power distribution system to meet the operation requirements in normal and power outage states under reproducible power generation uncertainties by utilizing distributed robust joint opportunity constraints.

[0021] Referring to step 132 in Figure 1A, hardware processor 155 constructs a decision-dependent moment-based ambiguity set for modeling reproducible prediction uncertainties using the sample mean, the sample covariance, and the lower and upper bounds in all dimensions of the support.

[0022] Step 134 includes using hardware processor 155 to cast the constructed model as a mixed integer second-order cone programming problem by applying convex approximation and the constructed ambiguity set.

[0023] Step 136 includes using hardware processor 155 to solve the cast mixed integer second-order cone programming problem to determine an optimal scheme for improving the resilience of the power distribution system.

[0024] Step 138 uses the hardware processor 155 to transmit the determined resilience enhancement scheme to the distribution control system 157, which controls and operates the power distribution system.

[0025] Still referring to step 140 in Figure 1A, method 100B includes using a distribution control system 157 to set up and start up renewable distributed generators, dispatchable diesel generators, battery energy storage systems, and switchable devices via a communication network at determined locations given by the determined resilience enhancement scheme. Method 100B further transmits a digital graph map of the power distribution network to the distribution control system (external system 101). In this case, according to the result of the minimized / solved objective function, candidates for dispatchable diesel generators, battery energy storage systems, renewable distributed power sources, and switchable devices are placed / determined on candidate locations on the digital graph map of the power distribution network, and as a result, when displayed on the distribution control system's display monitor, the distribution control system can instruct to set up and start up renewable distributed generators, dispatchable diesel generators, battery energy storage systems, and switchable devices at determined locations according to the determined resilience enhancement scheme. This allows control of the installation and setup operations of equipment located in the power distribution system 115.

[0026] Figure 1B is a block diagram of an automatic network configuration generation system for improving the resilience of a power distribution system, according to some embodiments of the present invention.

[0027] The automated resilience enhancement generation system 100 includes a human-machine interface (HMI) 167 connectable to a keyboard 111 and a pointing device / medium 112, a processor 155, a storage device 154, a memory 137, a network interface controller 163 (NIC) connectable to a network 151 including a local area network and an internet network, a display interface 161 connected to a display device 165, an input interface 139 connectable to an input device 135, and a printer interface 133 connectable to a printing device 131. The memory 137 is configured to load a resilience enhancement generation program 159 by associating it with the storage device 154 when performing method 100B. In some cases, the memory 137 and the storage device 154 may be referred to as memory.

[0028] The resilience enhancement generation system 100 can receive parameters 195 indicating the equipment settings and status of the power distribution system 115, as well as the settings and status of the entire system, via a network 151 connected to the NIC 163. The network 151 is connected to an external system 101 that can provide / transmit control signals (resilience enhancement commands) to the power distribution system microgrid 115 for performing resilience enhancement and resilient operation under normal and power outage conditions. Furthermore, the resilience enhancement system 100 can provide resilience enhancement commands (signals) to the external system 101 via the network 151 so that the external system 101 can control the installation and configuration operations of equipment placed in the power distribution system 115. In addition, the resilience enhancement system 100 is controllable by the user from the external system 101, and the user can use the external system 101 to transmit control data (command signals) to the resilience enhancement system 100 via the network 151.

[0029] The storage device 154 includes design parameters 158 for the resilience specification relating to the power distribution system 115 and a resilience enhancement program module 159. The input device / medium 135 may include a module for reading a program stored on a computer-readable recording medium (not shown). The design parameters for the resilience specification can be expressed in terms of costs, which include a first cost representing the first setup cost and size-based maintenance cost of a renewable distributed power source; a second cost representing the cost of electricity purchased from the main grid via a substation under normal conditions; a third cost representing the third setup cost, generation cost and emission cost of a dispatchable diesel generator; a fourth cost representing the fourth setup cost and degradation cost of a battery energy storage system; a fifth cost representing the fifth setup cost and switching cost of a switchable device; a sixth cost representing load limiting costs; and a seventh cost representing the expected adjustment cost for uncertainty inherent in the dispatchable diesel generator.

