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The problem statements cover key operational details such as scheduling objectives, state of charge, charging and discharging power, efficiency, and operating constraints. These examples turn storage requirements into optimization programs for code SFT, scheduling logic learning, and algorithm prototyping for flow battery energy storage systems.\u003C\u002Fp>","2026-10-09 19:03:54","2026-10-19 17:19:10","0.00",32,0,5000,"flow battery, energy scheduling, storage optimization, optimization code, code generation, code SFT, charge discharge scheduling, state of charge","Paired flow battery scheduling problems and optimization code covering state of charge, power, efficiency, and operating constraints for code SFT and storage-al","JSON","0.5GB","flow battery energy management, energy storage scheduling, power system optimization","code generation, energy scheduling optimization, constraint-based programming","V1.0",[583,588,593],{"id":573,"name":584,"field":585,"intro":586,"type":587},"File Name","file_name","File name","string",{"id":589,"name":590,"field":591,"intro":592,"type":587},7859,"Optimized Scheduling Code","optimization_code","Optimization program for flow battery energy scheduling generated from the scheduling problem description.",{"id":594,"name":595,"field":596,"intro":597,"type":587},7860,"Scheduling Problem Description","scheduling_problem","Source text specifying requirements such as scheduling objectives, state of charge, charging and discharging power, efficiency, and operating constraints.",[599,603,607,611,615],{"id":600,"question":601,"answer":602},5771,"What does the dataset contain?","Each example pairs a scheduling problem description with corresponding flow battery energy scheduling optimization code. The problem statements may cover scheduling objectives, state of charge, charging and discharging power, efficiency, and operating limits.",{"id":604,"question":605,"answer":606},5772,"Which model training tasks is it designed for?","The dataset is intended for text-to-code code SFT. It can help train models to interpret flow battery scheduling requirements and generate related optimization programs, and can also support scheduling logic analysis and algorithm prototyping.",{"id":608,"question":609,"answer":610},5773,"Does the dataset specify a programming language or optimization solver?","The available information does not specify a programming language, solver, or standardized runtime environment. Before use, review the code conventions in the examples and adapt or validate them for the target training framework or deployment environment.",{"id":612,"question":613,"answer":614},5774,"How can the data be obtained and used?","Contact the dataset provider for the files and delivery details. Preserve the pairing between each problem description and its code, and apply any required format conversion, quality checks, and dataset splitting for your task.",{"id":616,"question":617,"answer":618},5775,"What are the licensing terms and usage boundaries?","The licensing scope is governed by the terms published by the dataset provider. The examples are suited to model training, research, and scheduling algorithm prototyping; review them against device parameters, safety requirements, and engineering validation results before deploying a real storage system.",[620,628,634],{"id":621,"relate_table":622,"relate_id":623,"file_size":573,"file_name":8,"path":8,"duration":573,"cate":483,"file_format":8,"audio_rate":8,"audio_channel":522,"audio_bit_depth":522,"quality":8,"annotation":624,"cate_name":625,"optimization_code":626,"scheduling_problem":627},14645,"union_cubo",568161858,"{\"optimization_code\": \"import cvxpy as cp\\nimport numpy as np\\n\\ndef optimize_profile_tracking():\\n    demand = np.array([5.5, 5.2, 5.0, 5.4, 6.2, 6.8, 6.4, 5.8])\\n    renewable = np.array([1.0, 1.2, 1.8, 2.4, 1.7, 0.8, 0.3, 0.2])\\n    target_import = np.array([4.3, 4.0, 3.6, 3.4, 4.2, 5.0, 5.4, 5.0])\\n    n = len(demand)\\n    dt = 0.25\\n\\n    energy_min, energy_max = 0.8, 7.2\\n    initial_energy = 4.4\\n    charge_max = discharge_max = 2.0\\n    eta_charge = eta_discharge = 0.90\\n    ramp_limit = 0.75\\n    tracking_penalty = 120.0\\n    throughput_cost = 0.8\\n\\n    charge = cp.Variable(n, nonneg=True)\\n    discharge = cp.Variable(n, nonneg=True)\\n    energy = cp.Variable(n + 1)\\n    charging_mode = cp.Variable(n, boolean=True)\\n    deviation_above = cp.Variable(n, nonneg=True)\\n    deviation_below = cp.Variable(n, nonneg=True)\\n\\n    battery_net_output = discharge - charge\\n    net_import = demand - renewable + charge - discharge\\n    constraints = [\\n        energy[0] == initial_energy,\\n        energy[n] == initial_energy,\\n        energy_min \u003C= energy,\\n        energy \u003C= energy_max,\\n        charge \u003C= charge_max * charging_mode,\\n        discharge \u003C= discharge_max * (1 - charging_mode),\\n        net_import - target_import == deviation_above - deviation_below,\\n    ]\\n    for t in range(n):\\n        constraints.append(\\n            energy[t + 1] == energy[t]\\n            + eta_charge * charge[t] * dt\\n            - discharge[t] * dt \u002F eta_discharge\\n        )\\n    for t in range(1, n):\\n        constraints += [\\n            battery_net_output[t] - battery_net_output[t - 1] \u003C= ramp_limit,\\n            battery_net_output[t - 1] - battery_net_output[t] \u003C= ramp_limit,\\n        ]\\n\\n    tracking_cost = tracking_penalty * dt * cp.sum(\\n        deviation_above + deviation_below\\n    )\\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\\n    problem = cp.Problem(cp.Minimize(tracking_cost + cycling_cost), constraints)\\n    problem.solve(solver='SCIP')\\n\\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\\n        raise RuntimeError(f'Optimization failed: {problem.status}')\\n\\n    return {\\n        'objective_usd': float(problem.value),\\n        'net_import_mw': np.round(net_import.value, 3).tolist(),\\n        'charge_mw': np.round(charge.value, 3).tolist(),\\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\\n        'energy_mwh': np.round(energy.value, 3).tolist(),\\n        'tracking_deviation_mw': np.round(\\n            deviation_above.value + deviation_below.value, 3\\n        ).tolist(),\\n    }\\n\\nif __name__ == '__main__':\\n    print(optimize_profile_tracking())\", \"scheduling_problem\": \"Dispatch an 8 MWh flow battery in eight 15-minute intervals to track a requested site net-import profile. Site demand is [5.5, 5.2, 5.0, 5.4, 6.2, 6.8, 6.4, 5.8] MW, renewable generation is [1.0, 1.2, 1.8, 2.4, 1.7, 0.8, 0.3, 0.2] MW, and the target net import is [4.3, 4.0, 3.6, 3.4, 4.2, 5.0, 5.4, 5.0] MW. The battery starts and ends at 4.4 MWh, must remain between 0.8 and 7.2 MWh, and has 2 MW charge and discharge limits. Use 90% charging and discharging efficiencies. Limit the change in battery net output between adjacent intervals to 0.75 MW. Minimize absolute net-import tracking error weighted at 120 USD\u002FMWh of deviation, plus a throughput cost of 0.8 USD\u002FMWh. Use a 0.25-hour time step, permit net export if the schedule requires it, and prevent simultaneous charging and discharging. Implement the mixed-integer optimization in CVXPY with SCIP.