There are a couple of items worth noting that may help you lower your own LADWP bill. First, the rate you pay is partly determined by the time of day that you use power. This reflects the fact that it costs LADWP more to acquire or generate power to meet peak demand periods from 1 pm to 5 pm Monday to Friday. Second, there is a fixed monthly charge tied to your highest level of energy usage over the past year called the Power Access Charge. This charge can be lowered by reducing your overall electricity usage each year. If your annual monthly average consumption does not reach or exceed 3,000kWh in a year, you can choose to receive service under Rate A or B. The difference between Rate A and B can be seen in how prices are capped, how prices vary based on the usage tier (price for the first 500kWh, next 700 kWh, etc), and the service zone (set by zip code). The complete difference and breakdown of the rate calculation can be found here.
Depending on if you qualify there are also alternative pricing such as the Time-of-Use Rate (TOU) and Contract Demand Service. Under the TOU rate, your monthly bill may be lowered if you use 65% or more of your electricity during the base hours and your bimonthly electric bill is over $350. I suggest you use this link to check if you qualify for the Time-of-Use Rate.