[0030] To determine a resilience enhancement scheme for the power distribution system 115, the resilience enhancement system 100 may receive status and configuration data 195 of the power distribution system 115 via communication 180. This status and configuration data may include the on / off status and capacity limits of switchable devices, the charge status and power and energy limits of the battery energy storage system, the power output and power limits of the diesel and renewable generators, the load demand of critical and normal loads, and the power flow and power limits of line segments and other branch lines. The resilience enhancement scheme specifies the installation of additional renewable distributed generators, dispatchable diesel generators, battery energy storage systems, and switchable devices into the existing power distribution system.

[0031] According to some embodiments of the present invention, the power distribution system 115 may include a terminal bus connected to a line segment and a set of switchable devices attached to a portion of the line segment, a set of loads which may be identified as critical loads having special power-on requirements during a power outage, and a set of power generation resources which may include dispatchable diesel generators, renewable distributed generators, and battery energy storage systems. The power distribution system 115 is controlled and operated by a distribution control system (not shown). The distribution control system (attached to an external system 101) may include a human-machine interface (HMI) connectable to a keyboard and pointing device / medium, a processor, storage devices, memory, a network interface controller (NIC) connectable to networks including a local area network and an internet network, a display interface connected to a display device, and an input interface connectable to an input device. The memory is configured to load a distribution control program by associating it with a storage device. The distribution control system may further include a control interface configured to connect to sensors for equipment within the power distribution system 115 and to operate and control the power distribution system 115 by executing a distribution control program in response to receiving resilience enhancement commands from the resilience enhancement generation system 100, which indicate resilience specifications and renewable predictive uncertainty for setting up and starting up additional renewable distributed generators, dispatchable diesel generators, battery energy storage systems, and switches at candidate locations on a digital graph map representing the power distribution system 115 to meet specified resilience requirements under renewable power generation uncertainty. In this case, the resilience enhancement commands are sent from the resilience enhancement generation system 100 to the distribution control system. In some cases, an external system 101 may be referred to as the distribution control system, and the distribution control system is attached to the external system 101 to control the power distribution system via the external system 101.Furthermore, resilience enhancement commands may be sent to a display monitor, including a display interface (not shown) attached to the external system 101, to inform the operator of the external system 101 of status updates or warnings regarding the power outage status and the current resilience status.

[0032] The resilience enhancement generation system 100 uses resilience enhancement commands to display the resilience status of the power distribution system 115 on the display monitor of the external system 101 by sending resilience enhancement commands to the display interface of the display monitor attached to the external system 101. The resilience enhancement generation system 100 uses interface 153 to receive real-time or forecast data indicating resilience requirements and renewable power generation uncertainty via network 151 (communication network). Memory 137 can load a computer-executable program stored in storage 154, which includes a set of parameters 158 for resilience and uncertainty specifications and a resilience enhancement program (module) 159 configured to determine the optimal scheme for resilience enhancement of the power distribution system 115. At least one processor 155 is used in association with memory 137 and interface 153 to execute the resilience enhancement program 159 loaded from storage 154. For example, when the resilience enhancement program 159 is executed by the processor 155, the processor 155 receives data 195 from the power distribution system 115 regarding the minimum power-on period for loads with different priorities under a power outage, sample moments of the regenerative predictive error distribution, and risk factors for diesel power limit violations. The processor 155 then executes the resilience enhancement program to build an optimal model for improving the resilience of the power distribution system to meet operating requirements under normal conditions, power outage conditions, and regenerative power generation uncertainty by utilizing a distributionally robust joint opportunity constraint, and constructs a decision-dependent moment-based set of ambiguities to model the regenerative predictive uncertainty.After the optimization model and ambiguity set are constructed, the resilience enhancement program 159 further requests the processor 155 to transform the constructed model into a mixed-integer quadratic cone programming problem by applying convex approximation and the constructed ambiguity set, then solve the transformed mixed-integer quadratic cone programming problem to obtain the optimal scheme for resilience enhancement and strategically place dispatchable diesel generators, renewable distributed power sources, battery energy storage systems, and switchable devices within the power distribution system. The processor 155 then transmits the determined optimal scheme for resilience enhancement to the distribution control system to activate the actual resilience enhancement actions. Furthermore, the interface (NIC) 163 can receive data 195 indicating resilience and uncertainty specifications from the power distribution system 115 via the network 151 at pre-set intervals. If the resilience enhancement system 100 does not determine the required resilience enhancement for the power distribution system 115 while receiving the current resilience status of the power distribution system 115 and forecasts of power outages and uncertainties for the power distribution system 115, the resilience enhancement system 100 generates a normal status command and transmits the normal status command signal via the network 151 to the display interface of a display monitor attached to the external system 101, thereby displaying the sufficient resilience status of the power distribution system 115 on the display monitor of the external system 101. The sufficient resilience status and resilience enhancement command data generated by the resilience enhancement system 100 may be transmitted via the network 151 to the distribution control system (other control systems) so that they can monitor the resilience and operational status of the power distribution system 115.