\"}","文本","import cvxpy as cp\nimport numpy as np\n\ndef optimize_profile_tracking():\n    demand = np.array([5.5, 5.2, 5.0, 5.4, 6.2, 6.8, 6.4, 5.8])\n    renewable = np.array([1.0, 1.2, 1.8, 2.4, 1.7, 0.8, 0.3, 0.2])\n    target_import = np.array([4.3, 4.0, 3.6, 3.4, 4.2, 5.0, 5.4, 5.0])\n    n = len(demand)\n    dt = 0.25\n\n    energy_min, energy_max = 0.8, 7.2\n    initial_energy = 4.4\n    charge_max = discharge_max = 2.0\n    eta_charge = eta_discharge = 0.90\n    ramp_limit = 0.75\n    tracking_penalty = 120.0\n    throughput_cost = 0.8\n\n    charge = cp.Variable(n, nonneg=True)\n    discharge = cp.Variable(n, nonneg=True)\n    energy = cp.Variable(n + 1)\n    charging_mode = cp.Variable(n, boolean=True)\n    deviation_above = cp.Variable(n, nonneg=True)\n    deviation_below = cp.Variable(n, nonneg=True)\n\n    battery_net_output = discharge - charge\n    net_import = demand - renewable + charge - discharge\n    constraints = [\n        energy[0] == initial_energy,\n        energy[n] == initial_energy,\n        energy_min \u003C= energy,\n        energy \u003C= energy_max,\n        charge \u003C= charge_max * charging_mode,\n        discharge \u003C= discharge_max * (1 - charging_mode),\n        net_import - target_import == deviation_above - deviation_below,\n    ]\n    for t in range(n):\n        constraints.append(\n            energy[t + 1] == energy[t]\n            + eta_charge * charge[t] * dt\n            - discharge[t] * dt \u002F eta_discharge\n        )\n    for t in range(1, n):\n        constraints += [\n            battery_net_output[t] - battery_net_output[t - 1] \u003C= ramp_limit,\n            battery_net_output[t - 1] - battery_net_output[t] \u003C= ramp_limit,\n        ]\n\n    tracking_cost = tracking_penalty * dt * cp.sum(\n        deviation_above + deviation_below\n    )\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\n    problem = cp.Problem(cp.Minimize(tracking_cost + cycling_cost), constraints)\n    problem.solve(solver='SCIP')\n\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\n        raise RuntimeError(f'Optimization failed: {problem.status}')\n\n    return {\n        'objective_usd': float(problem.value),\n        'net_import_mw': np.round(net_import.value, 3).tolist(),\n        'charge_mw': np.round(charge.value, 3).tolist(),\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\n        'energy_mwh': np.round(energy.value, 3).tolist(),\n        'tracking_deviation_mw': np.round(\n            deviation_above.value + deviation_below.value, 3\n        ).tolist(),\n    }\n\nif __name__ == '__main__':\n    print(optimize_profile_tracking())","Dispatch an 8 MWh flow battery in eight 15-minute intervals to track a requested site net-import profile. Site demand is [5.5, 5.2, 5.0, 5.4, 6.2, 6.8, 6.4, 5.8] MW, renewable generation is [1.0, 1.2, 1.8, 2.4, 1.7, 0.8, 0.3, 0.2] MW, and the target net import is [4.3, 4.0, 3.6, 3.4, 4.2, 5.0, 5.4, 5.0] MW. The battery starts and ends at 4.4 MWh, must remain between 0.8 and 7.2 MWh, and has 2 MW charge and discharge limits. Use 90% charging and discharging efficiencies. Limit the change in battery net output between adjacent intervals to 0.75 MW. Minimize absolute net-import tracking error weighted at 120 USD\u002FMWh of deviation, plus a throughput cost of 0.8 USD\u002FMWh. Use a 0.25-hour time step, permit net export if the schedule requires it, and prevent simultaneous charging and discharging. Implement the mixed-integer optimization in CVXPY with SCIP.",{"id":629,"relate_table":622,"relate_id":630,"file_size":573,"file_name":8,"path":8,"duration":573,"cate":483,"file_format":8,"audio_rate":8,"audio_channel":522,"audio_bit_depth":522,"quality":8,"annotation":631,"cate_name":625,"optimization_code":632,"scheduling_problem":633},14644,610961066,"{\"optimization_code\": \"import cvxpy as cp\\nimport numpy as np\\n\\ndef optimize_peak_shaving():\\n    demand = np.array([4.0, 4.2, 4.5, 5.8, 6.2, 5.0], dtype=float)\\n    solar = np.array([0.5, 1.0, 2.5, 3.5, 2.0, 0.3], dtype=float)\\n    price = np.array([42, 38, 35, 76, 91, 55], dtype=float)\\n    n = len(demand)\\n    dt = 1.0\\n\\n    energy_min, energy_max = 1.0, 9.0\\n    initial_energy = 5.0\\n    charge_max = discharge_max = 2.5\\n    eta_charge = eta_discharge = 0.90\\n    import_limit = 8.0\\n    demand_charge = 18.0\\n    throughput_cost = 