[0033] In some cases, commands to initiate / execute resilience enhancement may be sent to the resilience enhancement system 100 using the keyboard 111 or from an external system 101 via the network 151. Model Formulation

[0034] This section first presents a planning model for a power distribution network consisting of normal conditions with reproducible predictive uncertainty and power outage conditions caused by extreme weather events. Next, moment-based ambiguity sets are introduced. Planning Model

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[0046] To address the disclosed models while incorporating the probabilistic nature and variability of reproducible uncertainty, the design of a clearly defined set of ambiguities is essential.

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[0051] As a result, (11) and (12) constitute a decision-dependent, moment-based set of ambiguities. solution

[0052] In this section, we will examine the solution method for our planning model. Reformulation of the objective function

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[0056] Furthermore, under the ambiguity set (11), each distributionally robust opportunity constraint (15a) acknowledges a deterministic quadratic cone programming problem, as revealed by the following theorem.

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[0058] By reformulating the joint opportunity constraint (2c) using (16), (2c) is ultimately transformed into a readily implementable quadratic cone programming problem. Reformulation of (8d)

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[0060] In this disclosure, the circular constraint (9) is approximated using two square constraints, which provides a sufficient level of accuracy for practical applications.

[0061] Figure 2 shows a circular constraint 210 approximated as two square constraints 220 and 230. Circuit constraints are used to restrict the variation of two variables to within a closed circle, with these two variables represented on the horizontal and vertical axes, respectively.

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[0063] In summary, by utilizing (13) to address the worst-case cost function (1h), using (16) to address the distributionally robust joint opportunity constraint (2c), and applying (17) and (18) to address (8d) and (9), the proposed planning model can be transformed into a manageable mixed-integer quadratic cone programming problem, which can be easily solved by commercially available solvers, as it significantly reduces computational complexity, memory size, and computation time while improving computational capabilities. A typical example of optimizing distribution network infrastructure.

[0064] This section describes a modified IEEE33 bus test system to verify the validity of our disclosed model.

[0065] Figure 3 shows the structure of a modified IEEE 33-bus test system having a network configuration represented by a digital graph map, which has nodes stored in memory that include candidate locations on the digital graph map for candidate resilience enhancement measures such as a dispatchable diesel generator 301, a renewable distributed generator (i.e., a wind farm) 302, a battery energy storage system 303, and a switchable device 304. The system is connected to the main grid via a substation 305 during normal operation and disconnected from the main grid during a power outage. The critical load 306 with the highest power supply priority will ensure the minimum power-on period after a power outage as defined by the resilience specification.

[0066] In Figure 3, two candidates for dispatchable diesel generators are located on buses 15 and 21, respectively; two candidates for energy storage systems are located on buses 7 and 29, respectively; and two candidate locations for wind farms are located on buses 17 and 31, respectively. Each bus except bus 0 is equipped with loads, with the critical load located on bus 19. Three candidates for switches are located on branch lines (2,22), (5,6), and (27,28), respectively.