1.0\\n\\n    charge = cp.Variable(n, nonneg=True)\\n    discharge = cp.Variable(n, nonneg=True)\\n    energy = cp.Variable(n + 1)\\n    charging_mode = cp.Variable(n, boolean=True)\\n    curtailment = cp.Variable(n, nonneg=True)\\n    grid_import = cp.Variable(n, nonneg=True)\\n    peak_import = cp.Variable(nonneg=True)\\n\\n    constraints = [\\n        energy[0] == initial_energy,\\n        energy[n] == initial_energy,\\n        energy_min \u003C= energy,\\n        energy \u003C= energy_max,\\n        charge \u003C= charge_max * charging_mode,\\n        discharge \u003C= discharge_max * (1 - charging_mode),\\n        curtailment \u003C= solar,\\n        grid_import \u003C= import_limit,\\n        grid_import \u003C= peak_import,\\n    ]\\n    for t in range(n):\\n        constraints += [\\n            energy[t + 1] == energy[t]\\n            + eta_charge * charge[t] * dt\\n            - discharge[t] * dt \u002F eta_discharge,\\n            grid_import[t] == demand[t] - solar[t] + curtailment[t]\\n            + charge[t] - discharge[t],\\n        ]\\n\\n    energy_cost = dt * cp.sum(cp.multiply(price, grid_import))\\n    demand_cost = demand_charge * peak_import\\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\\n    problem = cp.Problem(\\n        cp.Minimize(energy_cost + demand_cost + cycling_cost), constraints\\n    )\\n    problem.solve(solver='SCIP')\\n\\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\\n        raise RuntimeError(f'Optimization failed: {problem.status}')\\n\\n    return {\\n        'total_cost_usd': float(problem.value),\\n        'grid_import_mw': np.round(grid_import.value, 3).tolist(),\\n        'solar_curtailment_mw': np.round(curtailment.value, 3).tolist(),\\n        'charge_mw': np.round(charge.value, 3).tolist(),\\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\\n        'energy_mwh': np.round(energy.value, 3).tolist(),\\n        'peak_import_mw': float(peak_import.value),\\n    }\\n\\nif __name__ == '__main__':\\n    print(optimize_peak_shaving())\", \"scheduling_problem\": \"Schedule a 10 MWh flow battery over six one-hour intervals to reduce electricity costs and the billing-period import peak at a site with demand [4.0, 4.2, 4.5, 5.8, 6.2, 5.0] MW and on-site solar output [0.5, 1.0, 2.5, 3.5, 2.0, 0.3] MW. The import tariff is [42, 38, 35, 76, 91, 55] USD\u002FMWh, and the demand charge is 18 USD per MW of maximum grid import for this modeled period. The battery starts and ends at 5 MWh, has an allowed energy range of 1 to 9 MWh, and is limited to 2.5 MW charging and 2.5 MW discharging. Use 90% charging and discharging efficiencies, a 1-hour time step, and a cycling cost of 1 USD\u002FMWh throughput. Allow solar curtailment, prohibit grid export, and prevent simultaneous charging and discharging. Minimize energy charges, demand charges, and cycling cost using CVXPY with SCIP.\"}","import cvxpy as cp\nimport numpy as np\n\ndef optimize_peak_shaving():\n    demand = np.array([4.0, 4.2, 4.5, 5.8, 6.2, 5.0], dtype=float)\n    solar = np.array([0.5, 1.0, 2.5, 3.5, 2.0, 0.3], dtype=float)\n    price = np.array([42, 38, 35, 76, 91, 55], dtype=float)\n    n = len(demand)\n    dt = 1.0\n\n    energy_min, energy_max = 1.0, 9.0\n    initial_energy = 5.0\n    charge_max = discharge_max = 2.5\n    eta_charge = eta_discharge = 0.90\n    import_limit = 8.0\n    demand_charge = 18.0\n    throughput_cost = 1.0\n\n    charge = cp.Variable(n, nonneg=True)\n    discharge = cp.Variable(n, nonneg=True)\n    energy = cp.Variable(n + 1)\n    charging_mode = cp.Variable(n, boolean=True)\n    curtailment = cp.Variable(n, nonneg=True)\n    grid_import = cp.Variable(n, nonneg=True)\n    peak_import = cp.Variable(nonneg=True)\n\n    constraints = [\n        energy[0] == initial_energy,\n        energy[n] == initial_energy,\n        energy_min \u003C= energy,\n        energy \u003C= energy_max,\n        charge \u003C= charge_max * charging_mode,\n        discharge \u003C= discharge_max * (1 - charging_mode),\n        curtailment \u003C= solar,\n        grid_import \u003C= import_limit,\n        grid_import \u003C= peak_import,\n    ]\n    for t in range(n):\n        constraints += [\n            energy[t + 1] == energy[t]\n            + eta_charge * charge[t] * dt\n            - discharge[t] * dt \u002F eta_discharge,\n            grid_import[t] == demand[t] - solar[t] + curtailment[t]\n            + charge[t] - discharge[t],\n        ]\n\n    energy_cost = dt * cp.sum(cp.multiply(price, grid_import))\n    demand_cost = demand_charge * peak_import\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\n    problem = cp.Problem(\n        cp.Minimize(energy_cost + demand_cost + cycling_cost), constraints\n    )\n    problem.solve(solver='SCIP')\n\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\n        raise RuntimeError(f'Optimization failed: {problem.status}')\n\n    return {\n        'total_cost_usd': float(problem.value),\n        'grid_import_mw': np.round(grid_import.value, 3).tolist(),\n        'solar_curtailment_mw': np.round(curtailment.value, 3).tolist(),\n        'charge_mw': np.round(charge.value, 3).tolist(),\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\n        'energy_mwh': np.round(energy.value, 3).tolist(),\n        'peak_import_mw': float(peak_import.value),\n    }\n\nif __name__ == '__main__':\n    print(optimize_peak_shaving())","Schedule a 10 MWh flow battery over six one-hour intervals to reduce electricity costs and the billing-period import peak at a site with demand [4.0, 4.2, 4.5, 5.8, 6.2, 5.0] MW and on-site solar output [0.5, 1.0, 2.5, 3.5, 2.0, 0.3] MW. The import tariff is [42, 38, 35, 76, 91, 55] USD\u002FMWh, and the demand charge is 18 USD per MW of maximum grid import for this modeled period. The battery starts and ends at 5 MWh, has an allowed energy range of 1 to 9 MWh, and is limited to 2.5 MW charging and 2.5 MW discharging. Use 90% charging and discharging efficiencies, a 1-hour time step, and a cycling cost of 1 USD\u002FMWh throughput. Allow solar curtailment, prohibit grid export, and prevent simultaneous charging and discharging. Minimize energy charges, demand charges, and cycling cost using CVXPY with SCIP.",{"id":635,"relate_table":622,"relate_id":636,"file_size":573,"file_name":8,"path":8,"duration":573,"cate":483,"file_format":8,"audio_rate":8,"audio_channel":522,"audio_bit_depth":522,"quality":8,"annotation":637,"cate_name":625,"optimization_code":638,"scheduling_problem":639},14643,1200156640,"{\"optimization_code\": \"import cvxpy as cp\\nimport numpy as np\\n\\ndef optimize_arbitrage():\\n    prices = np.array([34, 30, 28, 31, 45, 72, 88, 61], dtype=float)\\n    n = len(prices)\\n    dt = 1.0\\n    capacity = 12.0\\n    energy_min, energy_max = 1.2, 10.8\\n    initial_energy = 6.0\\n    charge_max = discharge_max = 3.0\\n    eta_charge = eta_discharge = 0.90\\n    throughput_cost = 1.5\\n\\n    charge = cp.Variable(n, nonneg=True)\\n    discharge = cp.Variable(n, nonneg=True)\\n    energy = cp.Variable(n + 1)\\n    charging_mode = cp.Variable(n, boolean=True)\\n\\n    constraints = [\\n        energy[0] == initial_energy,\\n        energy_min \u003C= energy,\\n        energy \u003C= energy_max,\\n        energy[n] >= 6.0,\\n        charge \u003C= charge_max * charging_mode,\\n        discharge \u003C= discharge_max * (1 - charging_mode),\\n    ]\\n    for t in range(n):\\n        constraints.append(\\n            energy[t + 1] == energy[t]\\n            + eta_charge * charge[t] * dt\\n            - discharge[t] * dt \u002F eta_discharge\\n        )\\n\\n    energy_cost = dt * cp.sum(cp.multiply(prices, charge - discharge))\\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\\n    problem = cp.Problem(cp.Minimize(energy_cost + cycling_cost), constraints)\\n    