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[0068] The system has one substation located on bus 0, which is connected to the main grid. The purchase costs for active and reactive power are $0.08 / kWh and $0.00 / kVar, respectively. The bus voltage tolerance is 0.90 to 1.10 per unit.

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[0070] There are two candidate locations for the wind farm. Figure 5 shows typical hourly active and reactive power generation forecasts for a wind farm. It is assumed that active and reactive power generation are identical, and that the renewable forecast follows the same contour for the first 24 hours and the next 24 hours. The setup and maintenance costs for the wind farm are $0.4 × 10⁻⁶. 2 The price is $10 / kWh, and the capacity is 200kVA.

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[0072] The setup cost and degradation cost factors for a battery energy storage system are $0.1 × 10⁻⁶. 1 and are 0.0035. The charging efficiency and discharging efficiency are both set to 0.95. The maximum charging power and maximum discharging power are set to 100kW. The minimum and maximum charging power are set to 40kW and 180kW, respectively.

[0073] The system has 32 track segments. Figure 6 shows the corresponding resistance and reactance per unit, as well as the maximum capacitance, for each track segment in the system.

[0074] The three candidate line segments can implement normally closed switches. The setup cost, isolation cost, and connection cost for each candidate switch are 0.2 × 10⁻⁶, respectively. 6 The rates are $ / kWh, $10, and $10. The maximum number of switching cycles is 24. Setup performance

[0075] Figure 7 shows the setup performance of the diesel generator, energy storage system, wind farm, and switch.

[0076] In Figure 7, "1" means that the equipment will be installed, and "0" means that it will not. As shown in Figure 7, it can be seen that the setup decision is influenced by its cost. For example, increasing the setup cost of an energy storage system will result in completely different setup performance for these two energy storage systems. This is reasonable because there is a trade-off between setup cost and operating cost. If the setup cost is high, it becomes uneconomical to install the associated equipment. Compare with other methods

[0077] To further evaluate the effectiveness of the disclosed method (referred to as M1), the following two other methods are applied here for comparison.

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[0080] Furthermore, M2 and M3 can also be reformulated as quadratic cone programming problems by redefining the individual opportunity constraints (15a). 6 The cost and minimum reliability results for security constraints (2c) based on individual samples are reported in Figure 8.

[0081] As can be seen from Figure 8, M2 has the lowest total cost among the three methods because it incorporates uncertainty using a specific Gaussian distribution, which is often aggressive. Furthermore, M1 is more expensive than M3 because the decision-dependent set of ambiguities constructed in M1 explains uncertainty more accurately. Regarding reliability results, M1 and M3 can satisfy the reliability requirement (i.e., 90%), while M2 cannot. M1 has the highest reliability level, demonstrating the superior performance of the proposed method.

Claims

1. A system for automatically generating a network configuration for a resilient power distribution network to recover from power outages, The system comprises an input interface configured to receive design parameters for a resilient specification for a power distribution network in terms of the minimum power-on period for loads having different priorities under the aforementioned power outage, and the network configuration of the power distribution network, wherein the network configuration is represented by a digital graph map showing the locations of critical loads, buses, normal loads, branch lines of line segments, main grids, and substations on the power distribution network, the digital graph map of the power distribution network includes renewable distributed power sources, dispatchable diesel generators, battery energy storage systems, and switchable devices and connectable candidate locations, and the design parameters are, A first cost representing the first setup cost and size-based maintenance cost of the renewable distributed power source, A second cost representing the cost of electricity purchased from the main grid via substations under normal conditions, A third cost representing the third setup cost, power generation cost, and emission cost of the dispatchable diesel generator, A fourth cost representing the fourth setup cost and degradation cost of the battery energy storage system, A fifth cost representing the fifth setup cost and switching cost of the switchable device, A sixth cost representing the load limiting costs for the normal load and critical load, The system further includes a seventh cost representing the expected adjustment cost of the uncertainty inherent in the dispatchable diesel generator, and the system further includes, A memory for storing the design parameters, the digital graph map of the power distribution network, and a computer-executable program including resilience improvement planning for the power distribution network module. The computer comprises at least one processor associated with the memory that stores instructions for a program executable by the computer, and the instructions are transmitted to the at least one processor. The instruction causes the instruction to perform the step of formulating an objective function for determining the network configuration of the power distribution network based on the first cost, the second cost, the third cost, the fourth cost, the fifth cost, the sixth cost, and the seventh cost, the objective function taking a set of constraints, the set of constraints including a distributedly robust joint opportunity constraint-based power output limit and renewable uncertainty allocation constraint for dispatchable diesel generator candidates, a charge and discharge dynamics constraint for battery energy storage system candidates, a switching operation constraint for switchable device candidates, a substation power supply constraint for blackouts, a power balance constraint for the bus under normal and blackout conditions, a normal load and critical load constraint under normal and blackout conditions, a thermal capacity constraint for the branch lines on flowing apparent power, and a bus voltage constraint in terms of squared voltage amplitude, the instruction further causes the instruction to the at least one processor, To explain the uncertainty of the reproducible prediction error for the objective function, the steps include constructing a decision-dependent, moment-based set of ambiguities based on a series of observed samples, A system that causes a mixed-integer quadratic cone programming solver to minimize the objective function under the set of constraints, thereby placing the candidate dispatchable diesel generator, the candidate battery energy storage system, the renewable distributed power source, and the candidate switchable device at the candidate locations on the digital graph map of the power distribution network.

2. The system according to claim 1, wherein the output constraints of the candidate dispatchable diesel generators include time interval active and reactive power generation limits using corresponding minimum and maximum active and reactive power weighted by generator availability, and probabilistic constraints on joint upper and lower limits of active power generation taking into account regenerative prediction error, wherein generator availability indicates whether a candidate generator is selected.

3. The system according to claim 1, wherein the constraint on the excitation coefficient of the candidate dispatchable diesel generator is determined to compensate for the sum of the regenerative power prediction errors of the candidate dispatchable diesel generator.

4. The system according to claim 1, wherein the constraints of the battery energy storage system are the charging power and discharging power limits of the battery energy storage system, the charging and discharging binary state related to storage availability, the energy storage dynamics relationship between charging power and discharging power, and the minimum and maximum energy storage limits for storage energy, and storage availability indicates whether a candidate battery energy storage system is selected.

5. The constraints on the candidate switchable device are the maximum number of switching operations over the planning horizon, the relationship between the switching operation and the switching status, and the relationship between the switching statuses based on switch availability, and the switch availability indicates whether the candidate switchable device is selected, according to claim 1.

6. The system according to claim 1, wherein the constraints on the substation indicate that active power and reactive power will not be supplied to the substation during the power outage.

7. The power balance constraint for each bus indicates that, for each time interval of the planning horizon, the injected active and reactive power must match the corresponding extracted active and reactive power, wherein the injected power is power from branch lines, substations, dispatchable diesel generators, connected regenerative generators, and discharge power from storage connected to the bus, and the extracted power is power from branch lines, substations, dispatchable diesel generators, connected regenerative generators, charging power from storage, and demand from load-limited loads connected to the bus, according to claim 1.

8. The system according to claim 1, wherein the constraints on the load in the event of a power outage and under normal conditions are that there is no load interruption at any normal time interval for normal loads and critical loads, the minimum number of time intervals under the power outage without load limiting for critical loads, and the total load guaranteed for critical loads during the period defined by the minimum number of time intervals, and the total load condition indicates whether or not the load limiting exists.

9. The system according to claim 1, wherein the thermal capacity constraint for each of the branch lines indicates that the power flow on the branch line is limited by an apparent power limit weighted by the branch line condition, the branch line condition indicates the connection condition of the branch line, and the thermal capacity constraint is expressed as a circular constraint to limit the sum of the squared active power and squared reactive power flowing on the branch line using the product of the squared branch line thermal capacity and the squared branch line connection condition.