problem.solve(solver='SCIP')\\n\\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\\n        raise RuntimeError(f'Optimization failed: {problem.status}')\\n\\n    return {\\n        'objective_usd': float(problem.value),\\n        'charge_mw': np.round(charge.value, 3).tolist(),\\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\\n        'energy_mwh': np.round(energy.value, 3).tolist(),\\n    }\\n\\nif __name__ == '__main__':\\n    print(optimize_arbitrage())\", \"scheduling_problem\": \"Optimize an eight-hour energy-arbitrage schedule for a vanadium flow battery using the hourly electricity prices [34, 30, 28, 31, 45, 72, 88, 61] USD\u002FMWh. The battery has 12 MWh of usable capacity, must remain between 1.2 and 10.8 MWh, starts at 6 MWh, and must finish with at least 6 MWh. Limit charging and discharging to 3 MW each. Use a 1-hour time step, 90% charging efficiency, and 90% discharging efficiency. Prevent simultaneous charging and discharging. Minimize energy purchase cost minus discharge revenue, with a throughput cost of 1.5 USD\u002FMWh charged or discharged. Implement the mixed-integer optimization in CVXPY using SCIP and return the dispatch and state-of-charge schedule.\"}","import cvxpy as cp\nimport numpy as np\n\ndef optimize_arbitrage():\n    prices = np.array([34, 30, 28, 31, 45, 72, 88, 61], dtype=float)\n    n = len(prices)\n    dt = 1.0\n    capacity = 12.0\n    energy_min, energy_max = 1.2, 10.8\n    initial_energy = 6.0\n    charge_max = discharge_max = 3.0\n    eta_charge = eta_discharge = 0.90\n    throughput_cost = 1.5\n\n    charge = cp.Variable(n, nonneg=True)\n    discharge = cp.Variable(n, nonneg=True)\n    energy = cp.Variable(n + 1)\n    charging_mode = cp.Variable(n, boolean=True)\n\n    constraints = [\n        energy[0] == initial_energy,\n        energy_min \u003C= energy,\n        energy \u003C= energy_max,\n        energy[n] >= 6.0,\n        charge \u003C= charge_max * charging_mode,\n        discharge \u003C= discharge_max * (1 - charging_mode),\n    ]\n    for t in range(n):\n        constraints.append(\n            energy[t + 1] == energy[t]\n            + eta_charge * charge[t] * dt\n            - discharge[t] * dt \u002F eta_discharge\n        )\n\n    energy_cost = dt * cp.sum(cp.multiply(prices, charge - discharge))\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\n    problem = cp.Problem(cp.Minimize(energy_cost + cycling_cost), constraints)\n    problem.solve(solver='SCIP')\n\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\n        raise RuntimeError(f'Optimization failed: {problem.status}')\n\n    return {\n        'objective_usd': float(problem.value),\n        'charge_mw': np.round(charge.value, 3).tolist(),\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\n        'energy_mwh': np.round(energy.value, 3).tolist(),\n    }\n\nif __name__ == '__main__':\n    print(optimize_arbitrage())","Optimize an eight-hour energy-arbitrage schedule for a vanadium flow battery using the hourly electricity prices [34, 30, 28, 31, 45, 72, 88, 61] USD\u002FMWh. The battery has 12 MWh of usable capacity, must remain between 1.2 and 10.8 MWh, starts at 6 MWh, and must finish with at least 6 MWh. Limit charging and discharging to 3 MW each. Use a 1-hour time step, 90% charging efficiency, and 90% discharging efficiency. Prevent simultaneous charging and discharging. Minimize energy purchase cost minus discharge revenue, with a throughput cost of 1.5 USD\u002FMWh charged or discharged. Implement the mixed-integer optimization in CVXPY using SCIP and return the dispatch and state-of-charge schedule.","{\"optimization_code\":\"import cvxpy as cp\\nimport numpy as np\\n\\ndef optimize_profile_tracking():\\n    demand = np.array([5.5, 5.2, 5.0, 5.4, 6.2, 6.8, 6.4, 5.8])\\n    renewable = np.array([1.0, 1.2, 1.8, 2.4, 1.7, 0.8, 0.3, 0.2])\\n    target_import = np.array([4.3, 4.0, 