10. The system according to claim 1, wherein the bus voltage constraint for the bus is expressed as a linear function of the branch connection status and the squared voltage amplitude by using minimum and maximum limits for the squared voltage amplitude in the bus and the drop in the squared voltage amplitude between terminal buses for each branch, and the drop in the squared voltage amplitude is expressed as a linear combination of active power and reactive power using branch resistance and reactance parameters. 【Request Item 11】 【Number 1】 [Request Item 12] [Number 2] [Request Item 13] [Number 3] [Request Item 14] [Number 4] [Request Item 15] [Number 5]

16. The system according to claim 1, wherein the seventh cost, representing the expected power generation cost in the worst case, is reformulated as a linear function of the excitation coefficient of the diesel generator using a sample mean of the sum of renewable power prediction errors for each time interval. [Request Item 17] [Number 6] [Request Item 18] [Number 7]

19. The system according to claim 1, wherein the at least one processor transmits a resilience enhancement command to the distribution control system in order to display to the operator of the distribution control system status updates or warnings regarding the power outage status and the current resilience status.

20. The system according to claim 1, wherein the at least one processor transmits the digital graph map of the power distribution network to a distribution control system, and the candidates for dispatchable diesel generators, battery energy storage systems, renewable distributed power sources, and switchable devices are arranged at the candidate locations on the digital graph map of the power distribution network according to the result of the minimized objective function.

21. A method for automatically generating a network configuration for a resilient power distribution network to recover from a power outage, The process includes receiving, via an input interface, design parameters for a resilient specification for a power distribution network in terms of the minimum power-on period for loads having different priorities under the aforementioned power outage, and the network configuration of the power distribution network, wherein the network configuration is represented by a digital graph map showing the locations of critical loads, buses, normal loads, branch lines of line segments, main grids, and substations on the power distribution network, the digital graph map of the power distribution network includes renewable distributed power sources, dispatchable diesel generators, battery energy storage systems, and switchable devices and connectable candidate locations, and the design parameters are, A first cost representing the first setup cost and size-based maintenance cost of the renewable distributed power source, A second cost representing the cost of electricity purchased from the main grid via substations under normal conditions, A third cost representing the third setup cost, power generation cost, and emission cost of the dispatchable diesel generator, A fourth cost representing the fourth setup cost and degradation cost of the battery energy storage system, A fifth cost representing the fifth setup cost and switching cost of the switchable device, A sixth cost representing the load limiting costs for normal and critical loads, The method further includes a seventh cost representing the expected adjustment cost of the uncertainty inherent in the dispatchable diesel generator, and the method further includes, The steps include storing the design parameters, the digital graph map of the power distribution network, and a computer-executable program including resilience improvement planning for the power distribution network module in memory, The steps include locating at least one processor associated with the memory that stores instructions for a program executable by the computer, wherein the instructions are to be executed by the at least one processor, The instruction causes the instruction to perform the step of formulating an objective function for determining the network configuration of the power distribution network based on the first cost, the second cost, the third cost, the fourth cost, the fifth cost, the sixth cost, and the seventh cost, the objective function taking a set of constraints, the set of constraints including a distributedly robust joint opportunity constraint-based power output limit and renewable uncertainty allocation constraint for dispatchable diesel generator candidates, a charge and discharge dynamics constraint for battery energy storage system candidates, a switching operation constraint for switchable device candidates, a substation power supply constraint for blackouts, a power balance constraint for the bus under normal and blackout conditions, a normal load and critical load constraint under normal and blackout conditions, a thermal capacity constraint for the branch lines on flowing apparent power, and a bus voltage constraint in terms of squared voltage amplitude, the instruction further causes the instruction to the at least one processor, To explain the uncertainty of the reproducible prediction error for the objective function, the steps include constructing a decision-dependent, moment-based set of ambiguities based on a series of observed samples, A method for causing a mixed-integer quadratic cone programming solver to minimize the objective function under the set of constraints, thereby placing the candidate dispatchable diesel generator, the candidate battery energy storage system, the renewable distributed power source, and the candidate switchable device at the candidate locations on the digital graph map of the power distribution network.

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