3.6, 3.4, 4.2, 5.0, 5.4, 5.0])\\n    n = len(demand)\\n    dt = 0.25\\n\\n    energy_min, energy_max = 0.8, 7.2\\n    initial_energy = 4.4\\n    charge_max = discharge_max = 2.0\\n    eta_charge = eta_discharge = 0.90\\n    ramp_limit = 0.75\\n    tracking_penalty = 120.0\\n    throughput_cost = 0.8\\n\\n    charge = cp.Variable(n, nonneg=True)\\n    discharge = cp.Variable(n, nonneg=True)\\n    energy = cp.Variable(n + 1)\\n    charging_mode = cp.Variable(n, boolean=True)\\n    deviation_above = cp.Variable(n, nonneg=True)\\n    deviation_below = cp.Variable(n, nonneg=True)\\n\\n    battery_net_output = discharge - charge\\n    net_import = demand - renewable + charge - discharge\\n    constraints = [\\n        energy[0] == initial_energy,\\n        energy[n] == initial_energy,\\n        energy_min \u003C= energy,\\n        energy \u003C= energy_max,\\n        charge \u003C= charge_max * charging_mode,\\n        discharge \u003C= discharge_max * (1 - charging_mode),\\n        net_import - target_import == deviation_above - deviation_below,\\n    ]\\n    for t in range(n):\\n        constraints.append(\\n            energy[t + 1] == energy[t]\\n            + eta_charge * charge[t] * dt\\n            - discharge[t] * dt \\\u002F eta_discharge\\n        )\\n    for t in range(1, n):\\n        constraints += [\\n            battery_net_output[t] - battery_net_output[t - 1] \u003C= ramp_limit,\\n            battery_net_output[t - 1] - battery_net_output[t] \u003C= ramp_limit,\\n        ]\\n\\n    tracking_cost = tracking_penalty * dt * cp.sum(\\n        deviation_above + deviation_below\\n    )\\n    cycling_cost = throughput_cost * dt * cp.sum(charge + discharge)\\n    problem = cp.Problem(cp.Minimize(tracking_cost + cycling_cost), constraints)\\n    problem.solve(solver='SCIP')\\n\\n    if problem.status not in (cp.OPTIMAL, cp.OPTIMAL_INACCURATE):\\n        raise RuntimeError(f'Optimization failed: {problem.status}')\\n\\n    return {\\n        'objective_usd': float(problem.value),\\n        'net_import_mw': np.round(net_import.value, 3).tolist(),\\n        'charge_mw': np.round(charge.value, 3).tolist(),\\n        'discharge_mw': np.round(discharge.value, 3).tolist(),\\n        'energy_mwh': np.round(energy.value, 3).tolist(),\\n        'tracking_deviation_mw': np.round(\\n            deviation_above.value + deviation_below.value, 3\\n        ).tolist(),\\n    }\\n\\nif __name__ == '__main__':\\n    print(optimize_profile_tracking())\",\"scheduling_problem\":\"Dispatch an 8 MWh flow battery in eight 15-minute intervals to track a requested site net-import profile. Site demand is [5.5, 5.2, 5.0, 5.4, 6.2, 6.8, 6.4, 5.8] MW, renewable generation is [1.0, 1.2, 1.8, 2.4, 1.7, 0.8, 0.3, 0.2] MW, and the target net import is [4.3, 4.0, 3.6, 3.4, 4.2, 5.0, 5.4, 5.0] MW. The battery starts and ends at 4.4 MWh, must remain between 0.8 and 7.2 MWh, and has 2 MW charge and discharge limits. Use 90% charging and discharging efficiencies. Limit the change in battery net output between adjacent intervals to 0.75 MW. Minimize absolute net-import tracking error weighted at 120 USD\\\u002FMWh of deviation, plus a throughput cost of 0.8 USD\\\u002FMWh. Use a 0.25-hour time step, permit net export if the schedule requires it, and prevent simultaneous charging and discharging. Implement the mixed-integer optimization in CVXPY with SCIP.\"}","MOBIUSI INC","https:\u002F\u002Fstatic.mobiusi.com\u002Fmobiwusi\u002F20250829\u002F7bf4ac62b4533e2b809998a6f1c5491e.png?Expires=1792463130&OSSAccessKeyId=LTAI5tH8MQqhgeiAtrzCHrxM&Signature=v6Tr8jBrdm4s5wU1SnnyGsYg%2Bhw%3D&x-oss-process=image%2Fresize%2Cm_fill%2Cw_35%2Ch_35",[644,650],{"type":645,"title":646,"count_data":647},"bar","Length distribution",[648],{"name":649,"value":483},"1k lower",{"type":651,"title":652,"count_data":653},"pie","Language distribution",[654],{"name":655,"value":483},"English"]